pestle/assets/jsonqb/Physics 2025 QB merged.json

[
  {
    "question_id": "19M.3.SL.TZ1.1",
    "Question": "<div class=\"specification\">\n<p>In an experiment to measure the acceleration of free fall a student ties two different blocks of masses <em>m</em><sub>1</sub> and <em>m</em><sub>2</sub> to the ends of a string that passes over a frictionless pulley.</p>\n<p style=\"text-align: center;\"><img src=\"data:image/png;base64,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\"/></p>\n<p style=\"text-align: left;\">The student calculates the acceleration <em>a</em> of the blocks by measuring the time taken by the heavier mass to fall through a given distance. Their theory predicts that<em> </em><span style=\"background-color: #ffffff;\"><span class=\"mjpage\"><math alttext=\"a = g\\frac{{{m_1} - {m_2}}}{{{m_1} + {m_2}}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>a</mi>\n<mo>=</mo>\n<mi>g</mi>\n<mfrac>\n<mrow>\n<mrow>\n<msub>\n<mi>m</mi>\n<mn>1</mn>\n</msub>\n</mrow>\n<mo>−<!-- − --></mo>\n<mrow>\n<msub>\n<mi>m</mi>\n<mn>2</mn>\n</msub>\n</mrow>\n</mrow>\n<mrow>\n<mrow>\n<msub>\n<mi>m</mi>\n<mn>1</mn>\n</msub>\n</mrow>\n<mo>+</mo>\n<mrow>\n<msub>\n<mi>m</mi>\n<mn>2</mn>\n</msub>\n</mrow>\n</mrow>\n</mfrac>\n</math></span></span> and this can be re-arranged to give <span style=\"background-color: #ffffff;\"><span class=\"mjpage\"><math alttext=\"g = a\\frac{{{m_1} + {m_2}}}{{{m_1} - {m_2}}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>g</mi>\n<mo>=</mo>\n<mi>a</mi>\n<mfrac>\n<mrow>\n<mrow>\n<msub>\n<mi>m</mi>\n<mn>1</mn>\n</msub>\n</mrow>\n<mo>+</mo>\n<mrow>\n<msub>\n<mi>m</mi>\n<mn>2</mn>\n</msub>\n</mrow>\n</mrow>\n<mrow>\n<mrow>\n<msub>\n<mi>m</mi>\n<mn>1</mn>\n</msub>\n</mrow>\n<mo>−<!-- − --></mo>\n<mrow>\n<msub>\n<mi>m</mi>\n<mn>2</mn>\n</msub>\n</mrow>\n</mrow>\n</mfrac>\n</math></span>.</span></p>\n<p style=\"text-align: left;\">In a particular experiment the student calculates that <em>a</em> = (0.204 ±0.002) ms<sup>–2</sup> using <em>m</em><sub>1</sub> = (0.125 ±0.001) kg and <em>m</em><sub>2</sub> = (0.120 ±0.001) kg.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Calculate the percentage error in the measured value of <em>g</em>.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Deduce the value of <em>g</em> and its absolute uncertainty for this experiment.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>There is an advantage and a disadvantage in using two masses that are almost equal.</p>\n<p>State and explain the advantage with reference to the magnitude of the acceleration that is obtained.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>There is an advantage and a disadvantage in using two masses that are almost equal.</p>\n<p>State and explain the disadvantage with reference to your answer to (a)(ii).</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.ii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>error in <em>m</em><sub>1</sub> + <em>m</em><sub>2</sub> is 1 % <em><strong>OR</strong></em> error in <em>m</em><sub>1</sub> − <em>m</em><sub>2</sub> is 40 % <em><strong>OR</strong></em> error in <em>a</em> is 1 % ✔</p>\n<p>adds percentage errors ✔</p>\n<p>so error in g is 42 % <em><strong>OR</strong></em> 40 % <em><strong>OR</strong></em> 41.8 % ✔</p>\n<p><em>Allow answer 0.42 or 0.4 or 0.418. </em></p>\n<p><em>Award <strong>[0]</strong> for comparing the average value with a known value, e.g. 9.81 m s-2</em>.</p>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><em>g</em> = 9.996 «m s<sup>−2</sup>» <em><strong>OR</strong></em> Δ<em>g = </em>4.20 «m s<sup>−2</sup>» ✔</p>\n<p><em>g</em> = (10 ± 4) «m s<sup>−2</sup>»</p>\n<p><em><strong>OR</strong></em></p>\n<p><em>g</em> = (10.0 ± 4.2) «m s<sup>−2</sup>» ✔</p>\n<p><em>Award <strong>[1]</strong> max for not proper significant digits or decimals use, such as: 9.996±4.178 or 10±4.2 or 10.0±4 or 10.0±4.18« m s<sup>−2</sup> »</em> .</p>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>the acceleration would be small/the time of fall would be large ✔</p>\n<p>easier to measure /a longer time of fall reduces the % error in the time of fall and «hence acceleration» ✔</p>\n<p><em>Do not accept ideas related to the mass/moment of inertia of the pulley</em>.</p>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>the percentage error in the difference of the masses is large ✔</p>\n<p>leading to a large percentage error/uncertainty in g/of the experiment ✔</p>\n<p><em>Do not accept ideas related to the mass/moment of inertia of the pulley.</em></p>\n<div class=\"question_part_label\">b.ii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>Atwoods machine a) is a quite straightforward question that tests the ability to propagate uncertainties through calculations. Almost all candidates proved the ability to add percentages or relative calculations, however, many weaker candidates failed in the percentage uncertainty when subtracting the two masses.</p>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Many average candidates did not use the correct number of significant figures and wrote the answers inappropriately. Only the best candidates rounded out and wrote the proper answer of 10±4 ms<sup>−2</sup>. Some candidates did not propagate uncertainties and only compared the average calculated value with the known value 9.81 ms<sup>−2</sup>.</p>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Q 1 b) was quite well answered. Only the weakest candidates presented difficulty in understanding simple mechanics.</p>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>In part ii) many were able to appreciate that the resultant percentage error in “g” was relatively large however linking this with what caused the large uncertainty (that is, the high % error from the small difference in masses) proved more challenging.</p>\n<div class=\"question_part_label\">b.ii.</div>\n</div>",
    "topics": [
      "inquiry",
      "tools"
    ],
    "subtopics": [
      "i-1-3-controlling-variables",
      "inquiry-1-exploring-and-designing",
      "tool-3-mathematics"
    ]
  },
  {
    "question_id": "19M.3.SL.TZ2.1",
    "Question": "<div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">A student investigates the electromotive force (emf) <em>ε</em> and internal resistance<em> r</em> of a cell.</span></p>\n<p><span style=\"background-color: #ffffff;\"><img height=\"196\" src=\"data:image/png;base64,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\" width=\"213\"/></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">The current <em>I</em> and the terminal potential difference <em>V</em> are measured.<br/></span></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">For this circuit <em>V = ε - Ir</em> .<br/></span></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">The table shows the data collected by the student. The uncertainties for each measurement<br/>are shown.</span></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\"><img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOcAAADqCAYAAABZalL+AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABI9SURBVHhe7Z1Nb1zlGYanFSyQQGbHAmJLFXRR4qhiQ9LYioTEoglbqhCzL3F/AEl/QKGLkhVOf0CdVqiLIsEaCVuEbWOxRbKbFSuD2IHk+jrnPJnXJ+drJjP287xzX9LRmTnvGRPmnvv9OHPmuX9xdMxICOGOX1Z7IYQzZE4hnCJzCuGUx9acy8svVY+EEKfJwcHD6lFJoznrJ4kYSLu4NGmnaa0QTpE5hXCKzCmEU2ROIZwicwrhFJlTCKfInEI4JYw5r1xZL74LSrebN9+rWoXIjzDmfOGFF0bPPPNM9Ww0unjx4uiNN96onpXcuPHOaG3td9Wz2cHftQ5hd3enOiqmZXX11db38tq1q0Xb559/Vh0Z06Yvx3jN3btb1ZGS77//vvO/5Z0w5vzkk3+PnnvuueLx+fOrxfO33/5D8dzY23twLNR69Ww2HBwcnBD2s88e/9CIyVhdvVDseW9TMCQa0n7t2lvV0TFt+m5svFvs69rw9zDo8vLyzD8Xp0EYc/7www+j7777bvT000+P3nzzzeroGAyEEBculMKnIBK9J70yU2Ee06NynM16V3rmOrSDiWvPxfRgFtjf3y/2xtZWOfJtbm4W+5Qufc3ImDc1vJnVzBuNMOa8f/+r0VNPPVVMbS9evFQdHbO3t1fsu3pIxDNzIfQHH/xldOvW+8Vj4ANQnxptb/+j2POBoUfn3Hv3totjYjpWVlaKvWkG6NI9arbrm46Mpq/NeJaWlo473Y3iWDTCmPOLL74Y/fzzz8UIeunS4+bc2dkpRLJeuY179/55LPQ3hWgIiKjccGwfiMPDw2IPiMs5Jv5bb5XnaGr7ZKyurhb7g4PxyNk1akKfvuvrpTmtM01nPGgdkTDm/Prr+8X+lVd+XezrtK1HUsxkiGWCbWyUvWrTdMlMaMalB+Z1ZloxHemak5lI36gJffqaNjZimnbWoUYkjDm//fbbYv/6668X+xTEaFuPpCwtPV89Gj/u6lWt92Wqa+tUmwJbm5gc3nMbATFd36g5RF/+ppl3e3u7+Lv8N9rMHoEQ5rx//35xIejZZ58dXblypTo6Zsh6c1JYV5oRm7Dpk5iO5eVy3Ykx+0fNYfraKGkdZ2RjQghzfvrpf0Y//fTT6Mcffzxebz7+PdfQ9eYk2LTo9u0/H0+VHj7a0vUqPbqYDlt32nvYNmrCUH0xY3pO5CktuDbnw4f/G7388q9OXB197bXfFsdT+tYjk5Iab21trdgbGNPWTLowND12xRa6Rk2YRF/7O5xvOkXFdZkSprN37vytejbmo4/ujF566Vz1TBietBOT0aSdaghlhLSLS5N2Ya7WCrFoyJxCOEXmFMIpMqcQTglhTm5O183mMeBrqHn8pnYRCWFOjIlBh2K32/Grk1ljPy9jLx4HY2LQIaAr7yUbP+fj+8wu+s5H91Sf+i+M+AzR1lRBw37kXX/NWZLVtJbb7Xjj52FK4MNht/Sx12g+Pdxil3a4GK2r7Ezf+ZgK3VN9eJ7eA213DO1W9+oadCZmdE+3/GVlTnptxOi6MwTBrPe08iP0mghkI25bD2p3BNndKrpDaHq4JQ/s9kg0Q4O2Dq/vfLvX2dpNI3sdcIzb+zBmalp7bO1ecGnOdPrCZqTHmqZOCHb37t8H3VOJILvVLXr0mjduXD8x4vI4nTbx3+N8bt/78MO/FnueN/07Fo1UFyM9lh437L232yNNs3p1BKPvfBsJbeSz33emtwlCU0kTM7b9fNALLs05ZH3Z1MPxQ+qh0xJez03smBkwmfW69rdT41nvyt+n3XrmtAcWwzEzLVe/Tumj73y0NO04F8PRgdY/D2ZuzG4dLnte52lKC1lNaycBc6U3sfP45s3ylxFN02LrXa1Htp5bPx2jExv/asdIj6XH5w1GY7lina11tAbamr50rDbt9WZMcGnONmGbjk0LZkz3XVjvCqxVmabZxQjrfcVk2PuelirpYsj5pTGvF8sRZkRttYOsY2VqazOfIUuh02ZhR85J6LvwowtDk2PT093d3WJv72F9jWj0nW/GZI8xu0ZCK2mCiTk/HU09IXMOwHpX1rTp6G3rVa07J8cuvtjVc4zCFNRGOztuV837zuc6BUYDm92kM5wUjGnXDMDjqAkuzWlvrG1GesyEmDf23SYfhFRQoHdGaNoX+TvPVBcjPZYeN3jv7Ko3MHJZZ9dE1/l8FiZdWpgh+Xt2rcEbLn/P2SRmnbP+N3rkrLSTXk9Ok3b6sXVGSLu4NGmnNacQTpE5hXCKzCmEU2ROIZwicwrhFJlTCKfInEI4pfF7TiHE6aObEDJG2sVFNyEIEQiZUwinyJxCOEXmFMIpMqcQTpE5hXCKzCmEU2ROIZyyEOakvgxRDXzRy5ZWdk8jGOrbpHVpxOSU1e9e7a3BRBG1uj7UpzX62iOSvTkRH5Eow88dGOV28MigFHcaH39YVA636t/1gl5itlBBj3KWVs29iwcPHhSapFpRDdHoa49I9ua0spVpgWEqr7X11JiWDwuV3sT84P2nbOXQ95l6tRcutNeW7WuPyMKsOa2kooEB6blTmMbyoaGMf/18MXvu3fvX8SyluYh0HbQi+iKdsqYjbl97RLI3pwXX2EjJlHZrqyxUXBdve3u7MGVbGX8xO3iP6zkmbVgnmk5bV1dXCwNCX3tY+FVKyrlzL1aP8uG4Rz06f/43xf/b5cuXjra2Pi4e7+x8WZ1xdLS/v18coy0qEbWz9x2NJgHteN2DB/+tjpykr90bTdotxLSWXtoi4nZ3v6qO8jOd8ZTK1qY20ooY9E1dI09tF2bNmXJ4eFhMqdJpFVf7vAbaLDr2dVdqNHvMMqSvPSrZm5P1CMJZIA7PGSUt4dgozxu2BhKnC2tJTJZeYSdljON0pn3tUcnenIjD1VdLp7p27WphzHp4DReKZE4/cNOIXdBBF0KLMBwasoEFGfW1R0VlSjJC2sWlSbuFXHMKEQGZUwinyJxCOEXmFMIpMqcQTpE5hXCKzCmEU2ROIZwicwrhFKWMCeGE+h1Cun0vI6RdXHT7nhCBkDmFcIrMKYRTZE4hnCJzCuEUmVMIp8icQjhF5hTCKVmZsy2xipiFtpQxoPIehb+s/dat96sWMW/aNKvTlyLG6/k7aZtVgo9KNuZEiKbEKsRHqLaUMc4nUIfSirSRTIXQVkpTzI82zZroShHj9ehJpUWOUzj84GD/UexGVLIwJ2ZqS6zqSxljVMWst2/fLp4T+4fIOzvK5pwnXZo10ZUihoYY1P4WpTIxMscjk83I2ZdYVa/8jZjldLbsja34MB8ajmNgMV9mlTJG5wpp3eGVlZWi3doikoU5uxKrJkkZQ3TWmxhVwbnzZZYpY7mS1QWhJjAa0x2r+M4ap21UNOEZZYeuhcT8sbUklfuN9fX1wrRm3BzJ3pwwJGUsZXOTKPqDrIXPhZw70IUwZ500ZSzXhKqc6NPIpsdpZ0p72haR7M2JYAjbljLGOgYRbU0KJFwzlbKLROJsadIoTRHj+gDt6AbMerh4FP26wUKsObtSxsrR82RCVflBKL9DE2fDJClj6IXGmJc2Xru09PyJNWpEVKYkI6RdXJq0W8g1pxARkDmFcIrMKYRTZE4hnCJzCuEUmVMIp8icQjhF5hTCKQoyEsIJ9ZsQdIdQRki7uOgOISECIXMK4RSZUwinyJxCOEXmFMIpMqcQTpE5hXCKzCmEU2ROIZyShTmpqNeVEkbhp6EJVOR3UCBKnA5UyhuSMpbSpFFfCllEwpuT+qRdKWG0D02gQmALPhLzhw5y0sr6bRp1pZBFJbw5d3tSwmhH/L4EKjNx5CLEkaADnSRlDLo06kohi0p4c1pvaQWgEZ0e2fJQMC6kgjYlUCE6f0sBRqfHJClj0KURmrelkEUlqwtCiDJNShjTJEbSzc0/VUfEvJkkZQy6NLLrB+m0NocUsqzMacKw/hy6lrGpEtXBeZ3wR59Gdj0hrfCeQwpZVuY0JkkJ29r6uBhl6XWFT55Eo8hT2/DmfNIEKqZLrFNtrcJjjM3jdE0qzo4+jXJNisvighACIJiRpoTR49LelkBVfrUyvvxuayEeT7ImEvOjT6Omz0CaQhaV8OZEnK6UMB7nmECVO2nKWB9NnwGwFLKoqIZQRki7uDRpl+UFISFyQOYUwikypxBOkTmFcIrMKYRTZE4hnCJzCuEUmVMIpyhlTAgn1G9C0B1CGSHt4qI7hIQIhMwphFNkTiGcInMK4RSZUwinyJxCOEXmFMIpMqcQTsnCnFTW6woy2t3dKWrSWDs1UFOo7mZttkUvSBwFCq7NIsiI1w8Nq4pCeHNSArEryAjxEWpj492ivdwOThg0xxCcCGCeWQQZ8Xr0tOLSXWFVkQhvTkZFzNYWZGRCUk7RIEcl7alzDMHxDu//rIKM+AzQ1hdWFY3w5rQRz+qTIjo9sgUZGYysKYhp0x72uYXgRGBWQUZ0zpCatimsKhpZXRDCWPUgo7W1tWJvIyVi2XQnNWg6rc0hBMc7swwyypWszGnmYpS0tQxGZbpTTocYFa+fGFVtnZJbCE5OoCP6tQUZ5UpW5jTqQUb00nt73xQm5GKB0Tel0tTWB4saNhXenNOE2BweHhZTKrZcQ3BygiktyxJ0YuMxnS+Py313WFVUsrgghAi2poQ0yAjBENG+WuE5YvPVCjS9PocQnJzoCzJiVEXDtrCqqIQ3Zzn6tQcZYTDWKrbm5GYFjHnz5mbR3vR6iB6CE51JgozQO8ewKpUpyQhpF5cm7bK8ICREDsicQjhF5hTCKTKnEE6ROYVwiswphFNkTiGcInMK4RSZUwinKGVMCCfU7xDS7XsZIe3iotv3hAiEzCmEU2ROIZwicwrhFJlTCKfInEI4ReYUwikypxBOyc6cTQlUVNxLU8g4x8pfWmnMpm03eNZGBKiUNyRlrK5hPUmOioqpdmzRq/ZnZU4EYquDGYlY4A4MNoSmGl/ZRgHqcdlFik9TkY/SmNFLK3oHHYakjNHelSQHOSbFZWNOBCzLX54sIkzPzJamiGG6tlGRv8HfmiT9SkwO5hqaMoZWaNiWJAc5JsVlY05M1TTaYVY2elYDsZtGRY7zoVm0TI6zYmjKmI2IVuQbjRh108wbnueWFJeFOZnKYqy2BCp6ZwQ14dpGRiqGY8o0y1PMh0lTxgz0qyfJYUxIp7U5JMWFN6dNZ9tGO6ZDTJ9oHwt34VjIq9UZJZyHyRcpYi4ipmHZiY6T5DiWVnjPISkuvDn7EqgwHAKmo+HGBqljJ4WzC0mW5yl8U0+SayPy1Da8OTFVOmXlMaLxmL3Rt4ZkTUoPbOsa4Ye+JLhck+LCm7MvgcpG1PSyO6FFdSPSA0+zBhLzBw0xGR2vkSbJNbXnkBSXxQWhLjAc33elKWL0qvUUsXK0lTm9kKaMoUtXklxTO0RPilOZkoyQdnFp0i77kVOIqMicQjhF5hTCKTKnEE6ROYVwiswphFNkTiGcInMK4RQFGQnhhPpNCLpDKCOkXVx0h5AQgZA5hXCKzCmEU2ROIZwicwrhFJlTCKfInEI4ReYUwilZmJMKfHyJm25pQWEKTlOTxtosJ8WguFdb0JGYL9RumkWQEa/n71g7+veVzfROFubsCrFBfITa2Hg3aT84YdCuoCMxP3ifZxFkRDt6UWmP9rIi4/5oa2tccTEiWZizK8TGikWnRaXJ2LCeGqOyDQ06ErOB939WQUa0Y1D7W1Tjo7OOrmEW5qQH7guxqRcXpp3XISTbkKAjMVtmFWSEcQEdjZWVlUJja4tIeHMiEqTT2jTExuIV0pHSpjtm4KFBR2J2zDLIKFfCm9PWGW0hNrRjNNYk5ah6/UR0HGYdEnQkfGAaMRMasl6NTBbT2jZMOHppEqsRlYsFBlOqoUFHwhdDg4wiE96c04TYHB4eFlOqdFrVdq44e/o0Nh1To9KetkUkvDlZayKCrSkhDbFBMIS1y+48Z7TkqxXgPOgLOhJnR5PGaZARa0/aOQaMqFwgDL8mpRJCyrlzL1aP4rCz8+XR1au/L/7tbO+998eqpWRr6+NHbWw8T6m//p13rh/t7+9XrXHg3x4N3mf+3cdmqo6UXL58qdDBaNL4eAZUtR4Vr7c2Ns6NpCH/5joqU5IR0i4uTdplfUFIiMjInEI4ReYUwikypxBOkTmFcIrMKYRTZE4hnCJzCuEUmVMIpyhlTAgn1O8QesycQggfaForhFNkTiGcInMK4RSZUwiXjEb/ByhOQADxeBboAAAAAElFTkSuQmCC\"/></span></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">The graph shows the data plotted.</span></span></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\"><img src=\"data:image/png;base64,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\"/></span></span></span></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">The student has plotted error bars for the potential difference. Outline why no error bars are shown for the current.</span></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Determine, using the graph, the emf of the cell including the uncertainty for this value. Give your answer to the correct number of significant figures.</span></p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Outline, <strong>without</strong> calculation, how the internal resistance can be determined from this graph.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\">Δ<em>I</em> is too small to be shown/seen<br/></span></p>\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\"><em><strong>OR</strong></em><br/></span></p>\n<p><span style=\"background-color:#ffffff;\">Error bar of negligible size compared to error bar in <em>V</em> ✔</span></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\">evidence that ε can be determined from the y-intercept of the line of best-fit or lines of min and max gradient ✔<br/></span></p>\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\">states ε=1.59 <em><strong>OR</strong></em> 1.60 <em><strong>OR</strong> </em>1.61V«» ✔<br/></span></p>\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\">states uncertainty in ε is 0.02 V«» <em><strong>OR</strong></em> 0.03«V» ✔</span></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\">determine the gradient «of the line of best-fit» ✔<br/></span></p>\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\"><em>r</em> is the negative of this gradient ✔</span></p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>Almost all candidates realised that the uncertainty in I was too small to be shown. A common mistake was to mention that since I is the independent variable the uncertainty is negligible.</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>The number of candidates who realised that the V intercept was EMF was disappointing. Large numbers of candidates tried to calculate ε using points on the graph, often ending up with unrealistic values. Another common mistake was not giving values of ε and Δε to the correct number of digits - 2 decimal places on this occasion. Very few candidates drew maximum and minimum gradient lines as a way of determining Δε.</p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.</div>\n</div>",
    "topics": [
      "inquiry",
      "tools"
    ],
    "subtopics": [
      "i-2-1-collecting-data",
      "inquiry-2-collecting-and-processing-data",
      "tool-3-mathematics"
    ]
  },
  {
    "question_id": "19M.3.SL.TZ2.3",
    "Question": "<div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">A student uses a Young’s double-slit apparatus to determine the wavelength of light emitted by a monochromatic source. A portion of the interference pattern is observed on a screen.</span></p>\n<p><span style=\"background-color: #ffffff;\"><img src=\"data:image/png;base64,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\"/></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">The distance <em>D</em> from the double slits to the screen is measured using a ruler with a smallest scale division of 1 mm.<br/></span></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">The fringe separation s is measured with uncertainty ± 0.1 mm.<br/></span></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">The slit separation d has negligible uncertainty.<br/></span></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">The wavelength is calculated using the relationship  <span class=\"mjpage\"><math alttext=\"\\lambda  = \\frac{{sd}}{D}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>λ<!-- λ --></mi>\n<mo>=</mo>\n<mfrac>\n<mrow>\n<mi>s</mi>\n<mi>d</mi>\n</mrow>\n<mi>D</mi>\n</mfrac>\n</math></span>.</span></span></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">When <em>d</em> = 0.200 mm, <em>s</em> = 0.9 mm and <em>D</em> = 280 mm, determine the percentage uncertainty in the wavelength.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Explain how the student could use this apparatus to obtain a more reliable value for λ. </span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"text-align:left;\">Evidence of <span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"\\frac{{\\Delta s}}{s}{\\text{AND}}\\frac{{\\Delta D}}{D}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mrow>\n<mi mathvariant=\"normal\">Δ</mi>\n<mi>s</mi>\n</mrow>\n<mi>s</mi>\n</mfrac>\n<mrow>\n<mtext>AND</mtext>\n</mrow>\n<mfrac>\n<mrow>\n<mi mathvariant=\"normal\">Δ</mi>\n<mi>D</mi>\n</mrow>\n<mi>D</mi>\n</mfrac>\n</math></span> used   <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">✔</span></span><span style=\"background-color:#ffffff;\"><br/></span></p>\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\">«add fractional/% uncertainties»<br/></span></span></p>\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\">obtains 11 % (or 0.11) <em><strong>OR</strong> </em>10 % (or 0.1) ✔</span></span></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\"><em><strong>ALTERNATIVE 1:</strong></em><br/></span></p>\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\">measure the combined width for several fringes<br/></span></p>\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\"><em><strong>OR</strong></em><br/></span></p>\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\">repeat measurements ✓<br/></span></p>\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\">take the average<br/></span></p>\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\"><em><strong>OR</strong></em><br/></span></p>\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\">so the «percentage» uncertainties are reduced ✓<br/></span></p>\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\"><em><strong>ALTERNATIVE 2:</strong></em><br/></span></p>\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\">increase <em>D</em> «hence <em>s</em>»<br/></span></p>\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\"><em><strong>OR</strong></em><br/></span></p>\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\">Decrease <em>d</em> ✓<br/></span></p>\n<p style=\"text-align:left;\"><span style=\"background-color:#ffffff;\">so the «percentage» uncertainties are reduced ✓</span></p>\n<p style=\"text-align:left;\"><em><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\">Do not accept answers which suggest using different apparatus.</span></span></em></p>\n<div class=\"question_part_label\">b.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>A very easy question about percentage uncertainty which most candidates got completely correct. Many candidates gave the uncertainty to 4 significant figures or more. The process used to obtain the final answer was often difficult to follow.</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>The most common correct answer was the readings should be repeated and an average taken. Another common answer was that D could be increased to reduce uncertainties in s. The best candidates knew that it was good practice to measure many fringe spacings and find the mean value. Quite a few candidates incorrectly stated that different apparatus should be used to give more precise results.</p>\n<div class=\"question_part_label\">b.</div>\n</div>",
    "topics": [
      "inquiry",
      "tools"
    ],
    "subtopics": [
      "i-3-2-evaluating",
      "inquiry-3-concluding-and-evaluating",
      "tool-3-mathematics"
    ]
  },
  {
    "question_id": "19M.2.HL.TZ1.2",
    "Question": "<div class=\"specification\">\n<p>A beam of electrons each of de Broglie wavelength 2.4 × 10<sup>–15</sup> m is incident on a thin film of silicon-30  <span style=\"background-color: #ffffff;\"><span class=\"mjpage\"><math alttext=\"\\left( {{}_{14}^{30}{\\text{Si}}} \\right)\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mrow>\n<mo>(</mo>\n<mrow>\n<msubsup>\n<mrow>\n</mrow>\n<mrow>\n<mn>14</mn>\n</mrow>\n<mrow>\n<mn>30</mn>\n</mrow>\n</msubsup>\n<mrow>\n<mtext>Si</mtext>\n</mrow>\n</mrow>\n<mo>)</mo>\n</mrow>\n</math></span></span>. The variation in the electron intensity of the beam with scattering angle is shown.</p>\n<p style=\"text-align: center;\"><img src=\"data:image/png;base64,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\"/></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Use the graph to show that the nuclear radius of silicon-30 is about 4 fm.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Estimate, using the result from (a)(i), the nuclear radius of thorium-232 <span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"\\left( {{}_{90}^{232}{\\text{Th}}} \\right)\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mrow>\n<mo>(</mo>\n<mrow>\n<msubsup>\n<mrow>\n</mrow>\n<mrow>\n<mn>90</mn>\n</mrow>\n<mrow>\n<mn>232</mn>\n</mrow>\n</msubsup>\n<mrow>\n<mtext>Th</mtext>\n</mrow>\n</mrow>\n<mo>)</mo>\n</mrow>\n</math></span>.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Suggest <strong>one</strong> reason why a beam of electrons is better for investigating the size of a nucleus than a beam of alpha particles of the same energy.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline why deviations from Rutherford scattering are observed when high-energy alpha particles are incident on nuclei.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.iv.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>read off between 17 and 19 «deg» ✔</p>\n<p>correct use of <em>d</em> = <span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"\\frac{\\lambda }{{\\sin \\theta }}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mi>λ</mi>\n<mrow>\n<mi>sin</mi>\n<mo>⁡</mo>\n<mi>θ</mi>\n</mrow>\n</mfrac>\n</math></span></span> = 7.8 × 10<sup>−15</sup> «m» ✔</p>\n<p>so radius = <span class=\"mjpage\"><math alttext=\"\\frac{7.8}{2}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mn>7.8</mn>\n<mn>2</mn>\n</mfrac>\n</math></span> «fm» = 3.9 «fm» ✔</p>\n<p><em>Award ecf for wrong angle in MP1.</em></p>\n<p><em>Answer for MP3 must show at least 2 </em><em>sf.</em></p>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>R<sub>Th</sub> = R<sub>si </sub> <span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"{\\left( {\\frac{{{A_{{\\text{Th}}}}}}{{{A_{{\\text{Si}}}}}}} \\right)^{\\frac{1}{3}}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mrow>\n<msup>\n<mrow>\n<mo>(</mo>\n<mrow>\n<mfrac>\n<mrow>\n<mrow>\n<msub>\n<mi>A</mi>\n<mrow>\n<mrow>\n<mtext>Th</mtext>\n</mrow>\n</mrow>\n</msub>\n</mrow>\n</mrow>\n<mrow>\n<mrow>\n<msub>\n<mi>A</mi>\n<mrow>\n<mrow>\n<mtext>Si</mtext>\n</mrow>\n</mrow>\n</msub>\n</mrow>\n</mrow>\n</mfrac>\n</mrow>\n<mo>)</mo>\n</mrow>\n<mrow>\n<mfrac>\n<mn>1</mn>\n<mn>3</mn>\n</mfrac>\n</mrow>\n</msup>\n</mrow>\n</math></span></span> or substitution ✔</p>\n<p>7.4 «fm» ✔<br/><br/></p>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>electron wavelength shorter than alpha particles (thus increased resolution)<br/><em><strong>OR</strong></em><br/>electron is not subject to strong nuclear force ✔</p>\n<p> </p>\n<div class=\"question_part_label\">a.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>nuclear forces act ✔</p>\n<p>nuclear recoil occurs ✔</p>\n<p>significant penetration into nucleus / probing internal structure of individual nucleons ✔</p>\n<p>incident particles are relativistic ✔</p>\n<div class=\"question_part_label\">a.iv.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>This question was left blank by many candidates and many of those who attempted it chose an angle that when used with the correct equation gave an answer close to the given answer of 4 fm. Very few selected the correct angle, calculated the correct diameter, and divided by two to get the correct radius.</p>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This question was also left blank by many candidates. Many who did answer simply used the ratio of the of the mass numbers of the two elements and failed to take the cube root of the ratio. It should be noted that the question specifically stated that candidates were expected to use the result from 2ai, and not just simply guess at the new radius.</p>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This question was very poorly answered with the vast majority of candidates simply listing differences between alpha particles and electrons (electrons have less mass, electrons have less charge, etc) rather than considering why high speed electrons would be better for studying the nucleus.</p>\n<div class=\"question_part_label\">a.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Candidates struggled with this question. The vast majority of responses were descriptions of Rutherford scattering with no connection made to the deviations when high-energy alpha particles are used. Many of the candidates who did appreciate that this was a different situation from the traditional experiment made vague comments about the alpha particles “hitting” the nucleus.</p>\n<div class=\"question_part_label\">a.iv.</div>\n</div>",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-3-wave-phenomena"
    ]
  },
  {
    "question_id": "19M.2.HL.TZ1.3",
    "Question": "<div class=\"specification\">\n<p>A beam of microwaves is incident normally on a pair of identical narrow slits S1 and S2.</p>\n<p style=\"text-align: center;\"><img 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\"/></p>\n<p style=\"text-align: left;\">When a microwave receiver is initially placed at W which is equidistant from the slits, a maximum in intensity is observed. The receiver is then moved towards Z along a line parallel to the slits. Intensity maxima are observed at X and Y with one minimum between them. W, X and Y are consecutive maxima.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Explain why intensity maxima are observed at X and Y.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The distance from S1 to Y is 1.243 m and the distance from S2 to Y is 1.181 m.</p>\n<p>Determine the frequency of the microwaves.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline <strong>one</strong> reason why the maxima observed at W, X and Y will have different intensities from each other.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The microwaves emitted by the transmitter are horizontally polarized. The microwave receiver contains a polarizing filter. When the receiver is at position W it detects a maximum intensity.</p>\n<p style=\"text-align:center;\"><img 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\"/></p>\n<p style=\"text-align:left;\">The receiver is then rotated through 180° about the horizontal dotted line passing through the microwave transmitter. Sketch a graph on the axes provided to show the variation of received intensity with rotation angle.</p>\n<p style=\"text-align:left;\"><img 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\" style=\"display:block;margin-left:auto;margin-right:auto;\"/></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">d.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>two waves superpose/mention of superposition/mention of «constructive» interference ✔</p>\n<p>they arrive in phase/there is a path length difference of an integer number of wavelengths ✔</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>path difference = 0.062 «m»✔</p>\n<p>so wavelength = 0.031 «m»✔</p>\n<p>frequency = 9.7 × 10<sup>9</sup> «Hz»✔</p>\n<p><em>Award <strong>[2 max]</strong> for 4.8 x 10<sup>9</sup> Hz</em>.</p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>intensity is modulated by a single slit diffraction envelope <em><strong>OR</strong></em></p>\n<p>intensity varies with distance <em><strong>OR</strong></em> points are different distances from the slits ✔<br/><br/></p>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><img src=\"data:image/png;base64,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\"/></p>\n<p>cos<sup>2</sup> variation shown ✔</p>\n<p>with zero at 90° (by eye) ✔</p>\n<p><em>Award <strong>[1 max]</strong> for an inverted curve with maximum at 90°.</em></p>\n<div class=\"question_part_label\">d.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>Many candidates were able to discuss the interference that is taking place in this question, but few were able to fully describe the path length difference. That said, the quality of responses on this type of question seems to have improved over the last few examination sessions with very few candidates simply discussing the crests and troughs of waves.</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Many candidates struggled with this question. Few were able to calculate a proper path length difference, and then use that to calculate the wavelength and frequency. Many candidates went down blind paths of trying various equations from the data booklet, and some seemed to believe that the wavelength is just the reciprocal of the frequency.</p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This is one of many questions on this paper where candidates wrote vague answers that did not clearly connect to physics concepts or include key information. There were many overly simplistic answers like “they are farther away” without specifying what they are farther away from. Candidates should be reminded that their responses should go beyond the obvious and include some evidence of deeper understanding.</p>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This question was generally well answered, with many candidates at least recognizing that the intensity would decrease to zero at 90 degrees. Many struggled with the exact shape of the graph, though, and some drew a graph that extended below zero showing a lack of understanding of what was being graphed.</p>\n<div class=\"question_part_label\">d.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion",
      "c-wave-behaviour"
    ],
    "subtopics": [
      "a-5-galilean-and-special-relativity",
      "c-2-wave-model",
      "c-3-wave-phenomena"
    ]
  },
  {
    "question_id": "19M.2.HL.TZ1.5",
    "Question": "<div class=\"specification\">\n<p>The moon Phobos moves around the planet Mars in a circular orbit.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline the origin of the force that acts on Phobos.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline why this force does no work on Phobos.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The orbital period <em>T</em> of a moon orbiting a planet of mass <em>M</em> is given by</p>\n<p style=\"text-align:center;\"><span style=\"background-color:#ffffff;\"><span class=\"mjpage mjpage__block\"><math alttext=\"\\frac{{{R^3}}}{{{T^2}}} = kM\" display=\"block\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mrow>\n<mrow>\n<msup>\n<mi>R</mi>\n<mn>3</mn>\n</msup>\n</mrow>\n</mrow>\n<mrow>\n<mrow>\n<msup>\n<mi>T</mi>\n<mn>2</mn>\n</msup>\n</mrow>\n</mrow>\n</mfrac>\n<mo>=</mo>\n<mi>k</mi>\n<mi>M</mi>\n</math></span></span></p>\n<p>where <em>R</em> is the average distance between the centre of the planet and the centre of the moon.</p>\n<p>Show that <span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"k = \\frac{G}{{4{\\pi ^2}}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>k</mi>\n<mo>=</mo>\n<mfrac>\n<mi>G</mi>\n<mrow>\n<mn>4</mn>\n<mrow>\n<msup>\n<mi>π</mi>\n<mn>2</mn>\n</msup>\n</mrow>\n</mrow>\n</mfrac>\n</math></span></span></p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The following data for the Mars–Phobos system and the Earth–Moon system are available:</p>\n<p>Mass of Earth = 5.97 × 10<sup>24</sup> kg</p>\n<p>The Earth–Moon distance is 41 times the Mars–Phobos distance.</p>\n<p>The orbital period of the Moon is 86 times the orbital period of Phobos.</p>\n<p>Calculate, in kg, the mass of Mars.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The graph shows the variation of the gravitational potential between the Earth and Moon with distance from the centre of the Earth. The distance from the Earth is expressed as a fraction of the total distance between the centre of the Earth and the centre of the Moon.</p>\n<p style=\"text-align:center;\"><img src=\"data:image/png;base64,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\"/></p>\n<p style=\"text-align:left;\">Determine, using the graph, the mass of the Moon.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>gravitational attraction/force/field «of the planet/Mars» ✔</p>\n<p><em>Do not accept “gravity”</em>.</p>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>the force/field and the velocity/displacement are at 90° to each other <strong><em>OR</em></strong></p>\n<p>there is no change in GPE of the moon/Phobos ✔</p>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><em><strong>ALTERNATE 1</strong></em></p>\n<p>«using fundamental equations»</p>\n<p>use of Universal gravitational force/acceleration/orbital velocity equations ✔</p>\n<p>equating to centripetal force or acceleration. ✔</p>\n<p>rearranges to get <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span class=\"mjpage\"><math alttext=\"k = \\frac{G}{{4{\\pi ^2}}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>k</mi>\n<mo>=</mo>\n<mfrac>\n<mi>G</mi>\n<mrow>\n<mn>4</mn>\n<mrow>\n<msup>\n<mi>π</mi>\n<mn>2</mn>\n</msup>\n</mrow>\n</mrow>\n</mfrac>\n</math></span></span>  ✔</p>\n<p><em><strong>ALTERNATE 2</strong></em></p>\n<p>«starting with <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:center;text-decoration:none;text-indent:0px;white-space:normal;\"><span class=\"mjpage\"><math alttext=\"\\frac{{{R^3}}}{{{T^2}}} = kM\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mrow>\n<mrow>\n<msup>\n<mi>R</mi>\n<mn>3</mn>\n</msup>\n</mrow>\n</mrow>\n<mrow>\n<mrow>\n<msup>\n<mi>T</mi>\n<mn>2</mn>\n</msup>\n</mrow>\n</mrow>\n</mfrac>\n<mo>=</mo>\n<mi>k</mi>\n<mi>M</mi>\n</math></span><span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">»</span></span></p>\n<p>substitution of proper equation for T from orbital motion equations ✔</p>\n<p>substitution of proper equation for M <em><strong>OR</strong></em> R from orbital motion equations ✔</p>\n<p>rearranges to get <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span class=\"mjpage\"><math alttext=\"k = \\frac{G}{{4{\\pi ^2}}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>k</mi>\n<mo>=</mo>\n<mfrac>\n<mi>G</mi>\n<mrow>\n<mn>4</mn>\n<mrow>\n<msup>\n<mi>π</mi>\n<mn>2</mn>\n</msup>\n</mrow>\n</mrow>\n</mfrac>\n</math></span></span>  ✔</p>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"{m_{{\\text{Mars}}}} = {\\left( {\\frac{{{R_{{\\text{Mars}}}}}}{{{R_{{\\text{Earth}}}}}}} \\right)^3}{\\left( {\\frac{{{T_{{\\text{Earth}}}}}}{{{T_{Mars}}}}} \\right)^2}{m_{{\\text{Earth}}}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mrow>\n<msub>\n<mi>m</mi>\n<mrow>\n<mrow>\n<mtext>Mars</mtext>\n</mrow>\n</mrow>\n</msub>\n</mrow>\n<mo>=</mo>\n<mrow>\n<msup>\n<mrow>\n<mo>(</mo>\n<mrow>\n<mfrac>\n<mrow>\n<mrow>\n<msub>\n<mi>R</mi>\n<mrow>\n<mrow>\n<mtext>Mars</mtext>\n</mrow>\n</mrow>\n</msub>\n</mrow>\n</mrow>\n<mrow>\n<mrow>\n<msub>\n<mi>R</mi>\n<mrow>\n<mrow>\n<mtext>Earth</mtext>\n</mrow>\n</mrow>\n</msub>\n</mrow>\n</mrow>\n</mfrac>\n</mrow>\n<mo>)</mo>\n</mrow>\n<mn>3</mn>\n</msup>\n</mrow>\n<mrow>\n<msup>\n<mrow>\n<mo>(</mo>\n<mrow>\n<mfrac>\n<mrow>\n<mrow>\n<msub>\n<mi>T</mi>\n<mrow>\n<mrow>\n<mtext>Earth</mtext>\n</mrow>\n</mrow>\n</msub>\n</mrow>\n</mrow>\n<mrow>\n<mrow>\n<msub>\n<mi>T</mi>\n<mrow>\n<mi>M</mi>\n<mi>a</mi>\n<mi>r</mi>\n<mi>s</mi>\n</mrow>\n</msub>\n</mrow>\n</mrow>\n</mfrac>\n</mrow>\n<mo>)</mo>\n</mrow>\n<mn>2</mn>\n</msup>\n</mrow>\n<mrow>\n<msub>\n<mi>m</mi>\n<mrow>\n<mrow>\n<mtext>Earth</mtext>\n</mrow>\n</mrow>\n</msub>\n</mrow>\n</math></span></span> or other consistent re-arrangement ✔</p>\n<p>6.4 × 10<sup>23</sup> «kg» ✔</p>\n<p> </p>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>read off separation at maximum potential 0.9 ✔</p>\n<p>equating of gravitational field strength of earth and moon at that location <em><strong>OR <img src=\"data:image/png;base64,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\"/>✔</strong></em></p>\n<p>7.4 × 10<sup>22</sup> «kg» ✔</p>\n<p><em>Allow ECF from MP1</em></p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was generally well answered, although some candidates simply used the vague term “gravity” rather than specifying that it is a gravitational force or a gravitational field. Candidates need to be reminded about using proper physics terms and not more general, “every day” terms on the exam.</p>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Some candidates connected the idea that the gravitational force is perpendicular to the velocity (and hence the displacement) for the mark. It was also allowed to discuss that there is no change in gravitational potential energy, so therefore no work was being done. It was not acceptable to simply state that the net displacement over one full orbit is zero. Unfortunately, some candidates suggested that there is no net force on the moon so there is no work done, or that the moon is so much smaller so no work could be done on it.</p>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was another “show that” derivation. Many candidates attempted to work with universal gravitation equations, either from memory or the data booklet, to perform this derivation. The variety of correct solution paths was quite impressive, and many candidates who attempted this question were able to receive some marks. Candidates should be reminded on “show that” questions that it is never allowed to work backwards from the given answer. Some candidates also made up equations (such as T = 2𝝿r) to force the derivation to work out.</p>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This question was challenging for candidates. The candidates who started down the correct path of using the given derived value from 5bi often simply forgot that the multiplication factors had to be squared and cubed as well as the variables.</p>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This question was left blank by many candidates, and very few who attempted it were able to successfully recognize that the gravitational fields of the Earth and Moon balance at 0.9r and then use the proper equation to calculate the mass of the Moon.</p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion",
      "d-fields"
    ],
    "subtopics": [
      "a-2-forces-and-momentum",
      "a-3-work-energy-and-power",
      "d-1-gravitational-fields"
    ]
  },
  {
    "question_id": "19M.2.HL.TZ1.6",
    "Question": "<div class=\"specification\">\n<p>A small metal pendulum bob is suspended at rest from a fixed point with a length of thread of negligible mass. Air resistance is negligible.</p>\n<p>The pendulum begins to oscillate. Assume that the motion of the system is simple harmonic, and in one vertical plane.</p>\n<p>The graph shows the variation of kinetic energy of the pendulum bob with time.</p>\n<p style=\"text-align: center;\"><img 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\"/></p>\n</div><div class=\"specification\">\n<p>When the 75 g bob is moving horizontally at 0.80 m s<sup>–1</sup>, it collides with a small stationary object also of mass 75 g. The object and the bob stick together.</p>\n<p style=\"text-align: center;\"><img 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\"/></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Calculate, in m, the length of the thread. State your answer to an appropriate number of significant figures.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Label on the graph with the letter X a point where the speed of the pendulum is half that of its initial speed.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The mass of the pendulum bob is 75 g. Show that the maximum speed of the bob is about 0.7 m s<sup>–1</sup>.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Calculate the speed of the combined masses immediately after the collision.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Show that the collision is inelastic.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Sketch, on the axes, a graph to show the variation of gravitational potential energy with time for the bob and the object after the collision. The data from the graph used in (a) is shown as a dashed line for reference.</p>\n<p style=\"text-align:center;\"><img src=\"data:image/png;base64,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\"/></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p style=\"text-align:left;\">The speed after the collision of the bob and the object was measured using a sensor. This sensor emits a sound of frequency <em>f</em> and this sound is reflected from the moving bob. The sound is then detected by the sensor as frequency <em>f</em>′.</p>\n<p style=\"text-align:left;\">Explain why <em>f</em> and <em>f</em>′ are different.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">b.iv.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>identifies T as 2.25 s ✔</p>\n<p>L = 1.26 m ✔</p>\n<p>1.3 / 1.26 «m» ✔</p>\n<p><em>Accept <span style=\"text-decoration:underline;\">any</span> number of s.f. for MP2.</em></p>\n<p><em>Accept <span style=\"text-decoration:underline;\">any</span> answer with 2 or 3 s.f. for MP3</em>.</p>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>X labels any point <span style=\"text-decoration:underline;\">on the curve</span> where <em>E<span style=\"font-size:11.6667px;\"><sub>K</sub>  </span></em> <span class=\"mjpage\"><math alttext=\"\\frac{1}{4}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mn>1</mn>\n<mn>4</mn>\n</mfrac>\n</math></span> of maximum/5 mJ ✔</p>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"mjpage\"><math alttext=\"\\frac{1}{2}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mn>1</mn>\n<mn>2</mn>\n</mfrac>\n</math></span> mv<sup>2</sup> = 20 × 10<sup>−3</sup> seen <em><strong>OR </strong></em><span class=\"mjpage\"><math alttext=\"\\frac{1}{2}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mn>1</mn>\n<mn>2</mn>\n</mfrac>\n</math></span> × 7.5 × 10<sup>-2</sup> × <em>v</em><sup>2</sup> = 20 × 10<sup>-3</sup> ✔</p>\n<p>0.73 «m s<sup>−1</sup>» ✔</p>\n<p><em>Must see at least 2 s.f. for MP2</em>.</p>\n<div class=\"question_part_label\">a.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>0.40 «m s<sup>-1</sup>» ✔</p>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>initial energy 24 mJ and final energy 12 mJ ✔</p>\n<p>energy is lost/unequal /change in energy is 12 mJ ✔</p>\n<p>inelastic collisions occur when energy is lost ✔</p>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>graph with same period but inverted ✔</p>\n<p>amplitude one half of the original/two boxes throughout (by eye) ✔</p>\n<div class=\"question_part_label\">b.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>mention of Doppler effect ✔</p>\n<p>there is a change in the wavelength of the reflected wave ✔</p>\n<p>because the wave speed is constant, there is a change in frequency ✔</p>\n<div class=\"question_part_label\">b.iv.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>This question was well approached by candidates. The noteworthy mistakes were not reading the correct period of the pendulum from the graph, and some simple calculation and mathematical errors. This question also had one mark for writing an answer with the correct number of significant digits. Candidates should be aware to look for significant digit question on the exam and can write any number with correct number of significant digits for the mark.</p>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This question was well answered. This is a “show that” question so candidates needed to clearly show the correct calculation and write an answer with at least one significant digit more than the given answer. Many candidates failed to appreciate that the energy was given in mJ and the mass was in grams, and that these values needed to be converted before substitution.</p>\n<div class=\"question_part_label\">a.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Candidates fell into some broad categories on this question. This was a “show that” question, so there was an expectation of a mathematical argument. Many were able to successfully show that the initial and final kinetic energies were different and connect this to the concept of inelastic collisions. Some candidates tried to connect conservation of momentum unsuccessfully, and some simply wrote an extended response about the nature of inelastic collisions and noted that the bobs stuck together without any calculations. This approach was awarded zero marks.</p>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Many candidates drew graphs that received one mark for either recognizing the phase difference between the gravitational potential energy and the kinetic energy, or for recognizing that the total energy was half the original energy. Few candidates had both features for both marks.</p>\n<div class=\"question_part_label\">b.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This question was essentially about the Doppler effect, and therefore candidates were expected to give a good explanation for why there is a frequency difference. As with all explain questions, the candidates were required to go beyond the given information. Very few candidates earned marks beyond just recognizing that this was an example of the Doppler effect. Some did discuss the change in wavelength caused by the relative motion of the bob, although some candidates chose very vague descriptions like “the waves are all squished up” rather than using proper physics terms. Some candidates simply wrote and explained the equation from the data booklet, which did not receive marks. It should be noted that this was a three mark question, and yet some candidates attempted to answer it with a single sentence.</p>\n<div class=\"question_part_label\">b.iv.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-4-rigid-body-mechanics"
    ]
  },
  {
    "question_id": "19M.2.HL.TZ1.7",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that during an adiabatic expansion of an ideal monatomic gas the temperature\n   <span style=\"background-color:#ffffff;\">\n    <span class=\"mjpage\">\n     <math alttext=\"T\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n      <mi>\n       T\n      </mi>\n     </math>\n    </span>\n   </span>\n   and volume\n   <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">\n    <span class=\"mjpage\">\n     <math alttext=\"V\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n      <mi>\n       V\n      </mi>\n     </math>\n    </span>\n   </span>\n   are given by\n  </p>\n  <p style=\"text-align:center;\">\n   <span style=\"background-color:#ffffff;\">\n    <span class=\"mjpage\">\n     <math alttext=\"T{V^{\\frac{2}{3}}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n      <mi>\n       T\n      </mi>\n      <mrow>\n       <msup>\n        <mi>\n         V\n        </mi>\n        <mrow>\n         <mfrac>\n          <mn>\n           2\n          </mn>\n          <mn>\n           3\n          </mn>\n         </mfrac>\n        </mrow>\n       </msup>\n      </mrow>\n     </math>\n    </span>\n   </span>\n   = constant\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the efficiency of the cycle.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The work done during the isothermal expansion A → B is 540 J. Calculate the thermal energy that leaves the gas during one cycle.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the ratio\n   <span style=\"background-color:#ffffff;\">\n    <span class=\"mjpage\">\n     <math alttext=\"\\frac{{{V_C}}}{{{V_B}}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n      <mfrac>\n       <mrow>\n        <mrow>\n         <msub>\n          <mi>\n           V\n          </mi>\n          <mi>\n           C\n          </mi>\n         </msub>\n        </mrow>\n       </mrow>\n       <mrow>\n        <mrow>\n         <msub>\n          <mi>\n           V\n          </mi>\n          <mi>\n           B\n          </mi>\n         </msub>\n        </mrow>\n       </mrow>\n      </mfrac>\n     </math>\n    </span>\n   </span>\n   where\n   <em>\n    V\n    <sub>\n     C\n    </sub>\n   </em>\n   is the volume of the gas at C and\n   <em>\n    V\n    <sub>\n     B\n    </sub>\n   </em>\n   is the volume at B.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the change in the entropy of the gas during the change A to B.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c.ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Explain, by reference to the second law of thermodynamics, why a real engine operating between the temperatures of 620 K and 340 K cannot have an efficiency greater than the answer to (b)(i).\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  substitution of\n  <span style=\"background-color:#ffffff;\">\n   <span class=\"mjpage\">\n    <math alttext=\"P = \\frac{{nRT}}{V}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mi>\n      P\n     </mi>\n     <mo>\n      =\n     </mo>\n     <mfrac>\n      <mrow>\n       <mi>\n        n\n       </mi>\n       <mi>\n        R\n       </mi>\n       <mi>\n        T\n       </mi>\n      </mrow>\n      <mi>\n       V\n      </mi>\n     </mfrac>\n    </math>\n   </span>\n   in\n   <span class=\"mjpage\">\n    <math alttext=\"{P_X}V_X^{\\frac{5}{3}} = {P_Y}V_Y^{\\frac{5}{3}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mrow>\n      <msub>\n       <mi>\n        P\n       </mi>\n       <mi>\n        X\n       </mi>\n      </msub>\n     </mrow>\n     <msubsup>\n      <mi>\n       V\n      </mi>\n      <mi>\n       X\n      </mi>\n      <mrow>\n       <mfrac>\n        <mn>\n         5\n        </mn>\n        <mn>\n         3\n        </mn>\n       </mfrac>\n      </mrow>\n     </msubsup>\n     <mo>\n      =\n     </mo>\n     <mrow>\n      <msub>\n       <mi>\n        P\n       </mi>\n       <mi>\n        Y\n       </mi>\n      </msub>\n     </mrow>\n     <msubsup>\n      <mi>\n       V\n      </mi>\n      <mi>\n       Y\n      </mi>\n      <mrow>\n       <mfrac>\n        <mn>\n         5\n        </mn>\n        <mn>\n         3\n        </mn>\n       </mfrac>\n      </mrow>\n     </msubsup>\n    </math>\n   </span>\n  </span>\n  ✔\n </p>\n <p>\n  manipulation to get result ✔\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.i)\n </div><div class=\"card-body\">\n <p>\n  e « = 1 −\n  <span style=\"background-color:#ffffff;\">\n   <span class=\"mjpage\">\n    <math alttext=\"\\frac{{{T_c}}}{{{T_h}}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mfrac>\n      <mrow>\n       <mrow>\n        <msub>\n         <mi>\n          T\n         </mi>\n         <mi>\n          c\n         </mi>\n        </msub>\n       </mrow>\n      </mrow>\n      <mrow>\n       <mrow>\n        <msub>\n         <mi>\n          T\n         </mi>\n         <mi>\n          h\n         </mi>\n        </msub>\n       </mrow>\n      </mrow>\n     </mfrac>\n    </math>\n   </span>\n  </span>\n  = 1 −\n  <span class=\"mjpage\">\n   <math alttext=\"\\frac{340}{620}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mfrac>\n     <mn>\n      340\n     </mn>\n     <mn>\n      620\n     </mn>\n    </mfrac>\n   </math>\n  </span>\n  » = 0.45 ✔\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.ii)\n </div><div class=\"card-body\">\n <p>\n  heat into gas «is along AB» and equals\n </p>\n <p>\n  <em>\n   Q\n   <sub>\n    in\n   </sub>\n  </em>\n  «= Δ\n  <em>\n   U\n  </em>\n  +\n  <em>\n   W\n  </em>\n  = 0 + 540» = 540 «J» ✔\n </p>\n <p>\n  heat out is (1−\n  <em>\n   e\n  </em>\n  )\n  <em>\n   Q\n   <sub>\n    in =\n   </sub>\n  </em>\n  (1−0.45) × 540 = 297 «J» ≈ 3.0 × 10\n  <sup>\n   2\n  </sup>\n  «J» ✔\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    [2]\n   </strong>\n   for bald correct answer.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.iii)\n </div><div class=\"card-body\">\n <p>\n  <span style=\"background-color:#ffffff;\">\n   <span class=\"mjpage\">\n    <math alttext=\"{T_B}V_B^{\\frac{2}{3}} = {T_C}V_C^{\\frac{2}{3}} \\Rightarrow \\frac{{{V_C}}}{{{V_B}}} = {\\left( {\\frac{{{T_B}}}{{{T_C}}}} \\right)^{\\frac{3}{2}}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mrow>\n      <msub>\n       <mi>\n        T\n       </mi>\n       <mi>\n        B\n       </mi>\n      </msub>\n     </mrow>\n     <msubsup>\n      <mi>\n       V\n      </mi>\n      <mi>\n       B\n      </mi>\n      <mrow>\n       <mfrac>\n        <mn>\n         2\n        </mn>\n        <mn>\n         3\n        </mn>\n       </mfrac>\n      </mrow>\n     </msubsup>\n     <mo>\n      =\n     </mo>\n     <mrow>\n      <msub>\n       <mi>\n        T\n       </mi>\n       <mi>\n        C\n       </mi>\n      </msub>\n     </mrow>\n     <msubsup>\n      <mi>\n       V\n      </mi>\n      <mi>\n       C\n      </mi>\n      <mrow>\n       <mfrac>\n        <mn>\n         2\n        </mn>\n        <mn>\n         3\n        </mn>\n       </mfrac>\n      </mrow>\n     </msubsup>\n     <mo stretchy=\"false\">\n      ⇒\n     </mo>\n     <mfrac>\n      <mrow>\n       <mrow>\n        <msub>\n         <mi>\n          V\n         </mi>\n         <mi>\n          C\n         </mi>\n        </msub>\n       </mrow>\n      </mrow>\n      <mrow>\n       <mrow>\n        <msub>\n         <mi>\n          V\n         </mi>\n         <mi>\n          B\n         </mi>\n        </msub>\n       </mrow>\n      </mrow>\n     </mfrac>\n     <mo>\n      =\n     </mo>\n     <mrow>\n      <msup>\n       <mrow>\n        <mo>\n         (\n        </mo>\n        <mrow>\n         <mfrac>\n          <mrow>\n           <mrow>\n            <msub>\n             <mi>\n              T\n             </mi>\n             <mi>\n              B\n             </mi>\n            </msub>\n           </mrow>\n          </mrow>\n          <mrow>\n           <mrow>\n            <msub>\n             <mi>\n              T\n             </mi>\n             <mi>\n              C\n             </mi>\n            </msub>\n           </mrow>\n          </mrow>\n         </mfrac>\n        </mrow>\n        <mo>\n         )\n        </mo>\n       </mrow>\n       <mrow>\n        <mfrac>\n         <mn>\n          3\n         </mn>\n         <mn>\n          2\n         </mn>\n        </mfrac>\n       </mrow>\n      </msup>\n     </mrow>\n    </math>\n   </span>\n  </span>\n  ✔\n </p>\n <p>\n  <span style=\"background-color:#ffffff;\">\n   <span class=\"mjpage\">\n    <math alttext=\"\\frac{{{V_C}}}{{{V_B}}} = {\\left( {\\frac{{620}}{{340}}} \\right)^{\\frac{3}{2}}} = 2.5\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mfrac>\n      <mrow>\n       <mrow>\n        <msub>\n         <mi>\n          V\n         </mi>\n         <mi>\n          C\n         </mi>\n        </msub>\n       </mrow>\n      </mrow>\n      <mrow>\n       <mrow>\n        <msub>\n         <mi>\n          V\n         </mi>\n         <mi>\n          B\n         </mi>\n        </msub>\n       </mrow>\n      </mrow>\n     </mfrac>\n     <mo>\n      =\n     </mo>\n     <mrow>\n      <msup>\n       <mrow>\n        <mo>\n         (\n        </mo>\n        <mrow>\n         <mfrac>\n          <mrow>\n           <mn>\n            620\n           </mn>\n          </mrow>\n          <mrow>\n           <mn>\n            340\n           </mn>\n          </mrow>\n         </mfrac>\n        </mrow>\n        <mo>\n         )\n        </mo>\n       </mrow>\n       <mrow>\n        <mfrac>\n         <mn>\n          3\n         </mn>\n         <mn>\n          2\n         </mn>\n        </mfrac>\n       </mrow>\n      </msup>\n     </mrow>\n     <mo>\n      =\n     </mo>\n     <mn>\n      2.5\n     </mn>\n    </math>\n   </span>\n  </span>\n  ✔\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    [2]\n   </strong>\n   for bald correct answer.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c.i)\n </div><div class=\"card-body\">\n <p>\n  Δ\n  <em>\n   S\n  </em>\n  «=\n  <span class=\"mjpage\">\n   <math alttext=\"\\frac{Q}{T}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mfrac>\n     <mi>\n      Q\n     </mi>\n     <mi>\n      T\n     </mi>\n    </mfrac>\n   </math>\n  </span>\n  =\n  <span class=\"mjpage\">\n   <math alttext=\"\\frac{540}{620}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mfrac>\n     <mn>\n      540\n     </mn>\n     <mn>\n      620\n     </mn>\n    </mfrac>\n   </math>\n  </span>\n  »= 0.87 «JK\n  <sup>\n   −1\n  </sup>\n  » ✔\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c.ii)\n </div><div class=\"card-body\">\n <p>\n  the Carnot cycle has the maximum efficiency «for heat engines operating between two given temperatures »✔\n </p>\n <p>\n  real engine can not work at Carnot cycle/ideal cycle ✔\n </p>\n <p>\n  the second law of thermodynamics says that it is impossible to convert all the input heat into mechanical work ✔\n </p>\n <p>\n  a real engine would have additional losses due to friction\n  <em>\n   etc\n  </em>\n  ✔\n </p>\n</div>\n",
    "Examiners report": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  The algebraic manipulation required for this question was well mastered by only the better-prepared candidates. Many candidates tried to find the required formula via randomly selected equations from the data booklet.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.i)\n </div><div class=\"card-body\">\n <p>\n  The efficiency of the Carnot cycle was well calculated by most of the candidates, but the thermal energy that leaves the gas was well calculated only by the best candidates. Many candidates were able to establish that the heat added to the gas was 540 J - but struggled to then link this with the efficiency to determine the thermal energy leaving the gas. In iii) the better candidates used the formula given at i) to appropriately calculate the ratio but many were not able to manipulate the expressions to achieve the desired outcome. The reciprocal of 2.5 (0.4) was a common error in the final result and so was the incorrect use of the formula for isobaric expansion. The change in the entropy was well calculated by many candidates with ECF being very prominent from part biii). A complete and proper explanation in ii) was well formulated only by the better candidates. However, many were able to recognize that the Carnot engine was ideal and not real. Many answers referred to heat being lost to the environment but not to “additional losses” that make the engine less than its ideal capacity.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.ii)\n </div><div class=\"card-body\">\n <p>\n  The efficiency of the Carnot cycle was well calculated by most of the candidates, but the thermal energy that leaves the gas was well calculated only by the best candidates. Many candidates were able to establish that the heat added to the gas was 540 J - but struggled to then link this with the efficiency to determine the thermal energy leaving the gas. In iii) the better candidates used the formula given at i) to appropriately calculate the ratio but many were not able to manipulate the expressions to achieve the desired outcome. The reciprocal of 2.5 (0.4) was a common error in the final result and so was the incorrect use of the formula for isobaric expansion. The change in the entropy was well calculated by many candidates with ECF being very prominent from part biii). A complete and proper explanation in ii) was well formulated only by the better candidates. However, many were able to recognize that the Carnot engine was ideal and not real. Many answers referred to heat being lost to the environment but not to “additional losses” that make the engine less than its ideal capacity.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.iii)\n </div><div class=\"card-body\">\n <p>\n  The efficiency of the Carnot cycle was well calculated by most of the candidates, but the thermal energy that leaves the gas was well calculated only by the best candidates. Many candidates were able to establish that the heat added to the gas was 540 J - but struggled to then link this with the efficiency to determine the thermal energy leaving the gas. In iii) the better candidates used the formula given at i) to appropriately calculate the ratio but many were not able to manipulate the expressions to achieve the desired outcome. The reciprocal of 2.5 (0.4) was a common error in the final result and so was the incorrect use of the formula for isobaric expansion. The change in the entropy was well calculated by many candidates with ECF being very prominent from part biii). A complete and proper explanation in ii) was well formulated only by the better candidates. However, many were able to recognize that the Carnot engine was ideal and not real. Many answers referred to heat being lost to the environment but not to “additional losses” that make the engine less than its ideal capacity.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c.i)\n </div><div class=\"card-body\">\n <p>\n  The efficiency of the Carnot cycle was well calculated by most of the candidates, but the thermal energy that leaves the gas was well calculated only by the best candidates. Many candidates were able to establish that the heat added to the gas was 540 J - but struggled to then link this with the efficiency to determine the thermal energy leaving the gas. In iii) the better candidates used the formula given at i) to appropriately calculate the ratio but many were not able to manipulate the expressions to achieve the desired outcome. The reciprocal of 2.5 (0.4) was a common error in the final result and so was the incorrect use of the formula for isobaric expansion. The change in the entropy was well calculated by many candidates with ECF being very prominent from part biii). A complete and proper explanation in ii) was well formulated only by the better candidates. However, many were able to recognize that the Carnot engine was ideal and not real. Many answers referred to heat being lost to the environment but not to “additional losses” that make the engine less than its ideal capacity.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c.ii)\n </div><div class=\"card-body\">\n <p>\n  The efficiency of the Carnot cycle was well calculated by most of the candidates, but the thermal energy that leaves the gas was well calculated only by the best candidates. Many candidates were able to establish that the heat added to the gas was 540 J - but struggled to then link this with the efficiency to determine the thermal energy leaving the gas. In iii) the better candidates used the formula given at i) to appropriately calculate the ratio but many were not able to manipulate the expressions to achieve the desired outcome. The reciprocal of 2.5 (0.4) was a common error in the final result and so was the incorrect use of the formula for isobaric expansion. The change in the entropy was well calculated by many candidates with ECF being very prominent from part biii). A complete and proper explanation in ii) was well formulated only by the better candidates. However, many were able to recognize that the Carnot engine was ideal and not real. Many answers referred to heat being lost to the environment but not to “additional losses” that make the engine less than its ideal capacity.\n </p>\n</div>\n",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-4-thermodynamics"
    ]
  },
  {
    "question_id": "19M.2.HL.TZ2.10",
    "Question": "<div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">A small magnet is dropped from rest above a stationary horizontal conducting ring. The south (S) pole of the magnet is upwards.</span></p>\n<p><span style=\"background-color: #ffffff;\"><img 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\"/></span></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">While the magnet is moving towards the ring, state why the magnetic flux in the ring is increasing.</span></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">While the magnet is moving towards the ring, sketch, using an arrow on <strong>Diagram 2</strong>, the direction of the induced current in the ring.</span></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">While the magnet is moving towards the ring, deduce the direction of the magnetic force on the magnet.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">the magnetic field at the position of the ring is increasing «because the magnet gets closer to the ring» ✔</span></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">the current must be counterclockwise «in diagram 2» ✔<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><em>eg</em>:</span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><img height=\"182\" 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\" width=\"209\"/></span></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">since the induced magnetic field is upwards<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><em><strong>OR</strong></em><br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">by Lenz law the change «of magnetic field/flux» must be opposed<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><em><strong>OR</strong></em><br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">by conservation of energy the movement of the magnet must be opposed ✔<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">therefore the force is repulsive/upwards ✔</span></p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was well-answered.</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Answers here were reasonably evenly split between clockwise and anti-clockwise, with the odd few arrows pointing left or right.</p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>The majority of candidates recognised that the magnetic force would be upwards and the most common way of explaining this was via Lenz’s law. Students needed to get across that the force is opposing a change or a motion.</p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-4-thermodynamics"
    ]
  },
  {
    "question_id": "19M.2.HL.TZ2.11",
    "Question": "<div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">In an experiment to determine the radius of a carbon-12 nucleus, a beam of neutrons is scattered by a thin film of carbon-12. The graph shows the variation of intensity of the scattered neutrons with scattering angle. The de Broglie wavelength of the neutrons is 1.6 × 10<sup>-15</sup> m.</span></p>\n<p><span style=\"background-color: #ffffff;\"><img src=\"data:image/png;base64,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\"/></span></p>\n</div><div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">A pure sample of copper-64 has a mass of 28 mg. The decay constant of copper-64 is 5.5 × 10<sup>-2</sup> hour<sup>–1</sup>.</span></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Suggest why de Broglie’s hypothesis is <strong>not</strong> consistent with Bohr’s conclusion that the electron’s orbit in the hydrogen atom has a well defined radius.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Estimate, using the graph, the radius of a carbon-12 nucleus.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">bi.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">The ratio <span class=\"mjpage\"><math alttext=\"\\frac{{{\\text{volume of a nucleaus of mass number }}A}}{{{\\text{volume of a nucleon}}}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mrow>\n<mrow>\n<mtext>volume of a nucleaus of mass number </mtext>\n</mrow>\n<mi>A</mi>\n</mrow>\n<mrow>\n<mrow>\n<mtext>volume of a nucleon</mtext>\n</mrow>\n</mrow>\n</mfrac>\n</math></span> is approximately A.<br/></span></p>\n<p><span style=\"background-color:#ffffff;\">Comment on this observation by reference to the strong nuclear force.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">bii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Estimate, in Bq, the initial activity of the sample.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">ci.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Calculate, in hours, the time at which the activity of the sample has decreased to one-third of the initial activity.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">cii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">«de Broglie’s hypothesis states that the» electron is represented by a wave ✔<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">therefore it cannot be localized/it is spread out/it does not have a definite position ✔</span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><em><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\">Award MP1 for any mention of wavelike property of an electron.</span></span></em></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">«<span class=\"mjpage\"><math alttext=\"d\\sin \\theta  = \\lambda  \\Rightarrow \" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>d</mi>\n<mi>sin</mi>\n<mo>⁡</mo>\n<mi>θ</mi>\n<mo>=</mo>\n<mi>λ</mi>\n<mo stretchy=\"false\">⇒</mo>\n</math></span>» <span class=\"mjpage\"><math alttext=\"d = \\frac{{1.6 \\times {{10}^{ - 15}}}}{{\\sin 17^\\circ }}/5.47 \\times {10^{ - 15}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>d</mi>\n<mo>=</mo>\n<mfrac>\n<mrow>\n<mn>1.6</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>15</mn>\n</mrow>\n</msup>\n</mrow>\n</mrow>\n<mrow>\n<mi>sin</mi>\n<mo>⁡</mo>\n<msup>\n<mn>17</mn>\n<mo>∘</mo>\n</msup>\n</mrow>\n</mfrac>\n<mrow>\n<mo>/</mo>\n</mrow>\n<mn>5.47</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mn>10</mn>\n<mrow>\n<mo>−</mo>\n<mn>15</mn>\n</mrow>\n</msup>\n</mrow>\n</math></span> </span><span style=\"background-color:#ffffff;\">«m»</span><span style=\"background-color:#ffffff;\"> ✔<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"R = \\frac{d}{2} \\approx 2.7/2.8 \\times {10^{ - 15}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>R</mi>\n<mo>=</mo>\n<mfrac>\n<mi>d</mi>\n<mn>2</mn>\n</mfrac>\n<mo>≈</mo>\n<mn>2.7</mn>\n<mrow>\n<mo>/</mo>\n</mrow>\n<mn>2.8</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mn>10</mn>\n<mrow>\n<mo>−</mo>\n<mn>15</mn>\n</mrow>\n</msup>\n</mrow>\n</math></span> «m» ✔</span></p>\n<div class=\"question_part_label\">bi.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">this implies that the nucleons are very tightly packed/that there is very little space in between the nucleons ✔<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">because the nuclear force is stronger than the electrostatic force ✔</span></p>\n<div class=\"question_part_label\">bii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">number of nuclei is <span class=\"mjpage\"><math alttext=\"\\frac{{28 \\times {{10}^{ - 3}}}}{{64}} \\times 6.02 \\times {10^{23}}/2.63 \\times {10^{20}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mrow>\n<mn>28</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>3</mn>\n</mrow>\n</msup>\n</mrow>\n</mrow>\n<mrow>\n<mn>64</mn>\n</mrow>\n</mfrac>\n<mo>×</mo>\n<mn>6.02</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mn>10</mn>\n<mrow>\n<mn>23</mn>\n</mrow>\n</msup>\n</mrow>\n<mrow>\n<mo>/</mo>\n</mrow>\n<mn>2.63</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mn>10</mn>\n<mrow>\n<mn>20</mn>\n</mrow>\n</msup>\n</mrow>\n</math></span> ✔<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"A = \" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>A</mi>\n<mo>=</mo>\n</math></span><span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">«<span class=\"mjpage\"><math alttext=\"\\lambda N = 2.63 \\times {10^{20}} \\times \\frac{{5.5 \\times {{10}^{ - 2}}}}{{3600}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>λ</mi>\n<mi>N</mi>\n<mo>=</mo>\n<mn>2.63</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mn>10</mn>\n<mrow>\n<mn>20</mn>\n</mrow>\n</msup>\n</mrow>\n<mo>×</mo>\n<mfrac>\n<mrow>\n<mn>5.5</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>2</mn>\n</mrow>\n</msup>\n</mrow>\n</mrow>\n<mrow>\n<mn>3600</mn>\n</mrow>\n</mfrac>\n</math></span>» <span class=\"mjpage\"><math alttext=\"4.0 \\times {10^{15}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mn>4.0</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mn>10</mn>\n<mrow>\n<mn>15</mn>\n</mrow>\n</msup>\n</mrow>\n</math></span> </span></span><span style=\"background-color:#ffffff;\">«Bq» ✔</span></p>\n<div class=\"question_part_label\">ci.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"\\frac{{\\text{1}}}{{\\text{3}}} = {e^{ - \\lambda t}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mrow>\n<mtext>1</mtext>\n</mrow>\n<mrow>\n<mtext>3</mtext>\n</mrow>\n</mfrac>\n<mo>=</mo>\n<mrow>\n<msup>\n<mi>e</mi>\n<mrow>\n<mo>−</mo>\n<mi>λ</mi>\n<mi>t</mi>\n</mrow>\n</msup>\n</mrow>\n</math></span></span><span style=\"background-color:#ffffff;\"> ✔<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><em>t </em>= 20«hr» ✔</span></p>\n<div class=\"question_part_label\">cii.</div>\n</div>",
    "Examiners report": "",
    "topics": [
      "c-wave-behaviour",
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "c-3-wave-phenomena",
      "e-1-structure-of-the-atom",
      "e-2-quantum-physics",
      "e-3-radioactive-decay"
    ]
  },
  {
    "question_id": "19M.2.HL.TZ2.4",
    "Question": "<div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">Three identical light bulbs, X, Y and Z, each of resistance 4.0 Ω are connected to a cell of emf 12 V. The cell has negligible internal resistance.</span></p>\n<p><span style=\"background-color: #ffffff;\"><img src=\"data:image/png;base64,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\"/></span></p>\n</div><div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">When fully charged the space between the plates of the capacitor is filled with a dielectric with double the permittivity of a vacuum.</span></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">The switch S is initially open. Calculate the total power dissipated in the circuit.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">The switch is now closed. State, without calculation, why the current in the cell will increase.</span></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">bi.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">The switch is now closed. <span class=\"mjpage\"><math alttext=\"{\\text{Deduce the ratio }}\\frac{{{\\text{power dissipated in Y with S open}}}}{{{\\text{power dissipated in Y with S closed}}}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mrow>\n<mtext>Deduce the ratio </mtext>\n</mrow>\n<mfrac>\n<mrow>\n<mrow>\n<mtext>power dissipated in Y with S open</mtext>\n</mrow>\n</mrow>\n<mrow>\n<mrow>\n<mtext>power dissipated in Y with S closed</mtext>\n</mrow>\n</mrow>\n</mfrac>\n</math></span>.</span></p>\n<p> </p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">bii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">The cell is used to charge a parallel-plate capacitor in a vacuum. The fully charged capacitor is then connected to an ideal voltmeter.</span></p>\n<p><span style=\"background-color:#ffffff;\"><img src=\"data:image/png;base64,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\"/></span></p>\n<p><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\">The capacitance of the capacitor is 6.0 μF and the reading of the voltmeter is 12 V.</span></span></p>\n<p><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\">Calculate the energy stored in the capacitor.</span></span></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Calculate the change in the energy stored in the capacitor.</span></p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">di.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Suggest, in terms of conservation of energy, the cause for the above change.</span></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">dii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">total resistance of circuit is 8.0 «Ω» ✔</span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"P = \\frac{{{{12}^2}}}{{8.0}} = 18\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>P</mi>\n<mo>=</mo>\n<mfrac>\n<mrow>\n<mrow>\n<msup>\n<mrow>\n<mn>12</mn>\n</mrow>\n<mn>2</mn>\n</msup>\n</mrow>\n</mrow>\n<mrow>\n<mn>8.0</mn>\n</mrow>\n</mfrac>\n<mo>=</mo>\n<mn>18</mn>\n</math></span>«W» <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">✔</span></span></span></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">«a resistor is now connected in parallel» reducing the total resistance<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><em><strong>OR</strong></em><br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">current through YZ unchanged and additional current flows through X ✔</span></p>\n<div class=\"question_part_label\">bi.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">evidence in calculation or statement that pd across Y/current in Y is the same as before ✔<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">so ratio is 1 ✔</span></p>\n<div class=\"question_part_label\">bii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"E = «\\frac{1}{2}C{V^2} = \\frac{1}{2} \\times 6 \\times {10^{ - 6}} \\times {12^2} =»  4.3 \\times {10^{ - 4}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>E</mi>\n<mo>=</mo>\n<mrow>\n<mo>«</mo>\n</mrow>\n<mfrac>\n<mn>1</mn>\n<mn>2</mn>\n</mfrac>\n<mi>C</mi>\n<mrow>\n<msup>\n<mi>V</mi>\n<mn>2</mn>\n</msup>\n</mrow>\n<mo>=</mo>\n<mfrac>\n<mn>1</mn>\n<mn>2</mn>\n</mfrac>\n<mo>×</mo>\n<mn>6</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mn>10</mn>\n<mrow>\n<mo>−</mo>\n<mn>6</mn>\n</mrow>\n</msup>\n</mrow>\n<mo>×</mo>\n<mrow>\n<msup>\n<mn>12</mn>\n<mn>2</mn>\n</msup>\n</mrow>\n<mo>=</mo>\n<mrow>\n<mo>»</mo>\n</mrow>\n<mn>4.3</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mn>10</mn>\n<mrow>\n<mo>−</mo>\n<mn>4</mn>\n</mrow>\n</msup>\n</mrow>\n</math></span>«<span class=\"mjpage\"><math alttext=\"{\\text{J}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mrow>\n<mtext>J</mtext>\n</mrow>\n</math></span>» ✔</span></p>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><em><strong><span style=\"background-color:#ffffff;\">ALTERNATIVE 1</span></strong></em></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">capacitance doubles and voltage halves ✔<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">since <span class=\"mjpage\"><math alttext=\"E = \\frac{1}{2}C{V^2}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>E</mi>\n<mo>=</mo>\n<mfrac>\n<mn>1</mn>\n<mn>2</mn>\n</mfrac>\n<mi>C</mi>\n<mrow>\n<msup>\n<mi>V</mi>\n<mn>2</mn>\n</msup>\n</mrow>\n</math></span> energy halves   <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">✔</span></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">so change is «–»2.2×10<sup>–4 </sup>«J»  <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">✔</span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"> </span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><em><strong>ALTERNATIVE 2</strong></em><br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"E = \\frac{1}{2}C{V^2}{\\text{ and }}Q = CV{\\text{ so }}E = \\frac{{{Q^2}}}{{2C}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>E</mi>\n<mo>=</mo>\n<mfrac>\n<mn>1</mn>\n<mn>2</mn>\n</mfrac>\n<mi>C</mi>\n<mrow>\n<msup>\n<mi>V</mi>\n<mn>2</mn>\n</msup>\n</mrow>\n<mrow>\n<mtext> and </mtext>\n</mrow>\n<mi>Q</mi>\n<mo>=</mo>\n<mi>C</mi>\n<mi>V</mi>\n<mrow>\n<mtext> so </mtext>\n</mrow>\n<mi>E</mi>\n<mo>=</mo>\n<mfrac>\n<mrow>\n<mrow>\n<msup>\n<mi>Q</mi>\n<mn>2</mn>\n</msup>\n</mrow>\n</mrow>\n<mrow>\n<mn>2</mn>\n<mi>C</mi>\n</mrow>\n</mfrac>\n</math></span>  <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">✔</span> </span><span style=\"background-color:#ffffff;\"><br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">capacitance doubles and charge unchanged so energy halves ✔<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">so change is <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">«</span><span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">−</span><span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">»</span>2.2 <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">×</span> 10<sup><span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">−</span>4 </sup>«<span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">J</span>» ✔</span></p>\n<div class=\"question_part_label\">di.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">it is the work done when inserting the dielectric into the capacitor ✔<br/></span></p>\n<div class=\"question_part_label\">dii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>Most candidates scored both marks. ECF was awarded for those who didn’t calculate the new resistance correctly. Candidates showing clearly that they were attempting to calculate the new total resistance helped examiners to award ECF marks.</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Most recognised that this decreased the total resistance of the circuit. Answers scoring via the second alternative were rare as the statements were often far too vague.</p>\n<div class=\"question_part_label\">bi.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Very few gained any credit for this at both levels. Most performed complicated calculations involving the total circuit and using 12V – they had not realised that the question refers to Y only.</p>\n<div class=\"question_part_label\">bii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Most answered this correctly.</p>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>By far the most common answer involved doubling the capacitance without considering the change in p.d. Almost all candidates who did this calculated a change in energy that scored 1 mark.</p>\n<div class=\"question_part_label\">di.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Very few scored on this question.</p>\n<div class=\"question_part_label\">dii.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-5-galilean-and-special-relativity"
    ]
  },
  {
    "question_id": "19M.2.HL.TZ2.6",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <span style=\"background-color:#ffffff;\">\n    Define\n    <em>\n     proper length\n    </em>\n    .\n   </span>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (bi)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <span style=\"background-color:#ffffff;\">\n    In the reference frame of the train a ball travels with speed 0.50\n    <em>\n     c\n    </em>\n    from the back to the front of the train, as the train passes the platform. Calculate the time taken for the ball to reach the front of the train in the reference frame of the train.\n   </span>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (bii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <span style=\"background-color:#ffffff;\">\n    In the reference frame of the train a ball travels with speed 0.50\n    <em>\n     c\n    </em>\n    from the back to the front of the train, as the train passes the platform. Calculate the time taken for the ball to reach the front of the train in the reference frame of the platform.\n   </span>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p style=\"text-align:left;\">\n  <span style=\"background-color:#ffffff;\">\n   the length measured «in a reference frame» where the object is at rest ✔\n   <br/>\n  </span>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (bi)\n </div><div class=\"card-body\">\n <p style=\"text-align:left;\">\n  <img height=\"47\" src=\"data:image/png;base64,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\" width=\"304\"/>\n  <span style=\"background-color:#ffffff;\">\n   <br/>\n  </span>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (bii)\n </div><div class=\"card-body\">\n <p style=\"text-align:left;\">\n  <em>\n   <strong>\n    <span style=\"background-color:#ffffff;\">\n     ALTERNATIVE 1:\n    </span>\n   </strong>\n  </em>\n  <span style=\"background-color:#ffffff;\">\n   <br/>\n  </span>\n </p>\n <p style=\"text-align:left;\">\n  <span style=\"background-color:#ffffff;\">\n   <img height=\"115\" 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\" width=\"265\"/>\n  </span>\n </p>\n <p style=\"text-align:left;\">\n  <em>\n   <strong>\n    <span style=\"background-color:#ffffff;\">\n     <span style=\"background-color:#ffffff;\">\n      ALTERNATIVE 2:\n     </span>\n    </span>\n   </strong>\n  </em>\n </p>\n <p style=\"text-align:left;\">\n  <span style=\"background-color:#ffffff;\">\n   <span style=\"background-color:#ffffff;\">\n    <span style=\"background-color:#ffffff;\">\n     <em>\n      v\n     </em>\n     of ball is 0.846\n     <em>\n      c\n     </em>\n     for platform ✔\n     <br/>\n    </span>\n   </span>\n  </span>\n </p>\n <p style=\"text-align:left;\">\n  <span style=\"background-color:#ffffff;\">\n   <span style=\"background-color:#ffffff;\">\n    <span style=\"background-color:#ffffff;\">\n     length of train is 68m for platform ✔\n    </span>\n   </span>\n  </span>\n </p>\n <p style=\"text-align:left;\">\n  <span style=\"background-color:#ffffff;\">\n   <span style=\"background-color:#ffffff;\">\n    <span style=\"background-color:#ffffff;\">\n     <img height=\"45\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAjEAAAA2CAYAAAA29chlAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABkkSURBVHhe7Z0PcBTXfce/KKnjThUSO26Hk2nNGAykAxk8omSSeqYH1Ec8rh0KJW4dOBwxKfaAB1u1ThE2DomdUDjNNXbRJJA5RYCT2JBV5T+MkdoTqodxLeXkOBatcqrCACPdOXXsWH8c/ln3+t7evr29vd293ZNOQuj3mXmI29vbP+/v9/3e7703i3FAEARBEAQxzSjT/hIEQRAEQUwrSMQQBEEQBDEtIRFDEARBEMS0hEQMQRAEQRDTEhIxBCeN0b52NNauwaxZs9RQsbkezd0p/o0Fo31ob6zFSu3cWbPWoLaxHX2jlmcTBEEQREmg2UkznstIte/B/at3o0M7kiWAulgjnl51c1btjnah/p61qOlIaQey+IJNaG/YhMXlpI0JgiCI0kOtzQwnPfgKntjIBYy/DkpiCELTMnYJyc79CPrasGdjAzqGpYXlIvqO1nMB8xkEoz0YUc/lYSyJzkgQOFyHHUf7rK03BEEQBDHBkIiZ0VxEf+vzaEzdjXB9COsWztaOXwffii14/OkNQKoNrfH3M4fTZ3HqhVOA7x5s/rs/R3nmKM9FPqzYshmbfCm0vfA6+knFEARBEJMAiZiZjBQlgXW49/ZPawcl12Nh1VEwFsfeVTdpxwrjWzYPcyhXEQRBEJMANTczmdEkEj2pjPD4fa6zrqVjb9mtWLN1HXypl3HoZ/+DUe0w0il0RQ/hSKoSm9Z8DtKeQxAEQRClhBx7ZzDpvkbctWgLeoLV+IfzP0Ukz1l3CaqUV/DDdbcY1O4w+pr/GVvX78l1BPYFET70OB68c2F2mIkgCIIgSghZYgikDkcQwSY0xZMYU511xzCSUBDyv4fG7WG0DF7WzuSMJnG6szt/JlPqTfScfhcj5A9DEARBTBIkYgjOBkQPfAubK31ahihD+cK1eHzXA/ClmnGg9UxmWCl9Ds07NmD9kTmIdErBI8IQEso9OF+9AfdHurLDTARBEARRQkjEzGDK5szDMh//T+BLuGPB9ZmDOlzIzF2ApUihJ5FUhUm6P4YDje8h8HQddqyQgkcwGwvXVWNXqAIdkRZ06VOyCYIgCKJ0kIiZyZRXYNFSoWLckMboQD96tE/5lGPuoltzp2QTxBTyUXc9FuirSmfDgvpufKSdQxDE9IZEzEym7CbMW1YBtDXjpV98oB2USNEiZxxJy4wdoxhInOF/b8WiueTaS0w9H698DP36kOclDCjb4PPvxsGvLsXHtXMIgpjekIiZ0dyIFV/5Kvw4jprH9qG5b1g7LvZSasF3nmpCyhfAmuU3qkfLFnwR9wW45jnyIzS92I2UPmokZixF8NS+bpuhKYKYWsTK1E9ufwObdm3DKt912lGCIK5W2MVBdB8/hGfr61Hf9AbetZtHLaZY64wlWfxkgo1oH/kBNhSrYz74WCDayz8R1x5DrDdaxdMYIouYQoDVxQYM6T7GRnqbWNBndS4Pvm1MGbiknUuUkrFknCnhYDbd/CEWjRnLrgtEeW85yEJ+nyENgyysxFmy1IV9pJOF/fMd6pUhlohFc59NvGNLMc92gSWiGxgCUZa4RisxkR9ajoVNZTPAQlGFxRJD2llmzjMlON9wvlVYwoJhhcWTVK5LwwiLh/0W8e5n4bin0nxtceUMUx6s1OLiT9md4TfYUFr7zkRWxIz1smiAVxg5BZ1EzMzgEkvGFRYOLtEyjY/5Q1Hbyi+vAVUry5epopskxgYUVmUpJHm61bW5a+THBlisLmBxjUzwVSlsoFQFXr+3Xb1yiQ0o22yENX/HcKc3sTYUYyFfJQvF3tUOXEMIIdoUYn7LuJKBl0+lNz/OrsRZeL7V+RbBv5vFqHyXnrGzTKmq9J7HrykusHPKDnablvfK7/wX9vOhj7Tv8smKGLWg8x9dw70Vgpj2qJWcEJu8YWrqNAiWIZZQ6nhjtoRVKWcLdDhk54SLlWCEtelidYyNJBTN+uHmOt4ZS55iEYNYthQxsi4SVqE2aV3iQrtzf8bS4KtjsaHMr67Ew2y+Vtnlhq1MSV7hZ2jvavjNNUMBIZob7uY9+99pP8wwloiygOW5VsFLR1bkoxiLhgzPVqQVLa/DNFmWQhX+HvEIL1MbWDRxQTuWi2oBixpFpOgAHmQt8aTLuDKiiXd/hMVHrrG86oH0b15ljy4uz8Rn+ZdZ+OfvMRsjjAqJGIKYRsiGxxeKcdli5l0WC1W6KMPaeTaVs/M9iiTHYhBg1aH7bSy8TtZf+Z0Xq0rGXD+h73JVYLZWmYd9hJA4YbCumuv2rJAV380Px5mQfLlw4RjbrTfQ7uJQNvzaPU3BF2xiva4aaH4dh6Fr99cpFuP9bUSMOiRqGO7MCUV0Aq5li6Fb0v/HXntypRaHzsNIEi5icjOzDJkMa1WhGCvAoWzvSPzG0KsbS3ayJl2JiwJ2giWsMl3euPx4lGzx6CZ66dehZ1B7FU4QXtEFghyu0a0ObvyJnBp4geb7Md48W4oOjXpNUbYP84b2gsN7yHewrsy9Cyzh97HEJr5ycV8HuPHXke8hG7NsPTshQ3UyjdT78/o12mM9/JDT0BrfQz6fOG7fcBqtNa7iXL+feQiLx1lbhLcVdnnXhI3FMWvJK2FjnzdEZ1WeDOlptGYaf6uXHzu/Fx6CCkuqP7z2/bYKk2YXTh9g95ZrcfMXT7HX3rcfRpKMQ8TwzBWuzlfcvjrW1nuC1RkLuBosxrJHeljU2FPICWan0hKiFxj5jL/jme5u9TncV5YE4QI9r8nGTTYmFuUjD7ciZnwVfKbhsr7H2EALq9tl53cjnMR3s4hp2EKFV+5vvik7Jk7v4Wwl4j/0JrBUvw8X8eG6DnByhM9NwzxRJP0OLYZ2vJFbZzuLIqNYMTqLGp16reLaLNTciI9C+VNLWxdDe/ZitdA9xsdYsk1ru0THO6pZsqzixymfFsjDVqh5w8nRfQaQPseUry3m8SbyWyV76OXzjsNIkgLDSVYZRiYQP9cXZJFOrWLSx2fnM78/YLC8WI9lZwsXL/hq70z2QoWT6eFM4ZmU2S4Gs6x6vwsGc6iHTEgQrjCY27X8nXXULdy4SYFhKXj0hngcIkZew7bsiUZ8KwvkORDbHbdiEkWMKzzUAfL+/jqmWPkS5dRxBiGkCg3Dfcbl92CogwvWUVdYUtmqnWsQMV6cekVwVRdn63Trxlh+X2y9KuJZGyJz9TxeyeTL+cEwU9SRAIe8aDkRRiLzt4dymFRYsOh44Xc0CWZdjJnjKW/kgwdbK6KsZ+T7FBLM4yHNPozXsy9oz1T+ZR6vl91ImHGJmPyMqpse8xLWIjM4ZgJ5LbvCwJHPq720Y3Co8LINiJZgBvMrWWEIR4rNg3qPXFYS2cauYOOm/9Zkrh9JsDbdAbJYESOtDIXG882CxYuAETiIGP39bCp0GecT6KjrqQ6wFDH26HWiFKj6tW2EqBuMAsShbstgHMrIipjsc7kIvioW7XVTEzqkq4psB7zmT6M1icebw8xJFSHE6562SR/Rqf4+C0XcxL2DiLFsLyWF4iEf1UG92Dytj2ho98uzKkoM9UxeMJ2r121avtWvWRqHf5YeYC8/KK4v7hlg3/kvZ2deI+MQMfkJKwtGfuOf/xu3haikQkJPGH4vVbH+xpDINpUoQYwbWa5EPstUEtnyUKiScHB49FezsOqHVoyIyQoYW/+KHKRweZ61HfQiYAROlbxDwyFwbDyKwHMdIJ9Pi3MefLznfkw5ae3zZzxfFagfZhvkYq0Jaq9du7/uU2GD0SdGbySN+c8uCLFwkCle1x6S6WO00gty/Ey85s/8OC805Vu1RASqcp+B51kxgy8Q3M86XU0Xt8+Lenl1FDGT0RE2d4AuGKyKJlEk0yYn7uysiAbhqF73Sp4F2TNXBth/PruNrZx/A7vtgSZ2ekT6u6TZZR6fX9Z8YW74msIG3SoYzlW/Ym/qrbN4p1T7CZZ9Crd89hbtQ2HMe7BQmDmh5PzRpzGX1zzAezhz5jf4vXrQijKUL96Eho4YoiFejaosQTCsIP6Tb+LeRZ/inz1u/ZAeRPvODfjsli7cGf0pGqqWoPCvZ2PxA4/gvu5HEfjmjaj9xmr4puP63x7rAOAmrNr1E7SFg1CTi5M6XIMN61di0SfnYmVtM/pGnSqsMp7Uf5L5beoszrxjn9KueOcDjNje7jIG2w4j0pFSP/k2/TWWzxaJdBnvnO1H5mgluKAQnVnhHwkukMEFMieFjq5R3LJigYu8YGD2HXjkud3wpw6j+vMV+JgsQx+rwPK6AayolnnWCzzO98a1Z7yEZIxfv2M3Vt/fgG6buC7z3Ymnm6qAhh14on0QaQzjV40hPNy5HP/a8BBWXBOrNqcx2v0jPFZznP9/CaoeXovbEt/HxvUNPPX45/1b4VfT20TH62h99SU0N7+I9r5RlC9ch70nk2DJ72KVfv71WPiVx8AFMD8/jMd+8CZw+zo8zOsGpBqw/clXMOi1Xb44gK5/ewknf/07/G/TdvxtzYs4/5HQLcN4+6VjeFHsMowvYee21ajwUuWqUkYwRZaY0ivVApjNuzScRJQaQ+8/M8bsYTjJEa2cuTZLG3ph5uGpgpTKElPAb0Krpya0bBZdBwjn1xamKLmzK43vlB2q0ixs5ntp53lCH3IT17XzozJb7IznOTn1GqduF/uMwq/RvHim8Hvk8eWUtq6RecSFRWeklymhtczv/6L7hSB17Ns66/ZS4pS/JxJDOs4Ps/gVY7rKdZKMmKflyyCcmJ+3GKIzDkWK613S3kt8Lsbam2ZXzinswdu0NWAwj937/V+yD987wR7R8qkXXxjJlIkY/X7Fmqbk79XIKBAcTc9Z01/mWcixl3BJUXmQNy7jcOyV97R0sJPfuWrgDWuAuPTvyFJCn5iivxsPE1MH5A8xlMqx1+TbkLMoIGckwWLmBdiMYsToU2MleI0iqdj62RKvItsOLyJG+ItwATPRIkbGkaOIKaah94KhLtFE8hWDf5ddGVEX6MsR3jKY6h+z4M7rfGnneeIjNvJWQ3Yadfld7J9q7mM3qPdfwh58ecC1L4wkX8TkZDCrSmOCRIyxgOesGpqJ5MwqjRNdWdmgJ44s7IZnm8geH0HoeU36vsgK2WWvV/99ruUkW2ZcCCGOLpw8LydvJ1i8CJkCYkSvi0wr9spZi6XoXLisA/Q6zlRnCZ+PzkhunaXHsRQCujhwl0ZOZIVv4WBeGE4XWyJY+tSMwxrjQmQ7dyoFhcSqg7gwkFlTZoO2VIeWP0OKje+SFU730b6zFHky75Qgn+ZhELSFfGIsEdbYk0zRRG82r5sF9wT4xOh8yH79/EP6tgJ6WLybvVaEuM2KmBwTpXyZUooYjuM6MfmFr5TkVTi6Cp2MjEjMFPQyIit5vcF2WzGYhwmMwcIpVy/Xxl6hLI9W1zAEi0qw6HVicijUSBmcCvOCx0bVA+7qAEOjYRV0USjfQYpV+c6GtB8XTvlABh5XeY129jnEOdYr9XJkvhTnebGcFBTZLq0TMu4dHITt41E0zAoL5Tn2ZqyPAdftipOIMaSn0VHY6MBcUKxNEAYBrpanPEGunWYnwHm5zWxZwr+Tbbee/prg1q9ZaOKBS3I2eBThBvaFcBeXN97JihiZ8GqhlQlQYhEjcDVvnSCILKKs5u5NI2bIZNa2MGElYowNlFMYt9nfjkIihmNVLwjLzKTtm+OA1bOJRnsKNkFVhwY87V5tFIhOgsIo1rwMiziJK96o5lnqss+T227w6+hDJRbByYIoGtxST7EW6CLX4vkmqrF3iVmAW68TU0CA6+earcMTLcAFZv+Yu9kzbxXXNTGIGIIgCIIYL9Yi+5jldG07ESMQ1znJjpk3gDxmN519oikgYjiqiMzxP3J616uAq0iAq/4x53/JXoudZG/8d5Jd8OoMozFL/MNfhCAIgiAIYloxHVd2uEoYRl97I2pXVmTXE1lZi8YXu5HyNH/efJ0KrKxtRHvfsPa9E5cx2LwdFbOWo7b9t9oxE6N9aG+sxUr5jBWbUd/s9RknAfNzqvHwQ7zYnYK3RzXH51Jsrm9Gd+qy9j1BEARxzaDaYwiP2M23F8GL46HDGGXBpb6NY8/WY9bZzcxM17Ycm55CdKcx83OK4GEmh75/l8V1PM/CIQiCIK52yBJTDMOn8Oz2BqR8QYTbEuCChYvBS0h27kfQl0JHpAVdw4XtB+m+ZuysOQ5fsAm9I2NCUGavg0Zs2fEz9NldZjSOHzxUh8OZZTfzSZ9DyxPV2NOxFCGlV3tGhrHkKUSCn0HHnjp8r8PGejOppDHccQDbG0/zeIigLTGUiYexJDojYlXU44gcfROF7VKXMdiyBxv39MAfUpCQ8Smv07EbG793ysV1CIIgiGkDr+gJTzjNrJDfufHmlw5tVucWcCiTlgv/bhYNr7W8RmammLVVyH4W2VTg9K7ad25mychZOFaLiMnvSjbbhiAIgpgKyBLjGbnvSAWWzbvJ5FRUhvK5C7AU3TjS+vb4e/2+BZg3x7zHxwfojmzD+lf/Cspzj+KOG/9AO27kIvpPnUAb7sCmez+Xt/dJ2cIqtDKG5N5VmK0dy2Llo3OkdD4l6d/i7FtJm3ctx9xFtwKpNrTG39eOWZPufx0vtAGBTXfh9nJTti5bjKpW894gkjRG+9rRWLtGe18eVtbikGdfHIIgCGKyIRHjmVEMJM7wv9ab7JXNmYdlPt7uFty48nosWPP3qPJxwXPoOH6lb2R2GamuF3DoSLdhwzYJ/679GTxWcwV1z9Vh7c12m5hpz6gKg4u5osTJsVfbCHDR6i3Yp20ap24Ety+I5Q6brY2L0SQSPfxeSxdgrll84DrMmbcAPiTx1tnfOogKLkQG+tGjCssb8fscUeLk2Cvi8yncs2g1tuzjCkjSsQ8PLP86It0faAcIgiCIqxESMVNI2c1r8UyHgk3n6/DZT35Ma3Q/gYrP/wCoPoGOXf4cS0l68BU8sfEAEH4KO1fdbJ940rqBc2j91n25oiR1GDXrl6Py682mXUiFhWcrVqs+JYcRT17SfEoGEKsLqDuZ7jzad5VaJ6R17BLeaf22SZScxuGa9VheWY3mQaOQETvANuD+1bvR4Q+hKZ7EmHhfuUsujqNmZ7O9TxJBEAQx5ZCI8YouEArQ04+BgpaLUSRPx9GlWz0kp/Hv/PcfjHykfeaMdiGycTtevWs/nqte4W57/NRPsC8ChJo6kRzLOPaykV4ooQBSjd/Eky3nsqJk+E0cjRwH/DWo3/VVVMqt6stuxqpv1CLkS6EnkeRPPLGk3zmLt+yck3Xc3psLln3N/IUNIowNIaHUwZ+3ffz76Dr6Y3TgboTr67C50qcVhuvgW7UNu0KVLtOQIAiCmCpIxHil7CbMW1ahfXDAcnjEiFjjZSf861/Gn0VOZUUGG8NIQlhnvoPPyyEcMczz3V2oSazD/m//DW52nWo+BKLPYM/mFfDJ35QvxrrHhSg5jcYDMfSrbXQaw/H/wJFUJUK7NqHS/NyzV2Fv0s6HZnzI4TdnfFi6qMKdcAs8jQN7+DtIEcafeOG6alWUpBqfR2v/xczh4bfRKobsQtX4x8pPZ47p3IRVe+M2PjQEQRDE1QLV0FNF+gxaDzQjFXgUj+/4y6zI4ElSvnAtHt/1AHwdP8bRrveR7m/F3j1tQKoB6+d+Qht2EuEPsWjLMf6bbuxb/cf881fQ2McbaV1o3YH77piXn8jlFVi0lCsH3dLwPuKtbUj5Aliz/MbMOW4ZbkdthXyeAmFNY4mGZ6TvDBdt930RC/JfOOMgjDNIDAh7Tla0bVrzuQkXZgRBEMTkQCLGM7JBdMa3bB7mOMWudGi1JHeW05B21D3unlHH7RCZFZqVJmNFKhBaq7DQHCdSUDliNRPMiIwvt0gfGoIgCGI6QyLGM7LXfwovnDprcnSVPXwXwx+OjbecbZO5zqe0KdH5wuACEtEN/PxKhGLv8s9HUbXwev45+4xHXno735dEE1D67CeHIbL0YDO2VMxCRW17aRaKk/duO4FTcqhHR7MQ2cwEM5IZlkqh7cir+EWeH4ucrSUtTTJ+LEifQ/OWpZhVsRPtLhYsJAiCIKYQ3hgSXhmKsZC67XmQhdvkbqWXWDJ+WNsd1H7X0yxysTvzDqJi51bF5XUcFszTt4nn11d6swvejfQyRd1d1vgbw9br+nYExvfxsPS/ZwzbvAcjrE1uny92W23SdocNRFmi4Bp1cgsH/g4hxbDL7RBLKHXqdYyL+8kF/4zbEYwlO1mTGjdeto4gCIIgpgoSMUWR3T4+P+Q3gHqDaV4xdqSHRYN2ewYtYVXKWdOKwGacVv017q1kDkaxoqGLHvO5S1gw2lPaBl2uqJt3bxHMAiob93krDjvFZ97eSfb7VvmCTax3Urb6JwiCIMYDiZhiEZaCloOapUJrAIVlRonnbaxoK2IE4jpK2CA2hCXhIGuJJwsIGIGTiMkwlowzJRzMblbpD7FoTFqPcjGf6wuGmeLqOcaPuHdLVLO8ON7fQcQI8uJTWLpiBsuMAfO5NulHEARBXJ3MEv/wCpwgCIIgCGJaQY69BEEQBEFMS0jEEARBEAQxLSERQxAEQRDENAT4fx7MStj5Kk9rAAAAAElFTkSuQmCC\" width=\"468\"/>\n    </span>\n   </span>\n  </span>\n </p>\n <p style=\"text-align:left;\">\n  <em>\n   <strong>\n    <span style=\"background-color:#ffffff;\">\n     <span style=\"background-color:#ffffff;\">\n      <span style=\"background-color:#ffffff;\">\n       ALTERNATIVE 3:\n      </span>\n     </span>\n    </span>\n   </strong>\n  </em>\n </p>\n <p style=\"text-align:left;\">\n  <img height=\"121\" src=\"data:image/png;base64,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\" width=\"511\"/>\n </p>\n</div>\n",
    "Examiners report": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Proper length is quite well understood. A common mistake is to mention that it is the length measured by a reference frame at rest.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (bi)\n </div><div class=\"card-body\">\n <p>\n  Because there were three frames of reference in this question many candidates struggled to find the simple value for the time of the ball’s travel down the train in the train’s frame of reference.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (bii)\n </div><div class=\"card-body\">\n <p>\n  Almost no candidates could use a Lorentz transformation to find the time of the ball’s travel in the frame of reference of the platform. Most just applied some form of t=γt’. Elapsed time and instantaneous time in different frames were easily confused. Candidates rarely mention which reference frame is used when making calculations, however this is crucial in relativity.\n </p>\n</div>\n",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-5-galilean-and-special-relativity"
    ]
  },
  {
    "question_id": "19M.2.HL.TZ2.8",
    "Question": "<div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">Monochromatic coherent light is incident on two parallel slits of negligible width a distance <em>d</em> apart. A screen is placed a distance <em>D</em> from the slits. Point M is directly opposite the midpoint of the slits.</span></p>\n<p><span style=\"background-color: #ffffff;\"><img 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\"/></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">Initially the lower slit is covered and the intensity of light at M due to the upper slit alone is 22 W m<sup>-2</sup>. The lower slit is now uncovered.</span></span></p>\n</div><div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">The width of each slit is increased to 0.030 mm. <em>D</em>, <em>d</em> and λ remain the same.</span></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Deduce, in W m<sup>-2</sup>, the intensity at M.</span></p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">P is the first maximum of intensity on <strong>one</strong> side of M. The following data are available.</span></p>\n<p><span style=\"background-color:#ffffff;\"><em>d</em> = 0.12 mm </span></p>\n<p><span style=\"background-color:#ffffff;\"><em>D</em> = 1.5 m </span></p>\n<p><span style=\"background-color:#ffffff;\">Distance MP = 7.0 mm</span></p>\n<p><span style=\"background-color:#ffffff;\">Calculate, in nm, the wavelength λ of the light.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Suggest why, after this change, the intensity at P will be less than that at M.</span></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">ci.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Show that, due to single slit diffraction, the intensity at a point on the screen a distance of 28 mm from M is zero.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">cii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">there is constructive interference at M<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><em><strong>OR</strong></em><br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">the amplitude doubles at M ✔<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">intensity is «proportional to» amplitude<sup>2</sup> ✔<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">88 «<span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">W m</span><sup style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:11.6px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">−2</sup>» ✔</span></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">«<span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"s = \\frac{{\\lambda D}}{d} \\Rightarrow » \\lambda  = \\frac{{sd}}{D}/\\frac{{0.12 \\times {{10}^{ - 3}} \\times 7.0 \\times {{10}^{ - 3}}}}{{1.5}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>s</mi>\n<mo>=</mo>\n<mfrac>\n<mrow>\n<mi>λ</mi>\n<mi>D</mi>\n</mrow>\n<mi>d</mi>\n</mfrac>\n<mo stretchy=\"false\">⇒</mo>\n<mrow>\n<mo>»</mo>\n</mrow>\n<mi>λ</mi>\n<mo>=</mo>\n<mfrac>\n<mrow>\n<mi>s</mi>\n<mi>d</mi>\n</mrow>\n<mi>D</mi>\n</mfrac>\n<mrow>\n<mo>/</mo>\n</mrow>\n<mfrac>\n<mrow>\n<mn>0.12</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>3</mn>\n</mrow>\n</msup>\n</mrow>\n<mo>×</mo>\n<mn>7.0</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>3</mn>\n</mrow>\n</msup>\n</mrow>\n</mrow>\n<mrow>\n<mn>1.5</mn>\n</mrow>\n</mfrac>\n</math></span>    ✔</span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"\\lambda  = 560«{\\text{nm}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>λ</mi>\n<mo>=</mo>\n<mn>560</mn>\n<mrow>\n<mo>«</mo>\n</mrow>\n<mrow>\n<mtext>nm</mtext>\n</mrow>\n</math></span>»  <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">✔</span></span></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"> </p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">«the interference pattern will be modulated by»<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">single slit diffraction ✔<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">«envelope and so it will be less»</span></p>\n<div class=\"question_part_label\">ci.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><em><strong>ALTERNATIVE 1</strong></em><br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">the angular position of this point is <span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"\\theta  = \\frac{{28 \\times {{10}^{ - 3}}}}{{1.5}} = 0.01867\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>θ</mi>\n<mo>=</mo>\n<mfrac>\n<mrow>\n<mn>28</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>3</mn>\n</mrow>\n</msup>\n</mrow>\n</mrow>\n<mrow>\n<mn>1.5</mn>\n</mrow>\n</mfrac>\n<mo>=</mo>\n<mn>0.01867</mn>\n</math></span>«rad»  ✔</span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">which coincides with the first minimum of the diffraction envelope</p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"\\theta  = \\frac{\\lambda }{b} = \\frac{{560 \\times {{10}^{ - 9}}}}{{0.030 \\times {{10}^{ - 3}}}} = 0.01867\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>θ</mi>\n<mo>=</mo>\n<mfrac>\n<mi>λ</mi>\n<mi>b</mi>\n</mfrac>\n<mo>=</mo>\n<mfrac>\n<mrow>\n<mn>560</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>9</mn>\n</mrow>\n</msup>\n</mrow>\n</mrow>\n<mrow>\n<mn>0.030</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>3</mn>\n</mrow>\n</msup>\n</mrow>\n</mrow>\n</mfrac>\n<mo>=</mo>\n<mn>0.01867</mn>\n</math></span> «rad» <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">✔</span></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">«so intensity will be zero»</span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"> </span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><em><strong>ALTERNATIVE 2</strong></em><br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">the first minimum of the diffraction envelope is at <span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"\\theta  = \\frac{\\lambda }{b} = \\frac{{560 \\times {{10}^{ - 9}}}}{{0.030 \\times {{10}^{ - 3}}}} = 0.01867\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>θ</mi>\n<mo>=</mo>\n<mfrac>\n<mi>λ</mi>\n<mi>b</mi>\n</mfrac>\n<mo>=</mo>\n<mfrac>\n<mrow>\n<mn>560</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>9</mn>\n</mrow>\n</msup>\n</mrow>\n</mrow>\n<mrow>\n<mn>0.030</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>3</mn>\n</mrow>\n</msup>\n</mrow>\n</mrow>\n</mfrac>\n<mo>=</mo>\n<mn>0.01867</mn>\n</math></span>«rad»   <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">✔</span></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">distance on screen is <span class=\"mjpage\"><math alttext=\"y = 1.50 \\times 0.01867 = 28\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>y</mi>\n<mo>=</mo>\n<mn>1.50</mn>\n<mo>×</mo>\n<mn>0.01867</mn>\n<mo>=</mo>\n<mn>28</mn>\n</math></span>«mm»  <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">✔</span></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">«so intensity will be zero»</span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"> </p>\n<div class=\"question_part_label\">cii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was generally well answered by those who attempted it but was the question that was most left blank. The most common mistake was the expected one of simply doubling the intensity.</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was very well answered. As the question asks for the answer to be given in nm a bald answer of 560 was acceptable. Candidates could also gain credit for an answer of e.g. 5.6 x 10-7 m provided that the m was included.</p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Many recognised the significance of the single slit diffraction envelope.</p>\n<div class=\"question_part_label\">ci.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Credit was often gained here for a calculation of an angle for alternative 2 in the markscheme but often the final substitution 1.50 was omitted to score the second mark. Both marks could be gained if the calculation was done in one step. Incorrect answers often included complicated calculations in an attempt to calculate an integer value.</p>\n<div class=\"question_part_label\">cii.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-2-forces-and-momentum",
      "a-4-rigid-body-mechanics"
    ]
  },
  {
    "question_id": "19M.2.HL.TZ2.9",
    "Question": "<div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">A planet of mass <em>m</em> is in a circular orbit around a star. The gravitational potential due to the star at the position of the planet is <em>V</em>.</span></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Show that the total energy of the planet is given by the equation shown.</span></p>\n<p><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"E = \\frac{1}{2}mV\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>E</mi>\n<mo>=</mo>\n<mfrac>\n<mn>1</mn>\n<mn>2</mn>\n</mfrac>\n<mi>m</mi>\n<mi>V</mi>\n</math></span></span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">ai.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Suppose the star could contract to half its original radius without any loss of mass. Discuss the effect, if any, this has on the total energy of the planet.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">aii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">The diagram shows some of the electric field lines for two fixed, charged particles X and Y.</span></p>\n<p><span style=\"background-color:#ffffff;\"><img src=\"data:image/png;base64,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\"/></span></p>\n<p><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\">The magnitude of the charge on X is <span class=\"mjpage\"><math alttext=\"Q\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>Q</mi>\n</math></span> and that on Y is <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span class=\"mjpage\"><math alttext=\"q\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>q</mi>\n</math></span></span>. The distance between X and Y is 0.600 m. The distance between P and Y is 0.820 m.</span></span></p>\n<p><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\">At P the electric field is zero. Determine, to <strong>one</strong> significant figure, the ratio <span class=\"mjpage\"><math alttext=\"\\frac{Q}{q}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mi>Q</mi>\n<mi>q</mi>\n</mfrac>\n</math></span>.</span></span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"E = \\frac{1}{2}m\\frac{{GM}}{r} - \\frac{{GMm}}{r} =  - \\frac{1}{2}\\frac{{GMm}}{r}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>E</mi>\n<mo>=</mo>\n<mfrac>\n<mn>1</mn>\n<mn>2</mn>\n</mfrac>\n<mi>m</mi>\n<mfrac>\n<mrow>\n<mi>G</mi>\n<mi>M</mi>\n</mrow>\n<mi>r</mi>\n</mfrac>\n<mo>−</mo>\n<mfrac>\n<mrow>\n<mi>G</mi>\n<mi>M</mi>\n<mi>m</mi>\n</mrow>\n<mi>r</mi>\n</mfrac>\n<mo>=</mo>\n<mo>−</mo>\n<mfrac>\n<mn>1</mn>\n<mn>2</mn>\n</mfrac>\n<mfrac>\n<mrow>\n<mi>G</mi>\n<mi>M</mi>\n<mi>m</mi>\n</mrow>\n<mi>r</mi>\n</mfrac>\n</math></span>  ✔</span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">comparison with <span class=\"mjpage\"><math alttext=\"V =  - \\frac{{GM}}{r}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>V</mi>\n<mo>=</mo>\n<mo>−</mo>\n<mfrac>\n<mrow>\n<mi>G</mi>\n<mi>M</mi>\n</mrow>\n<mi>r</mi>\n</mfrac>\n</math></span>   <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">✔</span></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">«to give answer»</span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"> </p>\n<div class=\"question_part_label\">ai.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><em><strong>ALTERNATIVE 1</strong></em><br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">«at the position of the planet» the potential depends only on the mass of the star /does not depend on the radius of the star ✔<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">the potential will not change and so the energy will not change ✔<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><em><strong>ALTERNATIVE 2</strong></em><br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">r / distance between the centres of the objects / orbital radius remains unchanged ✔<br/></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\">since <span class=\"mjpage\"><math alttext=\"{E_{Total}} =  - \\frac{1}{2}\\frac{{GMm}}{r}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mrow>\n<msub>\n<mi>E</mi>\n<mrow>\n<mi>T</mi>\n<mi>o</mi>\n<mi>t</mi>\n<mi>a</mi>\n<mi>l</mi>\n</mrow>\n</msub>\n</mrow>\n<mo>=</mo>\n<mo>−</mo>\n<mfrac>\n<mn>1</mn>\n<mn>2</mn>\n</mfrac>\n<mfrac>\n<mrow>\n<mi>G</mi>\n<mi>M</mi>\n<mi>m</mi>\n</mrow>\n<mi>r</mi>\n</mfrac>\n</math></span>, energy will not change <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">✔</span></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"> </p>\n<div class=\"question_part_label\">aii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"\\frac{{kQ}}{{{{(0.600 + 0.820)}^2}}} = \\frac{{kq}}{{{{0.820}^2}}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mrow>\n<mi>k</mi>\n<mi>Q</mi>\n</mrow>\n<mrow>\n<mrow>\n<msup>\n<mrow>\n<mo stretchy=\"false\">(</mo>\n<mn>0.600</mn>\n<mo>+</mo>\n<mn>0.820</mn>\n<mo stretchy=\"false\">)</mo>\n</mrow>\n<mn>2</mn>\n</msup>\n</mrow>\n</mrow>\n</mfrac>\n<mo>=</mo>\n<mfrac>\n<mrow>\n<mi>k</mi>\n<mi>q</mi>\n</mrow>\n<mrow>\n<mrow>\n<msup>\n<mrow>\n<mn>0.820</mn>\n</mrow>\n<mn>2</mn>\n</msup>\n</mrow>\n</mrow>\n</mfrac>\n</math></span>  ✔</span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"\\frac{Q}{q} = « \\frac{{{{(0.600 + 0.820)}^2}}}{{{{0.820}^2}}} = 2.9988 \\approx » 3\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mi>Q</mi>\n<mi>q</mi>\n</mfrac>\n<mo>=</mo>\n<mrow>\n<mo>«</mo>\n</mrow>\n<mfrac>\n<mrow>\n<mrow>\n<msup>\n<mrow>\n<mo stretchy=\"false\">(</mo>\n<mn>0.600</mn>\n<mo>+</mo>\n<mn>0.820</mn>\n<mo stretchy=\"false\">)</mo>\n</mrow>\n<mn>2</mn>\n</msup>\n</mrow>\n</mrow>\n<mrow>\n<mrow>\n<msup>\n<mrow>\n<mn>0.820</mn>\n</mrow>\n<mn>2</mn>\n</msup>\n</mrow>\n</mrow>\n</mfrac>\n<mo>=</mo>\n<mn>2.9988</mn>\n<mo>≈</mo>\n<mrow>\n<mo>»</mo>\n</mrow>\n<mn>3</mn>\n</math></span>  <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">✔</span></span></span></p>\n<p style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"> </p>\n<div class=\"question_part_label\">b.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was generally well answered but with candidates sometimes getting in to trouble over negative signs but otherwise producing well-presented answers.</p>\n<div class=\"question_part_label\">ai.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>A large number of candidates thought that the total energy of the planet would change, mostly double.</p>\n<div class=\"question_part_label\">aii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>The majority of candidates had an idea of the basic technique here but it was surprisingly common to see the squared missing from the expression for field strengths.</p>\n<div class=\"question_part_label\">b.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion",
      "d-fields"
    ],
    "subtopics": [
      "a-4-rigid-body-mechanics",
      "d-1-gravitational-fields",
      "d-2-electric-and-magnetic-fields"
    ]
  },
  {
    "question_id": "19M.2.SL.TZ1.3",
    "Question": "<div class=\"specification\">\n<p>A beam of microwaves is incident normally on a pair of identical narrow slits S1 and S2.</p>\n<p style=\"text-align: center;\"><img src=\"data:image/png;base64,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\"/></p>\n<p style=\"text-align: left;\">When a microwave receiver is initially placed at W which is equidistant from the slits, a maximum in intensity is observed. The receiver is then moved towards Z along a line parallel to the slits. Intensity maxima are observed at X and Y with one minimum between them. W, X and Y are consecutive maxima.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p style=\"text-align:left;\">Explain why intensity maxima are observed at X and Y.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p style=\"text-align:left;\">The distance from S1 to Y is 1.243 m and the distance from S2 to Y is 1.181 m.<br/><br/>Determine the frequency of the microwaves.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p style=\"text-align:left;\">Outline <strong>one</strong> reason why the maxima observed at W, X and Y will have different intensities from each other.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>two waves superpose/mention of superposition/mention of «constructive» interference ✔</p>\n<p>they arrive in phase/there is a path length difference of an integer number of wavelengths ✔</p>\n<p><em>Ignore references to nodes/antinodes</em>.</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>path difference = 0.062 «m» ✔</p>\n<p>so wavelength = 0.031 «m» ✔</p>\n<p>frequency = 9.7 × 10<sup>9</sup> «Hz» ✔</p>\n<p><em>If no unit is given, assume the answer is in Hz. Accept other prefixes (eg 9.7 GHz)</em></p>\n<p><em>Award <strong>[2 max]</strong> for 4.8 x 10<sup>9</sup> Hz.</em></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>intensity varies with distance<em><strong> OR</strong></em> points are different distances from the slits ✔</p>\n<p><em>Accept “Intensity is modulated by a single slit diffraction envelope”</em>.</p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>Many candidates were able to discuss the interference that is taking place in this question, but few were able to fully describe the path length difference. That said, the quality of responses on this type of question seems to have improved over the last few examination sessions with very few candidates simply discussing the crests and troughs of waves.</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Many candidates struggled with this question. Few were able to calculate a proper path length difference, and then use that to calculate the wavelength and frequency. Many candidates went down blind paths of trying various equations from the data booklet, and some seemed to believe that the wavelength is just the reciprocal of the frequency.</p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This is one of many questions on this paper where candidates wrote vague answers that did not clearly connect to physics concepts or include key information. There were many overly simplistic answers like “they are farther away” without specifying what they are farther away from. Candidates should be reminded that their responses should go beyond the obvious and include some evidence of deeper understanding.</p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-1-simple-harmonic-motion",
      "c-2-wave-model",
      "c-3-wave-phenomena"
    ]
  },
  {
    "question_id": "19M.2.SL.TZ1.5",
    "Question": "<div class=\"specification\">\n<p>A small metal pendulum bob of mass 75 g is suspended at rest from a fixed point with a length of thread of negligible mass. Air resistance is negligible. The bob is then displaced to the left.</p>\n<p>At time <em>t</em> = 0 the bob is moving horizontally to the right at 0.8 m s<sup>–1</sup>. It collides with a small stationary object also of mass 75 g. Both objects then move together with motion that is simple harmonic.</p>\n<p style=\"text-align: center;\"><img src=\"data:image/png;base64,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\"/></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Calculate the speed of the combined masses immediately after the collision.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Show that the collision is inelastic.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Describe the changes in gravitational potential energy of the oscillating system from <em>t</em> = 0 as it oscillates through one cycle of its motion.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>0.40 «m s<sup>−1</sup>» ✔</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>initial energy 24 mJ and final energy 12 mJ ✔</p>\n<p>energy is lost/unequal /change in energy is 12 mJ ✔</p>\n<p>inelastic collisions occur when energy is lost ✔<br/><br/></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>maximum GPE at extremes, minimum in centre ✔</p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Candidates fell into some broad categories on this question. This was a “show that” question, so there was an expectation of a mathematical argument. Many were able to successfully show that the initial and final kinetic energies were different and connect this to the concept of inelastic collisions. Some candidates tried to connect conservation of momentum unsuccessfully, and some simply wrote an extended response about the nature of inelastic collisions and noted that the bobs stuck together without any calculations. This approach was awarded zero marks.</p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This straightforward question had surprisingly poorly answers. Candidate answers tended to be overly vague, such as “as the bob went higher the GPE increased and as it fell the GPE decreased.” Candidates needed to specify when GPE would be at maximum and minimum values. Some candidates mistakenly assumed that at t=0 the pendulum bob was at maximum height despite being told otherwise in the question stem.</p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion",
      "d-fields"
    ],
    "subtopics": [
      "a-2-forces-and-momentum",
      "a-3-work-energy-and-power",
      "d-1-gravitational-fields"
    ]
  },
  {
    "question_id": "19M.2.SL.TZ1.6",
    "Question": "<div class=\"specification\">\n<p>The Moon has no atmosphere and orbits the Earth. The diagram shows the Moon with rays of light from the Sun that are incident at 90° to the axis of rotation of the Moon.</p>\n<p style=\"text-align: center;\"><img 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\"/></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>A black body is on the Moon’s surface at point A. Show that the maximum temperature that this body can reach is 400 K. Assume that the Earth and the Moon are the same distance from the Sun.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Another black body is on the Moon’s surface at point B.</p>\n<p>Outline, without calculation, why the aximum temperature of the black body at point B is less than at point A.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The albedo of the Earth’s atmosphere is 0.28. Outline why the maximum temperature of a black body on the Earth when the Sun is overhead is less than that at point A on the Moon.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline why a force acts on the Moon.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline why this force does no work on the Moon.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">c.ii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><em>T</em> = <span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"{\\left( {\\frac{{1360}}{\\sigma }} \\right)^{0.25}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mrow>\n<msup>\n<mrow>\n<mo>(</mo>\n<mrow>\n<mfrac>\n<mrow>\n<mn>1360</mn>\n</mrow>\n<mi>σ</mi>\n</mfrac>\n</mrow>\n<mo>)</mo>\n</mrow>\n<mrow>\n<mn>0.25</mn>\n</mrow>\n</msup>\n</mrow>\n</math></span>   </span>✔</p>\n<p>390 «K» ✔</p>\n<p><em>Must see 1360 (from data booklet) used for MP1.</em></p>\n<p><em>Must see at least 2 s.f</em>.</p>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>energy/Power/Intensity lower at B ✔</p>\n<p>connection made between energy/power/intensity and temperature of blackbody ✔</p>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>(28 %) of sun’s energy is scattered/reflected by earth’s atmosphere <em><strong>OR</strong></em> only 72 % of incident energy gets absorbed by blackbody ✔</p>\n<p><em>Must be clear that the energy is being scattered by the atmosphere.</em></p>\n<p><em>Award <strong>[0]</strong> for simple definition of “albedo”</em>.</p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>gravitational attraction/force/field «of the planet/Moon» ✔</p>\n<p><em>Do not accept “gravity”</em>.</p>\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>the force/field and the velocity/displacement are at 90° to each other<em><strong> OR</strong></em> there is no change in GPE of the moon ✔</p>\n<p><em>Award <strong>[0]</strong> for any mention of no net force on the satellite.</em></p>\n<p><em>Do not accept acceleration is perpendicular to velocity.</em></p>\n<div class=\"question_part_label\">c.ii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>Many candidates struggled with this question. A significant portion attempted to apply Wein’s Law and simply stated that a particular wavelength was the peak and then used that to determine the temperature. Some did use the solar constant from the data booklet and were able to calculate the correct temperature. As part of their preparation for the exam candidates should thoroughly review the data booklet and be aware of what constants are given there. As with all “show that” questions candidates should be reminded to include an unrounded answer.</p>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This is question is another example of candidates not thinking beyond the obvious in the question. Many simply said that point B is farther away, or that it is at an angle. Some used vague terms like “the sunlight is more spread out” rather than using proper physics terms. Few candidates connected the lower intensity at B with the lower temperature of the blackbody.</p>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This question was assessing the understanding of the concept of albedo. Many candidates were able to connect that an albedo of 0.28 meant that 28 % of the incident energy from the sun was being reflected or scattered by the atmosphere before reaching the black body.</p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was generally well answered, although some candidates simply used the vague term “gravity” rather than specifying that it is a gravitational force or a gravitational field. Candidates need to be reminded about using proper physics terms and not more general, “every day” terms on the exam.</p>\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Some candidates connected the idea that the gravitational force is perpendicular to the velocity (and hence the displacement) for the mark. It was also allowed to discuss that there is no change in gravitational potential energy, so therefore no work was being done. It was not acceptable to simply state that the net displacement over one full orbit is zero. Unfortunately, some candidates suggested that there is no net force on the moon so there is no work done, or that the moon is so much smaller so no work could be done on it.</p>\n<div class=\"question_part_label\">c.ii.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion",
      "b-the-particulate-nature-of-matter",
      "d-fields"
    ],
    "subtopics": [
      "a-2-forces-and-momentum",
      "a-3-work-energy-and-power",
      "b-2-greenhouse-effect",
      "d-1-gravitational-fields"
    ]
  },
  {
    "question_id": "19M.2.SL.TZ2.1",
    "Question": "<div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">A student strikes a tennis ball that is initially at rest so that it leaves the racquet at a speed of 64 m s<sup>–1</sup>. The ball has a mass of 0.058 kg and the contact between the ball and the racquet lasts for 25 ms.</span></p>\n</div><div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">The student strikes the tennis ball at point P. The tennis ball is initially directed at an angle of 7.00° to the horizontal.</span></p>\n<p><span style=\"background-color: #ffffff;\"><img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAjQAAACzCAYAAACeoYZKAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAB57SURBVHhe7d1tdFXVve/x2TtGX5UAcuigXAFP5fJYeQpgqtDykBq8QpDUlniAU05F7jVBvQrnXpPW8lQkwTbYgyVhNNBeLHAk1nERxCPhgCARjZAUhAJNShmKiJxykIDvufnNvebOymbvnR3ITrJ2vp8x1lhrzvW0szZk/TMfv3KjkQEAAAiw/+KtAQAAAouABgAABB4BDQCgw40Y8S0zYEA/s3v3m83SJ058ZNNIPXl5T9jvuKys1Mu5PQQ0AAAExCeffGIDARf4RZPIMamIgAYA0OmcOPGnxhfzp2bEiJFeDmT69P/eYqCSyDGpiIAGANCuGhoazJw5/2CrG7QUFa329jSJrHLSC3r69IfC52iJrKrQdfz7XJWG8nVPt8/l63qiY939tEyceL/Ztm2r3af7u3z/cbqGFBQ812x/NP576xhdX9taRwYekZ9F13f0eXUt0f3dZ/CLdYzy/J9V94j1eR3/8Vr0nUVWAUZe0z03SeQ7i+T/Dv3fQyIIaAAA7UovxqqqQ14q9BJ3L+Fo3Ms48mWql5974Wnb/7JU2n8PPxdE9OjRw267gMdRlY3up7Wf/zidF/nCjXdPR8e467r7ONqO/Cy6vgu8boeeuf+z6h66l//+ftoXGUzoZ/MHUdGuqevp2bjteN9ZJB3v/w7d83HfV0sIaAAA7UYvRfeSKyvb0PjS+tQUF6+x6VgUeLgqKLcMGDDA7nMvf/eSzMvLt/t3737LpqMpLPyJPaawsLAxWJjR7LpVVYe9o3Ttq95WiDtP54jurfvos7nPc+LECbuOxd1v27Z/tWldQ89Di/sZ9Dx0jK4d+tk/si96lxY9Oy2Roh2jc3UNfUbt17X1s4ju6b4PPxd0uefpFvd89D1qCQWFza+5devWhL4zP91Pn0Xn6R463v270PUSQUADAGg37oWvtjEuMJgzZ274ZRePXsz6C18lA+6FK3ohu5dkfv4iu/ZfP5LL97fP0XVD137Uy7mZPqe4zzpgwF32GnoJ9+jR0+a1JD8/364nTvyOPc+pqqqya+W7+/h/ho8//tiub8VHH4UClrlz54V/ZgUq8YKwuXNDn0HPXNU/euZ6Pu65u3PcMxAX/LhgTWJ9Z5FcUKXv0VXJudKjaAFXNAQ0AIBOTS9CveS2bt1i0yp18AcjreUPJFSdoZenXtA9e/ZsTP+bt6dliQRhQaXASiUsClK0VFUdssGJGhzHC0yctvzOFOREK9WJREADAGg3I0aMsGv91e3aRuhFGe8lqeO0X6UgoWqfj+3i6EXpgpTS0vV27b9+PK46Q59LL+5Y7TuSzT0XBQ7uM/h/hpEjQ8GASkRaEnmMO1fBhSvt8D9zBS/R6JnqebuqNgVwCiz0mWJ9j64xb0vfWSQX7OiergrLv/iD0FgIaAAA7UYvz6YqiqZeSPG4l5lenjo+WiNZV03jXqqJNqR1pSzuPH0Wd79ESgXaip6LCyxU1eJ+Bn0GPS/38zl6dqrGiccd46r0FGC4Xkfumbt9kXSejvMvTQHQxGafN/J7VNVWIt+Znz6Dqtf087rP6BZ/Q+R4CGgAAO1KbSzcy1BUMhLvL3C9dP0vdL34XIPRQ4dCvYpUCuBvM6P9/nvEovP8xynt7tVSA9+2puei+/ufhT6LSiwc1wZHYj2zyGO0qCrN/wyVp3vFapCtz6LvxU/PyV91pGOiXVPnKd+/L9p3FknX9p8jSis/Ecy2DQAIPI2B4kozFACE/tIPtfdwL1mkNkpoAACB50pZXBWHAhx/FQlSHwENACDwolVXqLTmdnrXIFiocgIAAIFHCQ0AAAi82yqhuXjxosnIGO+lmpv+0AyzdNky07dvXy8HAAAgOdqkhKZ0fZkd+MYt1dVHzNm/njUrV6zwjgAAAEiepFQ5qVRm/vz5Zvdbb9pSHAAAgGRKehuatLQ0bwsAACA5khLQ1NbWms2bN9t2NN26dfNyAQAAkiNpjYI1hfuTTz5FQAMAAJKuTQIaNQqekZ3t5QIAALQvxqEBAACBR0ADAAACj4AGAAAEHgENAAAIPCanBAAAgUcJDQAACDwCGgAAEHgENAAAIPAIaAAAQODdckDz5Zdfml/96iUzevRIM2BAP7v+7W83eXsBAADazy33clqyeLF57Q8VXqrJ4wsWmqXLlnkpAACA5LulgObs2bNmypRJXupmR47UmD59+ngpAACA5EoooFGVkt/y5Ssal9ilMJv/7ytm/j/9yEuFfPLJp97Wzddz+yLzJda+ZF2vM3wG6Yjr+Y8HACBIEi6h+cEjj5iePXuajZs2mddeqzBLliz29twsLS3NfPWrXzWZU79nvnXPt8zYsePMqFGjvL1IpscXLDBPPf00zxsA0KUk1Ch4z9tvmw+PVJvKvXvMe1VV5rvfjV3d1KtXL1NdfcS8/vr/M1lZWebT85+an69caUsC9LJVQ2Jd49KlS94ZAAAAt6fFgEa9mZ4r+D9eypily5aar33ta6b8Nxu9nObWFL9ounXrZgYOHGimPfigbSD8h9dfN6dOnbElB927dze/+93vzPjxY01m5tRQ4+LXKszx48e9KwRLbW2tDdZiLbGUlZU2O66woMA+ayfefnfP9PQxpr6+3uYBANClqcopnk2bNt7o3//OZovy5NixYzdWLF9+Y8Fjj9m10q3xl7/85UZFxXZ77tSpU+y1dS1dv+rQoRvXr1/3jgyWA++8Y3+WLVt+7+U0t2vnzmb7a2pqbLq0dL1Nt7S/qGi1zdNxkfcYNWrEjc8//9xLAQDQNcRtQ6NqIZWkRFK10p49e9u8J5NKII4fO2aOHD1iTp44aau4Bg0abCZ9d5IZNnyYSU8fa0t+OjP9DN//fo4ZePdAU7Zhg5fbnEpbzp07Z17dvt3LaZ7X0n6V0MyaNdP07v11s317ReMzGuQdFWrkS+NeAEBX02JA0/jXvt3Ozp5udu3abbflG9/4Rrt0zVZVVF3dn80H739gjh0/Zv7zPy+bcWPHm/sn3G8bGyvAURVXZ7F16xZTWFhg9u17p1mg4fdobq4ZPWa0KSgo9HKazlPVnNoaxdsf7+cloAEAdEVx29AoYFFvGddjxm1raa9xZnSvH/5wtilZu7YxSNhvS4Z+/OMfm2vXrtnGxsOHD7U9sFauWGEbL3dkY2OVzpSUlJj8/EUxgxmpq6/ztpr06N7Drq9fv97ifgAA0Fzg5nJSIDVh4kTzzDPP2sbGKo342dKlpl//fqaystJMm/aAnYZBjY01FUN7NjZ+440d5vLlv5msrGleTnQ6Jp6W9sdCzzEAQFcVuIAmGpXiPPbYAluKc+zYR7YUJ7LLuEpxkt1lfNfOXWboULX1SfdyolPbl3ha2h+LqgezHogfTAEAkIpSIqCJpFKcyC7jKsVxXcZVitPWXcZV3XT4/fdMTk6OlxPb4EGDTcPVBi8V0nAtlNaghC3tBwAAzaVkQBNJjWhdKY5GOlYpzm9+U26+fd+3zelTp83ixc/aUhz/wH9uzJdE1Rw9atfDhw2363i++c1v2h5LfmoTdP99E+xnbWl/LGo8PWDAAC8FAEDX0SUCmmjUO0qNjVWKo8bGKsVRY2NXiqPGxirFUWNjleJoQs54Pr0Q6lk0eMgQu47nwQcftKU56rkk6oZdXl5uJk0OjcDc0v5Y1GBYbYkAAOhqEp7LqSt2B47sMl5fX2fbqETrMl5cXGRKS9dHfUauy/WOHTvD7Ws0rszWbaGARaY/NMP84pe/DF+vpf3RKPjSeD0K1AAA6EoIaFpBjYn/Ul/fbOC/e8dnmJEjR5qMjAzz3wYN6tCB/5iYEgDQVRHQ3CaV4tTUHDV/Ovkns2//v9u8jpplXN3VkzGCMwAAnR0BTRtTKc6xP/7RnD5z2lQdqrKzlKsUZ+J3JpphQ4eZ0WPGJCXgUCNmtfvhOwIAdEUENEmmQEMNilWKc/i9w+ZozRHzd3/X24weNdr2sho8eEiblOKopEhj7qibOgAAXQ0BTQdQgKO2ONXV1ebguwfDjY3vGXGPGT9uvG2L09pSHPXEUuNlDS4IAEBXQ0DTCagUR7OM/7nuz7YU51ZmGdf4OepyrrF2RFVftKUBAHQVBDSdlEpxamtronYZH6JqqtGjm3XhjuzhpO+r/Dcb7YjJAACkOgKagGipy/jC//G4HRxQQY7a02RnT7fnEdQAALoCApoAc13Gjx45agMcBTPjxo63+5R2CGoAAKmOgCaFuC7jJWtLzJkzp73ckMWLl5hnnnnWSwEAkFq67FxOqcjNMv4f/3HJy2ly/pPzNuABACAVUUKTYhS0jB8/1vTq1ct8P+cRk5mZeVMDYgAAUg0BTYpRQPP5558znxMAoEshoAEAAIFHGxp0OvX19SY9fYyXAgCgZQQ0KW7r1i22dE1LVtYDpra21tvT3MWLF20QUVxc5OV0jDd37TK5ubPN5ct/83IAAGgZAU0KUzCzefNmU119xFYXTp061cyaNdMGL5GefeaZThNEbNy4ydsCACAxBDQpSvNDlZSUmJycHNO3b1+b9+STT9n1/v377NopKys1dfV1XqpjzcjODn9eAAASRUCTourq6myJy/e+94CXY2zXbZXUzJ07z8sJtVcpKlptXlr7kpdzM1UDqcqqsKAgXH31aG6uOXjggF27vGjVVf4qLy26hoKtyHwtug8AALeCgCZFfXbhgl1/+GG1bRujgEFrf9CgwGLRonxTWPgTM2nyZC83tnPnztn5olSFdfj998w//mieyZ6ZbYOkoqJiU1q6vlkbHQU8hYUFpnR9mT1m3753zNZtW8zvf/+KDaqU519UOgMAwK0goElRDdca7HrXzl1m9+63bMCwcsVKk78oLxx0vLBqlV3n5eXbdUvy8vJsKY+qhO6/b4IZOnRYuLTn3nsz7NoFUvLphVA3/7S0NLseNGiQ/RyJ3g8AgEQR0KS4nzcGLa5NikpAFIRUV39gq3xUWrJ+fandl4jBQ4Z4W8bccccdZuDdA71UqDor0sMPz7KBj0pyVEKkKqlEqpX0eRX4AACQKAKaFNXvzn52HdnAVkHIR8c/MlWHqmw6M3NKuA2LqNpI3bvbgoKcV7dvt1VN+fmLzLE/HrMlRGpHAwBAWyKgSVFjx42zazUO9qv+sNqMHDXSlG3YYEtB/Iso8Kis3Gu324qqmgoKCm1wo/Y6KhmK1nUcAIBbRUCTolQ6ouDkxTVrvJxQbyX1fJo1K8fLSS7Xk8m12VEj5IMHDtpqL7pmAwDaEgFNClOpyOgxo8NVSuteXmd27NjZbsGEGgwrqNJgfrr/8OFDbdub1rTbAQAgEUxOCQAAAo8SGgAAEHgENAAAIPAIaAAAQOAR0AAAgMAjoAEAAIFHQAMAAAKPgAYAAAReUgIajRCbnj4mPKDbo7m5cYe61wiymt/Hf3x9fb23N7Q/74knwvu16B4AAADS5gHNwQMHTGFhgVmyZIkdiK+6+ojNnz//R3Ydza9//bI5d+5ceE6hSZMnmUWL8r29of1n/3rWjnKr/UVFxfYeuhcAAECbBzRvv/22natHw96LhtnPy8szZ86cjhmAaIbn7JnZXsqYjIxvNzu+oqLC5OTkmPT0dJvWtXv3/ro5dfqUTQMAgK6tzQOaouLiNp2tWdVNmlCxf7/+Xk5Ixr0ZdqJDv+LiIlvV5a+e0rYCo6ysB8J5mqQRAACkjnZpFPz+B+/b9dhx4+w6kiYw3LWzKciorv7AlvLo+Fhtb+76+7vMlS+ueKkmCn60T1VTpevLzO633jTPLn62MdhZY/OmPzTDLF221AZKAAAgNSQ9oFHjXlUpqd1Lt27dvNzm5s//J1NXXxcuQSkqWm2efuppe/z169e9oxL35JNP2fXkKVPsevbs2eHqqonfmWiDnlu5LgAA6JySGtCodCU3d7aZO2deuE1NJJWUTJ/+kA06XKNglazkL8oztbW1Ji0tzTsyMSrZcYGTW/fv31Rd1aN7D28LAACkiqQFNCqZUc8mtXVRu5pYDrzzji0xeeSRH3g5xszIzraBSWXlHtuoWBquNdi103C1wfS6o5eXAgAAXVlSAhqNEZOZOcUMvHugKduwwcuNL1Z1lPLVo+natWteToi6eat7NwAAQJsHNApmNEaMqpkSCWbUzkUBy7p/+RcvJzSWjbptZ2VNs+mFCxea8vJyWwUlusfh998zw4cNt2kAANC1tXlAU1JSYtdbt20JN/J1ixvd13WrFpXAbN9eYUtc3HEvrH7BtqNxDXlnzcoxgwcNblzPtPsVMBUW/sRMmjzZ7gcAAF3bV2408rbjUiChBrsAAACdTVJ7OQEAALQHAhoA6CTUO5SRzIFbQ0ADAJ2EJuU9+aeTXgpAaxDQAACAwCOgAYA2oKoidZ7QJLmux6YmxfVXIWn0dP/kuf792tZwFZoqRvsAtA4BDQC0oWN/PGaqq4+YU6fO2NHMNRmuo9HTv/jiC7tPvUanTp0anualsnKvHSFdk/XSoxRoPQIaAGhDeXl5dsoWjbGVPTPbTu2ikhk3YOjPV60Kj4xeUFBo7r9vgnmtosKmAdw6AhoAaEODhwzxtppPhvvphVCpi6aFcVVOWjTquQYWBXB7CGgAoB256ib/8ur27d5eALeKgAYA2oErrak5etSuAbQtAhoAaAeaiFeNfjVXnQbQE/VwSk8fE57nThquNnhbAFqDgAYA2oEaAm/e/IoZePfAcDsa9XBasmSJmTt3nj1m/vz54Yl91ZAYQOKYnBIAAAQeJTQAACDwCGgAAEDgEdAAAIDAI6ABAACBR6NgAEgy/f6MpN+nkfn+37Gx9sW6lvj38fsaXQ0BDQAkWbwgJJ7MzKlm0ncnmaXLlnk5AGKhygkAOqHXXqsw9fV1ZuOmcnP8+HEvF0AsBDQA0Ml8+eWX5oUXVnkpY15et87bAhALAQ0AdDIbN5abK1eueCljKvfuMXvefttLAYiGgAYAOpFLly6ZtWtLvFSTF3/xoi25ARAdjYIBIMla0yhY7WVqakIzci9fvqxxWWG3Zfr0GaZPnz5eCoAfAQ0AJNmt9nLi9y6QOKqcAABA4BHQAACAwCOgAQAAgUdAAwAAAo+ABgAABB4BDQAEkMakyXviCdsTyi1bt27x9kan/e7Y9PQxMY+vr6+3x9TW1no5IW/u2mXPc9d4NDfXHgt0BgQ0ABBAv/71y+bsX8+aHTt22q7dRUXFprCwwBw8cMA7ojkFL9rvjn/33UNm185dNwU1ClByc2d7qSYXL140+YvyzLSsafb86uoj5soXV8zPnn/eOwLoWAQ0ABBAFRUVJicnx6Snp9v03LnzTO/eXzenTp+y6UgKXubOmRc+vlu3biZ7ZrYpKWkalbi4uMgsWpRvg5ZI+/fvs+ufegFM3759zfz5883h999jBGN0CgQ0ABAwCiAuX/6b6d+vv5cTknFvhjl44KCXak6BR4+ePbxUSI/uPex1VPoi+/fvN5s3v2ImTJhg037Xrl0zQ4cOs4GQM2zYcLuuORoa2djJynrAVkdpcdVTZWWlzaq8dAzVVWhLBDQAEDAuAIl019/fZauBorn/vgmm4WqDlwppuBZKu+tVVu61JS/RfPLxJ95WE3fs9evX7dpPAdS8efNs9VR+/iJTVLTalhKpqkqLrPWVDgG3i4AGAAImWgDRElUv7ancEy4VUYNff3VTS65eveptJUYB1IzsbLt937fvs2sFOAqCtIxNH2vbAAFthYAGAAImLS3N20qc2tgsXLjQZGZOsVU+L65ZY9OSyPV69uzpbSVm9JjR3lbj9bt3t+v/eueddi2R1V/A7SKgAYCAcVU9rsrIUZVSrzt6eamb5eXl2yogLa9u3266e4FGrGomvwF3DTCXL1/2UiGuMfCtBFhAWyOgAYCAUcNc9WhSQ12/c+fOmUmTJ3mp5goLCmxDXL+TJ07aqiF/Q99YFPyoAbG/R9NnFy7Y9dhx4+wa6EgENAAQQKouKi8vDw9+px5Eaog73Ot5FEk9l86cOW0HxxOt1aYmLy/Pplvy8MOz7Pp///M/27UaEpeVlSUcEAHJRkADAAE0a1aOGTxocON6pm0To0HzCgt/YiZNnmz3K9BRvhs4Tw10NfieBsdT/rqX15mVK1aGj2+Jghadv/utN+35GRnjbf7PV62ya6CjfeVGI287Lv0DVr0rAKB19PszUiK/T/m9CySOEhoAABB4BDQAACDwCGgAAEDgEdAAAIDAI6ABAACBR0ADAAACj4AGAIAUpdGhi4uLvFRqixvQXLp0yRw/ftwu4ra1aB8AoG3F+73rn3YAQHNxB9bTf6Ds7OleqrkjR2pMnz59vBQAIJbWDKwX6/dur169zJ49e/m9i1ZRCc3UqVNNQUGhl5O64pbQjBo1yjy+IDS9vN/ixUv4TwUASaDfu1kPTPNSTZ5++n/xe7cT0VxY6eljbLCqRZN/aq0pJ7RP23lPPGHXOs6d82hubvgcbdfX14f3KU9zZDn+PC3a1jUVpLhruKktRCV47p7u2MgZ0lNZi21o/mfjA9FfBo62H3/85iAHANA2Xli92tsKGTRosJk9O9dLoaMpCNGcWLNnz7YlbTt27LQTfUbq2bOn3b9x4yYb6OicO+64w+ZVVx+xx+Tmzm5VVWL1h9WmuHiNvUZ+/iI7h5cLijRx6Nm/njX79r0TLgHUDOldRYsBjf4i0F8Gzk9/+jwzqwJAEun3rkrCHU0iye/dzuO3mzaZ3r2/Hq7GSU9PN0uWNH1fzoMPPmjX2v9aRYU9p2zDBpvXt29fO7GnAo433thh8xKhWdZ1PXnkkR/Y9Z/PnLFBjSYOnT9/fmMAPMjm/+KXv7TrriKhXk6PPbbA/oVw7/gM88MfzvZyAQDJopJwlYir+mnCxIleLjqDc+fOmYx7M7xUSL87b24nlda9u7dlTE1tzU3nuMDj/Pnzdp2I/v36e1uhGdCdzy5csOthw4bbtWj/0KHDvFTqS2i2bdXFAQDQVbkqHFEbloF3DwyXtsjBAwfMP/5onq1+UnCh6iVtu9KUaOeI3q+qOrrnW/fYc1QVpdIbURsalycZGeNN6foyMyM726bVrsblpaWlhe/v7ildqVGwUUADAAASU/DcczfGjBntpUK2bPn9jf7977xRU1NzY9fOneFtJ9o5dXV19jid685RnlNaut7mffbZZ3bRto5z/HluW9dyrl+/bvOKilZ7OaktoSonAAAQ8tiCBbbtixuwTg1+S0pK7HYs7hz1PBKVrvzs+edtu5qHH55lhgwdavNff/0Pdq1rlpeX2+1EqFRn7px59nP4Gwl3JbcV0LxXVWVWrljhpQAAfhpTRr8jGRAvtajti6p5KioqbJXR448vCLePUdVPNDpH1UFffPGFPUdVRerxtH17hW3rov1FRcWmtHS93V9Q8JztRdUaRcXFZlrWNJOZOSXcVEQBU1eRUBuaSGfPnjVFq1ebyr17bIO1jZs2eXsAAI4bJE+Ne9VbVB0skJo0Hoy6UJ86dYYeaR2kVSU0+ivjV796yUyZMskGMwCAll25csUsX76s8S/nqbZkG8FWVlZqS0Bc1Y7WmzdvNtMfmkEw04ESLqHR/CJz5vxD4xdX5+UAAG7F8uUrKK0JMP1x/8KqVWbrtqZRetV+5afPM05bR2pVlZO+xI0by83atU2Nn6hyAoDoIudl0nhea9e+ZKc3ANC2WlXlpMjzmWeetRNTRptrBABwM7WhUanMvn37CWaAJLmlXk4allulMv+67VUzYMAALxcAEEkT/FZVHaaKCUiyW+rlBAAA0JkwsB4AAAg8AhoAABB4BDToVDQ4lRvhMpLGetA+DQkej7uGlvT0MTYNAEhtBDToNDSzrEbajEbBTG5uy8OAu9E6NcS4Zsd9991DZtfOXQQ1AJDiCGjQ4TRJmyZs27Jli7n/vglebhNNALdoUb6do6QlCl40wJWbPl9DDWTPzG5x4jgAQLAR0KDDKaCRV7dvN6PHjLbbfvv37zebN79iJky4OdiJdPj990yPnj28VEiP7j3sLLfuPqJtVUkpkFK1lKuesqVEBQXhKqtHc3OZWBAAAoCABh1OpSllGzZ4qZtVVu61U+MnQiU8DVcbvFRIw7VQ2h/QONUfVtvZblU91bt3b5O/KM9cvXrVplVtpQDpjTd2eEcDADorAhqkFFUv7ancE540Tg2I41U3LVy40E7bLzk5OXa9dNkyu1agpan3z58/b9MAgM6LgAYpZe7ceTZIycycYquMXlyzxqYlLS3Nrv369+vvbRnTvXt3u/aXBqnUBgDQ+RHQIOXk5eXbKiMtapcTLVABAKQWAhqkFDXozcp6wEuFnDxx0ratYVp/AEhdBDRIKeoJdebMadtbSbRWm5q8vDybBgCkJgIaBJoa/aqtjBs4b0Z2tikqKra9lZS/7uV1ZuWKlWbS5Ml2PwAgNTHbNgAACDxKaAAAQMAZ8/8BA4H3YwNFRnkAAAAASUVORK5CYII=\"/></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">The following data are available.<br/></span></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">Height of P = 2.80 m<br/></span></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">Distance of student from net = 11.9 m<br/></span></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">Height of net = 0.910 m<br/></span></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">Initial speed of tennis ball = 64 m s<sup>-1</sup></span></span></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Calculate the average force exerted by the racquet on the ball.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">ai.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Calculate the average power delivered to the ball during the impact.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">aii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Calculate the time it takes the tennis ball to reach the net.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">bi.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Show that the tennis ball passes over the net.</span></p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">bii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Determine the speed of the tennis ball as it strikes the ground.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">biii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">The student models the bounce of the tennis ball to predict the angle <em>θ</em> at which the ball leaves a surface of clay and a surface of grass.</span></p>\n<p><span style=\"background-color:#ffffff;\"><img src=\"data:image/png;base64,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\"/></span></p>\n<p><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\">The model assumes<br/></span></span></p>\n<p><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\">• during contact with the surface the ball slides.<br/>• the sliding time is the same for both surfaces.<br/>• the sliding frictional force is greater for clay than grass.<br/>• the normal reaction force is the same for both surfaces.<br/></span></span></p>\n<p><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\">Predict for the student’s model, without calculation, whether θ is greater for a clay surface or for a grass surface.</span></span></p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"F = \\frac{{\\Delta mv}}{{\\Delta t}}/m\\frac{{\\Delta v}}{{\\Delta t}}/\\frac{{0.058 \\times 64.0}}{{25 \\times {{10}^{ - 3}}}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>F</mi>\n<mo>=</mo>\n<mfrac>\n<mrow>\n<mi mathvariant=\"normal\">Δ</mi>\n<mi>m</mi>\n<mi>v</mi>\n</mrow>\n<mrow>\n<mi mathvariant=\"normal\">Δ</mi>\n<mi>t</mi>\n</mrow>\n</mfrac>\n<mrow>\n<mo>/</mo>\n</mrow>\n<mi>m</mi>\n<mfrac>\n<mrow>\n<mi mathvariant=\"normal\">Δ</mi>\n<mi>v</mi>\n</mrow>\n<mrow>\n<mi mathvariant=\"normal\">Δ</mi>\n<mi>t</mi>\n</mrow>\n</mfrac>\n<mrow>\n<mo>/</mo>\n</mrow>\n<mfrac>\n<mrow>\n<mn>0.058</mn>\n<mo>×</mo>\n<mn>64.0</mn>\n</mrow>\n<mrow>\n<mn>25</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>3</mn>\n</mrow>\n</msup>\n</mrow>\n</mrow>\n</mfrac>\n</math></span>  ✔</span></p>\n<p><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"F\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>F</mi>\n</math></span></span><em><span style=\"background-color:#ffffff;\"> =</span></em><span style=\"background-color:#ffffff;\"> 148«<span class=\"mjpage\"><math alttext=\"{\\text{N}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mrow>\n<mtext>N</mtext>\n</mrow>\n</math></span>»≈150«<span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span class=\"mjpage\"><math alttext=\"{\\text{N}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mrow>\n<mtext>N</mtext>\n</mrow>\n</math></span></span>»  ✔</span></p>\n<p> </p>\n<div class=\"question_part_label\">ai.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><em><strong><span style=\"background-color:#ffffff;\">ALTERNATIVE 1</span></strong></em></p>\n<p><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"P = \\frac{{\\frac{1}{2}m{v^2}}}{t}/\\frac{{\\frac{1}{2} \\times 0.058 \\times {{64.0}^2}}}{{25 \\times {{10}^{ - 3}}}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>P</mi>\n<mo>=</mo>\n<mfrac>\n<mrow>\n<mfrac>\n<mn>1</mn>\n<mn>2</mn>\n</mfrac>\n<mi>m</mi>\n<mrow>\n<msup>\n<mi>v</mi>\n<mn>2</mn>\n</msup>\n</mrow>\n</mrow>\n<mi>t</mi>\n</mfrac>\n<mrow>\n<mo>/</mo>\n</mrow>\n<mfrac>\n<mrow>\n<mfrac>\n<mn>1</mn>\n<mn>2</mn>\n</mfrac>\n<mo>×</mo>\n<mn>0.058</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>64.0</mn>\n</mrow>\n<mn>2</mn>\n</msup>\n</mrow>\n</mrow>\n<mrow>\n<mn>25</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>3</mn>\n</mrow>\n</msup>\n</mrow>\n</mrow>\n</mfrac>\n</math></span>  <strong>✔</strong></span></p>\n<p><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"P = 4700/4800«{\\text{W}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>P</mi>\n<mo>=</mo>\n<mn>4700</mn>\n<mrow>\n<mo>/</mo>\n</mrow>\n<mn>4800</mn>\n<mrow>\n<mo>«</mo>\n</mrow>\n<mrow>\n<mtext>W</mtext>\n</mrow>\n</math></span>»  <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:bold;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">✔</span></span></span></p>\n<p> </p>\n<p><em><strong><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\">ALTERNATIVE 2</span></span></strong></em></p>\n<p><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"P = {\\text{average}}Fv/148 \\times \\frac{{64.0}}{2}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>P</mi>\n<mo>=</mo>\n<mrow>\n<mtext>average</mtext>\n</mrow>\n<mi>F</mi>\n<mi>v</mi>\n<mrow>\n<mo>/</mo>\n</mrow>\n<mn>148</mn>\n<mo>×</mo>\n<mfrac>\n<mrow>\n<mn>64.0</mn>\n</mrow>\n<mn>2</mn>\n</mfrac>\n</math></span>  <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:bold;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">✔</span></span></p>\n<p><span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span class=\"mjpage\"><math alttext=\"P = 4700/4800«{\\text{W}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>P</mi>\n<mo>=</mo>\n<mn>4700</mn>\n<mrow>\n<mo>/</mo>\n</mrow>\n<mn>4800</mn>\n<mrow>\n<mo>«</mo>\n</mrow>\n<mrow>\n<mtext>W</mtext>\n</mrow>\n</math></span>»  <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:bold;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">✔</span></span></p>\n<p> </p>\n<div class=\"question_part_label\">aii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color:#ffffff;\">horizontal component of velocity is 64.0 <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">×</span> cos7° = 63.52 «<span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">ms<sup>−</sup></span><sup>1</sup>» ✔</span></p>\n<p><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"t = « \\frac{{11.9}}{{63.52}} =» 0.187/0.19 « {\\text{s}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>t</mi>\n<mo>=</mo>\n<mrow>\n<mo>«</mo>\n</mrow>\n<mfrac>\n<mrow>\n<mn>11.9</mn>\n</mrow>\n<mrow>\n<mn>63.52</mn>\n</mrow>\n</mfrac>\n<mo>=</mo>\n<mrow>\n<mo>»</mo>\n</mrow>\n<mn>0.187</mn>\n<mrow>\n<mo>/</mo>\n</mrow>\n<mn>0.19</mn>\n<mrow>\n<mo>«</mo>\n</mrow>\n<mrow>\n<mtext>s</mtext>\n</mrow>\n</math></span>»  <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"> ✔</span></span></span></p>\n<p><em><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\">Do not award BCA. Check working.<br/></span></span></em></p>\n<p><em><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\">Do not award ECF from using 64 m s<sup>-1</sup>.</span></span></em></p>\n<div class=\"question_part_label\">bi.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><em><span style=\"background-color:#ffffff;\"><strong>ALTERNATIVE 1</strong><br/></span></em></p>\n<p><em><span style=\"background-color:#ffffff;\">u<sub>y </sub></span></em><span style=\"background-color:#ffffff;\">= 64 </span><span style=\"background-color:#ffffff;\">sin7</span><span style=\"background-color:#ffffff;\">/7.80</span><em><span style=\"background-color:#ffffff;\"> «</span></em><span style=\"background-color:#ffffff;\">ms</span><sup><span style=\"background-color:#ffffff;\"><span style=\"text-align:left;color:#000000;text-indent:0px;letter-spacing:normal;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-variant:normal;font-weight:400;text-decoration:none;display:inline !important;white-space:normal;float:none;background-color:#ffffff;\">−</span></span><span style=\"background-color:#ffffff;\">1</span></sup><em><span style=\"background-color:#ffffff;\">»</span></em><span style=\"background-color:#ffffff;\">✔</span><em><span style=\"background-color:#ffffff;\"><br/></span></em></p>\n<p><span style=\"background-color:#ffffff;\">decrease in height = 7.80 <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">×</span> 0.187 + <span class=\"mjpage\"><math alttext=\"\\frac{1}{2}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mn>1</mn>\n<mn>2</mn>\n</mfrac>\n</math></span> <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">×</span> 9.81 <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">×</span> 0.187<sup>2</sup>/1.63 «m» ✔<br/></span></p>\n<p><span style=\"background-color:#ffffff;\">final height = «<span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">2.80 − 1.63</span>» = 1.1/1.2 «m» ✔<br/></span></p>\n<p><span style=\"background-color:#ffffff;\">«higher than net so goes over»<br/></span></p>\n<p><span style=\"background-color:#ffffff;\"><em><strong>ALTERNATIVE 2</strong></em><br/></span></p>\n<p><span style=\"background-color:#ffffff;\">vertical distance to fall to net <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">«</span>= <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">2.80 − 0.91</span>» = 1.89 «m»✔<br/></span></p>\n<p><span style=\"background-color:#ffffff;\">time to fall this distance found using <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">«</span>=1.89 = 7.8<em>t</em> + <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span class=\"mjpage\"><math alttext=\"\\frac{1}{2}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mn>1</mn>\n<mn>2</mn>\n</mfrac>\n</math></span></span> <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">×</span> 9.81 <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">×</span><em>t</em><sup>2</sup>»<br/></span></p>\n<p><span style=\"background-color:#ffffff;\"><em>t </em>= 0.21 «s»✔<br/></span></p>\n<p><span style=\"background-color:#ffffff;\">0.21 «s» &gt; 0.187 «s» ✔<br/></span></p>\n<p><span style=\"background-color:#ffffff;\">«reaches the net before it has fallen far enough so goes over»</span><em><span style=\"background-color:#ffffff;\"><br/></span></em></p>\n<p><em><span style=\"background-color:#ffffff;\">Other alternatives are possible<br/></span></em></p>\n<div class=\"question_part_label\">bii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><em><span style=\"background-color:#ffffff;\"><strong>ALTERNATIVE 1</strong><br/></span></em></p>\n<p><span style=\"background-color:#ffffff;\">Initial KE + PE = final KE /</span></p>\n<p><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"\\frac{1}{2}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mn>1</mn>\n<mn>2</mn>\n</mfrac>\n</math></span> × 0.058 × 64<sup>2</sup> + 0.058 × 9.81 × 2.80 = <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\"><span class=\"mjpage\"><math alttext=\"\\frac{1}{2}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mn>1</mn>\n<mn>2</mn>\n</mfrac>\n</math></span></span> <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">×</span> 0.058 <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">×</span> <em>v</em><sup>2</sup> ✔<br/></span></p>\n<p><span style=\"background-color:#ffffff;\"><em>v</em> = 64.4 «<span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">ms<sup>−1</sup></span>» ✔</span><span style=\"background-color:#ffffff;\"><br/></span></p>\n<p><span style=\"background-color:#ffffff;\"><em><strong>ALTERNATIVE 2</strong></em><br/></span></p>\n<p><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"{v_v} = « \\sqrt {{{7.8}^2} + 2 \\times 9.81 \\times 2.8} » = 10.8 « {\\text{m}} {{\\text{s}}^{ - 1}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mrow>\n<msub>\n<mi>v</mi>\n<mi>v</mi>\n</msub>\n</mrow>\n<mo>=</mo>\n<mrow>\n<mo>«</mo>\n</mrow>\n<msqrt>\n<mrow>\n<msup>\n<mrow>\n<mn>7.8</mn>\n</mrow>\n<mn>2</mn>\n</msup>\n</mrow>\n<mo>+</mo>\n<mn>2</mn>\n<mo>×</mo>\n<mn>9.81</mn>\n<mo>×</mo>\n<mn>2.8</mn>\n</msqrt>\n<mrow>\n<mo>»</mo>\n</mrow>\n<mo>=</mo>\n<mn>10.8</mn>\n<mrow>\n<mo>«</mo>\n</mrow>\n<mrow>\n<mtext>m</mtext>\n</mrow>\n<mrow>\n<msup>\n<mrow>\n<mtext>s</mtext>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>1</mn>\n</mrow>\n</msup>\n</mrow>\n</math></span>»  <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">✔</span> </span></p>\n<p><span style=\"background-color:#ffffff;\">« <span class=\"mjpage\"><math alttext=\"v = \\sqrt {{{63.5}^2} + {{10.8}^2}} \" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>v</mi>\n<mo>=</mo>\n<msqrt>\n<mrow>\n<msup>\n<mrow>\n<mn>63.5</mn>\n</mrow>\n<mn>2</mn>\n</msup>\n</mrow>\n<mo>+</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10.8</mn>\n</mrow>\n<mn>2</mn>\n</msup>\n</mrow>\n</msqrt>\n</math></span> »</span></p>\n<p><span style=\"background-color:#ffffff;\"><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"v = 64.4 « {\\text{m}} {{\\text{s}}^{ - 1}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>v</mi>\n<mo>=</mo>\n<mn>64.4</mn>\n<mrow>\n<mo>«</mo>\n</mrow>\n<mrow>\n<mtext>m</mtext>\n</mrow>\n<mrow>\n<msup>\n<mrow>\n<mtext>s</mtext>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>1</mn>\n</mrow>\n</msup>\n</mrow>\n</math></span>»   <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">✔</span></span></span></p>\n<p><em><span style=\"background-color:#ffffff;\"> </span></em></p>\n<div class=\"question_part_label\">biii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color:#ffffff;\">so horizontal velocity component at lift off for clay is smaller ✔<br/></span></p>\n<p><span style=\"background-color:#ffffff;\">normal force is the same so vertical component of velocity is the same ✔<br/></span></p>\n<p><span style=\"background-color:#ffffff;\">so bounce angle on clay is greater ✔</span><em><span style=\"background-color:#ffffff;\"><br/></span></em></p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>At both HL and SL many candidates scored both marks for correctly answering this. A straightforward start to the paper. For those not gaining both marks it was possible to gain some credit for calculating either the change in momentum or the acceleration. At SL some used 64 ms-1 as a value for a and continued to use this value over the next few parts to the question.</p>\n<div class=\"question_part_label\">ai.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was well answered although a significant number of candidates approached it using P = Fv but forgot to divide v by 2 to calculated the average velocity. This scored one mark out of 2.</p>\n<div class=\"question_part_label\">aii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This question scored well at HL but less so at SL. One common mistake was to calculate the direct distance to the top of the net and assume that the ball travelled that distance with constant speed. At SL particularly, another was to consider the motion only when the ball is in contact with the racquet.</p>\n<div class=\"question_part_label\">bi.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>There were a number of approaches students could take to answer this and examiners saw examples of them all. One approach taken was to calculate the time taken to fall the distance to the top of the net and to compare this with the time calculated in bi) for the ball to reach the net. This approach, which is shown in the mark scheme, required solving a quadratic in t which is beyond the mathematical requirements of the syllabus. This mathematical technique was only required if using this approach and not required if, for example, calculating heights.</p>\n<p>A common mistake was to forget that the ball has a vertical acceleration. Examiners were able to award credit/ECF for correct parts of an otherwise flawed method.</p>\n<div class=\"question_part_label\">bii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This proved difficult for candidates at both HL and SL. Many managed to calculate the final vertical component of the velocity of the ball.</p>\n<div class=\"question_part_label\">biii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>As the command term in this question is ‘predict’ a bald answer of clay was acceptable for one mark. This was a testing question that candidates found demanding but there were some very well-reasoned answers. The most common incorrect answer involved suggesting that the greater frictional force on the clay court left the ball with less kinetic energy and so a smaller angle. At SL many gained the answer that the angle on clay would be greater with the argument that frictional force is greater and so the distance the ball slides is less.</p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-1-kinematics",
      "a-2-forces-and-momentum",
      "a-3-work-energy-and-power"
    ]
  },
  {
    "question_id": "19M.2.SL.TZ2.14",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <span style=\"background-color:#ffffff;\">\n    Show that, when the speed of the train is 10 m s-1, the frequency of the periodic force is 0.4 Hz.\n   </span>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <span style=\"background-color:#ffffff;\">\n    <span style=\"background-color:#ffffff;\">\n     Outline, with reference to the curve, why it is unsafe to drive a train across the bridge at 30 m s\n     <sup>\n      -1\n     </sup>\n     for this amount of damping.\n    </span>\n   </span>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <span style=\"background-color:#ffffff;\">\n    The damping of the bridge system can be varied. Draw, on the graph, a second curve when the damping is larger.\n   </span>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <span style=\"background-color:#ffffff;\">\n   time period\n  </span>\n </p>\n <p>\n  <em>\n   <span style=\"background-color:#ffffff;\">\n    T = «\n    <span class=\"mjpage\">\n     <math alttext=\"\\frac{25}{10}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n      <mfrac>\n       <mn>\n        25\n       </mn>\n       <mn>\n        10\n       </mn>\n      </mfrac>\n     </math>\n    </span>\n    »\n   </span>\n  </em>\n  <span style=\"background-color:#ffffff;\">\n   = 2.5 s\n  </span>\n  <em>\n   <span style=\"background-color:#ffffff;\">\n    <strong>\n     AND\n    </strong>\n    f =\n    <span class=\"mjpage\">\n     <math alttext=\"\\frac{1}{T}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n      <mfrac>\n       <mn>\n        1\n       </mn>\n       <mi>\n        T\n       </mi>\n      </mfrac>\n     </math>\n    </span>\n   </span>\n  </em>\n </p>\n <p>\n  <strong>\n   <em>\n    <span style=\"background-color:#ffffff;\">\n     OR\n    </span>\n   </em>\n  </strong>\n </p>\n <p>\n  <em>\n   <span style=\"background-color:#ffffff;\">\n    evidence of f =\n    <span class=\"mjpage\">\n     <math alttext=\"\\frac{10}{25}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n      <mfrac>\n       <mn>\n        10\n       </mn>\n       <mn>\n        25\n       </mn>\n      </mfrac>\n     </math>\n    </span>\n    ✔\n   </span>\n  </em>\n </p>\n <p>\n  <em>\n   <span style=\"background-color:#ffffff;\">\n    <span style=\"background-color:#ffffff;\">\n     Answer 0.4 Hz is given, check correct working is shown.\n    </span>\n   </span>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  <span style=\"background-color:#ffffff;\">\n   30 m s\n   <sup>\n    –1\n   </sup>\n   corresponds to\n   <em>\n    f\n   </em>\n   = 1.2 Hz ✔\n   <br/>\n  </span>\n </p>\n <p>\n  <span style=\"background-color:#ffffff;\">\n   the amplitude of vibration is a maximum for this speed\n   <br/>\n  </span>\n </p>\n <p>\n  <span style=\"background-color:#ffffff;\">\n   <em>\n    <strong>\n     OR\n    </strong>\n   </em>\n   <br/>\n  </span>\n </p>\n <p>\n  <span style=\"background-color:#ffffff;\">\n   corresponds to the resonant frequency ✔\n  </span>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  <span style=\"background-color:#ffffff;\">\n   similar shape with lower amplitude ✔\n   <br/>\n  </span>\n </p>\n <p>\n  <span style=\"background-color:#ffffff;\">\n   maximum shifted slightly to left of the original curve ✔\n  </span>\n </p>\n <p>\n  <em>\n   <span style=\"background-color:#ffffff;\">\n    <span style=\"background-color:#ffffff;\">\n     Amplitude must be lower than the original, but allow the amplitude to be equal at the extremes.\n    </span>\n   </span>\n  </em>\n </p>\n</div>\n",
    "Examiners report": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  The question was correctly answered by almost all candidates.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  The answers to this question were generally well presented and a correct argument was presented by almost all candidates. Resonance was often correctly referred to.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  A correct curve, with lower amplitude and shifted left, was drawn by most candidates.\n </p>\n</div>\n",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-4-standing-waves-and-resonance"
    ]
  },
  {
    "question_id": "19M.2.SL.TZ2.15",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <span style=\"background-color:#ffffff;\">\n    Identify, on the HR diagram, the position of the Sun. Label the position S.\n   </span>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (d)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <span style=\"background-color:#ffffff;\">\n    During its evolution, the Sun is likely to be a red giant of surface temperature 3000 K and luminosity 10\n    <sup>\n     4\n    </sup>\n    L\n    <var style=\"color:#222222;font-family:sans-serif;font-size:13.93px;font-style:italic;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">\n    </var>\n    <sub style=\"color:#222222;font-family:sans-serif;font-size:80%;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;line-height:1;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">\n     ☉\n    </sub>\n    . Later it is likely to be a white dwarf of surface temperature 10 000 K and luminosity 10-4 L\n    <var style=\"color:#222222;font-family:sans-serif;font-size:13.93px;font-style:italic;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">\n    </var>\n    <sub style=\"color:#222222;font-family:sans-serif;font-size:80%;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;line-height:1;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">\n     ☉\n    </sub>\n    . Calculate the\n    <span class=\"mjpage\">\n     <math alttext=\"\\frac{{{\\text{radius of the Sun as a white dwarf}}}}{{{\\text{radius of the Sun as a red giant}}}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n      <mfrac>\n       <mrow>\n        <mrow>\n         <mtext>\n          radius of the Sun as a white dwarf\n         </mtext>\n        </mrow>\n       </mrow>\n       <mrow>\n        <mrow>\n         <mtext>\n          radius of the Sun as a red giant\n         </mtext>\n        </mrow>\n       </mrow>\n      </mfrac>\n     </math>\n    </span>\n    .\n   </span>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <span style=\"background-color:#ffffff;\">\n   the letter S should be in the region of the shaded area\n  </span>\n  <em>\n   <span style=\"background-color:#ffffff;\">\n    ✔\n   </span>\n  </em>\n </p>\n <p>\n  <em>\n   <img height=\"463\" 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\" width=\"740\"/>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  <img height=\"117\" 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\" width=\"205\"/>\n </p>\n</div>\n",
    "Examiners report": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Locating the Sun’s position on the HR diagram was correctly done by most candidates, although a few were unsure of the surface temperature of the Sun.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  Calculating the ratio of the radius of a white dwarf to a red giant star was done quite well by most candidates. However quite a few candidates made POT errors or forgot to take the final square root.\n </p>\n</div>\n",
    "topics": [
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "e-5-fusion-and-stars"
    ]
  },
  {
    "question_id": "19M.2.SL.TZ2.2",
    "Question": "<div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">A container of volume 3.2 × 10-6 m<sup>3</sup> is filled with helium gas at a pressure of 5.1 × 10<sup>5</sup> Pa and temperature 320 K. Assume that this sample of helium gas behaves as an ideal gas.</span></p>\n</div><div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">A helium atom has a volume of 4.9 × 10<sup>-31</sup> m<sup>3</sup>.</span></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">The molar mass of helium is 4.0 g mol<sup>-1</sup>. Show that the mass of a helium atom is 6.6 × 10<sup>-27</sup> kg.</span></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Estimate the average speed of the helium atoms in the container.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Show that the number of helium atoms in the container is about 4 × 10<sup>20</sup>.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Calculate the ratio  <span class=\"mjpage\"><math alttext=\"\\frac{{{\\text{total volume of helium atoms}}}}{{{\\text{volume of helium gas}}}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mrow>\n<mrow>\n<mtext>total volume of helium atoms</mtext>\n</mrow>\n</mrow>\n<mrow>\n<mrow>\n<mtext>volume of helium gas</mtext>\n</mrow>\n</mrow>\n</mfrac>\n</math></span>.</span></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">di.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Explain, using your answer to (d)(i) and with reference to the kinetic model, why this sample of helium can be assumed to be an ideal gas.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">dii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"m = \\frac{{4.0 \\times {{10}^{ - 3}}}}{{6.02 \\times {{10}^{23}}}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>m</mi>\n<mo>=</mo>\n<mfrac>\n<mrow>\n<mn>4.0</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>3</mn>\n</mrow>\n</msup>\n</mrow>\n</mrow>\n<mrow>\n<mn>6.02</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mn>23</mn>\n</mrow>\n</msup>\n</mrow>\n</mrow>\n</mfrac>\n</math></span>«kg»</span><em><span style=\"background-color:#ffffff;\"><br/></span></em></p>\n<p><em><span style=\"background-color:#ffffff;\"><strong>OR</strong><br/></span></em></p>\n<p><span style=\"background-color:#ffffff;\">6.64 <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">×</span> 10<span style=\"font-size:14px;\"><sup><span style=\"text-align:left;color:#000000;text-indent:0px;letter-spacing:normal;font-family:Verdana , Arial , Helvetica , sans-serif;font-variant:normal;font-weight:400;text-decoration:none;display:inline !important;white-space:normal;float:none;background-color:#ffffff;\">−27 </span></sup></span></span><span style=\"background-color:#ffffff;\">«kg»</span><em><span style=\"background-color:#ffffff;\"> ✔</span></em></p>\n<p> </p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"\\frac{1}{2}m{v^2} = \\frac{3}{2}kT/v = \\sqrt {\\frac{{3kT}}{m}} /\\sqrt {\\frac{{3 \\times 1.38 \\times {{10}^{ - 23}} \\times 320}}{{6.6 \\times {{10}^{ - 27}}}}} \" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mn>1</mn>\n<mn>2</mn>\n</mfrac>\n<mi>m</mi>\n<mrow>\n<msup>\n<mi>v</mi>\n<mn>2</mn>\n</msup>\n</mrow>\n<mo>=</mo>\n<mfrac>\n<mn>3</mn>\n<mn>2</mn>\n</mfrac>\n<mi>k</mi>\n<mi>T</mi>\n<mrow>\n<mo>/</mo>\n</mrow>\n<mi>v</mi>\n<mo>=</mo>\n<msqrt>\n<mfrac>\n<mrow>\n<mn>3</mn>\n<mi>k</mi>\n<mi>T</mi>\n</mrow>\n<mi>m</mi>\n</mfrac>\n</msqrt>\n<mrow>\n<mo>/</mo>\n</mrow>\n<msqrt>\n<mfrac>\n<mrow>\n<mn>3</mn>\n<mo>×</mo>\n<mn>1.38</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>23</mn>\n</mrow>\n</msup>\n</mrow>\n<mo>×</mo>\n<mn>320</mn>\n</mrow>\n<mrow>\n<mn>6.6</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>27</mn>\n</mrow>\n</msup>\n</mrow>\n</mrow>\n</mfrac>\n</msqrt>\n</math></span>  <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">✔</span></span></p>\n<p><span style=\"background-color:#ffffff;\"><em>v</em> = 1.4 <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">×</span> 10<sup>3</sup> «<span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">ms</span><sup><span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">−</span><span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">1</span></sup>» ✔</span> </p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"N = \\frac{{pV}}{{kT}}/\\frac{{5.1 \\times {{10}^5} \\times 3.2 \\times {{10}^{ - 6}}}}{{1.38 \\times {{10}^{ - 23}} \\times 320}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>N</mi>\n<mo>=</mo>\n<mfrac>\n<mrow>\n<mi>p</mi>\n<mi>V</mi>\n</mrow>\n<mrow>\n<mi>k</mi>\n<mi>T</mi>\n</mrow>\n</mfrac>\n<mrow>\n<mo>/</mo>\n</mrow>\n<mfrac>\n<mrow>\n<mn>5.1</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mn>5</mn>\n</msup>\n</mrow>\n<mo>×</mo>\n<mn>3.2</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>6</mn>\n</mrow>\n</msup>\n</mrow>\n</mrow>\n<mrow>\n<mn>1.38</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>23</mn>\n</mrow>\n</msup>\n</mrow>\n<mo>×</mo>\n<mn>320</mn>\n</mrow>\n</mfrac>\n</math></span></span></p>\n<p><em><strong>OR</strong></em></p>\n<p><span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"N = \\frac{{pV{N_A}}}{{RT}}/\\frac{{5.1 \\times {{10}^5} \\times 3.2 \\times {{10}^{ - 6}} \\times 6.02 \\times {{10}^{23}}}}{{8.31 \\times 320}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mi>N</mi>\n<mo>=</mo>\n<mfrac>\n<mrow>\n<mi>p</mi>\n<mi>V</mi>\n<mrow>\n<msub>\n<mi>N</mi>\n<mi>A</mi>\n</msub>\n</mrow>\n</mrow>\n<mrow>\n<mi>R</mi>\n<mi>T</mi>\n</mrow>\n</mfrac>\n<mrow>\n<mo>/</mo>\n</mrow>\n<mfrac>\n<mrow>\n<mn>5.1</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mn>5</mn>\n</msup>\n</mrow>\n<mo>×</mo>\n<mn>3.2</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>6</mn>\n</mrow>\n</msup>\n</mrow>\n<mo>×</mo>\n<mn>6.02</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mn>23</mn>\n</mrow>\n</msup>\n</mrow>\n</mrow>\n<mrow>\n<mn>8.31</mn>\n<mo>×</mo>\n<mn>320</mn>\n</mrow>\n</mfrac>\n</math></span>   <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">✔</span></span></p>\n<p><span style=\"background-color:#ffffff;\"><em>N</em> = 3.7 <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">× </span>10<sup>20</sup> ✔</span></p>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>«<span style=\"background-color:#ffffff;\"><span class=\"mjpage\"><math alttext=\"\\frac{{4 \\times {{10}^{20}} \\times 4.9 \\times {{10}^{ - 31}}}}{{3.2 \\times {{10}^{ - 6}}}} =» 6 \\times {10^{ - 5}}\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n<mfrac>\n<mrow>\n<mn>4</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mn>20</mn>\n</mrow>\n</msup>\n</mrow>\n<mo>×</mo>\n<mn>4.9</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>31</mn>\n</mrow>\n</msup>\n</mrow>\n</mrow>\n<mrow>\n<mn>3.2</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mrow>\n<mn>10</mn>\n</mrow>\n<mrow>\n<mo>−</mo>\n<mn>6</mn>\n</mrow>\n</msup>\n</mrow>\n</mrow>\n</mfrac>\n<mo>=</mo>\n<mrow>\n<mo>»</mo>\n</mrow>\n<mn>6</mn>\n<mo>×</mo>\n<mrow>\n<msup>\n<mn>10</mn>\n<mrow>\n<mo>−</mo>\n<mn>5</mn>\n</mrow>\n</msup>\n</mrow>\n</math></span>  ✔</span></p>\n<div class=\"question_part_label\">di.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color:#ffffff;\">«For an ideal gas» the size of the particles is small compared to the distance between them/size of the container/gas<br/></span></p>\n<p><span style=\"background-color:#ffffff;\"><em><strong>OR</strong></em><br/></span></p>\n<p><span style=\"background-color:#ffffff;\">«For an ideal gas» the volume of the particles is negligible/the volume of the particles is small compared to the volume of the container/gas<br/></span></p>\n<p><span style=\"background-color:#ffffff;\"><em><strong>OR</strong></em><br/></span></p>\n<p><span style=\"background-color:#ffffff;\">«For an ideal gas» particles are assumed to be point objects ✔<br/></span></p>\n<p><span style=\"background-color:#ffffff;\">calculation/ratio/result in (d)(i) shows that volume of helium atoms is negligible compared to/much smaller than volume of helium gas/container «hence assumption is justified» ✔</span></p>\n<div class=\"question_part_label\">dii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>The mark was awarded for a clear substitution or an answer to at least 3sf. Many gained the mark for a clear substitution with a conversion from g to kg somewhere in their response. Fewer gave the answer to the correct number of sf.</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>At HL this was very well answered but at SL many just worked out E=3/2kT and left it as a value for KE.</p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Again at HL this was very well answered with the most common approach being to calculate the number of moles and then multiply by N<sub>A</sub> to calculate the number of atoms. At SL many candidates calculated n but stopped there. Also at SL there was some evidence of candidates working backwards and magically producing a value for ‘n’ that gave a result very close to that required after multiplying by N<sub>A</sub>.</p>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was well answered with the most common mistake being to use the volume of a single atom rather than the total volume of the atoms.</p>\n<div class=\"question_part_label\">di.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>In general this was poorly answered at SL. Many other non-related gas properties given such as no / negligible intermolecular forces, low pressure, high temperature. Some candidates interpreted the ratio as meaning it is a low density gas. At HL candidates seemed more able to focus on the key part feature of the question, which was the nature of the volumes involved. Examiners were looking for an assumption of the kinetic theory related to the volume of the atoms/gas and then a link to the ratio calculated in ci). The command terms were slightly different at SL and HL, giving slightly more guidance at SL.</p>\n<div class=\"question_part_label\">dii.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion",
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "a-3-work-energy-and-power",
      "b-1-thermal-energy-transfers",
      "b-3-gas-laws"
    ]
  },
  {
    "question_id": "19M.2.SL.TZ2.7",
    "Question": "<div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">The average temperature of ocean surface water is 289 K. Oceans behave as black bodies.</span></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Show that the intensity radiated by the oceans is about 400 W m<sup>-2</sup>.</span></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color:#ffffff;\">Explain why some of this radiation is returned to the oceans from the atmosphere.</span></p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">b.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>5.67 <span style=\"background-color:#ffffff;\">×</span> 10<span style=\"background-color:#ffffff;\"><sup>−8</sup> <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">×</span> 289<sup>4</sup></span></p>\n<p><em><strong><span style=\"background-color:#ffffff;\">OR</span></strong></em></p>\n<p><span style=\"background-color:#ffffff;\">= 396 «W m<sup style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:11.6px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">−2</sup>» ✔</span></p>\n<p><span style=\"background-color:#ffffff;\"><span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">«≈ 400 W m</span><sup style=\"color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:11.6px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">−2</sup><span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">»</span></span></p>\n<p> </p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color:#ffffff;\">«most of the radiation emitted by the oceans is in the» infrared ✔<br/></span></p>\n<p><span style=\"background-color:#ffffff;\">«this radiation is» absorbed by greenhouse gases/named greenhouse gas in the atmosphere ✔<br/></span></p>\n<p><span style=\"background-color:#ffffff;\">«the gases» reradiate/re-emit ✔<br/></span></p>\n<p><span style=\"background-color:#ffffff;\">partly back towards oceans/in all directions/awareness that radiation in other directions is also present ✔</span></p>\n<div class=\"question_part_label\">b.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was well answered with candidates scoring the mark for either a correct substitution or an answer given to at least one more sf than the show that value. Some candidates used 298 rather than 289.</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>For many this was a well-rehearsed answer which succinctly scored full marks. For others too many vague terms were used. There was much talk about energy being trapped or reflected and the ozone layer was often included. The word ‘albedo’ was often written down with no indication of what it means and ‘the albedo effect also featured.</p>\n<div class=\"question_part_label\">b.</div>\n</div>",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-2-greenhouse-effect"
    ]
  },
  {
    "question_id": "19N.3.SL.TZ0.1",
    "Question": "<div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">A student investigates how the period<em> T</em> of a simple pendulum varies with the maximum speed <em>v</em> of the pendulum’s bob by releasing the pendulum from rest from different initial angles. A graph of the variation of <em>T</em> with <em>v</em> is plotted.</span></p>\n<p><span style=\"background-color: #ffffff;\"><img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAsgAAAGzCAYAAAAypuHpAAAgAElEQVR4Ae29v4skSZbvG/9GyKmWVowyUkipNMM+pZUrhJBKCSXNhUlIrWFZliUgYdmWBhJqBx48GIK9yoXegtAaLgmhjZAkqzQ1SSjN0iTJ7aYogvOwiLAMCws/djzL0n+YxyehcDc/bmZf+xw7bqfcPT1Hwg8EIAABCEAAAhCAAAQg8Exg9LzHDgQgAAEIQAACEIAABCAgJMhMAghAAAIQgAAEIAABCAQESJADGOxCAAIQgAAEIAABCEDgKEEejUbCPxgwB5gDzAHmAHOAOcAcYA6cwhyo+u9AZYJcdSLHIAABCEAAAhCAAAQgMCQC7j8AVT9HR7UTqypzDAIQgAAEIAABCEAAAqUS0PJeEuRSPYpuCEAAAhCAAAQgAIEsAiTIWfioDAEIQAACEIAABCAwNAIkyEPzKOOBAAQgAAEIQAACEMgiQIKchY/KEIAABCAAAQhAAAJDI0CCPDSPMh4IQAACEIAABCAAgSwCJMhZ+KgMAQhAAAIQgAAEIDA0AiTIQ/Mo44EABCAAAQhAAAIQyCJAgpyFj8oQgAAEIAABCEAAAkMjQII8NI8yHghAAAIQgAAEIACBLAIkyFn4qAwBCEAAAhCAAAQgMDQCJMhD8yjjgQAEIAABCEAAAhDIIkCCnIWPyhCAAAQgAAEIQAACQyNAgjw0jzIeCEAAAhCAAAQgAIEsAiTIWfioDAEIQAACEIAABCAwNAIkyEPzKOOBAAQgAAEIQAACEMgiQIKchY/KEIAABCAAAQhAAAJDI0CCPDSPMh4IQAACEIAABCAAgSwCJMhZ+Kh8igT+/d//XX799ddTHDpjhgAEIAABCJwEARLkk3Azg3wtAj/++KO4oJnP56/VJO1AAAIQgAAEINAzAiTIPXMIcvpN4B/+4R82CfLvfvc77iL321WogwAEIAABCHw1ARLkr0ZHxVMj4O4e+wT5T3/6E3eRT20CMF4IQAACEDgZAiTIJ+NqBppLwCXH/hWL+/t74S5yLlHqQwACEIAABPpJgAS5n35BVc8I+LvHTpYPGu4i98xJyIEABCAAAQi8EgG/1sfNjY4OjI4OxadQhsBgCfi7x26APmi4izxYdzMwCEAAAhA4cQJ+rY8xHGXD2olxRcoQGBqB8O6xG1sYC9xFHpq3GQ8EIAABCEDgcK0PeZAghzTYP2kCLgl2SbL/CRNkdxfZ3V3mBwIQgAAEIACB4RAI1/pwVCTIIQ32IRAQ0IImOIVdCEAAAhCAAAQKJqCt9STIBTsV6c0S0IKm2V5pHQIQgAAEIACBtghoaz0JclseoJ/iCMRB8y//8i8HYwjLbr/pcth52Jc7nir3SVsbWkIW4X5JnGKtbXBjfm3jKJwzdbjX5VanrZf2bZ3fJ211tbjzrHG9tr2uNtdv2HdYj/1yCcRrvR8JCbInwRYCEQEtaKLTKEIAAhCAAAQgUCgBba0nQS7UochunoAWNM33TA8QgAAEIAABCLRBQFvrSZDboE8fRRLQgsYP5i9/+Yvfrdym7Cmba8yyW4/5rPope8qGNt3ncKsMg83BFJuU7ZTnWy4Xq37ONcRqO9desjY9CrD0lYC21pMg99Vj6OqcgBY0XljOIpBT1/Wfs4C4+qn+UzarLtocgeofiys+hVtIwJovufac+Zbbt1W/ZG2hD9kvg4C21pMgl+E/VHZAQAuaDqTQJQQgAAEIQAACDRDQ1noS5AZg0+QwCGhBM4zRMQoIQAACEIAABLS1ngSZuQEBhUAcNPFjwbDs9psuhzLjR5Bh3+68sNwnbW1oicdel1sb2kItoU53POVTtO3Jpbi1wSnsP9x3CuNy6NNT17b34DGnrrnV1eZ0hj4N67FfLoF4rfcjIUH2JNhCICKgBY0/Lb6o++N+m7KnbK6+Zbcu0lb9lD1lQxu/pOfnd7jNmTM5dZ2GocZCLherfg43q+1ce8nawrhgvwwC2lpPglyG/1DZAQEtaDqQQpcQgAAEIAABCDRAQFvrSZAbgE2TwyCgBc0wRscoIAABCEAAAhDQ1noSZOYGBBQCWtD403MeI+bUdf3nPIJ09VP9p2xWXbQ5AtU/Fld8CreQgDVfcu058y23b6t+ydpCH7JfBgFtrSdBLsN/qOyAgBY0Xop1kU/ZUzbXvmXPWUCs9q2+LTva/Aw53MLtkIcvWVws+1DnmzXuXHsOt9y+rfola/Pzmm05BLS1ngS5HB+itGUCWtC0LIPuIAABCEAAAhBoiIC21pMgNwScZssnoAVN+SNjBBCAAAQgAAEIOALaWk+CzPyAgEIgDpr4sWBYdvtNl0OZ8SPIsG93Xljuk7Y2tMRjr8utDW2hllCnO57yKdr25FLc2uAU9h/uO4VxOfTpqWvbe/CYU9fc6mpzOkOfhvXYL5dAvNb7kZAgexJsIRAR0ILGnxZf1P1xv03ZUzZX37JbF2mrfsqesqGN7yD7+R1uc+ZMTl2nYaixkMvFqp/DzWo7116ytjAu2C+DgLbWkyCX4T9UdkBAC5oOpNAlBCAAAQhAAAINENDWehLkBmDT5DAIaEEzjNExCghAAAIQgAAEtLWeBJm5AQGFgBY0/vScx4g5dV3/OY8gXf1U/ymbVRdtjkD1j8UVn8ItJGDNl1x7znzL7duqX7K20Ifsl0FAW+tJkMvwHyo7IKAFTQdS6BICEIAABCAAgQYIaGs9CXIDsGlyGAS0oBnG6BgFBCAAAQhAAALaWk+CzNyAgEJACxrldA5DAAIQgAAEIFAYAW2tJ0EuzJHIbY9AHDTxe3Nh2e03XQ5HHr+jF/btzgvLfdLWhpZ47HW5taEt1BLqdMdTPkXbnlyKWxucwv7DfacwLoc+PXVtew8ec+qaW11tTmfo07Ae++USiNd6PxISZE+CLQQiAlrQRKdRhAAEIAABCECgUALaWk+CXKhDkd08AS1omu+ZHiAAAQhAAAIQaIOAttaTILdBnz6KJKAFTZGDQTQEIAABCEAAAkcEtLWeBPkIFQcgsCWgBY3nE78354/7bcqesrn6lt16D86qn7KnbGjjT037+R1uc+ZMTl2nYaixkMvFqp/DzWo7116ytjAu2C+DgLbWkyCX4T9UdkBAC5oOpNAlBCAAAQhAAAINENDWehLkBmDT5DAIaEEzjNExCghAAAIQgAAEtLWeBJm5AQGFgBY0/vScx4g5dV3/OY8gXf1U/ymbVRdtjkD1j8UVn8ItJGDNl1x7znzL7duqX7K20Ifsl0FAW+tJkMvwHyo7IBAHTXxRD8tuv+lyiCBeQMK+3XlhuU/a2tASj70utza0hVpCne54yqdo25NLcWuDU9h/uO8UxuXQp6eube/BY05dc6urzekMfRrWY79cAvFa70dCguxJsIVAREALmug0ihCAAAQgAAEIFEpAW+tJkAt1KLKbJ6AFTfM90wMEIAABCEAAAm0Q0NZ6EuQ26NNHkQS0oPGDiR8L+uN+m7KnbK6+Zbce81n1U/aUDW185s3P73CbM2dy6joNQ42FXC5W/RxuVtu59pK1hXHBfhkEtLWeBLkM/w1c5Vqe7n+Q2fSNuInq/o2n1/Lx/rHWuNerj3I1OZfZ8ik637U7l8vJeNfuuVx+uJXVOjpNKWpB40/PWQRy6rr+cxYQVz/Vf8pm1UWbI1D9Y3HFp3ALCVjzJdeeM99y+7bql6wt9CH7ZRDQ1noS5DL8N2yVjwu5HI9lcjmX+6e1yPpBFlfnMhq/l/nD5+TY16sf5XqTWE+OEuT1w1wuxudytXiQtXyW1eI7mYzeyMX8J6mTI2tBkxSEEQIQgAAEIACBYghoaz0JcjEuHKrQL7Kav5PR6J3MV1/2g9wlzec3d0oy+yj3H69lejaV2Z8vZTKKE+SfZXH5VkbnN3L/nA3vjk3nstr3pO5pQaNWwAABCEAAAhCAQFEEtLWeBLkoN56QWDNB/iTzi/dyc/cosprLNE6QvyxldjYWPcG2WWpB42tajwlT9pTNtW/Zcx5BWu1bfVt2tPkZcriF2yEPX7K4WPahzjdr3Ln2HG65fVv1S9bm5zXbcghoaz0Jcjk+PCGla3lcXMl49FYuFz/b465KkDcJ9pn8j9n/Kx8uz5PvILvg0P6FnccX7bDs9psu19XizmtaS9x+XW1tcOqztrqc+uzDPms79fnF3N9e+2IOVrluXMbzK6zHfrkESJDL9d3pKX+6ldlkLOOLuTw8vx6RwFCVIG+OjWQ0nsr17Wrzmsb2l/nOat9V1oImoQQTBCAAAQhAAAIFEdDWeu4gF+TEk5C6/knmF29kPP0gd+4X9ur8qAly/IrFb3J/862MzmayDF531rrQgkY7n+MQgAAEIAABCJRFQFvrSZDL8uOw1T7dydy9DjH5Thar9NcrDkBUJcibd5DPZDr/FJy6+4XA8ZUsHu3kWwsa36D1Hl3KnrK59i17+MjQ6wm3Vv2UPWVDG99BDueZ38+ZMzl1Xf9DjYVcLlb9HG5W27n2krX5mGBbDgFtrSdBLseHA1a6/17xePq93L4kOXZUqhJkcV+s+L1MZrey/zry7g7ywZctdKxa0PgaOYtATl3Xf84C4uqn+k/ZrLpocwSqfyyu+BRuIQFrvuTac+Zbbt9W/ZK1hT5kvwwC2lpPglyG/watcvu94pGMJteyrPtaRUikMkFey9PyWibji+2XLkRk+w7yW76DHLJjHwIQgAAEIHDCBEiQT9j5/R767tvE2pck/DeLN0nwSM5mSzl6fbgyQXaj/iyr5V8O/5Le/C64o5wmowVNuhZWCEAAAhCAAARKIaCt9dxBLsWD6GydQBw08WPBsOz2my6HAOJHkGHf7ryw3CdtbWiJx16XWxvaQi2hTnc85VO07cmluLXBKew/3HcK43Lo01PXtvfgMaeuudXV5nSGPg3rsV8ugXit9yMhQfYk2EIgIqAFjT8tvqj7436bsqdsrr5lty7SVv2UPWVDG7+k5+d3uM2ZMzl1nYahxkIuF6t+Djer7Vx7ydrCuGC/DALaWk+CXIb/UNkBAS1oOpBClxCAAAQgAAEINEBAW+tJkBuATZPDIKAFzTBGxyggAAEIQAACENDWehJk5gYEFAJa0PjTcx4j5tR1/ec8gnT1U/2nbFZdtDkC1T8WV3wKt5CANV9y7TnzLbdvq37J2kIfsl8GAW2tJ0Euw3+o7ICAFjReinWRT9lTNte+Zc9ZQKz2rb4tO9r8DDncwu2Qhy9ZXCz7UOebNe5cew633L6t+iVr8/OabTkEtLWeBLkcH6K0ZQJa0LQsg+4gAAEIQAACEGiIgLbWkyA3BJxmyyegBU35I2MEEIAABCAAAQg4AtpaT4LM/ICAQiAOmvixYFh2+02XQ5nxI8iwb3deWO6Ttja0xGOvy60NbaGWUKc7nvIp2vbkUtza4BT2H+47hXE59OkQtLlrYtW/OmPbe/CYU9fc6mpzOkOfhvXYL5dAvNb7kZAgexJsIRAR0ILGnxZf1P1xv03ZUzZX37JbF2mrfsqesqGN7yD7+R1uc+ZMTl2nYaixkMvFqp/DrclrY65PrXHn2i1uYVywXwYBbT6TIJfhP1R2QEALmg6k0CUEIACB3hDg2tgbVyDkFQho85kE+RXg0sQwCWhBM8zRMioIQAAC9QhwbazHibPKIKDNZxLkMvyHyg4IaEHjpeQ8qsup6/q3HvPltJ9TF21+dhxvLa749JiZO3Kq3Kxx59pz5luT10bn8xxtuVys+pa26lnM0T4T0OYzCXKfvYa2TgloQdOpKDqHAAQg0AKB1PUvZXPSLHsL8ukCArUJaPOVBLk2Qk48NQJa0JwaB8YLAQicHoHU9c/Zfv31VxVKqq5aCQMEOiKgzVcS5I4cQrf9J6AFTf+VoxACEIBAHgHt+ucSY2f7wx/+oCbJWt08RdSGQDMEtPlKgtwMb1odAIE4aOJ308Ky22+6HCKN34ML+3bnheU+aWtDSzz2utza0BZqCXW64ymfom1PLsWtDU5h/+G+UxiXQ5+Wps1d/3L+hSzC/SpOsb1tbvvZdezDUJvbD7WF9dgvl0C81vuRkCB7EmwhEBHQgiY6jSIEIACBwRHQrn/+DvIf//hHdcxaXbUCBgh0SECbryTIHTqFrvtNQAuafqtGHQQgAIF8AqnrX8rmerbs+epoAQKvR0CbryTIr8eYlgZGQAuagQ2T4UAAAhA4IpC6/qVsriHLftQZByDQIQFtvpIgd+gUuu43AS1ovOrw3TR/LNym7Cmba8OyW+/BWfVT9pQNbfyp6XCO+/2cOZNT1/U/1FjI5WLVz+HW5LUx16fWuHPtFjcfE2zLIaDNZxLkcnyI0pYJaEHTsgy6gwAEINArAlwbe+UOxGQS0OYzCXImWKoPl4AWNMMdMSODAAQgYBPg2mgz4oxyCGjzmQS5HB+itGUCWtB4GTmP6nLquv6tx3w57efURZufHcdbiys+PWbmjpwqN2vcufac+dbktdH5PEdbLhervqWtehZztM8EtPlMgtxnr6GtUwJx0MQXzrDs9psuhzDii3TYtzsvLPdJWxta4rHX5daGtlBLqNMdT/kUbXtyKW5tcAr7D/edwrgc+nQI2tw1sepfnbHtPXjMqWtudbU5naFPw3rsl0sgXuv9SEiQPQm2EIgIaEETnUYRAhCAAAQgAIFCCWhrPQlyoQ5FdvMEtKBpvmd6gAAEIAABCECgDQLaWk+C3AZ9+iiSgBY0fjDxY0F/3G9T9pTN1bfs1mM+q37KnrKhjc+8+fkdbnPmTE5dp2GosZDLxaqfw81qO9desrYwLtgvg4C21pMgl+G/gatcy9P9DzKbvnl+v208vZaP94+1xr1efZSrybnMlk+H539Zyuzs+J25s9lSvhyeWVnSgsafnLMI5NR1/ecsIK5+qv+UzaqLNkeg+sfiik/hFhKw5kuuPWe+5fZt1S9ZW+hD9ssgoK31JMhl+G/YKh8Xcjkey+RyLvdPa5H1gyyuzmU0fi/zh8/Jsa9XP8r1JrGeHCfIq7lMR2/lcvFzsg3NqAWNdj7HIQABCEAAAhAoi4C21pMgl+XHAar9Iqv5OxmN3sl8FdzX3SXN5zd3sq4c9aPcf7yW6dlUZn++lMnoOEH+spzJ2ehbubn/rbIF66AWNFY97BCAAAQgAAEIlEFAW+tJkMvw3+mpNBPkTzK/eC83d48imzvFcYL8m9zffCuj8ZUsHqtTbAuqFjS+nvWYMGVP2Vz7lj3nEaTVvtW3ZUebnyGHW7gd8vAli4tlH+p8s8ada8/hltu3Vb9kbX5esy2HgLbWkyCX48MTUrqWx8WVjOu+HlGZIP8si8u3Mhr/Xia/H+/ebT6Xyw+3soryZRcc2r8QenzRDstuv+lyXS3uvKa1xO3X1dYGpz5rq8upzz7ss7ZTn1/M/e21L+ZglevGZTy/wnrsl0uABLlc352e8qdbmU3GMr6Yy0OUzFbCqEqQ13dycz6W0eRalu69Zvfz9De5mb6VyexWol/nq2xWC5rKkzkIAQhAAAIQgEBxBLS1njvIxbly4ILXP8n84o2Mpx/kzie21pCrEuTKOi977UILmsqmOQgBCEAAAhCAQHEEtLWeBLk4Vw5Y8NOdzC/PZTT5Thar9NcrDijUTpCVXwg8aGxf0ILGn2G9R5eyp2yufcsePjL0esKtVT9lT9nQxneQw3nm93PmTE5d1/9QYyGXi1U/h5vVdq69ZG0+JtiWQ0Bb60mQy/HhgJW67yDP5dK9VjH9Xm5fkhw7KlUJcuUv+e3uIJ/fyH2NVze0oPGOyFkEcuq6/nMWEFc/1X/KZtVFmyNQ/WNxxadwCwlY8yXXnjPfcvu26pesLfQh+2UQ0NZ6EuQy/DdoleuHuVyMR4fvC79kxFUJsvwiy9k3B21u/6DIW7mY/6R8Ou6wUy1oDs+iBAEIQAACEIBAqQS0tZ4EuVSPDkb37msT2pckpnNZubFukuCRVP4VvMoEWUTWK1l+cN9I3n2lYjyV2cf7Wr+g57rUgmYw6BkIBCAAAQhA4MQJaGs9CfKJTwyGrxOIgyZ+LBiW3X7T5VBp/Agy7NudF5b7pK0NLfHY63JrQ1uoJdTpjqd8irY9uRS3NjiF/Yf7TmFcDn166tr2Hjzm1DW3utqcztCnYT32yyUQr/V+JCTIngRbCEQEtKDxp8UXdX/cb1P2lM3Vt+zWRdqqn7KnbGjjl/T8/A63OXMmp67TMNRYyOVi1c/hZrWday9ZWxgX7JdBQFvrSZDL8B8qOyCgBU0HUugSAhCAAAQgAIEGCGhrPQlyA7BpchgEtKAZxugYBQQgAAEIQAAC2lpPgszcgIBCQAsaf3rOY8Scuq7/nEeQrn6q/5TNqos2R6D6x+KKT+EWErDmS649Z77l9m3VL1lb6EP2yyCgrfUkyGX4D5UdENCCxkuxLvIpe8rm2rfsOQuI1b7Vt2VHm58hh1u4HfLwJYuLZR/qfLPGnWvP4Zbbt1W/ZG1+XrMth4C21pMgl+NDlLZMQAualmXQHQQgAAEIQAACDRHQ1noS5IaA02z5BLSgKX9kjAACEIAABCAAAUdAW+tJkJkfEFAIxEETPxYMy26/6XIoM34EGfbtzgvLfdLWhpZ47HW5taEt1BLqdMdTPkXbnlyKWxucwv7DfacwLoc+PXVtew8ec+qaW11tTmfo07Ae++USiNd6PxISZE+CLQQiAlrQRKdRhAAEIAABCECgUALaWk+CXKhDkd08AS1omu+ZHiAAAQhAAAIQaIOAttaTILdBnz6KJKAFTZGDQTQEIAABCEAAAkcEtLWeBPkIFQcgsCWgBY3nE78354/7bcqesrn6lt16D86qn7KnbGjjT037+R1uc+ZMTl2nYaixkMvFqp/DzWo7116ytjAu2C+DgLbWkyCX4T9UdkBAC5oOpNAlBCAAAQhAAAINENDWehLkBmDT5DAIaEEzjNExCghAAAIQgAAEtLWeBJm5AQGFgBY0yukchgAEIAABCECgMALaWk+CXJgjkdsegTho4vfqwrLbb7ocjjx+Ry/s250XlvukrQ0t8djrcmtDW6gl1OmOp3yKtj25FLc2OIX9h/tOYVwOfXrq2vYePObUNbe62pzO0KdhPfbLJRCv9X4kJMieBFsIRAS0oIlOowgBCEAAAhCAQKEEtLWeBLlQhyK7eQJa0DTfMz1AAAIQgAAEINAGAW2tJ0Fugz59FElAC5oiB4NoCEAAAhCAAASOCGhrPQnyESoOQGBLQAsazyd+b84f99uUPWVz9S279R6cVT9lT9nQxneQ/fwOtzlzJqeu0zDUWMjlYtXP4Wa1nWsvWVsYF+yXQUBb60mQy/AfKjsgoAVNB1LoEgIQgAAEIACBBghoaz0JcgOwaXIYBLSgGcboGAUEIAABCEAAAtpaT4LM3ICAQkALGn96zmPEnLqu/5xHkK5+qv+UzaqLNkeg+sfiik/hFhKw5kuuPWe+5fZt1S9ZW+hD9ssgoK31JMhl+A+VHRCIgya+qIdlt990OUQQLyBh3+68sNwnbW1oicdel1sb2kItoU53POVTtO3Jpbi1wSnsP9x3CuNy6NNT17b34DGnrrnV1eZ0hj4N67FfLoF4rfcjIUH2JNhCICKgBU10GkUIQAACEIAABAoloK31JMiFOhTZzRPQgqb5nukBAhCAAAQgAIE2CGhrPQlyG/Tpo0gCWtD4wcSPBf1xv03ZUzZX37Jbj/ms+il7yoY2PvPm53e4zZkzOXWdhqHGQi4Xq34ON6vtXHvJ2sK4YL8MAtpaT4Jchv8GrnItT/c/yGz6RtxEdf/G02v5eP9Ya9zr1Ue5mpzLbPmkn/90K7PJWM5mS/min3Vg0YLGn5SzCOTUdf3nLCCufqr/lM2qizZHoPrH4opP4RYSsOZLrj1nvuX2bdUvWVvoQ/bLIKCt9STIZfhv2CofF3I5Hsvkci73T2uR9YMsrs5lNH4v84fPybGvVz/K9SaxnugJ8vonmV9sk+/XTJCTwjBCAAIQgAAEINB7AiTIvXfRqQr8Iqv5OxmN3sl8Fdzb3SXN5zd3sq5E8yj3H69lejaV2Z8vZTLSEuTP8jB/L+PdnWkS5EqYHIQABCAAAQicJAES5JN0e8GDNhPkTzK/eC83d48iq7lMlQR5/TCXi/G5XP3wV/nnsxGvWOymROoRZ8rmqlv2nMejVvtW35YdbdXXBLh9HZcmuVlt59pzYiG3b6t+ydqqZxJH+0yABLnP3kFbRGAtj4srGY/eyuXi58hWUdQS5Ke/yc30rUxmt/L0ZSkzJUF2waH9C3uLL9ph2e03Xa6rxZ3XtJa4/bra2uDUZ211OfXZh33Wdurzi7m/vfbFHKxy3biM51dYj/1yCZAgl+u701O++4W68cVcHqrfrzhkUpkg/yLL2TcymlzL0r3XnEiQDxvbl7Sg2Z/BHgQgAAEIQAACJRPQ1np+Sa9krw5R++4X6sbTD3LnEts6P0cJ8lqeltcyGX0js+Uv2xZIkOuQ5BwIQAACEIDASREgQT4pdxc62Kc7mV+ey2jynSxW6a9XHIzwKEF+kuVsor42MTqbyTL4fcCDtoKCFjT+FOs9upQ9ZXPtW/bwkaHXE26t+il7yoY2voMczjO/nzNncuq6/ocaC7lcrPo53Ky2c+0la/MxwbYcAtpazx3kcnw4YKXuO8hzuZyMZTz9Xm5fkhw7KkcJcgWqBu4g5ywCOXXd6HIWEFc/1X/KZtVFmyNQ/WNxxadwCwlY8yXXnjPfcvu26pesLfQh+2UQIEEuw08nqXL7pYnR/n3hl1LoKEF+qUzOhwAEIAABCECgXwRIkPvlD9Q8E/hZFpdv9dchpnNZuXM3SbDymTYS5Gea7EAAAhCAAAQgUJ8ACXJ9VpwJgQ2BOGjix4Jh2e03XQ7dEj+CDPt254XlPmlrQ0s89rrc2tAWagl1uuMpn6JtTy7FrQ1OYf/hvlPoyu66of0Lz3f7TZf31A6vCfF861pLyKHP2pzOOE5DxuyXSe4K+NIAACAASURBVCBe6/0oeAfZk2ALgYiAFjT+tPii7o/7bcqesrn6lt26SFv1U/aUDW38kp6f3+E2Z87k1HUa+hwLOdeQXC5W/RxuVtu59pK1hXHBfhkEtDglQS7Df6jsgIAWNB1IoUsIQKBAAlxDCnQakk+OgBanJMgnNxUYcF0CWtDUrc95EIDAaRPgGnLa/mf0ZRDQ4pQEuQz/obIDAlrQeCk5jxFz6rr+cx5Buvqp/lM2qy7aHIHqH4srPh0et5xriDVfcu058y23b6t+ydqqZzFH+0xAi1MS5D57DW2dEtCCxouyLvIpe8rm2rfsOQuI1b7Vt2VHm58hh1u4HfLwJYuLZe9yvlnXiBy7Ne5cew633L6t+iVr8/OabTkEtDglQS7HhyhtmYAWNC3LoDsIQKCnBKxrRK69p8NGFgQGRUCLUxLkQbmZwbwmAS1oXrMP2oIABMolkLpGLBaLzefe/v73v6sDTNVXK2GAAARelYAWhyTIr4qZxoZEIA6a+LFgWHb7TZdDtvEjyLBvd15Y7pO2NrTEY6/LrQ1toZZQpzue8ina9uRS3NrgFPbvrhG5//zImtDu23bbULcrh/Otib7D/sL9Ki2xva/anM5QW8iX/XIJxGu9HwkJsifBFgIRAS1ootMoQgACJ0ogdY34x3/8x03y7O4kaz+p+lodjkMAAq9LQItDEuTX5UxrAyKgBc2AhshQIACBDALWNSLXniGNqhCAQE0CWpySINcEyGmnR0ALmtMjwYghAIEqAtY1Itde1SfHIACB1yWgxSkJ8utyprUBEdCCxg8xfm/OH/fblD1lc/Utu/UenFU/ZU/Z0MafmvbzO9zmzJmcuk5Dn2Mh5xqSy8Wqn8PNajvXXrK2MC7YL4OAFqckyGX4D5UdENCCpgMpdAkBCBRIgGtIgU5D8skR0OKUBPnkpgIDrktAC5q69TkPAhA4bQJcQ07b/4y+DAJanJIgl+E/VHZAQAuaDqTQJQQgUCABriEFOg3JJ0dAi1MS5JObCgy4LoE4aOL36sKy22+6HOqO39EL+3bnheU+aWtDSzz2utza0BZqCXW64ymfom1PLsWtDU5h/+G+U+jK7rqh/QvPd/tNl/fUDq8J8XzrWkvIoc/anM44TkPG7JdJIF7r/ShIkD0JthCICGhBE51GEQIQgAAEIACBQgloaz0JcqEORXbzBLSgab5neoAABCAAAQhAoA0C2lpPgtwGffookoAWNEUOBtEQgAAEIAABCBwR0NZ6EuQjVByAwJaAFjSeT/zenD/utyl7yubqW3brPTirfsqesqGN7yD7+R1uc+ZMTl2nYaixkMvFqp/DzWo7116ytjAu2C+DgLbWkyCX4T9UdkBAC5oOpNAlBCAAAQhAAAINENDWehLkBmDT5DAIaEEzjNExCghAAAIQgAAEtLWeBJm5AQGFgBY0/vScx4g5dV3/OY8gXf1U/ymbVRdtjkD1j8UVn8ItJGDNl1x7znzL7duqX7K20Ifsl0FAW+tJkMvwHyo7IBAHTXxRD8tuv+lyiCBeQMK+3XlhuU/a2tASj70utza0hVpCne54yqdo25NLcWuDU9h/uO8UxuXQp6eube/BY05dc6urzekMfRrWY79cAvFa70dCguxJsIVAREALmug0ihCAAAQgAAEIFEpAW+tJkAt1KLKbJ6AFTfM90wMEIAABCEAAAm0Q0NZ6EuQ26LfYx/r+Rs4Tf+p0NBrL+c2drI80/SyLy4lM55+OLKd6QAsazyN+LOiP+23KnrK5+pbdesxn1U/ZUza08Zk3P7/Dbc6cyanrNAw1FnK5WPVzuFlt59pL1hbGBftlENDWehLkMvz3lSpd0vtWRuc3cn+cER+2+biQy/G3cnP/2+HxVkprebr/QWbTN+Imqvs3nl7Lx/vHWr2vVx/lanIus+XT4fnrlSw/XMrkK9p0DWlB4zvJWQRy6rr+cxYQVz/Vf8pm1UWbI1D9Y3HFp3ALCVjzJdeeM99y+7bql6wt9CH7ZRDQ1noS5DL893UqvyxldjaS8eVC0qnmWh4XVzKuk0h/nZJ0rU1yPpbJ5Vzun9Yi6wdZXJ3LaPxe5g+fk3XXqx/lepNYT6IE+bM8zN/LeHwhN3ePL2rTd6gFjbezhQAEIAABCECgbALaWk+CXLZfk+q3r1uc1Xht4kmWs3Pl1QsRebqXj7OpjP2rG+OpzD7eS3S/NqlFN36R1fydjEbvZL76sj9tlzRXvw7iTnuU+4/XMj2byuzP7i5xlCCv7+TmfHz4n4PVXKajOjy2MrSg2YtkDwIQgAAEIACBkgloaz0JcsleTWrf3RWOE8eqOptk8vdyufi5wrp7TWPynSxW7m7uo9zdXMh41PDrGGaC/EnmF++3d4c3iW+UIFeMRF45QbYeE6bsKZuTbtlzHkFa7Vt9W3a0VU0+fFpNxeZyqvPNGneuPSdOc/u26pesTZvnHO8vARLk/vqmIWW/yf3NtzIaX8niMf0C8uZOs3reJ5lPz2Q0uZale/2hlR+f3L9VkvZIRJ0E+elO5pfnMnpO9PdtuODQ/u3POn7vN7yIu/2my3W1uPOa1hK3X1dbG5z6rK0upz77sM/aTn1+Mfe3176Yg1WuG5fx/ArrsV8uARLkcn33lcp3ia35XvE2kdbfU17L090HmY79L8/N5K/z/y3Lzd3kr5RmVXu6ldlkLOOLuTzUycmTCbJ/hcPpfyPT6x9lVafNGr+kZw0DOwQgAAEIQAAC/SZAgtxv/7y+utq/oFf3826Pcr/4XzL/62yXLJ/L1eKh4nNxmUNZ/yTzizcynn6Qu7p3rJMJ8l7P9msX9RNvLWj2LbIHAQhAAAIQgEDJBLS1nneQS/ZqQnvtX9D7ms+77X4BbjSdyyqh4cWmxGsQybZqJsgiu9dO4l8IVBrXgsafbr1Hl7KnbK59yx4+MvR6wq1VP2VP2dDGd5DDeeb3c+ZMTl3X/1BjIZeLVT+Hm9V2rr1kbT4m2JZDQFvrSZDL8eELlPp3eK1fXKvxebfnO7rfy+3mtQr/yoX2B0deIPP5VPcd5Llcutcqpr6fZ6O9U5UgV/6SX/33sl2nWtB4QTmLQE5d13/OAuLqp/pP2ay6aHMEqn8srvgUbiEBa77k2nPmW27fVv2StYU+ZL8MAtpaT4Jchv9eqNJ9tm1S4xf0jM+77Xpdr27lg/sFt+dfZjuXyw+3td/ltcSvH+Zy4d5x/tpfBKxKkOUXWc6+OWhz+4rFmUxmt7U+UacFjTUe7BCAAAQgAAEIlEFAW+tJkMvw34BV7j4j95x8R1+U8K9xbJLgkZzNlhJ8LXnLpTJBFpHoL+mNXvj9Zi1oBuwMhgYBCEAAAhA4KQLaWk+CfFLTgMG+hEAcNPFjwbDs9psuh9rjR5Bh3+68sNwnbW1oicdel1sb2kItoU53POVTtO3Jpbi1wSnsP9x3CuNy6NNT17b34DGnrrnV1eZ0hj4N67FfLoF4rfcjIUH2JNhCICKgBY0/Lb6o++N+m7KnbK6+Zbcu0lb9lD1lQxu/pOfnd7jNmTM5dZ2GocZCLherfg43q+1ce8nawrhgvwwC2lpPglyG/1DZAQEtaDqQQpcQgAAEIAABCDRAQFvrSZAbgE2TwyCgBc0wRscoIAABCEAAAhDQ1noSZOYGBBQCWtD403MeI+bUdf3nPIJ09VP9p2xWXbQ5AtU/Fld8CreQgDVfcu058y23b6t+ydpCH7JfBgFtrSdBLsN/qOyAgBY0Xop1kU/ZUzbXvmXPWUCs9q2+LTva/Aw53MLtkIcvWVws+1DnmzXuXHsOt9y+rfola/Pzmm05BLS1ngS5HB+itGUCWtC0LIPuIAABCEAAAhBoiIC21pMgNwScZssnoAVN+SNjBBCAAAQgAAEIOALaWk+CzPyAgEIgDpr4sWBYdvtNl0OZ8SPIsG93Xljuk7Y2tMRjr8utDW2hllCnO57y6alpc7Gn/Utxa4NT2H+4H8dd7NNT15aa+zHHMBba4FZXm9MSagvrsV8ugXit9yMhQfYk2EIgIqAFTXQaRQhAoEECxGGDcGkaAhDgDjJzAAIvJcDC/FJinA+B1ydAHL4+U1qEAAT2BLRrDHeQ94zYg8ABAS1oDk6iAAEINEqAOGwUL41D4OQJaNcYEuSTnxoA0AhoQePPj9+b88f9NmVP2Vx9y269B2fVT9lTNrTxp6b9/A63OXPGqmvF4VBjweKSa8/hltu3Vb9kbWFcsF8GAe0aQ4Jchv9Q2QEBLWg6kEKXEBgsASvOcu2DBcfAIACBVyGgXWNIkF8FL40MkYAWNEMcK2OCQFcErDjLtXc1LvqFAATKIKBdY0iQy/AfKjsgoAVNB1LoEgKDJZCKs8VisfkN8//4j/9Qx5+qr1bCAAEIQGBHQLuGkCAzRSCgEIiDJn5vLiy7/abLocz4Hb2wb3deWO6Ttja0xGOvy60NbaGWUKc7nvLpkLW5OMv957m2wSn0W7jvNMTl0Kenrs37qIpT19zqanM6Q5+G9dgvl0C81vuRkCB7EmwhEBHQgiY6jSIEIJBBIBVn//Vf/7VJnt2dZO0nVV+rw3EIQAACnoB2DSFB9oTYQiAioAVNdBpFCEAgg4AVZ7n2DGlUhQAEToCAdo0hQT4B5zPEryOgBY1vLX4s6I/7bcqesrn6lt16zGfVT9lTNrTxmTc/v8Ntzpyx4izXnqMtp67jkxOnuX1b9dEWzuD9fi63fUvslUJAu8aQIJfiQXS2TkALGi/EupCm7Cmba9+y5yxuVvtW35YdbX6GHG7hdsjDlywuVhwOdb5ZXHLtOdxy+7bql6zNz2u25RDQrjEkyOX4EKUtE9CCpmUZdAeBkyZAHJ60+xk8BBonoF1jSJAbR08HpRLQgqbU8aAbAiUSIA5L9BqaIVAOAe0aQ4Jcjg9R2jIBLWi8DOsxYcqesrn2LXvOI0irfatvy442P0MOt3A75OFLFhcrDoc63ywuufYcbrl9W/VL1ubnNdtyCGjXGBLkcnyI0pYJxEETX9TDsttvuhwOP15Awr7deWG5T9ra0BKPvS63NrSFWkKd7njKp6emzcWe9i/FrQ1OYf/hfhx3sU9PXVtq7sccw1hog1tdbU5LqC2sx365BOK13o+EBNmTYAuBiIAWNNFpFCEAAQhAAAIQKJSAttaTIBfqUGQ3T0ALmuZ7pgcIQAACEIAABNogoK31JMht0KcPg8Banu5/kNn0zfNj1fH0Wj7ePxr1tub16qNcTc5ltnw6PP/pXj7OpjL2j2vHU5l9vJforMM6QUkLGn9K/FjQH/fblD1lc/Utu/WYz6qfsqdsaOM7yH5+h9ucOZNT12kYaizkcrHq53Cz2s61l6wtjAv2yyCgrfUkyGX4b9gqHxdyOR7L5HIu909rkfWDLK7OZTR+L/OHz8mxr1c/yvUmsZ5ECfLPsrh8K6PJlcw3ifZnWS2+k8nojVzMf5J1stWtUQsaXzVnEcip6/rPWUBc/VT/KZtVF22OQPWPxRWfwi0kYM2XXHvOfMvt26pfsrbQh+yXQUBb60mQy/DfgFV+kdX8nYxG72S++rIf5y5pPr+5U5LZR7n/eC3Ts6nM/nwpk1GUIK/mMh2dyXT+ad+m7JLm8xu5r5Eha0ETNMguBCAAAQhAAAIFE9DWehLkgp06aOlmgvxJ5hfv5ebuUWSTDEcJciUcEuRKLByEAAQgAAEInCgBEuQTdXyZw17L4+JKxqO3crn42R5C3QR5k3SPZHy5kPDtZhcc2r+w8/ixX1h2+02X62px5zWtJW6/rrY2OPVZW11OffZhn7Wd+vxi7m+vfTEHq1w3LuP5FdZjv1wCJMjl+u70lD/dymwylvHFXB5qvApR7w7yL7KcfVPrvWYPXAsab7feo0vZUzbXvmUPL/heT7i16qfsKRva+CW9cJ75/Zw5k1PX9T/UWMjlYtXP4Wa1nWsvWZuPCbblENDWel6xKMeHp6F0/ZPML97IePpB7twv7NX5Me8gf5aH+XsZjy+2r2TUaVNkc1e55qmcBgEIQAACEIBAgQRIkAt02slJfrqT+eW5jCbfyWKV/nrFAZtkgvwo9/MrmYzO5WrxoPzC30FrzwUtaJ5PYAcCEIAABCAAgaIJaGs9d5CLdutQxLvvIM/l0r1WMf1ebl+SHDsEWoLsE+7xVK5vVy9Kjl2zWtB46jmPEXPquv5zHkG6+qn+UzarLtocgeofiys+hVtIwJovufac+Zbbt1W/ZG2hD9kvg4C21pMgl+G/QatcP8zlYjyS0eRalnVfqwiJVCXIu1c1RqNvZLb8JTy79r4WNL4B6yKfsqdsrn3LnrOAWO1bfVt2tPkZcriF2yEPX7K4WPahzjdr3Ln2HG65fVv1S9bm5zXbcghoaz0Jcjk+HKjS3afXtC9JTOeyciPfJMEjOZstJfha8pbJUYLsv4KhfZ0i+uayQlYLGuV0DkMAAhCAAAQgUBgBba0nQS7Mkchtj4AWNO0poCcIQAACEIAABJokoK31JMhNUqftognEQRM/FgzLbr/pcggzfgQZ9u3OC8t90taGlnjsdbm1oS3UEup0x1M+RdueXIpbG5zC/sN9pzAuhz49dW17Dx5z6ppbXW1OZ+jTsB775RKI13o/EhJkT4ItBCICWtD40+KLuj/utyl7yubqW3brIm3VT9lTNrTxHWQ/v8NtzpzJqes0DDUWcrlY9XO4WW3n2kvWFsYF+2UQ0NZ6EuQy/IfKDghoQdOBFLqEAAQgAAEIQKABAtpaT4LcAGyaHAYBLWiGMTpGAQEIQAACEICAttaTIDM3IKAQ0ILGn57zGDGnrus/5xGkq5/qP2Wz6qLNEaj+sbg24VM3h6v+xQq70OY1WH1b9ia49UGbNe5cew633L6t+iVr83OHbTkEtLWeBLkcH6K0ZQJa0HgZ1kU+ZU/ZXPuWPWcBsdq3+rbsaPMz5HDbJbfcuYxPD33pS0361Go7157j09y+rfola/Nzg205BLTrIwlyOT5EacsEtKBpWQbdQSCbAHM5GyENQAACAyWgXR9JkAfqcIaVT0ALmvyWaQEC7RJgLrfLm94gAIFyCGjXRxLkcnyI0pYJxEETPxYMy26/6XI4/PgRZNi3Oy8s90lbG1risdfl1oa2UEuo0x1P+TRXm5vLYX9V7XWlrUpLrLWutjptxW3nltG2vd5YHFOcwrruvDAWnC20N1Guq831HWoL67FfLoF4rfcjIUH2JNhCICKgBU10GkUI9IJAar6mbE68Ze/FABEBAQhAoAEC2vWPBLkB2DQ5DAJa0AxjdIxiaARS89XZfv31V3XIqbpqJQwQgAAEBkBAu/6RIA/AuQyhGQJa0DTTG61CII+ANl9dYuxsf/jDH9QkWaubp4jaEIAABPpPQLv+kSD333co7IiAFjReTvhenD8WblP2lM21Ydmt9+Cs+il7yoa2/v6paTdfc/6FczfeZ77FRLZlK1ZyuFlt59rR1oxPq1vlaJ8JaGs9CXKfvYa2TgloQdOpKDqHgEJAm6/cQVaAcRgCEIBA4ncwSJCZHhBQCGgJh3I6hyHQKYHUfHU23kHu1D10DgEI9JSAdu0kQe6pw5DVPQEtaLpXhgIIHBNIzdeUzbVk2Y974wgEIACBYRDQrn8kyMPwL6NogEAcNPE7f2HZ7TddDocYvz8Y9u3OC8t90taGlnjsdbm1oS3UEup0x1M+zdXm5nLYX1V7XWmr0hJrrautTltx27lltPEd5HAOsF8egXit9yMgQfYk2EIgIqAFTXQaRQj0ngBzufcuQiAEINARAe36SILckUPotv8EtKDpv3IUQuCQAHP5kAclCEAAAp6Adn0kQfaE2EIgIqAFjT8tfDTrj4XblD1lc21Y9vhxfNhvnfqp9lO2Om2jLfbGtmxxbZJb7lxuUpvFxbIPVZs17lx7Drfcvq36JWurjn6O9pmAdn0kQe6z19DWKQEtaLwo6yKfsqdsrn3LnrOAWO1bfVt2tPkZcrjtgpubw1X/DpUx32Ievmz5zLLnxILVdq4dbd7Lh1uLq8XtsDVKJRDQ1noS5BK8h8ZOCGhB04kYOoUABCAAAQhA4NUJaGs9CfKro6bBoRDQgmYo42McEIAABCAAgVMnoK31JMinPjMYv0pACxpfwXoUl7KnbK59y2495rPqp+wpG9r6+6emU35L2fBpP32a6zOrfs41xGo7116yNr8+sC2HgLbWkyCX40OUtkwgDpr4oh+W3X7T5XD48QIS9u3OC8t90taGlnjsdbm1oS3UEup0x1M+RdueXIpbG5zC/sN9pzAuhz49dW17Dx5z6ppbXW1OZ+jTsB775RKI13o/EhJkT4ItBCICWtBEp1GEAAQgAAEIQKBQAtpaT4JcqEOR3TwBLWia75keIAABCEAAAhBog4C21pMgt0GfPuoReLqXj7OpjP2nqcZTmX28l6c6tdcPsrg6l7PZUr4cnf9ZVovvZHI2k+Wx8ehsf0ALGm+PHwv6436bsqdsrr5ltx7zWfVT9pQNbf18X9XyCz71UXm8TbFJ2Szmzp4Tp7l9W/XRdjwXXsOn1a1ytM8EtLWeBLnPXjspbT/L4vKtjCZXMr9/FJFdUjt6Ixfzn2SdYrFeye31NrE+TpA/y+r2e5mORzIiQX6mmFo8UzbXgGXPWXit9q2+LTvanqfAwQ7cDnA8Fywulj1nvllt59rR9uzmgx2Lq8XtoDEKRRAgQS7CTScscjWX6ehMpvNPAYRd0nx+I/eVGfJanu5/kNl0ItPZv8rlZHx4B3l3R/ps+s/y58vzV0+QA6HsQgACEIAABCBQIAES5AKdhmQrQf4iq/n/lOnN3+RJPsl8enaYIK/mcjH9IHdPn2U1f0eCzISCAAQgAAEIQOCAAAnyAQ4KRRB4XMjleCTjy4W4ly7SPxUJ8nMFl0jrCbILDu3fcxMV7xOGj9rcftPlulrceU1riduvq60NTn3WVpdTn33YZ22nPr+Y+9trX8zBKteNy3h+hfXYL5cACXK5vjtR5b/IcvaNjMbvZf7wuQaDr0+Qtca1oPHnW++qpewpm2vfsocXfK8n3Fr1U/aUDW38kl44z/x+zpzJqev6H2os5HKx6udws9rOtZeszccE23IIaGs9v6RXjg9PSOlneZi/l/H4Qm7u7HvHWzDtJ8gn5BCGCgEIQAACEBgkARLkQbp1iIN6lPv5lUxG53K1eEh/veJg+CTIBzgoQAACEIAABCBgEiBBNhFxQucEnu5k7r42MZ7K9e3qBcmxU95+gpzzGDGnrhttziNIVz/Vf8pm1UWbI1D9Y3HFp3ALCVjzJdeeM99y+7bql6wt9CH7ZRAgQS7DT6ercv2TzC/eyGj0jcyWv3wFBxLkEJq1AKXsKZvrw7LnLG5W+1bflh1t4SzZ78NtzyLcs7hY9pz5ZrWda0db6On9vsXV4rZvib1SCJAgl+Kpk9S5lsfF1f4v6B19VeKdzFdfRDbfSh4dfsrtmVf7CfJz1+xAAAIQgAAEIFAkARLkIt2G6C4JaEHTpSb6hgAEIAABCEDg9Qhoaz1fsXg9xrQ0MAJx0MSP3sKy22+6HOKNH/OFfbvzwnKftLWhJR57XW5taAu1hDrd8ZRP0bYnl+LWBqew/3DfKYzLoU9PXdveg8ecuuZWV5vTGfo0rMd+uQTitd6PhATZk2ALgYiAFjT+tPii7o/7bcqesrn6lt26SFv1U/aUDW18B9nP73CbM2dy6joNQ42FXC5W/RxuVtu59pK1hXHBfhkEtLWeBLkM/6GyAwJa0HQghS4hAAEIQAACEGiAgLbWkyA3AJsmh0FAC5phjI5RQAACEIAABCCgrfUkyMwNCCgEtKDxp+c8Rsyp6/rPeQTp6qf6T9msumhzBKp/LK74FG4hAWu+5Npz5ltu31b9krWFPmS/DALaWk+CXIb/UNkBAS1oOpBClxCAAAQgAAEINEBAW+tJkBuATZPDIKAFzTBGxyggAAEIQAACENDWehJk5gYEFAJa0CincxgCEIAABCAAgcIIaGs9CXJhjkRuewTioInfmwvLbr/pcjjy+B29sG93Xljuk7YmtDg/af9CDo5LilsT2sL+w/3YR2jbfz6vyg+Oj/+JOYY+raobnt+E3ety27AvV0bblk7MxSq3zS3lw1Cr2w+1hfXYL5dAvNb7kZAgexJsIRAR0IImOo1ijwjgsx45AykQgAAECiCgrRskyAU4D4ndENCCphs19FqHAD6rQ4lzIAABCEDAE9DWDRJkT4gtBCICWtBEp1HsEQF81iNnIAUCEIBAAQS0dYMEuQDnIbEbAlrQeDXhu2n+WLhN2VM214Zlt96Ds+qn7Clb37VZPoNbOEP3+5bP4bZnFe41yc1qO9ee49Pcvq36JWsL5wf7ZRDQ1g0S5DL8h8oOCGhB04EUutwRsHySawc0BCAAAQicFgFt3SBBPq15wGhfQEALmhc0wamvTMDySa79leXSHAQgAAEI9JyAtm6QIPfcccjrjoAWNN0poueUTxaLxeZzb3/84x9VUKn6aiUMEIAABCAwWALaukCCPFiXM7BcAnHQxO/NhWW333Q5HE/8jl7YtzsvLPdJW64W55PcfyHHLjmFfTtNKZ/mcqtTX+NSkrY64wy5v8b5dbm9Rl8v1d4nbSkt4bji+dYGt7ranJY4TsO67JdJIF7r/ShIkD0JthCICGhBE51GsUUCKZ/8+uuvm+TZ3UnWflL1tTochwAEIACB4RLQ1gUS5OH6nJFlEtCCJrNZqmcQsHySa8+QRlUIQAACECiQgLZukCAX6Ewkt0NACxrfe/xY0B/325Q9ZXP1Lbv1mM+qn7KnbF1rs3ySa88Ze05dx/VUfQo3f8U43OZysernzDer7Vx7ydoOvUipBALaukGCXIL30NgJAS1ovJicRSCnrus/ZwFx9VP9p2xW3a61WT6Dm/PQ8Y/lc7gdM3NHmuRmtZ1rz/Fpbt9W/ZK1Vc8UjvaZnphnoAAAH1xJREFUgLZukCD32Wto65SAFjSdiqLzJAF8lsSDEQIQgAAEIgLaukGCHIGiCAFPQAsab2fbPwL4rH8+QREEIACBPhPQ1g0S5D57DW2dEtCCxouyHhOm7Cmba9+y5zyCtNq3+rbsXWqzfNaltj5zQ5uP6sOtxcWy58w3q+1cO9oOfe1LFleLm2+HbTkEtHWDBLkcH6K0ZQJx0MQXzrDs9psuh8OPL9Jh3+68sNwnbU1ocX7S/oUcHJcUtya0hf2H+7GP0PYXh2DzU+UHb3PbmGPo06q64flN2NG29YnFOcUprOvOa9undbU5naG2sB775RKI13o/EhJkT4ItBCICWtBEp1GEAAQgAAEIQKBQAtpaT4JcqEOR3TwBLWia75keIAABCEAAAhBog4C21pMgt0GfPgwCa3m6/0Fm0zfPj8rH02v5eP9o1Nua16uPcjU5l9ny6fD8p3v5OJvK2D+CH09lNl/Kan14mlbSgsafHz8W9Mf9NmVP2Vx9y2495rPqp+wpG9r2rwJ4P/st3DyJ422KTcrmWrLsQ40Fa9y59hxuuX1b9UvWdjz7OdJ3AtpaT4Lcd8+dgr7HhVyOxzK5nMv901pk/SCLq3MZjd/L/OFzksB69aNcbxLrSZQg/yb3N9/KaDyV69uVrOWzrBbfyWT0Vi4XPyfb9EYtaLzdusin7Cmba9+y5ywgVvtW35YdbX6GHG7hdsjDlywuln2o880ad649h1tu31b9krX5ec22HALaWk+CXI4PB6r0i6zm72Q0eifz1Zf9GHdJ8/nNnVTf8H2U+4/XMj2byuzPlzIZRQny+k5uzsdyNlvKc6u7Y+PLhdS5N60FzV4kexCAAAQgAAEIlExAW+tJkEv26pC1mwnyJ5lfvJebu0eR1VymcYK8qX8m0/mngNKTLGcTGZ3fyH111h2cK5vXPQ4OUIAABCAAAQhAYFAESJAH5c6hD2Ytj4srGdd9HaIqQd4cUxLks5ksn28rbxNhFyBV/0LS8WO/sOz2my7X1eLOa1pL3H5dbW1w6rO2upz67MM+azv1+cXc3177Yg5WuW5cxvMrrMd+uQRIkMv13ekpf7qV2WQs44u5PNS401t5B/kFCbIGWAsaf771Hl3KnrK59i17eMH3esKtVT9lT9nQxi/phfPM7+fMmZy6rv+hxkIuF6t+Djer7Vx7ydp8TLAth4C21vOKRTk+PA2l659kfvFGxtMPcud+Ya/OT+YdZK0LLWi08zkOAQhAAAIQgEBZBLS1ngS5LD8OW+3Tncwvz2U0+U4Wq/TXKw5AVCXIX5YyO1NeseAd5AN8FCAAAQhAAAKnSoAE+VQ9X8S43XeQ53LpXquYfi+3L0mO3fiqEuTKL1Z8kvn0TF7rKxY5jxFz6roh5zyCdPVT/adsVl20OQLVPxZXfAq3kIA1X3LtOfMtt2+rfsnaQh+yXwYBEuQy/HSSKtcPc7kYj2Q0uZZl3dcqQlJVCbL47yBfbL90wXeQQ2IkyAc09gVr4U7ZUzbXg2XPSQqs9q2+LTva9nMk3GuSm9V2rj3Hp7l9W/VL1hbOD/bLIECCXIafTlDlz7K4fFv5BQk3aUfTuawclU0SPDr8rrGnVZkgi4h/ZeP5CxXncvnh9tX+kp7vni0EIAABCEAAAmUSIEEu02+o7pCAFjQdSqJrCEAAAhCAAARekYC21vNLeq8ImaaGRSAOmvixYFh2+02XQ7rxI8iwb3deWO6Ttja0xGOvy60NbaGWUKc7nvIp2vbkUtza4BT2H+47hXE59Ompa9t78JhT19zqanM6Q5+G9dgvl0C81vuRkCB7EmwhEBHQgsafFl/U/XG/TdlTNlffslsXaat+yp6yoY3vIPv5HW5z5kxOXadhqLGQy8Wqn8PNajvXXrK2MC7YL4OAttaTIJfhP1R2QEALmg6k0CUEIAABCEAAAg0Q0NZ6EuQGYNPkMAhoQTOM0TEKCEAAAhCAAAS0tZ4EmbkBAYWAFjT+9JzHiDl1Xf85jyBd/VT/KZtVF22OQPWPxRWfwi0kYM2XXHvOfMvt26pfsrbQh+yXQUBb60mQy/AfKjsgoAVNB1LoEgIQgAAEIACBBghoaz0JcgOwaXIYBLSgGcboGAUEIAABCEAAAtpaT4LM3ICAQkALGuV0DkMAAhCAAAQgUBgBba0nQS7Mkchtj0AcNPF7c2HZ7TddDkcev6MX9u3OC8t90taGlnjsdbm1oS3UEup0x1M+RdueXIpbG5zC/sN9pzAuhz49dW17Dx5z6ppbXW1OZ+jTsB775RKI13o/EhJkT4ItBCICWtBEp1GEAAQgAAEIQKBQAtpaT4JcqEOR3TwBLWia75keIAABCEAAAhBog4C21pMgt0GfPookoAVNkYNBNAQgAAEIQAACRwS0tZ4E+QgVByCwJaAFjecTvzfnj/ttyp6yufqW3XoPzqqfsqdsaONPTfv5HW5z5kxOXadhqLGQy8Wqn8PNajvXXrK2MC7YL4OAttaTIJfhP1R2QEALmg6k0CUEIAABCEAAAg0Q0NZ6EuQGYNPkMAhoQTOM0TEKCEAAAhCAAAS0tZ4EmbkBAYWAFjTK6RyGAAQgAAEIQKAwAtpaT4JcmCOR2x6BOGji9+rCsttvuhyOPH5HL+zbnReW+6StDS3x2Otya0NbqCXU6Y6nfIq2PbkUtzY4hf2H+05hXA59eura9h485tQ1t7ranM7Qp2E99sslEK/1fiQkyJ4EWwhEBLSgiU6jCAEIQAACEIBAoQS0tZ4EuVCHIrt5AlrQNN8zPUAAAhCAAAQg0AYBba0nQW6DPn0USUALGj+Y+LGgP+63KXvK5upbdusxn1U/ZU/Z0MZn3vz8Drc5cyanrtMw1FjI5WLVz+FmtZ1rL1lbGBfsl0FAW+tJkMvwHyo7IKAFjZeSswjk1HX95ywgrn6q/5TNqos2R6D6x+KKT+EWErDmS649Z77l9m3VL1lb6EP2yyCgrfUkyGX4D5UdENCCpgMpdAkBCEAAAhCAQAMEtLWeBLkB2DQ5DAJa0AxjdIwCAhCAAAQgAAFtrSdBZm5AQCGgBY0/3XpMmLKnbK59y57zCNJq3+rbsqPNz5DDLdwOefiSxcWyD3W+WePOtedwy+3bql+yNj+v2ZZDQFvrSZDL8SFKWyYQB018UQ/Lbr/pcjj8eAEJ+3bnheU+aWtDSzz2utza0BZqCXW64ymfom1PLsWtDU5h/+G+UxiXQ5+eura9B485dc2trjanM/RpWI/9cgnEa70fCQmyJ8EWAhEBLWii0yhCAAIQgAAEIFAoAW2tJ0Eu1KHIbp6AFjTN90wPEIAABCAAAQi0QUBb60mQ26BPHwaBtTzd/yCz6RtxE9X9G0+v5eP9Y6Leo9x/vJbpeHv+aPRGprO5LFef93XWK1l+uJTJrs3R5FI+LFey3p+R3NOCxleKHwv6436bsqdsrr5ltx7zWfVT9pQNbXwH2c/vcJszZ3LqOg1DjYVcLlb9HG5W27n2ErT9+OOP8t///d9hGLBfKAFtrSdBLtShg5L9uJDL8Vgml3O5f1qLrB9kcXUuo/F7mT8ECW8w6PX9jZy7pPj6R1m5KquPcjUZy/hyIdu0+hdZzr6R0eQ7WeyS5u05/4/Mlr8ELem7WtD4GjmLQE5d13/OAuLqp/pP2ay6aHMEqn8srvgUbiEBa77k2nPmW27fVv0StM3n883NnH/7t38jUQ4nboH72lpPglygM4cl+Yus5u9kNHon89WX/dB2SfP5zV3FHd/f5P7mWxmdzWT5XGV3bHwli8e1SGX9J1nOJkESve+uak8LmqpzOQYBCEAAAqdFwN1BdgmyWytIlMv1vbbWkyCX69NhK69McP2Qf5bF5VsZTeey8odE5MtyJmejb+Xm/jeR1VymozOZzj+FZ2yT8YPEOjBHu1rQRKdRhAAEIACBEyZAoly287W1ngS5bL8OVP1aHhdXMh69lcvFzxVj/CTz6ZlUJ8gTmS2flDvIu8Ta32XeteyCg38wYA4wB5gDzIHXnAMVixeHekjA+bzq5+iodmJVZY5BoBECT7cyc+8TX8zlofI36mokyBK/g/xZVrff736pL3qdQxlEn2MBbYrTjMNwMwApZrgpYIzDcDMAKeY+c1Mkbw7f39/Ln/70J/nd734n//mf/5k6FVuPCGjzjQS5R05Cioisf5L5xRsZTz/InfuFvcqfOgmya2slt9dTGW/uELtfAvz/ZHFzEb27XNnB5qAWNHqN9ixo+zrWcIPb1xH4ulrMt+FxqxpRmBi7X9779ddfq07jWE8JaHFKgtxTh52krKc7mV+eH3x5oprD9pftql+x2L2DXFlx94rF+Y3ca7l3UE8LmuCUznbR9nXo4Qa3ryPwdbWYb8PjFo6IxDikUe6+FqckyOX6dEDK3XeQ53LpXquYfi+34beMK0cZfbFic87uaxj+/eL1ndych599c3eU3bEzmcxu5amy3cODWtAcntVNCW1fxx1ucPs6Al9Xi/k2PG5+RP/0T/+0eZWCO8aeSLlbLU5JkMv16WCUrx/mcuH+4MfkWpbqaxWHw33+DvLN3zbJ7vF3kH0SfSE3d+7LyLs/LHKmf1v5sAfZ/OJefKwvZS2g+6APbV/nBbjB7esIfF0t5tvXcfO1/v73v/MqhYdR+FaLBRLkwh1bvvzdaw/alyT8p9w2n20bydlsKdtPHz/K/fxq/1fyRu4d478c/SW9/TvIdf463yFNLWgOz+qmhLav4w43uH0dga+rxXwbHrevGxG1+kxAi1MS5D57DW0QgAAEIAABCEAAAo0RIEFuDC0NQwACEIAABCAAAQiUSIAEuUSvoRkCEIAABCAAAQhAoDECJMiNoaVhCEAAAhCAAAQgAIESCZAgl+g1NEMAAhCAAAQgAAEINEaABLkxtDQMAQhAAAIQgAAEIFAiARLkEr2G5tch8HQvH2f+T06PZDSeymy+lJX61/R230x232befH7ujUxn88NPyL24TW0oNfo6qOr+qMoPMpu+2Wmr+nzd7i8Nxp/OO5vJcvuNvIMW9UJVXzOZL1eiovuylNmZ57bf7j/P9xVtagJf5IPdH5KJmfiy/5ygqV8Tox/ffqP7XGZL48/TmON56VzRNT1b1g+yuDoPPp/4bIl2qvr+Qe6D75Z/Wc7kzPN83k7scUc97YufZbX4TiY15q3Zt8l232vdvVp+3X2ecnsd2cfDtvxO5isXkE3G67V8vHffgdd+qvwaXusajteP94k/2lTVdzSeBuJVI8Xx4RIgQR6ubxlZkoD/gyFTub51id1u0R29lcvFz5U1n/8IyfWPmyRa/yMk9dus7Mj9cb/7GzkfvZGp2ldU83Ehl2P3zef5NjnZJTijcfgHUD7JfHom48uFpJbGqOXjov9rhP6vGz73dSWLRyVF3iQEOtvtXzMM/mJinTaPlYnIy/163Mwvspx9I6Ox/2MyImLpP24keWS9+lGuN/+ZsRJFezwvnitJZW7yrcR/J3z/H5iqSmt5XFzJeHQul/O7wz/MczGXh81UiP6SZVUzLzr2WVa338vU/SfVTJCtvm22L5K2QVfXr3HLa3laXsvExfzujxyJvFK81ro2HOox59TXXAMOu9iVdt+7n1zJfJOw++vwG7mY/1T9H+4643nleK2UzsHBEyBBHryLGWAlgd0F/iAB8Bf9ygRyt5geLMp+gd0lhi9us1LZPslL9XVQ1d8F9XeedsbdQnJ+c7ddaDZ3VcbyXD5oo35hu3geJnbbY3oCvL2T963c3P9W2dHXtFnd0PZPidf3a9zKPlEJF2hLf9yKXt7dmTubyuzPlzIZHXI8qmfOqRrz8qhR7YC/MzeR6exfN3/i/YDjUbVtAjfyd9k3dp80e1/v7oKe38i98n+no2a1A7u7vWfTf5Y/X57XSJCNvk22mpCq4y/0a9zE063MJmMZP//HQkReJV5rXhsO9Nhz6tXidZPInsl0/ilQsEuaK+dMvfG8XrwGstg9OQIkyCfncga8IbBJHuMLc2pB3V20D5IBt4a5x8e7ZODFbWq+qNGXVjU8HiXIVhIbVtX3fQIUJePJxTz6j8RR41/T5lEj2wO5Plj/JPOLN9GfN7f0K1oqD3+S+cX77Z853yQHRoJsjueV5spGq0s+/ufuDuY2+U0nyFUD9L7cxUTyP51V9RPHVnO5mH6Qu6fPspq/sxNkq2+TbULLkemFfj2o/1ke5u9lPPpGZstfni2vE6/PzR3uRNeGQ6M1p/7v7snBS64Bhz2kS7v+KxNkpebBeF4zXpX+OHwSBEiQT8LNDPKIQOWdi12CfHDn1tesulvmE+RdkvPiNn3b8bZGX3GVo7JPVPxdXV8+k8nk7e495Yo/w33UTnxAuYOze+evOqHaLXjj38vk9+Nd3+dy+eF2977317QZ69qVs3xQffdYxNKvaLEO10mQzfG8xlypEvq1CbJntXuqsklcRjKeTOT3/v3jyaV8SL2vXiXn4NhuvlTGaXCi1bfJNmjrJbt1/Bq2V3X3WF4rXsOO/L5v218b/HG/tebUL9v/oIyqEuRRjffWfT/K1vut8kleVZ14PH4OatebqjY4BoFjAiTIx0w4cgoEXrw4WovG0+49VeWutLWYHzCv0dfB+RWFo0V3d1fl4C7Vo9zdXMh4ci3L4JeqKloLDn1FMru7kzcK+3n6m9xM38pkditP8hVtBooOdl/s17C2X1ijd6lN/WEbL9ivk0iZ43mFuVIpedtu9X94Kiu4N3Cf36P1r6ds74KOd3529dbydPdBpuPDu6Vai9XH6yXIZt8m2+rezaN1/PrcSJzcecNrxatvL9geXRsC22bXmlNNJsj+/f/wdydifVE5Hk9T8Rp1S3H4BEiQh+9jRlhF4MWLo7Vo9ChB3r0mMN48jk6/+Pnyx7ivlcyGj0F3j8xf447Ui/0aTI6Dx7TB8crdUH+acWV1d7BOImWOp8a8VAWkDC9PkNcPc7kYh79kprRvvfqgVNsfrpcg788P9sK+TbZBvZfs1vHrc3u7/5TVfJ3g5fH63NF2p9a1wZpTTSXIu1dNwl+OjeQfFWuNx9V6hXg96pwDQydAgjx0DzO+agKbVwKUu72Vi9Xu9YvUO8gvbrNa2vPnnVJ9qVXvZO5+gWnynSxWn7Wz9scrk4S9uWpv+9511ePVl/wC4GGi/Tpt+l9seolf/Qi1O3neHm8P9cfWWuU6iZQ5p2rMy1pi4pNekiC7X+6by+XkTCZXHxOfSfR9VCdg3mpvMxLk3ZchNr9YaLK1lVSeUcevvuJLXyf4inj1XclT3WuDPadeLV6fxT3K/fxKJqNzuVo8VH+94vnc3U7t8bjzXyFe4/4pD54ACfLgXcwAKwmEd5KeT9gu3NWfQau6A7G76I4Pv2JxWD/V5nPH0U6NvqIam0fXmyQl+FTawTnVd6q2d6T8FwcOKqiFyrtYm4Vbeaex8s7sboy7/4y8uE1N3Yv96huqYr6z1dDvW3nRtk4iZY6nSnc0L18kyp9cN0H2ic2b508S+hbcnNx+Bi6aX5sxnWV8TaVOglyjb5PtfiQv2qvj112DlfN+Y3u9eLWvDfHo7DlVqTt1DYi7CMs+0R37z2OGxqp9/x8y5VrXVLxWSeHYoAmQIA/avQxOJ+AXAf+tW//9TSXJc29P+m8T775Tqn8HuX6bmj67r8Oa28fbo+jrC+E5/v3Q4N3P3beGDz4tFVbR9n1i4V/hML9ZvHuvMHgHecvu7f5bpy9uUxP3cr9uW6pOSLa2Gvo1OanjtRIpezwvnSspSXtbnQTZf30hfMd438Jmb/N+6FnwDvIuzg6+zx3VMYt1EmT3dzbcp9NSfdtsTSlVJ9Tyq6uoJPGbNl8vXu1rw/EgzDn1WvHqvxpz8LsRx3rCI/Z4GorXUAT7J0GABPkk3MwgKwn4Oxf+t+vdHzx4/rKCf0c0/K1sf7fM/+Wriq9AWG1WCqk6aPW1TWC2fyxhl9w9j8Pr222fX9X4LKvlXzbft3WBP3J/lGB2+FfPqpQcH9vfwdm24xLz8MsEuwQm/MbveiXLD+67vztN7q8WHvy1LKvNYxXqEcsHmwQm9KtracfzmVXUuqk/Or9OsTKRCv26a8Qaj1hzpY6Y+JyqBDny6+71gOc54H272e5fc1mvbuWDe+1nZx9Po796FndtlpUEucKvZt8mW1PM8Ql1/Wo+9n+NeK1zbYj8uhmRNadeI179fxCi69XzPNq9xnXg1zrjcf/3sK43x27jCARiAu6aVfVzdFQ7saoyxyAAAQhAAAIQgAAEIFAqAS3vJUEu1aPohgAEIAABCEAAAhDIIkCCnIWPyhCAAAQgAAEIQAACQyNAgjw0jzIeCEAAAhCAAAQgAIEsAiTIWfioDAEIQAACEIAABCAwNAIkyEPzKOOBAAQgAAEIQAACEMgiQIKchY/KEIAABCAAAQhAAAJDI0CCPDSPMh4IQAACEIAABCAAgSwCJMhZ+KgMAQhAAAIQgAAEIDA0AiTIQ/Mo44EABCAAAQhAAAIQyCJAgpyFj8oQgAAEIAABCEAAAkMjQII8NI8yHghAAAIQgAAEIACBLAIkyFn4qAwBCEAAAhCAAAQgMDQCJMhD8yjjgQAEIDAIAr/IcvatTOefBjEaBgEBCJRFgAS5LH+hFgIQgEBDBNbyuLiS8XQuq4Z6qN3s0718nE1lPDojQa4NjRMhAIHXJECC/Jo0aQsCEIBAsQR+lsXl7+X85k7WXY/h6V4Wi6UsZt+QIHftC/qHwIkSIEE+UcczbAhAAAIHBB4Xcjn+Vm7ufzs43F3hSZYkyN3hp2cInDgBEuQTnwAMHwIQGB6B9f2NnI8mMls+7Qe3/knmF29kdH4j9xW3iL8sZ3Km2GQ1l+nojUxn/yqXk7G4hWM0nsr1/1nK/7l2r0KMZDQay+RyLvdPFY0/vzLhztvWnX28l6dNu7tjmzbc/juZr76ICAny3nnsQQACbRMgQW6bOP1BAAIQaJrA5m5w+P7uWp6W1zIZfSOz5S8Vvf8m9zffyvhyIY8V1m2CPJLR5Erm948iT3+Tm+mbbVJ89VFWa9/+uOIVDffqxlsZTb6TxeqziDzK3c2FjEfW3WoS5CpXcAwCEGiHAAlyO5zpBQIQgEB7BNZ3cnM+lrPZUty9WNndPR5fzOWh4gavbM7/vVwufq7WuLnTGya/24R6f7dXRL4sZXY22vf53NInmU/PZDS5lmXV3eXn8+IdEuSYCGUIQKA9AiTI7bGmJwhAAAItEdjdtd18kWL3dYrEHdvNKxnjK1k8VmXPIts7yOEd6S+ymr+T0dlMlpsMPJUgr+Xp7oNMx9tXKcbTmfx1/r9lubmb3BIOuoEABCDwQgIkyC8ExukQgAAE+k9gd4fXJbC/3MpsciaT2a0EbyQHQ6jxebfNHeSvTZB9V49yv/hfMv/rbJcsn8vV4qH7L2Z4eWwhAAEIBARIkAMY7EIAAhAYBgF/1/h/yD/PLmQ8fi/zB/f+b9VPjc+7vUqCHPS9ewVk1IdvLgey2IUABCDgCZAgexJsIQABCAyIwPZLFu61hnHi7rH7nbkan3fLSZD9+8/T7+V281qFf+UifKd5QOAZCgQgMAgCJMiDcCODgAAEIBAR2CS17pNqiXeLN68OJz7v5pvMSZDd7wiubuXD5fn2E2+bz7mdy+WHW1kprzz7btlCAAIQ6IoACXJX5OkXAhCAAAQgAAEIQKCXBEiQe+kWREEAAhCAAAQgAAEIdEWABLkr8vQLAQhAAAIQgAAEINBLAiTIvXQLoiAAAQhAAAIQgAAEuiJAgtwVefqFAAQgAAEIQAACEOglARLkXroFURCAAAQgAAEIQAACXREgQe6KPP1CAAIQgAAEIAABCPSSAAlyL92CKAhAAAIQgAAEIACBrgiQIHdFnn4hAAEIQAACEIAABHpJgAS5l25BFAQgAAEIQAACEIBAVwRIkLsiT78QgAAEIAABCEAAAr0kQILcS7cgCgIQgAAEIAABCECgKwIkyF2Rp18IQAACEIAABCAAgV4SIEHupVsQBQEIQAACEIAABCDQFQES5K7I0y8EIAABCEAAAhCAQC8JkCD30i2IggAEIAABCEAAAhDoigAJclfk6RcCEIAABCAAAQhAoJcESJB76RZEQQACEIAABCAAAQh0RYAEuSvy9AsBCEAAAhCAAAQg0EsCJMi9dAuiIAABCEAAAhCAAAS6IkCC3BV5+oUABCAAAQhAAAIQ6CUBEuReugVREIAABCAAAQhAAAJdESBB7oo8/UIAAhCAAAQgAAEI9JIACXIv3YIoCEAAAhCAAAQgAIGuCJAgd0WefiEAAQhAAAIQgAAEekmABLmXbkEUBCAAAQhAAAIQgEBXBEiQuyJPvxCAAAQgAAEIQAACvSRAgtxLtyAKAhCAAAQgAAEIQKArAiTIXZGnXwhAAAIQgAAEIACBXhIgQe6lWxAFAQhAAAIQgAAEINAVARLkrsjTLwQgAAEIQAACEIBALwmQIPfSLYiCAAQgAAEIQAACEOiKAAlyV+TpFwIQgAAEIAABCECglwRIkHvpFkRBAAIQgAAEIAABCHRFgAS5K/L0CwEIQAACEIAABCDQSwIkyL10C6IgAAEIQAACEIAABLoi8KIE2Z3MPxgwB5gDzAHmAHOAOcAcYA4MfQ5UJeejqoMcgwAEIAABCEAAAhCAwKkSIEE+Vc8zbghAAAIQgAAEIACBSgIkyJVYOAgBCEAAAhCAAAQgcKoE/n8nxrrH52IK4wAAAABJRU5ErkJggg==\"/></span></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Suggest, by reference to the graph, why it is unlikely that the relationship between <em>T</em> and <em>v</em> is linear.</span></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Determine the fractional uncertainty in <em>v</em> when <em>T</em> = 2.115 s, correct to <strong>one</strong> significant figure.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">The student hypothesizes that the relationship between <em>T</em> and <em>v</em> is <em>T = a + bv</em><sup>2</sup>, where <em>a</em> and <em>b</em> are constants. To verify this hypothesis a graph showing the variation of <em>T</em> with <em>v</em><sup>2</sup> is plotted. The graph shows the data and the line of best fit.</span></p>\n<p><span style=\"background-color: #ffffff;\"><img src=\"data:image/png;base64,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\"/></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">Determine <em>b</em>, giving an appropriate unit for <em>b</em>.</span></span></p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">The lines of the minimum and maximum gradient are shown.</span></p>\n<p><span style=\"background-color: #ffffff;\"><img src=\"data:image/png;base64,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\"/></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">Estimate the absolute uncertainty in <em>a</em>.</span></span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">d.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color: #ffffff;\">a straight line cannot be drawn through all error bars<br/><em><strong>OR</strong></em><br/>the graph/line of best fit is /curved/not straight/parabolic etc.<br/><em><strong>OR</strong></em><br/>graph has increasing/variable gradient ✔</span></p>\n<p><em><span style=\"background-color: #ffffff;\">NOTE: Do not allow “a line cannot be drawn through all error bars” without specifying “straight”.</span></em></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color: #ffffff;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>v</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>15</mn><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">m</mi><mo> </mo><mo> </mo><msup><mi mathvariant=\"normal\">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math>  <em><strong>AND </strong></em> <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>∆</mo><mi>v</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>05</mn><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">m</mi><mo> </mo><mo> </mo><msup><mi mathvariant=\"normal\">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> ✔</span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mn>0</mn><mo>.</mo><mn>05</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>15</mn></mrow></mfrac><mo>=</mo></math>»0.04 <span style=\"display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;\">✔</span></span></span></p>\n<p><em><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">NOTE: Accept 4 %</span></span></em></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>use of 2 correct points on the line with Δ<em>v</em><sup>2 </sup>&gt; 2 ✔</p>\n<p><em>b</em> in range 0.012 to 0.013 ✔</p>\n<p>s<sup>3 </sup>m<sup>–2 </sup>✔</p>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>a</mi><mi>max</mi></msub><mo>=</mo><mn>2</mn><mo>.</mo><mn>101</mn></math> «s» ±0.001 «s» <em><strong>AND</strong></em> <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>a</mi><mi>min</mi></msub><mo>=</mo><mn>2</mn><mo>.</mo><mn>095</mn></math>«s» ±0.001 «s» ✔</p>\n<p>«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mn>2</mn><mo>.</mo><mn>101</mn><mo>-</mo><mn>2</mn><mo>.</mo><mn>095</mn></mrow><mn>2</mn></mfrac><mo>=</mo></math>» 0.003 «s» ✔</p>\n<div class=\"question_part_label\">d.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">d.</div>\n</div>",
    "topics": [
      "tools"
    ],
    "subtopics": [
      "tool-3-mathematics"
    ]
  },
  {
    "question_id": "19N.2.HL.TZ0.11",
    "Question": "<div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">Monochromatic light of very low intensity is incident on a metal surface. The light causes the emission of electrons almost instantaneously. Explain how this observation</span></p>\n</div><div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">In an experiment to demonstrate the photoelectric effect, light of wavelength 480 nm is incident on a metal surface.</span></p>\n<p style=\"text-align: center;\"><span style=\"background-color: #ffffff;\"><img 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\"/></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">The graph shows the variation of the current<em> <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>I</mi></math></em> in the ammeter with the potential <em><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>V</mi></math></em> of the cathode.</span></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\"><img src=\"data:image/png;base64,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\"/></span></span></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">does not support the wave nature of light.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">does support the photon nature of light.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Calculate, in eV, the work function of the metal surface.</span></p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">The intensity of the light incident on the surface is reduced by half without changing the wavelength. Draw, on the graph, the variation of the current <em><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>I</mi></math></em> with potential <em><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>V</mi></math></em> after this change.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b(ii).</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color: #ffffff;\">«low intensity light would» transfer energy to the electron at a low rate/slowly ✔<br/>time would be required for the electron «to absorb the required energy» to escape/be emitted ✔<br/></span></p>\n<p><em><span style=\"background-color: #ffffff;\">NOTE: OWTTE</span></em></p>\n<div class=\"question_part_label\">a(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color: #ffffff;\">«in the photon theory of light» the electron interacts with a single photon ✔<br/>and absorbs all the energy <em><strong>OR</strong> </em>and can leave the metal immediately ✔<br/></span></p>\n<p><em><span style=\"background-color: #ffffff;\">NOTE: Reference to photon-electron collision scores MP1</span></em></p>\n<div class=\"question_part_label\">a(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>ϕ</mi><mo>=</mo><mfrac><mrow><mi>h</mi><mi>c</mi></mrow><mi>λ</mi></mfrac><mo>-</mo><msub><mi>E</mi><mi mathvariant=\"normal\">K</mi></msub></math> <span style=\"background-color: #ffffff;\">✔</span></p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>E</mi><mi mathvariant=\"normal\">K</mi></msub><mo>=</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo>«</mo><mi>eV</mi><mo>»</mo></math><span style=\"background-color: #ffffff;\"> ✔</span></p>\n<p><span style=\"background-color: #ffffff;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>ϕ</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>24</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow><mrow><mn>480</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>9</mn></mrow></msup></mrow></mfrac><mo>-</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo>=</mo><mo>»</mo><mo> </mo><mn>1</mn><mo>.</mo><mn>1</mn><mo> </mo><mo>«</mo><mi>eV</mi><mo>»</mo></math><span style=\"display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;\">✔</span></span></p>\n<p><span style=\"font-size: 14px;\"><em><span style=\"background-color: #ffffff;\"><span style=\"text-align: left;color: #000000;text-indent: 0px;letter-spacing: normal;font-family: Verdana,Arial,Helvetica,sans-serif;font-variant: normal;font-weight: 400;text-decoration: none;display: inline !important;white-space: normal;float: none;background-color: #ffffff;\">NOTE: Allow reading from the graph of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>E</mi><mi>k</mi></msub><mo>=</mo><mn mathvariant=\"italic\">1</mn><mo mathvariant=\"italic\">.4</mo></math>leading to an answer of 1.2 «eV».</span></span></em></span></p>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color: #ffffff;\">similar curve lower than original ✔<br/></span></p>\n<p><span style=\"background-color: #ffffff;\">with same horizontal intercept ✔</span></p>\n<p><span style=\"background-color: #ffffff;\"><img height=\"246\" src=\"data:image/png;base64,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\" width=\"401\"/></span></p>\n<div class=\"question_part_label\">b(ii).</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b(ii).</div>\n</div>",
    "topics": [
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "e-2-quantum-physics"
    ]
  },
  {
    "question_id": "19N.2.HL.TZ0.6",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a(i))\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <span style=\"background-color:#ffffff;\">\n    Show that the pressure at B is about 130 kPa.\n   </span>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a(ii))\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <span style=\"background-color:#ffffff;\">\n    Calculate the ratio\n    <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mfrac>\n      <msub>\n       <mi>\n        V\n       </mi>\n       <mi mathvariant=\"normal\">\n        A\n       </mi>\n      </msub>\n      <msub>\n       <mi>\n        V\n       </mi>\n       <mi mathvariant=\"normal\">\n        C\n       </mi>\n      </msub>\n     </mfrac>\n    </math>\n    .\n   </span>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b(i))\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <span style=\"background-color:#ffffff;\">\n    determine the thermal energy removed from the system.\n   </span>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b(ii))\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <span style=\"background-color:#ffffff;\">\n    explain why the entropy of the gas decreases.\n   </span>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b(iii))\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <span style=\"background-color:#ffffff;\">\n    state and explain whether the second law of thermodynamics is violated.\n   </span>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a(i))\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     P\n    </mi>\n    <mi mathvariant=\"normal\">\n     B\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      250\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <msup>\n      <mn>\n       5\n      </mn>\n      <mstyle displaystyle=\"true\">\n       <mfrac>\n        <mn>\n         5\n        </mn>\n        <mn>\n         3\n        </mn>\n       </mfrac>\n      </mstyle>\n     </msup>\n    </mrow>\n   </mfrac>\n   <mo>\n   </mo>\n   <mo>\n    «\n   </mo>\n   <mi>\n    from\n   </mi>\n   <mo>\n   </mo>\n   <msub>\n    <mi>\n     P\n    </mi>\n    <mi mathvariant=\"normal\">\n     B\n    </mi>\n   </msub>\n   <msup>\n    <mfenced>\n     <mrow>\n      <mn>\n       1\n      </mn>\n      <mo>\n       .\n      </mo>\n      <mn>\n       5\n      </mn>\n      <mo>\n      </mo>\n      <msub>\n       <mi>\n        V\n       </mi>\n       <mi mathvariant=\"normal\">\n        A\n       </mi>\n      </msub>\n     </mrow>\n    </mfenced>\n    <mfrac>\n     <mn>\n      5\n     </mn>\n     <mn>\n      3\n     </mn>\n    </mfrac>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <mn>\n    250\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     3\n    </mn>\n   </msup>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <msub>\n     <mi>\n      V\n     </mi>\n     <mi mathvariant=\"normal\">\n      A\n     </mi>\n    </msub>\n    <mfrac>\n     <mn>\n      5\n     </mn>\n     <mn>\n      3\n     </mn>\n    </mfrac>\n   </msup>\n   <mo>\n    »\n   </mo>\n  </math>\n  <span style=\"background-color:#ffffff;\">\n   ✔\n  </span>\n </p>\n <p>\n  = 127 kPa\n  <span style=\"background-color:#ffffff;\">\n   ✔\n  </span>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a(ii))\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    «\n   </mo>\n   <mn>\n    127\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     3\n    </mn>\n   </msup>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    5\n   </mn>\n   <mo>\n   </mo>\n   <msub>\n    <mi>\n     V\n    </mi>\n    <mi mathvariant=\"normal\">\n     A\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mn>\n    250\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     3\n    </mn>\n   </msup>\n   <mo>\n   </mo>\n   <msub>\n    <mi>\n     V\n    </mi>\n    <mi mathvariant=\"normal\">\n     C\n    </mi>\n   </msub>\n   <mo>\n    »\n   </mo>\n  </math>\n </p>\n <p>\n  <span style=\"background-color:#ffffff;\">\n   1.31 ✔\n  </span>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b(i))\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n </p>\n <p>\n  work done\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    ∆\n   </mo>\n   <mi>\n    W\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mo>\n    «\n   </mo>\n   <mo>\n    -\n   </mo>\n   <mo>\n    »\n   </mo>\n   <mn>\n    250\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     3\n    </mn>\n   </msup>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    5\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      3\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <mo>\n    «\n   </mo>\n   <mo>\n    -\n   </mo>\n   <mo>\n    »\n   </mo>\n   <mn>\n    375\n   </mn>\n   <mo>\n   </mo>\n   <mo>\n    «\n   </mo>\n   <mi mathvariant=\"normal\">\n    J\n   </mi>\n   <mo>\n    »\n   </mo>\n  </math>\n  <span style=\"background-color:#ffffff;\">\n   ✔\n  </span>\n </p>\n <p>\n  change in internal energy\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    ∆\n   </mo>\n   <mi>\n    U\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     3\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    300\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    8\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    31\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mfenced>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      150\n     </mn>\n    </mrow>\n   </mfenced>\n   <mo>\n    =\n   </mo>\n   <mo>\n    «\n   </mo>\n   <mo>\n    -\n   </mo>\n   <mo>\n    »\n   </mo>\n   <mn>\n    561\n   </mn>\n   <mo>\n   </mo>\n   <mo>\n    «\n   </mo>\n   <mi mathvariant=\"normal\">\n    J\n   </mi>\n   <mo>\n    »\n   </mo>\n  </math>\n  <br/>\n  <em>\n   <strong>\n    OR\n    <br/>\n   </strong>\n  </em>\n  <em>\n   <strong>\n    <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mo>\n      ∆\n     </mo>\n     <mi>\n      U\n     </mi>\n     <mo>\n      =\n     </mo>\n     <mfrac>\n      <mn>\n       3\n      </mn>\n      <mn>\n       2\n      </mn>\n     </mfrac>\n     <mi>\n      P\n     </mi>\n     <mo>\n      ∆\n     </mo>\n     <mi>\n      V\n     </mi>\n     <mo>\n      =\n     </mo>\n     <mfrac>\n      <mn>\n       3\n      </mn>\n      <mn>\n       2\n      </mn>\n     </mfrac>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      375\n     </mn>\n     <mo>\n      =\n     </mo>\n     <mo>\n      «\n     </mo>\n     <mo>\n      -\n     </mo>\n     <mo>\n      »\n     </mo>\n     <mn>\n      563\n     </mn>\n     <mo>\n     </mo>\n     <mo>\n      «\n     </mo>\n     <mi mathvariant=\"normal\">\n      J\n     </mi>\n     <mo>\n      »\n     </mo>\n    </math>\n   </strong>\n  </em>\n  <span style=\"background-color:#ffffff;\">\n   ✔\n  </span>\n </p>\n <p>\n  thermal energy removed\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    ∆\n   </mo>\n   <mi>\n    Q\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    375\n   </mn>\n   <mo>\n    +\n   </mo>\n   <mn>\n    561\n   </mn>\n   <mo>\n    =\n   </mo>\n   <mn>\n    936\n   </mn>\n   <mo>\n   </mo>\n   <mo>\n    «\n   </mo>\n   <mi mathvariant=\"normal\">\n    J\n   </mi>\n   <mo>\n    »\n   </mo>\n  </math>\n  <br/>\n  <em>\n   <strong>\n    OR\n    <br/>\n   </strong>\n  </em>\n  <em>\n   <strong>\n    <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mo>\n      ∆\n     </mo>\n     <mi>\n      Q\n     </mi>\n     <mo>\n      =\n     </mo>\n     <mn>\n      375\n     </mn>\n     <mo>\n      +\n     </mo>\n     <mn>\n      563\n     </mn>\n     <mo>\n      =\n     </mo>\n     <mn>\n      938\n     </mn>\n     <mo>\n     </mo>\n     <mo>\n      «\n     </mo>\n     <mi mathvariant=\"normal\">\n      J\n     </mi>\n     <mo>\n      »\n     </mo>\n    </math>\n   </strong>\n  </em>\n  <span style=\"background-color:#ffffff;\">\n   ✔\n  </span>\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    ∆\n   </mo>\n   <mi>\n    Q\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mo>\n    «\n   </mo>\n   <mi>\n    n\n   </mi>\n   <mi>\n    C\n   </mi>\n   <mi>\n    p\n   </mi>\n   <mo>\n    ∆\n   </mo>\n   <mi>\n    T\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mo>\n    »\n   </mo>\n   <mfrac>\n    <mn>\n     5\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <mo>\n    ×\n   </mo>\n   <mi>\n    n\n   </mi>\n   <mi>\n    R\n   </mi>\n   <mi>\n    T\n   </mi>\n  </math>\n  <span style=\"background-color:#ffffff;\">\n   ✔\n  </span>\n </p>\n <p>\n  thermal energy removed\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    ∆\n   </mo>\n   <mi>\n    Q\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    300\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    2\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    5\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    8\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    31\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    150\n   </mn>\n  </math>\n  <span style=\"background-color:#ffffff;\">\n   ✔\n  </span>\n </p>\n <p>\n  <span style=\"background-color:#ffffff;\">\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mo>\n     =\n    </mo>\n    <mn>\n     935\n    </mn>\n    <mo>\n    </mo>\n    <mo>\n     «\n    </mo>\n    <mi mathvariant=\"normal\">\n     J\n    </mi>\n    <mo>\n     »\n    </mo>\n   </math>\n  </span>\n  <span style=\"background-color:#ffffff;\">\n   ✔\n  </span>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b(ii))\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n </p>\n <p>\n  <span style=\"background-color:#ffffff;\">\n   «from b(i)»\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mo>\n     ∆\n    </mo>\n    <mi>\n     Q\n    </mi>\n   </math>\n   is negative\n   <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">\n    ✔\n   </span>\n  </span>\n </p>\n <p>\n  <span style=\"background-color:#ffffff;\">\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mo>\n     ∆\n    </mo>\n    <mi>\n     S\n    </mi>\n    <mo>\n     =\n    </mo>\n    <mfrac>\n     <mrow>\n      <mo>\n       ∆\n      </mo>\n      <mi>\n       Q\n      </mi>\n     </mrow>\n     <mi>\n      T\n     </mi>\n    </mfrac>\n   </math>\n   <em>\n    <strong>\n     AND\n     <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n      <mo>\n       ∆\n      </mo>\n      <mi>\n       S\n      </mi>\n     </math>\n    </strong>\n   </em>\n   is negative\n   <span style=\"display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;\">\n    ✔\n   </span>\n  </span>\n </p>\n <p>\n </p>\n <p>\n  <strong>\n   ALTERNATIVE 2\n  </strong>\n </p>\n <p>\n  <em>\n   T\n  </em>\n  and/or\n  <em>\n   V\n  </em>\n  decreases ✔\n </p>\n <p>\n  less disorder/more order «so\n  <em>\n   S\n  </em>\n  decreases» ✔\n </p>\n <p>\n </p>\n <p>\n  <strong>\n   ALTERNATIVE 3\n  </strong>\n </p>\n <p>\n  <em>\n   T\n  </em>\n  decreases ✔\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    ∆\n   </mo>\n   <mi>\n    S\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mi>\n    K\n   </mi>\n   <mo>\n    ×\n   </mo>\n   <mi>\n    ln\n   </mi>\n   <mfenced>\n    <mfrac>\n     <mrow>\n      <mi>\n       T\n      </mi>\n      <mn>\n       2\n      </mn>\n     </mrow>\n     <mrow>\n      <mi>\n       T\n      </mi>\n      <mn>\n       1\n      </mn>\n     </mrow>\n    </mfrac>\n   </mfenced>\n   <mo>\n    &lt;\n   </mo>\n   <mn>\n    0\n   </mn>\n  </math>\n  ✔\n </p>\n <p>\n  <em>\n  </em>\n </p>\n <p>\n  <em>\n   NOTE: Answer given, look for a valid reason that S decreases.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b(iii))\n </div><div class=\"card-body\">\n <p>\n  <span style=\"background-color:#ffffff;\">\n   not violated ✔\n  </span>\n </p>\n <p>\n  <span style=\"background-color:#ffffff;\">\n   the entropy of the surroundings must have increased\n   <br/>\n   <em>\n    <strong>\n     OR\n    </strong>\n   </em>\n   <br/>\n   the overall entropy of the system and the surroundings is the same or increased ✔\n  </span>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-4-rigid-body-mechanics"
    ]
  },
  {
    "question_id": "19N.2.SL.TZ0.1",
    "Question": "<div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">The graph shows the variation with time<em> t</em> of the horizontal force <em>F</em> exerted on a tennis ball by a racket.</span></p>\n<p><span style=\"background-color: #ffffff;\"><img height=\"356\" 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\" style=\"margin-right: auto; margin-left: auto; display: block;\" width=\"457\"/></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">The tennis ball was stationary at the instant when it was hit. The mass of the tennis ball is 5.8 × 10<sup>–2</sup> kg. The area under the curve is 0.84 N s.</span></span></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Calculate the speed of the ball as it leaves the racket.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Show that the average force exerted on the ball by the racket is about 50 N.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Determine, with reference to the work done by the average force, the horizontal distance travelled by the ball while it was in contact with the racket.</span></p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Draw a graph to show the variation with<em> t</em> of the horizontal speed <em>v</em> of the ball while it was in contact with the racket. Numbers are <strong>not</strong> required on the axes.</span></p>\n<p><img src=\"data:image/png;base64,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\"/></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">d.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color: #ffffff;\">links 0.84 to Δ<em>p</em> ✔</span></p>\n<p><span style=\"background-color: #ffffff;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>v</mi><mo>=</mo></math>«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mn>0</mn><mo>.</mo><mn>84</mn></mrow><mrow><mn>5</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup></mrow></mfrac><mo>=</mo></math>» 14.5 «m s<sup>–1</sup>»✔<br/></span></p>\n<p><em><span style=\"background-color: #ffffff;\">NOTE: Award <strong>[2]</strong> for bald correct answer</span></em></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>use of Δ<em>t = </em><span style=\"background-color: #ffffff;\">«</span>(28 – 12) × 10<sup>–3 </sup>=<span style=\"background-color: #ffffff;\">»</span> 16 × 10<sup>–3</sup> <span style=\"background-color: #ffffff;\">«</span>s<span style=\"background-color: #ffffff;\">» <span style=\"display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;\">✔</span></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mover><mi>F</mi><mo>¯</mo></mover></math> =«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mo>∆</mo><mi>p</mi></mrow><mrow><mo>∆</mo><mi>t</mi></mrow></mfrac><mo>=</mo></math>» <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mn>0</mn><mo>.</mo><mn>84</mn></mrow><mrow><mn>16</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow></mfrac></math> <em><strong>OR</strong></em>  53 «N» ✔</span></span></p>\n<p><em><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">NOTE: Accept a time interval from 14 to 16 </span></span></em><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">ms</span></span><em><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\"> <br/>Allow ECF from incorrect time interval</span></span></em></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><em>E</em><sub>k </sub><em>= <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mn>1</mn><mn>2</mn></mfrac></math> × </em>5.8 × 10<sup>–2 </sup>× 14.5<sup>2 </sup>✔</p>\n<p><em style=\"color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: italic;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;\">E</em><sub style=\"color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 11.6px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;\">k</sub> = <em>W <span style=\"display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;\">✔</span></em></p>\n<p><span style=\"font-size: 14px;\"><em><span style=\"text-align: left;color: #000000;text-indent: 0px;letter-spacing: normal;font-family: Verdana,Arial,Helvetica,sans-serif;font-variant: normal;font-weight: 400;text-decoration: none;display: inline !important;white-space: normal;float: none;background-color: #ffffff;\">s = </span></em><span style=\"text-align: left;color: #000000;text-indent: 0px;letter-spacing: normal;font-family: Verdana,Arial,Helvetica,sans-serif;font-variant: normal;font-weight: 400;text-decoration: none;display: inline !important;white-space: normal;float: none;background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mi>W</mi><mi>F</mi></mfrac><mo>=</mo><mfrac><mstyle displaystyle=\"true\"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>5</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>×</mo><mn>14</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup></mstyle><mn>53</mn></mfrac><mo>=</mo></math>» 0.12 « m » ✔</span></span></span></p>\n<p> </p>\n<p><em>Allow ECF from (a) and (b)</em></p>\n<p><em>Allow ECF from MP1</em></p>\n<p><em>Award <strong>[2]</strong> max for a calculation without reference to work done, eg: average velocity × time</em></p>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><img height=\"241\" src=\"data:image/png;base64,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\" width=\"370\"/></p>\n<p><span style=\"background-color: #ffffff;\">graph must show increasing speed from an initial of zero all the time ✔<br/>overall correct curvature ✔</span></p>\n<div class=\"question_part_label\">d.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">d.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-1-kinematics",
      "a-2-forces-and-momentum",
      "a-3-work-energy-and-power"
    ]
  },
  {
    "question_id": "19N.2.SL.TZ0.3",
    "Question": "<div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">The solid line in the graph shows the variation with distance <em><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>x</mi></math></em> of the displacement <em><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>y</mi></math></em> of a travelling wave at <em>t</em> = 0. The dotted line shows the wave 0.20 ms later. The period of the wave is longer than 0.20 ms.</span></p>\n<p><span style=\"background-color: #ffffff;\"><img height=\"296\" src=\"data:image/png;base64,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\" style=\"margin-right: auto; margin-left: auto; display: block;\" width=\"612\"/></span></p>\n</div><div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">One end of a string is attached to an oscillator and the other is fixed to a wall. When the frequency of the oscillator is 360 Hz the standing wave shown is formed on the string.</span></p>\n<p><span style=\"background-color: #ffffff;\"><img height=\"172\" 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uz1pOvieVRLRlmlZrFbAXHfddSyP7qZMbUQzm3q9ifN9yUwmkI6QiUjSG9lDDz3Udr4lnebgpIZNLRFTJ4FlYtGmkKkKkcW+nywIXkdaB+7Pnz+fKrQRpkI2d911V7tlsXEPRPmQKWwquE+bNi2Wrz2ETCAdIRORohFnnUvmzchInN+4CklHoKgD7e3ZVOer2PbZRJXaiWbYeKzyi/s9OjSYVlVVxetbjnU0IDxp0iTn87ggZALperv/AqGnYiVXXHFFW8BUp+DAgQNO+XQCZvA0O6PjXzZt2uR0DDSzWVpa6hTDUGca4aSZGbUTPVZqM8ifefPmOff7jBkznBCD8FHoUbjU46SAqZUae/bssaVLlxIwc0Azwjpjt76+3nnP1oxxeXm5U0iLNgLEnGYygTBrbGxsV5hGhUsoxJBfqQUxkqEzkQyf7q0IA7UTf/ErXaYwTX6piJbahvcYqM1QQCs8/MWb9Djpc+SXio/528jChQtj8Trl/T0dfQDFiGc+QkudMzoF4ZIa+HVZ16Gw1HHztxMGAApHr1v+Kpt6PAj7haVBSX9V5bgEm6iK46Cl97d09AEUI575CCU6BeGWOhpN+C8stQ+vnTBzFg7+1zBWXhRGaphhFUy4xGnQ0vsbOvoAihGFfxAqqYV9kkHGHn74Yao3hpAeqxUrVrQVdFDRDO1J4ziHwtDjwd7k8OFxKYzUwj7JsGmTJ0/msQih1Aq/NTU1kSsMROEfIB0hE6FBpyCaVIV25syZke4gRInaiY6YKSsr41iZCNJRMocPH6Yido6kDlQy+BUNKsikc0q9o7P0uC1ZsiQyR8kQMoF0VJdFKOj8vlK32p9mL+vr653z/OiEhZ9mmbdv324LFy50PlflQFXXVKcBwfLaiTpi77zzjnstokSPoc4OVAVgqmsGS/fnlClT2gKmBrxWrlxJwIwAhUlV+PWqmWsg7eqrr3ZmOQFEEyETBaUgokCiYCIKKgoslJKPFg0GqEy9jgKggxC81Hais2EnTJjgXEa06AggzdJo5l8DBprZRM/5Byo1y6+BSlZURM+4ceNs48aNbcedjB8/3hYtWuTMUAOIGC2XBQrBXzxG/6r8P6JPxTb8xRwoRtMzuu9oJ/GSWpBGbQTZUUE4Hdfj3Zeq7MvrTTyo4qz3uOq1L8xFm7zfs6MPoBgxk4m804ikRvNHjx7tjFRqxFIjlxT3iQfNanrLnkSFgbSE7c0333Q+R/ckO9E2aNAg2kmMqI1oO4A384/saD+4Vkxo5YTuR92f3//+99lmEROa1WxsbGw3868ZawDRQOEf5JWCxoIFC5xOgVAkJt70eKvT5xVzUvBUxwEAekLLjP3FfaJUJAbdo4Hp6upqZy+zaMBN/YgwDSZQ+AdIx0wm8ubZZ591AqU36syemfhTwY1169Y5ewiF/TUnp9kZjdZTOKk4qXgNj3/HvP3JXsBUFXIV9yFgxpfCpAYrd+zY4fQdVPiMwllA+BEykRcadfYvj6W4T/HwOggsnz05tZMRI0Y4BX7279/vXotisnfvXufx1zJQDTjgBIWK1OWxWnaM4qAjmzQA418+S3E5ILwImcgpzVj5R521PFb79dgzU3y8/TWq/Kjls5rF1uw20tuJZmcYhClOqhrsdaI14MAetFa6HxQqdL/o/mF/cnHS6ph777233eoY1XhgdQwQQtqTCeRCMlBQFRNpUqvPqspmMVN1TNoJUqlKqtdGirn6rF4v9Pd79wXVY+HxV5+dPn2681paKN7v0dEHUIwo/IOc0AyVlseKRp3nzZvHgdhox1+4I4yFHPLFayu0E6Tyv44W41u19l/Onj27rVCc9uRpySTg0bYLrYrRDLeWUK9du7Ygq0Ao/AOkI2QicP7wsHDhQrv11ltZHouM1InW80MdBC2j1bKnYgtZ6khr/+XgwYNpJ0jjPT+Kbfm09l9ef/31beFBy2UZgEEmWip7yy23tA1GFKKKOSETSEfIRGD0Qq+ZGFV+E44nQVekjkQ//PDD7LUCiljqShiOJ8HJqP/hP+ZEezZVcC5fCJlAOgr/IBAabddIogKmgoKWNREw0RWanVC1YXUmFTRV7CSuFQO9Aj/qkFB+H9nQjJ6eP5r1jyP9XV7AVFBQkRcCJk4mtYq5wmZVVRUFgYACImSixzQT5S8rr04Q+2bQHeogZKoYGCdqJzrbzWsnVI9FNoYMGeL8q050nM6c1d+hv8ebidJKGIUGlpCjO7RMVkfb6DVWg94a/Oa4LKAwCJl5pJmLuJ17pmVN2kumGSjNRGlGin0zyIY3Eq3OpcRpJFrt3lsSrHai4xeAbGgpuXcovc6cVSc66m1Ev7/+Dv09wkoY9ITaiAa71UY0qKfnEkETyD/2ZObRV7/6VXvmmWfswIEDsVj+oyWNmnESCvwgSKl7sjTLGdXnljo3GoiRYq6ii2DpeeXfy7xz5073lmhJ/Tso8IOgeIMX+ahOzJ5MIB0zmXmiTrMCZv/+/Z2D1qNOSxm9gKkljnPnzqXjjMCoI9DY2Ng2Eq1lplEeidbfoXaydOlS2gkCoSCmGXENwgwaNMi9NlpSZ/gJmAiSXms1QKlBcNHAZVz3+wNhxExmnnizmJ6ozmZqZHDFihXtljWx/xK5omCpJbQbNmxwglqhzkADEKw4rVZA+GlgPJeVZ5nJBNIxk5kH3iymJ6qzmf59M+rwEzCRa5rVWLdundMJ1WxHaWmp057CTO1E+6/1L5BvGpgJe+VizVimVpAlYCKXUivPKnTyGg3kFiEzD+bMmeNeanXo0CG77bbbnGM/osI7ooQKssi3KC158gZiFIa13BfIN7UVPf/CWp1Zv1d5eblz2ZtRImAiH1R5VoPjoqCp12qCJpA7hMwcS53F9ERpNlMj46lHlLBvBvmkTqj2/apTKmE84kTtZMqUKW3tZODAge4tQP6UlZU5/3qzNWGhzrx+H2/JomaVgl6yCJyMBsfr6+ud12i9VhM0gRzSnkzkzuWXX66F+B1+HDhwwP3KcGpsbEwkX4yd33X69OmJY8eOubcAhbF69eq29pMMne61hZXaTvQ5UCg7duxoayOzZs0q+Ou2fr7ahfc76fcDCsn/ml1WVtbj12zvud3RB1CMmMnMoY5mMT1hn83U7+8/A5N9MwiDioqKdkuewnCWpr9CptoJM/0oJM3W+A+kV7G2QvGWkHsz/OzlRxjoNVqrsvSarcJynKUJBI/qsjmUWlG2I2GsNKuA6S/MMG3aNAImQsX/HC30IIiCrgaNOCsWYaJOs9rF8OHDncGZfNPP91eHZqsFwiZ1ECTb5yjVZYF0hMwc8XeAO6OO6Y9//GOncxoWqQGTfTMIK52zN3PmTGbbgZBRwPRm+AmYCDN/0JRsZtsJmUA6QmaOdHUW0xOW2cw1a9ZYZWWlc5mAiSjwd2ZV9ETFRXLdmfWWVdFpRtToeBMVpcrl+42/TWrwZ968ebQVhJ6/MFV3gyYhE0jHnswc0ExgdwJm3759Q7E3Uy+wXsCk8h+iQp1XzZJotiQfe2s0EKO9ypo1BaJGx5uoWniu2ohWF/gDJnuUERXq83gVzLWaS305ANkjZOZAd1+Yjh49am+//bb7WWGkjuDpPCkgKrygqZlMdW5zFTT9AzHeURFAlCj4eW1EgTBIeu8bMWJEu4DJ8nVESWrQ1PsKgOywXDbPtKQibHd5T5aIAGESVBGHTGgniAO1ES1fVdVZCeq57N/LT8BE1Om9o7y83Lncla1DLJcF0hEy8yxMITOIze5A2OTieb1582YbP368c5l2gjjwD5o0Njb2aDDGHzDZy4+46M7zmpAJpGO5bJFKnfFRJ4OOM+JAsyeaRdFsigSxt6alpcX5l4CJuPAvCzx27JjzbzY0AEPARBzptV6v+aIBGQ3MAOg6ZjLzLAwzmblcUgiERa6WBQJo5Z8NJWAirlJnNDOdG85MJpCOmcwiQ8BEsVAnYOnSpW2zNUHMaAJoRcBEsfBmNNVn0nNefSj1pQB0jpBZRA4ePEjARNHxLwvsStBU52HGjBnOyHQuj0IBwkbvCXren2xZoD9g1tTUEDARewqaah/qO6kPRdAETo6QWSTUWdbZaHpx1NELBEwUk9Sg2VEnOnWmnzaCYjJkyBDn3872n/kDpmZ3dBQKUAz0fkDQBLqOkFkEFDD9h2OvW7eOzjOKjj9oZupEZ5rpB4rJxRdf3Gmhk9SAyR5nFBuCJtB1FP7Js3wX/kkNmJxdhmLn7yj795Jdeumlbe1EBYMYiEGx8hc6Wb16tU2ePLltAEYImCh2qX0rr210hK42ihEhM8/yGTIJmEBm/nMvFTSvu+46O/PMM2kngMsLmrfeeqsdOXKEgAmk8PexToauNooRITPPThYydXvQrrnmGnv00UfpOAM+qWXpKV4CtOffoywETKA9bbOYPXs2M5lABuzJDCG9GAXx4XniiSds9+7d7mcARJ3l1P1n7K0BWqUWwaqvrydgAik0eM/WCiAzQmbM+StqAmilZU5VVVX26quvtguaFHEAMp+nPGzYMKfNLFq0iDYCuFasWGHz5893PwPgx3LZHNDyif3797uftVdaWuqMCKfq06ePMxoW5J5N7//S/rOWlhZn7wBQ7BoaGuz666939tHojD+1C//SWfZlophlCpjeTI2/OBZtBDBn0GX9+vUn3ZdJVxvFiJCZAwsWLOj2yJbetFeuXJmTkAmglT9MLly40Clq4nWUCZoodv5CJqkBUygmB2R2snoa9MVQjFgumwNTpkxxL3XdjTfe6F7KPc20ajYHKCbPP/98W4jUMvK5c+e26yBrv1ljYyPnn6EonSxgij7njEAAQFcQMnNAe1e8c/i64vLLL89rQYVt27Y5y3ZTD9oG4uy1115z/u2skiydaBSjrgRMj9dGysrKnDaigRmgGGiAXstj16xZ414DoDMsl80RzRQqyHWFvyx8PpbLakZnxIgRzmWObkCxUEf62LFjziDQyfg73epMa0Cmo043EGXZLoHV4IsC5uDBg1kyi9jztxNttdBKGD+WywLpCJk5pFkQr7prRzSL+fvf/979LD8hUzrbmwage7M7QBRlGzCBYtKVdkLIBNKxXDaHujJDuHjxYvdSfnlnBKrzfOeddzpluIE40ZImHbmgDkI2/Etn1blQJyPb/wsIGw00Bhkw9f/1pL0BYcRADJA9QmYOnWxvZr73YqbSz/Y60YcOHXKvBaJPy1srKytt2bJlPZp91Pdu3LjR6VwQNBEX3kqWIDvO77zzjtPe1Eb0/wNxsHPnTgImkCWWy+ZYZ3sz/XsxPflaLgvElQKmN7iTqY1lI/XswLVr13ZpbycQNv6tErNmzXKO3Aqi46w2ohUxWhkjQbU9oJDUh9u7d69NmDCh03bCclkgHSEzDzLtzUzdi+khZALZy0XA9PiDptCJRtT4A2auir7lsg0CYUXIBNKxXDYPMr2RF2ovZlf0dC8bUAgacVbnVjONuejcahRby6W0bErUWWdZIKJC4S/XAVP0/3qDqhs2bHD+BaJC1fe1jQhAzzGTmSf+2cyOZjElDDOZOgdKS57UWaeiJqJCM4319fU2cODAnD5n9XOqq6uZrUFk+GcXcxkw/TZv3mwXXngh7x+IDPV3ysvLncvd7TsxkwmkI2TmiX9vZmed0jCETPafASfn77ivXr3aKioqnMtAmPifpzU1NU5hHgDt9fT1nJAJpCNk5pGC24svvmi/+93v3GvShSFkCvvPEHZazq2l3ddee23BBkEKMUMEdIVew+fNm+dUfJVCv4ZrlqilpcUmT55MhU6Eiv91PNt2QsgE0rEnM4+WLFnijCRHgToBK1euZG8NQsk7u0zLulX5r1AUKjdt2uRcVidFnRWg0LxBwrAETNGAkI4V0u+l3w8IAy3r7mnABJAZITOPFNwGDBjgfhYNXie6rKzMvQYoLBXb8R+OrdLyhTRu3DincyLqrMyYMYNONArm4MGD7bY7aJ9yGDrOGoDR76Pfi6CJsOjbt69zlM+ePXsImEDAWC4bMmFZLguEkf8IhoULF9qtt94amqV3+t30+3BwNwrFm+HXczCMhdv8v58GLhU8KQyEOGC5LJCOmUx0mzrT6rwwEo1885Ztaxn33LlzQxXiNAquduHN1kyZMoVjgJA3qQEubAFT9Pvo99IgjNryzp073VuA/NBMP30XID+YyQyZKMxkekecMFuDfFNHet++faFe1hT22STEj3+GPwqvy+rk79692y644ILIbSFBdOkMzJkzZzqvzUH3jZjJBNIRMkMmCiGTJU9A59SJ9u+LW7FiBft9kBMqXDJ+/HjnsvaWLViwgIE/IEXqQIwKGwaJkAmkY7ksus1b8qSAqSVPCpwsC0TQFNQ0a66qlFGjTr5mk9SZ0WCMOjcKA0CQNMDnBUwtIV+6dGkkA6beP6qqqiLZ1hF+el55AVPtJOiACSAzZjJDJgozmR7/bI3wVEJQ/LPlmp1R5zmqFAQ4SxNB0muvZse1bUF0NJbaS1Rpn9yZZ57pXA5bQS9Em3+mf/Xq1VZRUeFcDhozmUA6ZjKRNW+2Ri/c3nmaQE9p34wXMDUTeMcdd7i3RJNCpXc+rsKmZmcVEoBseIN7XsDU8TlRDpiifZneMUD6uzjiBEFpaGhw/tXzK1cBE0BmzGSGTJRmMoGgKWCOGDHCuRy3/WWpe4KWLFlC0RN0S9yLSqX+fRs3bqSNIBKYyQTSMZOJwGnpkzrUjESju5588knn3yjvL+uICv80Nja2HXFy9dVXs5cZXabXVP8MfxyrFuvvUbD09jLv37/fvQXoGvU/AIQDM5khE4eZTG8PBMc3oLs0MKEgNmzYMPea+FEnaPbs2W17mbWMi8qz6IxeR8vLy53LxVBBthheBxA8r+9RiH38zGQC6ZjJROAuv/zytpHowYMHOyPwQFeo4xz3jqWW/2kvswqciJbQUlUTmShsaQ+vFzDjOMOfSTG8DiA4aif+SsvDhw93/gVQWIRMBE4dhNROtN4AAD8NPmj0d+LEie41xUNtZO7cuU7RLKmsrHSOcGCJOTxaSp1a4KdYKxOreIteK2bMmMESc7SjlSFqJ14Fbwr8AOFByEROeJ1of1VNr8oboEEHrwhO1Ctj9oQ6Q+oUaWn5smXLbMqUKXSi0VZhWUuq9dzQ0tFiXlI9cODAtr3Mul90/wCive1eO6mvr2frARAi7MkMmTjsyUylDsELL7xgY8eOZX9mkUvdjxj18/2ComCpWaoNGzY4nSWdgUhnqTj5919q24FWhcR9eWxXaJbffy5zLs88RHRoBUj//v3tpptuKmglYvZkAukImSETx5AJeNQh0IydgtTDDz9sF198sXsL1In2H7Cv/XfTpk0jYBQJPf7z5s1z2ofo8S/W5bGd0f5lLS+XPXv28BqCUCBkAukImSFTLCFTHYXDhw/TiS4yqv5XV1dX8FHnMEudyVLwYAVAvDGT3T3az719+3a79tprKRBURLTl5vXXX3eKC4at30DIBNIRMkOmWEKmCjh4+yjWrl1LRwHwUWfq+uuvbzuUntARXwwqACfnbyfaexm2PgMhE0hH4R8UhDpS3jEnpaWlzhsI4kV7cbU8luM5uk8dKM3U6Lw3tRGvQjPVZ+NDj6Xah/94Eu2/JGBmR/eljnvhMP540eOZ2k50NBqA8CNkoiDUkVKHSm8YojcQzW4i+tR5ViAaMWKEs7+sX79+7i3oDi0H05mI/grNVJ+NBw3AXHHFFW37k73jSdg6kD3N/ms/s6qNcjZzPOgx1eNJOwGiiZCJgtEbhd4wVLxBbyBe1UBElzoFCkLemWVUj+053X86wqKsrMzZs6dRfGb+o0kDMJrZ1wCMZqi1mmPjxo0shQ7AqlWr2s38a1aTmf9oe/zxx9vaiV7zaCdAtLAnM2SKZU9mKi2JUehkhDK61KHr06ePc1mBSLNw7LUNju7f6urqtgDP/r1o0QCMlv1poEAYgMkN/949hU69DiGatGrj2LFjkXgfYU8mkI6QGTLFGjIz0ZKyo0ePMnoZERoouPvuu2348OE2efJkBgxyRO1i5syZzgi/EFbCTYMDjz32WNuxGwzA5J7CiWaMTz/9dI6BiQi1E63Y0EqNKL53EDKBdITMkCFknuC9aGs0+o477uDIC8ClDpn/TE1mNcMpdfZy9erVDMAAKfwDZ5s2bbJx48a5t0QHIRNIx55MhJY2+Wuvpjb9a/M/+9DCQ52CiRMn2qWXXuoEHuSXQsrcuXPb7Wf29mryeBSeHgMVv1LlbAVMzV7q2IWKigoCZoGoGJCCgEI/FWjDQY+D9s56e5TVTkaNGuXeCiDqmMkMGWYy2/OWYCpoit6E1q9f71xG/vF4hI8CjX+vph6T+fPn28UXX+x8jvzavHmz3XXXXSxnDhktofUffaHHZcKECYT+Aonbsn9mMoF0zGQi1LREVvuXvFlNzQpoCRryT53nM888sy1gqlOwbt065zIKR51k7TvTTJkCptqIZgaYsckvvS7pGKbx48c7HWct89ceMwJmOGgp+YEDB5zHRVQcSJWweT8pjEceeYR2AsQcM5lZONmIVbHI91PHWwbIyHNhaGms1ylgj2x4acmsZpv9MwTM2OSOgrw6zN5MsgbDtF+WgmXhpVk0zfZrQEZnNVMcKP/0fq5wGZcCWMxkAukImVmIwzLUngrLfaAOtaoIfu9734tksYAo0XIzobhM+GUKPhoYYLYgOOokP/XUUwT6iPJCzsCBAxkwyyHvtUiuu+662N7XhEwgHSEzC4TM8NwHCpj+owE0y8YMQs9o+ZgKybz33nu2ZMkSOmAR5j2W/j20tJGeyRQuFy5caDfddBNtJeK8Gc6rrroq1oEoH9RO/Ef3iM68jOsADCETyEAhE93D3Rau+2DHjh2JZOfZ+Z30ocv19fXuregq3WfJANJ2P375y192b0HU6bFNbSNqN+i6ZAc5UVNT47QL735Ue+G1Jj727NnT9tjq47777kscOHDAvRVdVYztxP+8yfQBFCOe+VngBSOc94H/jU1vaug6f7jUhzpX6lQjXjINyOg6HuuOES6LS+pgmz42bdrk3oqTaWxsLMp24n++ZPoAihHLZbPActnw3gdaorN792674IIL0pY6aW8Iy5/S6X5R1dhkJ9opgPHNb36T+ynmdGagltCq8InosdeezTFjxvDYu7y9ZFqS7y2LTXaabfr06bEpVoKO+Zea6zFfuXKlews6470Hn3XWWUXVTlguC6QjZGaBkBm9+8CrjKq9U9/4xjeK9gxBFe/ZuXOnDR8+vF0HQB0DoWBJcdEeNAUpb8+mqNqmimgVa5DKdJ/odePaa68lXBYhvWb6i515Iero0aN2+eWXF+Vrpu6DZ555xh588EFnoEpHjBX7Pm9CJpCOkJkFQmb07gN/gSApKytzKm0Ww6yd1yFQEQaNzIs6zXPnznUuA5q10TmoXjVaURtR1eZRo0bFvo1o1vLXv/61U63aP7tbUVFBARi0o9fTPn36uJ+1DsqMHj26KAYuM71OqJ2o3RR71XFCJpCOkJkFQmY07wOvI3n//fe3qwoZ57ClDoEOh/dTp2jixIkcRYI0aiPbtm1zBmW8sCVaJqrQeckll8Rm5kZ/a11dXbvBF9HSyBtvvDFWfyuCpdnuBx54oN3zRmFr48aNsR2QUHvRtgoP7aQ9QiaQjpCZBUJm9O8DdRKefPJJu+KKK9ot8/E62VpeG7UQpt9db/b+N3wFao060yFAd3mzFv49iaLAqSMeojjD6S0X1xEkqQFB+5HHjh3L4Au6TK+5/hnw1GWjmV6Tw04ztfX19c5yYP/fouurq6vt9NNPp51kQMgE0hEys0DIjO99sGjRIrvzzjudy+p4asZPnekLL7wwdG+q6sC89NJLtmfPHnv66aedTo5+5+3bt7fr1KhzQLBEtvT80R40Pa+8tuHR7KYC54gRIzIW2yo0hcp9+/Y5bSQ1LKutaDlssSx1RG6lvs5qIFPtQjTIN2HCBGcv/ODBg0P3eqwBpb1799of/vCHdnuR2WvZdYRMIB0hMwuEzPjeB+qUrl+/PmOHNExLoTRyXl5e7n52Qk1NjbPXFMgVdZ7V+fQGNvwUOrUK4Pzzz3c61AMHDsxbm9GgyxtvvGGvvfaa01nWigR/GxZvL/ZXvvIVivggpxQ6b7nllnYz5p7GxsbQDFpmei/xQjHvJV1HyATSETKzQMgsjvtAgfNPf/qTs29LS4SmTZvWNgKtDu3UqVOdTrY6ruqwqlPdr1+/Hi219ZbziTrK7733ntNJSd076nUMtHRRHebUarFAPqgdqH3oQ8/b1NDp0fO0f//+TviUIUOGtBVP6UoQVbs4duyYc1n/KkiKv41kEvaZVsSftxJAs+l//OMfnY+1a9e2vV7rua2l2k1NTc4RQv52oqCX7aynlrq3tLQ4/68GX7xBl9T3Eq+a8uc+9znaSQ8QMoF0hMwsEDK5D2TGjBkZO7ea9fSCoqgToRHh1FkVSV2O5B21kopqsIiC1NlELcPrKHgGTbMvf/3Xf902ixrGZYlAKoVQ1QbI9Lq/evVqZ0m3p6qqqm05a9++fZ19k6Ln/r333tv2fFe7Ky0tdS6n2rRpk3NEEYJFyATSETKzQMDiPvDTG7poT4tolsa/x6s7IVOjyt4szdlnn+0caE1nGVGX2kZefvllO3TokHO5s5lIjzrRZ5xxhnNZMy6DBg1yVg2ce+65zowoRUgQdRqg2b9/v73++uvODKRoZtM/q+gVchN/yFTFcM2G+nkzmbST/CBkAukImVkgYHEfAAAACCETSNfb/RcAAAAAgB4jZAIAAAAAAkPIBAAAAAAEhpAJAAAAAAgMIRMAAAAAEBhCJgAAAAAgMIRMAAAAAEBgCJkAAAAAgMAQMgEAAAAAgSFkAgAAAAACQ8gEAAAAAASGkAkAAAAACAwhEwAAAAAQGEImAAAAACAwhEwAAAAAQGAImQAAAACAwBAyAQAAAACBIWQCAAAAAAJDyAQAAAAABIaQCQAAAAAIDCETAAAAABAYQiYAAAAAIDCETAAAAABAYAiZAAAAAIDAEDIBAAAAAIEhZAIAAAAAAkPIBAAAAAAEhpAJAAAAAAgMIRMAAAAAEBhCJgAAAAAgMIRMAAAAAEBgCJkAAAAAgMAQMgEAAAAAgSFkAgAAAAACQ8gEAAAAAASGkAkAAAAACAwhEwAAAAAQGEImAAAAACAwhEwAAAAAQGAImQAAAACAwBAyAQAAAACBIWQCAAAAAAJDyAQAAAAABIaQCQAAAAAIDCETAAAAABAYQiYAAAAAIDCETAAAAABAYAiZAAAAAIDAEDIBAAAAAIEhZAIAAAAAAkPIBAAAAAAEhpAJAAAAAAgMIRMAAAAAEBhCJgAAAAAgML0SSe7lgunVq5d7CQAAAAAQZieLkKEImQAAAACAeGC5LAAAAAAgMIRMAAAAAEBgCJkAAAAAgMAQMgEAAAAAgSFkAgAAAAACQ8gMk4932fLzelmvXudZZW2je6U0Wm3lec5RL+ct32Ufu9cmv8Gaa29yru913nLbdeIGAAAAACgIQiY6cdgafrvCKqfVWrN7DQAAAAB0hpCJDrTYruVlVjruNlvDDCkAAACALiJkhskpI+32VxKWSLxiqycNdq8EAAAAgOggZAIAAAAAAkPIBAAAAAAEpghC5nFradhmtY8vt8pBqtzqfYy32atqbWvDYffrMvnImnc9aY8vr7RBbd+X/BhUacsf33CS75XM3z+ocrk9vrXBWtyvatNhddme6OjvT358bbatqt1mDS3H3a8Vr2LtaTZq1rbWq9aUu79/pt8ry/u3udYqna+7yWqbD7YWGGr7/kH2tbm/tWb/rwUAAAAgEmIeMg/by6tm2LDSr1n55Fm2pl2J1M22dFq5XVl6mVWu2pse+Jzv/a6NHPW3NnnWmvbVVZvX2KzJEzv53qSWl6129jU2KMP3N6+ZZZOvHGPX5DpIHW+2nSv+sYO/P2nbUptW/jUrveantrX5I/fK7ujJ/es5Yg3/OsvGqMCQ7/s/dd5gO5t5dgAAACByYtyNVwC61cZOW5UMeCU2pqrattS/b4mECut8Ykfqt1h11bjk1+21NdOm2M3tgtBxa9lVbd91vne4VSzbaPVHPnG/N2GfND1nv2j73p/Yrxo+bP02z/F9VvvDyVa+dHPyk5TvP1Jvm5dVJH+jZtu2uNKuu2dnJwGsJz6yt9YvtIm3KeCOs6rqLR38DUnb5tv1/2dH8h6TU6xk0kPJrzlidcvGONdYRY01Od/nL0jUk/vX7xGbM+spK62qcX+/P1tT3VpbNGEIa7kBAACAKEqGglj6pL46kYw4CbOSxJg5mxNNn7g3+H3yZmLLnHHJr9HXTU5U13/g3nAkkQxYrdePq07UZ/re97ckqkpa//9x1S8lTnzJJ4kjdfckkvGs9Wcvey75v6V6N7GlamTr/18yJ7Hlffe7/1KXWDZU3zc0UVHzRut1jjcSNRVDna8fuqwu8Rf32uQ3JJpqvtP6/wxdlqg7cUO73y/z75D0yUuJ6nEl6b+Hw3cfVNQkkiGznZ7dv0lNNYkK5/pMPxsAAABAVMV0suhDe2XHRtM8opXcaD+640oryfSX9v4fNvaO2ZYMY0k77NEdr1va6tUXX7E32+1ZdJ0+1pY0adauyTZNPd8363bQdv7qX83ZzaifPXOU9XOu9xtoX/3W39tQXWzebJvqDjrXBue4Ha572n7pLD8dbTf83Rcz/A5Jvc+xL329tPVy80E7dLSra3cDvH+TSm64ykadzrwlAAAAEAfx7Nkff912PLrDuXjSAHP6F238DSOTF5pt86P/115xUlAf+5+X/C9zslHzYruybI6tqu1KoZ+kj/fZ7ppdrZe/Psou6OBnnzLydnvFWVpaZ0vGDnSvDUrvZAZe5C5x/ZVNHXaqe32qU+y0AWe5l7uhx/evX4ldVDoocwgGAAAAEDkxDZlH7eCrrVVk+pz1mWRk7Myp9pmzTmu9+OpBO+KEoGRIG3OzrZ3j7VlUgRwV+vmM9ep1kVUuf8RqN+zKXLTn2Pv27rHWi0Mv+rxlEeFyqLXabW1tbfLjcVs1u8xKpz3m3tYNPb5//frYX/XvG9MnIgAAAFB8Yt63H2qXDfmsneJ+ltmpNmiIu2TUT0s9Fz1m9Vv+zZZVDHevlL22ZtY/WPnEUTbovylwbmp/BMjRQ/Z2uyqrhXTYGrY+assrL3KPBvnvTrXb8vLy5Mdkm+YUJuqJHty/AAAAAGIp5iHzVXv2tf9nH7ufZfahNb1W715OdboNG/ttu331i5b4pMnq1tdYTXWVuTVXkxQ4r7YxP1xvb2Wa1Syk42/Z1rmTrfTKv7dZa/a6VyaNqbLqmuTfUbPettS/Y/XVk90bstHT+xcAAABA3MQzZPbuawOGOjsq7di775u7erUDH9r77x5pvTh0gJ3W0T3Su8RGlk2ySVOX2O/aHdFh1rxqkd27bb9z2c76vF3kVPRJRrAX99m7rRczaLTayvNaZxjHr7KGQEOqji9ZbNcv1kzlOKv6xXPW9In2ZyY/frfEpk5K/h2TymzssD525GDHv2GHcnH/AgAAAIiFmIbMc230t0c7F5t/+bTVHe4kwR1+wTb9UoV6Smzct/+3nad75ONdtvw8LS8dZONXvZyhImpv6zdsrE2906ucesjePvSBc4ud8nm7pFyFbpJ+W2cvdfSzD/+nPffbV5MXfD83MO/Ycxs2mlbtllTNtjsrL81c/fX4m/bH32Yxy9jT+xcAAABAbMW0y3+qnTf6anPmGZt/YT+9e0vmIj1aUnr3ElvqHvXx7dHntt4hbUGx2Tb/8inbk+kIk6Tjb79uzzvfO9gu+vwZznVmA+zSb/1D65Ja/eyH66zFud7vkO16+J70n5tXH1nztkftl5u7sIH07UMpBXt6eP8CAAAAiK3Y9vl7D7vW/ql6qpUkg+K2xZV23ZxVviNIjltLw1ZbNWeqXeksKR1uFdU/tm+1HfUx0MbcMtemapZy2212zc33WO2uZt+MpgrqrLI537mr9azIcTfY343wDuHobf1GfMt+5FSmTf7sWdPsZn9xoOPNtmv1Yrt91m+Sn5TYmGW3+35uUM6y4Vdc4lxqXvpD+8GKZ30hUH/7Nnt8+QwbeeX81vM8HfX2WtOH7mXxFex5cbftbf4oeaHFmptbI3PP7l8AAAAAsZWItfcTL1VPTSSzYkJ/auaP4YmK6hcTR9zvOOHPiaYt8xNjMn6P72PM/MSWpj+73+Nz5KVETdW4zN/jfJQkxszZnGj6xP16+UtdYtlQ3TY0UVHzhnulvJGoqRjqfN/QZXWJv7jXJr8h0VTzndb/b+iyRN2JG5I//8VEdcVw92dl+kj+/Ko1iee23J9IxuHk5yMTVVvedb+51Sf11e5tJz7a//we3L9NNYkK5/bUvxUAAABAlMV89eLpdv7UldZQ/7uUqrBJJRW27LHfWF3TLls9dbh585AnfMpKxs6zLU11tv6xZVbRWufGVWJjqh62mvV11rRlno0t+ZR7vU+/823Skiesqe439tiyiuR3eFq/d33dLtuy6OuZ90oGod9wm/ovm61u/cNWNcb/y4+zqurHWn/+khvs0jHftO8k/36zXfbLTS+YNxcpvYddb7+oW9Pu+9sXM+rJ/QsAAAAgjnopabqXAQAAAADoEeqwAAAAAAACQ8gEAAAAAASGkAkAAAAACAwhEwAAAAAQGEImAAAAACAwhEwAAAAAQGAImQAAAACAwBAyAQAAAACBIWQCAAAAAAJDyAQAAAAABIaQCQAAAAAIDCETAAAAABAYQiYAAAAAIDCETAAAAABAYAiZAAAAAIDAEDIBAAAAAAEx+//FiA+86hvq5gAAAABJRU5ErkJggg==\" style=\"margin-right: auto; margin-left: auto; display: block;\" width=\"521\"/></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">Point X (not shown) is a point on the string at a distance of 10 cm from the oscillator.</span></span></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Calculate, in m s<sup>–1</sup>, the speed for this wave.</span></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Calculate, in Hz, the frequency for this wave.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">The graph also shows the displacement of two particles, P and Q, in the medium at <em>t</em> = 0. State and explain which particle has the larger magnitude of acceleration at <em>t</em> = 0.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">State the number of all other points on the string that have the same amplitude and phase as X.</span></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">c(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">The frequency of the oscillator is reduced to 120 Hz. On the diagram, draw the standing wave that will be formed on the string.</span></p>\n<p><img src=\"data:image/png;base64,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\"/></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">c(ii).</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><em>v = </em><span style=\"background-color: #ffffff;\">«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mn>0</mn><mo>.</mo><mn>05</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>20</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow></mfrac><mo>=</mo></math>» 250 «m s<sup>–1</sup>»✔</span></p>\n<div class=\"question_part_label\">a(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color: #ffffff;\"><em>λ </em>= 0.30 «m» ✔<br/><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>f</mi></math> = «<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mn>250</mn><mrow><mn>0</mn><mo>.</mo><mn>30</mn></mrow></mfrac><mo>=</mo></math>» 830 «Hz» ✔</span></p>\n<p><em>NOTE: </em><em><span style=\"background-color: #ffffff;\">Allow ECF from (a)(i)<br/>Allow ECF from wrong wavelength for MP2</span></em></p>\n<div class=\"question_part_label\">a(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Q ✔<br/>acceleration is proportional to displacement «and Q has larger displacement» ✔</span></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color: #ffffff;\">3 «points» ✔</span></p>\n<div class=\"question_part_label\">c(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color: #ffffff;\">first harmonic mode drawn ✔</span></p>\n<p><span style=\"background-color: #ffffff;\"><img src=\"data:image/png;base64,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\"/></span></p>\n<p><em><span style=\"background-color: #ffffff;\">NOTE: Allow if only one curve drawn, either solid or dashed.</span></em></p>\n<div class=\"question_part_label\">c(ii).</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c(ii).</div>\n</div>",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-1-simple-harmonic-motion",
      "c-2-wave-model",
      "c-4-standing-waves-and-resonance"
    ]
  },
  {
    "question_id": "19N.2.SL.TZ0.4",
    "Question": "<div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">A proton is moving in a region of uniform magnetic field. The magnetic field is directed into the plane of the paper. The arrow shows the velocity of the proton at one instant and the dotted circle gives the path followed by the proton.</span></p>\n<p><span style=\"background-color: #ffffff;\"><img 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\"/></span></p>\n</div><div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">The speed of the proton is 2.0 × 10<sup>6</sup> m s<sup>–1</sup> and the magnetic field strength <em>B</em> is 0.35 T.</span></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Explain why the path of the proton is a circle.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Show that the radius of the path is about 6 cm.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Calculate the time for <strong>one</strong> complete revolution.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Explain why the kinetic energy of the proton is constant.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color: #ffffff;\">magnetic force is to the left «at the instant shown»<br/><em><strong>OR</strong></em><br/>explains a rule to determine the direction of the magnetic force ✔</span></p>\n<p><span style=\"background-color: #ffffff;\">force is perpendicular to velocity/«direction of» motion<br/><em><strong>OR</strong></em><br/>force is constant in magnitude ✔</span></p>\n<p><span style=\"background-color: #ffffff;\">force is centripetal/towards the centre ✔</span></p>\n<p><em><span style=\"background-color: #ffffff;\">NOTE: Accept reference to acceleration instead of force</span></em></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>q</mi><mi>v</mi><mi>B</mi><mo>=</mo><mfrac><mrow><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup></mrow><mi>R</mi></mfrac></math><span style=\"background-color: #ffffff;\">✔</span></p>\n<p><span style=\"background-color: #ffffff;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>R</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>27</mn></mrow></msup><mo>×</mo><mn>2</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow><mrow><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>35</mn></mrow></mfrac></math> <em><strong>OR</strong></em> 0.060 « m »</span></p>\n<p><em><span style=\"background-color: #ffffff;\">NOTE: Award MP2 for full replacement or correct answer to at least 2 significant figures</span></em></p>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi mathvariant=\"normal\">π</mi><mi>R</mi></mrow><mi>v</mi></mfrac></math><span style=\"background-color: #ffffff;\">✔</span></p>\n<p><span style=\"background-color: #ffffff;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mn>2</mn><mi mathvariant=\"normal\">π</mi><mo>×</mo><mn>0</mn><mo>.</mo><mn>06</mn></mrow><mrow><mn>2</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfrac><mo>=</mo><mn>1</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>7</mn></mrow></msup></math> « s » ✔</span></p>\n<p><em><span style=\"background-color: #ffffff;\">NOTE: Award <strong>[2]</strong> for bald correct answer</span></em></p>\n<div class=\"question_part_label\">b(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color: #ffffff;\"><em><strong>ALTERNATIVE 1</strong></em><br/>work done by force is change in kinetic energy ✔<br/>work done is zero/force perpendicular to velocity ✔ <br/></span></p>\n<p><span style=\"background-color: #ffffff;\"><em>NOTE: Award <strong>[2]</strong> for a reference to work done is zero hence E<sub>k</sub> remains constant</em><br/></span></p>\n<p> </p>\n<p><span style=\"background-color: #ffffff;\"><em><strong>ALTERNATIVE 2</strong></em><br/>proton moves at constant speed ✔<br/>kinetic energy depends on speed ✔<br/></span></p>\n<p><span style=\"background-color: #ffffff;\"><em>NOTE: Accept mention of speed or velocity indistinctly in MP2</em><br/></span></p>\n<p> </p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion",
      "d-fields"
    ],
    "subtopics": [
      "a-2-forces-and-momentum",
      "a-3-work-energy-and-power",
      "d-3-motion-in-electromagnetic-fields"
    ]
  },
  {
    "question_id": "19N.2.SL.TZ0.5",
    "Question": "<div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">An electron is placed at a distance of 0.40 m from a fixed point charge of –6.0 mC.</span></p>\n<p style=\"text-align: center;\"> </p>\n<p style=\"text-align: center;\"><img src=\"data:image/png;base64,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\"/></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Show that the electric field strength due to the point charge at the position of the electron is 3.4 × 10<sup>8</sup> N C<sup>–1</sup>.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Calculate the magnitude of the initial acceleration of the electron.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Describe the subsequent motion of the electron.</span></p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">b(ii).</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>E</mi><mo>=</mo><mfrac><mrow><mi>k</mi><mo>×</mo><mi>q</mi></mrow><msup><mi>r</mi><mn>2</mn></msup></mfrac></math> <span style=\"background-color: #ffffff;\">✔</span></p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>E</mi><mo>=</mo><mfrac><mrow><mn>8</mn><mo>.</mo><mn>99</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup><mo>×</mo><mn>6</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow><mrow><mn>0</mn><mo>.</mo><msup><mn>4</mn><mn>2</mn></msup></mrow></mfrac></math>  <em><strong>OR  <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>E</mi><mo>=</mo><mn>3</mn><mo>.</mo><mn>37</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">N</mi><mo> </mo><msup><mi mathvariant=\"normal\">C</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> </strong></em><strong><span style=\"background-color: #ffffff;\">✔</span></strong></p>\n<p><em>NOTE: <span style=\"background-color: #ffffff;\">Ignore any negative sign.</span></em></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>F</mi><mo>=</mo><mi>q</mi><mo>×</mo><mi>E</mi><mo> </mo></math><em><strong> OR  <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>F</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup><mo>×</mo><mn>3</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup><mo>=</mo><mn>5</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">N</mi><mo>»</mo></math> </strong></em><strong><span style=\"background-color: #ffffff;\">✔</span></strong></p>\n<p><strong><span style=\"background-color: #ffffff;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>a</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mn>5</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup></mrow><mrow><mn>9</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>31</mn></mrow></msup></mrow></mfrac><mo>=</mo><mo>»</mo><mo> </mo><mn>5</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>19</mn></msup><mo>«</mo><mo> </mo><mi mathvariant=\"normal\">m</mi><mo> </mo><msup><mi mathvariant=\"normal\">s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>»</mo></math><span style=\"display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: bold;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;\">✔</span></span></strong></p>\n<p><em><span style=\"background-color: #ffffff;\">NOTE: Ignore any negative sign. <br/>Award <strong>[1]</strong> for a calculation leading to </span></em><span style=\"background-color: #ffffff;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>a</mi><mo>=</mo><mo>«</mo><mo> </mo><mi mathvariant=\"normal\">m</mi><mo> </mo><msup><mi mathvariant=\"normal\">s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>»</mo></math></span><em><span style=\"background-color: #ffffff;\"><br/>Award <strong>[2]</strong> for bald correct answer</span></em></p>\n<p> </p>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color: #ffffff;\">the electron moves away from the point charge/to the right «along the line joining them» ✔<br/>decreasing acceleration ✔<br/>increasing speed ✔</span></p>\n<p><em><span style=\"background-color: #ffffff;\">NOTE: Allow ECF from MP1 if a candidate mistakenly evaluates the force as attractive so concludes that the acceleration will increase</span></em></p>\n<div class=\"question_part_label\">b(ii).</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b(ii).</div>\n</div>",
    "topics": [
      "a--space-time-and-motion",
      "d-fields"
    ],
    "subtopics": [
      "a-2-forces-and-momentum",
      "d-2-electric-and-magnetic-fields"
    ]
  },
  {
    "question_id": "19N.2.SL.TZ0.7",
    "Question": "<div class=\"specification\">\n<p><span style=\"background-color: #ffffff;\">A stationary nucleus of uranium-238 undergoes alpha decay to form thorium-234.</span></p>\n<p><span style=\"background-color: #ffffff;\">The following data are available.</span></p>\n<p style=\"text-align: left; padding-left: 30px;\"><span style=\"background-color: #ffffff;\">Energy released in decay                         4.27 MeV<br/>Binding energy per nucleon for helium      7.07 MeV<br/>Binding energy per nucleon for thorium    7.60 MeV</span></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Radioactive decay is said to be “random” and “spontaneous”. Outline what is meant by each of these terms.</span></p>\n<p><span style=\"background-color: #ffffff;\">Random: </span></p>\n<p><span style=\"background-color: #ffffff;\">Spontaneous:</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Calculate the binding energy per nucleon for uranium-238.</span></p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span style=\"background-color: #ffffff;\">Calculate the ratio <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mi>kinetic</mi><mo> </mo><mi>energy</mi><mo> </mo><mi>of</mi><mo> </mo><mi>alpha</mi><mo> </mo><mi>particle</mi></mrow><mrow><mi>kinetic</mi><mo> </mo><mi>energy</mi><mo> </mo><mi>of</mi><mo> </mo><mi>thorium</mi><mo> </mo><mi>nucleus</mi></mrow></mfrac></math>.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b(ii).</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color: #ffffff;\"><em>random:</em><br/>it cannot be predicted which nucleus will decay<br/><em><strong>OR</strong></em><br/>it cannot be predicted when a nucleus will decay ✔<br/></span></p>\n<p><span style=\"background-color: #ffffff;\"><em>NOTE: OWTTE</em><br/></span></p>\n<p> </p>\n<p><span style=\"background-color: #ffffff;\"><em>spontaneous:</em><br/>the decay cannot be influenced/modified in any way ✔<br/></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: italic;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;\">NOTE: </span><span style=\"display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: italic;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;\">OWTTE</span><br/></span></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color: #ffffff;\">234 × 7.6  <em><strong>OR </strong></em> 4 × 7.07 ✔</span></p>\n<p><em>BE</em><sub>U </sub>=<span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\">« 234<span style=\"display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;\"> ×</span> 7.6<span style=\"display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;\"> + 4 × 7.07 – 4.27 =</span>» <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>1802</mn></math> « MeV » ✔</span></span></p>\n<p><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mi>B</mi><msub><mi>E</mi><mi mathvariant=\"normal\">U</mi></msub></mrow><mi>A</mi></mfrac><mo>=</mo><mo>«</mo><mfrac><mn>1802</mn><mn>238</mn></mfrac><mo>=</mo><mo>»</mo><mo> </mo><mn>7</mn><mo>.</mo><mn>57</mn></math> <span style=\"display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;\">« MeV » ✔</span></span></span></p>\n<p><span style=\"font-size: 14px;\"><em><span style=\"background-color: #ffffff;\"><span style=\"background-color: #ffffff;\"><span style=\"text-align: left;color: #000000;text-indent: 0px;letter-spacing: normal;font-family: Verdana,Arial,Helvetica,sans-serif;font-variant: normal;font-weight: 400;text-decoration: none;display: inline !important;white-space: normal;float: none;background-color: #ffffff;\"> NOTE: Allow ECF from MP2<br/>Award <strong>[3]</strong> for bald correct answer<br/>Allow conversion to J, final answer is 1.2 <span style=\"display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;\">×</span> 10<sup>–12</sup></span></span></span></em></span></p>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span style=\"background-color: #ffffff;\">states or applies conservation of momentum ✔</span></p>\n<p><span style=\"background-color: #ffffff;\">ratio is «<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><msub><mi>E</mi><mrow><mi mathvariant=\"normal\">k</mi><mi>α</mi></mrow></msub><msub><mi>E</mi><mi>kTh</mi></msub></mfrac><mo>=</mo><mfrac><mstyle displaystyle=\"true\"><mfrac><msup><mi>p</mi><mn>2</mn></msup><mrow><mn>2</mn><msub><mi>m</mi><mi>α</mi></msub></mrow></mfrac></mstyle><mstyle displaystyle=\"true\"><mfrac><msup><mi>p</mi><mn>2</mn></msup><mrow><mn>2</mn><msub><mi>m</mi><mi>Th</mi></msub></mrow></mfrac></mstyle></mfrac><mo>=</mo><mfrac><mn>234</mn><mn>4</mn></mfrac></math>» 58.5 <span style=\"display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;\">✔</span><br/></span></p>\n<p><em> NOTE: Award<strong> [2]</strong> for bald correct answer</em></p>\n<div class=\"question_part_label\">b(ii).</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b(ii).</div>\n</div>",
    "topics": [
      "a--space-time-and-motion",
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "a-3-work-energy-and-power",
      "e-3-radioactive-decay"
    ]
  },
  {
    "question_id": "20N.3.SL.TZ0.1",
    "Question": "<div class=\"specification\">\n<p><span class=\"fontstyle0\">A spherical soap bubble is made of a thin film of soapy water. The bubble has an internal air pressure <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>P</mi><mi mathvariant=\"normal\">i</mi></msub></math></span><em><span class=\"fontstyle0\"> </span></em><span class=\"fontstyle0\">and is formed in air of constant pressure </span><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>P</mi><mi mathvariant=\"normal\">o</mi></msub></math><span class=\"fontstyle0\">. The theoretical prediction for the variation of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfenced><mrow><msub><mi>P</mi><mtext>i</mtext></msub><mo>-</mo><msub><mi>P</mi><mtext>o</mtext></msub></mrow></mfenced></math></span><span class=\"fontstyle0\"> is given by the equation</span></p>\n<p style=\"text-align: center;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>(</mo><msub><mi>P</mi><mi mathvariant=\"normal\">i</mi></msub><mo>-</mo><msub><mi>P</mi><mi mathvariant=\"normal\">o</mi></msub><mo>)</mo><mo>=</mo><mfrac><mrow><mn>4</mn><mi mathvariant=\"normal\">g</mi></mrow><mi>R</mi></mfrac></math></p>\n<p style=\"text-align: left;\"><span class=\"fontstyle0\">where </span><span class=\"fontstyle2\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>γ</mi></math> </span><span class=\"fontstyle0\">is a constant for the thin film and </span><span class=\"fontstyle3\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>R</mi></math> </span><span class=\"fontstyle0\">is the radius of the bubble.</span></p>\n<p style=\"text-align: left;\">Data for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfenced><mrow><msub><mi>P</mi><mtext>i</mtext></msub><mo>-</mo><msub><mi>P</mi><mtext>o</mtext></msub></mrow></mfenced></math><span class=\"fontstyle0\"> and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>R</mi></math>  were collected under controlled conditions and plotted as a graph showing the variation of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfenced><mrow><msub><mi>P</mi><mtext>i</mtext></msub><mo>-</mo><msub><mi>P</mi><mtext>o</mtext></msub></mrow></mfenced></math> with <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mn>1</mn><mi>R</mi></mfrac></math>.<br/> </span></p>\n<p style=\"text-align: left;\"><span class=\"fontstyle0\"><img height=\"662\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA2MAAALZCAYAAAA6F/muAAAgAElEQVR4Aey9iZdf11Xnmz/FsjXYDknoDEAn6RcIizCEOCYTAZp+dILDAwI0L716NaxmaN4CmgWPMDQ0zesQx5ZlyZZkWdZUqnlQzaUaNJVUmkpjqVSa58nnrc/96fzO994693eu24qsKu29Vkn1u79d33vO9wz7nHvP3vt9zsQYMAaMAWPAGDAGjAFjwBgwBowBY+ChM/C+h35Hu6ExYAwYA8aAMWAMGAPGgDFgDBgDxoCzzZh1AmPAGDAGjAFjwBgwBowBY8AYMAbeAwZsM/YekG63NAaMAWPAGDAGjAFjwBgwBowBY8A2Y9YHjAFjwBgwBowBY8AYMAaMAWPAGHgPGLDN2HtAut3SGDAGjAFjwBgwBowBY8AYMAaMAduMWR8wBowBY8AYMAaMAWPAGDAGjAFj4D1gwDZj7wHpdktjwBgwBowBY8AYMAaMAWPAGDAGbDNmfcAYMAaMAWPAGDAGjAFjwBgwBoyB94CBhpuxAwcOuC9/4Yv2YxxYH7A+YH3A+oD1AesD1gesD1gfsD5gfeAd9IGbN28mt3cNN2NtrW3u1371BTc8NGQ/xoH1AesD1gesD1gfsD5gfcD6gPUB6wPWByr0gec++7Pu5IkT724z1tLc7F742teTIKZgDBgDxoAxYAwYA8aAMWAMGAPGgDFQY+BTn/ikO3bsWJKOhm/GbDOW5M8UjAFjwBgwBowBY8AYMAaMAWPAGMgxYJuxHB32wRgwBowBY8AYMAaMAWPAGDAGjIGHw4Btxh4Oz3YXY8AYMAaMAWPAGDAGjAFjwBgwBnIM2GYsR4d9MAaMAWPAGDAGjAFjwBgwBowBY+DhMGCbsYfDs93FGDAGjAFjwBgwBowBY8AYMAaMgRwDthnL0WEfjAFjwBgwBowBY8AYMAaMAWPAGHg4DNhm7OHwbHcxBowBY8AYMAaMAWPAGDAGjAFjIMeAbcZydNgHY8AYMAaMAWPAGDAGjAFjwBgwBh4OA7YZezg8212MAWPAGDAGjAFjwBgwBowBY8AYyDFgm7EcHfbBGDAGjAFjwBgwBowBY8AYMAaMgYfDgG3GHg7PdhdjwBgwBowBY8AYMAaMAWPAGDAGcgzYZixHh30wBowBY8AYMAaMAWPAGDAGjAFj4OEwYJuxh8Oz3cUYMAaMAWPAGDAGjAFjwBgwBoyBHAO2GcvRYR+MAWPAGDAGjAFjwBgwBowBY8AYeDgM2Gbs4fBsdzEGjAFjwBgwBowBY8AYMAaMAWMgx4BtxnJ02AdjwBgwBowBY8AYMAaMAWPAGDAGHg4Dthl7ODzbXYwBY8AYMAaMAWPAGDAGjAFjwBjIMWCbsRwd9sEYMAaMAWPAGDAGjAFjwBgwBoyBh8OAbcYeDs92F2PAGDAGjAFjwBgwBowBY8AYMAZyDNhmLEeHfTAGjAFjwBgwBowBY8AYMAaMAWPg4TBgm7GHw7PdxRgwBowBY8AYMAaMAWPAGDAGjIEcA7YZy9FhH4wBY8AYMAaMAWPAGDAGjAFjwBh4OAzYZuzh8Gx3MQaMAWPAGDAGjAFjwBgwBowBYyDHgG3GcnTYB2PAGDAGjAFjwBgwBowBY8AYMAYeDgO2GXs4PNtdjAFjwBgwBowBY8AYMAaMAWPAGMgxYJuxHB32wRgwBowBY8AYMAaMAWPAGDAGjIGHw4Btxh4Oz3YXY8AYMAaMAWPAGDAGjAFjwBgwBnIM2GYsR4d9MAaMAWPAGDAGjAFjwBgwBowBY+DhMGCbsYfDs93FGDAGjAFjwBgwBowBY8AYMAaMgRwDthnL0WEfjAFjwBgwBowBY8AYMAaMAWPAGHg4DNhm7OHwbHd5ZBm45+YGv+P+05c/5T6yYoX7wId/zH31d/7GbT98o1qJbxx2W/786+6nP/q0W778g+5TX/hd97/6Zt2deX99wx3Z/Ofuhc98zL3/yRXuBz/xRfetf+5zs/MV5/2lXTAGjAFjwBgwBowBY8AYWJwM2GZscbar1aoiA9d3/pV77pml7oe+/Efu5S2trvm1b7tf/9Fn3PKP/rp749S9xij3TrsNL/wrt/QDX3B/srrD9fducf/0659yzzz5Y+7/6bsif3vPnX7jBffRJz7ovvTHq11nX6/b+o+/4T697Cn34/+136mm/JH9agwYA8aAMWAMGAPGgDGwyBmwzdgib2CrXgMG7p1yq/7ts275x3/PdV0Oercn/tL91FPL3M/940F3N1ye99uNvv/i/vUTH3K/teVC+O7OtHvpKyvc8s/+kzvi93I3+twffmyJ+/BvbnFB846bfvEr7tknf9b9z8NeMcDYb8aAMWAMGAPGgDFgDBgDi58B24wt/ja2GpYxcLPP/eXnP+l+8o963E3RuXvwH9zzS5e6n/nrPZHjhl7xthv4g4+4pT/wu67tur/G/2+7udf/nXv6ic+6fzpU22Td7v9D90NPfMB9qzWn6N6eW+t+ZekS99w/HlIA+90YMAaMAWPAGDAGjAFj4DFhwDZjj0lDWzXTDNy7eckdG1nv/uzLH3HLP/RL7qWDDd6L3TvlXv7Sk27Z5/4/d7TwYuvuzj91n3xihfutbdecc/fcqZe+7JYtec59p/6q7H5Z7o66P/uRJe7Z39yWLpxpGAPGgDFgDBgDxoAxYAwsOgZsM7bomtQq9L/FwNWN7jeeXuKWPrHELV3+o+5bG465242A7u51f/2pJe7pX1kvRw9rf3Dv8P9wzz3xlPvFV8445+66vX/1o27p0n/v3ghnFL2i+6efWeKW//yqRndy169fd7/01V9wX/j88/N+nv/cc+5HPvpDbvfuvXWMrdu2u41vbXEzM9y/JuvWv+nWr9/oP7ojR45mOm3tXfVrwyOjbs2adW5iYnf9WtP21kzv5MlT9WtgrROs6eljmU5rW0ddZ+fOsQxrbGyifq25uS3TO378RP3a2nUb3OtrN9Q/Hzt2PNNpbmmvXxsdm8iwdo6O1a+1tHZketzbC/WjbF4oMzxQBy/jE7vdmtfWOerqpa29M9M7cnTaX3Lr38hjnTo9k+ls29Zc19m1e49b9errbnBopH6tvaMr0zt8+Gj9Glhr14Vy0S6Ua8vW7XWdPXv2ZeXqHxiuX+vs6sn0pg6GN6c1rMDX7Nmzmc6mzWFDv3ffpFvz2nrX1zdQx+ru6c30Dhw4WL8GV6+9vr7+eW7uXKbz1qat9Wv7JvdnWDt6++vXduzoz/Qm9x+oX3tjw1tu7doN7vz50MmpIz9e9h+YyrAoi5fevoFMZ9++/f6Se3Pj5qxPUB4vRSw4eXX1WtfR0e1VXF//YIa1Z+9k/Rp/R/+anT2bu6blOnToSMaDYg0ODmdYtLEXOH597Ru5cVUs1+EjRzOs1rZO/2duaHhnhqXjavOWbVl706+8FLGOHj3mXnv9DdciY2Fk51iGpeOqaXtLpnfixEkPleloHRlzYG1vDmNhdHQ809s5Ol7/u+3NbZke49BLsVwnTp5yq9esy/XfsfGJDIvyeaHc3JN6eCliUX843bIljIWJXbszLHjz0t7elfGq46qIxbgCa5P0X+ZF9AYGw7hivNN3aHcvRSz6C/2G617oV3zu7x/0l1xX9w732mvr3dRUGFdFrHPnzmdjY8Obm+p/x7hCr7c3jNGeHX3Z+GCcePFYOq4YszrPMQ7RY1x64XfmAO7jhXGN3tm5OX/JMf8yp3ihHuhQLy99/UNZX9VxtXlLU6an44o5TrEOHjqc6XR29ngoNzAwlM2ZzHdemAe558yZWX8pq59i0e7oML96oX8wl0/sCmN0W1NLpnfq1GmvlmGpvTp6dDrTaZMxSr/F9o2P76r/HWOFe+q4ok/AmRdv+7BHXrBTYDG+vGDPwNJxRZm0HY+fOJnpMAa9jI3vyuqo4wo7C9ZRtX1Fe3XqdKYDH16Yf7BXQ2KvsP9gsR7wAu/rIvaKdYUXxhXcDw4G20c7g0W7ewFL+TozO5vp0H+80K8ye1UYV2BNTQXbx/307/zfL5b/bTO2WFrS6vGuGHj76pTr3d7pura+7P70qz/sVjz1w+4brx4uP6Z4d8z9xceXuKdf2DQvAMe94991X1rypPvid1jQ3HXjf/4Jt3TpN9zmYqSOe8fdi88/6ZY9/y/Jsk+Mj7udIyPzfro6u9yKp5a6K1eu1jEwkGfOzLqbN8Phy+GRMTc2FgzNtWvXMx1d8F64cCFbYF2+HBzozp6dy/Ru3AjRJVm86QKOzSL3U6xLly5lEyf/e4lhDQ/vzC2Url+/kWGh6+XSpctZuS5cuOgvubm5Wrm4txfqRz29UGbKpVjUbeu25tymgXKjp1jjE7uyRbTHgkt0dPEB5+vfeCtXb48Fv15YLKgBjGNdcU3b23ILJRZx3PPqVd6w1gQjqAvLW7duZTroebly5YrDoGtZz5+fj7Vr127X1R02RnGsq46FxMxMwGdhWCtX6HMY1L6+QXf7dniEgY6W6+rVq661tdOdngkbEI+l/Xdy8oBjk0Z5vBSx4BfDfOxY2NjTf9Gj/l5Y2Pbs6E9gXXMs9k+cCA8c6GtgXb4csNgA9vT05cZVrFwdnd25RdfFi5fuY4VxdWDqYMarjtEiFv2xs3OHm54OGyOPxZjwcuTIdKanY7SIxXedXTvc4SPhgQNjEz0doyzwOjp7HOPQSwyLxef+/WHTQHnQo3xejh0/kS2edVwVsag/7XNQHjgwRmtYYbzTNq1tXU7HVQyLzc3+/WFjRPuhp3MHi1421o3KRd+jP++VhwT0qyLW6dMzrqW1PTdGi+W6deu2Y0OjGxD6O3q6yeIz45Zx4sVj6bjiYcbERJjL0S9iMfaZT3RceSwdV0NDw7nNDHMNesw9Xpg/WdTruIpiDe/MPci7dm0+FvMjmxCtY9ReDY86NiJeYvbqfMReeawbN4LtYyPDAz0vtDvlV3t18eLF+/YqjKuYvWIe17k8YKm9qtk+HQseS8cVD1R0kxWzVzXb15zrv97GaP+Fq6Hh8ICR+lNHtQG0H9zPzYW29Vg6rti06YOQmL1iXG1ranVn5YGZt1e0u5ddu/Y6Hmx5uXmzZq9mZ4M9oVyZ7ROb77HU9nV19dpmzDn3Pk9m7P+W5mb3wte+HvvKrhkDC4+BG6PuL39ymVv2kW+5lmAX8/W4t9f97adrb8bCkqGm4t+M/cJKns7dc/u+/enam7H5irU3Y19Zmcd+B5+Y+J5dvuId/IWpGgPGgDFgDBgDxoAxYAw8KgzYm7FHpSWsHI8QA3fc+H/7cbdi6c+4v9tX4jf29oxb9fNPuWWf/46bjvqMLXe/uZUnRG+7mZVfdcuXPO/+ZZ5izWfsmf8rHAt7pyTYZuydMmb6xoAxYAwYA8aAMWAMPDoM2Gbs0WkLK8lDZuDuwe+6r33io+4X//lwIYT9bTf0J//GLV/2JfedY4WdVr2Md9zwH3/MLf3Af3Rd4UTE/WiKv+yefuIn3T9M1f72ztAfux954oPuP3XkFOvRFH/678Nxnzp8xV84xvDMsuVJbfw8TosPWewP7t2750ZHw3GOmA7XTp467dTXpUyPo4xvv/122dfZdfxJ9Lx6mTLlonyNBJ8R6pkSjnTcvVuyyb7/xxzxUF+BMkx8M/QIUUyPoyJ6nC6mwzWOM6awOO4yLf48ZVi7du/NHc2L6XHEiiOBKdm9e1/uaF5Mn2MlHJdLCccZr8uR15g+R7fwvUoJR1z1GFZMn+Np6hsU0+EaPOiRmJgex44OHgz+EDGdDGv/lLsiR81iehwbxX8xJfsPHMwdD4vpc2RIfQFjOlw7MHXIXZJjlzE9+NTjhzEdrnHEdU6OssX04LNK/6J99BhhDIsjWXpkMKbDNXyL9OhfTI8jcoNDwR8tpsM1+vO58+FIV0yPI1y7xf8ppsM15jk9HhbTu3nrlmPcpoT2UZ+omD5HI3eJL1VMh2vMS3qULaZ3586dSn2V45/Mm40ELHzjUsLcO3Mm+DzH9DN7JccPYzpcO3nytDt9ujEWdkqP3pdh4VesvsVlelVsH2WibCkZHduVtn0V7RXc3759p+EtacPjx4P/aZky89ftO42xZmfnKtk++qoen43dc3Jyf+7IY0xnIV+zzdhCbj0r+7tj4MYO90cff8o9/VN/5XbJPuntC23u9z7xlHvms3/vJhus2W/2/YH7kSd+0P321guuvuW4O+1e/soKt/Qn/tbt9397s9/90UeXuI98c6u7EBTd9Pe+4p594jPu7xrdJFFDFogrli5LaDnHIpjFWCPBuL21KQSCKNPdN3nATYq/SJnexre2JjdjODkPy1n3MizKldqM4exLPVOyect2x6KgkeCErEFRynRfXrk6uVFhgTgxEZzMy7A4g68+RDE9FnXqSxHT4Rq+J+pTENPDn6qrKzjqx3S41tzSkdyoYLxHxF+vDAu/n8vi0xXTI/CK+j/EdLiGc7j6tsT0eGgwIE7mMR2u4ZuV2hDgN9ffP1QGUb+OH15qEc9iE9/FlOBPpb4tMX026Bq8IabDtR29A25W/DJievDZ3Z1eLDc1tTh8whrJ+QsXMz+1Rjp8R/vwYKCR8NCpXYK1lOkODe1MLnDxLdSAOmVY+J+ywWgkbOw0eEOZLovz1AOZa9evu+3NIXBRGVZ3d29yk4vPkAYuKsPCPyj14INFcpW+ykYy9eADrJdebhywirLiX6eBi2Ll54GaBi6K6XCNTTwPNRoJmzHsVUrw8VI/rzL9KraPByhVHjBs2tyUfHg4dfBwpYcCL738qsNvq5HQhvh6pWTrthbHA4RGwgON8fH0Qyf6qvq8xjAJaEWAnsUqthlbrC1r9arAwD136s3fdJ98arn75C/9qVu1td21bfgn9x9/+oNu+fs/7/566HLYZF15w/3a8iXumS//izvuX9DcO+XW/fsPuaU/8Jz7g5VtbqBvm/tf3/xR98yST7r/0hUc2bPw9q9/zX34iQ+453//Fdfe3+ea/vmb7tPLnnSf+v0up5oVCp1TeSdvxjS6Yg7k/ofak8bgNB3T4dqpUzOV3ozxNiv1ZoxoVFXeqFR6OljxzRjG4YG9GesdSL7N4smzRpAs4xUDmH4zdq7SmzE2kqknjQTSqPIWhCf/qU0ii3iilKVk7979Fd+MpbGIiJl8M3bxojskkS3Lyjc5OeXU8TymV/XNGJxWeTNG1MCUEOhDAyfE9HkzptH8Yjpc42FFtTdjjReuYPEkO7URvnrtWqWHNrQPARQaCQ8WNOJmmW7tzVhjLNpZAxSUYfEGJLWpZlzs2RsiA5ZhERglxRcLW95Cp6T2Zqzx5pV5pMpbNuYlIrI2Eh5cVemrtTdjaawdld6Mnar0ZqzKgylOcqROhWCnqpwKYY6rMs9VsX3YY8qWEuqYehBJJEoNQFSGWTvJ0fhB5Jkz2KvGDyHAz05yJB5q8qAo9RACLPpqyvYRNVQjF5fVcaFet83YQm05K/cDYuCmO9byt+53nv837sPLl7lnP/Bx99yv/qlbv+dS2Ihxp9hmjOvXD7q3/uzr7qc/+rRbtuQZ94nnvun+e9fpSBTG6+7gxj9zL3zmY+79S550P/DDn3e//Xdd7nTjeTFZR/MZS1JkCsaAMWAMGAPGgDFgDDyyDNhm7JFtGiuYMZBmwDZjaY5MwxgwBowBY8AYMAaMgUeVAduMPaotY+UyBiowwNGpp5cuy+Vt4WgAR+P0bDg+S+pPxbEfdPToDPmG8H/Qo1/k80JP87ZwnE6P05A7pYYVkvRydAoszVmG70sNK+Qw4riQ5iHh3Dg66ifDMS2S6Go+JI+leVuo37j4ZlHmGlbIAUPd2tq6csei4AA99bEicbKedec4Ejpw6wV/kZrfUqh3DAvHY5LieqFd5mNdc+0dPbl6E4gAPT0+h6+eJhPlKCI6/HghcALn68/K8aMYFsdMuiW5K07/RSzuTQLYM4KPzw16GvCCI3D42OhRk/lY1x05kvS4LH5aNayQQ4IgGfiMUR4vRSzaijxjepzGY2n/PXTosMOPSI9sFrHIsdOzY8BpYnPGFXp6RJAjcPRVHVdFLMrV2zeY8zWi36LHmPBSyzPWljv+OR/rRpafSo/5cCy5hhXyIZGHjDxWOkaLWIyr/oGhXKJYj8X/XvADo/zqvzEf66Zrbe3IBQ1hnKOnWPjF4aemY7SIxbgib9PhwyEBMzyhRxt4IdBBT09/bozOx7qVtTVt7oX2K2JRrmKesSIW/YX+rEln6Vc1rHAMEj9CfAR17ihiMSZGdo7n+GLuQE/9FPnMuNWcTx5Lx1VPT28uoAbjsIYVEq4zT5EvTucOj6XjilxXGmQFffQ0CMq5c+dcW3t3brwHrOAzRMJkPUpKPWpYIQgK8yOJjnXuiNkrgkPsFf9f+AWraK+wCzreA1ZwAmee0yArwV6FctFv59s+b68C1vw8Y/Ptlbd9Oha8vdJxtWfPZC7HW9z2XZ1n+2gPuNBxBVcpewVPcK8cxuwVicI1+XXcXl3NfDgVi6BElEv7L31Lc7yV2Sv6qiYjj9kr7JAlfbY8Y35ut/+NgUeKARYsBPDQiIQDA8OO5KdMjl6am9tzjuY4zKOjC3smThyP1QmbhSx6ugkhCXBLS4eHzhICo7NzZ0i4jHMyWLqYIVAHekzYXjZu3OLefHOz/5hF40JnZCQksAQDrAMHQtRJ7oWeRu/CmFJPL5QZHerghbqBpYsGOEBPI26x2CQIhheMDjqDEgyCxfmL33sltzFlcYMefnVeSHS8fXvAwtCgMzAQgkHgN0eQEo2AhnFFTzcJbW2dWYJMj42vDTokqPWCHx6LTY3Wx2YcPd28bNm6PRfIgE3DfKzjDgdy9afAHw093SS0tXe5pqbW3IYDHX684J+yeXNTLtAHjvroaGJjAjUQzEQ330Us/CNWvrImF1CDBQl6BDnx0tnZ47Zta8kteotYRKYjqIv6I9A/0KONvbBxxWldx1URi3EFrxroAx8f9HRc8UBg9Zq1uYVREYtN65atzbm2ZVyhp1Ed8QNBT8doEYsxt3Vrs9vR2++rk41N9HSMshEDS8dVEYv7rFmzLnuo4cEoD3oa1REOtmzZntt8F7EYV7QPCV29sDFDTzcJjDvaSMdVEYtxRXJigrF4YV5ET8c75Vq5cnUuImERi00SfbBDgobQr9DTTQJBaxgfbPC8FLFYlBOggMTiXujv6OlDLeYOsNS/1GPpRn7dujfdli1NHiobhzWsEHRhbGxXNp/ouGKOQE83ucxLbGi8UA90COzhhTmJuUnHFRyip5tJ5kvmOi9soNHRhT0P8r774sqcnzDzIHq6ASzaK9odHTjyQpsyl+sYpZ+gpw/z5turM5nOzp3jHirznQVLN/JEawVLx9WbGzc7frwwTtDR4EX4b9bsVfC9xJ6hp+MKG0rZvDBG0eG+XhhXYOlYoNzo6UOtou2j/uiovWL+efHFlbnk48H2FeyV2D7mO7BYV3hhXNEnNJE57YyeRoikb6nto7+go/Mj/Qos7XP8jp76wa1duyGbM30ZFtv/9mZssbWo1eexYoAnv1VC21+4eDH31DpGEk7MuliP6XANY37xUnhqXabHU/ZUAA8WY2o4y7AoVwqLRQ/1TAkLjpRDNE/6daFRhonxTgUDYSGlC40yLDZdKSyebqaCCoCPY3gqYiSbHTXoZeViIZQKh8yT7irtSHRDfcofuydP56tgselMBRYhQp0upmL34xo86NuzmF7tiXp4MxrTybDOzKbLde1apTQMLN5SdeSNmC7yysrF2019exbT415VsOir+nYjinXrVqX+Rfvom6UYFm9zUkEY+Dv6jT6Zj2Pdyr0hjOl4LIKQNBL6sm4Qy3SZ51J8MV6rBHSgfXRDFbsn84g+xInpcI15KRXdFCzdbJZiXbiYexgT0wOLSLUpYe69dDm8sY3pM4enol3yd3Clb6liWNiWVHRQ/m7u3LnsJ4ah16rYPsqUakcwqWPKXsFVFXsF9ykbU7NXFexoRXv1oGwfc3SV4CnaDgvpd9uMLaTWsrIaAwUGWLg+u3xF4ap9NAaMAWPAGDAGjAFjwBhYCAzYZmwhtJKV0RgoYcA2YyXE2GVjwBgwBowBY8AYMAYWAAO2GVsAjWRFNAbKGOCYgyV9rrGD74sGKSnjzJI+15ixpM+hh1jS5xoXHKezpM81Lizpc40Hju9a0ucaF5b0ucYD/1rS58DFg/jNNmMPgkXDMAbeIwZsMxaIt81Y4AJn+pQfjm3GAl+2GatxYZux0CdsM1bjwjZjoU/YZixwYZuxwMWD+M02Yw+CRcMwBt4jBuyY4ntEvN3WGDAGjAFjwBgwBoyBB8CAbcYeAIkGYQy8VwzYZuy9Yt7uawwYA8aAMWAMGAPGwLtnwDZj755DQzAG3jMGqoa25zij5qqJFZjwvidOnop9lbtGSN5UqGD+AKxUOHrC3nI0KiVVsKhflVDB5EFJhQom3DM5vFJCvpVUqGDC0VcJO0yI7BQWyWLPXwjJXcvKR76rZGj7y5crhTEn/1oKi3DiVdqR8MSp0PYcr6yCRT4mTcAc44Jw9FXC5BMuPBXanqSslbBIuH4rJMONlQu+yG+WktnZuWRoe8LRo5eS2bNz7sbNkMA2pu8TvMa+02uUPRX2HT6rhMmHU01gq/fxv9NnZs7M+o+l/9NvUsdzKZfmyCsDAysVJp9xUSXkPvNcldD2jNuUkI8qNf8yj5BGIiXMS5o0OaafYVXoq6QV0STpZViHj4TcfTEdrlWxV8zhVcL3k4YlFSa/qu0jrUiV1CLkx0rZPtKnVEkRQx2T9qqi7YP7lI2hDavZq9MVsCravtNp28dccuzY8bIus+Cv22ZswTehVeBxZsD7jGniSxIqkghWF7T4EGmiZow+Opr4cnKylkRTE1+SNBI9zdVEQk5NVskCGx1N1OyTPmsSWJIvo6dJn0mgueHNTfUmZMJFhwTRXnzSZ5LneuFe6HFvL9RPEzVTZnQ08aVPoqlJYEkgjY+PMiUAACAASURBVJ4uhDIsSdTMghEdTXxJclqSPpPI1AtJNNHThTYJOZsEi4UZOpr40id9JjmzFxK3oqc5fkiqSgJZLxhNdEiQ6YUkmps2bcslWyWJJnqaUJbEsWvXbfB/li2Aili1BNIkfQ4JUkkCi54aRpJRkyRXN/zo8OOFe5PUFl8cLySQRkcTypIcl+S9urEuYsEJSZ/7+kLibBKQ1rCmPbzr6OjJHM11cVHEYnOeJX0eDElN6R/o0cZeurpI+tycG1dFLDbUJDrWtiVhK3o6rkiGunr12tzmrohF3yYBs7YtYwA9TdTc01NL+qzjqojFd2Bx3QvJafmsY5R7kbRaN1FFLMbV6jXrcsmCKQ96OkZJMgyvOkaLWIwrfE/g1gvJadHTRLeMu1rS57CBLWIxrkgg3dHZ46GyhMDoaaJm+szLK1fnktMWsegv9MH29u46FjmO0NNEt8xDtUTNIelzEYuNEwnRSfTthXGFHv3fC2OMZO26UfRYOq7WrnszS57u/45xiJ4mjA9Jn0MCdNoWPR1XzEskuPdCPkd0NFEzc0ct6XMYV7QtejquSO7LXOeFTQQ6mqg5lvTZ2yvaz0vRXjGfgqXzEG1aS9Qcxujg4HCmpw9NivaKh0tgMe97oa+BpcnUh4Zqtk8fdLz55mbHjxdv+9ReBdsX7BXfc08dV9hQyuaFMYoOdtJLzF6RYBo9HVdF2+ftFXx4YVyRcFv7HPYfrJzta+3IJWpmHYGOzmmsN+gTikU7o6cb5Pn2qmb76D9eGFfFpM/0P7DU9r2+doN7dfVa/2eL7n/bjC26JrUKPU4MYFifXros99SViZgFkz7pH5/Y7fbsmaxTw5NodNQAgrW9ud3x9sWLx9LEsxO79rhdsojgjQFYuvnj6RpYuojge/Q08SyGp38gLKjjWFddc0tH7mlwwLrhi5rVb3x8d/0zZeZ+apipGwsGXUTAAXr6dB5Dz4LGC28M5mNdcyyMtN4B67r/U7dvcr8bHZuof6ZdilgcN21r73Lnzp2r6124UCuXPp1n0bBzNCwiSIYLFj9ewOro6Ha8CfFCfdHhOy8ssjplEczbhyIWT/NZ3OoiIoZ1YOpQtoHWt15FLO7d2dXrWAx5oc+hp28Npg4ezhYkjbGuZwZck5QHrNB/WYAMDI7kxkKxXLxJYUOjiwgSYqOnbw14C9o/MJzAuuF29LLpDYtzFuM1rCu+2tkGiMWrvtkrloux0Ns3kNv08jQdPR1X09PHHYsbHaPzsW66vv7B3KYXjCIWGwHKz729FLG4DwtJ3cQFrJCol4VUz44U1q2sfXTTC+fcU9/+sBgnyqO+9SqWi3E1OLTTHTwUFucBKySpp1wsvFNYQ8Ojjn7thbmDe9LPvLAg7ujckXuDViwX/ZgF9P4DB/2fZf29hhXevp85czZ7eKBj1GPpWOjq7nU6z6GPns5pc3Nzrr2jKzfeY1jMSzyE88JcU8RifuPhQaxcamOYL/fuUxtTw1Ibc/78eceiWrG8jclhje/ORcalrSiXYtEO2AWdOzyWjgUecO3evc9XMevbNaxwIoNxVbR93sYoFg/29OFemb0qt31hXO3es8/pwzfsIuVSe0Kfo476Bs2XS8doZq/G1V7FbR/cnzsXNr3BXoVy7duH7Wtsr+C8rb0z1x4BK9g+7JVuoL3to55e6Av01bNzavu8vQpY2CE2bYtVbDO2WFvW6vVYMMBEZkmfH4umtkoaA8aAMWAMGAPGwCJkwDZji7BRrUqPDwO2GXt82tpqagwYA8aAMWAMGAOLjwHbjC2+NrUaPUYMcJTnmWXLkzU+eep00gEeJ2GOM6aE8+VVnNbHxnclnZjxd1B/obJ7U66UEzNH6ahnSjhmmXJi5vy+Hlsrw+Tolx4hiulxJEPPvsd0uMaxlRQWx3COHT9RBlG/TvJrPfZT/0J+4YiVHjWTr3K/7t27P3ecLvfl/Q8cUcEPJiX7Jg/kjsDF9DludeRoGovjmnqkNobFUabDR4KvS0yHa/v3H8wdNYvpMdb0OF1Mh2sHpg4mywVfetS3DIsjm3pUMqbHkWD1dYnpcA0dAtM0EvhUf7Qy3T179iYDGVy9dj13NK8Mi/bRo38xPY4QT4rPaEyHa/he6nG9mB4PsDg2mJKj08dyx7Bi+hxh27svHPOL6XBt+tjx3PGzmB7jtUrSenz91McnhsU8or5tMR2uMS/pkbGYHkFKqvRVgiyp32IZVl9f8G+N6XANP84zs40DtmAPOGqdEgKZzMw0xiLYBvYqJcxxVea5KraPMlUJssJRxqTty+xV2vZxnPn27TsNq0kbEoAkJfSJ23caY509ey53ZLsMk76asn3kxRweCb7kZVgL9bptxhZqy1m5jYH7UadWLF2W5AIjr/4PsT9gwq9yJpsFdZWFEX4ZqYhSnCdX5+dYubhGuVIGiUVklcUMgQBS0QEPHjqcc04uKxeBANSnIKaHs7P6BsR0uEYAjBQWG9cqiwZL+lxjmcUOPmMpsaTPNYbwR8E3KyVNTS3JhwLnL1zM+SSWYdI+qc0FG+H2jhBMowwLH1QW8o0EX0x8PVNiSZ9rDLFJJHBNSlic46PZSMB66eVVjVSy71icTx0M/nqxP+CBGgFPUsJmWf31YvrYKexVSizpc2DIkj4HLh7Eb7YZexAsGoYx8B4xwCLl6Qpvxo6fOJkLnBArLpudkZ0hal5Mh2ssdqq8geLpc2ozxpPsKm8bKFdqM0ZgCOqZktHRieSbsZkzZ3KRB8swu3t6k0/0eGNHkIWU4JSfejpIZC+e2KdkYtfu5JuxU6dPO40qWYZJBDQNuhLTm5s7n0Wui32n13Ckvy7BIfQ7/ztO/ockiqG/Xvx/cGgk+daIDUGVt0a8/dNAAMV78Zm3N1XeGvGw4ooEwYlhsempsqnmoYcG64hhEXxAoxjGdLjGgjQV4pu3cBrFsAyLaGcaGCemB59V3hrRPum3WdcrPWhhM8Bbx0bC2z+Nilqmy0OUuUTaDYIoVHlrxDyX4ot0CLy1Twntk9pwEtinyikH5qXUGygeXFXpq7yx10A/sXqA1dUdImfGdLhGAJzU6QvswU6J8lqGxRu71Bso7FSVt6WEhq8Smr+K7eMBBGVLCXVM2r4Z7FXa9hH8JfVmjDbUiJ5l5aNPpN6M8Zatku2bSNsrgsNosK+yci3U67YZW6gtZ+U2BpzLolJZAA/rCsaAMWAMGAPGgDFgDCxMBmwztjDbzUptDGQMWAAP6wjGgDFgDBgDxoAxYAwsXAZsM7Zw285KbgxkR6fIM6a5qM6dv5Adr9EADgSH4PiUF46dcQRHjwfh3E9iUhzvvXgszYeEX5YeP7pxs4bFkTAvV8hD0taVO67F99xT/aJIOjk8EpJcxrBqOU26HYEKvHgs9L1QP80nQ5m5H3XwQt3wPbl4KeRDggP09Cgex770+BFcFrHgnITV5y8E/AsXL2V6ehSP42F6/IgjRBmWHIG6dv16dnxHj1jVsa6HHDAHpg67McmlxrFGsPjxQrAD/H70Gnlq+Mx9vNCO5JTyUorV0+9mz4YcMHBXxOJY4c7RidyxFXS0DHDSs2PAnZk962+Z5ZLKsKTPcTyMfqFHNotYHA/b1tTsTp4Kx3w4gofeVcmlRnAIfH9u3b5dv2cMi0AspyT/2aXLV2pYV0NetqPTx93Q8M7c8c8YFrnI9Bgv4wo9xoQX+CJRto7R+Vg33cDASM6Z/vKVq/exQi41jubid6VjtIjFmCMHlx7j5UhiVq4rAevEydNZLjUdV/OxbmU58fCr9MKxTPQon5eTp2ZcX/9QblwVsag/TvkasIXxnmFdDuOdI2vkXNPcSvOxbjt8ejRgi8eiPb1QLhJbN8S6fTvrz3pcln7FPfWo5+zZs667h1xqYR4qlotjYaNju5zyxdyBns5DZ+dq/no6d3gsPQ62o3cgC/bj68OYLmKdO3/ecSRNcyfWsWQscJxZ/anQz7AklxrzGzmedO7wWDqudu3ekzsuSz3QYx7zwrz9xoa3clgc2UWPedEL8/jk/mCvYli0aVt7d9T2ceTTy+49k1muR//Z276cvbpy9b7tC2OUuZhy6bgq+oyV2itsn4yFuL3a7yibF2+v1AbQ56ij9t86lvQ5uNIEzNSfshdtH9zn7FXU9h10tKWXMttHjkrlsG6v5Bg6fup6XJb+Qrn48VKzfb25snIkHB3tv+QsrOK76HEX2v+2GVtoLWblNQaEASYtAnjoooGISd09fbnoXU3b27JErf5PsySqPX3ZQtVfY4OFEzMR3LywsARLEwgTHIKkll5YKKFDklQv+LqARQQkLyTLRE/9Cja8udm9sWGTV8kiPqLDwtELEf/AUl8WFsXoqV8BiWippxfKjA518ELdwNJAHyzW0VO/giIW/h7osLj0gn/Ki997JbfRwlijp4txknY2bW/1f5a1Czq9fYP1a2xACFKiyVxJyIqeLqBJWE2gDy9sJNHBUHnBPwUsTTTN+X70NBLjps1NWQJW/3f0pSIWAUPQU19CjCt66gvQ0trptjW1OPyXvKDDjxciZ4KlEbHwR0NHF+OtbV0O53DK46WIhX/EylfW5Dhk85xhSfRENt4YcF2AFLHw2yCoi/oj0D/Q04AELEi3bG3OjasiFuMKLG1b/PLQ03FFO766em3Oj6iIhU8JmwYW314YV+gRsdELn9HTSHZFLMYcZee6FxbhfFZ/MzbnlJ9Im16KWNxn9Zp1WfJ0r8OiCz1dQMMBWBqco4jFuKJ9Ort6PFTm44eePvBhDG/e0pQbV0UsFvX0Gw30wbyIno53ykXgHfXXKWLRX8AiEbsXxhV6+sCHOY8+fVwinBax8OtlbJA42QvjCj19SMPcwbgl8qIXj6V+g2vXbcgFrmAcoqeLXh6MgKWRapkj0NNxxbzE/OSFeqDD5tELuGBRfy/0SfR0XNWwgl0gIh866tc1PrHHfffFlTn/UtoDPTaQXor2ivkUHTjyQpAP5nLd5DKG0Ts7F5IKz7NXp2cyHZ2H9k3et32S5Htg8L7tk4dHPHzjx0uwfcFeMZ4yeyXRP7FnlGvmTIjqiA2lbF54SIWOBhzCRxUsHQv0OfTwkfZStFfUHx2d0/DNhHt9yFi3fRKFuMxesa7wwriiT+wSH0famXtqJMaivWKjiY7Oad5eqV8i/Q899YN7fe0bbvXqtb4Ii+5/24wtuia1Cj1ODGCkq4S2ZxJUIxzjCCfmKsEh2ADoG7UYFtdYCKQCeBBWWReRpVjTaSzqp08Vy7BY7KQcoi9dupRbdJdhsVFMhclnMcZCMSVslFJYtHcqEAD3YQOXihh54eJFd+rUTKpYmXFNOX3zFDgVIpsbsQDWp+mxm/M2o0qfwJFe30jEsDjGq2/iYjpcgwd9Ah7T422GPkiI6WRYp2ecvlmK6RFEooqTPIs9fYMTw+J73TzFdLiGjr51ienBp26eYjpcY9GuT/5jevBZpX/RPrRTI+HpvD7gKNOl39B/GglvCXn4kRIe5qQCsfD2VhefZZiMjRRfjFd98FKGRfuk5t87d+7mNohlWOfOncu96YvpMSdV6avMccx1jQSsA/KArkw3s1eXwsOYmB5zeJUw82wY9e1cDCuzfRXSadCOVea5KrYvs1dyqiJWLq6x2U7ZK04+6FuwMqwHaq+OPUB7dfxE0l7xoEsfOpfVcaFet83YQm05K7cxYAE8rA8YA8aAMWAMGAPGgDGwoBmwzdiCbj4r/OPOgAXweNx7gNXfGDAGjAFjwBgwBhYyA7YZW8itZ2V/7BngqIMlfa51A0v6HIaDJX2ucWFJn0OfwE9DfT/DN+E3jppZ0ucaH5b0ucYDR0SrBE7AF0l9LEOvCr+BZUmfa3xwZFB9wQJL+d/wSUwdX8cflSBdKXnp5VeTx7FpQ3x5U2JJn1MMvbPvbTP2zvgybWPgkWLANmOhOWwzFriwzViNC9uMhT5hm7EaFxcuXHBr170ZiCn5zTZjNWJsMxY6SDGaYvgm/xtBN1L+0rYZC5wR/CXlG0uQH4J4LFaxzdhibVmr12PBgB1TfCya2SppDBgDxoAxYAwYA4uUAduMLdKGtWo9HgzYZuzxaGerpTFgDBgDxoAxYAwsTgZsM7Y429Vq9ZgwQCLkZ5avSNaWRKWp0Mocq6gS1prw6iSyTQlHxFJHNWph8kPS5DJMypXCon6akLUUa+ZMMlQwocdTYZrBJ3dW6jw/obY5TpoSctCksNh8V8EiBHsKi75TJUzzmTNnk2GHr1+/ngy3Tf0JPa4JbGOckOhT8xfFdLh2kjD5ktw1psfRlyrpDuBBk87GsW5WSlFwdu5cslzwVSUcPWkMUnXMksXOhaTcsbJzjSSqqfD93KtK6oQzZ87kEvfG7gmfVfoX7ZM6okQI+ZS/G2UASxPFxst1K5djLKbDNeYm2qmREI6+SuoEsEiN0Eju3L1bKXUC7aN5x2KYjP0qaRiYS1KpAAirXqWvMl8ybzaSLBy95FEr0wUrlVbgndirKrZP80yWlatmry6WfV2/XsX2UaZUOwJIPrGk7ator0jrcvfuvXo5Y79UtX30ibv3UlgPzl4xl5w4cTJW5EVxzTZji6IZrRKPKwPeZ0wTcpJcmQSNugglKWRra0g6ygSPztjYRJ06n6xSc/AMD49merpAa2npyCV8xeiDNTo6XsfyySr538vIyFimpzmkNr61xb25cbNXyRbrYO2U5J4kq+QMPmfsvezcOZ5h6YKD+lFPL5QZLOrg5fDhI7WEnJMH/KWMA/R0wUGC1mZJbE1gA3SGJBk1nJP0WZPAjo3tyvR0U9vW1plL7km7gDU4GJJRk5emlkQzOE5PTOzO9Nh0eCEJ7XZJbE37g9UvyajJS4PTtyaBxSEbPTVmW7c2u3XiO8MCqIjlEzVrP6G+6Gmi2/b27iyxtS4u0OHHCwk8SdxL23nZu3cy0+E+Xjo6elxTU2tuM1zEghOSPg8MhCTcHktzD3V27cgS7rKI8lLEIn/Nli3bc4nGSTCOno6r7u5et21bS25cFbFod5IrD0iiccYVejqu2tu7ssTJmn+uiDUzM+toI000znhCjzHhpbd3INPTjU8RizFHEAZ0vYCBno7Rvr6hrPxswL0UsbjPmtfWOerg5dChGpaOURI1k4yaengpYlF/EiLDrRd4Qk+TUQ8NjcxLIF3EYlyREL2ra4eHytoPPU0YT59Z+cpqR7t7KWLRX+iDJPr2Qr9CjyTeXujLjDXNNVbEIhE6SYw1GTX9HT0SF3th7qglkA4LTo/FgxMv69a/mfHqPzMO0dN5aHx8Vzaf6LhijkCPHIpe8C1tawvtSD3Q0WS+u3fvzbB0XNG/0dNxxXypia3hFx1NZA8WiYc1GTXzIHqN7dVMpgNHXmgH7IKOK+ZnsBrZK+Z5dEZH59s+DUDibZ+Oq40btzh+vHjbp3NazPZhz7in2j4SImvCbe6DzshIsFeUhzrqWMDOolfF9qm9gqcXv7fSMU96YV4HSxNIF21fsFcj/s+ycYW90v5LO4Ol44q+pYmt6S/o6PxIvyomkKb/oae2j2TnlvTZuffVWyHyS0tzs3vha1+PfGOXjAFj4PvJAIvxp5cuyz1hY8Jnoia5qZedo+NuYmKP/5g9pUVHjRYTJRGSWDx4wUCgp0+uR8d2ubHxYBR5elzEwuCDpYY/hsUCYUdvv79d9lQbLDWAbBJYZF28GBbUc3O1cumTa+qnRpEyF7H8wkgNPxygp1hsXtg8eoFLdNSYsvFYvWZdrqweS5+CE+VKDWwMi8UWhlnxWahyT31yjSEdGt7pi5W9NUGHHy9gtbZ2ON5eeDl/fj4WRr2tPWzQeSsyH+uqYzOpm0u4q5UrPAWfnNzvBgZHHG8wvBSxeOLa3tGVM9YeS59c799/wLGQ1zdC87GuuQ1vbsot6gjMgJ4uXPcfOJgZ9UZYvG3s6Nzh2Cx6YSyApZvLqYOHHEEwdFwVy0W7d3X15pLRMkZrWGFcTe7fny2oG2HRH4lseOTotC9W9lYULMaEFxZZ3T19uTFaLBdjoaenP7dwZWzWsMLi/Oj0tOvq7s29XYphsbHTTQnlQY+6euEpPJthHVdFLOrf2zeYe9DCGK1hhfFO27BJ13EVw2LjqgtX2g893TRQrjc2vJVLNF3Eor+wYNRNHP2qiMXCkwckOkbnY912PCBTvujv6Ok8RILv1raO3Nslj6XjijGkD6sYV0UsPrPY13HlsXQsDI+M5qLwUQ/09CEBc/H25vbcuIphMV8SUdEL4yqGxYJax2jUXu0cdxO70vYKu6D2ymNpMng2XbohpD9SLrV99NuavQrjKmav2CDw4yVgzflLmc0rs3361paHZbohjNkrb/u0/3obo+MKrkbkIRf1p45qT+AJ7s+eDW/RPZaOKzbMVWwfDz7VTnt7Rbt72bNn0g2PBHvFm/laufL2ir6qZfVYOq6wQ8z5i1XszdhibVmr12PBABPfsxWOKT4WZFgljQFjwBgwBowBY8AYWGAM2GZsgTWYFdcYUAZsM6Zs2O/GgDFgDBgDxoAxYAwsLAZsM7aw2stKawzkGODowTPLlueuxT5wzEyPAcR0cK7miEJK8AEh2ERKOLKScjzm+JH6NZRhUi7K10ionx6nK9Pl6EQquAXHL/TsexkWviw48TcSjoKcPBn8U8p0SQCawuL4xgnxISvD4niVHkeK6Z2Znc35HsV0uDa5fyoZ+IFjNMeOnSiDqF/n2OANOT5b/0J+4TgqR8lSgl+MHmOJ6V+8dNkdnT4W+yp3bWrqcO4IXO7L+x848qY+ZDEdrh08dNhdlaM6MT34Ut+NmA7XDh0+kju2FtPjKBq+kCnhOKMeW4vpw6f6zcR0uMaRu1SQFY4+kYw2JbSPHruM6XOE64D4n8Z0uIa/pB6VjOnxAEt9IGM6XKM/6/GwmB7HLPVYZEyHa8xzeiQxpsd41WORMR2u4Z+nfngxvdu377h9k8G3LabDNXxy9LheTI85qUpfZb7UY2tlWINDwVc2psO1zF6dDX6LMb3MXu1J2yuOf6aCrGCn9Ihl7H5cO3b8RPZT9r2/XsX2ZfZqJhwl939b/J9j7knbh706PVP803mfByvYq6q2b+/etL2amzuf8/uaV6D7F+irehQ3pscx8dGx4G8c01nI12wztpBbz8r+2DPAwmPF0mVJHvbsnUwuZpjwcaRNyb7JA9kCPaVXJfElfksaYKMMk3KlDBKO09QzJZu3bE9uelhQV9mYvrxydc6HKHZvFsHqrxfT4Rr+D+pDFNPD8V399WI6XLOkzzVmWKDgy5aSzs4dyYU3C2ANlFKGic/VufPny77OrhNIBb+rlPTs6E8ullk87dgR/C7LMC3pc40ZS/oceghBgg4fORouRH5jk1ilr7IBSW3kwXrp5VWRu+QvERiCxXcj4YHaps1pe8VDLh4CNRI2Y9irlFjS58AQfnE3E9FseXil/nrhr/O/WdJn52wzlu8T9skYWFAM8ET56aXpN2M80Tsp0cNilWSzo9GXYjpcO37iZKW3MzyFS70Z44m+RoYruyflSm3GeDJLPVOC03rqzRhPZnnKnpKOju7kEz2id2n0sDJMgqykng4S5S61eAJ/dGwiubHjqbhGwyor19j4bqcO8TE9nMKrtOP4xJ5cQIcY1rlz5yq9UenrH8wF2Ihinb+QCw4R0+EakehSYbl5S1LlLQgPBFKpH3gbwcIuJSwkNUBBTJ85QINDxHS4xkMU3hQ2Et7+VXkLwkOU1FsQQpPzVD8lRGBMvTXiLVuVNxc8kNHgE7F70869fSGqZEyHa/Rn0hQ0Et7YVVls8oYzxRcPYgiOlBLaR6OixvRJK0AbpeTo0Wk3I4F+YvrMSVX66tHp47mofGVYBCBJCaclTp1ufJqAOVyDGZVh8lYydTIBO4W9SgkP6fhJSRXbR5koW0qGhtP2iodOVU4TwH3KxhBZ8ejRtO0jYEgKi2AdVU4T0FdTJzl279mbC/aV4m2hfW+bsYXWYlZeY0AYMJ8xIcN+NQaMAWPAGDAGjAFjYIExYJuxBdZgVlxjQBmwzZiyYb8bA8aAMWAMGAPGgDGwsBiwzdjCai8r7WPKwOS+fW505+i8n+6ubrfiqaW5nDkch8E5mJweXsi/o0c6yFGCjh7pwZeCBKyaW4l8XujpMTVyQKkfDrlTaljhSE8tPwp5xsKxKI5m1bBu+GK53t5+19PTV//MsR901KmcY1qUS53pPZbmbeEoo/r0UOYaVsgBQ904n67HouAAPc3bgh8b+Y+8cIQIHT1qxEaYhNUcq/MSw+KID/46XmiXIhaBFfDzUnzKiB738UJemh07Al8c7UCHHy9gkQNGndZjWBzXzOcZuz0PiyNd5D+bmQnO4fQT7qfBMwimga+UHlsplgt9sDQwCm1awwo5y8jxBhZHrbwUsWgr/EX0aI7H0iAVHMPs7OrJHYEpYnEEjvxOGkgGX0z0NB8SRwE7Ortz46qIRbngVI+lks8LPR1XYNGn1UdwPtaNLIfVocPBp4fxVMMK4+rgwUOurb07N0aLWIwrdA4dCn44HkvHKMfpyJuFvpciFmVu2t6SOxrJGEVPsY4cPZYlAdYxGsOCUw02AU/oaSAO2oZcRDpG52PdyvKa7dkbjkbSfkUs+gx9p1G5GFf0QU1+TL+qYYX8Zxylo0/rGC2WizEBliZhZ1yhp3Max8MYtzquPJaOK/oXY9cL+jWsC/6Sm52ddc0tbbmjtx5LxxW+hnoEkXqgp/MjR5CZm3RcBaxgYzj6qeViXNWwgv8k+Q6ZM5WvqL3qG3TDkk+RdgdL7RUBZIr2KmCFHJvYBPK8eQn2KpSLvlbE8jZGbR8+nOqf6bHUXjEGwNIcmwErjCuOMubtVcz2XcmwtJ9gb+BC+y9caf6zmL2in9TsVah31F6NYPtS9upK1ie03rQt5aLdvZAPT/kqt1fYvmDDYvaK5V8ouQAAIABJREFU8f/WprRfn7/3QvvfNmMLrcWsvI8dAxiiL/3cF9zzn3tu3s/nfuazbtmSJ92u3SFB5patTdmke1oW0K+ses2tevX1Onf4HTExt7aFpL9EBnzp5Vfd+ETwW8CooKcR/MDixwvR0NBpaW33l9zIztEMC98lL9ubWzM99evifurQzUIJrObmNv9nDl8q9DRxcktLe6Y3LZHyqJ+WizKDRR28sGkAS33jWIijp2fbM6xX1vg/yzYQ6Gzdtr1+jUSb//Ldl3ObNhay6LGo9fLqq6+7lYKFDxk6m7c0eRXHeXjKpUawo7Mn08MPxsurq9fmsDB+YKmRwqcErB7ZtHV178j09h+Y8lDulVVr3Ivfe6X+GcMK1sa3ttSvsWkAi7/3Ai56Gvlt9Zq1jmAmuohDhx8v+FuB1d7R7S+53t6BTGfvvhB45bXX38iw1NAXseAE7tlYe+nrq2GpH9zadRsyLCJHeiliEZ2OcrEQ9jIwOJyVSxPPkiiYOuq4KmIRrAUsNiteGFfo6bhat/5N990XV+Y2pkUs/HnA2ro1BPpgDKCn42rTpm2ZHr6cXopYjDmwNm8OfY5xhZ4mEGbuQE83uUUs/JUoO3XwQnnQ08U4Dv5gUQ8vRSw25nCqyVwJKoGe+vCwGQBLx1URi3EF1vr1G/3tsnkRvf6Bofo15gP6Du3upYhFfwHr9bVveJXMvxI9fBW94INDuQ5MhQARRay5c+fcyldWu9deW+f/LNvIoqcJ77u6dmRY6pfosXRcMWZ1PmEcolcc75RLfQkZ1+jpAx9wXl0d7AL1QIcHGF4Yo2DpuGIzi56OK7DUxuBzhw6bbS/UF+6Z77wwD6JH+3lhblIs2h0d5lcv9A/KRX/xQqAR9NQ/umb7gr0iiTo6zPte6LdgjY0He8UYRk/989Dhxwv2Bx2dO9jcosP48oI9Q0/H1apX83b0+PETmY7OaUT9BEvHFZsSsHRc1WxfsFfUHx0NvMLDALjX/ov9R0/9kMHS/sV8hw5zgxfWG5RLxxXtjJ76DtO3FAsfMnQ08Ar9CiwdC/Q/9HRcvfi9le67L77si7Do/rfN2KJrUqvQ48QAT5GrhLZnY5IK+06ADBaTKWGi17cbZfpgpQJ4YBir3BOdVAAP6qebxkblSgbwmDmTM8JlWBiSlOMxUfh0oVyGRR31CXhMj8WPbmZjOlwDS9+6xPTgakoWkTEdj6VvSmJ6LPB0oRHT8VjXrocnpzE9NmFVgqew6dQ3MTEsnvzqhj2mk5XryLQj4EQjYUFcJUw+m3p9CxbDhC/dzMZ0uMb4SNWRJ/DopQSdi5cuNVSj3PpQokyZsvMgoJHwJqUKFu2jm40YJk/1Dx9J15F+o5v4GBZvy6oEKaE/68YlhsW4qDJ/ESZ/dja8oY9hMV6rYPEgQjcIMaxbt25XwiKARCpNye07dyphUSbdUMXKxfymm7qYDtdOnEjbK+bwKnwRKCMV9h07VQWL/lylT4OVsn2UKRVYBC7AStqr09irU2V01q/X7FU4cVD/Qn6hDVP9C3XKlbRXZ2Ydm8yUgJWyo2zMqkRLTt3rUf3eNmOPastYuYyBCgxw3OPZ5SsqaJqKMWAMGAPGgDFgDBgDxsCjxoBtxh61FrHyGAPvgAHbjL0DskzVGDAGjAFjwBgwBoyBR4wB24w9Yg1ixTEG3gkDVZM+40BOEI9GcufOnUqJLzMnZglIUYZJEs3U0cItW7c7fF5SAhblayTUj3qmBKzUsTt8hjo7g99EGSZn8FPHyPBPUz+pMizKlcLCH6G1LfhNNMLCobqR4AemPjFluiTcTh3XIteS+k00wjotviExPfJJbW8O/lsxHa7hO8PxlkbCsRb1wSjT3bS5KXn8c3JyKud/WIZFUvHUsUF8U9SXogxry9bmnJ9UTA8fDfRSgs7UweAnFdPnCBblTwk+PeoTE9OfPnYi5xcZ0+Ea7ZM6NshxLtooJdu3t2U54xrpcSxSfSXLdOnPGnQjpsdRTcZHSvDzGUvkECNROHNAStau3ZCcm7ALVbDa27tzgZ1i9+b4bhUsfFw1UEYMi8AlzJkp6ezakfNHiulzrK1Kubp7+nJ+vTEs7FQVLPzb1Nc3hsU1sFK2jwBRlC0lYKWO8BFUC85SAvepI9S0YUdH2vZRrlQ+RQJhqZ9fWfnAungxBMaJ6eFLjK/qYhXbjC3WlrV6PRYM2GYsNLNtxgIXGDfbjLnMx8A2Y7V+YZuxGg+2GQvzhG3GalzYZiz0CduMBS4e5m+2GXuYbNu9jIEHzIAdU3zAhBqcMWAMGAPGgDFgDBgDD5EB24w9RLLtVsbAg2bANmMPmlHDMwaMAWPAGDAGjAFj4OExYJuxh8e13ckYeOAMEKa5SjRFQkdr4shYQTiqQR6QlIBFws2UgJUK74vPRSpENvcBK3UGn/qlQmSDRSjnVKjgCxcv5hKMltWV0NApXzaOkmqy0jIs6pjCIoz53FxjXzDPVyrsMMcYU+kOMqzZs0mfBfwQUiHFPVYq5D5+CGfnQiLtMr4Iv6wJRmN6hFdP+bvxd/TB65LoOIaFv0tlrET4/kuXL1cKa0049FQdeSCTCpteq+OcuyoJxGN19Ml1Y9/pNdJbpPwbfUJc/bvY73CqCYVjOj6Be+w7vVbDuqKX5v1OHauE7qY/p/xr8OXR5Orzbnb/Algpvm7dvl1p/iU5dGo+YR6pMpeDw/zUSO7cufvgsO7erRTqHP+5B2mvUljYqSp8vRN7lbJ9Ve1VVdsHZykhzHzKxjxIewXW3Ll0uarYvix1jeRSTNV1oX1vm7GF1mJWXmNAGGCyW7F0mTt69Fj9Kk6zAwPDuY0J/iLbtoVEtOS+QofAC15INoqvkeZR2blzPNPThTZJaEno6gUDBZY6qBNUACxNADk6OpHp6YJ29Zp1jkTGXlhUgoWul0OHjmRYBw6ExKrcCz3dyFE/DWRAmdGhDl6oG+XSZKhwgJ4a421NrW6LBDJgk4fOyMiYh8o4xyFak45OTOzJ9DTfTlNTay4oAkYYLE08TX4kyqXtsXv33kxPc7o1bW/LYdH+YKnjPDmNwFIOyS+D3smTIRcNyXFJbOuFxWIRi80mWFpvgi2gpwtagh0QYEEX1ejw44U8OGBpWWkHdDQXTXNLR4ali9ciFpzgzK3JqMl9hd6xY8f9LV1ra2cWIAaevBSxMPKUC4d6L/v3H8ywdFy1tXdnwRp0w1/Eot3femurI8iNF/JCoafjisA1BJFohEV/JDhEtwSlYTyBpYFLOjt3ZHo6RovlYsyBha4XxhV6/O+lu7svK7+OqyIW9/neS6tySWApD3o63nfs6M941XFVxKL+BPBpk6A08ISejve+vsEMS8dVEYtxRTJZ2twL7YeeJlKGT8atPogoYtFf6M8tLSExMP0KPc0Pxxim72i+qCIWGzqwmiUoDeMKPZ2HGGNgab4oj6Xjivlyw5shmTrjED0NgjI2vivD4j5eGHfo6bgiWIv6VFIPdHbv3uf/zDEPUS4dV9QbPR1XYDFveoFfdHbtCgmeSfYM95pH0GPphimzV03BxtDuYDG/epncfyArlyY/hkP0dLMKltor+iM6OtcemDqUYem4itm+19ducPx4aWT7NFiOt3360KRor86enW+vKA/c7z8w5W/pxsdrtu/MmZDnj0TmavuoP3XUeZtxBffaT7ztYz3ghTbUID7e9rGu8MK4olx79oZ+QjtzTx1XZfZKbR/9CqyJXaFt6X9gqe0j4JEF8HDufb4RYv+3NDe7F7729dhXds0YMAa+jwxgDJ9euixnYDFcTIg8TfZCpCuN3MTTdHR00TU3N+dYJKqBxXChx1NuL0Rt0qiFPLkvYmFYwdLFZsAKSX9ZPG18a4uHdjy1rmEF40CUJbAonxfKjZ6+NaB+1NMLZUZHF4PUDSytd8C65v/UsZDUCIhEXwRLF4MsatjM6KaERS96JKn10ts7mFts8mYohkW54lghGTFBSlpksemxwPNy+fLlrI6a7JgFNDq6qGtpbXdEZvPCU3508lhXMqwjR0LUwoAV3kAMDg07NlEkm/VSxOIt7tZtze7gwUNeJVs0oadvIDDURFPUCGLzsa66V1atdkRe9MICpIZ12V9yIyOjjgh7+jauiMUbL8qli2z6LXq6cCV6IFg6ropYjCsWRrrguXChhqXjqr9/yL26+vVcVM8yLK0j4wo9xWKB2tTUko0dX/EiFuOKRbc+OGBcoaeLYDbtlF/H1XysG2716rWuVyKqUp4i1t59+922pmYHJ16KWIwrOCVKqBfe/qKncwebY9pIx1URizbe3tzmdNFI+xWxqOPKV1Y72t1LDIsHDENDI17FMa7Q04U+G1nGrY6rIhb9mGiKA4Mhmi39vYjFpqKGFcaVx9JxtW79xgzPF4xxhZ5uxo+fOJVh6bgKWLf8n2bzkj6EoB41rDDXnp6ZuY8VxtXMTG2e0HHFw4od0ifgFyx9+MZn5kwdV95eKVZ7R0/ugQbtXsTy9or+4uXMGW/7gr3q6Czaq/m279z5C1kddVwFexWw2FTz46Wh7ZPTI7Oz3o4G2zffXtVsX8xeadvG7BUPf2L2Cj68wBPc82bVSwyLNqQtvTDfwX3R9tFXue4l2L4wrvr6hnLRf2njIpa3VyfkQSFti56OKzbBjNvFKvZmbLG2rNXrsWCAhU6VY4qPBRlWSWPAGDAGjAFjwBgwBhYYA7YZW2ANZsU1BpQB24wpG/a7MWAMGAPGgDFgDBgDC4sB24wtrPay0hoDOQZ4xf/MsuW5a7EPhw4fcUeng19ZTIegFhzhScnhI9M5/5cyfbBSQTfwmdAjXY2wUkE3qB/1TAnlSgW3mD523B061DhBLvcZHBzOHTWL3RsfLvWlielwjXKlklEfP3HS4YOUErD0eFhMH67wP0gJiZP1SFdMH1+T/eLTF9PhGliXLodjWDE9jqdwLC0lHCHTI2MxfY7WTO4P/hYxHa7RB/W4XkwPHw09yhjTybD27XcpZ3p899SfowyL8TF3rnEwE3xN1PeoERa6jQQ+OV6YEo4V6pHamP75Cxfd3n2Tsa9y12gfPQKV+/L+B46PVZkn8A3TY1gxLI4/6vHDmA7X6M8EKmkkHKOiT6fkwNTBnF9ZTJ/xyrhNCWM2NTdxRLsKFvPSseMnGt7y5q1b1bAOHc75lcVAObLJnJkSjn/qMeuYPoEoqtQRv6sj4lMdw8JOVcGiP1fp02ClbB9lUh+1WLm4BlYq6AY+eOr7WYZVs1fBfSGmhw9XZXt1szEWvsBTciw9dj9fR45SNxL8IAfl2HAj3YX4nW3GFmKrWZmNgfsMsEghgEdK8PHC36iRMOHjSJsSzqerb0CZPlgpg8S5cxz4UwJWyiBZ0ufAInxZ0mdL+hx6hMsc/DWogH7nf8fJX533/fXi/6+sWuPwoWsk08dOuM1bgn9NmS6+bKmNFpt99dUpw8L/TINPxPQs6XNgxZI+17jATlWxffTnKn26iu3DV0/9uEOr5H8DS/1n89/WPvUPDDt8uVNCAA/1I4zpW9LnGCvf/2u2Gfv+c2x3MAa+bwzgCE0Aj5QQEWvf5IGGarx5YlJPCU+C9+5NPz0HK7UZGxremYuuV3ZvsFJvxqgf9UwJWCnjxhP2XRLdqQyTgAGpN1BEhdPACWVYlCuFxWJ6TCJgNsLCsb+RwFVPT28jley7gcGRXMCI2B/whFejN8Z0uAaWBmaI6RGpa6dE04zpcI0AJKm3ILzh1OAQZVg8cZ09G4IWxPSITEdAkJQQgGRGHOdj+ocPH3Ht7V2xr3LXhoZHc07yuS/vfyDiGHopQSf1poc3VBrprAyzvaPLHUy8OT4zO1fpDRTto5H6YvcknUOVp+JEwNMImDEsAiTQd1JCfz4sgWti+gRBoU+nZHRsIvkWhJQOzAEp6enpS85NBLyogsW8xFu7RkLKh0pYu/bkolbGMLOALc1tsa9y1whaQ7TERsLphirl2r1nX/JtL3aqChZvVKu8VQUrZft4A03ZUgJW6iQHb5c10E8ZZs1eNX4Dhe3TqJVlWJTrWuJtFqc4xidCxOZGWKnTF909vY6gOotVbDO2WFvW6vVYMMDi3QJ4PBZNbZU0BowBY8AYMAaMgUXIgG3GFmGjWpUeHwZsM/b4tLXV1BgwBowBY8AYMAYWHwO2GVt8bWo1eowYIHcIxxQ1RwtHF/m5fftOnYnhkVE3OhqCNXBMDx3N48Hv+JZpHiXOl9ewQv4ojhWpv0jACsfiOI4CluYn81iaM4cErJ2SG4zvuJ+ea/dYeowhhjU6tiuXY4ijHfOxbmblunQplJV6o6dHF3EW1qNfMSw4J0caR6i8xLBIZjk4tNOrZO3C/fjxAhZ8abAGj3XzZsgLtItkmHIsCj+6+Vi3MizNpQZ36Gk/4bhNc0s4MlSGxfEQzVfDEagiFk7t/f3D7s6du75K88oFv/hInDoVctN4LO1zHDclD5f6CBbrCBY56jSRcgyLIzf4ZqSwenr6HYFWvJA/iHtqQBUSw5JbS8dVrFxgabAcj6VjgeNJ+Evq8aMo1o7+XB1xckdPsTjyiB9nY6zbbkdvf87JP2CFY0tHjk47yq9jtFgu7rN12/bcUTnKg57mJyOoQA0r9N8YFu2jCZ5jWAQLoe/oGJ2PdSfzi9UgK7RfrVwh19n09LR7axN+OGFOK2LRX+iDGsyEPlrE4lhnqlwZ1sCw27MnBPrwWPRZL4xX5oBYHfWINjnLyOvnhTFNuRSLQCxg6dzh66hjgaOfmmw3YIVcURzFrILFkfPxiWBjuDf3ZB7zAhZzps5Dvlw6rsgVx3zuBU6KWOBSLp07vF3QsVCzfRMeKuO3iMVYqIJFknlNNN/IXukY9eXSPscxWMrmhTJTrrztq9kF5ZDj5+hpP6lq++BeAxV5G6NYHCukLb3QLtyPHy+0H3zRnl48lvY5EkHjg+aFvjcfq2avNOhRzF5xxJJxu1jFNmOLtWWtXo8FAz6Ah0bYY3FAAsizcyFyGs7v6phPgkV0BiSyFT5SOAvvPxCiz7GAQ08TURax8FlBp38gBAjBIR8sdcxn0YXe6ZmQdHLVq6+7V1a9Vm8rIumh09c/WL/G4hwsPV/PQgk97u2F+qmTP2VGhzp4YXEOlkYRhAP0iHDnpYiFPxE6+Gt4YXGOQ7QaVBY36BH10EsWpEQShZLAEx2MmReiV1EuxWJBgh5+T162bG12b0nAE/yv0NENLVG1wNK2ZQONnm4SXnt9vXvp5Vc9dGak0dHE2fiCgaXtwUYcPd0IkZCXcl2UBKzo8OMFXx6wtD3Y9KKjUTC3bmvJsHTRUMSCE7hvbevw8FmbonfwUIioua2pNTPgGnWxiEXEL8qliyzGAnq0sRcWA+jpuCpinThxKtMhaa0X+i16Oq42btzsXvzeKzk/tSIW/l3cr018yxhP6OmGgyTg6M2cCYnSi1iMOXRa2zp9sbIIjOjphoN7oXdKkrkWsRhXlP3NjZvrWJQHPY0syGew1E+tiMW4QgduvbAxQ0/9PwlOgJ6OqyIW44rFWlNTq4fKIo+ipxuO1tbOrO/Q7l6KWPQX+jN90Qv9Cj31gSGQEeVi4+mliMUcXcRiXKGHL5kXxhhYbIi9eCxdCDNnkvjZC+MQPX1AxmIaLI3Wx7hGT8cV8yVzihfqgY7OQyM7xzMsHVe0B3o6rop2gSiN6OjCnvoybjVaH/MgeprYuIhFu6OjfoP4NVFH3cj75Mf6IKqIRTAYsAbEP48xCpZGXqVt0dNxtea19Y4fL972aXAsxhNYavtoW7Cwb16KNoaNPTqaTJ3ygKVjATuLno6rIhb1Rwc+vBAdFO7HpM9526cJl4tYzHdgsa7wwnqDcmn/pZ3R0+ic9C3490J/QadLgo3Qr8BS3176H3o6rkhY/d0XV3qoRfe/bcYWXZNahR4nBniKViW0PcEHMEKNBIfjVLQ1/p6n1Dp5l2GC9fbbb5d9nV1nEa6GuUwZrJRDNPWjnikBS58Ox/QxsvqmJKbDNRZ5+iQwpocB1g1VTIdrlCuFhcE+Kgu/Rlj6Viemx2I05STP39E++sYjhoXxPyqLyJiOx9I3nDE9Fui6II3pcA2HdV1YxvRYSBxJBGHg71gQXLocnvzGsFhIpAI68HdshlmAN5Izs7Nuz9608/6hw0eTdbxw4YJDLyXonL9woaEa5a4SInvv3n25RWoMlA1EFSzaRxfiMSyeuutmIKbDNTYmZxOBWDhNUCXYAf1ZF/Wxe3JMvMr8xYMIfaAVwyJQBnNASniglJqbmEeqYLHY1Q1C7N68zamCRZn0rXcU6/bt3MY4psM1FvS62Yjp8bawSrnYyOmDthgWdqoKFv25Sp8GK2X7KJM+XIiVi2tg6ZvRmB5c6SYopsM17JW+BYvp0Yap/sXfUa4UFgGWdEMVu5/H0relMT0e+FQJqhX724VwzTZjC6GVrIzGQAkD5jNWQoxdNgaMAWPAGDAGjAFjYAEwYJuxBdBIVkRjoIwB24yVMWPXjQFjwBgwBowBY8AYePQZsM3Yo99GVkJjoJQB7zNWqnD/C87l67n2mD5H9zi7nRJL+hwY4gy++nOEb8Jv5G3i/HtK4D6Fxbn61rZ0fiqwLOmzJX3WPof/RuooFsf88BlJiSV9rjHEMUb14SzjjaAbYxKQIqZHAIMq8+/atRtyPqIxLOxCFSxL+lxjjyPwVfiypM+ht8EXufEaCX7P6vNapguWBgOJ6b32+hvmM+ace1+MHH+tpbnZvfC1r/uP9r8xYAw8JAZsMxaIZrOpQTHCN/nfmPhT/lQ4NmtQjDxC+GSbsRoX4+O7KyXkZOGqAVwCk+E3/Hm2N6eTexJEQgMUBITwGwElmraHgA7hm/xvOJmnfC4mJ6fctqYQ0CGPED6xmUn5vI2NT7iVr6wJf1TyGxsoDW4SU8NnSYMwxHS4ZpuxGjPT08eyACRlPPnrJJjVYB3+uv5vm7HABgFCNHJe+Cb8hr8oc2ZKCBCiAaFi+vgrVdlAEXiC4FGNxDZjgR3asEMCEIVv8r/ZZizPx7v9ZG/G3i2D9vfGwHvIgB1TfA/Jt1sbA8aAMWAMGAPGgDHwLhmwzdi7JND+3Bh4Lxmwzdh7yb7d2xgwBowBY8AYMAaMgXfHgG3G3h1/9tfGwHvKAAkgn12+IlmGCxcvJv2ROKqRCgvNjTgayU9KwEqF9yXJcSqsNfcBKxXaHn8r6pkSsFKhgjOsC2ksQuCnwuRfvnw5GZ7c1zGNdcWRWywlhHTXxKcxfbhKhe7m72ifFBahx6uUC6xUOGSOMp2rUEdCcmti1VgdSYSruZBiOr6ON27eLPs6u054/8pYN240xGLckqYgJXPnzifrSMJa9FJSwwoJnmP6HN+tMh5nzpxJ+ouQjLcKFpxqwuJYuQjV/qCwqGMqnDtloD/TrxsJYd+rlKsKFmNMc9iV3Zcxm0rpwDxSZS4Hh/mpkTBXVsVK+byCpbkhy+5LuVJY78heSf7D2D2xU1XqSFtXaW+wUraPnIxV7Wgl21fRXj0o20cdU1ik3kml06A9wCqzfdSdH+ZL0gH4zyl+Y+38KF+zzdij3DpWNmMgwYD3GTsmiYFJ/kkCRjXYJOUlAa4X8hyho/l2DkwdzM7ga2JgfFvQ00UoiVDVd2b27NlMRxOr4ufCmXL1dxmf2JXpqTFb89o6t3rNWl8sd3ZuLtNRXw1yO4E1NRVy8Ezs2p3pqQGlftTTC2Wm7NTBC3UDS5N77tq9J9M7M3vWq2V+RuqHg0EBa3RsvK7jEw9rvXfv2ZvpaaJQEtqS+NkLmyCwNMkl/kqUS7HIQ4WeLhybW9pyARZYsKCjSVrJXQOW1ptEpOjpQmj9G285Eml6wXDWsHb6S1k+ObBI/OqFJNzoae4eAhTgd3Xlali8osOPF3LhgDU8Eq6RMwkdctd5IZEzWJTHSxELTkgAqj6CJFVGT5P54jwOliajLmJh5CmX+qhMHTyUYWl+OIKwbNq8LTeuiljkksIvjoSxXg4eOpxh6biin+LzpguVIpb3R+rZEZKtMp7QU5+07p4d2T15sOGliMWYo1zKF+MKPc2dxr3Q03FVxGJcfe+lVTk/NcqDno53OCAJs274i1jUn/bRADf4dKGn+btoG9pIx1URi3EFlgYMYF5Ej7nNS3dPb+a3pJvhIhb9BSxNkk2/Qo/kuV6GhkezcmmS7CIWQQ4I/MAY8UKeRvQ0zx/zNnXU/FoeS8fVq6vX5hJuMw7RY1x68QmRNR8k4w493XwxL2nCbeqBzt59kx4qy4dHuXRcMXehp+OK+bJpe0jejW8oOppPDx9OfMbUP7OOJQ/SGB/q60m7g8X86oXxTrnoL15IQoyePhiq2atg++iP6DDve6GvgaW5EklIj57avtfXbnD8eGGcoIM98oIfK1iajwx7hh72zUvNXgUfVMYvOtzXC+MKLJIse8FGoIfd9QJXOXt13turvO2D+3379vs/y+w/WKwHvNCGisU6Ah1NKs64olx79wasur2Sh0yZ7ZOAQPQXsNT20a/A2r075F2k/23d2uQ+8qEfdEufWBL94SF0Z0cYU778C/V/24wt1JazchsD999SrVi6LPeEjQU3BlqDVLCo0IAUvH1ARxOR8ntxscmiFz2evnshApcunniqjY4ubjCGYJ2TBeLMTA2Lo5VeNm7c4t7YsMl/dHxXhqWLOv+UTLE6O3fkFk+UGSzdzGBYKBdl8UK90dNkxF1dO3KLJ97A1LBC4myiP7Gg1qSWHkufqONATjAAL7QLWLoxYlNNuRSL+qLHWxQvO3r7c8EtSJSJDj9eSGoLliY79li6wcGAsxn2Ese6nGHpwpgFCPfTRR3BU8DTt17FcqHPonRqasrf0s3N1bD0KXj/wHD24ECTgBax4IQNAYFDvLDhQI/6exkaHnHbtrU43tJ4mY91NSuXLkDpt+hphK/hkTG3bVtkscunAAAgAElEQVRzblwVsehDLHB37QqLRhZz6OnDESKSEsBD3+zNx7qWYemDCcZVDSu8HWXTzT01MXcRi3HCApfFqhePpQtXFvE1rDBGi1iMq1dWvebY1Hgh8TR6GsFz9+69bsvWptxbr/lYN7L2YYHmBc7R00Xwvsn9WRvpuCpiMa54SDQwOOKhsnkRPX0ARNvQdxpj3cz6IH3RC/2qiDU1dTAbHzquiuXirR4L3D4JIkF/R083vYcPH7mPFd5UeSwdV2wGtktQGsZVEYvNDnOAjiuPpeOKeYn5yQv1QE/nWj7XsMK4CjYmjCs2m7rZZ4zWsMJC/+TJ09mcqW+EAlZ4m5zZq64dvlhZW4Gl9ooyUi4dozF7xea8XQJSeHt15kx4M03/AEvHaAxr41tbHD9eGtkr7b8xe0XAE42My/iljjF7dVY2Xh5L3yYT8KSltdMXK7PXMSzsFde9eHuVs33dvTnb18he6WZ/drZmR9Ve8XCnWYIxMQ9zf7V93l7pBp22nTow5X7/P/+e++av/0b286Ef+IBbtuSp+udv/YffdYcPhU2qr9NC/d82Ywu15azcxoBz2ealyjFFI8sYMAaMAWPAGDAGjIGFyMD/+W9/2X3w2fcvxKJXKrNtxirRZErGwKPJAE/mbDP2aLaNlcoYMAaMAWPAGDAG3j0DthmrcWh5xt59XzIEY+CBM8ARlWeWLU/iksz12LETDfVwxtXz5GXKR48ec0enj5d9Xb8OVsrxGJ+hSfF1qP9x4RewUs7C1I96pgSsVEAKzrGnclhxH3y19Ahc7N74Q6kvTUyHa5QrhcURj4OHjpRB1K+DpUdL61/ILxxjVL8J+Sr3K74oeiQm9+X9Dxytwc8qJWClEoVyDEd9JMow8TvQo0AxPY7hqL9QTIdr9MELiaA0s7Nz7oD4C5Vi7Z/K+azE9E6dPp07MhjT4RrjI1VHjlihlxJ09LheTJ8ji+pPGdPh2tjYRM63KaZ34cKlnE9UTIdrtI8eP4vpcdyuyjxBv5mZCcfiYlgcqVSflZgO1+jPemQspsfxLvXViulwjWO+p06Fo9ExvWvXr1eafzn+mZqbOFrGHJAS/JrUXzOmf/PWrUpYlOn48eD7GcPiuKX6t8Z0uIYfox5bi+kR8KFKHY8cPebU9zOGhZ2qgoWPn/r5xbC4BlbK9lEmypYSsMqCW/i/hSv1/fTXi//DvR5TLX7PZ9ow1b/Qo1wprBMnTuV852L381j02Ubyxed/zr3/6WcaqSzo7+zN2IJuPiv8486AD+CR4oGz/Pj1NBImfBxpU4K/iwYoKNMHK2WQ8E/ZtGlbGUT9Olgpg2RJn+t0Ze2o/jvhm/BbV/cO9/raN8KFkt+KAR1iapb0ObBiSZ9rXEwfO5H5eQVm4r/ha7h3bwgYEdPC14iAGinZvr0tFwggpm9JnwMr+P+qv174JvxG8JAqdsGSPgfOqtg+ElGrv1746/xvYKnPYP7b2id8G/EbSwkBPNS/Mab/qCZ9/qmf+En3TIXI0bE6LYRrthlbCK1kZTQGShjgifHTS5eVfBsuE4GJSFaNhDdPGIiUEIFx954Q+ahMH6zUZmxgcNj196fvCVbqzRj102iEjcqVMm4EDBiXqFZlWARFSL01mpyccmNjIUJWGRZ1TGHxFmHnaAjC0AhLA2zE9IgA1tnVE/sqd62vfzAXICb35f0PPGEfGRmLfZW7Bta5843DsPOEl2AZKWERn3rbwFvc1GKT+/T3DzmNphm7N29eB4dCcIiYToY1MOyIJNdIiLDY0hqCupTpEoxCnd1jerwt1aAVMR2uoaMO9zG906fPOA1aEdPhWmtre/Lt5ZkzZ3MRKsuwaB/aqZGcPXsua6NGOnw3PDyafDtO4Ab6Tkroz6k32gR8oE+nhDdxGgQnpn/p8uVK8y/BhVJzE2/sqszlzEupN6G8Ya+ENb4r+fYSLObMlBC0RgPqxPQ53VClXLuwfXsa2z7sVBUsonpq1NVYubgGVsr2USbKlhKwUic5iJargX7KMOFeA/3E9HgDXdVe8Ta3kfA2XoMGlelSRw0iEtN77rOfc8+ueDr21aK4ZpuxRdGMVonHlQHzGXtcW97qbQwYA8aAMWAMPB4MmM9YrZ3NZ+zx6O9WywXGgG3GFliDWXGNAWPAGDAGjAFj4B0xYJuxGl22GXtH3caUjYGHwwA5OjimiJO1FwIk8KM+Vhxt02MMt27fznT0aAAbO/zB1CkXfwGw9JgERxg0MaXH0sSkYIClTrkxLPJmab4i7sP9YliUz0sMiyOKmpiyEZaem4cD7kk9vJCLSJ38b9+5UyuX5PyCc/JmaeLeq9eu1bCkPTjWqcfuaBfux48XsODr3PmQPyqGxVFMEs16iWFxBBMscnh58VjaTziGRYJlL3fu3p1XLrBoI00wSjtQdsXCqR1fAz1KWqwj/OJrSIAOLxxzybBuhnxFHG0Bi/J4KWLRtlu3bneaSDmGdWDqUHbsTsdCDKu3d9AdPxHy73CcCr0bUi6OmXFEKYnVN5gLlnP9xo0aljioc6yIo3L0Ky/RcvUN5uoYwyJoTfEoUwyL43Tq5O+x+N8LQQWqYJHniiSvXhjn3FOxjh0/6eBV54555bpzJ2sfDf4C5xmWHIE6depU1ncaYdEuHMXUpMweS49TkbAWX9UUFn1QgzUwp1EuxSLwCH1a545iHenHg0MkZQ4BNWJYjFfGbQxLx1V7e5cbGQlzAOMwK5fMjwQpybBkHvLl0nFFQAdNpOyxmC+8YGNKsaT/Mp9ofj3mDu6Zw7qfa1Dnjnq5BGvnzrHckfMYVt1eSR3rdkGwOCY3JvkI4TcrlySop/9Sx5TtQ4cfL/QhsGL2KmX78LPVI3yNsPRooa+j9hNsX9ReSR3hHHtFe3optX1yTDxmY8CCh4uXQk48b2NoKy+4M2jAlhgW+mDRZ714LO0nn/uZn7Vjis4524z5XmL/GwOPEAM+gIdGecORl6SZmlCUhJbqAH/8xMlMR4N6sFnDWVgXIDgYgzVzJkQoK2Lhs4JOb99AnZk9e/ZlWOpbxoSLnkYoI3ksyW+94B+DjgYIwbmfcun5eu6F3slTIQkz9aNsXigzOuokzXl4sIgG54VFKnoaVQyjReAKLyShRIegF172H5hyOEQPiR8Ri3X0iMbopYh1du5cpoPDuxeiwFEu9Unid7B0w0FwCC0XkfbQae/o8lCZbwpY6tuALw16R46GaJNrXlvvXnr51frfsalEhySpXvAFA4sFuheMPnoacYvFLeXSZK7o8OOFTQNY2h5sntHBh8oLfg1g6Sa3iAUncK/JtFnYoKcL+63bWrJ7akTCIha+YJRL24OxgB5t7IXNE3o6ropYRCJDR9uDfouejqsNb252L35vZS65bhEL/y6wuO6F8cRnNnNe4AA99VMrYjHm0CExrxfGFXrqS9ra2pnpqZ9aEYvNNMljqYMXIquhp+O9ra0rw1I/tSIW44pyqQ8XPkzoqf8nbYOejqsiFuMKHRI/e2FeRE99rOCAvqPRZYtY9Bf6oPo30a/Q0wU0cxr3VJ+3IhZ+ZWAxRrwwrtDTh0eMMbB0w+yxdFytevV1t279Rg+VjUP0dDHO3AEW9/HCuEZPk3xTLuYUL9QDHfWz5EESWDqu2ju6Mz0dVzWsEGSFjT1Y6s/IJgvuNVoqbYueRvpkHmfe9EK7o6NzGpsZyqWRRAlUhZ76f9bsQsCiP6Kjvn48MANLI2PWbZ88PGLO5McL9ges3t75tg8b6AV7hp6Oq2K5GL/okCjZCxt4ykUydi/0E/Swu17gSm0f9UdHk3AzruBe+xz2Hz3WA17m2auzc5mOBghhXFGunTvH/Z9l7QyWRq4s2qu5c972ddf/jn4Flm7a6H9g6bj6zI//hAXwsM1Yvd/YL8bAI8UAb3iqhLafnj6em3BjleDpqxq2mA7XWMSkwg6jB1bKiRmjrBvJsnuCpU+HY3oYFOqZErD07UZMH4OthiCmw7XR0fHc09SYHkZTN0ExHa5RLn0yG9PDmB+uEL4frFRoe6LK6duN2P2ych04mCUXL/ue6yzQU8EOPNaVK1cbQWVhznURWabMhloXljE9Fvu60YvpcI0+eFGeGMf0CCKRCsKQYU0dcizAG8npmRk3MbG7kUr2HeMjVUcWxLq4LQNFRxfPMT3KzdvElBD85dTpxqHa2UBUSStA+9BOjYR5rso8Qb8hcEgjuXjxYu5hTJku/Vnf4sb0CLijb+JiOlzjwQXBURoJ45VxmxI20am5iXmkChYPSE6eCov62L1v3bpdCYsy6QYhinX7djZnxr7Tazxs0Ydj+p3/nTm8Sh3ZHKRC7mOnqmDRn6v0abBSto8y6cbF16v4P1hJe3XiVO6hXRHDf8Ze6Zsrf13/pw1T/Qt9ypXCwl5VSTcDVsr2ffH5L7gfsND29mZMO6v9bgw8KgxwVMOSPj8qrWHlMAaMAWPAGDAGjIEHzYD5jNUYtWOKD7pnGZ4x8AAYsM3YAyDRIIwBY8AYMAaMAWPgkWXANmO1prHN2CPbRa1g746Bm+5Y69+73/3Sj7kfema5e+bpD7tPf+G33d81T7sQUqDsDnfd1D88555+YolbWvxZ/g33Zu401g13ZPOfuxc+8zH3/idXuB/8xBfdt/65z80G//2ymzS87n3GGio5l50dV/+wmD5HITi7nRL8JNSnq0wfrNRRDUv6HNiDL/LGNZKav1bw6SrTBcuSPrvMH0r9kcr4wn8jdfSWfHHqj1SGZUmfa8xY0ufQQ/BTS+VuIv9elfl37doNrlP8TcNdwm/YhSpYlvS5xhl2qgpf+FOpL1tgPP8bWCnbh++X+s/mEcInsFLHAS3pc+Brof5mecYWastZuR8AA/fczFu/4z751HL3f/y7/+ZWb+t0XdtWub/45U+4Z5761+63N55y9xre5Zrb+s0PuOUf/ar7w7/+tvvbb8vP373lJutBhe6502+84D76xAfdl/54tevs63Vb//E33KeXPeV+/L/2uxBTr+HNol/aZizQwmZTHZbDN/nfMG4a6Sr/be0TyahTCx40cYhObaCGhnY6HN5TQrlSWLYZCywSREKDiIRvwm8Ep7DNWI2PLVub3dTBECglsBR+w79DAzqEb/K/vbJqTS4QQP7b2ifbjAVWbDNW44LofcyZKSFYhAbriOmzQWHOTAkbHg1AFNO3zVhghSiiHR0huFT4Jv8b3BNJspEQOEoDQpXpgoUvpwrRJV9ZudKdna0FD/upn/jJegAP2v7VV1a5ubON/UMV71H/3TZjj3oLWfm+fwzcGXd/+eNL3TOf/Ru3V1+D3dzlvv3Ty9yKT/+FG2/05urObvftzyxzH/jGBtfwfcaNPveHH1viPvybW1wI3nrHTb/4Fffskz/r/ufhxlu+RgQQDKGKzxiLfA3nHsPEIKUc/Pm7S5fBaljjDB6st99+O3ar+jWCE6QCFKAMVupJI/VLbWYqY10BK4QArhe48AsO/nfuhBDsha+zj7QRm+aUUMck1tV3gtWo87qMK41gVlY+2kfDgMf0CGRwoWBMY3pgERCgkXD0NhUAg78nrPiNGzpw56MSEroKFuVKOZATYKEqlobEn18q51iUpoJW8HeUK/XggO/RSwk6Gno+pg+fVbBIdUAdGgl8VsGCUw3dHcNk8fWgsCgXfScl9Gf6dSNhXFQpFwvNJNadO5XmX8Zsam7ilEOVuZx5KRVQh8BJlbAugdV4cQ5WKigKfD9Qe1XB9mGnqtSRtq7S3mClbN8DtVcVbR/cpwJh0YZV7VUa63/fXh09ejQ7cfQTn/60m52ddb/48191H3jm2ewt4Td+9Vez79avXddoeC6o72wztqCaywr7IBl4e3a9++2Pf9g99//ucvll6y3X9Z8/5pbNO2pYuPul9e7Xnl7mPvc3+1yj5fjt/j90P/TEB9y3Wq/nAN6eW+t+ZekS99w/pqOX5f5QPpjPmJBhvxoDxoAxYAwYA8bAomDgu9/5l/qG7Be+8vPug8++3/mN2P/9O/8hubFcSCTYZmwhtZaV9eEwcPeg+x/PLXPLP/5Hrr/BQ/zbI3/qPv3Uh9yv//dV7k9+6cfch5evcP/qE593v/XtFnes/sD+njv10pfdsiXPue8cKbwBuzvq/uxH/n/23sQ/r6u6++2fEiceklAopS1tgQKBQgmBJFCgwy3wljQtb2mhtPe9L6UMpZTyTr1t6UR7S5vEdjzb8SjLsq3JsmRbsiRL8mx5lm1ZtuzYiQ0Z9v18z+P1nN9ztM/ZOylJNOz1+egj6Tzr+Z211977rLPOWcM8d/8X8n5Wr3SAyRl7pRpL/EkDSQNJA0kDSQNJAzNBA+aQUdZ+4d33ZM7ZbHPEmIfkjM2E1ZhkfB018KI7t+px9/Z5C92D/6u/oojHy27i6U+7+++6x93/C7/hvrO4ybXt2OB+8NWPu7ffPd+98/Nr3bnM93rRHfw/73Xz5/+2W1eMJHpp1H3/w/Pcwl97unJ8hEd99StfcV/+4pem/Hzh8//VLZh3d0OfoV27ul1bW2dDE81ly1e75SvyV/r0EoFn797e+rmHhw86mjAflUa3u3f3ZHwa1lPEopcIWHv27Ktj0QsHrMOH8+a03d17Mz4NU6Hp8JNP5eOnOS1YPT15k2EaNYOlTTR7evZlfNpEk/EhmxEyg8UYjOhnApY2kEYH8GmPHBp7KhaNfuFBt0b0bSL/oa+v3w5lDaDh0x45K1etdTRqNSLMCJ7Ozt12KOtfhVw0RTUi3h6+M2fy3mkrV61rwCJkBh7Nb6PXEljauBVc+OgtZgTPfzyxxP7NQvCKWORkwadzS68a+LR/zKrVz7inl61sCBOFhx8jeteA1SXzQTNeeEZH8+a0a9dtzPg0JLCIhU7Q/Y6deRNjw9IeZc+s35RhaQhSEYuGssilOmR9wKf9uzZuasr4NLSziHXu3FjGs7M1b9TMuoVP99W6ZzZm8msD6SIWaxu5tm9vNRU69hV87Amj5m3bMz7do0Us9hxY8BrRqBk+fhvRQBo+bcxexOI86H7dM5vsa5k88CGfEU1bwdI9WsRi/PBs2pTn/tBPDD6uR0Zt7Z0Zn+6rIhbzAtb6DXkzauYPPt3vNLZGfm0gXcRivbCemScj1hV82h+Oawvn1P6GRSxCvtj/q9esN6gs1xE+bT5PjhRYp6Qxu2Fp+DV7lpw9I/YhfOxLIxrRg6U5laxv+HRfIRfXJyPGAY9e07h2gKX7qqOjK+PTfbVs+aqGhsjoF6ze3v0Gn13f0L326+M6CJ/uq6KNYd7hYVxGzClyaf+5rq6avdIQ4CLW+fNmr3Lbxx4FC/tgRCNnzqn7Clul9spsH/bIiP0Elu4r7BlYuq+K9oo9Co82kDZ7pXuBazF8uq+KWIwfHvRhhJ7QvdqYcts31V4VbR9j1DXHPHNO3VdFe8V6gYf1Y2T2Sps+s/7gs3311f/+lcwJo1Da73/+87PqjZjpITljpon0O2nAveTGd37TPXTv3e6nHv1b11+ZEvGCG/6HT7p3vO0T7h9H6q/BnHM3Xe93PuDunffz7k9bAXjRDX73nW7+/N91m4vh9C+ddU88erdb8Oi/V+qe2PONGza4dWvWTvlZumSpW3jPfDc+PlHH4OLGTYjmdHDjtH7DljoPNwjwaHNHGh1z8dSmqRhz+DTfDKxn1uc3POQv1LBO1/ExLGBduJg3OuWmoYaV55txQV+yNL+x4KYDHr3Rv3hxPMM6P3ahjs8NC3yaO8H49OYJmeHRGxLGhlxnz+YODjqAT+PkN2zc4tau21A/H3kV8OgNCQaveGOB8YBPb3g2bmxya9bmWOSOwKM3JNyUIpc2KMbhgE9zFKj6p1jk2hSxuKkBS2/+MZDw6c3TqtXrHEUwjHD64eHHyLD0xoJmpUUsikOsXvNMQ35TEYtzI9eQ3GTjvMCnN2LbWnY6nDvkMSpioRN0r0n+ONPwqYODIwMWb5CNiljMFXL17c9vZrnRgU9v6ijCApbuqyIWuUFg7d2X34ByAwaf7qutzS2Z/JqvMxXreoalY6RxcA0rz3nq6tqT8ekeLWKR44nsWgWVPQofv416enozLL35n4p1w/3HE4sbKktywwqfNjbe19uXYem+KmIxfuRqbc0rhKJz+MbG8qbS+/sHMyzdV0Us9hVY23fkjjDXxRpWfu3gBpS1U4XFemE9b2vZYarJ1hVY+tBmZORgJpfu0aJczz9/K3PEmra21LFY7/Cpc3no8NEMS/eoYWneIM7AqlXr6ljww6eNjbnxZh3qvjIs3VdcS3jIYMQ44Dtz5pwdypq5g6X7imsXfLqvuF5qQY3JScPKr7UnRkcz3fuwNKeOBzJqr5grzmc35wjHNQ25dI/yUAc+3Vc125fbK5/tG7twIcNSx8tn+7BVjfaqZvsa7ZXZvnz9mu3TfcVDA32g4bdXNdun68Rnr9AVOjMye6UPucxenTiRF/HxYTGHaxvslc/21eyV2lazV8y70aZNWwv2qtz2HTue2x3WH/O4edNm9/FHHq07Yjhjv/zAA1kOmZ1jtvxOzthsmck0jv+kBm67U8/8ifvgorvdWz/6Hdd5uRBS+ArQXzz8Pffw/Hvc+77Nk7eX3KG/eV/tzVhjsSDn7M3Yp/K3E6/gNBlrClN8pRpL/EkDSQNJA0kDSQNJA9NVAx1t7e4TH/t45oQR+YMT9va3/Yy7b8HC7G8r6jFd5X81ciVn7NVoLX1ndmng5atu7/d+0/383fPdL376+27/9eoKgDb4F29fdxNXb04p3vHypSXuMwvvdm//7zyhfdldXPLrbuG8R92/ny44eHdyxu77fP5k0rBjfydnLFZTiS9pIGkgaSBpIGkgaWC6aqC9rc194tGPZQ7Xonvmu3e/453Z3+SIfeb/+q2sgIflkOGQpdL2hZnc3tLiHv/cY4Wj6d+kgRmggZfGXes3H3Rvnnef+9B/2+BOacRhlfgvHHR/96H5btED33X9jaUY3Qv933W/fM8C98g/1OLPX9j35+4X7nqL+3/aGsGtmuKDf5/HqVed0vcZoQ08LQrR8RMn3ejJU5VslEPWmPkyZkL1ToxWY/FdsELl6InV13j4snOChXxVxPg0zK+MF6xQE03CSjSMsAyLmHkN1fHxZaEggf5OfA+5QlgWBuk7jx4DK1RmmjBG8qxCBJaGg/r4aZh89Nhx30cNx8C6Oll8RdzA4s6eO9+QB9L4af4futcQu/yT/C9CyjSnJP+k8S/kujxxpfFg4T9CF48cjRvjpfHq/jfk7vUPHCicYeq/yHUxUIYdHcAXImTXsGEfP6GUMVjIrrlNPixC0WKwmB8N/fNhEYoXi0XoaxURrqW5LmW8rGfNf/HxEfIWJVch9M+HRc+mGCz2bIiPkL8QDzIQCsb1qYpohxCDxfVSw/V8mIRbxugerJC9oq1AjFzYKw2n88mFnYrBGh456PgJEVgh24dMGvZehglWqLXI6CuyV3n4t++csbYPuZ6TUHIfloVB+j7TY0uXPO0+9vAjmeN17/wF7s/+9E/d7q7ddUeMEvoff+RjjiIekDlkpG7MFkpvxmbLTKZxvAoN3HaH/vmT7q3z3uQe/naHmyi8uKoG/KHr+8v3uoV3v9t9o+O6q79Le3nCbfvjd7iFCz/m/uX4nYL3t3vcN392nvuZP2hyk3XGF93pJz/l7r/rg+57h6sK41dLwc3AovkLqpmcc83bdjoS6qsotonmtpZW17I9L5xQhknseagPCcnjWlikCivkQDG+mAa/yBVyVGhUubU5L3ZQJhe5J5r/4OOjgWbT1jAWcoWwaGpNflaIwLpwIc+T8fFv2tzkKKASIrBCN6XkIm3e0hyCynJKuHGoIpp3kxsXInSvxRR8/Hv39blNm8PVShnj4YBD09s34DZuisMaHjnkE6d+rKOzq6F4Sv2Dwh/IdWBopHC08d/BweGGXJ3GT/P/kH0g4HwPDx+KwqKIBEU1qogcKOQPEfPDPFXRsWOjkVjNrmdPXpjBhzly8FCWt+T7TI+xnnd379FDU/4mTyZmjDTS3iXFFKYAOefIW4rBWrx4mdu4Mc//9WHhcMZgNTW1uLb26ga/Vycno7C4Xra2Vq8J8onYtyHa2rwjaK/IfYsZIzmoNN2uIuxUDNaKlWscPyECK2T7kAnZQgSW5vn5+HfsxF7l+Y0+Ho6he80j9PExh1sj7dXElas+iPqx9vauSntVfBOGE3bubJ6vyN/Wr+2D7/+Au2/Bojo2n4Uc3jrzDPgjOWMzYJKSiK+NBl46u9h95v55bsGbH3H/7X//jfu7vyn8fG+tG7a8/xvr3O8tnOfu++S/u7N3nLaXLm1xf/LOBW7hWz/mvv6DTa51xzPu+3/0oHvr3W9xv/aPB9ytutgvubFVn3Nvu+vN7tGvLnWtPd2u+V//wL1vwd3uPV/tcOF2wHWgKX/wxoInSSHas7fPabUiHz9P30I3DHyP4gT7evMKgj4sjoEVMkhUnQsZSsMKPR1kfHukOmSVXKE3UH37B4I3deBv3tzcUAjAd87+/gOOwgghQl9aVMDHz800zkqIwJqYyIu6+PipahjjcIKlie0+LByG0I0r3wPrvBRm8GHhyGihCR8Px9B96O3lwUOHG6o3lmEh12mpWunjO3z4WEN1Mh8Px8AKPdUfGDwQ5byCxVvtKkIH8IWIymqaJO/j52l9DBaOSugNx6nTZ6KwWIfMUxVRnCJGLtbNyEg11smTp7K1U3U+PmM9Dw1XO8K8lYyRa3f3XnfgQDXW5YmJKKzm5u2uqyuv6uobB05PjFxUAeT6VEUUf4nC2tPr9ksRHB8mWOzbEOFQh+wVzbtj5MLRpzJtFWGnYrCo3qoVXMswwQrZPmQKPYQAH6xQQ3oeFIUeQoCF7rWgjk9+5jDWXl27nhfj8mGxtnz2Sp0w7l9+53OPuZGR6v3xkQc/7O5fdK/vNLPiWJWyJiQAACAASURBVHLGZsU0pkG8cg287C5npennZa/CSRCd8rPwM27F5TuvsjzOGOf80bk2949f/FX3wE8tcvcufIt710OPu/+x9pB7tv4GzCR73h3f8Ffu8Q/+nHvTvLvdT/78I+6L3+twF6oj7+zLpb9TzlipatIHSQNJA0kDSQNJA0kD00QDRSes+CasSszP/tans5yxKp6Z/Flyxmby7CXZ57wGkjM255dAUkDSQNJA0kDSQNLAtNWAzwk7fy4PR4wRPDljNS39RJWyUgGPKu2kz5IGXjsN0LeE1/wawoeDxo+GSezbt7+hjxL88GgsOn8TTuPD0uIZNBPWEBI+K2KR3wWWhleAD59ikXdCfpZRFVZR1iIWfaIYp5FhwWfE2JDr2WfzJnIml46bUA0NISnD2rq1xV25msfN+7AodkCYqBHzgkw+ubTHEMnu8KhcJO/vkZyYKiztPefDIgyrRXIWqrC08IMPa2joYNbzS9dccYzoEN2fH8sLLBiW5gOSIE9vrRAWutcwRR8WTYgJkwlhIZc2xGbdIr/KdfjI0SCWra/R0TwvzofFPBIiik6MyvSlRWkMS/cVRRiQP4TV3bPXHZUecj6sEydORWEhu4a3+bBOnjodhcX8HJTG0+gcXegY6TsUGiNzDBY5YUY+LEIxWTtV+gKLNci6NjIs1pkRvdBi5AJrUMIUfVgUTynD0vXLntXGwKw59KVycR0BS68dtr4Ui+uSFpLxYRHWFoPF9ZJ+cEaGpddtwurRfUguQuE15NGHRY/FMrl0brEJhPEZ8Rm6ULlYa0Usu5YrFr0G+THyYTG3YN2+/UNjy87FORULmXz2SuVi3GAxViOfXDV7FbZ96H7yWp4YYVg6H8zh3kh7FcL69x/8h/uVX/5AvTDHV7/yFXf82PFM/zYeG+NVsaN2LVe5PvLgQylM0TmXnDFbOel30sA00oAV8NBKUBiLlu2tbvxyXtGNJGAtPkBBBng0z2dgYChLYtYGv+0dXRmfVq0rYlG9DCyNuaexL3za4Lezc3fGR1U6o8VLlrvFS/IiEjR2BqtzV54TQcVFsLRYA+eCj0bVRowPPiNkhocxGDE2eNTQk2cCnzZNLWKRMwWPJrtzc05C9J49eQ5Xd/fejI/EfqMiFkU6wFInlEp3yKUNfskBgE+r1hWxuOmCR4uzcHMOFkbciBsl+DSX6ellqxqaPtPwFR7N4cPZAYt8IyOccfi0EpjJRdNjI3j4MeImGCyKkBiRmweP5jKRjwSfNtItYnGjj+61YAtzCp9WddzSVMPSpPUiFhUqOZ/OB7l58DHHRhROgU/3VRGLqpLwaOPhwQPDGZbuK5qqUgRDc/GKWDR6BUuL5bCf4Bs5mOdFoQP4aC5tVMRiz8GjBQPIzYNPq5nyP3xa3bCIhWOO7NoUHXngG5JiI6wjsLRhbRGL8cOjDZEp/AEfejNibuDTfVXEYl/BowVuuC7Cpw4HjZxZO9pAuIjFegFLi9KwruBTh6OjY3fGp1UEi1jkb4HFHjFiX8GnD7XYY/CdGM1zBA1L83yWPr0ya1BsWOxD+NiXRuSCgaUPK5gP+HRfFeViHPBo7i248Om+4noDn+6rIhY5g/DoNY08KXSvVUmZW/i0eFERi3mHh+urkdmrw4fzPcr1GT7dV0UsqrXCo3mp2Bb4NHeRIjvw6b5atny148cI+wPPLsnhYz+BpY489gw+7JuRXTPtf84Dj14feZgE1sBgnk/FOoFP91URy2evDh0+kuleHdPsgVxm+/K3VEUsrnecT51Q9hVyaS4e8wwf897W2up+9dFas+aFd9+TVUfkTRjrBR691rKuwNKHn6w/+HRfFQt4mN5my+8UpjhbZjKNY05qgITomNL23KDrzbNPWTy1O3QoN2w+Ho4dOz7aYOTL+MAKVTvi5k2drCosfaro42N8jDNEyMXTyyrihkhvPsp4+/r6G57y+fhwQmLKqyMXT0+rCCdEb2TKeMEKVYzkJiZUhAF8sHgDW0Xc2IaqERpWqEgJb0EolhEidH/x0qVKNm689GatjJkxXr5cXdoeBwVHIURghUrb42DjiIYILH0Q4uPnJg6+ECH7mDhsPn5u4mKwkF0dex8WN3ExWMyP3lj6sHjoEId1zOEQVxGVBlk7IWI9h4q64CRFyXXkWHaTWnVO2pTEYLFn1bH3YXIdicHiuhSaR95SRGEdOx4sIQ9WjO55gxuyV7w1iZGLBz36dtmnL+xUDNaBoWHHT4jACtk+ZNKHUGWYYOkbIh8futK33j4ejqH755/P3+z6+F6JvaLtgZI6YdyXfOkPv+g6d+UP35RX/2aMIdv38UcedW+6U9pevztb/k7O2GyZyTSOOakBLmD3L8zLvc5JJaRBJw0kDSQNJA0kDSQNvCEaKDphX/vqV90rzQkLCZ5yxmoaSmGKoZWSPk8aeAM0kJyxN0Dp6ZRJA0kDSQNJA0kDc1wDr4cTZipOzlhNE8kZsxWRficNTCMNWM5YSCQaNWucto+f0D3Na/DxcIwcFs2JKeMDS5PFfXyrV69zNH4OEVih0ELGpzkxZZhghUL4iI/XfKQyrCeeXNqQ6+Djo/FlTENO5NK8CR8WuQcxDaTBCjV93rxlq1uydIXvNA3HwAo1fSY/bUvTtobv+f4BK9T0mVw5muSGCN1rjpKPn3wXzfvx8XAMuUJhlhSIiWlGDRZ5jlVE6M6TTz1dxZJ9Blao1xX9q+ALEbJrHpaPH7ljsJC9vaO6WTBhkTFYzI/mO/nkoulzHNa2hmI5PiwKfLB2QsR6puhJFZHLFCMXeWyao+TDpOlzDNbSpSvcpk15bqwPi1DMGCya+2pOrQ+Lps8xWFwvaXBfReTPxei+edvOoL2i+ESMXOQeaU6tTz7sVAzWqtVrHT8hAitk+yzvLgZLi3r4+He2Yq/CDaTRveb5+bCYw+ZAA2mcsPe954GsMAfhiGVvwsipjLVXl8bHfeLUj2U5Y7M4CiiFKdanOv2RNDDzNBDrjHGhDhkknB0SaUOEY6dFBcr4wQoZJByx5SvWlEHUj4MVcsYYX4wDBVbIGcOxi2mITDJ6yIHCuMUYJOQKYZHcrQUK6goq/AFWyBnbtLnJPbU4L55SgKj/C1bIGeNGM8bpASvkjFERL8bpQfehfEOSwjdtDjsqyBVyxkh8j7lhA4viGFVEcQCKYIQILBpqV9HgYK34QBUPnyE7hUmqaHi4ViyniofPkJ1KqFWEM4b8IWJ+NHnfx48zFofVHGx+izPG2gkR61kLHPn4ccZi5OLhghY48mHhjMVgLV68zG3cuMUHUT+GMxaD1dTU0lCUqA4gf+CMxWBxvWxtrV4TOGMxuufhVche4aDEyMUDOi1KJEOr/4mdisFasXKN4ydEYIVsHzLFPDwEK+SM7diJvdoREivTfcgZYw5x0n2kb8IW3TPf/d9//CeV4Yg8iIy1V1HO2ILZm5KRnDHfikvHkgZmiAZwKmJyxkiA1ypavuGRcBxyBvjelauTQSz4wHr55SndrxtOPT4+3lD5quFD+QesUEI042OcIQIrVAyEG5AYLKrUhZKrKVgRg4VcQaxr19xEzBgnrgSdV4xyqDgEurw8caWhzLhPvzwUCBl5wyomfRfxKBYSg0Xhihs38hYFRRz+v/5sHBZj1PLRPiwKLMTIBdbNm9WFWCavXWuo0uY7H8fAunGzeozoAL4QIXtIX8gdg4XuQ4VYCKGOwUIu5qmKuBmNxgoUm2GMyB8i5Lp2PS8D7uO/det2tFzskSq6/cMfRmGxZycmJqqg3A9/+KO4a/mVq8F5/NELL/zYsLjuajXdskHE2CucHa6ZIaL1SMj2YadisHAYQk4D8oAVsn2ZvZJy7mXjACvk2MXavldrr1p37nQU0Jh/17ysYBhvwoaGhsP2ajLSXl2eCNqr3/jUr7k333d/mZpm/PHkjM34KUwDmMsaSDljc3n209iTBpIGkgaSBpIGXhsNFJ2wr3/1z9zY+fOvzckCqClnrKaglDMWWCjp46SBN0IDyRl7I7Sezpk0kDSQNJA0kDQwOzUwnZww03ByxmqaSM6YrYj0O2lgGmnAcsa0Tw85JjQ51bAYcnC0KAKhD/AcPHSkPhr6nhCfrn16aDILH2F7RkUswnng0Ua0NH4ES5s2kkcDH2EjRjQw1SIShKfUsPKcG3r9gHX8eN4MlXPBx7mNSLjXXCNkhkcbT1tT3qNH835k6AC+yxL6U8PKc40IK4NH83foYUX+gzb3pLEmfNoYmIa2m6TAwvXr1zMeLaZA81DGqMUayGECSxuYkpeheUuEzsGjuUA0FgVrUPKD6E0Gn4Ylrly1rqGIBCFs8PBjRF8qsCheYUQ/G3g01ItcPeTS8LwiFs2CwdJiDfSsg09Dl8ijAEtD6opYFy+NZ7on98qI9Qvf+fN5Y1WS9zkn/fiMiliWX6NNsum1Ax9zbLRzZ3uGpfuqiMW+4nyaH8QegE/3FXlS5F2xroymYN1pPEwSvNGpU2cyLO1/1dbelZ1TQ7GKWOw55ILXiN5w8LFXjTo6uzM+DYUtYnEeZNdcPHKnMqxTOVbX7loTYw0vLGIxfuTasaPdRMiar8On/a+sibHuqyIW+woszWflugifNlKm+Tz7lnk3KmKxXliDWhSBdQWf9qza19ufnZP1aFTEIswULM3pYV/Bp32maCaN/OwTI8O6Kf0HuV6uWbveWLJ9CJ/2meI6BZb2lTMszZdFLm24zTjgO3I07/PH9REs3VeDB4YyPt1XrAdy0IzotQeWNk6nPxq653pnxHUQPu1lyHVcCwIx7/BwfTWy5va6R7l+wqchtEV7xXqER20fa40x0uPQiObN8Om+Wr5itePHqNL2nTptbI48RbA0XB173GCvrtbs1fDIwfr3kAe5TpwYrR+jMTVYjbavpQGL8cOj9oS8X3SvfRfrtu9OuCdO2PulMAdvwg7fsWlq+9hXyHVQ+hsyz5xTeyySK80aMyIcGR61fawrsDTPlvW3fUer+6V3vDMLTSQ8ccG8u7MwSf7m52ff+tNud1d+PbNzzNTfKUxxps5ckjtpwLnM4Vo0f0GDg3Pm7NnsBuu555+v64gkWr0Z4CaemzAa2RqNjdVuvPVGjAs4fHqTDZYWpHj2Rg1LDazdlOoND0YTLM2BWbZ8lcMhM+IGHB51LjGeXKyRz4hzZVg3btihbHyaLIzM8GjxiYkrNSw9ZljoxAjnQp1X3kCCpTfU3OBi3NRJxBGCT3NgcC7U6JL/Ao/eUGPwGePx47nRJaEfPs1b4UazAevWrYwHPiNLuD9yJL+hwnHKsCRvZe26DQ3OGA1Z4VEsjHpmdA8eNvjsZhEedSRItsfo3r59u85XxMKJAevAUH6zQdNm+NTZp5IlWMhjNAXr+vVM9z179hmL40ayiNXWvivD0kanRSxuApFrvzRh5oYCPn1wQCVL+HRfFbG4OYVn7779dbm4kYRP99W2bTsyh4Z1ZTQF68aNDGvPnl5jyXJRMix5CNHdvTfjuym5ZUUs9hxyqcPJvoJPH0Ls2duX8akjXMRiX+GMaYEbbgwzLMnh6e3bn2FxfTAqYjF+5FKHkxtW+PTawQ0cfLqviljsK9YNc27E/MGneT779vVma0dv/qdi3cqwtAItaxQ+dbxGRg5mcukeLWLdun07c1y1IAX7KsMSx8sKnui+MizdV0uWLHfr1m20IWb7ED514uzBmjolhqX7imuJFpFgHPCpE8cDAHSve5RrF3y6r7heqvOKfjOssfzhyOnTZzLdq4OTY6m9AisvSMG8g8X11YgHOMilDg7XZ/h0X9VsX16QwmeveOAFFvbByOyV7iuKTWnBKRxbzndOQvfYT2Dp+sWewaf7iv3TaK9qtk+dS7NX+uCrbq9kX6ErdV699upKzV4xn0bYf+TasnlLPSeMwhyf/fRn6+GIXO/g4b7CyB7ucNyI+eB/3VcU+2qwV8/XbEyD7btTIEYfmLD+hodH3B9+4Q8cb8T4eecvvMO9/Wd+rv7/7z72O+7okdw5Nzlm6u/kjM3UmUtyJw04lxmdmAIeSVlJA0kDSQNJA0kDSQNJA6aB6RiOaLLNtd/JGZtrM57GO6s0wBOw5IzNqilNg0kaSBpIGkgaSBp4zTSwc8cO97GHH6lXR3wjC3O8ZoOcYcDJGZthE5bETRpQDRBaR9PFENHbSUMKfPyUz9UcBh8Px8iBOSmhDmV8YIXK0ROPTh5BiMAKlfdlfJpnUoYJVqhnGfk05A2FiD5XoZLo5NOciMBCrhAW4ZUnTuS5c2XygaW5IT6+4ydOOPIiQgSW5ob4+M+dG2vIa/DxcAysSQmV9PGRQ6B5OT4ejqF7DQXy8RHuEoOFXBru5MMiDEzDSH08HAOLMN0qYh41B6OMF6zQGC9duhy1b5Fd8w9950RuzhkiZGddVxFhmTFYzI+GxfkwCWuLxdJQNh8WYWSh/nR8jzwdQsKqiJCsGLnYsxp+5sNkv8ZgsWePB+aIh3QxWMgVmkfCGmOwuF5y3awisGJ0D1bIXtEGJEYu7JWG5vnkw07FYJGzpnlrPiyOgRWyfcikOdVVWKGWJ6ci7dW//+A/3CMf+WjdCfvGn32tHo5o54+1fYxRw1Tt+/qbnLdYe6V5kYphf7PuY9aO8c+038kZm2kzluRNGhANWAEPOeT9MzV9ztVCPH/IUUlNnxv1pTl2+Sf5X6npc64L1pcmo+ef5H+lps+5LlLT55ouUtPnfE2Q36w5dvkn+V/kCLLXQkRO3Fxv+qxvwu6dv8D5nDDTY1XTZ+PhN7rXPFj9zP7+cTZ9fmrxsizf0LBn2+/kjM22GU3jmVMaoIIYF9cQdffsaygq4OPn6VtHZ165zcfDsZ49vY5E/xCBFXqbtX17a0MCeRkmWKGngxRN6O7ZWwZRPw6WJnjXP5A/qPhHYYQQbdi4paFyl4+/r2+goXCCj4djyKUJ9z6+/f0HHI5PiMAKNYbt3LXbbd7SHILK5NIqjL4vUB1rV1e376OGY8h1TqodNnx45x8KfFAsI0TonopqVUQVsxgs5Ao9iafyWGdnWC6wQk+DqZy3cVP4RhKs0BN7KoPCFyJkp6pmFSF3DBay9+3vr4JyJ0+djsJifpinKuIJe4xcYGn1VB8mhQJYOyFiPYeexF+8eDFKLqprasVT37l5Yxczxi1bml2nVBH1YfEmMQZr9+49rk8K1/iwKJ4Rg8X1sre3ek3UCtyEdQ+WFsHxycVbthi5KPKzN2CvsFMxWC3bdzp+QgRWyPYhkxYgKsMES4uu+Pgy2+exV+qEEUHzmd/6jDt8OC/G5MNiDmNsH3JpZVkf1v79g9H2Sosl+bCwVTH71vfdmXAsOWMzYZaSjEkDJRpIOWMlikmHkwaSBpIGkgaSBuagBopOWNWbsDmonmk55OSMTctpSUIlDcRpIDljcXpKXEkDSQNJA0kDSQOzWQNeJ2ysOu9xNutjJo0tOWMzabaSrEkDBQ2QQE6Y4gsvvFD/hJAGfjRMglA5evUYwQ+P9q/hf0IQg1j7Bx3hckY+LEIKwdJCGT65yJ1pl75AyFyUC3ywOG6E3PyvsjI+xmlkWPo9w9J+Lz4sQop6+/KQmzIs8hG0Z44PixA+msMalWExRu3l48OicMI+6WFVhaVhij4sQmQ0L4OEc3Tl0xdFIox8WCMjh9zefX0NSetlWNozh/UBn4agHjx4OAoL3WvBFh8WvZsIqUVPRmVynTmTN3j2YRHiF4ulBQN8WENDw46G1DFyaSEZH9aJ0dFsf1Rh8RmyazETdI4uwDQ6dep06TXAeMBCdm3c6sOil1DZ9USxkIsG50Y+LPo0xWAR+qXNfH1Yp06fzkKj9dpRXBOMkfWsjex9WJcuXQrKxb7at6+voViOD4viKWVj1GIQNB+nCbYR40B+9qXR1clrUVhcl3QefViEKZbJpWuO66WGYvqwKDjFvvXpvogVslcUj4iRizDM/oC9+uEPa/YqJFd7R5fjx8g3RuYWucA0smumjhGZNESUz4rrEHywtFCGYams//ZvP3AffP8H6oU5vvbVP3MnT57M8EwG+NH9tWvP2qFszXBOxcpsX6S90r5/PrkI8yXk36hqjNpfz4eFrUL+2UrJGZutM5vGNSc0YAU8Dh8+Wh8vFy2aQGoVNpJtNdmZClrwaJ5Pf/9gxsPNsBENeOHTG+giFlXC4CEHyQinAb4DQ8N2yLV37Mr4tNrZ4iXLHYm5RlQvA6tDDB45IGANDAwZWxbfD582hy7KhczwMAYjbq7g6xWnDR3Apw2di1hUoYNHm8BSVYumz+TjGXXt7sn4tKoY+TXgGTEvYGlSOTej8CgW+W/wnTyZV3Wkqa1i0WwXHm6OjY4ePZ7x7N7dY4cygw6fNtZ8etkq98STS+s8VBOERw0eOVmcT/OuuEmFTysLmlya8wYPP0bkI4GlNzMYaniOHstzmQxLqxsWsXDC0H1zc97MlZtB+I4czW/saTjKObWxcRELxwmenTs7TFRHThd8WjmNpqrw6b4qYuGAwKNzy80NfLqv1qzdkDVO1uqGRSyKpoDV0pLPLTc38A2P5FUwaR4LH01XjYpY7Dl4mrfl+mJfwTc0NGJfy5r2wqdVBItY7CuaPjMGIwqWwKc39sgNlhZ/KWJZs11tfnvw0OEMa0AeHm3f0Z5h6b4qYjEvnE+btXNdhI/5NEJfrB11mItY1riX4iJGrCv4+uQhDWuZc6rDXMTiYQ08rGsj9hV8eqPK9RM+dZgNS/fV0qdXupWr1hlUtg/hY18a0dwbLM2pZF/Dp/uqKBfjgEedPXDh031Fri98uq+KWOQMwrO7O89x5UESulfnm70C37hUIK1h5ddM5h0erq9GPBCET53v1taOjE9zXOHhx4j1CJZe07At8PBQyaitvWb7tNLnsuWrHT9G2B+wNN+sbvsO5PsKewaf7quiXOxfeLRpOfLAp04u6wS+s2fPux3bt9dL1C+av8B982tfd2NjY47xw4M+jLj+oHvN66vbPqmMatdf+57ZK31wx75CLl2/zDPnZN6Nilg8cIBHr4+sK7C0uT3rDz592JYKeNS0+hOmXN/v7S0t7vHPPeb7KB1LGkgaeA01QEJ0TGn7I0eONRhmn0g8HRsZyR0xHw/HeEPADX+IwNInuj7+wcGhhjd2Ph6OgaVP73x83HgwzhCBpW8DfPwUTTh8JHdwfTwc40bl5s2bZR9nx48fP+nUWS5jRq6bN58r+zg7Tol83vaECKxnb9yoZMM469u/MmawQonaGGC9KarC0jeJPj4KaRw8GG53gO4vXLzog6gf46GDOkH1Dwp/MMbx8VA5+vMNb0oKEPV/wbp4abz+v+8PbjJ4WxIisPRBiI+fmzj4QsSDCH0Q4uPnJi4GC9mPB1osXBofj8JifijQUUU8dIiRi3WjDpsPEwdQHRcfD8dYz7wprCKcpCi5Dh0JljHnLUMMFs6gOg0++biOxGBxXQrN4/O3bsVhHTna8IDGJxdvYWJ0j7OmjqQPizdQMWPkZl8f9viwsFMxWAODBxw/IQIrZPuQSR3cMkywGKsSTtijH304exNGn9E/+sMvuV3yMFR59W90TxXKKuIhW6y90jd2PkwewMXaq5Dtw1bFrB2fHDPhWHozNhNmKcmYNFCigZQzVqKYdDhpIGkgaSBpIGlgFmmg6ITZm7BZNMQ5O5TkjM3ZqU8Dnw0aSM7YbJjFNIakgaSBpIGkgaQBvwaSE+bXy2w6mpyx2TSbaSxzTgOEj8X0GSPnQmPRfYoidE/zLXw8HNuxs8PtbM3zsMr4wNKEZR/f2nUb3Oo1630fNRwDKxRayPg0Fr0BQP4BK9T0mVwQzcOSrzf8SRy7Fspo+PDOP/R32iZ5Pz4ejiFXCKuWkxZOYgaLHkhV1LR1myNvLERgaW6ej59cN3JxQgTWyVNnKtko6NC0NYyF7oeH89wpHyihLU1bW3wfNRxDrlAPLnJUNLepAUD+ASsUstm1u9uRLxkisEINpIeGDkbtW2Qnn6WKCPPjnCFCds0R9fETMhyDxfyEwmUJ9Y3D2h7sT0UeoOap+mTnGOs51AeK/KMYuWhiHOrdRMhtDNayZascvcaqiNycGKxt23Y25E75MCkqFIPF9bKjI88b9mFNTk5G6b5le1vQXhFuFyMXuU6aN+yTCzsVg7Vm7XrHT4jACtk+ZNI8LB8mTtgD735vPRyx7E1YWzv2qs0H0XCsZq+uNBwr/sMcap5q8XP7nzGGmj7v2kU+dpy9Gr+cF4myc+hvbFXMvtXvzKS/kzM2k2YryZo0UNCAFfAoHJ7yLxfE0IUfZ4dE2hDhWMRc+MEKGaSVq9a65SvWhE6ZyRVyxhgfSb8hQq6QM0ahjhjngoRobnyqqK1tV5RzgVwhLBLFYxwCsC5cyAs6+OTbtLkpyriBpUUYfFg0oo5pIA3W6MnqPBwcOwpvhAjdh5rykmOgRRjKMJFLiwr4+Cj6okUYfDwcAyvkQFFFlCIYIQIr5EANDg5H7Vtk10IAvnMPD9cKBvg+02PIToGDKiJXBPlDxPyEckGOHRuNxGrOitVUnZMG06ydELGetfiEj5+cxJgxcuNK4+cqGrtQK7JSxcNnixcvcxsDTautmEkIq6mpJej04IzFjJHrZWvgIR3OWIzucV5D9gpnLEYuCpeEHtJhp2KwVqxc4/gJEVgh24dMWixJMfVNGIU5/uwrf5oV5lAe/ZsHpOgsROie/MsqYg63RjwMY4whZ6y9vSvaXpFjWkU4YjFrpwpjOn+WnLHpPDtJtqSBgAZwKkjgDRE3+aGLMAnHWt2tDPPyxJUgFt8F6+WXXy6DyY5TnECrVZUxgxVKiGZ8IWcGfIorhIqBYGRisKhoFXISqV6mlcKqxhjCovhFqNAE+OiL8sBVND4+7s6fD/egAYvE+yrihk2rDJbxgvVcIIGcoggxWFTxpFR2FfGwIgYLuUKFWK5dss9N7QAAIABJREFUv+4ujVc/vUUWsELO/tWrV4NvGw0rNEY+55whQnYtRe3jR+4YLN6UalU+L9bNm1FYzE+oQAzJ/TFygaWVB71y3bjhWDshqmFNVrJRwCBWrlDhGvZrDBZ7NsTHdSTEw8C4loTmkeIRMVhcL2OwQg92kCvGXuHsRMk1EbZ92KkYLOxVqKAO8oMVsn2ZvZpofJBHMTwtzMGbsKEDQ0HHbmIi1l6di7JXMbaPMWr5ft9GyWxfoDCS6eu2tNjwYbHuY/at77sz4VhyxmbCLCUZkwZKNJByxkoUkw4nDSQNJA0kDSQNzAAN4IQ98pGP5uGIX/9GMLJhBgwrifgKNJCcsVegrMSaNDDdNJCcsek2I0mepIGkgaSBpIGkgbAGkhMW1tFc4UjO2FyZ6TTOWakByxk7fz7PD6IhLM1Xr19/tj5mcnBoWmtEiAQ8midDw0/iwLVYA72J4NPQH3IpNNmZUAR4tJ+INb89fTov1kBRA/g0XIcGpkuWrjCx3JWrNSwtgEAzZuQ6cSJvfsy5wNKwGHKpNNcImeFhDEaEOYB19NgJO5T1E4NPwziLWOgZHs0FImyCGHY9RtEC+DTMg2IUKhfzAg9Nd42sKa8286UPDXwaZkdegOYt0UsMHs0rIuyTMXLciL5p/K+hOKtWr3NPPvW0sbgbN29mPPq9CxcvZVj9/XlvHZrSwqONVclJRC4eDhjBo1iEhyKXFmugCTU8GvpD8jhYyGNUxCLkDt1rs1V6sMGnYa/WLFhD/YpYhJAilza6pW8afBrGSdEa+HRfFbEI4YWnS/KD6JsGn+4r9hB5VxqeV8SauFLD0kIZ7Cv4NNTLGg8TKmpUxGLPIZc23GZfwac9vmiECx/70KiIxb5Cdl3ThOvCh3xG5BGCxTiMiliMHx5yXoxojAufNmXu2dOb8em+KmIxL2BpfhDXRfhOSp4i+mTtaOhwEYv1whps2Z4XH2BdwacNnvv6BrJzar5LEYsQS7A0n5V9BR99mIzoX4X82qPOsHRfcb3UhtvsQ/i0WTTXEbA4j5Fh3biR76tNm7Y25LMyDvj0+mi5f7qvuN7Ap/uK9aCFdyjIkGFJT0r6V6F77XfHdRA+DaEFS3NjmXd4tI+kNZHXRspci+HTfcVea7B9V8z25f0a2e/oS8PgfLZv+YrVjh+j3PblfRHN9rHvjcz22b7CCXvg3e9peBN2+EjNPmpfRLNXuubM9mm+Voy9OneuZq9Uh9h/9KW2r8xeqW1iX6Ev7UdG71GwtBAHWKx9I9YLPGr7zF7R7N2I9QefhoWnnLGadlLTZ1sl6XfSwDTSAEaHBF+9MJ86fTYrkvDcc3lzR4yRFqTgxoVCCmp8zp2v3cRzQ2mEYYFPb4y58KvR5QILz5mzeR4GDkR2Y3Exz2U5feZcDUtuBpYtX+VwyIxwLmpYeRNYu1k+P5bnN3Eu+PRmgPGp0UVmePQG0W6WSbw3Qgfw6c0AN07qcHJDBQ+6NSJOnxsLHB2js+fGaljiCJOkrTeuzAtYWlUQo46+tNHpufMXMr7Ja9cNPiucoljkrNSw8qIYV+7ceGvTam5+4FOnmhs6dcZo7goPP0Z2E68NUcfGLmY8VyevGVuWbI/RvSV5akUszs0YGx3HSxkWMhtRPAUs5DGagnXteqb77u59xpLdeMJ35UqORYXNjZuaGhqdFrHIBUOuvv0DdSxuiOFjjo06O3dnfLqviljmEGhBikuXLmdYuq+am3dkDo02Op2C9eyN7HzdPb0mQnZzAp86EhSZQH69yS5i8Rk8OEhGYGRYktOx547To/tqCtbNm5nsej3hZhk+vXna17s/O+d1yesrYjF+5FInET3Bp07J/v7BGpbsqyIW88K6oWCOEdfFDEuuQ3v29mZrh3k3KmJRHAIs1qIR6wo+dXCGhkYyuXSPFrFu3bqdYe3Y0W5Q2QMp+NTBOXT4cIal+8qwNP9zyZLlbu26jTnW5LVMLvalEdcR9KoPvgxL9xXXEi0iwTjg04d7NCgHS/cV1y74tIEw10t1OLFN8KizRBNtrpn6EM2wdF+Bpesrt1e5DeBBCXKpI2G2T/dV0V6xHpFLbR8OLViXL6vtm2qvKDalBaf8tq/2cEfXLw8+OOfGjRvr4YhUQf7tz/52PRyRPQoPdtIIeZBL58Nv+8L2in2F7vXBRN32yb4q2j6zVw227469wok1Yp6RXx1hin2pvSJfGJ5G21d7UHTixKhBZeOFT/dVcsZq6knOWH2ZpD+SBqaPBlKY4vSZiyRJ0kDSQNJA0kDSQFEDKRyxqJH0f1EDKUyxqJH0f9LADNJAcsZm0GQlUZMGkgaSBpIG5owGtm9LhTnmzGT/JweanLH/pALT15MG3kgNECZx34KFQRFOnz7rCJWoIkoFa2x6GS9YGkpRxgdWqBw9eVFHjh4rg6gfByvUt4XxaY5a/cuFP8AKlZAnJ0dj/gsQ9X9HRg41hOrUP5A/yBXS/Bf5qOFP5NKwn4YP7/xDKIiGhvh4OAZWqFQ74UeHDuW5DlVYoVLtY2MXGsJfqrCuSUiMj4/8MUJUQoTuNYfIx0/4EeMMEfrSkC4fP/l28IUIHs2T8vEzj5rL6OPhGFga3ujjy0IEI+XS8EYfFiFfMWNEds2B82ERehqDxfxo/qEPixDXOKzT7sKFPE/Kh3XlyhXH2gkR4Vz0/qqiLEwtQvdgaZ6UD5P9GjNG9uzoaJ5r5sPiOhKDRdhgaB4JPY7COn3GkTtYRYRbxuiea2/IXtGeJEauzPZJ6J9PPuxUDNbRo8ccPyFaunipe/ihj9Rzwv78G9+shyPad8nVRLYQIVeoFQu6irdXefi379zMYbS9klByHxZ5arH2KtTyhHUfs3Z8csyEY8kZmwmzlGRMGijRgOWMlXxcP5yaPtdVkcXgh5yL1PS5UV9aMCL/JP8rNX3OdUGOhxZ1yT/J/0pNn3NdpKbPNV2kps/5mpipTZ95E2ZO2H0LFzmfE2ajrGr6bDz85noSekiXmj6rxmbm38kZm5nzlqROGsg0gDNGInCIuFmmIlkV0dyzta2ziiX7bHf3XtfdkxdOKPsCWKG3Wc3btrumrS1lEPXjYCFfFTG+rt09VSzZZ2BpdTLfF/bs7XO7pCKej4dj657ZGHyjsm/ffte5K06u0NsZqrd1dnaXiVM/zhgvX65uUNzeQXXALfXvlP0B1sWLeXEAH1//wAGHgxEisChyUkWDg8MNBR3KeNF96Ck1VbvaO/KCDmVYyKWJ7T4+3gZRECREYB07niej+/j7+vrdM+s3+T5qOAYWVcqqiOpo8IUI2bWoi4//2LHRKCxk39fb54OoH+ONV4xczI9WV6sDyB+8QYjD6nKDB0bkm1P/pOogaydErGcqHFYRb3Fj5KLqJ0VIqogqdDFYGzducW2B+aZARgwW1xIKrVTR9evXo7C4Xu7dW70mwIrRPVghe0Uj+pgxUuBGK6X6xoqdisHa2tzi+CmSOmH3L1zkHn/scXf+XHUkCjIhW4iQi7FWUc+eeHulRZx8mMzhrkh7pQU2fFi9vf3R9ioUTYCtilk7PjlmwrHkjM2EWUoyJg2UaCDljJUoJh1OGkgaSBpIGkgaeA01UHTCqt6EvYZiJOhZoIHkjM2CSUxDmLsaSM7Y3J37NPKkgaSBpIGkgddfAz4nLBQ98PpLmc44kzSQnLGZNFtJ1jmrAXKcrl69OuWHghWEKWqCLyEN/GiIII129+/Pw2Tgh0f719CzivBDDQf0YREq1xfAokAGWIrvwyKscFdXHnaHzEW5kAcs5DMCFz4dN+PThsKGBZ+RYWlxCy9W/4GG8B0fFufe2druCL0x8mENDBxwhCoa+bBMLu3R4sOiEab2sKrC0pBHHxbhSe0SdkcSu82RyWpyaf8dHxZhZvRv0oItRSz0xTzSd8uIdQIf5zEiHJB+V1VYjBvda5K/D+vQ4SNuz559DXuhTC5t8OzDIlywJxJL+9j5sGhw2traESWXJtP7sEZHT2d6RSdGxTHyGbLTGNsIncMHphHnYo50X/mwkF2T6X1Y5BnGYDE/WsTHh0UPrTis3obm8z4sChSwdkL6Yj2Hxkg/xZBcrGPCnoeG8/BJn1z0RCvD0r3Ant23Lw8HZK6YI/al0eTkZIbFeYxsHhULHK5PRj4s+i8ilw9Ldcj1RJvD+7CwY+jet74ascL2igeRMXIREhyyV/SCi8H6++/9g3v/ex+oF+b45te+7k6fPt2ge/YTWDofds3UMSITshnxmc2RHUPnYGlxC8NSHe7fj72qxoK/Zq9uGHwmI+dULOYw1l5pb06fXAMDQ9H2avJa3rfSh9XW3pnJXxd+lv2RnLFZNqFpOLNPAyTvvuPtP+9++s1vmfLz1p98s1sw725HbLbRylVr3ZKlKxoqW/3HE0vcE08uNRZHngk8JAcbde7anTVz5SbEaPWa9RkfVbeMwOLHiKbHYK3fsNkOua6unoynu2dv/RiNSuHTSmA0oeTHiMaP8Kx7Js+nIUeN82k+2DPrN2d8x6XhMuNTuZAZLMZgxNjgoYGvEbHo8GluThGLylfwrFq9zr6WOWvIro1hN23amvEdPny0zlfEosIUWNo8FAcXuTCWRjSwhm/kYF75rYhF01h4nl62yr7m+vsHM6zt21vrx2igCp/m5nA+1T0V7eDRJtwDg0MZljaG5W/4cAyNTC5uTo3g4ceIBrmcU5u5ksQODzlnRjT3hE8r7BWxuElGdl1zO3a2Z1iam7Nk6fIMi2qPRkUsqnRxPppDG2H44dN8mmXLV2d8WjGuiMW+AkvlIl8IPt1X6Bj5WVdGRSwqjYKleRLk0sCn+2r16mcyvpNSNbKIxZ4Da83afC+QrwKfNoKmETh85FUZFbGojobs6MOI/Bf49MEKcoPFOIyKWIwfnuUrciweNsCnjaDZo/Dpvipisa/g0fXLdRE+zQci3w35tZJoEYv1Ahbrx4h1Bd/OnfkebWpqyfiGRw4aW8YDnxFVOMFiXRuxr+BpKexR+LQpusml+wrZ4TNiH8LXuEdrTcU5jxF6gU/3FTjsXSPGAY/m8bKv4NN9xdzDp/uqiMUDB3g2b2k2+Kw5PPJzvTPiOgifNocuYjHv8HB9NWJ9wKcPp1atfibjO30mr1JYw8r1xXoES/NlWbfw8cDCiL0AH7mkLc3b6oU5Ft2zwH3rm9/M8mixP/Bo/id2CizNB8OewaeNjZ94stGOkmMJD+c1Qh6wdu3KH1hybYGPxt5Gdv21/xk/POjDiFwwdN/aljcyx/7Dx3XLqIjF9Q4e7iuM2FfIpbmLzDN8zLtREYvm1fCo7WNdgbVzZ5t9LVt/8GkhJGTnZ7ZScsZm68ymcc0JDTz77LNRpe0PHT7a8PTZpxyezOnNuo+HYxjGw3LxLuMDS5/C+vhwHPr254bZx8MxsPSpoo+Pp+u8CQkRWPqU18ePY3Ywouw7N6GhYiAYzYMH4+QKVc3iJjmmJDpj1Ld/vjFy46U3Mj4ejoHFOqsiyi/rW4QyXrAmJ/M3iT4+bn7UCPt4OIbu9cbSx8cbKr1R9vFwDLlCJeS5KRkezm+6q7AuiVPq4zsxerLhxs/HY3JdvDRe9nF2nCISyB8iZIe3ii5eHI/C4iZRHTYfJiX3o+QaOehC1TopSBGHdcidCpQLHx8fDxZ0YDys51BZ7uvXn42Sa2TksGPOq+jGzZtRWLzNGpa3bD5Mrkkx+jp48HDDTb0PizcnUViHjrijR3MHoQyLfRsirr36ttTHzzU8Ri7slTobPizslA9LnTAKc/zB73/Bbd+x0wfRcAyskO1DJn240AAg/4AVsldHXpG9el7Qp/7JHMbaK9ZGFVEQKNZe6ds/Hya2Kmbt+L47E44lZ2wmzFKSMWmgRAMpZ6xEMelw0kDSQNJA0kDSwKvQQNEJszdhrwIqfSVpIEoDyRmLUlNiShqYnhpIztj0nJckVdJA0kDSQNLAzNJAcsJm1nzNJmmTMzabZjONZc5pILbP2M7WzmAfKBKPt27dHtRha9uuqH5LYIVCC4m1J5csRGBpoQEfP32BNH/Lx8MxsEJNn8mfI1ciRORhTExcqWSjZ8v2HWEs5AphkT/Xsj2PrS87MVih6l70eFuxck0ZRP04WFrcov6B/EGBAs1ZkY8a/gQrFEZGIjpNykOE7kOhkfv7B1zzth0hqGxNaA6G7wsko9OMNkSMkbDgKiKfRPP8ynjBCoX5DA8fitq3yO4LxdJzHzp0NAoL2TU/TDHsb3JzkD9EzA/zVEUnTpyKxNrpeiUfyYdJrzXNK/PxcIz1HArjPXfufJRc21pag32zLly8GIW1cuUatzXQm5EQ0Rjdb9/eFuynSGGFGCyul5rb5NPrtWvXonRPE+NQ30JCumPkIl8w1GuwuWmre+8vvbtemKPsTRh5kJrD6Rsjx5ArZPuQSXMZq7BC4evkpaKzELHuCfmtIuZwR6S9unJ1sgrKdXXtibZX9NmrImxVzL6twpjOnyVnbDrPTpItaSCgAZyxRRFNn7m5DTkXODta0KPs1NxYxDgEYIUMEknBmsxbdk6wQs4Y44u58QYr5Izh1GmhiTK5SCjmxqeK2tp2uaaIm1LkCmFhdLc0TW06Wjw/WBcu5EUrip/z/6bNTQ1FBXw8HAMrlNNDEQhN1K/CGj2ZF4Px8VE9bNPmPOnfx8MxdH9Aioj4+LiZ3rQ5T/r38XCMMYbyILnJ3ygFBKqwQjlv3GiStB4i5NKCDj5+mmTDFyJk14IOPn4cuxisLHm/vbrRNA5pDBbzE3J6yD2Jw2oOOj0UxIkpBMB61iIMPn2Rkxgj1+Yt24JOz9iFC1FYixcvczR+riIKfsTIRQGSUCPzq5OTUVhcL1tbq9cEVR5jdM+Dg5C9wkGJGSNONYWCfJS9CfvwQ5kTRlXiMifMvotDEPMAC7lCtg+ZYh5ggRVyxnDEYh4UofvQAz/mMMbJRS4qgFZRe3tXtL26NF6dG0sBnJi1UyXPdP4sOWPTeXaSbEkDAQ3gVNy3cFGAyzkqemlFLt8XMB5U5wsRWFqevIwfrFASM0+Wz547XwZRPw5WyLgxPmQLEVhaytfHD9bFS5d8HzUcoxT47dt5afCGD+/8g4MVKjQBK3IFsSauRGOFkqsp5qBVx3yym1yhmwGM8oWLYX0xxps3nys7VXacJ7cXLoSx0L22AvCBUt4/VLTCxvjsjbzksw9rcvJaNBaFHaro8sSEO3X6TBVL9hn6uiatE3xfQAfwhQg9hPSF3DFYyB56cPDsszeisJBL2zD4xnHjxs1IrEsu9LSectzaLsB3Po6xnkNvEZ577vk4uS5eCt4Es19jdI8DGFrTlAaPweK6FJpHHoJFYV265MbHqx9MgRWje4rW/FjtVaGgzrbmZvfwHSeMwhw4YQeG8uqwZWsCe8VPiNBXyPZR5CfWXsXYvlChH2RG96GHmsxhrL0KYb0y25e3ZvDpF1sVs3Z8350Jx5IzNhNmKcmYNFCigZQzVqKYdDhpIGkgaSBpIGlANFB0wv7iz//cXYp46CYQ6c+kgddEA8kZe03UmkCTBl4fDSRn7PXRczpL0kDSQNJA0sDM1EBywmbmvM0lqZMzNpdmO4111mnAcsY0bIXeMfQU0t5Q5D9orhHhN/Ack4ashAAQB05jRiP6oMCn4U3kP9CQ2IgQI3iOHs0bR5JjBJY2tT1ypIZFuJfR08tqjUjtf8PSvjCEhYBF/ykjzsU5NbyJ8WmuETLDo71cKEQBFjkoRvQUg09DkopYhG/Bo41iaXhKDPtBacpMEQj4NC6ffDGVi/AteJgnI+YPufTY8eOjGZ+GETU372jIWyJ8CywtZEGICVg0WTY6ceJkxqehPzSwfvKpp40lCx8Eix8jwmjAGpCmzPQUg0dDbMh9ICeJsC2jIhbnBqu3b9BYsjmFT8NiaIQLloYzFrHQCbrv7MybodLku4hF3gnn1BzBIhZzBU/PnrzZ+enTZzIsbWpLERz4dF8Vsa5cqWFprlHW62z4YMO+2rKlOcsZ03DGqVhXs/NpoQz2FXw0ODbq7OzK+HRfFbH4DNnJOTRiX9Ww8rArmrXDp/uqiMW+ImdMcwTZV/BpbiHFZsDSfVXEYvzwaOEddA4fejPas6cv49N9VcRiX4GlxXLYV/Axn0ZdXd3Z2qnCYr2wBjU3ljUKFuvMaP/+weycuq+KcvHADCzND2LvwKeNugfu5P75sHRf0QxXGwMbFvvSiKIv6EL3qMml/Qe5LmluLOeGT5sTHzlyPMPSPcr1Bj7dV2Bpbix7FB6uY0Zca9m3fnuVhwmDpfaKuQJLi+zQJJkx6h7l+gzf9TuhvThh73lXXpiDN2FHDtd4kMXo9Ola7p8WKsptX26vaE6uDcp99op+hMjVaPv89gpbasQeRXafvdJ+d2avrl7N87Wm2qua7fPZK3qSGWH/Oafu0an2qmb71DaZvdJecD57xdrSnF3WC+dTm2n2Svt6sv7gU9uXcsZqs/YTNnm+39tbWtzjn3vM91E6ljSQNPAaasCcMXJQjDBSNGTVm1ku+mooyUOBR3OGuMHDiGhVI4wAfGp0ufA3STUvbqgyLLnhIX4dLDW6p07XsLhpMlq2bFVDhSTyOcDSfBoSe8HSWH0+h09vZhmfGjdkhkcNGWMDS2PP0QF8mptDMrRicQMDD7o1MoeAqnFGZ87ewbqWNzamqIg6Yzefey7D0iawNBxGLsXixpZzkvRu1NKys8G40SgTHsWauOMQHDqcO3vk5cGnN9lr1q5vcMbIC4OHHyOMNHINDR+yQ+7c+bGM54rcDHADzA2n5qkVsTg3WINSdOP8WA0LmY127uzIsDRPbQrWnUIA3PAbnR+7kMmlN9lU/uScejNbxKJaHDxUcTQi5wM+vRlo79id8em+KmKxH8Haszd37Mg9gk/3FTcpODR6Y1zE4oYSrO6efIzkMcKnye4UT4FPc96KWOaoUN3MiBv1DEvyLGnmDBb70KiIxb5Cdr0GkP8Cn+ZZUmEzw5KctyIW44dHq92hJ/ioLmhEY3j40K/RFKzM6WlqqFDHdRE+zXmiQAwOAfNuVMRivbCetUId6yrDGssfVh04MJLJRZELoyLW87duZVhaRIJ9BZ/e/FNYhDHqvjKsW7fyfBqcMa1ACz987EsjGvdmWFJgwbB0X3Fd0qJHjAM+zePlQQ5Yuq+43sCn+4rrJQ+LjHAu4Dlz9pwdcjiM6F4brBsW10UjsNRJZN5rWLmDbk7PuBRQwrk9dvyE27B+fT0njMIcj/32Y/VwRPYVWGr7xsZqD8PUETbbp/uKYlNacMpsn9orv+27Y69kX2Gv9KEm50GuBnt15wGW2r7TZ6baPnSl9ooG4hmW2Cv2FbpXp91n+5hDxeJ6B1aD7ZuYyNaEHmOe4dOHQtu2Ya/yYkw8mICnwV7dsX3qaNftleyr5IzVdkdyxuwqkX4nDUwjDaQwxWk0GUmUpIGkgaSBpIE3RAMvv/yy403YRx/8cL1EfcoJe0OmIp30VWgghSm+CqWlryQNTBcNJGdsusxEkiNpIGkgaSBp4PXWQHLCXm+Np/O9FhpIzthrodWEmTTwOmmA8KP7FiwMno0QAg118H2B8rkaIuHj4RjhIfyECKxQeV9CFggrCRFYofK+jE9DYsowwfrRj35U9nF2nJAfzVkpYz50+Ih7/vlbZR9nx8nB05CYMmbkCmGRH0F+Q4jAwlGvIsJGNTevjBcsctOqiFL0mpdTxguWhsD5+Mgh0LAfHw/H0L2GTvn4CMWLwUIuDa/xYVHyWcNbfTwcA0tDzXx8zKPmhvh4DCvUywcdcM4QIXtIX4TPxWAhu4bY+c59dfJaFBbzo7lNPizC1GLkAitU4ptcG9ZOiFjPoXYNhGzGyMWe1ZBt37kJ04vBYs9q3poPi1DEGCzk0hxhHxZl8mOwuF6G1gRYMbon3ypkr7iGL168pOFN2Le/9a16OKKNhXBvDbu04/obOxUzxuPHTzh+QgRWyPYhk+ZYlmGCFWrFQoqB5qiVYaF7DSX38TGHMbYPuTR81o8Vb680fNaHxbqPWTu+786EY8kZmwmzlGRMGijRADcpqelzTTmp6XO+SMjxSE2fXdZMWBPIcw01/oW+UtNn51LT53xdpKbPNV1Mt6bPvAlr3rrVPfShB+vhiD4nzGayqumz8fCgj2tAiFLT51xDWR6h5CTmn+R/pabPuS5CfyVnLKSh9HnSwDTWAM4YCcoh6tzV01AIwMdPA0eKJ4RoV9ceR9GAEIEVepvVtHVbQ1W2MkywQg0mKXTQuSuvrleFpYUTfHwUMuiUynM+Ho5RBEOrWvn4qASnVex8PBxjjCGsfb37XXtHVxlE/ThY4+PVDbBb2zrcM+s31b9T9gdYoaf6VJVra+8sg6gfByv0lLp/YKihCEP9y4U/0D0VOquIRq6tbXFyaWK7DxNHhYqKIWKMR49VPz1nHteu3RCCytZE6O0lb6k4Z4iQPfRkmcIPMVjIrkVKfOcmST8Gi/kJNdw9depsNBZVCauIN/GsnRCxnvf355U/ffy84YwZY1v7LkcRkiqiKEsM1vr1m9zOne1VUFl1vBisjo4uR6GVKqKwUQwW18s9UpHUh0nxjBjdUyVVC9eAZU6Y5oT93u/83pQ3YcXz7urqcVrdtPg5/2OnYsa4pYkqj3lBCh8Wx8AK2T5kQrYQgRV6m0VRGq0sW4ZZs1d5sRkfH3MYY/uQi7ffVbR3b7y90iJOPkxsVcza8X13JhxLzthMmKUkY9JAiQZSzliJYtLhpIGkgaSBpIEZrwGfE1b1JmzGDzgNYE5qIDljc3La06BniwaSMzZbZjKNI2kgaSBpIGnANJCcMNNE+j0XNJCcsbkwy2mMs1YD9Dm5d8HChpAIkn350QRiejsNSTNfPjM+Uw5hgH19A0EsQoq0obAPi2NgaeKxnU/lIhRlt4Q8+rAI9wBLwxR9WIyHHlRqAAAgAElEQVRvUEKUqrCeey4vuuHDGh455AYHh0w1mS6Nzw4iV1tbZ0NBCuPRMdKAdSACizFq3zQfFo0x+6UBc9UYtT+ZD4uwKQ2f5ObH+HSMyKWFH4xHw3AOHzmehXSBYWR89j+ygkVPKiMw4FMsmpoSHhbCQveaaO7DohFp3/7Bhr1QJhd9yox8WITdxWJpgRsfFs1YCV3TdVImlxZ/8WFRtAK9BrH2DzYUIPFhUQAnBgvZtQmsD4siODFY6JRCPkY+LArExGCxbjRE1IdFmCxrJ6QvsLRBrg9rYmIiKBfruL9/sKFgiw+LEOWyMepeIISsry/viWdYrB8jGpODxWdGtr503IQEc30y4jPjs2MUFonB4hrHddPIh8XDQ3RfJRdj/dfv/6v7wAPvr+eEUaL+/PnzDfaEYiAxcmW2byhvZO+TizHHYBFaqCGPPizGBpbOh+kUfqOhoYMNPRersG7f/qF9rT4/ikWD5Fh7pSH6PrmYw1h7FcLiGsEaM6oaI2vWyCcXtoq1M1spOWOzdWbTuOaEBqyAx8hIblCzpo2bmx1V6YxIttUEZSqrbd7c7NrbdxlL1vQWHoyE0fbtrRkfuRFGRSxuiMFqlXya/v4D2fnUcdixoz3j0ypZi5csdzRzNKK6FFgav4+R4Zyac9Ha2pHxaQWpolzIDBZjMMKJhG+v5Em0te3K+LQaYBGLm0GwaGJpNDJyKGuiqflz5GDAd/JkXt2uiEXlOHiam7cbVHZjC59i7drVnfHRdNWoiEVTYrCamlqMJbvpg0/j/ru6ejI+bay59OmV7oknl9a/h8MF1pYt2+rHyFcCS/PUurv3Znw4TUYmF9X4jMDix4hzw6c5XHv27Mt4tLLgxjtrVR3AItaJE6OZ7rXxMLkO8OHoGFG8g3NqM9ciFrli8LRsb7Ovud7e/RkWc2xE81L4dF8VsahyB0+zrBNuzODTfbV6zTNZ42TWlVERi0p3YNGA3Ih9Bd8BaZxN81j4tJJdEYs9B482fmdfwTcgN0ucCz6t8lbEovoeTZ9Xr8nzrpAHPpwOI3QAllb/LGIxfngolmHEjSV86M2IuYFP91URi30FjzaZ5boI3759+w0q00Gx+W0Ri/UCFo2fjVhX8Om1g2sefDj9RkWsK3easMNnxL6Cr6dnnx3K9hg8x6SJvGFps3b27cpV6+rfYx/Cx740skbgmm/IvoZP9xXnU7kYBzy7duW5TOQjwaP7auvW7Rmf7qsi1ujoyYxHr0Pk4qJ7deS5DnJO9tXWpib3kQdrhTmoEvyX3/qLLPeVeYeH66tRb29/JhfrxailxexV3jC8KBfrESy9sbem4jTxNtq+vS3j0321bPlqx48R9gcs7JHRwMBU24c9g0/3VVEuKiLCs2NHfh2ypuLk5BohN3y6r4pYNLGGB30YoSd0v3dfniOI/YdPq8QWsZgXeLShN/sKPs03ZJ7hY96NilisF3hYP0asK/h0/bL+4NN9lZo+1zSWmj7bykm/kwamkQZ4mhRT2p6L56HD1cUOeBqlb5bKhsmTVN7QhAgsfXrn4+emV2+UfDwcAwv5qojx6c1zGS9YPFWtIpwDfcpbxouTo08HfXzcEFH8IUTIFSohz1N/fcNZhgkWyfJVxA10MUnexw9WKFGbNxsHhvIbGR8Ox8AKJWqfGD3l9KaoDAvd642Sj4/yy+q4+HhMrosXqwue4KzzlD1EjHHsQn4z6OPHMe3and/w+ng4BlZojDha8IUI2c8EWlLwACMGC9mPHD1WeUrKwsdgMT+hUu3cxMVhjbhQIRaK0bB2QsR61gchPn6cpCi5hkbcMXHYfFg8WIvB6unZ2/AWxIfFdSQGixv00DxScjwKa+SQO3y4ek1QiKKoe96EqRP2pkX3ui9/6Y/c7sD+oLR9jFzYK3UkffrCTsVgUXiHnxCBFbJ9yKRvJcswwQq1YsH2xdqrUAl55jDWXj33/PNlYmfHeVAQa69CdhRbVVw7lSefYR+mN2MzbMKSuEkDqoGUM6baSH8nDSQNJA0kDcwEDficMHsTNhPkTzImDfw4NZCcsR+nNhNW0sDrrIHkjL3OCk+nSxpIGkgaSBp41RpITtirVl364izWQHLGZvHkpqHNfg3E9hkj4T7Ug4sCGTTIDBH5Q1r4oYwfLE3U9vFt3LjFrd+w2fdRwzGwtIBHw4d3/mF8Mb2uwAqFRND/RXObfOfj2PIVq7OePmWfc3z37r1R/amQS3OufJg9e3rdjoieUmBdupTnI/mwWrbvdKtWP+P7qOEYWKFQOUJ3tkuuQwOA/APW6TPn5MjUP3v7Bhryt6Zy1I6ge8098fGRs9giOYM+Ho4hlxaR8PER5qc5GD4ewwo1kCZ3hgayIUKuUEgwIcjwhQjZQ6FMhCjFYCG7FjLwnZt+XjFYzI/mlvqwRkdPR2K1ZUVWfBh2jLA81k6IWM+EUVcRRSVixrh9R3tDro4P8+KlS1FYq1c/41pa8jxCHxZ5YTFykcu0W3LNfFiT165FYXG97Ooq7z+JE7Z2zRr3rl98R1aYg3DEsjdhYIXsFeF2MWNs79jVkD/rGyN2KgZrw8bNjp8QgRWyfeRYIVuIwAqFFtJHNNZehXpZMoea/10mH3JpLqOPr7t7X7S9ujwx4YOoH8NWxezb+hdm2B/JGZthE5bETRpQDVgBDz3m+5tk+h2BRqE4OyTShmhbS2vUzTJYIYO0ctVat3xF+KYUrJAzxviat1XfpDA2sG7cuFE5zJ2tHW6rFNgoYyYhmiIaVUSBEC2cUMaLXCEsnOAtUqyjCuvChbzoio9v0+amhuIpPh6OIZcmnvv4KBigRRh8PIY1KsVNfHwUDNAiDD4ejqH7UD4YyeoU8QgRYww5UDiJWtChDBOskNPT0dmVFcEow7DjYIVy8cgpgS9EyK5V0nz85IrEYFHAI/TggzyWGCzmR4sK+OQ6dmw0EqvZ8cCiikYO1grvVPHwGes55HBSvChmjJu3bAs2+B27cCEKa/HiZY6HWFVkBUiqePiMwj88qKuiq5OTUXJxvfTdxBffhN07f0GpE2ZyUEgmZK9wUGJ0j9MQelCEnYrB4iFEzEMUsEK2D5mQLURghZwxHtBpoZ8yTK6ZWsDFx8ccaoENHw/HkGtCCjb5+Nrbu6LtFU3PqygV8KhpJxXwqFol6bOkgTdIAzgVMQU8KCigVeB84mI8qOgUIhLgtQpcGT+lrUNJzJTtpjR3iJArZNwYX6hwAucBK5QQnWFJBcky+UjwDxUDocqbVqMsw0KuINb4Zacl2KuwQgact12jJ0+VQdSPIxfhsFU0fnki+PaM74MVKlJyeeJKFBa6n5y8ViVWViwk9FbP5NK2Aj5Q3lqypkPEGHlIUkXceFAqP0RghcbI5/CFCNm5sa4i5I7BQnbWdRWhzxgs5idU1OXZZ2/EY01cqRIrm5tQYQ4AkCv0cOTmzeci5brgxserH9qwX2P0dfLkKacVaX2DvXXrdhQW16XQPPIQLEYusLQITtEJ400YJer3STU/n+wcoxpgyF5R0ClGrsxeSWVh3zmxUzF7myI+WnXXh8Ux5ArZPgrcIFuIwAoVr6rZqzBWjL1iDuPtVV5y3zcO1lasvaK4SxVhq2L2bRXGdP4svRmbzrOTZEsaCGgg5YwFFJQ+ThpIGkgaSBp43TSAE9a0ZYt76EO1EvU4Yd/5i2+7y4E3H6+bgOlESQPTUAPJGZuGk5JEShqI1UByxmI1lfiSBpIGkgaSBl4rDSQn7LXSbMKdCxpIzthcmOU0xlmrAcsZ05AOemRR2IDQHiNyFjTXiCReeLSpIuEXxIFr6MTRo8cyPu1ZVcSanJzMeLShMKEVYJ09d95EcPQc4ZzXruWhZU8vW+WWLl1R5yHkCh7FIlwILO1FxOfwaQgX+Q+at4TM8DAGI8JfwNJwB3QAnyYj00yYppNG9HODR5uooidi8LWHDc2I4dNCHORSaA4UoaXwaKNj5g+5tFgDzTPh0xh/cv80b4lCJPCoDISGgKX9XQhtgk/Drmg8/ORTT9sQs1BEePgxstwTzc1iHuDhMyOKMCCXhkYWsTg3cu2XxsCsOfg0VIpmq2BpaGQRC52gexpjG9EEtYhFLgXn1NDIIhZzBY82MKWZK3y6F1rbdmV8uq/KsLQowtmz56dgbWnaluWMsa6MilisR+TaJUUR2FfwaRhR567dGZ+GRhax2HNgdXTm+mJfwcdvI/qHwaf7qojFviJnbEtTvj+QBz4Nn7NmwbqviliMn/Np8QF0Dp/mKZJTBp/uqyIW+wqenZIby76Cj9wuI8bI2qnGupmtQc01Yo2Cpc12rcGv7quiXKxj1jO5tkbsHfi02S65gchfxFq5YlXWCPlDH/ig4+fN993vfuan3pr9zf+/+Wu/7vbu7W24PnI9AEv3qMlFaKUR1yXNjeXc8GmvtiNHj2dYukfBh499ZU7YL73jXfXCHLwJO3KkZoe0CTANrdG9z15pHi/XcW3ozlxxPq6vRjSCZoy6R7k+w6chx0V7xXqER20f+x0s3Ve5vcpDjikgoUUkquwV+97IZ6+wx8hmxP5FLs5rhDzIpevk+PGa7dN9ldkraZzO+MHy2SvyL41y23fVDmX5YmqvuN6B5bNXR6VBuddeNe8o2L5ye6X4rD/OOSFFPVLOWG2KUs5YfammP5IGpo8GzBlTo8sFlgu63oBy0dciEhgReNTBwXHiwq9GF6cFPr0B5UZSHTtkgAfjaISBBEvjxbnAwqeGMnPGnl5pX8saFcOjNwPmqOjNGc4FfHoDyvjUuCEzPOp4MTbk4vtGyF3Dyp1EkqEVC13CowYcnXNjoU1TMZrw6c1sc8Eg4UDVsE6YCNlNE3IpFjd98KnR3VZwxrjRg0edV3N6tKEoN6Pw6Q3o6jXrG5wxHCl4+DHC6UEudeyYB3jUSeSmlRtOjfsvYnFusAYGDxh8dvMOn96AkrhfdOyKWDxMQPe7u/PmvTgCRSxu8jmn3oBOxao5Pdp8HAcFPt1XJKODpfuqiMW8w0O1RCNuqODTfbV1a0vm0FRhsbbB6u7OK9Sxr8DSm1kqf8Knjl1RLvYcPLu6cmcMDPg0/5PqZ/Dpw5ciFvuq5oy12BAzeWpYed7Knj29GZbu0SIW4+d8WkQCPcGnN8a9vQMZn+6rIhb7aiPOWGtnXS7mDz51OGkey9rRfTUVq+ZAaREJ1ih8OMRGA4M1B0r3VRGLfcV65iGDEXsHPr1hp+gLurhyJc95g2fN6jXuQx/4gPvlB96X/cy/a567f+Gi+v+f+tVPuP37BxqcV4rRgKV71OR67rm8US833Vr0iHHApw4nVUbB0j3K9YYb/WfWrquHI5K7/Phjv1sPR0S/Naw8J5hcQ3Sv+wrnAj6tcFtur3IsK56i+8rsVaNjh+3L16rPXrE+GKPmvBmW7iuKTWnBqRwrtydm+3T95rYvd+xqDlTujLFH0YM6r8iDXI22z+yVYjXaPsYPVtH2oXt1aLH/8Om+ymyfPIgss33IdfxEnvfKgzWwdF/x8FAdO67D8PjslT40Ndun+yo5Y7WrR3LG7CqaficNTCMNpDDFaTQZSZSkgaSBpIHXWAM4Y59//Hdf47OUw9ubsJQTVq6j9EnSwCvVQApTfKUaS/xJA9NIA8kZm0aTkURJGkgaSBp4jTXwRjljyQl7jSc2wc9pDSRnbE5Pfxr8TNcA4Qgxpe0p26thE75xUzqe2PkQnT9/oSH8sIwfrFB5X8IFNSSxCitU2p7xxZQnRq5QaXtK5Gs4UplcxMxraJ6PjzCwGCzkCmERWqZ5eL7zcQwszd/y8RH6omGXPh7D0hAiHx+hQhpK4+MxrGcDPd4IYYrBQvehBqaEVsVgoS8Np/PJT8jXmbPh/QHW1UDJfeZRQ3V85zN9adiPj49QHs4ZImTXsB8f/9Wr16KwkF1zdXxY6DNGLuZHQ+B8WIRwxWKFSsgTkqW5Lr7zcQy5Qr2P2Bdxcp1vCFP1nfO555+PwsIZ++xvfdoHUT/GdSRGLkJ7NUy1DiB/3Lp92y1+arH78K98KMsJ+8l773Pf+fZf1sMRjZVrXGhNUCY/RvdghewV5d5jxkgIYggLOxWDRXn1mHYgYIVsHzJp+KzpsfgbrFBpe3KhY2xMzV7dLp6i4X/mMAYLuVgbVcTairZXgdL2WfqF5KhVnXcmfpacsZk4a0nmpIE7GuCGZ9H8BUF9pKbPuYqIddecgvyT/K/U9DnXRTFnIf8k/ys1fc51gb5S02fnUtPnfE2QA0VuXxXFNn3GGXv04UeqoOo5qJVMgabPvAnbsnmz+5Vf/kClE2bnKGv6bJ/zm2JP5C2FKDV9zjXE9ST0YC01fc71NVP/Ss7YTJ25JHfSgHPZ0/x7I5yxjo7djhvmKuKpZYskmZfxUpGtc1f1jQXfBSv0Nmvz5q1u46amslPVj4OFfFXE+Do6uqpYss/ACr3p2d29x7V37ApirVy1Nvi2oadnX0OBgjJQ5Aq9uaDin1aeq8IaD/T12bGzza1du6EMon4cuUJPlnv7+h0ObIjACr1dotoiNxchQvdaRdLHPzA45LQIg4+HY8ilye4+vgNDB932He2+jxqOgUUFuiras7fXrVq9rool+wwsnJoqOnjwSNS+RXYqlFXRkSPHo7CQvWfP3iooR+EH5A8R88M8VdHJk2cisTpcf39eIMaHydsB1k6IWM99+/sr2XizETNGsPb1VmPxFi4GC2fsVx/9eKVcvMWNwWpr62woNgOoOWH6Juz3Hv/8lDdhRQG4XnZ3V68JCsPE6L69oytor3j7FzPGjs7dQUcYOxWDtWlzk+MnRGCFbB/OObKFCKxQxAS2D52FCN2H3rQzh+3tYduHXKEIAIr4xNqry1I50TcObFXM2vF9dyYcS87YTJilJGPSQIkGUs5YiWLS4aSBpIGkgVmogdcqZ8znhPnCEWehStOQkgbecA0kZ+wNn4IkQNLAq9dAcsZeve7SN5MGkgaSBmaaBn7czlhywmbaCkjyzkYNJGdsNs5qGtOc0QCJ7RTw0GRh/uYHI2tEnyjtO8Vnxmc8FLUgxCeENTx8sCEnxocFBlgaqmHnU7loVrpHejJVYWnRDR8WIVhDQwdtONn4jc8Omlwa9mE8KhfNl4eGRuxrpVgdnV0NPdh8WIcOHXU0dDWqGqP2c/Nh0dtn8MCwQZXKhe61ubYPq3/ggOuSPJYqubRQhmHx24iCDoODQw1rzviMh/+R6/LlvI+S8SgWidqErel8GJ9h8Rm61ybDxqNY9OzpHwhjIZf27vJhnTx1OhpLE/N9WMwjzZpDY0Qu7UXlw6LQBHxBrIEhd1qaH/uwSNyPwUL2Q4eP2HTUryVgGlEEJwaL+dEiPj65Ll26HIXFutHeRz4sQm5ZOyF9gXXseN4L0IdFWHHMGAcHh7P+SqYbH9bktWsZFp8ZGZ/KijP2G5/6dWPx6p4iOchVhQXm9//5X9z73/uA5IR92126dKnhe/QlC2EhDNc4bVoPvslvwoKF7qvkgpdrr4bU+rAIW4+RC9unOZw+LOxUDBZhd/wY+bAYG1gh24dM2r+xCktD9E2n8BvVbF/YxqD7m8/lTb+9WIeORNurEBYh1rH2SvO4fXJhq5B/tlJyxmbrzKZxzQkNWAEPHCQjmkmS9Hvh4iU7lP3PMSNuLPlf83z27uvLjh2Qm30Kf8BHBUUj/lcsGjTyv+bm7N8/mB3jt1FLS2t2TG8uFy9Z7mjmaESFJrA0fh+ngWPkJRmR/8Ixvbnkf36MkJn/GYMRhoFjPWJQ0QHH0IkR//NjxI0l/2/dut0OZYaUZHRNzLcmw1pxq4hljTxpnm00cqfhq2KRA8B3jx0fNbbsf5WLyoP8r401uSHiWHtHno/Quas7O0bDTaOlT690Tzy51P51l+80eKZBrZEVYWhry3MIMIrg01jWiP/50Zw3O2Y85FFxTNfc7u692THN/bLvIY+RHbP/uUlG91u25Drs7qk1LNaHDoyF714av2xfzf7nmBG5YvzP+jTau7e2F/RmCR3DV7mvTtb2lTbSJVeI7+m+WrX6maxxMuvKCB5+jGggzv8UMzDq219rfjwwkOdYoQP41DEtYrHnOKbN2rlh5Bg5ekZ27WAfGhWxcDRp+swYjHBc4EM+I+TmGOMwKmLZvtL1y009fPt699vX3LaW2nUoZl/p+uW6CBa5lkbsu1rz27xhbVEu1kvxGOuKY+SAGtm1QytjFr9H/lbxmO2r3ZLHyx6DTxu/2/euXL1qp8wcp4cf+mj9f2vwrA9WbL9rvqHtBa4ZWzZtrldH5GHeX/3ld9zE5ctZhU/OqblM5M9yTPcVBUk4VrWvcIrhoVm6EflI6J7rnRHzAd/FS+N2KPufY0bMO/9r/tHeffuzY/qgy9ac5rjyPcWyfbVT8lKxLfDgNBvZmtPKgsuWr3b8GGF/+B5N743YTxxrsH3b27JjVfuKqoN8j/Ma2b5S24edhe/U6Yp9NVazfXrtOHBgJNO9OpO2fqtsH9c7zqeNs21faXN75hk+fRjC//wYUXWX/1k/RravNKed9Qef7qvU9LmmsdT02VZO+p00MI00YG/GQiLxxkiNqY+f8rl6Y+bj4Vj2pHE4N6ZlfGDxhKuKKGSgF/QyXrBC5X0Zn77NqsK6HSjJy5PGA0O5YS7DomCIPtHz8eFo6NNBHw/HGGMIixsvvWGowrp2/XrZx9nx/oFBt6uru5KHD5ErlPR99NiJYBEGwwolauN88rYkROheHRAf/4nszVh1QQeTK1Ti++TJ09kTb9959Bj60ocX+pn9zZuxmKe8YIXGSEEU+EKE83VanCwfP45WDBayH5Y3Yz4sHK0YLB626JsxHxY3cXFYjW/GfFjZm7GIYgfZm7Fj+ZsxHxYPH2LkAitU1GVy8noUVvHNmE+uGzduTsHiTQpO2IMf/JX6m7A//tKXXXdPdWEnKvnFjJHrJcVkqgismCJLOFghe8Xbohi5im/GfPJhp2KwiOLQSA4fFsfACtm+4puxKiyNCvHxoSt1Sn08HEP3pDZUEXOoD47KeBnjzeeeL/s4O36YN2Pi4JYxg8WarSJsVczaqcKYzp+lN2PTeXaSbEkDAQ2knLGAgtLHSQNJA0kDs0gDrzRnzOeE2ZuwWaSWNJSkgRmtgeSMzejpS8LPdQ0kZ2yur4A0/qSBpIG5pIFYZyw5YXNpVaSxznQNJGdsps9gkv8/qYHb7syOv3df/sQD7u33LXT33fs2976Pf9F9r+W0q+4tf+e0t0bdlu8+5h782XvdwoVvce/5+Jfdv3WPuxemSHXLndz8Xff4B3/OvenuRe6t7/xV9yf/2u3GpzJO+WbVAXLGovqMdXY7Yv+riLCPmD5K9BjT3KYyTLA0idnHt2VLs9u0Oc9R8vFwDCxNYvbxMT7NdfDxGFaoz1h3z96okAj6LWmelO+cPT29UT1gGGMIizyJtogeMGCF+oztbG1369Zt9InccAwszcFo+PDOP+QKtbaFe4OBdebseR9E/dj+/gMNeWX1Dwp/oHvCYKqI8FDNUSvjRa4To6fKPs6OE+4U0/8MLM3N84GSn7l6TZ5z5ePhGFiHj1SPkQIx8IUI2bXAgo8fuWOwkD0UXkzuSAwW8xMK4yXPJxYrFOJKn7GYHm+s5/2SA+fT19jYWJRc5Dpp3o8Piz5jMWPEGfvEx8r7jOGErVi+wr37ne+qhyOWvQmjn5Tmz/rkItw5Ri5CyDSfzodFn7EY3dMXM2SvKMIUIxf5c127q/tiYqdisDZv2er4CRFYIduHTMgWIrC04JSPn9xbdBYidB8KOWcOY8IBkSvcZ6wv2l5NBPqMYati1k5IB9P18+SMTdeZSXK9Dhp4yV3c+CX3rnsWund/5n+45VvbXcfWp93//PQ73X33/KL74oYxV5nx9NIF98zjP+3mv/nj7i+Wt7me3Vvc9//re9x9dz/gvt19Q+R/yV1Y97j72bve4j7x58tde/du1/RPv+/et+Ae9/5v9TjllC9F/WkFPELMFLHQAhs+fpwdTbb18XBsW0trQ4GNMj6wQgaJJo7LV6wpg6gfByvkjDE+LZxQ/3LhD7BCuVncIG5tzot1FCDq/5KMfvnyRP1/3x8k5jdJ4Q8fD8eQK4SFs6lFGKqwLlzIi674+GheqsVTfDwmFxX7qojk681bmqtYss8Y4+jJvFCK7wsU4tCCDj4ejqH7UG4DTk+Ms49cWpDEd87evgGnxSF8PBwDS6u3+fjIuaIIRojACuWCkJMBX4iQndylKhoePhSFhext7Z1VUFmz6hi5mB/mqYqOHRuNkot1E3IuRg4eytZO1fn4jPUccgjO3CngEMbaFnyANXahVnShiEWeVb80n8YZe/ThRzI2cl/ts+KbMC3MUcS0/5uaWoI3y1cnJ6N0z/WytbV6TUxOTkbpnsITIXuFXmLWFwUxtMCGjV1/Y6disFasXOP4CRFYIduHTFqsowwTLMZaRTxo0WIdZbxcMykoU0XMoRaqKuNFrokreWEZHx9FPWLtFQ8jqigV8KhpJxXwqFol6bOZqYEXBt3/fv98d99Df+sO6muw20Pubx5c4Ba973+6wYo3V7e6v+Z+8a6fcn+4ZTIf/wun3VOfWuQWPvR9d9I8uVvd7hs/N8+97QtbXM75gjv9xKfc/Xd/xP3LqDHmMLF/4VRgdENERajzY9U35xgPrU5YhgnWufNjZR/Xj4MVSmKm9DjV7EIEVsi4Mb5QsQPOQ/XHUEI0b4KobhUiKp+FnlqOjV1sKE9eholcISyKTFCwIURghRK1uZHUalVlmGCF3iRSCU0rhVVhafl+Hx9lzGOw0H3oTeL4ZbDO+k7TcIwx8mCjinCUY/YHWKGnzxcuXAy+PUMWsLSSnk8+dABfiJA9dPOE3DFYvEHDeagiSrXHYDE/zFMVUagoDutcQ4U/HybOhVYs9PFwjDVI4ZAqouhArOJYQJ4AACAASURBVFzaOsGHyX71YT31xBPZG67v/e3fZV/DGfvsb30629+//slPZZ8teWpxQ2GOb3/rL9zAQLhwDQ9ZtKKnTy4cPp9cRV6ul6E36GDF6B6skL2ioFOMXJntC9gr7FTM3qYgED8hAitk+yiWo5UayzAZY6h4FbqKt1d6szP1rJntC0Qv8C3kuhUohMV1LtZehRxObFXM2pk6oplxJL0ZmxnzlKR8DTTw8vha98V3vM09/NdDhbDCH7qOr/ycW7Dwd9360gI/P3J7vv4zbv5PftntbHho9bKbWPUZd+9dD7nvn6g5WT/q+YZ7+11vdn+yo4HRvTyx2v2X+fPcw/9UXbGraugpZ6xKO+mzpIGkgaSBma0B3iY9/OGH6g4Zztjjn3vM/fonP5kd+9m3/nT2+yfvvc999zu1EvUze8RJ+qSBuaeB5IzNvTlPIw5p4MXj7p8fXuAWvuObrudHJcwvjbnFn7jbLfjo/+dOFV5svbj/O+5ddy1yf7iVErIvubGnPukWzHvY/aD+quwO5ov97q9+YZ67/wvhGPQSKbKno/cvXFT2cTqeNJA0kDSQNDDDNaAOGc7YW+5/U+aA8Xdywmb45Cbxkwacc8kZS8sgaaBBAy+6c6sed2+ft9A9+L/6y4t4vHjQ/b/vmefu/S9rJfSwBvTS6D+7h++6x/3mUpouv+gO/p/3uvnzf9uty2MUjdF9/8Pz3MJfe7pBguI/hHZ8/5/+2f3NX//1lJ/vfuev3MK773Ga00NeCAUVrl27VoeiQeuatevr/9P4Ex7yJ4yOHx/NGlpquAaJ9fBp2BVYq9fkWIRvwTM8kjeepicTzTFPSSNlcl/g01CpYtNn4tnh0Wa7JO+DpeEhNJ2ET3tWMT5N8EVmeLQ4AGMDiyR+IxqQwjcuuV9r1m5wK1etMxY3OXkt49GcG8IviMEnz8aIfi9gaTPUtes2NmARDgcP/ZWMCDFBLm2GSn8y+DS8ad0zm9yKlWvta+76s89mPNojhxBSsLRPGkUgwCJsxGj5itXuiSfzvKVnb9zIeOAzIvwFLJWVUBF4NCRp/YbNWS6FhjPCo1iEQ4GlhQyYB3gI2TEih4g8QuQxKmKhE3SvBVsIY4FPQ1VpKAsWYW5GRSxC0ZCLoi1Gx0+MZlgaYkM+Ili6r4pY7CuwtH8b6xY+3VfkbyE/68qoiMW+AkuT6U+ePJVhacNXcjzg05DNIhZ7Dtm1yAp7Ez5t+EqOB1iaV1LEImwS2ck5NEIe+LQpM8UJwNI8yCIW40cuzfUkbBE+3e/MDVi6r4pY7CuwNEeF6yJ8XNuMOnftzuTXEMQiFuuF3CDNN2RdwUfDcaO+vv5MLm0EXsQilJE9u37DFvtaFoIHnxZ6GRg8kGFp2KBh3bz5nLt69ar7pXe8s+6ELbpnfvYmbGS4dl3VEC5yKdGXhvoZloYJr1y51nF9MmIc8GmzaGwEWLqvuB7Ap/uK6+XatRsMKmviDM//z955+Nl1FPn+/SmSULQs2xgbYxtsEIsJu4AXMGmBhQW8S8773mPJLJnFNiYtbwHbkpWDlfNoZqQJmhlNUJ6gHEYajbKsYFmq9/meq7qn7pk+p1tW8IzU9fncz7333Lq/U13dfarrnK4qmzRm8+Ytie7tljrFstuEwbL2in4Hy9Ye6+7uSeSyW5rL9upYamzz7VV63Wa7PG3cbQopc/3knHab8KTJU4WXEvYHHmuvmE9gMVeV+B0+O6+wobZwOvMXHhsjijxg9ZgxRzwqfHZeZe0VW3Hhydo+5i01NJXoW/i4binRh9b2cb2Dx9o+5hVybdmaYtHP8Nni3STdqLBXJ0r2ytoTxhVYVoeMP7DsvCJOFflvVorO2M3as7Fdr0ADF6Wv6vvy92NHyJ2PPiltuVsU8bHa5RcPDJexn104IAHHxb1/kw8MHyHv/wtxHC9Lx88elJEjH5dF6dqyJNvFvfLMoyNk1KN/LZSVWKnfP/20PPXEEwNev/jZzwc4Yx0dG5MsYHbR6HLGyBS2xeGM2RgbjDp8PmcMHgytkssZoyAzfHbR6HLG4MHZUlJnDIOpxO/w2QxMLmcMHpvkgbZx4ceQK+EAwVdk3Fg0woNulTBIGAfrjGHo4Kswbg5nDB4b06EGKeuMwVfkjJ08eTI5X5sp+otjkxg3U7S6s7Mr4Styxog/5Hy8lHC4wLKydnV1Jzw+ZyyLxbnBss4Y/QCfyxmzSVayWHnOGHx20ehyxrJYLmds+/YdiVz2JofLGctiuZwxxi18dl65nLEsVp4zBp9dNLqcsSwWc87ljMFnb5jU1A50xrJYOAVZZwx54LMLUBxS+tvOqyxWnjMGn53vZHgDy86rLFaeMwafdcbWOpyxLFaeM1bCMs5Ya8kZs3M0i+Vyxpg78LmcMTtH4cHhmz1rtrz9795WdsR4IvaLn/0smaYpVrdO2+RGDPqyc1TlKnLGaAd8NkupyxnjegBfkTPGvIKHm0pKXN8YO3aOKlaRM0a/g2UdCW6+0EbrjKm94kmikssZA8teayk6DpadVxs3qu1Lk1RknTHsD1iV9uqyM2ZuRKb2Kk2e4XLGwMJOKpWdse3pzYQwe3UskStr+9C91SH2n3PaeeVyxuDJ2j70ZR1t+hk+e5PD5YzBY+2J2j57M5fxB5+dV9EZK42KmMBDZ0d8v0k1cE52vfANeWTMCLnr3T+RNYczew+zrb64RZ6aWHoylt7bLjHpk7GPTCbA/aJsfWJi6cnYQMbSk7EPpk8nsqfxfY8xYz4Nxd+jBqIGogaGngbIjrhowUJ5x9seSZywUcNHlJ2x1064I/msST2GXuuixFEDUQNWA/HJmNVG/HxrauDSUWn67UflvhEj5f6P/0laT1zy6+HSQZnyodfIqPf+RXZn/LZSzNho+cISYsYuycHJH5bRwx+Vvw5gLMWMjfu3dLuP/8SVHNEZq9RH/BY1EDUQNTCUNZB1wogJe/AN9yfO149/+MPk/dOf/FRFUo+h3N4oe9RA1ECMGYtj4FbXwMU+Wf39d8qE4ePkHd+aL7uKs74abV2Qlh/cKyMnfFNqK/5DNsWPy9hhb5ffd5e8tAvNP5A3DLtD/r26grGcTfGdT6fbS8wJgj6GprYnDsE+8neBsx0yJNUu22hIse4jYpd86X2Jo7HxL3mYyOVLbU/7bLxFEZYvtX2C5SkFAD5p+YnpKyK2bdjtQnm8tNGL1Xe4Ig6kCMuXKpitgTbGpwgLp7+IiLezWw3zeGkj27aK6HD/kSAsdG9jrlyY/UfCsJDLbrlyYbHVL6SkA1h2y5ULi5o6NibKxcMxsHxt5Hf4fITsxJIUEXKHYCG73Y7kwkSfIViMG/qpiNhaF4zlqaNEG0PKaSCX3WLpko9YrjC5eqWvr7geIfGWzz37XPlJ2IRxt8nPf/pT+cPvfl92xJCBLYqf/PgnxCb1oPi0pbNnzwXJxXXJ14/UdwxpI1gHDxaXAgArRPeUA/HZK9K9h8iV2KuDxfYKOxUyt9k2aLcyWp3bz8jls33EQ9ktqfb/9jNYvtT2JXuVxgPb/9vPIfaKPgy3V+ct/IDPjC0btziA4fIB2ugr64KtChk7eecY7Mfjk7HB3kNRvuuogXOy9Y+PyV3Dx8t7flwr/ZknXL4Tn2v4rrxh2F3y5SXHpPws7eXdMumDY2Tk256SzpcvI5xrlO/fM1xe98UlcixllN3PflBuG/aI/HabMvrOOPB3FhZjRo4a+EPmSCz6nCqEYpU2Hin9Jf0Uiz6nukBfNnYq/SX9FIs+p7pAX7Hos8Siz+mQkEWL84s+s2hfOH+B/N1bJiaOljphGg974sQJqamuLqPhjGnR55MnTkjVqlXl3/QDMUCMQx/Fos8lDXGjL0RfsehzOqLQl03Glf6SfopFn1Nd+D5FZ8ynofj7TauBi3snySduGy6jJrxXvvWrgckxnvrtHNmkDwROzZV/HT1cxj32V9mrTtvFAzL7U3fKyNvfI9+dXCXrGpbK/3zxzTJu+BvlO7W2gOxFOTDzX+TuYRPk0W8/L6sbG2TZn78oE0eNkIe/XSuW80qVjTM2NsAZq65ZK2Q3KyLuWuK0+YgLbE1tvY8twfI9zZq/YLG8MG9REBbyFRHtq65ZU8SS/EYbbdY/1x/W1jVWZJ5z8XCMIOYjnrv69fVNgnPnI+TyYTWua5ZVVTU+qET3hw4V3w1esbKqIvtkHihy+Z56NTW3yspV6YKxCGv3nuKi1S3r22XFSj9WEkBuMoO5zknWrhUrV7t+qjhGG7tNxr2KHy9/ITPZ8hVhWNs6i592N65rShJquM5jjyGXDZK3v+nnzZu3Bc1bZPc5idu2dQdhkQykvmGdiuB8J8EC8vuI/rHZ1Vz8O3bsDsSqlvWtHS6I8jGyDjJ2fMR4bm5pLWQj+UBIG1euqpGmpvUVWOqEaUwY2xH/7fHPVSQlqvjD5S84Y+9/9B9dP5WPkbUvRK6qqhqpb0iziJYBzAeKd4dgkamzrq54TJBUKkT3q6vXeO0VT/5D5KqpWVuRddU0rfwROxWCRdZYXj4Cy2f7yASLbD4Cy7fLYc1a7JXf9pXsVZqQxHVu+nB1qL06WvykvaGhKdhe2czILrnIlBwydlz/HQrHojM2FHopyngdNHBJDk/5uNw2bHhyNxIDN+A1+hMy/fDlR1kuZwypzvTIgp9+Wt55z1gZNXycPPieL8rvanszRaQTRumZ/1P57CP3yvjhI+T2+94rX/5trfReuLqmxZixq9Nf/HfUQNRA1MCN1EDWCcs+CfPJgp36t88+7mOLv0cNRA0MIQ1EZ2wIdVYUNWogq4HojGU1Er9HDUQNRA0MPg1crROmLYrOmGoivkcN3DwaiM7YzdOXsSW3oAaoMzVu1GhvyymWaWvHuP5AkLAtEuni4RjbpmztmDw+sFiAFBE1dHxbgfg/WL4gZtpni4LmnRcsX6IMtpnZOjR5WHX1jd4tj52dPd7tYdpGX3ILtn7ZumZ5ctFGCkIXEUVNqd/kI7B8SSR6tu+UjZvS+jh5mGD5kjVQ88cWPs3DQvf7M4kLsrwUYA3BQi5fIoPdu/fKhg1hbfQlkqFwsG+bH21BLt8WURIPwOcjZN+7d38hG4kTQrCQ3dbIcoGSVCAEi/6hlmARkUgjFGvHzt1FUHLw4EFh7PiI8exLskL9RZ9cXAP/+Ic/yVsffrMzJkzlOH78pBcLXpyxj37oI/o35/upUy8GYXEt6exKay66wNgi52sj/+N62enZnkuShhDds/XWZ69IwhQiF4WJt25La5252kgfhWC1rG8VXj4Cy2f7kMkWTc7DBMuXcIrtxejMR+jet+WRPgyxfcj14pkzhafkGhFqr0iGU0TYqpCxU4QxmH+Lzthg7p0oW9SARwOawMMWnVyydEUSjGyr1xNsawOUWaTy3cYyNTWvT47ZQpHsV4dv/35qppUoi8UilWM2lqm1tSM5xrvSihWrk2N2QZgt+kwBT7BszBDxJByzxYKJweAY2RiV+M5LCZn5bmMBMCAca1zXomyJDjiGTpT4zkuJxTXfly5dqYdk46YtSQFT4suU2LcPn81SmMVikcoxChIrYfw4ZrEowMsxG8uUxdJA/YWLlilU4izDZ+P6iKfjmF1APz9lhjzz7PPl/7HghYeCxEpbt3Ulx6qr09iGurrG5JiNi1K5bEFvPaZYLPo4Zscc8Socs869/s9mstNjioUzQwHTxYtTHTY0NidY1iGnLfz3UN9h/WvynWNKZOjiO+NTifgejtHHSuiYY4XzamdpXlEgWqm5pS35n51XFKKliKl12sDmpYSDwvely1Ks9a3tybH29rT4ODqAzxbSzWIx5zi2eMkKhZe2ttK8ajUFw/XaYQvpZrFw/pCdNii1d2xM8JFPCbn5r3W0slg6r+z4xTmDz96kWb6idB0KmVd2/HJdBGudiddi3jF2bGa2rFyMl+wxxhXH7A0MxjLHuEmipP9jMU5ijrdNfGviQN02ekxSqJnEHDqv6uvTGCvmGP8lpk1JsY4cTeN8cMbe8/fvVhZhHsLHvFTS+c55lHQuFM6r7u0JFvFMSjje4Nt5RUISjhXNK27QwEOMsRIxROjeLvbpD/gOHkozMfKdlxL9zncbF0WcKsfszRYdczYbYBZL51VVVRrHi22Br6MjvamhY85mbCRmycYtYX/4n42XZT5xrML2raxOjhXNq737SnOU8yrpvLK2DzsLvs1CzHdeSrSf7/bawc0YdL/uCm0f1zuwuDYo6bwihlmJfoaPflfiOy8lbnjxnfGjpPOKJFBKjD/47Lx6btLURH7ludneozN2s/VobM8tpQHSR48dNVqoTaPEZ33pMZwQu7DU3+3/uPtG8gR7zMXHotIaQBcPx8CyQcwuPoxzfUO6iHDxKJZ9Mubiw0C0G2Pq4lEsm0bXxUeiAwyhkouHYywOeDqp5OLjjqVdPLt4OIa+SOGt5OLDabHJDlw8ikWwvJKLj4Vz7Zp0oeTiUSy7GHTxcTeVxQe/KSmf/U4bbYpv5bH/6+ruCcJC9zbLowurZ/t2oZ0WX/mycvFUSEl57P+279gVjGUdIxcW/UiyGYuvfFYG9GUXcMpj/8fNEPjsMeWzWOjBLuCUx/4Ppy0EC9k3b9mq8Mm5FU8P8tQyBAu5tm/foX9zYpFuOwSLMWgXcCqTbSOLa8aOPaZ8KgTfwbKOkfLY/5EoIysX17z58+bJO/7ubeUnYV//6tdlnVm4urCOHjs+AMvFhzP24cc+pKI69XXi5KkgLK4l1jFynY+t8Nk2uvi4xtkEMS4esPJ0D78S116u50ouLBI6hciF7fPZKxznECwcU/tE2yUXx8CyT8ZcfMiEbEouHsWyyatcfCXbF2av7BMoJxa2z9zscfGoXD4sHK1Qe+Wzfdgqxs7NStEZu1l7NrbrltBAjBm7Jbo5NjJqIGpgkGuAxfeC+fMrnLBf/Oxn3gypV9qsGDN2pRqL/FEDg18D0Rkb/H0UJYwayNVAdMZyVRN/iBqIGogauO4auFFOmDYkOmOqifgeNXDzaCA6YzdPX8aW3IIaCK0zRixSQ2NxPRm2Qth4njx1Uoekrr4Yi/+CZbcpuvDYh273j7t4FMtu1XDx0b61dcW11BTLV2eMvfBr1qZxE67zcWz2nHlCEH8REX9kYzDyeNGXD4v4I2LJfARWX18ag+Hir66uDarxBlZvb7qFz4VFnAS17HwEFrERRcQWGRujlseL7js705gYFx9bgaoDtrYgl41HcmGxBStkmwxYXSaGyIVFPNScufNdP1UcA8tulav48fIXEh3A5yNktzFELv6uru1BWMje1JTGXbqwSH4RIhf9Y7eRubB27dobiLW2YquyC4t4Q8aOjxjPbe1pzGuWHyds0rPPyZseeLC8HTHvSVh1TV2yxTWLYb8zX0P0hTP2gX98v/3rgM/EboZg1dbWDah/lgU7TmHpgPHF9dLGI2Vx+E4B6xDdE/Pms1dsNQ+Ri1g6Xy017FQIFvFtNtbX1UaOgeWzfchk4/yKsOy2ehcf8bLozEfo/tixYntFH64xMYN5mLTRl9ipqak12F75EjtRjzRk7OTJO9iPR2dssPdQlC9qoEADmsCjgCX5iSQWNsGGix9nxwbbung4RvFYm2Ajjw8sn0GaMXNOUPFbsHzOGO2ziROK5Dp1Ko3NcvFhaJYuS5N1uHg4RkC0DYh38eFYLDGJP1w8HKONPiycOpuEoQirtzdNuuLiW7hoiRAU7SPksrFZLn6CrxctTpOIuHg4BpYv2x0LC5vQIQ8L3dukGC4+ktIsXJQmJHHxqFw2IYmLjzgQmxzCxaNYNnbGxUf8A0kwfIS+fI4KSQfg8xGy2zhIFz+Zz0KwkN1XYF2TVLjOY4/RP/RTEXV37wiSi3Fjk/O4MIl1Y+z4iPFs44OUP/skTBNzFBVs54aTTc6jWPb9QG8p6YI95vqMM/boe97r+ql8TBP7lA/kfFiyZIX3JsrRY8eCdM/1cvXq4pgeHIEQ3ZN4wmevyAoYMlZJiGETbLhUgZ0KwZo+Y7bw8hFYPtuHTDZZRx4mWL4MiKuqsFdpop88LHRPnGMR0Yc2UVUeL3L1H0kTy7j4SOoRaq8OeW4exgQeJQ3/L5ei9djKFSvks//yaf0a36MGogZukAYIeg1JbU8SAN8TCYyHzSiY14Q9e/d5U2TzX7BYuBRRT8/2ioD7PF6wfMaN9u0x2RWLsHypgknAYDM15mGRiOHMmbN5PyfHSU1OkgUf7dy52491oFd2BWKxhbWIdu3aLds8T5b4P3L5nFeenNmseXnnBYukM0VE9q4QLHTvW1iQvYt2+gi5SKBQRCxwQ+YHWDarpAtz/4HeigySLh6OgeVrI7/D5yNkP9zfX8iG3CFY6N6Xcp+nvCFY9I+vrAA3ncKw9gjJPoqIZDTI7yPGoH0inHXC7rhtvPznj34s7QVPz/QcYNnMmXrcvp9+8cWgNuKMfeKfPmb/OuAzi/cQfXFd8vUjZUCCsPbsFZt5cIBQIklJkRDdc+312SsSOoXMxxB7Rd+GYPFUlZePwPLZPpLlIJuPwLLJq1z86CrUXvmestGHofbq7NlzLnHKx8hoHGyvPGnysVUhY6d88iH2IT4ZG2IdFsWNGrAaiDFjVhvxc9RA1EDUwLXVAItqsiO+/a1/l2xHxAn75c9/fs0Tc4RKHWPGQjUV+aIGho4GojM2dPoqSho1MEAD0RkboJJ4IGogaiBq4Ko1MNicMG1QdMZUE/E9auDm0UB0xm6evowtuQU1oDFjbKFS6unZkRT3PXXqtB5KkmTYuCUCbykAbLdwsdWBfeB2yxCFUeGzNUBKQcxpAUhkgMduZWF7D1hsx1LasWNXwme3qU2ZOlMoPqxEgDdY8CppkWQbt7RzZwmLcyvRPpsMBJnBssVdtegk/1dCbvhsXS7231ssdAkPulVC5+zBtwkW2I4Enw1sXrZsVUUMFMlDSljpdheN8bBYbBWBzyb1WL68qiJuCWccHltbibgzdG+LtLJ9Ez67fW7W7Hny7HNTtDlJXAI8vJTYAgeWrVFHP8Bjt88R/0BMkt0Ck8Xi3GC1d2xQ+KRQMXw2Vo5YEbBsnEQW6+jRo4nubY06tpZmsUhawTltPZyBWKWYmObm1rJcbN2Cz84rLWpq51UWi37nfLYYKgVY4bPzaunSFUnMWBEWYxushoa0GCrzCizmhBKxSPDZendZuZhz8NgEN2DA19ubYjU0lApnMw+VsljMK2LGbCxIipUmeiERAOe0czSLRfvhsclf0BN8tnBvS0up2LWdV1ks5tWCpKh4GrdE/8Fnt+KRGIJ5a+eVxcIJmzljpjxw3/0VT8K6u0tzw27Fa+8oFai288pioUPGMeN55cpqVWkyd+Bjq5oScYbowsaewTN/3nz58GOPyQf+8X3JC2dswrjx5e+f/fRnpL2toyKuUwtB2zmqcr344hk9ZXJdsnG2tAM+u02tZ3spXs/OUa438Nl5RYydjVtCvyWsPeXzkdQF3dt5xVb1ElaIvUqxuKahLzuv1F7ZbdVcx23BYpe9YnyAZbe4KpadV9Omz66IcU6xUnuits+O39T2pfMqm7yKOYoeduxIiyYjD3JV2j61Vxar0vbRfrCytg/d25p+2H/47LxKbN+iNP43z/Yhly3wvHt3yfbZeUWsuo3/ZbxwPpe96jLFztX22XkVY8ZK0yjGjJUvJ/FD1MDg0QDGYMzIURWLM7KrbdmyrcKBwiDZxROLWXisc8HFlAusjZPgAgmfXZxlsQjKhsdeYFmwJEbEZM7jIgyfdXoSZ+z56WWFYhSyWGoorePIueCzRoRgdJtEApnhsRd5CvsilzVS6AA+a0QSQ2kMEgYZHoobK6EnjJvdx46hg88aEQLbrUHCUMJDPympw7nFxLJglOGzCyqMGws7JRag8FgZ1OG0DhTOJ3x2QTVr9gsVzhiOHTy8lNRJtIky6Ad47IJqxcrVAxyoLJY6iWReVGLMwWcXVCxaaSPyKGWx0Am6X2syiGHAs1gEttPf1unJYtFX8KxrSpNIEGMJn50Lq6vXJnz2xkQels3exoI7i8UNDRwau9DLYjEekWttXeqMMa/gsws9stjBZ52eLBZzDp7aNWnGNeYVfNZRqasvOXZ2XmWxmFclZyxdsCEPfLbYNYlYOKedV1ks2g+PzVKJzuGzC1ASfMBn51UWi3kFT1VVjQ6b5LoIn40lpY2MnSwWhXPtdsTbRo+Vz3/uC2XniDEKlnVU2ts3JOe08yorF+OY8UziIyXmDnw2NpJELcifxXp+8vPy4Bvul/vuuTd5jXnNKBk/Zlz5+7seeXtSUNpeH7kegGXnqMplHSiuSzZREeeGz94M68QhzDg94MNn51WCZRIVMUdLWKlzgUOL7u3NBLVXlQ7UsgoHir4CyzoS3ERDLjtHuT7DZ2/4Ze0V4xEea/uY72DZeZXaq9TpmTZ9lvBSKrJX1tF22SvsMbIpMX+Ri/MqIQ9y2XGC8wqfnVclxy6dj7QfHpe9IhmOUmr70kQcJO+w9orrHVgue9XVncrqtFeZG5GMF7Bc9sriM/7g6zcxrtEZK/VadMZ09Mb3qIFBpAEMPdm8IkUNRA1EDUQNXLkGBut2xCtvSfxH1EDUwFDVQNymOFR7LsodNSCSPD2IzlgcClEDUQNRA1emAZcT9quf/0LYNRApaiBqIGrgRmogOmM3UtvxXFED11gDbO0YF/BkjC02dsuKSwwWJ3bLh4uHY4cOHZZDJkYtjw8sMIuIbU12a1MebwgW7bPb3YqwfKmC+w73B2Ht2r1Hzp07n3eq5Dhbfw4eKk63DSNt9GGx9cdu8ck7MVg2fsvF13vwYMX2LRePymXjt1x8bCMKlYsU3kUEFuntfYTu7fZZFz9beUKw0NdJT+05tiTZ+CrX+TgGlt0m5eKjH9mi6aMSVrpNysXP9ib4fITsdiujix+5ZEkjXQAAIABJREFUQ7CQ3W6nc2GxvSkEi/6xW65cWGxvCsU64inCfuz4cfnrX/5akR3R5YQxnu1WRpdczIsQucDyFbVlvoZgseXSx0c6eh8P7UEuXz+ef+mlICyuvT4sSoowb30UYq8odRLSxhCsUNv3atkrX1mXvr5we+Wr10kfhtpRP1a4vWLMFhHjPmTsFGEM5t+iMzaYeyfKFjXg0QCLK2LGfBSLPqcaYg++jU9If0k/xaLPqS7Ql43fSX9JP8Wiz6ku0Fcs+iwy2Io+s+Ce98IL8uY3PVROzOFywrQn84o+6++8axIJe8z1mdiga1X0edKkqbJgwWLXacrHuDHFOPRRLPpc0hDOToi+YtHndEShr1j0OdXH1X6KztjVajD+P2rgVdQAztjYAGcM56Kmtq5QUu5y2YyLecwE21dXr837uXwcLN8dvRfmLZQ5cxeU/5P3ASzfXTjaV7U6Dd4vwvI5Y7Vr6mVVVZr9LA/r+SnTKxJsuPjWrm0Usg36iDbyxKSISAyxwmRly+MF6+DB4qcly5avrMgMVoRlkzy4+Eh+sXxFleunimPI5SsC2tzSKtw88BG637x5ayHb+tZ2sdni8piRq6s7zW7p4mtr31iRLc7FwzGwtm4rLipc37BOpkxNs4gWYdmsmC6+TZu2Bs1bsqTZpC4uLALrkd9HyG4zM7r4SfwQgkX/0E9FtH37rkCsKmlZ31YBpU7YIxPfmjhht48dJ5/85095tyMynkkcUkQ8KQlpI8k7Gte1FEEJT6pDsKZPny1k4ywinm6EYJEsx+ck8iQxBIvr5RqTIMYlH4lkmLc+IqOqz17xVDJErtXVtRXZOl3nxk6FYM19YYHw8hFYPttHBlFk8xFYvp0JNbXYK7/tQ/e+p7304apAe+V7Cl1Xty7YXvUdTjNCu3RCJsuQseP671A4Fp2xodBLUcaogRwNxAQeOYqJh6MGogZuaQ1knTCKNRc9CbullRUbHzUQNfCqaiA6Y6+q+uPJowauTgPRGbs6/cV/Rw1EDdxcGohO2M3Vn7E1UQO3ggaiM3Yr9HJs402rAer0jBs12ts+4jfYNlREJLXwbWPi/9u2dQtFRX0EFgujImpr65DW1rTuVB4vWL6kG7TPtz0MfLB8wcLUT7G1UPLkorgvtb6KKKkxY+qH5fEilw+LIpvUX/ERWLaGlYt/0+Yt3m1Y/A8stioV0Y6du2TzluItg4p1xJOtbueu3d6YK7DQ/QFP4goSTfjit1QuX4IbahGxJdBH6MuXzIQ6d+vWNfugEt1TG6+IKKzOOX2E7Pv2HyhkQ+4QLGTv7ine1kkSgBAs+sfW7nIJePjwES8W15rf//4P8paHHi6MCaONtii363wcYzzbQvYuPpK6hLSRrabbTSF7F9bxEyeDsJqb1ws10YqIWmIhcnEt8fUjiUVCsLhe2lqTLvnACtE9WD57RTKQELmoX2XrbbnkYuyEYFEj0dZJdGFxDCyf7UMmW1urCIu2FlFi+wJsDLr3bXmkD0NsH208c+ZskVhJLbdQe2Xr37lA2TIcMnZc/x0Kx6IzNhR6KcoYNZCjAU3gsXlzukBftmyVLFq0rGJBSLCtDVCmiCQ8NTVp7FdzS1vCs3FjauhXrlyd8NlimFksgtjBWr16TVnKtrZSMdS29g3lY6tW1SR8NnvipMnThGKOSiSKAKuqKt1L39GxMZHLxpWsXl2b8LFAVsrKhcxg0QaljZcLqzaZAr/Ev8Fns9tlschEB89yE8tEvBIFTEleoVRbW5fw2UVcFotFKljLlqWxORgs+CwWBY3hswWqs1jEhsBDIL4SBh6+NWvq9ZDU1TUmfHax9PyUGfLMs8+XeYhXA2uxKUTKggEsG7/R0NCU8NnipCqXzYoHFi8lzg2fLfDLoh4euyhZcHms2vi5LBbFX9E9xU6V1q1rSbDsQmLhoqXJOa2jlcWiwChy2Vi8lpbWBMvGpFEIFT7raGWxmFfw2Ji39evbEyw7ryi4TeFkm50xi4WDAhaxXkrMK/hsEW5iSuCzcX1ZLOYcPDYuhnkFX3v7RoVPzgWfTdiSxdq/vzeRfdbseeX/IQ983FxRQgdgWUcri0X74bHF2nE04ENvSvQNfHZeKRaLXhJzTHz4zYkTNn7MWPnVL36ZxIRxXYSvublVoRIdMHZsYWPFUiZNgGELrDOu4LPXDq55yGULCGexjhw5kvDAp8S8gq+xMXXImWPwUBhZSbHsvGLezpg5V1mSIsHwMS+VuI6AZZ0Q5jV8dl7BY+WiHfAQ56qkxbvtvKIwMHx2XmWxKAIMj70OsZhG93aBznUQPpvBL4tFv8PD9VWp5bK9so7pihVqr9IbGFksxiNY1dWpvcK2wLdhw2aFF+Lp4LPzauq0WcJLCfsDD/ZISQuBW9uHPYPPzqusXBR0h8fGayEPfPaGJXLDZ+dVFosbOPCgDyX0hO5tHCT2Hz5bVDqLxfUOHtYVSswr+IgVVqKf4aPflbJYjBd4GD9KjCv47Phl/MFn51Us+lzSWCz6rCMnvkcNDCINkIp67MjRFcHCPEHiZe/MYRg6NmwqS85vyqcHSZDR1NzqxcLYtHekCzgXFsHLYNk7eno+KxfB49ZYF2HZBB4uLNrX2pY6f0VYL754Rptd1oOVa8PGzRUGMA8Lw8kdbSWXXNxBbDUJCvKw0JdNPe7C4imCdUqLsGy9JBcWiTKsY1SE1d/fr00s68sGqG/Z2iUsji5dujSATw+ATxttmn8wkM1i8dQVLPiVVH79zm/o3jrQLiyecNJOHxZy2adGLqzunh3BWLv37FVRk7Zl24iTR8B9iFw2nbNLLhaqyO/DQg/WmXFhscALwUJ2uwh2Ye3duz8IC7nsTQIXFjdWsnJxPZgza7ZoYo47x98u3/jaN4QnR0ourD179yZjx6cvxiA7CpRcWNwMycqVHavMCZKKbNmSJnVxYTFf87DsvGIxbh1CxeK8StgFsPhNSeWy7eZaYp8I8Zvy6f94Wh+ChcPAdVMpD4t565OLp0/2hoMLi90NIXJh+9o7im0fbQ7BWrO2QXgpueSibWDZ/lCdwq+ETNZhK8KyOzlcWOjKPrHLw0L3lIlQcmIF2j7a6MPiGhFqr2w5EJdc2Crkv1kpPhm7WXs2tuuW0ECMGbslujk2MmogauCyBlhovjB3boUTpk/CopKiBqIGogaGogaiMzYUey3KHDVwWQPRGYtDIWogauBW0EB0wm6FXo5tjBq4NTUQnbFbs99jq28SDYTWGauvb5J1TcV1bthSSO0TH9U3NAtxBD4Cy25HcfEvX75KlprYKRcPx8CyWx5dfLSv3sRvuXgUCye2iNhXX1efxk3k8VInzcZzuPiam9u8tXz4H230YbHlw26TcZ1PsQ576rbU1q6VBQvTOJYiLBsn5eKjBhe12XxEG+12QBc/201ra/1Y6N7Grbmw2IJl40xcPBxDLhKHFBFJGGzsXB4vWDbWwcW3vrVN5s1b5Pqp4hhYbLUsos7OnqB5i+y+xDvIzTl9hOxsLywikrqEYNE/dqtcFhMn7C//81d54/0PJDFhbEfMexLGuLFb5bJYfO/ZvkMYOz5iPNvt2C7+3t6DYW1cUy/E+xURdZZC9LVw4RKpqUnjnVyY1JIKwSIulVjhIjpx8mQQFtdLG5vnwiSpUIjuiXnz2SuSgYS0kdqMvsQP2KkQLGoz8vIRWD7bh0zI5iOwaGsREbtl443zeNE9SWeKiD4kxthHyHXs+IlCNrb6htorYiuLCFsVMnaKMAbzb9EZG8y9E2WLGvBoQBN4eNiShAK+opDEYBBI6yMKmNpkB3n8YPkM0oyZc4IKD4NlY8Zc56R9IQV+wfIVfaZIdoiTSEA0cSNFRIIQmzghjxe5fFgsEBebZB1FWL29vXk/J8cXLlpSkTwljxm5bOC5i4+FgE3C4OLhGFg7dhY7PTj6JMvwEbq3cSUufpxqknj4CLl8jkrL+naxCR3yMMHyZXCsXVOXJMHIw9DjYPmci46OTUHzFtl9zgUZFzmnj0g+Uu1xCIi3CsGif2xSAT23Pgl728SJAxJzKE/2nXHjK65MlkTGjo8YzxTnLiKSF4W0cdHi5d4bMgd6e4OwJk2aKgsWLC4SK0msESIXiX98TsjRY8eC5OJ6aZM4uQQ8duxYkO5JWuOzV2QFDGkjxbtXemKNsFMhWNNnzBZePgLLZ/uQCdl8BJYvA+KqKuxVmmAjD5NxbxO4uPjoQ5tgw8XDMeTqP3I07+fkeE1NXbC9OtTXV4gVE3iU1BMTeBQOk/hj1MCro4GTJ08FpbYnWxILhyLCeNjMfXm8JBSwmZzy+MBiQVVEnV2kyU+D5PN4wfIZN9pns0IVYfkcO7Jk+Z6UgE+Ass9QksjAJk4oksuHRVY8nzMDPvrypckn65XNalYkF+OsiMiwZ7PT5fEil01S4uIjE1gIFrr3Oa+9Bw9VZPdynY9jyHXk6LG8n5PjJB7ZbjKF5TGD5Vvw0I8+h03l8rWxr68/aN4iu81+55IfuZHfR8juc9B5OhOCxTikn5SyThhPwn7y4/+syNSovNl3xo2v3AFttMlHshj6HSzKBhQRT3rC2rirIiufC5P5GoLFnCWbaBGRoCgEi+sS16ci4qlMENau3WKz27owwQrR/c4Ae8VOiRC5EnvlsX2MuRCszk7S5IfZK5/tI8mPTc7j0hfHkMu3K6Rkr/bkQZSPl+xV8VO2BMtzw0zlOuN5YsfYCrVXvt0qjPuQsVNu7BD7EJ+MDbEOi+JGDVgNxJgxq434OWogamCoasDlhP36l78SnqZEihqIGogauJk1EJ2x6927F3bIMx96g/zrC4clTfoscnbF1+V1w4cn2y9GDkvfR71mrNz94HvlS7+vk77ihwrXRPKrleN0/Xdl4jt+Je3FN1uuiawRZKAGojM2UCfxSNRA1MDQ0QBPvOfOmSO6HZEnYdEJGzr9FyWNGogauHoNRGfs6nVYgHBRdj/7Ibnr3X+UnrQEiIhckM2/eYeMMU6YdciSz8PvkE9O3i3X1x+7BnJc6pM5n7pL3vnrjXKuQBPxp+ujAY0ZO2zqQBE4T5C6rWhPzIKNWzp+4kTCY+shUXSSfeAEkiuxVQ8sG2NFzJIttkt9EHhszSe2dIFFgLvSrt0lLLvlberUmUIRUyWCxcGy2zfYSw6WLRbN7/DZ2iS0j3YqITM8drshbQPLbmdEB/ChEyX231ssthDBg26V2D7GHnybYIEaRgmWCWwmjs3GQJ1+8cWEx255O9xfKgxrsdgGBpZ9MrBiRVVFDNSLZ84MwOq/XGR267a0EPjeffsTPpsgZPacefLsc1O0Ocl2S87HS4mtZuhr46ateihJwAHPkaNpvMDKVTVJPJUNNM9icW6wbL27/QcOJOdDZiUKpBLfZLdsDsC6HHtiA+DZUgaf3SK4unptck5bVy6Ldez48YTHJjJgqxt8dotgTW19wmfnVRaL+UgbbfIBtuDBZ+cV8TXEXdmtpFmsEydKWA2NaZD/wUMlLBtfoQV+T55Kt5JmsZhzyFVXl8ZAUWQXPltsl6QC8DEPlbJYzCtkt9eAQ32HEyzkUyKpQIJl5pXFwgmbNnWq3P/6+8qJOXDCenp6Eqzeg+m1g8Q1YNktrhaLczKvCPK3tfO4LsJnty4Sk8i8pd+VsliMF8YgsThKjKsEy2xd1KK8xFUpZbHYygWWjVtiXsFnCwoTy0Yb7bxSrLNnU+s6+fnpMmfuAj1dwg+fTYzT1VUqsM55lBTLziuuSzbOlnbAx/VCiW1yyGXnFdcu+Oy84nppCwOTKAKePXv3KVSy/Rjdc71TUiz6TwksG7NLv5ew0q32bIFDrj4Ts7vzsu07dTqtpbV4SaXtY16BZW0fW6MTrL6Bts/Oq2nTZ1fEOKvts/bKbfsu2yszr7BXyKbEeZCrwl71leyVtX279wy0fejK2ivan2AZe8X1B93bLeAu20cfWiyud2BV2L7+/kRf9hj9DJ9NELJ8OfYqjf/l5jE81vYxrtC9rTVYtldmXsWYsdJIiTFjOmOu5P34EvnynXfLN1amRjL5+6UjMvOTY2XkqA/Js/usu3VRXjrTL50LvyPvGj1cxj7637Izrdl4JWcO471Gcpxv+7lMHPuYTNpr2xImQuS6Og2oM2adHt1bTTyDEsHoNvEDRpr9190mUxsOChdF4n+Utm3rSvjsIogLtTUiLLLB6urq1r8l8SRg2RgC9trDZy/WU6bOEBYXSorV2ZliYYjAsnFXnAss61zQPnvhR2Z4aIMSi5/ShT91OMjIB59duGSxMLrwbN2aFm6lEC3GbcuW1FHBoMBnFy4YXSsXC2N4bLwW/Ydc9hiZ7eCzDgGGkoWdEkU34aGIsBKZD8HaaAqwsqCCz8YMzZw1t8IZw+jCw0uJhTpYFPpWwpjDYxfxBKIjl12cZbE4N1gt6zsUKulT+Gy2xhUrVydY1unJYqkjvGZNWoB1167diVwWiyQAnNPeTMhi6WLAJn7gxgJ89LFS1eo1CZadV1ksMoJxPpv4gVhG+Oy8Wrx4WeLQ2JsJA7FKjvDaurSNOOjwceNEac2auuScdl5lsfgNuWzGyyRuLcFKF95kUYPPzqssFvMKZ8wmbGFewWfjyHCUwbLzCp6Ojo0VT8LGjxkrX/ril8s3HdA5fDbGdd26kmNn51VWLnU4uTGgxLyCz94oqqtrSOZtERbjhfFsExUxrsBinClR6Jg22nmVlYsFKFg2WQNzBz6cByWKAOdh2XnF9XL2nPn6t2QegmUX2WT+BMvOUZXL3gDgumSdHtoBn41JI1snWHZecb2Bz84rsOwNP+YoPDazKNdarplue5Wuk8Cy9oq+Assu2HEEkMvOUa7P8OFwKZXs1Qr9moxHeGwmVmKgwbLOcWr7Uqd92vRZwkvJZa/USay0fW57ZZ0e5ihyueyVddDUXlEkXGmgvSrZPpe96uxKs7Ni/zmnnaMD7VXJ9lnbpPaKmG8ll71ibNkESowXzmdtJuMK3W8xtpXxB5+1fdEZK2k6OmM64oLfL0rP798lY+/7gTSfz/zpfJ18774RMuZtv5ZNFU/MLvNd2CJPvn2kjJn4c2l3/Z6Be8Vfr5UcF3fIf79rlLzx++vi07FX3Bmv7I9xm+Ir01v8V9RA1MCN1UDcjnhj9R3PFjUQNTB0NBC3KV6vvrrQIb9843C57zuNkvXFXt7x3/L+kSPk/m+vcTov5zY/Le8fM1xu/9QM6beBZtdY1msnx0Xp+d07ZPSEr8mqdHfANZY2wrk0EJ0xl1bisaiBqIHBogGXE/Zfv/p1+UnYYJEzyhE1EDUQNfBqaSA6Y9dJ8xe3PimPDBsjX1o60Ds5tfALctfw2+Xz89JH6XLxvJzq65F1M38iH713pIwc/jr50oIjFUk/rrWo11KOC80/lAeGvVb+Y23W9bzWUkc8qwEe+982eow95PzMNg+7FcHFRDYzu93GxcMxsHz1ReAD69Kl4rsJbFGwaa3zzgmWL1Uw7bNbj4qwLlwofuQcikWchi9NPltZbIxEkVxerGPHKrZuFGGdO5fGmbj4KAptt/i4eDiG7m0smIuPLTZ2S4mLR7HOnCnO9sM2uBAsthTZbVKucxIHGIJFG+22SBcWWwptfIqLR9vI9tEiIjbHbonK40UuXxvZngefj5Ad3iJC7hAsZLdbGV2Y6Ou5Z5+rSMzhcsLoHxuv6cJim16IXAmWidd0YRFPE6J7sGxcmQuLeREql91G6sJivoZgMWd9fFxHfDzIQBt9/Uha9RCsko1JY+dcbQTLxra5eDgWYq9w8sPlSrf0uc6JnQrBwl7Z7ZouLI6B5bN9oTYGLNpaRKFYJXv1UhGUHDlyLNiOnn+pGCuxfSamL+/EtNFn+xj3IfM27xyD/Xh0xq5TDx2f8ykZO+wRebozG0f1krT+9C0yuih5x7Bx8si3FsuB7F+vqazXVo5Lh2fIP48cIe/+w/brnHTkmiphyIOxcB0zcpS3HcuWV3mLaHIxZO+2j2LR51RDSTC6x9jEos+pvhhfvrozsehzpb6GWtHn5EnY7Dny0INvLCfmcDlh2sq8os/6O+/d3TuCrk3EGtnYP4uhn2PRZ9WESCz6XNIFYzbE9sWiz+nYQV++m7Kx6HOqL9+n6Iz5NPSKfr8oXU89IiNHfFxmHs48Gbh0UCZ/ZPTAlPYjx8lr750o//iJb8qTczbKsczfUjHOyaIvTJBRhc5cKVX+bZ+cJubZWwrBp6uWoxJOXqqRfx83XO7+doMUP3PI/C9+vSoN4IyNDXDGCES3WcZcJ8UZW2QyH7l4OEaAvM0ylscHlu+OHhn9Zs56IQ+ifBws350z2kfyBx+B5XvaUF2ztiLgPg+TbITcXS6i2tp6wRn2EXL5sNbWNQqZHn0EVm9vmnzCxb94ybKKTJYuHo6BZbN5ufhwoGx2PRePYlHQtYjIwmeD9/N40b1NUuLia1nfWpFsxsXDMdpoA9tdfCRrsAH3Lh7FIoFCEZGUg4B0HyHXxk1bhKcmf/7Tf8vPfvKT5PXNr31dvvBv/5Z8/sZXvy5f+NwX5HBfXyEcsttMli7mzZu3BV0DkL12TV0FhDphf/eWiYl9m3DbePncv37eux2RZED0UxH19OwMkotx09RcjLVl67aKxDV552U8k12yiEhYQh/5iKQINvOni/9Ab28Q1pQpM2TRojSJjwuLJw0hcpEQyCZ1cWHxFDcEiwQlLL6LiMywNoNrHi83/Hz2iqyQIXKRxbJqdZoV03VOxm4I1qzZLwgvH4Hls33IZDNs5mGCZTNguvjIGovOfITufbtH6EOyIPoIuXzOGAmWQu2VzRDrOjdZl0PGjuu/Q+FYdMauSy+9LJt+8ZCMHPkZmZ/1hs5Vyf9+7QgZ+w9PS1fxk+ccyS5I14Kn5cnf/Mb7+u3cDc6YtAT4quXIiHehUb5353C57eurpfjBdeZ/8etVaSDGjF2V+uKfowaGhAZ27tiRbEceUALF3JRbvHDRq9KWrBN21+0TpOhJ2KsiZDxp1EDUQNTAINZAdMauS+dclO6n3y4jR3xMZmSejL289Sl59+XkHa9mdNU1l+N8tXxr7HC55zuN8cnYdRlTbtDojLn1Eo9GDdxsGiCV9e7du5PXY+97v0wYd1v5+0FTk+tGtTs6YTdK0/E8UQNRAze7BqIzdp16+MS8z8jYYRPlqS028OuSHJv1Gbl92Fj5zMzrm5yjuFnXXo5LfVPlYyNfI+/5884YM1as/Gv6KzWPxo0a7cWkNomt9+L6A4srW+vDxcOxru7tFfVe8vjA8iXd2LBhU1J3KA9Dj4Pl2/ZB+2ztGP1v9h0sAsmLiMKUtoZKHm9LS6t3Cwk1vmzdtDws5PIltyDeapupwVaEhaNeRFu3dUpra3sRS/Ibcvm2dVL01NbHyQMF6/iJtP6di49CpFtNbTgXD8fQ/aFDxYkr2EZGO32EXEeOFicfoE6YrduThwmWb7spdYNa1rflQZSPg8WWsyx9/KP/JHeOvz05fPBgX9C8RXZf8gHOxTmLiHn4m/96Qh5+45uS7Yg8CfvNr38tx00RZf5P0hofFnz0jy8wn0QAYVhdQp2nIqJvGDs+YjzbWmcufhKihMgFlm97LvW/QrCYs1u3Fm+DJeFJCBbXJVuA19VGtsgGYXV1C9e6IgIrRPdsGfbZK5IwhcjV1d0j3T3bi8RK7FQIVseGjcLLR2D5bB8yIZuPwPIlnEJXvm3WnKdkr4oTKF2JvbLFyF3toPZdqL3ybcVk3IeMHZccQ+FYdMauUy9d7H5a3jVstPxrxT7Fl6Tx+w/K6JHvkqe3vaI9itdI2msvx0sN35PXD7tXvt/waj7vu0bqGWQwXKQevO8NcteEOwa8WJCNHD5Cms3igiDjSZOnVRRgpUgrLyWMMDzz5y/WQ0nsADzr1rWUj82a9ULCZ4tOZrEoxAnWC/MWlv9HTAx8DQ1N5WMUKoXPGn8SYPBSwgmCZ87cBXpI6uvXJVjESynNfWFhwmeNbFYuZAaLNigRAwIfhXKV5s1flPBZ5yuLxaIMrBkz5+jfpLl5fSJ7VVVaZHbBwiUJn3VMnsnofu++/QnPtGlp8VAW5pzTYlFUl3Pags7PPPt8wqdCkGEKHvbTK7W2dSQ8K038HPEv8NkYK85ndc9CHR5bhJtiz/AtX5HGqS1bvirho3ivksplHQeweCmRiAIsG1tGjB88bW1pIWjikeCzjkMWa9PmrYns8+alW/OIv4BvvXEwJz8/LcHab4o3Z7FY7HA++k6JeBX46GOlKVNnJny2sHEWa1tnV8LDmFKqra1LsOy8or/QvV3sZ7G4sYBcc19IC/yuXduQYL3n799ddsZmzZqb8FEEVymLxZwDy8a71NWvS7Ao9KzEHIXPLoQVS5+EqRNGsWZ1whoamxKsNWvTAtVzX1iQYNkbJIql56P9nM8W0l3X1JJg1dSsVTaZN39xwmfnVRaLeQWWnQtcF+FbbWKGXnhhYaJ7u/jOYjFewGL8KDGu4FtVVa2HZMmS5QkfBWqVslgHD/UlPDZGkHkF34oVaWwOBXI5JzeolBTLzivGzd+eSa+ZzEP4mJdKy5evSrBssXbmNXy24DLne+bZ1C7QDniI41NiXsFn5xVzAT47r+DhpUSRYHhsLBa6Q357I4LrIHy2kHkWi36Hx87Rmtq1yfmamtI5OmPm3ISPIs5KWSzGI1h2jjJu4WtsTGMEZ82el/DZwtzIzksJ+wMWY10JOwUW80sJewYf9k0pKxeOCzyzZ89TFmFewbd2bX35GHYWPuvIZbFoPzzoQ4l5hew2fg77D5+9WZjF4noHD+sKJeYVfKur01g8+hk+Wxxa7YL+j5su8Ew1to9xBZadV4w/+Oy8yupeMW+W9+iMXa+efHmLPPGWEfK6/21qiV3cLX9532gZdc//kdrirNOXpbogdV8eLh+aWZyO+IqbcMVy+M4X0U87AAAgAElEQVRwUbY98VYZfde/S+0ZH2/8/ZVogCdgBD9nXyxmSOBhnxpx95GXPUZSBGsA+Q0emxSDNM0YEPvUyIXV1Lxemk2QvAsLDLD4v5ILiyQAJMtQUiz7P8Wy6dVdWLQPg6NUhGXTmKMD8OBXWr++rSJ434XFMYLWSaKi5MIi8YM18i4s7nyiLxeWvSva1r5BSJahxN1X1YUeUyy2tSmpXBYLx9QawCIs0uArubBYQJKgwN4NzpOLJzlKLqyNm7ZKfb0fC93zRE7JhUUiDZz5ELlsym3GHPJbfbEgpI/sOMm2kd/g2b0nlUuxeFciKQcL8RCsnTt369+Suck5P/aRj5adMe5kh8q13SwGXXJxriwWT1inT5smb33zW0rZEW+fIF/6wpekoSFdbLqw9uzdOwDLpS/6xz4JdWHt298biNUkmzenT/boP85pdc81k7Fj+zYrF+OF8bxx0+ay7l1YfX19iVwhWDYrpmIxZpX6jxzJxbLjlzlrb3K5sLAT9KNLLovFdYmbN0ouLGxPENa6Zlm/Pn3S7sQ6dSrRvWvc22NkxPTZK57+IZftW+1Hi5XYK3Ozkt/gs7rnewgWDiAvJcXi/0rIA5Y9xmdeVi4cGmRTKsKyT430Omex0JXNIurCoj8Y95ScUHJh0Yeh9urEyYFYdsy1tYXbK1tGQuWyWNwUQP6blaIzdt169qLs+vN7ZOzd/1fqip8KXzcJbhjwy53y9NtGycM/as5PGHLDhLm1ThRjxm6t/o6tjRpAA3ab4vXSCAu6ObNml52wvO2I1+v8ETdqIGogauBW0UB0xq5nTx9fIl++8w754qLjr/As1+nJ2BVLc0mONv9RPv+2O2XssLHy8Md+JbV9aSzcueYfyZvGPiaT9qbHrvgU8Q+vSAPRGXtFaot/ihoY0hq4ns5YdMKG9NCIwkcNRA0MQQ1EZ+y6dtrLsuuvH5C7/v4P0pPugLqCMw4SZ+zEcvnKPe+Un9Tsl9Nn+6Tlqcfkvk/MliRR5KXDMvfTd8ojP2+Tm/0B4BV03A1jPXEirM4YWxhsXJlLQLZX+GrO8L9169YL2x59BJbdSuHiX7lqtawIqI8Clt2O4sKifb66QPwPLF9yC7Z9sF/fR8QwHDtWfLOFbR++GkMqlw+LbYps6/IRbezvL65/trauviI2JA8TrEOHDuX9nBynflVdfRp7lMcMlo0zcfGxhc/GB7p4OIbuiVcsIgr8Er/oI+SyWx5d/Fu3domNiXLxcAwsGxfp4mtr75CFJkbNxaNY3T1pnInyWWcMHXBOHyG7jTPJ8jNX//THP8kD972hMDEH/0N2G0OUxeI7CStC5KJ/6Kci2rNnfyBWo2zaVIy1Y+fOitijvPMynjdsTOO3XHzENYa0kW1r7R3FWIf7+4OwiFNb4+lvEp6EyMW1xNePbEULweJ6abcpuvTFlkcb9+Xi4RhbsX32im3rIXIRq2m3A7rOydgPwSLGNaSWJVg+24dMNo7UJRfHwLJb9F18zS3Yq3T7uouHY+g+m2gny0sf2m2w2d/1O3LZbfV63L6zRT/UXh0x2+othn4mjixk7Cj/UHuPztj17rHz3fKX998vn5t/WHLrOOfKMDicsQtN35cHPjZTjqic51bKV+74ilSdFznd8H156yM/k/Wn9cf4fiM1wMVwTEDRZ4oOrzKJJlwysk97/oI0iYGLh2MUl6SItI/A8hkkEmJMm54GBudhgoV8RUT7bBB7Hi9YvuyABDkTUO8jgop9mfOqq9cKRV99hFw+LAxgSEFksHxFnxcuWhJUeBgsm7TC1Q4WmyQc8RFYZIQsIhYVCwMK6aJ7m+zAhcmCZ6GnQC7/Qy5f1q+W9e2yYGFxsV3FIsFIERErSdC6j5DLxhopv3XGOjo2Bc1bZG83SVcUizlqtyOOHzuunJhDebLvyF5dsyZ7uOI7cWDI7yP6x7dY7u7eEYi1rCJ2xnVuHD/Gjo8Yz/UmLs7FT/xZSBspuO27wUDR5xCsSZOmyoIFaeIll1wk/AjBWrJkRUXMrguLos8hWFwvV68uHhPEsoXonkLBPntFHFWIXMQZ+YorMwdCsEhiYRNZuPTFMbB8ti80BgosGzPmOueqKuxVmsDFxcMxdO8r+kwfLg20V76izxSQDrVXvqLPJMAJGTt5bR/sx6MzNqh7aLA4Y9/LOGMr5Ct3fU2q03j0Qa3Fm1k4UiuHpLYnU9OuXWlSAZdOMB6+Jw38j8W0TSrgwuIYWDZY3MVHum2bfcnFo1g+40b7aKePkMvn2PGUxPd0g/PwRIhA8iIis5Uv5TP/Ry4f1p69+6THkz5asXwOZ0/P9ooEBXltQC4b9O3iI5OdzcDn4lG5jpmEJy4+EmmEYKF7EigUEdkmaaePaKNvYdHbe8ibIpvzgNV3uPipJMktfI5kGcuT2v7Qob6geUvmN3iVmE/WCSMm7Cc//s+gcgfITgmCImLRhy58RP/QT0XEk54wrB1CCYIi4oYHY8dHjMF9+4rT5LMzIVQuX8p95msI1qZNm6XbkxKdJ/8hWFyXfP3IU5kgrB07xWYxdOkXrBDdbw+wV+yUCJGLLKM2G7BLLuxUCNaWrduEl4/A8tk+ZLIZUPMwwfLtCsH2oTMfoXufY3cl9spXioWbFaH26rSnFAvJdELGjk8Hg/X36IwN1p5J5BoczpicWCZfvvud8pPaA3Lm7GFZ//Rjct/HZ5W2KQ5q/d38wsWYsZu/j2MLowayGrBPxrK/+b67nLAn/uu/vNuXfLjx96iBqIGogaiBV6aB6Iy9Mr3doH8NEmdMLkp/w5Py6YfGychh4+QtH/uFVB98RUFwN0hvt85pojN26/R1bGnUgGrglThjOGGzZ86qyI4YnTDVaHyPGogaiBp49TQQnbFXT/fxzFEDV60BjRmjRo0SW+zY/mCTVBD8amOg2HYGD9vLlPbtP5jsdSeQXIktLPCdOp0GBbIH3MZAEZQND1volDRmwdaUKmOdSuvmTZ02s6JI68lTpwZiHS7FP1AwUolzcU62aSrRPlusFJnhsdtwaBt78Nk+obR3XwnL1kwh9ow4DyXqkoFlkzywDYs97LbwNPqEj+1LSsuXV1XEQLEVER67debIkaOJXHarDNv14LP1Vwget/FUbDkpYaVbVAiEpo22QC5JMxIsk2xk9px58uxzU1RMOXP2bMIDnxLbw8CyhafZUgYPsSRKq1bVJPFUZ029HXgsFslJwLIxUAd6DyY8NnibeD3im5BHaQDW8eOJ7hsa0qD13oOXsY6k9dWoYUfQt92ak8U6fuJEIpdNPnDw0KFELhtfQdIE5LfzKovFvILHxkCxNRA+O6+WLSsV5bX17gZgnSxhNTSmtfMO9R1OsD782AfLdcaIa+Kcp06lc9Ri4YQ9P3myvOGe15cSc0y4Q3DCerZvT7BsQeF165oTLDuvLBb9wbwiZsxeA9j6Bx/yKTU1tyZYdl5lsWg/stfUpkXYD/cfSbAolqxEIgD47LzKYjGvGDfV1WncEtdF+GwBcZImMG/pd6UsFuMFLFsglzkKH+NMiSLqyGXnaBaLrXlgrVyVFodnXsHH+Fdi+xtYdl4plq1ZNXnyNKGIsBL8CZbZ6tnVvb2EdTSdo4pl5xXXElu7iXbAZ6+1fEcu2q+kW+zsvOJ6aWN2sU3819bv27Vrd6J7F5bdog1Wpb0qYVl7hYzIZeeo2j47r7L2ivGIXFz3lRgfYNmY3dRepfOK+GYb48w8Actn+8r2ytg+5o+Np2L+glVhrw6X7JXdelvGMjW+iBfz2SvmFePeFrFO7VVaLyxr+7jeIVeF7TtyJNGXtWFqr2xSD8aWtVcvlu1VGjests8WxKZvOaedVzFmrDRa/5cOWtf7yhUr5LP/8mnXT/FY1EDUwHXUgDpj9mK9efOWJB7FxvlwQbSOCgaMuI/Ozu6ydMRbYZBsnATxXPDZLH8EttsLPxdTeOziXwPbd5uivMSHwcdCRGnKlBky+fnp+lUoVAwPvEokj0Cu7dtTJ4FzwWeNOobNXviRGR4bk0bbwGKxotTZWcKyRj2LhZ7Bsk4JBgPjZo+hT/isUcfoWrnoF3g2bdqiIiQxM8hlsYgLgc8uljG6LOyUiDOBh0WhUm9vyam2++uJy4HPxgzNnDW3whk7ffp0wgOfki5SKN6pROFgeOwClwQxyGUdFXgsFuemjbaY644dOxMeZFYiuyZYyKOUxUIn6J6EJkqMX/gsFgtgzmmdiywWfQWPLXTKohE+uyitWr0m4bPzKovFGAKrri7NLMkcgM/OK+YQDo1duGSxjlxe8Kxdm7aReQXfB9//gbIzhiPDOUmOoARPW1tH8iRs4sNvTpyw28eOk69+5Wvl7YjMK/j27EkXpWRcBMsWDM/KxbxCdjumiYcqYaU3OUjqAhbtUMpi0X54SECghM7hszGuZIOFz86rLJY6wjZZA9dF+GyM65q19cnYKcJivDAGbeY8xhVYNi6VTITIZWMXs3LhGIBlHRXmDnw2lpTkKmDZOapYdl5xvZw9Z76qK5mHJaw06yYJZMCyc1SxrNO+cOHSCqeadsBnbwpt6ywlYrHziusNfHZeMR4qHfTDCU9XV09ZVrCYtzZGkOtgCSt1CMCyjgp9BY+1V+iONto5yvUTPjuvmGvW9jEeS1hdZbkYa2DZOeqyfdOmzxJeSqntS+1VavvSuZDavtShRSZkU2L+IpfLXtkxF2L7XPZq376SversSm2+2itr+/LsFesKJeYV+rI2n35G/sOH0xsyYDH2lRgv8Fjbx7gCy8biMf7gs7YvOmMlLUZnTEdTfI8aGEQawEjfNnrMIJIoihI1EDVwPTRgEwJktyleupTm6tXtiOqE3XX5SZgvpfX1kDliRg1EDUQNRA34NRC3Kfp1FDmiBgatBqIzNmi7JgoWNXDNNLB792557YQ75E9/+GOCaZ2x1VVVcvcdd8rSxUsqnoThhD35m99UbO27ZgJFoKiBqIGogaiBa6aB6IxdM1VGoKiBG68BtqmFPBk7cvRYRSyCS1LuvLOv3EdsM7RbDfP4wbJ37F18bEOwcSYuHo6BZZ8MuPiInbCxRy6eBOtwv7cGDFux7BbIPCy2WPjSDodi0UYfFttPQuRi24kvfT/xNHYbU14bwbIxKy4+4m/sdjQXD8fAsjErLj62m9kYSBcPx9C93cro4iOeMQQLuWzMihvrVEV8iouHY2DZmBUXH0+p7LYvF0+KdTop+vqut78j2W74xz/8QdQZwxGjtMWEcbfJmx54sBwT5nLCkMtuUXOdE7nh8xGyM66LCH2GYNE/9FMREZsUimW3kbowSaEdonvGs41Rc2GdPXsuSC7mrN0658I6d/58EBZz1qeL8+dfCrqWI5evH1+6cOGaYV24cKFii6JLDxxDLhs75+LjCbDdauri4ViIvcJOhdg+7JXdOpd3zhDbFyIX+LSRthbR0UB7xfZQn425lvbqSrB89opxHzJvi/Q0mH+Lzthg7p0oW9SARwMY+Fj0uaSkWPQ5HSzswY9FnyVJpHGzFH3u7+8XdcgmPvywjB8zVsa8ZqSMGj6i0AnTUUHshqvos/7O+6ZNpVgje8z1ORZ9LmlF44NcOrLHiLGNRZ8liWskZsxHsehzqiGu5TZRSvpL+ikWfU51MVQ/RWdsqPZclDtqQCS52xrijC1fsVqqVqfZvFzK486UDbZ18XBsxcpqsUHyeXxg+e7okURi+ow5eRDl42D57pzRPpsZrPznzAewfAWRV1fXVgTcZyDKX1mU+u7OVlevFRYXPkIuHxYJK2yQfB4mWD5nbNHipTJp8rQ8iPJxsEj2UEQka7BB8nm8YFE0vIgaGpsrEsTk8aJ7gryLiKyGNkg+jxe5tplkNi6+lvXtFUkrXDwcA4sECkVUu6ZOnnn2+SKW5DewbPbJxCF75O2J8zVy2PDkncQcn//cF7xPcUiKEOKMcU4fIXt1TZq10MW/dVtX0PWE/rHZJ11Y3d07ArGWC8k+imjzlq1JApIiHn5jPJOpsohwxkL0RTKKEGcsBItsigsXLikSK3l6E4K1dOlKIeNoEfGEKgSLBCU2k6ULkyQVzFsfkRDIZ68046UPiyQsq6qqC9mwUyFtnDFzjvDyEVg+24dMNkFMHiZYPmeMrJ/ozEfo3vdUlT4k26uPkKvfZNh08dfU1AXbq0N9afZUFxa2KmTsuP47FI5FZ2xQ99Il6Z/5TzLqzU9K10W3oOer/4+8fnjJKKtxHjlshIwePV5e/9B75fHvPSstfcWPuN3I8ehQ0ECMGRsKvRRljBq4eg2wuJs1c6bc97p7ys7Y+977Xq8TdvVnjghRA1EDUQNRA9dTA9EZu57avWrsk7L4s6PlgR+3yYUcrJIz9hp5+J9/LE8+8YQ8dfn1xC9/Iv/3nyfKXcOHy/h3/ELWv5gDEA8PaQ1EZ2xId18UPmrAqwHibHDCNDsiN93YmqjbE4khixQ1EDUQNRA1MHQ1EJ2xwdx3Z6vlG+PulP9oOJ8rZckZGy0ffWa/DHh4dumkNP34bTJm2O3y+Cx/UHbuSeIPg1YDBL4TwO+j7p4dsn3HzkI2Fn22bkgec0/PDunZXozFf8HyJd1IasyYGll55wQL+YqI9tkCzHm8YPm2PFLXxdbaycOizhAOcRFR48jWNcvjRS4fFvVwbN2eIizfVkzqq7W1p/XDirB8SREoVGrr1xRh+RIGUNTU1hPKw0L3tiaTi4+6QSFY6N63fYfaOr6tjMgAli/InwKqra3tLpHLxxjvv/vt7wQjjQN2+7jbZPRrRsrr7rxL3vfeR+WO28aXY8h+/MMflf+X9wHZe3sP5f2cHEdu5PcRstvaXS5+ttyGYNE/1EAqIhI6hGJR86yIaCNjx0eMZ7YhFhExu0FydfXI7t3FWNRgCsFqb9/g5SN5SggW1xJfP1K0OgSL66Wth+XSG1ghugfLZ69IRBEiF/bK1nNzyYWdCsHauGmz8PIRWD7bh0zI5iOwfEk3tl+BvTpz5mzhKUNtH3L5kjElts/Umcs7MVg+24etChk7eecY7MejMzaIe+ilxu/KPWO+JKvO5AtZ6IyJyEtNP5I3jxgpb/t5anwuHGqUZ777GXnfQ6+TO0aNlLHjXidv/cDX5I+1vblP4PIliL+8mhrQBB5czJQ0kYVdEBIEzEuJRQZ7/NfWNeihpEgsPLbo5Gr2jy9fVZHFKIu1d9/+hIdiqkrEucC3YWMa01NTuzbh23+gV9mSmCWKOSrt238g4amtrdNDsnHTlgSrvX1j+RixU8hli3Rm5SLzEjy0QWnzlm0JFvE/SugAPpwApSwWi3542JuvtHVbZ1LAlBgnpbr6xoTPLrwWLKzUPf0Clo27Y6HMOS1WQ2NTwrdzZ1rsmn368CnhQIBlYw9YYMFTX58WHiaOBj67wJkydWZF3BILXnhs3B2LIrAoBqxEfA98diGhcllHCx5eSlqklSLFSs0trQlPV3daGFaxkEcpi7Vj565E98uWrVSWpJg0fNYpJE4K+Q/395f5slha8LXKFB5ubetI5KKPlYghAsvOqywWTik8tm+J04LPziuK9hL/YJ1JxdInYQ9dzo6IE/aTH/0ouelCuvr/+cvfEmfszvG3CzFkD1121ubOmauiJucDT4k5h1zLlqf6Yl7BYwuGE3cCH/NQSeXS78wrZLeFh4mRg88WGqd4N1g23jCLRfvhsQV+Kf4KH06HkhbvtvMqi0W/gGUL0nNdhI/+VFq6bGUydmxR6SwW4wUsm/yFcQXf+vVtCiVacNs6IVkssuaBxbhWYl7Bx/hX4voJX8/2dIGuWHZePT9lhsyYmfY18xA+G3dX39CUYHEeJeY1fHZeZeWiHfDYAujgwmfn1cqVqxM+O6+yWDt37U54bNxdc3Nront7U4O5wjn7DqdztISVXufod3i4viq1tm1I5NqyNZ2jq5PYqVUVWWLB4qXEeATLXtOwLfBQNFqJmEj4DpiC9FOnzRJeStgfeGzx+bLt25A6bdgz+Oy8yspFpkN4bAwf8sBnYz0ZJ/DZmw5ZG0PmQXjQhxLXH5KntLSk47ds+8xNB73+6v/UXrGuUGJeIZcdv/Qz56TflbJY3KCBx14fGVdgrTOxnow/+LjOK8WizyVNxKLPOiJu2PvLsuln98vof5knRQmEi52xS3J8/hfktcNGy2P/7/IEOdMiv3z7GBl9z0fkp5OXSO2aGlk6+Sfy8ftGysjbPiLP7R7wfO2GtTie6Mo1wBOLsSNHVTw14u4jLxtA3NTcWnFXiQUfPDZlOXfMMOL2CZQLq7mlTawz48LiTh5Y9gmUC4tEGdbBQeasXOCDZe/oITd8VlbumtFOJcWCT0mx7FMjFxaLt6am9fq3RJcqvx4Ea8nSFXL0aOo0uLC4o7cuAIs2+rAwyjZBQVEbDx8+rKIm/ZzVF8bTOl7cyXW1EbkOHkyDq11tZEGPAbV3g/OwWHQoMT7gs3d+N23eEoSF7q1z6cLC+captXMhTy670HdhbdvWHYxlHWgXVkfHRsEpsHIxJqdOmSITH3o4eRJ21+0T5Jvf+JZ0dGxI4sK+/53vyoaODYm+PvaRjwrOGNTcsl4e/8xnZeuWdCGZbSPnQQ92cY7O4UM+JRbj9LedVy4sZLdPVV1YODshWMhlF9QuLBbQIViNjU2yefM2bU4yrrJt3LlrVzJvfW1kPOOwKrnkYtHrk4s50biuuSIRiwuLRW8elp1XK1ZUVTgltIM2Mi+VcABDsLgu2X50YZHePw/Ljl+ul9bpdWOdzNV9Fss+BXFhkdQiRC4chvXm5psLizkQgoVzYx0cFxZ9C5adV3rNtG1EJuvM8Ft2roEPlk3goVj8ppTYvgAbwzXTllhwYYXaPuSypR9cWDi565rShDpFbbSlDFxY2Crkv1kpPhkbrD17sVuenjhcPjq1Ty4VyOh2xi7JhdN90lX9Z/n8G0fJyHEflL/uKCXxONf0K3n03gflawuOVeCeXPRFuXv4GHl89omCs8WfBpsGYszYYOuRKE/UwJVpgEXVzBkzUidswh1J7K9d6GQRtc5Y9nj8HjUQNRA1EDUw9DQQnbFB2mcX9/5VHh32D/KXPcVPqkrOWDabovk+bqJ8fdYOecnTzgsbfiXveM0Y+fjk4pgCD0z8+QZrIDpjN1jh8XRRA9dIA6/ECdNTR2dMNRHfowaiBqIGhr4GojM2KPvwkvRP/7CMLEhpr2KXnLFsNsWn5Hd/+B+ZOn+NdPa73LDz0r+tTpbMeEb++MsfyL8//hF5173jZNSw0fKx59ItRHqO+D54NcDdc7Yp+ii7TdHFz/aKurp0T76Lh2Ps+2eroo/AstsyXPxs+bB70V08HAML+YqotE0x3VqYxwuWL1i4tbWjYntFHhY1kmw8h4uvrW1DxdZCFw/HkMuH1dGxqSKeowiLeKIiqm9oTLbKFfHwG3LZ2CYXP9u52G7mI7AOHDhYyEb8EVtgfITut5v4Ghf/1q2d3lpR/A+5iPcqIuJcqKfmI7BsrEOWHyfsif96Qt5wz+tL2xELnoSB5Uo+YJ0xYobg8xGy+xLcsE0xBIv4ubb2NA7Lde5du/cGYbFdln4qor17DwRiNQlbU4uIbYohtecYzyQYKqJDhw4FyUUsqK0X58JkvobonjhJHx/1vHw8yMBWTLtN0SUXSaJCsNiOxnWziMAK0T3bJ+02RRcmW9lC5MJetZg4PxcWdioEi9pnvvpn4IPls33IhGw+Aou2FtH6xF75bR+6t9sUXZiJ7TPxWy4ejiHX8RMn835OjrNNkTHmI7DsNkUXP1ujQ8aO679D4Vh0xgZlL52QhZ8eJQ/8Z4c3oYZ7m2JBo05vkL995k0yfthwGTP+Pnnkvf8kn//3n8l///pxeeOI6IwVaG5Q/qQJPHzCEZjvc3rY404grY8oIE3hZx+B5TNIFNCcNn22DyqRy+7Bd/1BE5e4frPHkMvGjNnf9DNxbFz8fURAtK9QM0WfQwo1I5cPi0Bxm+wgTz6wfEWfFy5aIjZ5ShGWTcLg4mOhH2IokSuk6DOJN3yE7kOKPtskDHmYyGWTCrj4iJO0SRhcPBwDy1X0OfskbPyYsd7tiGC5FvHWGcNBh89HyG4TAbj4N20qJQxw/WaPkcAjpOhziFz0j00+Yc+jnyn6HIa1zHvjg6LPjB0fMZ5t8gkXP4mQQuQiqUhI0ecQrEmTpsqCBYtd4pSPaTKT8oGcD0uWrKhIGOFiY5EcIhfXy9Wr02RJLiycxBDdL122ymuviKMKkYtYI5swwiUXdioEa/qM2cLLR2D5bB8y2ZjdPEywbMyYi29VFfYqTdjj4uEYuvdljaUPKQbuI+QKKfocaq98RZ9jAo9Sj8QEHr6ReS1/P7NKvjrmTvlOQUp7Pd2VOWMvS9fT/yDjht8rj/9tkxxL4z/lfN135cHho+Wf4pMxVe2QeA9Nbc/dc5vxy9U4Fou+BSn/I6296259FhMsG3ie/Z3vmzdv8d59hg8s5Csi2mcz/OXxguVz7Hiy4XuKAH5bW4f3KRvpfW3ihCK5fE/sSIkelCa/s9vrcJLFikQSPkJfRfFL/H/Pnn1hKfc7u+XosaKURJJkCesMSIeM7kmgUERkL7NZ4PJ4aePh/uLyH2QkDEqT39kth/rS5ClZJ+y1E+6QH/3ghxWZTIvkOngoTZ6ifNYZQwfI7yNk7/Xo69Chw0FYPE2xWdNc505S24fI1dVdkWXOhZWktg/C6hGyuxYRjgpjx0dkJbUZVl383AwL0T1YvievJ0+dCsJizlKWoohOn34xCIvrkq8fSV8e0kaulyFp8kN0TykWn71ip0SIXGSntIl+XHrDToVgkVyIl4/A8tk+ZLKZM/MwwfLtCkFX6MxHJXtVkJ5bJOnDYHt1phgrKcViMnrmyUcbT58+nfdzcpxxHzJ2CkEG8Y/xydgg7JzzDd+Wu8d8WaqKx3ki+ZU5Y+dk+RzBkPUAACAASURBVJfHy8jR/yzT+01akEsnpP57b5Exw0bLR/6apvcehKqJImU0EGPGMgqJX6MGBokGXE7YU088KSdPXH2SJOuMDZLmRjGiBqIGogaiBl6hBqIz9goVd/3+dkHaf3yfjP70fAkx2VfmjF2UfZM/LncOHyMTH39aXqiqlZrFU+WpL71T7n3t6+Tu4aPkPb8t3rt//dodkV+JBqIz9kq0Fv8TNXD9NIATNmP6dHnLmx5KYsJ4EnatnDCVOjpjqon4HjUQNRA1MPQ1EJ2xwdaHFzvlqYdJaX+4IvV8nphX5oyJyMsHpfapz8uj90+QcSPHyGvv/3v5zPcnScv+RvnPN46UOz45Pe9U8fgg1IDGjB0xta727N0rbGd70WwhYN+23VN+8uSphGe/Ke5KYoXsPnBihcBi24sSWDYGiu018NiClmxRAostQUpsH4LvlNmOMHXaTKGIqdKpU6dLWGarEdvHwLKJHzhXgnXqlP41aZ/dn47M8Nh4p/4jJSx7TLHQiRIFJ23xWJxesOy2JXTOHvyenp36N2ErG3wnTqaBzcQF2Bgo9v/DY7ctaWFYu83yQG8J67h5kkKsXgXW2bMJFnhKGuNht9RRqBceG7w9Z+58efa5Kfq3pMYNPBaLhCLo3hYsZqsbPMeOp9sNidcjJskGmmexODdYGzam23wOHiph2eBtinSDRc0dpQFYJ04kuqd+kxLb+eCzWBRQBcvWqMtiUasPuVpb00LgbDOEz84risTCZ+eVxcIJe+7ZZ+X1r7u3wgnbsXNngmXjK5YvX5UUTrbbUi0WbWJecT5bDJV5Bd+HH/tguc5Yw+UCv3abTxaLOQeWTYzCvILPFu4lcQJ8zEOlLBbzipgxG1NJHEqCZQr3tqxvTbBoh1IWi/ZzvtratGA8WxLhs9cOtkXCZ+dVFot5RV/born0H3w2HqW5uSUZO/S70kCsswmWrYHIuILPbhtlmzVy2TmaxTp77lxSPNrG7DKvEiyzbXTr5UK6dl4plp1XkydPk7lzF6joyTyEz25BZfsbctmEQIpl5xXXEhu3RDvgs4WOtSi6nVdcu+Cz84rrJbHJSug3wTJ1BXfv3pPonuudUoqVbgUiQQzXYCX6HSyur0rUK6SNtog112f47Lwq2b40Bsplr7T4OPZBSe2VnVfEN9sYZ2KPOd++/enWWC0YbscvxaHhs/OK+VNpr0q2z26zVXvF9VupbK/MvEJX6EzJaa+OlOyVLXaO/UeuSttXVWn7Ltsr1hVKzCt0z3+V6A++23lFfHmFvTpTslcVtu9yTKLdSsr4A8vOqxgzVtJ0jBnTERffowYGkQbUGeNir0TAP4sXu/DmgmidCxZ18Nhiq8SBcYG1DgdZ8uCzhjiLxUIMHpvFjAspWDYegaQG8NkFLo7Y5OfTGwAY1hJWWsCWCzdY1unhXPDZYGSMkb3wIzM8tnArbQOrq2u7qivRAXx2UYqRtFgskOCxyRQwmjhjG41zsXVbZ8LXZwouU6jSJpEg/gqsjg2byjJgYJHLZm9jHz18NpMhBpwFpxJGFB6bmIEFC1gdG9J4MGKw4LMxVjNmzq1wxlgowMNLCaMIFtm6lIhZg8cuEFgMIJd12rNYLBbBsoVOiXOAzxaCZnEIll24ZLFYEKP72jV1KlYSfwHf/v3pgo0gec5JbKVSFotFEzzWUSEGAz67MKqqqkn47LyCh6xo9knY7eNuk29+/Zvl7YjE0cBn5xXjAYfGLryzculNCJK2KLGQgu+x972/7IxV19QlctkFbhZLF0/wKlHkGj67oKpdU3I4reOYxeI8yG7HNIksEqxd6eKsrr4xkcvG4mWxaD+6t47K3r37EyybkRKnGz47r7JYzCt4bHIhrovw2YXemjX1ydixi+UsFuOFMWgdFcYVfDbOh6yynNM6aFksHGGw7M0w5hV8Ni6V7JRgWadKsU6/mN4M43o5e8587cZkHsJnY0kpwg6WdaoUyyYvWrhwaUUhXdoBn42zJNMlWHZecW2Bz84rrpckBFHihgY820x8G9dH5i3XOyWug/DZRTxY1rmg3+Hh/0roDrnsHN24qWT7rBMKVoXtu2yvrO1jjoJF7KsS12LOaefVtOmzhJdSke2zTg9JY8CyjiMyWRvDeeCxMWnIg1w2a+yWrS7bl7FXx0r2Cn0ocQMS3W/blsYbogPOyXpAiT60cnG9g8faPuYVcm3ZmmLRz/DZeFlu2jL2lXCq4bG2j3EF1ubNqc1n/MFn51V0xkpajM6Yjqb4HjUwiDTAgvW20WO8ErHosYtI1x8IOLbGwsXDMXB8WPCBdemSiU10AGLMrEPlYEkOgeULiEYmu7gtwvJluuKOnDXoeVgYC19wNYuMECwWzC+9VJykBGMWjlVcCgBntc8Y4bw2skjwJTzBKSRTmo/Asnf5XfzcubbOv4uHYzipL76Y3k138TE/QrCQy97ld2Fxhxw+pbztiHsyT6WV376ziLXOgP3NfuZ8rjbabYrcBbdy2f/bz/DYRb39TT9zrhAsZLeLZ/2/fUefIVj0j3W8LYZ+Pnv23DXD4gmavcGh58i+M57tE4Ps73w/d+58kFzMWR/W+fMvBWGxcPbpleuIvenlkp1jyOXrR8Z5iF0IxbIL7CK5fDYm3F75bR92KqSNV2KvfLavZEfT3QV5ugi2fZ7ESOCje/qziK7EXl1LLJ8dxVaFXDOL2jaYf4vbFAdz70TZogY8GmAhFuKMeWDiz1EDUQOBGnA5Yb998qnyk7BAmKtis87YVQHFP0cNRA1EDUQNvOoaiM7Yq94FUYCogVeugeiMvXLdxX9GDVyJBgaDE6byRmdMNRHfowaiBqIGhr4GojM29PswtuAW1gBbHcaMHOXVQCz6nKqI/ek2biL9Jf0Uiz6nukBfNuFJ+kv66WYu+qxO2AP3vaGcmKPoSRj6chV9TrUlSawbcVc+AsvGaii/dcZi0WfViiSxLo3rWtIDjk+x6HOqlFj0uaSLWPQ5HROx6HOqixv5KTpjN1Lb8VxRA9dYA9EZSxVKEgCbgSv9pfJTdMZK+li4aIkQFO2jW9UZwwmbPm1aOUX9neNvly9+/kve7YjXwxkjZm/K5Ofl6ad+m7xImz9u1Ojk83e+/R352le/LsdNdktXnxJIbxO9uHg2bdqaBNO7frPHcCSra9bYQwM+a3bAAT9kDpAIpKl5feZo5dfu7lJ2wMqjA7+ReCA6Y5LE1jAOfRSdsZKGojOWjpTojKW6uJGfojN2I7UdzxU1cI01ELcpXmOFRrhbXgPqhL35jW9KnoTdfcedUvQk7EYorKenR0aPeE0iz8hhw53vL8ydeyNEieeIGogaiBqIGrjGGojO2DVWaISLGriRGojO2I3UdjzXzayBweiEWX3v37dPNm3alLza2tqkpaWl/B1nLVLUQNRA1EDUwNDUQHTGhma/RamjBhINkC6Z7Uo+ooYYtVSKiK0aXV3+Rd32HbuEOkw+AsuXjp5iwra+SB4mWL509LSPdvoILF+qduqj2doueZjtHRsqCoy6+Kg3Y2sTuXg4hlyuNOaWn5prtjC0/c1+BssW17a/6efu7h7ZYGqd6fHsO1i+tNzUhrI1k7IY+h0sX8rqffsOSHd3WgdO/5t9R/e+VMfUXPNh4YQ9/dTT8tADD5afhLEd0NZQ4tzUVbO1nLLy6HfaaOv26HH7Tl2ujo60Dpz9zX4Gy9dG0rTD5yNkP3iwr5Ctr68/CAvZbX0yFyhpwEPkon9snTkXFqncQ7FsDSsXFn3D2PER49nWsHLxkwY8SK6e7RV15lxYxLGGYDFnfXxcR3w8yMC1xNePFK0OweJ6aWtrudpIWYsQ3YfYK+ZtkFw7doqtWeeSCzsVgkW8IS8fgeWzfchk69/lYYJFW4so1Pahe1v024VJH4bYPuSi5EQRUcsw1F75bB/jPmTsFMkzmH+Lzthg7p0oW9SARwMaM9bZ2V3mZM/3ihWrKxZxxA/Y4oskZICnvn5d+X9t7RuTeBGKfCrV1NQlfLZYcBaLxTNYa9c26t+SQsjw2YLIFFuFzy68Jk2eJpNM3BIFIOFZs6ahjIWzBpYtFMm54OPcSrQPPiVkhoc2KGkB01ZTxLiubl3Ch0OhlMViwQtWdfVaZUmKZ1JEc9265vKxhoamhI/FtlIWi8UgWFVVtcoinZ09iewUt1VqbGxJ+HbtSp3oLBY1aMBatapG/5Y4H+jBFjFualqf8FknesrUmfLMs8+X/8eCF6yVK6vLxzCkYK2tS/u2ubk14bOOr8pl45bA4qXEucGyRYzXr29PeKzDtGjRsoTP1lLKYrH4QPc2RpA+hc8uqhYvKWHZWnaKpU/C3viGBxIn7I7bxicxWDhh7e0bEyxbIJVC4MhvnSPF0jZqkdaVpj9IsAGfnVcU7SXuyta7ymJpYVVbxJj5BN/mzdv0lIkOkMsW4c5iMefgsUWMiQ+DzxYaX75idcK33xTlzWL19h5KZJ8zNy08jDzwUWxYSQtu24L0WSzaj1wURlfaurUrwUJvSlWrSwW37bzKYjGvwKKflLguwtfWljpfy1esSsYOC0WlLBbjBaxFi5cpSzKu4LPXjpra+oTP3ujKYlGvDCzmiBLzCr6WljY9lMwx+Oy8Uix7A+P5KTOEgu1K8MPHvFRqbCwVybYLYeY1fHZeZeWiHfCsM0lQKNIOn51XXG/gs/Mqi8WiHh5kUaJINvOW650S10H47A2MLBb9Dg/XV6X29g2JXHaOcn2Gz86rLBbXeXi47ithW+Dj5qBSbW3J9tl5NXXaLOGllNq+1F4xn8CqtH0NyTlt4Wy9ZioW50Gu2tq0yDvygNVu5kJdndq+K7NXXH/Qfcv6dj1lYv85p03QlJWL6x08rCuUmFfIZccv/QyfdcizWIwXeKztY1yBZeNGGX/w2XkViz6XtB+LPusojO9RA4NIAydOnJCxI0dVFB7mDhMv+ySJoPYmY6wpCgqPLXTLlsc1axucWPbOHBfKdU1pwD2/ZbEoYAqWvQvHueCzWCtXrZYVK9MFexHWi2fSAr8uLBYj1plRLM6pRGFJ5Dpx8pQeSnQAjy24zAKkoTE1/BcuvJzInsUi+UD/kaOFWDgc1jGiX8DJYiFXf3+Khe5KcqXFm1kIWge6COvQocNlubiDmcVas7a+YhFchHWg92AhFokhyKj48ssXy3x5bbSLc5WL8aK0YeOmy1gv6yGnvtB9V1f6BM2FtXHT1mSRa+cCTzMmPTdJbEzYt77xrQqnhDv4yG+foG7Zum0A1sA2XkjGV495Qkth4CxWa1u74HQyrpSyWIxfxoR9GqdYvCt1dXUnfHZeubDW1jVIZ1d608aFRaIMzunDQnbGtZILiyfofqyXE53a7JPoHPltcXAcJ7DsHM22kT7mpoF1CF1Y3PVn7PiwGM8dG9Knl4xRzmmfBvDktSRXOn5dcoGFg6/kwuo92JeLZefV0qUrhBtbSlzTsnKx6M2Ty84Frku2H1Osswovx44fz9W9xeJ62bI+dS5dNoabNXm6r8RqFq7BSi6s06eL7FU6r7B9PnvFtTarL4qDo1c7F1au5GZVmL3iiaKSy14hk002w3k4H+dVUntFW5VcWCV7lTq9RfaK4txKimXnAn1onV76JTumVS7GhpILq2T7Uqe3CMsW3XbZPm7YMHZuVopPxm7Wno3tuiU0EGPGbolujo28BhpgsTN96tQKJ8y1HfEanCpCRA1EDUQNRA1EDQRrIDpjwaqKjFEDg08D0RkbfH1yK0l09OhR+cH3vi/f+OrXktfHP/JR+cgHP1T+/r3/+I4cOnToVVVJdMJeVfXHk0cNRA1EDUQNeDQQnTGPguLPt5AGLh6SJV95QG7/9Gw5EdTsl6X79++Rsa5U06Mfl3mnLchZ2bnoZ/LZR+6V8SPGyF0Pvl++8ecG6SuOy7UAzs9suWKboo/YJ97WnsZNuPjZetBg9ve7eDjG1oP1JuYqjw8su/XExVdTu1aqq9O96C4ejoGFfEVE++w2mTxesOxWEBcf8Qh2m4yLh2PLlq30JqQg9sXGc+RhIZeNDXHxUQDY7q138XAMrCNHjuT9nBxnS6fdIprHDJaNk7J8W7dsEWKt8tKt3zZ6jDQ3pds9wSLmqIi2bO2s2L6Tx4vud+zIT9iCE/bUk0/J/ffeV5iYA3zk2mNiBl3nZEukjX9x8SjWzl178n5OjtOPNt4tjxm5fMkHiBmCz0fIbuORXPw7d+4JwkJ2u4XPhUX8XJBc65plW2eXC6J8jFibMKwWob5ZEZGwgrHjo3VNLbLZxBC5+Pv6+oLkYkua3Yrpwuo/ciQIi21yjWYLtQuLrWgh+mpuXl8Ri+vCOnnqVBhWS2vFVkwXFklKQnRPbJnPXrGNNaSN2KvWtg6XOOVj2KkQLGrr+errAQqWz/Yhk90iWhYm8wEsu2U383PyFV2hMx+he9YMRcR22lB7deJkMdaGDeH2itjKIsJWhYydIozB/Ft0xgZz70TZbpwGzu2Sxf/xTrlj2HC5LdgZe1GWfHGCjL7nw/K93zwhTz1hXr9dINvKYR0XpXfuZ+WeYXfIB34wTWoa6mXJHz4vE0e9Rt76w0ZJo5euvLmawMP3z2XLq4SiyEVEfAWBtD4iyN8mFcjjB8tnkGbMnCPTps/OgygfB8vG75R/MB9i0edUGeirt7c3PeD4dK2KPtMvVVU1QkKHf3jHO+VN9z+QZJjkqW12EYFcOzxZPVl8ULzXRwSju7JB4rTb7YgTxo2X3/326QHZES0+cm0zSXDsb/qZGxo2CYMez76D5Vt4166pS5JgZP+b/Q4WjlsR4ezD5yNkj0WfJcmGx9jxEck76hvSeBcXP4klQnS/aPHyJJ7NhaHHDvSWkqzo97x3Eh4tWLA47+fkODdPQuSKRZ9LasROhehr+ozZwstHYPlsHwlubEKdPEywfDcPV1XVytJlq/IgyscZ9zbpSvkH8yEWfTbKuIEfozN2A5UdTzUYNXBG9lT/Wb7xzjtk1LARMmr4FThjFzbJE4+MkgmPvyCF94fONsj37h0ud39hsfx/9t7Eza7jOO/On0KQAEhR4i5Sa2JbSRxR1BYvUpwvkhd98iJZcSI5dizLkmKbsmLr02YtlERKFEGQBAECIPZ9gAEwmAFmMDPAzGDf930lAJIi+3t+fVG333um7+0GSQCzdD3PfebOOXXfU13dfarrnK6q8OznVbfvyU+4O2/9sPvJ7pD04Fo1ROa3nNT227bvTKaY5U2CZpNqJgsJBTT7XTM+sFLpfWvpakNgeyss5GtFZA6jnSlCrqqTUP0Nqeg1Q2X1vP3P27OLFxtegdqp+l/eRqQW+jAjVwqLtyRbt4YkDPWLVL6AVU3NXmFxW7ZsdT0bQxKG6nn7HyzNkmjH9S8ZtLZs3eY++qFH3L973/v0VMN3sE6dDrOg4eTVf0jWoJkHYzwcQ/ea6azqhFGs+dF/fNT1SCKAZljI1eztn/2GzGm8tUsRWJp9NMZPP3ZnyqVtjGEdPnw0a94iu2YyjWEhN/KnCNlTabmPHT+RhUVf7z9wsOUlT5w4lY21b39rrKPHjmW99WY8p9K+8wYqR1+8raNcRiviLUMO1saNfUm+CxcuJnmQhXtJqh9xBHLk4n6ZevMKVs6OA7ItaibImN6Y7zlybd+xM1l2AzuVg8Xb4NQbYWQFK2X7KJ2AbCkCK7UrxNs+yVDZDLNmr0IykBgffZhj+5DroiTHimGRQTfXXvHWtBVhq3LGTiuMkXyuOGMjuXeKbNddA6+fme4+M3mCmzj5/e6PH3vSffnXbst/M3ZupvuTOya5j3x3iwu5m4aL/ErnV91Dt9zlvrQ8ZEmC6/WTM9wfTJzgPvqjkBFu+K9bHykxY631U87eWA2knLHrIU3MCUu9CbsechTMooGigaKBooGigTeigeKMvRGtld+MGQ28fnae+9of/r2bOXjOvf7KRvfNX893xl7pedR94LZ73J/94Bn39//Pb7j7J9/u7nvfx9wXvrPM7a9ntX3NHX7qd92kCR91T+ypvAH7Va/7xrsnuDs//8bTtRZnbMwMxTHRkBvpjOGEPffMsw4jRswab8KKEzYmhlFpRNFA0UDRwLjSQHHGxlV3l8a21MA1OWOvu5PPfMrdectt7s53/557dMpCt3L5HPfEl3/LPXTrRPe+P53pDnrf61du6Fu/7iZO/EM3q7o767Xd7rEPTXCTP/lMS7HY7rBwwQI3c8YLwz5TpzztJt820R0/frKOwTYDthHqlrfZL85v2BNPrBk8WqCRbVgzZsx2Wp+KbQbwnZe6XGC9OCfELFDrrIYVtuGw3QksTdZAAccaVtjUSbyYFtEkuBgeLfZ49Ohxj6UFMymEDB/XNmJv/ewX59m/XmZ4tNAxbUOu/QdCwVd0AJ8mz5g7b6GbNTtgse0HHt2Gw7a2Xz71jKNukRFb7ODTWi7EPykWNWPg0W04FDxFLj1GPAp8WqSV2JOZs+ba5Xz9lyoWMQFgUX/KiKKe8GktF2K8KLptxBYiePgYGZZuG6RoahVr4aJljkLGH374Q/VtilUsro1cA4NDBu+LdsOncQwEaoOlcRKKhRP2xONPuAfuvc87YQ/cc693wmgvfFo8dvmKle6FmS/6GDa7qGJxjL5CLg3yZzsffLp1kYKyM154sWFeVbHYzgmW1vRjmyF8Oq8oPMzYYVwZDcc657G0FhHzqYZ13H7ma7JxTZ2jVSy2rCK7xkAxR+HTLZVcCywN8h+OdcE9NeWZhngXiuzCp/OdLUVg6byqYtF++keTIqBz+Nh+adTb2++xdF5VsZhXjBviZ4y4L9awQvxkd3eP130rLB5ygbV02QqD8uMKLC2ITUF62qhztCoX9ZfAWiRJQxjv8GnNPbZFgqVz1LC0XuPTU6e5mTNDwW344dOi9WzXBkvnlWHpvJo1a25DfCbtgI/kK0ZsYwRL5xX3KfjQkxH3uHlS2JqEDDWscK8l4Q7jPoaltbTA0hgu+gosLdTNPQ25dI6CD5/Oq5rtC/YqZvuY72BpseiY7asWfTbb12ivzPaF8Wu2T+fVnLkLHLIZMX+RvdFe1WyfjpOYvUJXamPMXmmCI7NXeiyGRR8qFusI5Gq0fTV7pbKavdJEHNQjbLRXzW0f2zaNGH9cU+cVtoqxM1apOGNjtWdLu65dA9fkjL3qBn7wu+699/+O++Fg/TWYc+6i6370P7o7JrzL/U0bC61fuf5/ep+bOPGP3fzqlujXDrgnP36rm/Txn7eUlfimv/rSX7ov/sX/GPb58z/7nJs04baGPfEUd2Vxo4YYI6KBxywo4Fm/obt+bRbJU595vmER37Gu0/MdOx4Wf2Bp0g0MGVhdXSGjGwVywdq6NcTYUBQUPl38PTXl2YYbLAtXeDq7Qga+rVu3e6zBoS11WckECB9B70a0Tx07ZIaHNhhR9Ba5tDDs+vXdnk8XWdOen+mefW66/cwvHsBCt0YYCwKiNe6K7GTwqfF8/vmZ7plnAxZZ0+Ch6LIRMWrIRTyIEZkh4cPIGT0/fVYDFsYKHrJSGrF4AktjkigyDN++fSHLHzy/ePJp+5l3SqpYxDbBR6Fvo96+fo+lMTDTZ8x2zzz7vHvkgw/XnTGw+BgRfwMWBXCN+vs3ex5dIGC84dPFMjgUCNc3Ye+44073xf/5xXpsHLEc8OmiAeccrFOnQzHtqlwHDh70PKtWBR1uHhj0WPSxEQkwwNJ5VcU6eOiw51nRFpLlsGCHT53jWbPn+rGji9IqFvOK62mRWeYVfJp9kAxj8OlCsorFnINHMziy+IePv0ZLl7Z5Po1Tq2JxHcb9bHlYgTzwIZ8RCXW4Ju0wqmLRfnjmzQsJSIijgU+d9pWr1ng+nVdVLOYVWC/OCQtcFnjw6XxfvnyVl59+N6piMV4Yz/STEeMKPk0a09HR6a+5T+ZoFYvFP/MfZ9iIeQVfX3/IcMs9Dfl50GRkWLqIZ85OfWaasfhYNPiYl0bch8DiOkY+c+2q1Q3zCrlIomREO8Dq2Rgy83FPAkvnFQlo4NN5xf2S+6YRzhI83T2heDNYjB3ud0bcB+Gj/4yq9op+h4d2GdGnyKVxV2s7avbq+IlQ8L5qryjUDRbZMo2wLWBpUXQeXMCn8wpnQB0C7A889J0RD67A0gdY2DP4dF5VH0QSywiPPjAhdgssnQtd66/aPplXNXs1w0RwtB8s9GGEntC92hjsP3zDbJ/aq5M1e9Vg+3bu8nLxkMSIfgaLfjeq2iseHMDD+DFiXNFGzYTM+INP5xXjHvnHKhVnbKz2bGnXtWvgmpyx5vC/2vp999GJt7kP/AM3+9fclu98oPZmLBSrr/3Y3ox9IiyIm6PGzxD0SvrwFHET1KdMMX7ewOniMMbDMbBSSRjgA+v1119vBuOPY+jU2DVjBisVEE37kC1FYKWSgeRiYdhTwdU4FScz5crCOhkWLc3aShtT2SdPnjzZsDhohXXlSj01aJSNBSdOSmqbInJdvqwPL4bDnT1Xw7Iz1e2I9iZsx46dTp+mG7/+ZRGrzpOe0+/IpW8M9Jx958n1iUzd6xsD+73+PXP2rDt8JDw513P6Hbn0Dbees+88BYcvRcieCpLnWjlYyK7OcuzaF196KQuL/lFnI4ZF3+TIlYNF36iDGLsex8DSt3oxPh6U5cr1VmGxoE9dk7mf4rE2pvqR+ZeDlWNjuO9yz0xRDhbZCt8qubBTOVjXYq9Sti/XxiBXKjNjLlaOvcrFQq630l6lsBj3OfM2NbZG6vnijI3Unily3XgNXKMz9qsr59zJ0xeHJe94/djT7tOTb3UP/TVPx193R5/+L27yhI+7n++Lx4y97U/DU+FrbTQLixxn7FpxC3/RwBvRQMoZuxbMmBP2w3/916RDcS3XKLxFA0UDRQNFA0UDN1sDxRm72T1Qrj9yNHAtztirQ+57H5zobv+Nf3K9lYzrr/b+5VjWFwAAIABJREFUk/sPt01yH/tBLWbn1Q1fd+++5W73Vysb3whYNsWH/zXE9lyrMoozdq0aK/zXUwNvhTNWnLDr2UMFu2igaKBooGhgpGmgOGMjrUeKPDdPA9fijLmXXc8//rqbfOu/c19tP+fqm/FeP+mWfPG9bvLk/+x+svNqwvsrne5r75zgHvjzhe5MnfFXbt8vP+HuvOU33fe3tkqM31odbH25feKk1kzOuVL0OaiIYOfUdq0VbRTRXBZ+1OQbe9hT21tI/ECCixQhVwqrfXWHW7BwaQrKB7/fqKLPCEMcGEVyU84YbWxW9NmcsHc/+FA9MUerN2HoXuN3YkpZv6HHzZufzlaKXKlacKXoc9Aw8RvEdLQiamuh1xTRP/RTK9qxY3cm1mKnCU9imMQH5cSelKLPNe2dPnMmS/fcLykY3IpI7pCjewoYE3PYiti6mjO+KKxMgeVWVIo+B+2Uos9BFzfyW3HGbqS2y7VGtgZaOWMXZrk/mTzBve13f+4OXN1t+NqxBe5L75vkJt/7n93fPTHPtS2f7R77Hw+7e2+9233yh5vc5XprX3OHp/+Ru/+Wu9zHvzzVtXWuc4t/+ufuA5Nudb/25XYX8gHWf5D9pThjQVUYb01QEM40fsOAF2fMuXnzFzoSqKQIfWlQdoz/zThjOGHPTn3GJ/4gRf09b7/L/fcv/EWyj4ozVuuJ/v6BrEUpCUj6+lsXWB8Y2JKFVZyxmu5JrpPjEJAFdc3akEwhNodIBpGDNWXKs27u3JAdMIZF5rwcrIULlzqSo7Si4owF7ZAkShNhhTON39B9Ks4LBxFHMUVgpeJZySCKA5si7pmpGNrijKW0eH3OF2fs+ui1oI5GDVyjM0YTXzm40v3wv/+2+417bnd3TL7bvf+Rz7pvztziztffgJkiLrmdc77hPvubD7q3T7jVveNdH3P//fvt7khli6Nx5/4t2xRzNVX4boQGUm/GVIaqE0ZijlZvwvS35XvRQNFA0UDRQNHAWNFAccbGSk+WdoxLDRRnbFx2+4htdI4zVpywEdt9RbCigaKBooGigZuggeKM3QSll0sWDbxVGiDd9tsmTU7CUXRSC2bGfsC2Ci06HOPh2J69+xuKRTfjAyuVjp76RMSWpAis1LYP2qfFN5thgpVK+059E63R0wyLWjepLSQUsNTimM2wkCuFRWHXXCxSi7ciilVTAytFyHX+QrVIXvgVBYWpr0V9s6ozpmnZccK+/93vu/e/570+Juyd997nfvSDHwzbjkj6Za1pFK7U+A3dnzjZOqU76ZC1KHcjQviPNpLSuRVRq0vrIzXjBSu1FYgaV9QySxFYqThCtqTBlyJkP3Y81F+K8SN3Dhay75d6QjEs0pPnYNE/Wn8phkX69TysPQ3FomNYtFHrjsV4OMZ41vpLMb5z58/nybV7jy9wHsOwYxcuXszCYs6mdMF9JMXDdbmXpPqR9P1ZWHv2NtREtHbpX7BydE9cacpekSY/Ry7qIVLjsBVhp3KwqHnJJ0VgpWwfMmmtxmaYYKVKsaCrZrG4iovuU6VF2Hqba2MuX2lMSqbX4jvb23OxUraPcZ8zdqoyjJb/izM2WnqqyFk0ENGAxYxt376zfnZV+1of/KyLOPadEzNidODgIc+zrjMUq+zfVIs90YKyq9es83xHj4Wiz1UsFizEa2mxSm6c8A3IYp+YCfh04fX01OfclKefM7F8HRF4tDDw0NBWj6U3Yq4Fn9asoX1c0wiZ4aENRhhSeHr7QrFVilHDpwVlq1gseOHRYpUUCGUPviYfoPgnfBpjVcWi3hM8GqtBcWHkWr8+JDIAFz5dSFSxWPDC07ay3ZroFxVgrVsX+ra7u9fzqfGnGOqTv5xa/x2xIWCRvMQIpwgs7Q+KXMOHke3v63OTJtzq/vzzX/B8j/ynD9aLPv/tl7/iz7WtWOFjwt77rnd7J+yed9xVd8I29vZ7LHVyiK/hmshjxPX4GKETdK8xF/QpPBT6NSLZCVjoyaiKhbMMjyYfYC7Ap0Vgia+BT+dVFQtnGZ5ly4OsjFv4dF5R2Jq4K8aVURULBxespctC8gHmE3xDW0KhZnQA35GjxwzK88BnxJyDZ8nSNjvkmFfwDA6FQs3EscCn9XyqcuGUIrsWRKbALXw63/kfLNphVMWy2CZNcEMiFfg2bQ7OatvK1R5L51UVi3nF9TTBDfdF+CgubkRha8YO/W5UxWK8gMVYNGJcwaf3Du4t8O3dGxb7VSwcyRrWYoPyDxvgY/wbMcfg04dAhqU1yqZOneamz5hlP/PzED4tPk9BY7D0oQbzGj596AAP9xQj2gHPhu5QqJnENfDpvKI/4NN5VcXigRY8XXJPQ0Z0r8XUuQ/Cpw8wqlj0OzxaXLnvaqwkhZGNSHAEnz50qGIxHuHhvm+0eWDIt1EfDNZtn8wr7pl8jLA/YHVIIXuzffw1om/h03lVvZczf+HR4soUZEf+TZvCXOhYV7NX+qCgikX7wUIfRswrdK9Fn7H/8LEeMKpicb+Dh3WFEfMKuRrHXM1eaaHmKhaFvcHS5D+MK7C6Zcwx/uDTeUV8M/KPVSrO2Fjt2dKucaGBc+fOuTsmTmp400NyCj76NA3npauLItQ14i0FPPrmguKx7e1rHU8vjTgPH/xGGDE1ijEsMMDSp10xrCVLVjQk3WiFpbLGsLq6ehocwlZYZ8+et+Z4HVTbyAJi7dquOg+6hIePEW/X5sxZ4E6cCAtqto3Co2/eNmzIw0JfutCPYXX39DYkAmgmF1i6OI9hrWpf4zMgWnt48xhrI1jq9CoW/cDbMBJv/OUX/9J95EOPeGfsl7940h976P4H3Pvf/R7//YF773N/9Zd/1eCUMD64po45Fs4shPRNaEwudK8ZEKNYmwb9gkTnQgyLNvImxCiGRXILFjetsBhzYG3fER6OXL582beRv0Y9PRvdnLkLsrC2bWuNxQMGrsm1japt9HKtXtvgxMXk2rZ9ZxYWsutDiBgWT/RTcqFLdKqOF2MB+fXewRtvsHReVdtoWCQ0MYph+QcfcxYksRiD6njFsHiAk5KLcQxWz8bgeMWwDh8+2lRfOhcWLFjiVknSDXSCLpiXRtyTmsmlWNzj1PGKYfFQpBmWzgWw9GFSMyzmbawfG7A6Gu1VDIs2V+Uyu6BYOC+aYTNmFxhrYNEvRoal8wp7xccohgUGWDrfY1jIhGxGrbCwzUYxLGyfPjCj/egHXiN0iO5PnQoPuWJY9GGO7aONp0+Hh1xqF+yajK21krjG5EI2I+QCK2X7yG6K/GOVijM2Vnu2tGtcaIAbYCn6PC66esQ2knTVH3n4Q97hes+DD7n777nXf7994kT/t9l2xBHboCJY0UDRQNFA0UDRwA3UQHHGbqCyy6WKBt5qDRRn7K3WaMF7IxrAIfvwww9754u3ZHzuv/ue+nbEN4JZflM0UDRQNFA0UDQwHjRQnLHx0MuljWNWA+fOnffbFFMNZItMqsYQ2yR0O0czzI29m1xvb4i5asYHlm6JifGtXtPRsBc9xsMxsHS7SIyP9uke9hiPYekWqBgfMUM9Pb2xUw3HiNfReI6Gk1f/Yb8/2wtTRBtTWAMDQ25Ddx6WbiGJXXv9hm6/Lz92To8hl24h0XN8p1++/a1vu7vvfHvdGfvk7/yu3yZT5QVLt09Wz/M/cRu6BS7GwzF0v2fP3man/XFivnKwkEvjJmKgFB7W+JcYD8fA0ji/GB/9uHRZiN+K8RiWxvnF+Ijd45opQvZUMD0xGjlYyL5pc9gOGLv2/gOHsrDoH43Ni2EdOnQkG0u3rsaw9u3f3xBrGOPhGNuLNTYvxkfMW46+NmzY2BCbF8M6dfp0FtYK4rC6QjxoDOvs2bNZWMSS6hbRGBZbynLayP0yVYQdLI3zjF2PYz09fUl7xXbAHLmIy9PtprFrYqdysIgZ1rjhGBbHwErZPmTSmMFWWLp9MsZH/Bw6SxG6Z83QiujDHNtHG8+dD9sNY5ibN+fbqzNnz8Yg6seIIcsZO/UfjLIvxRkbZR1WxC0aUA1YAg89Fvu+eMmK5MLb7ymXBBgxHI6RBECTCjTjIyg3ZZCenz7TPTfthWYQ9eNgIV8r4mZdij7XNIS+jhw50kpdb7roM07YM09PrRdr5m3Y5Ntu8w8H+P79735v2PWRK5X1i6DyefNDsoNhIFcPEMydWvyx0J83PyQoaIaFXKlFPIkMCEhPEViayCLGz4KOJBgpAiu1WC5Fn4MWGTepRfXg0JasRADEqGhSonCV8K0UfQ66WLR4WUMSnHAmfOMNek4SBgoYcz9vRTxQY36kiAU8iWlaEXYqB6sUfQ5aRF8nJTFSOBO+rVq1tiGhTjjT+A2sY8dDkrDGs7X/SgKPmh7+TUw5dmzZ0qXus3/0Gfu3/C0aKBq4QRogrXhOansWmppUICYewbWpRSS/I3sVgf4pAiuV3revj7dsIbC9GSZYGpQd46N9mrEuxsMxsFJPGgnyz0lhTNYyDZKOXZNEBpqlK8ZjcqWwSDKRelpvWCR3aUUsSjV4vxkv+iIjnJE5Yf/2ve/zb8Luetud/u+/fc973cO/+Z986nqLIas6ZGClDDhvZzTDn123+hfda3ay6nn+J7NXDhZyaQa2GBaZEgcHQ+bBGA/HwDpyJGQ2jPHRj5rsIMZjWKk28taIa6YI2TUDW4wfuXOwkJ1x3YqOHTuehUX/aAa2GCZvZnPkAmvvvgMxiPox3swydlJEtsnUW0mcixy5hoa2NWRJjF2b+ZqDRda5wcGhGET9GAkfcrDIgpnqx5cuXcrC4n7J2+NWhAOVo3uwUvaKh3M5bcReabbhmHzYqRys3j7esuXZq5TtQybNBBmTi2PIlXoQuf2a7FVI9BK7Jn2YY/uQK1U+ZefOfHvVqnwKcmKrcsZOrE2j4Vh5MzYaeqnIWDTQRAMlZqyJYsrht1wDVSeMxBxf/+pXvSP2H37jA+7YsWP1OmOa1GNdR0iv/JYLVQCLBooGigaKBooGRrkGijM2yjuwiD++NVCcsfHd/zei9TEn7Mc//KF/I8jT/O9957veEUMWLfqMQ/bdb3/bHU9sP7kRbSjXKBooGigaKBooGhipGijO2EjtmSJX0UCGBogZo86YJn5gWxPbkbTOCXFeWoiW7XDwsJXIiD3bFEzVLWkUi4VPE14QL6Z78C9efMnzUAzWiIU4WFoU9OjRGhYOpNGMF15sKGDKOa6nWBQpBUsL5HIePsVavpwA35AUAZnh0SLTtA0sPYYO4NMtgstXtDvi7IwuXbp8FSvEYREkT9Hqffv2GZvXJ1haF4YCqRrLRr/Ao9vP6D/kUizaW8MKQdIUyySewojtlvDwMcJBAksLvhrWeQm4njtvoXv22en2M791U7HYGvPEzx53D973gH/7xZswnLB9+/b767FF1ohaUcSMfPjhD9WLPisWfPAjF4VMjU6ePOmxNKicmkwUAdatpFUsEgGge03YQtFY+HR7JrV3wLp8OdQPGo510cul8WenTtWw6GMjYtko/KzzqorFGKKNmjCAOQCfziuKdFO8l3FlNBzrJY+lgfnMhRpWqBVEQheu+dJLlwzK88BnxDyBR7elGpYWASahQA0rzNGqXMwrZNeYHuY7fJo0prdvs8fi/mA0HOuy7x+tt4TO4dN7B0V5kUvnVRWLfqGvKS5vxLyCTwsKk4CIsdMa64rHWi1FcxlXVSy2fyOXzquqXFeuvOznrCZ+YLzDp4lxduzcfRUrzCvD0m1q06a94ObNC7FSzKsqFvcR5NJ5ZVg6rxYvXu64PxnRDvj0XktimxpW2PYcbEyYV9wvtWA8c7SGFWzMgYOHve5z7BX3YCP6Ciy1VzzkQS6do3F7VbV9NRvDm3wjtk6DpXM0hvXCzDmOj1HMXtVtn9Tgitkr7LEm8WH+0ka1TWavtD8MS+cVusqxfYx7tlsbxWwffai2r5W9Uiz6A/npd6OVKxvtFfdheNT2mb3CrhjF7BXFtpF/rFJxxsZqz5Z2jQsNYNRunzjJEUhuxIKKRZcaFpIYzF+wxFh8sCw8LHKM2MNOIK1mguvr3+SxdGFEkDzB7UbHT5zwPJpogJgYsNQh6N+02fPpwmjqM8833GBPnDzpechmaLR7z16PtV3iEcjkhvy6mKF9mqwBmeGhDUa0Dbl0T/zmgUHPpzFDYGmyBgqfgqXxAsS5VJNIDAySPWqjOypOLkZescgaBY86EvsPHPRyacFai+lS44wzoFgstsDSbI0snmijZuoizgw+NYLTnp/pfvnLqaYav6CEp7Ozy019+mlnMWF33/kO95Uvf6XurBL/Bh9G1WjRomX+mo988OG6MwYPHyMKRyOX7vsnZgIeiuca4bjCpwvcKhY6Qfe6kCQjH3wHDhw0KL9AAeusxM9VsVjcwLO2Iyzid+zc5bE0lomHEPDpvKpisbiBRxfxO3ft9lg6r+hDEngwroyqWCxIwNICv8wr+DSWaUXbas938tQpg/I88Bkx58BSfTGv4OGv0ar2tZ5P51VVLuYVslP42Qh54EM+Ixx0rqkLySoW7Ydn2fLwEIVFGXway4RTDZ/OqyoW8woeXZRyX4RP44/QJ2OHfjeqYjFewNJFKeMKPo2XJUEMfIePHDUozwOfEbEwPPjgYYXRwUOHPZ/GuDKHwdIC6ybXBSne+/TUaY6HWEbMQ/g0LpXMsmBxHaPuntp81IcojEPuT0a0A6yhLSE2kmLnYOm84t4Fn84rsNTGEJsHD/cxI+KM0D33O6M6ljz4qGLR72BxfzXi3oFcuojnIQh8+oChZq+C7WM8wsN93whHGKy9e8ODNXQIn9o+HAI+RswTeDSzKBlLwWq0fVft1cmT9lOvK01UxPwFS7MeM6/A0vGLnYUPu2s0zF6dNnvVaPvQPbGQRth/sDR5RhWL+x08ak8scY32bd1eybyq2j7GC1hq+xhXtFF1yPiDT+dVSeBR67WSwMNGb/lbNDCCNMBTqLdNvj0p0fETJxueDsd+QMCxLnZiPBzDAOlirRkfWK+//nqz0/44zoE6CM2YwUoFRLPgpJ0pOnr0eDIZiMc6HoxdM0wMiT61jvGdPHm6YUEa4+EYbUxhsTDQxW0rLH0CHuPDcVAniGurE2Zvwlis69ugGBaLHwy6blOM8dFGEgK0otNnzjY8AW/Gi+7VYYvxsUDXp+kxHo4hl74ZjfHx4CMXKxWMTj/q4jZ2PZMr1UYW18ifImTXNyUxfq6Vg4Xs6vzFsHAgcrCQS99uxLB4C5CLpc5yDIu3LDm6Zzzroj6GxZvNLLmOn0hiXb5yJQuLOZsah8zlHLm4l6QS6rBNORvrZHggENMXWOqIxXg4dvx42l6RAZF7eYq8vRInKMaPncpp47XYq5Tt48Fjlh09ejyZlbhmr9K2D93TB60o1/ahrxTWtdirlO1j3OfM21ZtG8nnypuxkdw7RbaigYQG2CZxZ4YzloApp8exBqpO2IP33e9+/KMfJZ2TmMpSzljsN+VY0UDRQNFA0UDRwHjWQHHGxnPvl7aPeg0UZ2zUd+FNa8Bb6YRZI4ozZpoof4sGigaKBooGigbyNFCcsTw9Fa6igRGpAYsZSwlH7IMG3Mf4WZyzdztFxGSUos81LbEHP7XVZOXKNT4ZQEqv6D6FRRyOxng0wwSrWdFnc8Leed/9PjFH6k0YWKntIcT0EEeYcsbAKkWfnStFn8PIJc6T2KtWRO0jxk6KStHnmobYfpijL2JQV65a01KtFtfXksk5HxPX1haSgcT4SW7BPTNFpehz0BD9qAm0wpnwjQQemtgpnGn8hu7ZhtiK6ENigFOEXKktrqXoc0qL4XxxxoIuyreigVGngeKMhS7D2dSsheFM4zeMiGZ8ajxb+4+MUhpwH+Ph2GhyxnDCnp4yxRdlnnjLBHfP29/h/vizf5Lcjoi+ijPmXHdPX0PylGZjAn2lCsgWZyxorzhjNV0cPlJLcBM0E/82Zcqzbq4kT4lxFWcsaGXJ0hUN2X/DmfCN+DPmbYqmPf+C45MisMBsRWQkRrYUgVWcMedKAo/aSCkJPFIzppwvGrgJGijbFG+C0kfZJatOWOpN2JtpXurN2JvBLr8tGigaKBooGigaGIsaKG/GxmKvljaNGw0UZ2zcdPU1N/RGOmEmXHHGTBPlb9FA0UDRQNFA0UCeBoozlqenwlU0MCI1QCrqt02anJRt374Dya1mbKvQmkPNQKm9tH9/qBPTjA+sVDr6HTt2OuqbpQis1LYPttLRzhRRByaVkpdilloXyjC3b9/unvjZz9zjP/2p//zx//vH7vvf/W79//VdXcZa/3vw4GG3d28oaFk/UfmCXFoEuHLa/0tNoRQWTtj3vvM99753v6ceE/bYj348bDvinj17Gwowx67HMeTSArkxvsOHj/raVylnDKxzUiw6hkUNsT17Qr2fGA/HBoe2JtOrU0uKdqYIuVIp0Y8dO5E1P8A6JQVfY9emH7XeT4yHY2ClYjyIM4QvRcyhVEwiqahzsJCdcd2KSAufg0X/pFKUsx07D2ufo75VK6IwNWMnRdR40jpHMX5KGGTJBdbhUDA+hkX6/hysrVu3Jfm4j+RgcS9J9eOVl1/Ow9q3v6GgcKyN3JtydL83w169+uqrWXJ5eyV1zWJyYadybB/1vrTmVwyLYzm2jzTzWsewKdbuvclSLDV7lbZ96D5V8sRjZdqrFNZbafu2bN2WNXaa6XGkHy/O2EjvoSJf0UALDVjM2I4du+pcq9es88VdT0igLvvOKaRpRDFQCsBqAd7Nmwf9vnmK5xpRCBc+rWtTxWKRAU9n1wb7mV9owqcLzo516z2fLpYoYDrl6efqv2MhDta6zvX1YxQzBUvjcDo7N3g+XeDQPviMkBksLeZrhUK1sCY6gI8FslEVi/pl8PyXT3zSOzjEXMU+OEDwUXjZiKQCKheLa3hIxmFEgVt4KHRp1N3d6/nUYFexWPCCRSFbexP2ngcf8rLde9fdDieMt6cU2YRPHUyKlz4pRZ9xRuDRgH4WdMhF3xlR/BM+dZgoFArfIx/8YL3oMzx8jFj4wcP4NKIf4NFiwQuuYqlzVMVCJ8TrLV0WigX3X8XauSsUHibZCdfEyTCqYuHEw0OiFSPmAnzbZV4RIA+fzqsqFosPeFa0rTIoP27h03k1a/Y8XzhZ6+JVsaxI9vIVK+tYzCf4tGg5CXW4ptZJqmIx5+DRgshbtmzzWBQEN1q2fJXnUyekisW8ougzbTBCHvh0oU1SAa6pRYyrWLQfHo3P5OEMfANSkJ6+gU/nVRWLeQXPQkk+wH0RPi1Iz5hh7GgcZBWL8QKWFjFmXMGnBenXrO30fPoQqIrFPbqKxbyCjyLFRswx+LSgt2FpfTjumdNnzLaf+XkInxblXb9ho8dSh4x5DZ/OK66nhYdpBzxaRL6np89j6byiODh8Oq9qWMHG4GzAo/c0ZET3WtCb+yB8+tABLLVX9Ds8muilf1PNXunDPPoDPq3FSMFtxTp0qGavurq66zrEtnDNrdvU9nV5LJ1X1aLPZvvWdYrt27LNY6ntw54hF/bNCJmQzYgHR/B0dIQHesiDXBRnNsLOwqfzapi9On7C86API4qVo3sdc2b7tDg4MZxc04j7HdfT+zbzCh4dc/QzfFpHrmqvGC/wtLevNXjHuAKLmFwjxh98Oq9KzFhNOyVmzEZJ+Vs0MII0gKG/Y+KkhqddGG4+r7zyal3StWs7GxbULNzh0TcevGXDYF++fKX+O47VsEKhyLVruxzZ84wC1gU75IsEg4UjYGRYL78csMjatHDREmNxnON68BpRcBgsPRbDwuCp8eHt13CsKx5LFyToAD7aYYRxVeNjWBj5nu5u171hg3vi8Se80/M3f/2//f8c27dv/zAsjH4j1queh2sa8YSRNqrTa3JduRLkWr9+Y4MTx9NhFjGP//Rn9cQcFGv+6//1127Xrt0G79+KcT19ktm2st3NFaMLFjyNcr3s5Tp4MLwJ5Ql+FatnY69jgfaRDz1Sd8aqWOiXNqpDaFg65jZu7PdYyGNUxUIns2bPdVu2bDcWF8Pq7dvsyOiVwkKuHTuDvl566ZJvoxa73rRp0GPpvKrKZW1Ux8uw9K1n1/oeN/vFeQ1vaJthaRsJ5IdPsXCAkF/f9g7HesXzDA5tqesrYIUi3Fu37vB8OkerWFwH2bvk4QvywEdbjXiDgFw6r2JY9A+OtFEMa9fuvRlYr/r+2dgbHBz6ryZXuA+xwGXstJKL8cJ45iGGEWO0isXCM9VGw+qWBy2GxZg1OnjoSFMs3RXAwrutrd1+5uc0cinW0aMnPJbeO0z3OhdWr+5w6pRwf6hhXazjU9ybNiax1qxzneLgwA+W2phTp0553et9yOTSecV9XB/I0VdVrHPXYK861sXsVWgjdoo26n3IbIzOK+yVZhpsZa9Stg+ZsKVGZmPUziEPctFWI5JPoQsdv9irNWvDQ65mWIx7LdZuNkax6MNcexXD0nHS1dUzzF5Zf1t74KeNavsuXqzZZB0n2CrkH6tU3oyN1Z4t7RoXGuCGX4o+35yu7lzX6Z2xJ3/+i5siAAZUsyOSmMPehN0UgZxLpra/WXKV6xYNFA0UDRQNFA2MVA0UZ2yk9kyRq2ggQwPFGctQ0nViuVnOGE7YlKeeqr8Ju5lO2Llz59y3/vlf3Ne+8nf+gyykzLf///mb33QnT568Tj1QYIsGigaKBooGigZGvwaKMzb6+7C0YBxrgFf+d2Qk8Ojr29wQNxFTGVsbdH9/jIdjff0DDXETzfjA0u01Mb6Ojs6GrYUxHo6BpdtFYnzEhfRJDEaMx7BSdVvYo69762NY5ozxNqoVDQxscbp1qhkvbaQ/mxFOGI7Pux540L+Ra+WEgUWiglbU3bPRrVwVYrqa8YLVzKEa2LzZv5mNxc9xbPKtt7l1HSE2DiyNwYhdk9gGjR+I8XCMunIgh2eZAAAgAElEQVSpZCY7du5qiH9phoVcGjcR4yO2gTi+FIGVSnBDPInGlTXDBEu3dcb40AF8KUJ2jUeK8SN3DhayDwyGOJYYFvFzOVjEh9BPrYgEMXlYfcmEQGwtZOykiC2KW7eFbbAxfhKi5MgFFrGvrYj5moO1atVqp1seY5hsX8/BYkuwxuLGsC5cvJiFxf1S4/xiWGw/y9E9WBrnF8NiC1tOG4lL3bRpIAZRP4adysEi/lhjkOsAlS9gpWwfMmnscgWi/i9Yul2vfkK+bNqctlewo/vziQRK9GGvbPWVyzR8RS7dUtlw8uo/g4NbHWMsRWCdPXu2JRu2KmfstAQZwSeLMzaCO6eIVjSQ0oAl8EjxLV6yInkjY7GvgbvNMEkCsHRZSCrQjA+slEF6fvpM99y0vCKayNeKuFHfyKLP5oz98F9/0EosnxhCkwo0Y0ZfsWx31Tdh977jLveTHz/WEI9XxQTryJHW2dvmzV/oC2lWf1v9HyxNdlA9f/7cOTd//iL3zLPPu2PHjjV8qgYWrN2JTInEP2hSger17H+C0VOLLAL+CUhPEXJp8H6MvxR9DlohgUfKkbfEO+FX8W+l6HNNL6XocxgfJMtJLbx5oMa8TVEp+hw0xD1TE6WEM+FbW9vqhri4cKbxG7o/KYmRGs/W/iMelCRKKQLr2PHjLdlKAo+aekoCj5bDpJwsGrg5GuApV05qezKmpRabBHannkbSShIKpJ7ywgdWKrX9xo19WW8uwNLA85i2ad/QlnTKarBSTxpJwKDZsGLXM2cMx6gVke1Ls8w140UuDXavOmEP3f+A+8aj38jWF1sIW9HmgcGG4P1mvMhF1sZWRDbE1FNxfg+WZiOMYeKsafawGA/H1q3rasiAGePjrVIOFnKl3tiRwXHz5tZvg5ABLM3yGZOLN0GaoCDGY1ia5TPGxxsorpkiZNdshDF+5M7BQvZUim8yOOZg0T+pt38kzsnF0iyf0TYeOeLHTuycHmM8794dMnPqOfvO26wcuXg7rtkI7ff69+y5c1lYJNzYvLn1mx7eWOTINTi4JdmPbIXPweJ+qZkNtW32HSzmbYrAStkr7o85cpE1VLOPxq6NncrBIlERnxSBlbJ9yIRsKQIr9SDS276Mcg3onreTrYg+TNk+fo9cmjQmhknWxdSbV8NKvbFj3OeMnZgco+FYeTM2GnqpyFg00EQDJWasiWJuwGFzxt7qBB51J+xqnTCcsNSbsBvQ3HKJooGigaKBooGigaKB66CB4oxdB6UWyKKBG6WB4ozdKE0Pv85b7YwVJ2y4jsuRooGigaKBooGigbGugeKMjfUeLu0b0xqwOmMaSEvxSIpLas0U9t9TV8oIJw4eLY5JAVb26msSCWp/wKd1jSjmukLq3FBbqIqFXGCdPh2CcgNWqEU0a9ZcN3PmHBPLEQdQwwr7x9luB9YJycqH3PBpXSPap3EGyAyP1i+hbWAR22QUsELNH+JhlklcHPWKwEK3Rm0r2nwije98+zt2yMd8wafbN6hXpDF2bJFULP7/2U9+6t557/0ez96E7d9/wPPptpL29o6Gwr2GBZ4R2z1o4+49e+2QjxOAR7dBLli42BGzZ4QzCE8j1gWPtVNqlhFzUMMKtW+oC0QsodanqmJRHwe5tAYXRUDh0/FL/R1iHHVrznCsi+6ZZ6e73r4QHB6wQhIU4s/A0m2pVSz0i1y6zZJtmfDpXFi/vsfHJOq8qmIxr8DSwsBnztSwmBNG7e1rHAVktY5ZMywNpqc+HnyKRXIIrqlJaapYnINHE6MQzwef1twjAQ58Oq+GY132spNIwgh5qlhsY6phhXlVxaL99I/Wp2K+w6dbY4eGtngsnVdVLPoYLPrciP6rYlHTjLGj86oZliZrYF7Bp4WOt2/f5eXSeVXFYhwzN9ZIsXPGexWLWmroi3liZFg6r6bPmOUWLlxsLJ4fPo0FIhELWDqvAlaIveW+tKo9FDunHTWskAGV4sJVuY4erd0ndF6BRb0oI/QLlsbBkogF3atcZq8Ui+LjGpNIv1exwK21Mcx37uvw6bwabq+G2z7GGlg634O9umxN8oXOtdh5S9t3Jti+48fNjgbbhw1FNiOzfTF7pQmUmtqr5SEpjdkrtXOMX3SvW6hjWKtWrWmwV9zv0KnaPvoPfWnhafoDPp1XFHemyLoRfTwcq2avtFg07YVP5xW2CvnHKhVnbKz2bGnXuNAAi6DbJ05ye/cdqLeXBRdFZU+LMaBQ6PwFwYATHwNP/6YQa8K+cwJpNePaxt5+z6eBugTca4IFbuhgkWXRiPgIsHZKIV0yZMGnxnnqM9PclKefs585HEJ4KNZrxCIFLI1H4FrwcW0j2kc7jZAZHtpgRDwJWLpXHx3Ap0Zw/oIlDVgYa3i0COyLL87xztOj//gNg/f76OFTw7VgYSMWi194Otatd1N++Uv3/qvbEe95x13u61/7ej0xB3Em8LGAMSIYWttInAk86zeEbHoYNdqoshKzBt+hQyGpx7TnZ7onfznVoN258+evYvXUjx04cMhjbRB84g/BIlbJiAQlXFONJzx8jMhWCM+6zm475GMP4eE6RosW17CQx6iKhU4IRtfitxQshk8zGZLQhWuq81LFOnLkmOfRoqlkdIRPY5lYbIKl86qKdfTocc/Tvnqtie6Im4BP5xUFTEmCoQ5HFevY8RMeSxe4zCv4du8OjjaLOuTSxXgVizkHjz5EYV7Bt2tXiItiIQYf89CoisV1kH3O3AXG4uWBT+c7Dw7Aoh1GVSzaD8/SpWHBtmfvfi/X9h0hw+KatV2eT+dVFYt5BRYJG4y4L8JHfxqtXLnGjx363aiKxXgBiwWnEeMKPo1lIo4FPl2UVrFYuMKjSXwY7/BpQW+yXcKnWT0NS+fV01OnuRkvzDax/DyEj3lpxP0TLJ1XJLOBTx0O7iWaYIF2wKNxPjjVYOm82tDd6/l0XtVszBITwS+mwdKYTeIWmbfEXxoZlj4UqGLR72Ahi5EliNGMqj0ba/ZKHWbsldq+Y8dq9kofmDDWaKMmFyIDLtfUecUDFD5GwfYFe2W2T4vI0x9g6bxCJk0uRCwtPJp5F3mQa9u2HXZJ13/V9um8qtor2g8W+jDi/oPutW/N9mm8bBWL+x1Y+iCHeYVcikU/w4cTZTTMXp2t2Sv63IhxBZb2B7hgqeNYEnjUNFYSeNjIKX+LBkaQBniK+rbJtyclwpipsxH7AZkPdVER4+EYC069eTfjAysVxEyWPn0i1gorlZmR9ulirSnWoSPJZCAYOhIQtCLbpvj4T3/Wis07jLrw4+mgOmG8CfvpYz9xvH26ciU8tY6B2tPH2Dk9hu716bCes+8YOnU27Hj1L1j61qV6nv9ZsBwWIxzj4RhY+nYjxocTrQ5ojIdjONapJCWnToMVHNBmWMilT+tjfDgOuVi64I1h0Y/qnMV4OIZcuuCN8XEevhQh+5lE+mjkzsFCdn0QErs2T+JzsJBLndIYFs5IHlbjm6sYFm1MJfngd4xnXYjHsHgzkiUXb4hOnopB1I9dunw5C2vfvv3Jcch9JEcuFs6pfqSkSBbW0WNZWHvkjX298ZUv3HvfOnuVxsJO5bQRe9Uqs6w1A6yU7cu2V4ePJLMS42Cm7BWyoXvdcWDy6l/Gg9orPaffaaO+sdVz9v348dobLvu/2V+w9M1ojA9blTNvY78dDcfKm7HR0EtFxqKBJhooMWNNFHMDDpszlpvAo5kTRh8WKhooGigaKBooGigaGJ8aKM7Y+Oz30uoxooHijN28jsx1xooTdvP6qFy5aKBooGigaKBoYKRroDhjI72HinxFAy00wBYlYsZSRGC7JreI8bN9gb3bKSpFn2saMmesWdFnc8IevC8k5mA7YrM3Yehe4+li/dC+uqMhxiPGwzGwblTRZ663tqOrIS6jlVwalxHjK0Wfg1boR42TCWfCN2JIcuYtcTh9/SG2JSCEb8Qp5mCVos81nZFkJ0dfxOGQ5KYVlaLPQTvE6qXsFVunc3Rfij4HvZaiz0EXI+1bccZGWo8UeYoGrkEDxRkLysJ4k7AhRRhwzVgW4yfRAYkkqvTo3/+D+4NPf9rHKqkzRjzb3/z1/3Z/+Onf93vfn3rySfe+d73bJ/i496673Ze++JfJuCvkKs6Y89nwNEFMtQ/sfxYWmzaFpDF2XP+StECD5PWcfkf3mphBz9l3AthxaFIElga2x/hJ8IFDkyKwijPm3I4du7MW3owbzcwY0+/g0BafyCB2To+RYIHMnq2oOGNBO9wv29pChs1wJnwjsyjzNkXFGQsa4h6QitklK6Mmmwm/bvxWnLFGfYyk/4ozNpJ6o8hSNHCNGijbFK9RYW+S/YnHH/cO1n/+6MfciuXL/fefP/GE+8LnP++///bHPl53wiwxR8qQvkmRys+LBooGigaKBooGigZGsQaKMzaKO6+IXjRQnLEbPwa+/a1vecfrP37g3/u/j3zwYf/37bff4f8WJ+zG90m5YtFA0UDRQNFA0cBo1UBxxkZrzxW5iwac89vt3jZpclIX1IRKpe5lq53Wf2kGCpbWwmnGB1Yqve/u3Xsa6hy1wkqltqd9Bw+GelVNsfYdSKa2J932gRZY5pBNvGWCd8D4ixNG8ebqmzDStGu9n1ZypdL7knI4pxTAvn0Hkqnt2WJFDawUgVVtU/U3lDrQOkTV8/Y/WKnU9qRpzsGieLTWJrJr6N/jJ8AKNY30nH5HrlRqewqR5swPsFLp6CnBoHXzVBb9DhZbu1oRaeHhSxGynzrdGgt95mAhu9YTil2bGng5WPSPFnSPYdE3eVgHG+qaxbAodq2Fx2M8HGMMptKr8zAsV65U2Q3mWA4Wc5b09q2IQr05WKRpT5WkIJY4C+vgoWTKfbBydM+9N2WvXn311Sy5vO07FGoixvSGncqZ27uwV7tDXb4YFsdybN+hQ4cbajU2xdp3IJnaHl21sleGje5T5VO87ZO6j/bb6l/GxJWXW5di4R7xVtkrxn3O2KnKOVr+L87YaOmpIue41QAG//c+8Qn3sQ9/ZNjnww9/yE2acKvbPBCKYS5YuNi9OGe+O3I0FF+ksDLFQo1279nreTRIesOGHkdhxf5NIcifOACw1PkCSws1U/8DnmXLQ+HWno29HksLLi9Zutzz6c2ZosMaO4MRA2upFG4FA7l6ekKhyGXL2jyfLkpon8qFzGBp7Fd//2aPtV6KES9fsdLzaQ2TKhYGCqyFi5b4mDDS2U++9ba6I/a973zXOyzEmsGnBruKxaIMHi1EOjA45OVa2xGC/Cn2C586TFOfed7zWT9SEwaeufNC4pWhoa2eZ/WaDmNzxCjBp8bsqSnPNMRvUFMJHi3mS3FsdE8xYCOKI8O3det2O+RMLq0XBQ8fIwqXgqWFhzs6ujzP0Jatxuaem/aC59MaT1UsdEL8w8KFocjsunU1rMHBLXUsCltzzWPHj9ePVbF27drteTTesGt9t5dL47VemPmi59N5VcWiGDPXW7hwaf16zCv4dF5NnzHTy8+4Mqpi7d27z2PpOGEOwEcBdaM5c+d7Pl2MVbGYc8g1d14o1My8gm/jxj6D8jFx8OnCtIrFAw90P336rPrvkAe+bpmjFDsHi3YYVbFoPzwvzJxjLD4OED7i/YwWL1nm+XReVbGYV2BNnxEKInNfhK+za4NB+TGD/PS7URWL8QLWtOdfMBbHuIJvXef6+rEVK1Z5vu07QlHpKtbJU6c8jxYLZl7B1zjfV3s+LfBrWDqvkP2pp56py8A8hE+Llre3r/VYWtyeeQ2fxqVOmfJsg12gHfCsag/zHRnRhc4r4jDh03lVtTEUAIdn5aoQR7Z27To/drjfGTG+4VNntYpFv8Oj9w7mKHJp3OjCRUs9nzpyNazn7HK+vh9Y3PeNurs3eqy+/jCvGHPw6QM+bFWDvbpq+5YuU9vX57F0XmHPwNJ59fTURjuKYwyP3of6+jZ5rA3dG01Ut2x5zV7pvKraGNoPFvowoqgyY0fjILH/8LEeMKpicb+Dh3WFEfMK3a9bF+YC/QyfFn6fOnWa57Pf8XADHo3jZVyBxdgwYvzBp/MK2fmMVSrO2Fjt2dKuMaWBgYEB19fbO+yzZvUad/ttE93Fixfr7cXYskjXJ2AYCxYORjyFhefUqdN2yH9fsHBpwxsC3gbAx5NWo6XLVnqDYP9funT5KlYoakphVbC0KC+L6xrWZfupvynPlQyOFCqGRxfiFI8FSxckhsW1jWifGkVkrmGdNBbfNrD0STw6gE/f/mD0ycJlxBsrjPKPfvgj996riTn0rRgxZLQ1htW2co1bskSxXvbX00URRW2RSzMg0l7kwhk3wkipseZJMzx8jAzrwMGDdsjrroq1dNkKN2v23DoPBTyrWIwr5FKnlzc18OkbrtVr1nmnlwKxRsOxXvJYOCxGvImpYYXxS2ZGHGjkMapi0VczXnjR4XgaGRbtN2IRvmjx0oZCp1UsCvfSRk3gwZst+DTRy/oNG/3iRudVFQu5wBoUuRgX8OmbNxYxOHf6JnQ41mWPtWlzWLgyr2pY562JjgcMXFPnaBWLecXCTLMpGhZ/jTZvHrqKFebVcKwrXnZd1DFH4VMs+ga5dI5WsWg//aOOF3qCT98u8iauhnXJRPU88BnRL4wbdbzovyrWlq1b/dhpJRfzCizGohHjqoZ11g75IrrIpXMUHpWLOUFyhTVrwmKTeQWPvtndf+CAb6POK8PSeTV79ly3RBIVwV/DCm89eeuCXGoXDEvnFTjcn4xoB3x6r2UxDpbOq4AV3oxwv9QEHsyrGlawMbxBZ95qG2P2ioy9aXt1ysul8ypgqb1qa3C8gr0KcvG2lDYqltkYnVc89NIHX4al9oo5AJaO34AV5hXOYKO9itm+Cx6r0U7X7KiO3xUrsFfBIWReofuqjUH36vRG7VXb6gx7VZNLC02fPl2zo/S70cqV+fZKHeiY7cNWIf9YpeKMjdWeLe0aFxrAeN45+fZx0dab1UgMm2ZHRN84Yr/7W7/t//7Bpz7l/5pDdrPkLNctGigaKBooGigaKBoYfRooztjo67MicdFAXQPFGaur4i3/ghP2y1+EFPUPPfBO93uf/KR3vD73J3/q1q5Z67+zZdFiyEhtX6hooGigaKBooGigaKBoIFcDxRnL1VThKxoYgRpgS8QdGQk8+jcNJmsfERDdI/EjzZpLHA3bmVIEViqBR2fn+oZ9580wwUK+VkRtJ/bFpwgstm01I5yw//tP/9cn5PCJOR54Zz0xB2nsqTWGLFZn7Cc//rGHeuJnP3P/52tfGwY7NLStYXvYMIarB5CL7V6taMvW7a6vL8T0NeMFK5X4YWNvn1u9OsSVtcLSbTgxvm3bd7revv7YqYZjyHVMtpY1nLz6z/Ydu5zGGsZ4OEaMQio5x85du7OwkEu3ycSuyfbKjRvz2phK2LJl67aGOLzY9TiGXKk2EkgPX4qQnfjOVoTcOVjEEGqcXwzz0KEjWVj0Nf3UikhckyMXWDt2tsYitk7jmJpdl/GcSrLCNu4cuYip01iw2DVPnzmThcWc1XikGBZ2IUcu7iVDW7bFIOrH2OqYg8V22cHBsG24DiBfwMrRPYXMU7X62EqaI5e3VwOt7RV2KgeLeEGNGZSmNXwFK2X7Ng8MJWsIAgoWbW1F3vb1p20futetmDFM+pC+TBFynZct4TF+YhZz7RUJf1oR4z5n7LTCGMnnijM2knunyFY0kNAA+9JvnzgpweXc4iUrnCbriP2AGz4FJlPE3nTixlIEVioD4vPTZ/qEDTlYKYP0Zos+V9+E3XfX3e7xnw7PjmiymjP2w3/9gR2K/mXf/MJFwwtIV5nRl+7xr57n//bVHT6GIHZOj4Gl8Wd6zr7Pm7+wIbjajlf/gkVweSsitkYTTTTjBWv3npDQIca3rnODK0Wfa5pBX5pEJKYvFq7wpYiC1RozFuMfGNiShUUSg9TCiAcHOXIRzK8xYzG5StHnoBWSbsydGxKxhDPhG/FCObon0QyJgloRTmIOFjF2GjMWwyxFn4NWSMShccnhTOM3dK/xzI1na/+Vos8xrYyuY8UZG139VaQtGmjQAE9Ac1Lb8+Qs9QSUtz05T7F4cqYJChoEkn/AOnDggOvd2Os/67vWu9Xtq+v/D2ze7Nav73aa2VB+3vAVrNSbMdqnWboaAOQfsPTNWNUJe9c7H3TfePQbjgxbrcicsZ/8+LFWbG7r1h1ZbxKRK/XUkjdQqcU5woBFUHorIrufJmFoxguWBpDH+HgboVnNYjwcA+v4iZBQJca3c9eerDecJERIOYlkCdMshrHrmVy8fWlFe/fuTzozhqXZR2OYZLXU7HcxHsPSLIkxPnSAXlOEI6aZTGP8pAHPwUL2rdtCNs0YFinTc7DoH83mFsMiC1se1oDbJQliYliHDh9uSKYR4+EY41kzw8X4Tp06lSXXpk2DDVlRY1hnzp7NwiJrKFn2WhFv2HP0tXnzYEPimhjmxZdeysMaGGrIsBrDYlu9JjKJ8XCMt0Ype8XDuZw2kq1PE/3ErslbrBwsHhqkHhyAD1bqzRgyaYbKmFyGlXoQia7QWYrQvSZiifGTnTNn5wttvCCJw2JYvA3OtVfnErtCsFU5Yycmx2g4Vpyx0dBLRcaigSYaGMkxYyxUyPSoWQer36nLdbPInLD3PvQuLyNOWKs3YVU5zRkjZqxQ0UDRQNFA0UDRQNFA0cAb0UBxxt6I1spvigZGiAZGsjP2+uuvu3lz5rrHfvRj//nIhx7xTs+/fu/7/n9irE5I/acbpdI364SZnMUZM02Uv0UDRQNFA0UDRQNFA29UA8UZe6OaK78rGhgBGiBm7I6Jkxq2HhAvwLYenA6jtpWr3ar2tfavoxYIPJqYga1oS5e2NdRWIoYJPt3WB5bGGbCfvYrFNhmwtNbK5//0z7wzRj0SIwrWzn5xnv3raxKBpbFTbN0DS2vfEDgPn+6lp9Apshkhs2KhD7YUPnDPfQ1vwqgfNgxrdUdDgVF+Cw+6NWpb0eZxKPhshD7h01orq1evc+zpN4phEdhOG7XAKP0BltbkWbO2syH2j+0r8PAxMiytDYbOq1jUd9K6LXGsl7xcu3aHOC/6oYYV6nlRN2vZ8lVO6yE1k2vHzl0mqu9T+HTrDHWiiKfQrTnDsV7yBXk1YQvxKDWsC3V8tsAS39gKiwca6F4L5FL/CSzdNrqhu9dj6byqykW/g6XbfJgDNayQnIW6bMRLtsJibIOlbTQsticbsV0IPp2jVbk4B48Wi6b+GXxaC5DtdPBpDaMYFrKvXh3uJ8gDn873waEtV7FC3aEqFu2nfzZsCFuCuXfUsMI2W+LPkEvnVTOsLinoTv/Bp/W82JpHMWf63aiKxXhhPBO/aETNsirWzp17rsrVCusVj9UhBXIZ72DpPY0ivrU2DsfSeUWBbAoSGzHfq1hskwVL7x3WRp0L3JcYi0bww6fbkqklVcMK8z2GRW1GTQiEfqtY1LhC98hsFLNXK9pW+0L1xpNrrwxLa4PVbF+Ii4vZK7Z000ad7zHbR+FsPkYBK2y9jtk+w9J5Rc3IVvaKa8RtX83GNNg+b6/U9g23V4xfdH/06FET39t/+kjnFX1I3TKjmL1i/KIvatAZmb3SebV6TaO9ohYg1zsuD2HNXh08dMSg/PiDT8cvtkqLsNeZx8iX4oyNkY4szRifGmDxQwKPPZIUgQUoi2M19ATva1IE4mPg0dgDC7jXorzd3b2eT522KhY3TbB6e0OmuR07dvmgb81G9gef+n3vvGh2uKenTnNTnn6u3nkYU7A0WxhxGwQxazYyMsPBx7WNaB+yGSEzPB0dXY6thLYd8d677naP/sM/1h05dACfFsMkGYViYWjg0UXj7Fkv+vY8+g+P2iV9rAB8R44EIzV/wZIGLPoFHuLljIhHoo29vSEWhJgV+CjgarRgIVghWQP9D0+nLBrJrgdWd0+v/cw7B/Cps4dhe/KXU+s8LKirWPQVWBrXR5IH+DRei4LC8OliBh4+RmTqg0cXuMRNwKNjgmQn8KnDUcVCJz//xZSGRYNhqRNKsV2wdDFexTp8+IjnaV8dFqXETcCn84rENWDpvKpi0e/wsNAyYtzCp/Nqzpz5jiQYuuitYh09etxj6YKNeQWfxjKRuIZr6gOMKhbzCh59KAAGfGAacS34jh0LDx2qWFwH2V+cM99+5nbtqmHpfOfhD1i0w6iKRfvh0YK16Ak+ne88hIBP51UVi36BZ/Hi5XY533/w0Z9GbSvb/dih342qWIwXsDTxDuMKPnXamXfwEWtnVMVicV7FYrzDpzFDxCLBp5k4DUuLj3PPnDFjtl3Oz0P4mJdGZJUES+cVssKnzjf3OO5PRrQDHhxWIx4GgKXzqqur2/PpvKpioV+wSDBjhLPPvOV+Z8R9ED6dVzWsxcbi+x0ejesiTgq5dF5xf4avlb3iPg+P3msZa2Dt2rWnfk2zfTqvnn1uhuNjZLZPs6zWbZ/MK+wZ12QeGlXtFdeBp0fu28iDXNhmI+wsfGr7qvbKbJ/aK/SE7jW2zGyfxss2t1c9JoKfV8jVME76a/ZK59WCiu1jvCA748eIcQWWrkXAhU9t31NTnvXy2+/G2t/ijI21Hi3tGVcawEjnJPA4fPio4wlnKyLzoS7Wm/ESmK8372Z8YGkQ8xf/4n9450Wf6HEjVsPcCiuVmZH2qSHgiZ46YcSEsTWShaM+aY5dE4OtWDEe26b4+E9/FjtdP4bRTKVNhxl96ZuSOoB8IS08KcNTBJbqOcZ/8NChhoVMjIdjYOnTzhgfSTnUcMZ4DEufisf4WJSkEmDwO/pRF4MxLBYlOVi0kUVzK8Jx0EV3M16w9A1RjI8nw7rwi/FwDKxUG3kjCF+KkF0XvDF+5M7BQnZdDMawcKZzsOgfXTzHsHDyc7FOnDwVg6gfwxlh7AB9Jy8AACAASURBVKSI8awL8Rg/yS1y5AJLF+IxLOZrDhaL6hQf95EUDzJwL0n148uvvJKFxf1SHe9YG7nv5ugerBtpr7BTOfqiNESqPATtBkttX0wX2FBsaYrAulbb1wwT3eub0RgffZiyffwOuVJY3vZl2quU7WPc54ydWJtGw7HijI2GXioyFg000QCL5Dsn397k7Mg6HHPGroeEzZww3cb1VlzXnLGSwOOt0GbBKBooGigaKBooGhifGijO2Pjs99LqMaKB4oyFjrxRTphdsThjponyt2igaKBooGigaKBo4I1qoDhjb1Rz5XdFAyNAAxYzlhJlJBR9jr0ZeyuKPpsT9sC9ITEH2xGbvQljf7rGYMR0RzA6RUxbkTljpeizc6XocxgpjC/q+rWi9tVrfdxVKx7OgZWq01OKPgctEofTKfEo4Uz4RmIRYmdSRBxOqg6fxVSmsZY44t5a0eEjtdjFVjycK0WfaxpiWyfzI0UUViYhUCtiG2AOFnG2OUkkwEptLSxFn0OPoK9jktQjnAnfSsxYTRf/Jqhk+LdlS5e6z/7RZ4afKEeKBooGrqsGxrMzZk6YJea47+573F/9r79u6oRZR3DjL86Yc/PmL3QYuBShL03WEeMvzljQCvoqzpjzSQfQRYrmzV+ULKS7Y0ctiU8aqzhj6MgStqT0tXDh0obMuDH+02dqiVFi5/QYD6/a2kJGPz1n34lvzHGESbxDYppWVJyxoB0S86CzFKH7VHwmfbhoUesHkVyHuX3yVMiMHLv2qlVr3YKFS2OnGo6BVZyx97v9+0NimwYFyT/FGRNllK9FAyNFA+NxmyJO2C+e+Ll7z4MP+YQglpij2Zuw69VX9masxIxdLw0X3KKBooGigaKBooGxr4GyTXHs93Fp4RjWwHhyxqpO2LvJjvj448k3Yder+4szdr00W3CLBooGigaKBooGxo8GijM2fvq6tHQMaiA3tT2p1bVGT0wV7HHXGjcxHo6R9pZU+SkCS9P7xmLGKHSqtZximDhh3/n2d+pvwpo5YbQvJ4U8cqVS23ssqe9lch04cMBNe+45N+3ZZ903H33Uv5n78899zv/PscHBUJ/HfkOa/Jy078hFW1vR0WPHs1K1g5VKbX/g4KGs9Opg4fS3IrZF5aSGBuuCFHyNYZImH9lStHPnrmTa9xMn87CQS+uaxa598uTprPkBViq1PSmftVZY7HocAyuV2p509fClCJ5UanuulYOF7FqXL3bts+fOZWHR16mtU6S2z5ELrFQ6evqGsZMixnMqHT1FaXPkoqwAZSla0UuXLmVhUVYgtW348pUrWVjcl1L9SPrynDaClSp5AlaO7km5/5baq0QKeexUThv3YK/27mvVjf4cWGr7Yj8grX1OCnmwUvFnNXuVLnmC7lPp6OnDbHv18suxptWPkSY/p7QIbUzZPsZ9ztipX3yUfSnO2CjrsCJu0YBqwGLGdu0OxSoplrh6zbqGgrIU0dSizxgBeLp7+upwg0Nb/T7wHTtDDR6C4eFjgWxUxaIeDDwbukOR4a1Xi2hu3RaKVf7+f/u0d160eGi16DPOBljrN2z0N2e2Iz54/wP+d++87/76m7AN3Rs9n9aiqRbRRGawNKCftrE/XYtVogP4tOZLFYvFIjyf/J1PeFkm3jIh+petk/CpUwiWxs5QrwqeDimITA0VeHo2hsLZvX2bPJ86JhTkVCwWz2BpcgCcW3jQoVFf/2bPt//AQTvknpvWWPSZsVTFsmLUqkOKwMJHcWkjilFzTa3VBQ8fI0t2QBFuo82bhzzPHikCawWk1aGpYmG8iX9YviIE5lPMFD517oljQS7iXoyqWCwW4Glf3WEsjrkAn9YCIwkOfFqouYrFvIKnbWUo+kyRYPh0Xs1+sVb0WZ2QKhYLLLBIJmPEvIJv+46ddsgtW14r+qyOQxUL5w8seI22bd/psbS4MteCTxfoVSyuQ9Fn2mC0fccuj6XzHR2ApYvqKhbthwfdGuHowUdRXyMSnsCn86qKZQWkNXaG+yJ89KfR8uWr/NjRRWIVy+KkGItGjCv4tLgycxi51DmqYuHkw0MBXCPmFXyanIU5Bt++/WFeGZYWU+eeOV2KPjMP4WNeGvVs7PNYWsORewR8Oq/mzl3YYBdoBzy9fZsNynEfQi6dV8SIwqfzqmoXcEDhoQC1ETIyb7nfGaFD+E6dDvFHVSz6HR7aZURcJnLtlJpxnV0bPB8PYYyqWIxHsLqluPKWrbUC0loAvWv9VdsnTnS16HOwfeFeawWkmatG3Iu5JvbNqGpjcNbh6VofiitbAWkK2hthZ+FTx7eKRfvhQR9GzCt0r+OkbvukAHoVy+wV6woj5hW67+8P44R+5ppai3F+xfbxMAgexo+R2auNvZvskB9/8HGfNyoJPGqaKDFjNiLK36KBEaQBDOsdEye5l166VJfq1OkzPrBWn4CtXLnGrWoPi83Ll694Hn3qzvely1a6ixGsK1fCE7CVq8BaW78eT2EJ5D195mz92IWLL3ksXUT8+Z99zjswBHEbzZm7wL04JyzqwMLw/ugHP6y/CXvXA+90//uv/sYdPRrexnEtrgm/UfvqdY52GiEzPOjDiLbRxpOnQmFY2u2xLgcsDEHbyhCMji7hwZFctXKlW9nW5hYvWuz+8kv/y70w4wX/P8e2bNnq+S5dvmyXdGvWrnNtsqB++eVXanJJ8DNPxZFLn5SeOXuuhnUpYJHdTRfnvOFDLj5GvBEDi7d4RrylgIfrGC1esty9MHOO/evfFjbD0kXd2XPnh2Gt6+z2AfevvPpqHa+KZW3cuTM8OGCh6uWSMbd+fU8N65VXmmJdunTZkYlzYCC8iTx3voZFIV4jnHayllG41qgqF32FvrZsDQ8Ozp2/4OXizYfRxo39NSx5GlzFIm4RrEHJpnj+Qg2LOWG0tqPTTZ8+q+Ep9XCsKx5L23j+wkUvl75d3LRpwPPpHK1i8dQZufr6w4L9gmFduGhi+cQj8Om8Go71spedOWKEPPAhn9Hg0DZ/Te41RlUs5hX90yMLY3Tusc5fsJ+57dt3eiydV8OxXvFYG+QhhGHRn0aDg0N+7LTEeuUVPwb1IQTjimsyzoz27NlTk0vmaFWuV1551WOtWxcWxtyv4WMuGe0/cOAqVpijhqXzauasOY65a8S8qmIdOny0OZbMBe4laztCPzKvPNbZcwbvEyswJvTeYXLpvGpb2e7WyJhAv/BxHzOi2DnzVrFY7MPHfdFo5crVjvu5UQzL7FXM9l2ROVqzV8Ntn9orHiLRRr134Dggl84rHBA+RjHbx5gDS21fzF5hj5HNyOyVvr1GHrDOng22tY4l8wpdqb2i/chetX3oXhNlxGwffdhor4ZjoXPk0oLhdXslto/7nNorxgty8TEyu6C7bVjXwMN4NMJWIf9YpfJmbKz2bGnXuNDAWIoZY8GoiTmabUccFx1bGlk0UDRQNFA0UDRQNDAuNFCcsXHRzaWRY1UDI9kZ4y3B3/7N37jOdbUnnBozxpPIr33l71xXZ5ffjvjzJ56ovwkrTthYHa2lXUUDRQNFA0UDRQNFA1UNFGesqpHyf9HAKNIA27zeNmlyUmLiaXTfeewHr776qo8PiJ3TY+zVHxwMe9j1nH5nz/39d9/j3n77HW51e7szZ+zYsWPutz/+cb9l8dP/7VPunVeLNbdywohbQL5WRPtoZ4rASqXBJ15F48qaYa5e3dGwHSXGt3Xr9obYkBgPx5BLt7bE+LZt3+E2bQpb82I8hqVbW2J8ff2bHNtIUoRcGicV4ye2oX9TiB+I8XAMLI0/jPERA0KMW4rQvcbqxPiJTcnBQi6NGYxhEdfWJ7E0MR6OgaXxSDE++nH1mrB1KsZjWBo3EePbv/9g1rxFduL2WhHxHsifImRnXLcith3lYNE/GkMUwyQRQC6WxvnFsEhOwNhJEeN5RyLRx6lTp7LkIk6HuLpWdObs2Sysjo5O15foIx525eiLe0mqH9kql4PF/XLLltZjgoeHObonljRlr9jimiPXwOBQQ8xgrA9ItpGDtX59t+OTIrBSCTyIY0S2FIGlIQcx/qEh7FUaC92namzShzm2D7nY6tyKtm7Nt1e6/TeGia3KGTux346GY8UZGw29VGQsGmiiAfZW3z5xUpOz4TAB8qkimtzwdT98+HXjtyVL2/x+8cajw/8Dq7e31913193eIftvv/dfvQP2sQ9/2P+9+863+7/3vuNux5uxVg4SWCmDRPs0lmK4RLUjYKUMEvvcSf6QIgKiU9nbiGNbmFlEM4VFkoncIppHjrTOrlWKPofeZUxowH04E74R7E4ygBSBVYo+l6LPOk5IvKNJdvScfT98pJb8xf5v9nfKlGfd3LkLmp32x0mywjhMUSn6XNMQ2Qpz9DXt+RccnxSBlcqASKzkkqUhcU0zTLBSmXFL0edm2hs9x4szNnr6qkhaNDBMA7wZuyPjzRhZuzSpwDAg5/ybJ818FePhGG+fNKNYMz6weDq4qb/fO2STJtzqnS/LRMibsK9/9euuXZKBtMJKvRmjfZqdrBVWK8eP3/HUksQIKVrVvib5NotseprBqhkm+kq9GcNh0CQMrbA0UUqMr7evvyHgPsbDMeTiDUArIrtf6mm9YR0/HjKdxTDJOpjzlBrdp970kPUrB4s2pt6M7d6zz/VKxq+Y7NZGzYAZ4yPrIBkCU4RcmgEzxk82PfhShOyaATPGz1u4HCxkZ1y3IhLx5GDRP5oNNobJm7FcrFTJgIOHDjnGTooYzzska2WMn2yQOXLxVpLsla2I+ZqDRYKF3t6QVTCGiV3IwervH0j248WLF7OwuF/yhqYVgZWje97YpewVD+dy2rh5YDD5cAQ7lYNFdkLNUNisrWCl3ozxwAbZUgRW6kEkO1Vydkyg+9SDSPowx/YhV+rNGG/Zcu3VuXMh0UtMJ4z7nLET++1oOFacsdHQS0XGooEmGhjJMWMqMnFj5oTdOfn25Jsw/W35XjRQNFA0UDRQNFA0UDQwVjVQnLGx2rOlXeNCA6PBGSN+wWLEcMiIcSOGrFDRQNFA0UDRQNFA0UDRwHjXQHHGxvsIKO0f1RqwOmNaD4mtM8Qe6dYG6oJpXSDqd8CjNU3YJkPcFVtJjAyLtPNGbFHS5ANs+QNLkzywFQKsw4cP1x2x//gbH7gaI3ZXPanHvPmLGvbqx7EueixqohhxLa6p2w1r2xjC1i9khoc2GNE25DopRUHRAXxa04T4jmoNmOFYL7kZM2Y31AYLWKFWEAUutQgw/VLFwqmu6SvEedEf8GkdHQpvaj0ZavPAw8cIfrB0exu6q2GFWldLl61ws2bPtZ/5OmPNsLTOWAyrq6vbrWhb7TEMsIpF3ANy7dwV6owxfuHT8UuBVGL2qKFmFMNC91qDK2CF8UuB1BUr2hvmQgwLubRgMVtm4NNtOGzLSWNd9m3UIsNsGathhVpXFL6e8cKLDTWMqnIxtpFL28iDDfh0Oyvbk+DTOToc64rn0e2yYFSx2BoGls6rKhbXQXaNgQpYoW4WSXDSWC97nfZsDAXj0TnXRG9G1BkDS2NnqnIxr+gfLT4fsMIWKOqMMXZatdFjta12XV2hAC/3Dq7JODPas2fvVblCPaSqXIxj5oZub2O817DCPY1iz83aqHNh9ovzHHPXiHsHWHp/JP4MLL13mFyKxX1JC/DCX8WiLlUNK9w7DEttDPdLHRP0FXxqY6hLhe6R2chsjGKxHY37uVEMK9ir4Vg6F6q2j36vyRVqXTGvaKPaPrMxioW94mNkWI22r2ZjwDQyLB1z2OOGep2Xa/ZKscxead/GsNasqdqruO1D91obLNirMH7XrO1qqNdJv6CvRjtas1dHjx2zJvp+hk/nKPe5mO2Dz8hsn8Y4BxsT7Ci2CvnHKhVnbKz2bGnXuNAACwMSeGg2ss7ODW7t2s4G54jEA/PmL67r5MiRo56HQrZGQ1u2esdo167ddshRgBcsvXlWsY4ePeZ5tHAri6fZL853j3zwYe+A/fM3v+l+/1Of9t+XLF5ST+rxzW/+i5vy9HP162EouF53d1ickamPIGYtysu14OPaRrRPEywgMzy0wYh4ErAGJOvixo19ng+dGFWxMERg4XQY7d69x5HAg0W6UW9vv+fT4s1gcU0jDCBY9JPRnj37PI/2B3Em8B08eMjYHIkAFAujBQ9GzwjHCR4tfksMAHyaffC5aS+4J3851X7mF5lVLIpcg6XtJtMWfBqvRVIR+NRJgIePEdeGh8LVRvQDPOrsLVxUw9JFbxULnaB7FlBGOBI1rH12yC1avNxfUxczVaxDh2qJE7TILPFQ8NHHRgTbI78ulqpYZBCERxcgZKuDT+cVhc5/8eTTDQucKhZjGywW8kbbtu3wWMwJo+XLV3k+kjYYVbEsoYPqi3go+JirRlyLa+qCrYrFvEJ25rcR8sCHfEYszsHSOVrFYl7Bs2RJcC7IhgifZvnj4Q98Oq+qWMwreOhzI+6L8GlmvhUrVvmxQ78bVbEYL2Bp4p29e/d5LI1l6li33vNpxssqFk4lWJp4h3kFn96HcPzgIzumkWHpvHp66jQ3XRalzEP4NAMe9xGwuI4R9wj4dF7NnbvQzV8Q7ALtgKdfspmS7RIs2m/EQyH4dF5V7QJZK+HRWFIeBjBvud8Zmb1Sp62KRb+Dxf3ViH5ALs2eSaZD+NRxqGIdOVKzV9z3jRhrYGm84YYNNdunMa7PPjfD8TEy26f2ivkEFhlTjTiPXDqvqjaGOQqP3rfNXvFgw6inp2avdF5VscxeaeZH9ITuNR6MccI1W9k+7nfwqL1iXtFGfbhDP8NHvxsxtuAzwoGGh/FjxLiCR+NxGX/wqe17asqzXn773Vj7W5yxsdajpT3jSgO8gcpJbU/KagLqWxHZn3SB3YyXtN26kGnGxxPo9z70Lvf//cu3PIultufJGUk93v/u97gf/uCHyeB9foxcqexUtE9v3s3k4gm0Ph2O8WH8U0kY+B2GV592xrAwdLpYi/FwDLkuXw5vIGN8R44ey8bSJ5QxLHSaSt1tcumbqxjW0WPHG97ExXgMKxVAfuz4iYYFaTMsdK8LuBjf8RNgtU7nbnLpIjWGdeLEqWwsXaTGsI4ePdrgBMV4TK5UG1ksMXZShB7UkYzxI3cOFrrXBVwMi9IKOVjIpQ97Ylg4NHlYB506pTEs2oj8KeLNsi6eY/wXLl7Mk+vAQUcSklbEW6mcNu7cuSs5DrmP5GBxX0r1I29GsrAOHnI8jGhFYOXonntvyl6R0ClHrhx7RbKNnPsED2f0AU2ztoKVSuCBDU2VwACfNqaSV6GrXHulb/pi8tOHufbqypWXYxD1Y2+l7cNW5Yyd+sVH2ZfijI2yDiviFg2oBnjFT0KM0UDqjI0GeYuMRQNFA0UDRQNFA0UDRQPXWwPFGbveGi74RQPXUQPFGbuOyi3QRQNFA0UDRQNFA0UDRQPXWQPFGbvOCi7wRQPXUwMWM5a6xs0q+qxbC2Nvxp6fPtMRu5Qi9pRrgHeMn3iYUvS5phn0pQHRMX2Vos9BK+irFH12vn4gukgRMWMrV4VYthg/MZ45WCREWL8hxHXGsHbsqMV6xs7pMWJnOiWuU8/Z98GhLVmxJ8S7aHyj/V7/sh0tp42l6HNNa8QMEbeUIuL+NL4xxs827BzdE+tJgeVWhJ3KwSpFn4MW0dfJUyEJSjgTvq1atbYhVjKcafwGFoliWlGJGatp59+0UtKypUvdZ//oM61YyrmigaKB66CB4owFpRZnLOgC41acMecX+Zr9LGio8Rv6Ks5YccZ0VBRnrKaN02dqiVFUN7HvixYvc22SbCbGU5yxoBUcRBzFFHFvSsX/Ll/R3pC4phkmjrAmN4nx0YeLFi2LnWo4hlzFGWtQyZv6p7wZe1PqKz8uGri5GijbFG+u/svViwaKBooGigaKBooGigbejAaKM/ZmtFd+WzRwkzVQnLGb3AHl8kUDRQNFA0UDRQNFA0UDb0IDxRl7E8orPy0auNka8KntM7IpUpMklaaZffOpdMK0lxTNpDJPEVia3jcWM0btKS1O3AwTLI0/i/HRPq29EuPhGCmFU6mCSa9OGvkUUfQ1lSqYVNvUtkkRbUylCiYFeCoVNdcBK5Vyn/T9e6UOUTP5wEptk2Hry2Gp09YKK5Umn60vqRTZ4FOriOLMrejUabBal3Tg97RRaznFMEkxn4ulBYtjWPTjHqnbFOMxuVIp9zmP/ClC9jNnQ5HhGD9y52AheyqFPEVvc7CQK5W+n+LNeVhHk+n7aaPWuYrpgWOM59SWLtLRZ8l15Kg7IcXnY9e8dPlyFha1w1LjkPtIjlzcS1L9SBmQnFIm3C9zsLhnpgist85epbGwUzn6wl5prcZm7QBLbV+ML9teZdm+fHuVir2+Fnv18suvxJpWP0aNtlx7lbJ92KqceVu/+Cj7UpyxUdZhRdyiAdWAxYztFgNHAPvaji7HQtRoeOHLo55HCxZT6JZ94A1FNDds9Hy6kKhi4ZxxvR4pokk9ELC2ST2f3//U7/uiz1rPhQKmw4o+d3S57p7hRZ+3bttuzfHX4prqFFYLX7LghWf9ho313+3ctcfLNTC4pX4MHcCnDlMVCwcBni4pIE3hS/bgqw57KXzZ0dXgTBB7MndeSIrAwhOezq5E0ef+Ac+ntWiGFX0+e9bzUHzWCKOF7jd0h3Zv2jTo+bR+DMHoDUWfz50bhrVvXy1BAQVpjTZTqLmjq6EWWLToM0VmpRi1FX1e1xlkpR/g2bsv1Mmi0C7ynxVHCx7Fom4eutcg/8GhrTWsvaHQbbTocwWLhRPXG1b0uaOroZj6kqVtnk/nVVUuFvBgUfDYiFg0+HRe1Ys+SwB8FYsHC2BpHA7zCb4dO0NhdnQA3/ETJ+2Sngc+IxZY8Ki+fKHmji63XQpIt62MFH2u6It5RQIP2mCEPFxP5/uq9kjR5woW8wq5NHZm1+49HkuLPq9Zs87zqZNe1RfzCqzFWvR5z16PpUVzV7RdLfosDmwVi1pkYDUWfd7vsRhnRhSvhU9rPFWxcP5qWEvtZ455Bd/AQLgPcW+BTx9OGZY+KBhe9Pmgx2JeGoWiz2FecY8AT5177uXcn4xoBzwNxXzrRZ/DvFrXucHzaT09jzU/YOHAgUXRaKNo0eeuGpY65FUbQ7+Dxf3ViH5AX7t2B+du/foez6dOdBULRw8sdGTEHAVr564wr7h/wqfzaljR52M129fdEwpIb99Rs31aEwt7BpY6mFUbwxyFR+/bVvQZ22zUQ6FmbJ88LKxi0X540IdRvejz5kE75G0XfOowzZ+PvVpU5+F+B48mxmG9gb42CRb9DJ867tgrtX2MF3gYP0Z799bsVUPR501Xbd/BUEC6JPCoaawk8LCRU/4WDYwgDWBY75g4yfHk2AjHCQNy5eVQkJEAXxZaRpcuXfY8p06fsUP+iTKLVy3Ky00drMtXQjHiFW1gtdd/xxNdeLSg7PkLF3xAsb65+Pyffc47Y2p0Z82e62bOnFPH4m0OWBoYjDzIdVqcS87Dx7WNyO5GO42Q2WPJE2nDohiwETrwWJcUa01DBi6e2sGjTik6f+bZ6Q0FMgPWJYN37e1r3dJlIZsX/TIM6+JF30Z1lgich4+n70btqzvc0mVt9q/jySQ8fIwuXHzJY+2VNy+nz5y9ivWSsbkFC5c4slkavfzKcCzeYqH7XbvCggeDyvUuvhSwMLA4K1pMuyoX/GDp4v/M2XM1rIsBa926DX5xjjxGVSx0gu77+sJCz7AoxGvEAoJMovo0eBjWpUterqGhsDDGEYRP5xWLJLB0XlWxmFe0URcpLMbhY04YMSZY2OnT4GFYl2tYupg9d/4q1vmAxSKGa+ocrWJRBBgefXBw7vwFLxd/jVgseyyZV8OwrlzxsuNsGeEswId8RgODQx5L52gVi/aj0/Ubuu1n7vyFix7r7LmANTS0rYZ1KcyFYVgv17A6OwMW/QefOvabNg/4sfNSCyzGC+N5bUd4cMC48lhnw9tYFsvoS+doVS7mBFhr1nbW28i8gk/fVO7Zu9dj6bwyLJ1X02fMcgsXLQlYL13FOhPeeh48eKiGJfPKsHRecV9iLBrRDvi4XxjhvNBGnVd1LLExJKRYJQ8h0K/HEhuDA8G8Vay4vVrVkK2TN/Ngxe1VmO91LLFXw2yf2SuxJ9hR30aZo2ZjdF7Nmj3P8TEy26f2Kmb76lgyr7DHDfbq8lV7JQ9ozF6p7cPOogudVzz8WbZ8lYnld2vA02ivLnjdqxMX7FWwfava17plKXt1oWavjhwNRb6x61xT51V7O/Yq2D7mFTx8jBgL6J4HbEbBXoX5jq1i7IxVKm/GxmrPlnaNCw2UmLFx0c2lkUUDRQNFA0UDRQNFA2NUA8UZG6MdW5o1PjRQnLHx0c+llUUDRQNFA0UDRQNFA2NTA8UZG5v9Wlr1RjTw2jG38C/e697xmRdc2IiSALq82y34p8+4h995h5s8+W73a7/1P93j6467V4f97LLbM/+f3Gd/80H39ltvd/e+77fdl366zh0fzjjsl60OECT/tkmTW7H4c2zzSdVRIqkFsUUpIv6Cgq4pAkuDmGMJPHo29jbEhzXDBCuVdIP2DUk8RyusVHKLbdt2OI0NaYZFUVjd1hnjI3ZgcDDEmcR4OEYbU1g7du5yGu/WCku3iMb4Ng8Mui6JW4vxmFy6tTTGRzzCgMSsxHgMS7fOxPiIR9D4lxgPx9C9bm2J8bFVk3amCN0T+9iKiPPR7YfNeMFKJVigH4k3ShFYGjMY40cH8KUI2TW2KcaP3DlYyE5sTCtie1sOFv2jW2pjmMTT5GENJYP8Dx85kizmjAyMZ+LXWhHbx3LkAot41VbEVsocLObspk0DraB8MpocrMHBLcl+5IFfFtbQVrdtW+sxAVaqkDYN496bsldsecuRC3ulxFmaBgAAIABJREFU8YcxxWGncrB6enodnxSBpbYvxo9MGssY4+EYWLrNOsaHrvLtVdjWGcOiD7PtlWyDjWERl5prr1jLtCLGfc7YaYUxks8VZ2wk906R7cZp4Mpet+BvH3Z33zLB3ZnrjL12xM3+7H1u4l2/5f7+uZWus2OBe+zPfs297dbfcP+wLsRhOPeaOzLrs+6dt9ztfufrz7lV6zrcwh99zn1g0m3u3/+fTqec19pgS+CR+h1xGRq8H+Pnhk9QboqIf9B94M34wdIMiDFnjH3gz017oRlE/ThYKYNE+xYvWV7/TbMvYKWcHuLiKGKaIpJIkNCgFa1cuaYhEUAzXuRKYREzRrKMFIFVij6Xos86TgjK1/gzPWffSSjB2EkRCTyI0WxFPLDJwaIo9/oNIdFADHPHjt2ZWIsbEg3EsAaHtvjkL7FzeqwUfa5poxR9DqOCpEd8UsS4V9sX4y9Fn4NW0Nex460fhpUEHjV9lQQeYdyUb2NKA5fc/pU/dV96+G436ZZb3aQJ+c7Y5XVfce+55R73hQUhCYZ7dZ976hO3u8mPPOb2vHZVUZfXua8+OMHd//kFLnC+6vY9+Ql3560fdj/ZbYzXrliSA9yR8WaMRdhmyXwUuxJB4hu600/9+vsHXH/Gk3iwThw/7nbs2OE/n/2jz/gEHps3b/b/792zxz/pWiuB7TG5OAaWBrHH+GhfarFpWKlU7byZ0cxdsetxjMxs9EEr4umzZopqxksbU1g8SdUkDK2wzpwJoy3GxxNeDbiP8XAMuTQ7WYyPJ7OaTTPGY1jHjoXkKTE+MvL1SHayGA/H0D1pvlsRb6BynmTTRs0CFsPk7Z9m+YzxcAwszYgX4xvastW1tYVkMzEew+KNXCsiGxnXTBGyp9Lp799/MAsL2RnXrYg3ejly0T/0Uysi02keVl9DgpgYJlk9GTspYjzzhrwV8fAkS66N/cndBDg9OVjM2W7JlBqTj7fiOVi9vf3JfiTBQhZW36aG7JAxuS5evJil+96+tL2ipEiOXP39m5NvtHGccrDWdnQ6PikCK+WM8aYa2VIEVqp8yubN2Ks0FuNeM3PGrs0DmVx7pUmJYli8Ycu1V5pkJ4bFuM+Zt7HfjoZj5c3YaOilIuN108DrZ6a7z0ye4CZOfr/748eedF/+tdsy34y94rr+7gE38R3/060ICX+cc6+7k9M/7e645RH32K6ak/VK51fdQ7fc5b60vIHRvX5yhvuDiRPcR3/UeiHSqvEjOWaMLTx3Tr7dO2ATb5kQ/fvkz3/RqnnlXNFA0UDRQNFA0UDRQNHAmNZAccbGdPeWxqU08PrZee5rf/j3bubgOff6KxvdN3890xl77bCb8ju3ukkf+ZnbW3mx9auNj7r333K7+8Ii0nW/5g4/9btu0oSPuifqr8quSvWrXveNd09wd34+1PRIyVs9P5KdMfbMP/fMs+5b//wv/vN3f/sV94XPfb7+/3e//W138MDBapPK/0UDRQNFA0UDRQNFA0UD40YDxRkbN11dGprUwLU4Y78act/+tQnujj+YKVsPa1d4bfeP3Udvuc3916nHnHO/ckPf+nU3ceIfulnVXWOv7XaPfWiCm/zJZ5KiDQ4Ouu4NG4Z9VratdLffNtGx/cPo2PETvhiybm1gfzpxUEbUk6FgsiZToH7JwkVLG2oFUQ8EPuoUGVHPROPP2PJXxWLLAVhaFNSwtD4Kta606Ch1msDSOiTUGwJLk0icOFmTS7cb0r5ly0MNLmSuYlEHCSyNzUIH8Gl9FGrAaD0vas3Ag26N0Dl10o5KrRW283ksqQ1GzBhxdkb0SxWL7R7IRQFiI2rTwEdNIiNqAi1ZssL+9XF08PAxMiy2YxlRuLOKxZh4cc4CY4liUacJuXQ7ILVpwNJaQavXrPPxerqVtCoX/GBpUgT61GNJnbyOji6PpTGCVSzGL7onMY0R27zg060ztTpjyxpqg1WxqOuEXNukqDjj1mNJDS7qjBFHqPOqioVcYGkwPfXP4NMaXBT8nv3ivIbaYMOwLtWw2IJkRIyox5KtsWx14po6r6pYnEN23cbLHIVPtwdxLY8lNfeqWCS/QfZOKdzK9lqPJTW42IoJls6rYVhXrrjFS5Y1FGZHT/BpDS62C3osmVdVLPrl/2fvTZzsSq7zTv8pjSaA7qZEiqJJiRY1lsQZUZZtUU1LpKSZkMOmhpI8pBWekceOoa3FHku0IxxDi9pszZDqJva9G1sBVUChsNYKVBUKQBVQ2ApbYSvs3QB6QU788uFUfvdWvpsJk90qAHkiKvBw3/e+e/LczHsy781zDjGjWpyWLVmeS+pmTUwc932nSS9qycGlCQPoV3BpDa4zZ856vXSM1vWiFiAxu/v299pl9PXrPJfU4Jo6d95z6bgyLh1XjNkdUmsQPDitwUWdMeyldfKMS8cV9xItUE47wGndLAoCw6Xjyri05h73S61lybiqc5Ekh3Gb8ldwxfyVbpfmHo5eOq7M91X9VY/r7g7bUrnu6KW+j/uQ55JxZf5Kkz1t3brd8WcSfF+IG270fTKu0Il7sAljFL3U9zGu0KvSbvMxUieve1fNXz32feqv6Cctf8W8pCWzvk/Glfd9KX91p+Wv2D5sMuuvpP4kWwvVX1FXkDZqfJj5K01UNMslvo9+j/7PqpTF2LN6ZUu7ntwCT7QYG3H/6ScWuJe/unlOAo73z/+1++UFL7pf+g6xHu+50W9+1i1c+JtuSz1Tx/vn3WuvvugWvfrdRl254f/ql77sfvnVL875e/Uf/oJbtODFSiY7CoJu3LTVaXHHJUtXuqXLVs2eh0kEGHV4TDYJktVMXUxIwF28GAoywqNcTNTB7OwOjuXQoRHPNTJyePacXV3dHqeLhNdeX+ZIBmBy7tx5j9GFELFb6KUxSTgxzqmLBHSinSboDEaTelDUFi7aasI+dHAaT1PnujR92WO2bQvJM8gCRwIPLQxLMWy4Tp8ORZKXLV9d0YvrAoaFqAnxN+ilkz+K6oLTeJo6F8WrwZAEwYRJMFz79oXJ3959BzyOzI4mYNDfBIcP16bNIYHD+MRxz0UhUBNi/MBNyOKFYpzw6YIZDH8mx09MeozGStFeMOPjYVFFQhe4dAJS58Im6M5ExaS3b8Bz6UJo9ZoNnotsfCZ1LmLBOF9nV1jkDgwMeS7NxLhu/Zsep+OqzkUmSLhUL/oaOB1XFO5Ff/qVSZ2LWDC4tnaEyR9jAJyOq02btnocE3CTOhdjDi69tsQLgdOYjs1btnsc49CkzsWkCd1pg8nI6GHPpWO0o6PTc9EOkzoX7Uev9RvCJIuizOB0jHZ27vQ4HVd1Lq4LXGvXvWGn8/dFcP0DoRA01wb9ue4mdS76C1yrVoei6PQrcH19IQsm9w5wk5JZss7FQy4wK1ettdM5xhU4HjyYMN7BMU5MjEvH1V//9RKPMwzjEJzG3u7Zu99jOI8J1x4cD7JMuF9yTzGhHWD4vQk6opeOKx6ggdNx5bnEx5w8RdKVrZW4VOKtsL3GG3IfBMck3aTur7juYLi/mpD0Bb00wykPHMBpNtOly6q+j8ydYHSBRr+FS2O4Ortavk/HFb5K/ZX5Pl1UHRpucTG+TPBnnFPHVcuPBn9FplMweh/i4Ql6aawqfhbcWYmXneOvLk17jCah4v6D7TWLK/4fLuYDJstqftT8lRYaJzsoevXKAxkWXnBx3U3q/opFGBh9AEu/gktj8eh/4MjGaILu/D2rUhZjz+qVLe16cgs8yWLs/WPuTz7XejN2q3YmezP2a0t5y/G+G//W51pvxuYCW2/GvhwWIzWq5H958puT2p7A/FRaawKOdUHS7uQkJzh/Pkz82uHgSqX3PXnyVOWG28SVCoimfersmrhSafJxwDypTgmLCN6aNQmLwlQSBn5/5sxU5Q1kjJM3Z2cTCR0C1/0YxewxJiW6oJr9ovYBvdgO2yQ8PddJdzssXPq0PoYjJXoOF7YnLrFJrly5mkybzu/RizewTcKT+JzxAZe+EY5xkl5dF6AxDMfgSrWRyT64lKD79ZmZRhiT/hwudNe3uDFSbJDDRT/USX2MizcEeVznkiUKSGyTY3v6IP26SXjDk6uXLrxjnLyxyeHiDa5OnmNcvM3J4eK+pA/aYly8ScviOnc+WWoCrhzbc+9N+Svu4TnjMcdf4adyuHgIpA/HYvbiGFwp34cPTSX6Ma4c35frr/TNfkx/SmXk+ivedDUJSZF+UP4KX5XTd5r0mc/flcXYfL46RbcP1wJPshh7dNkt/5WPuEW/+B03FY0ZW+y+1sEE9pG7vPRX3eIFr7rvzgG2YsZe+e3wJuJJGzyfY8aetC0FXyxQLFAsUCxQLFAsUCzwvFmgLMaetyte2tveAk+yGHPvuqE//LRb+LF/6fZUXoyQTfHX3csv/Jz788nWKu3dwT90n3nh4+5f9VSAs9kUf/5Pw7aU9srFvymLsbhdytFigWKBYoFigWKBYoFigafBAmUx9jRcpaLjh2OBJ1qMOfeg9/fcZ174hPudjpvukWn43pRb8uWX3MKf/RN3/L3HBx/0uT/41AL3t7/e4W4GoJt6/cvuoy983n17woBGkv/v01T0OdaqUvQ5WIXCl5pYJHwTPpWiz8EWxA9oHFb4JnwirkTj6cI31U/YnlppTTJ0cMRRODklcB1J1OAiJkJjT9pxwqUxMTEcdf/ApaQUfW5ZqBR9Dj2lo6OrksAjfBM+laLPwRal6HOwBfccTfQSvgmfdu/e77Z2hLje8E31E1ya1KP6bet/xJWVmDHnStHnWO8ox54tCzQtxu5ucL+1eIF75UvfdedtW+L7l9y6f/ojbuEPf8H93tJu19+7zf1/X/9p98qCn3T/ds9tsc377tKar7hPvvAx9+o3lrldfb1u+1993X1u0Yvup76xxylSfpT1sSzGgpnI8KjJOsI31U/c+O/erWdTqWIIbNbg5+q34X84h9QCimyKHdt2hB+1+YReKa6yGAvGK4uxli3KYiz0CRKQaDbF8E34VBZjwRZlMdayBTFZ3H9TUhZjwULYqyzGgj2+30/lzdj3a8Hy+2fHAk+6GKPlb590m/74N9zPf+plt2jBK+6zX/i6+7M90+7dOVZ5253c+Mfuq5//tPuhBS+6H/7xX3S/8+09bnoucM4vmw6UbYpN1infFQsUCxQLFAsUCxQLFAvMbwuUxdj8vj5Fu2KBRguUxVijecqXxQLFAsUCxQLFAsUCxQLz2gJlMTavL09Rrlig2QJst3tl8UvNIOd86ujUFjhS8ZJWPCWkodbClO3wcKXS+5JWOZVaGf4cLtqXSpFtXKnU9nBpwcx2bSSdsBZRjeGol3XlSqhzFcNwjHouSa6ZG4507SmBK5XCGIzWfGvHCY5i3E1iRaWbMHwHF4WRm4T06hSHTQllDO7caU5H74s3Z/Rp9Eql3L9161aldl87/eCi5ESTzMzMZJVhgIu07k3iCy5ntlELPMc4fZHkDC5sr3XgYlzcm9A/JWBSpQB8MeIsrquVWnexc6NXTgkM6l6lygr4or85elGUeaa5DIMvUp/BxZhN2ZX7SAqDbbiXpK4jBadz/AL3y2vXmksnwJWTgr3FFeqhxa4jWwtz9MInpHzfo0ePsuz1JP4KziZ5En+VSm3/ZP7qnSa1/DXM8VfY/uE7zVwt35e+l9NXU76Pfp8zbhsbN4+/LIuxeXxximrFAikLWMyY1mUaHDzk+voGK5MSgveJpzDh5gdGi1xOTFA8tKNSsPjgwRGPU4dd58KhwzU8HAo8Uz8MrhNStPHQoVGPU8e4bHm1UDOOs8UVCmae8sVDO9xxKVjMucCp06B9mmABncHQBpNW8dCOSgHTkZExj9PJy5atnRUuJlJwDQ0NG5WvvUPcEr83IX4HnNYnqnNR5wjM4OBB+5kvXo29tJjv2NhRj6NWiwnB0NpGrj9c/f2hqC0OCy4twEuRTnDUkDGhoC1Ft02Y1M/luuC5SIRhQsFWcFprjpg4zqmxeGD4M6F2G5jevqDrsWPHPYY6eCbGpYuQOhc2wfZatJwaNOC0Rs627RRu7XAspEzqXFwrMHulSPbx45OeS+srtQq3dlTGVZ2LPgQXBXxNKLQNrl6wmAQeOkGvczGu4NrVs9eofE0+cFqwuFW4tRpvWOdizMG1szsUzT158rTXi39NOBc4fahR52JcofubG7fYz7w+4LRI6+49FBrvqDw8qHPRfjCdXbtmubA5OC1Qvs8XGu+ojKs6F+MKLo0b5b4IjnubCW2k7+gYrXPRX+DSuFH6FTitddTXP+hx+kCpzsUDA7g0bpT+Du7YsQlTyxe5BqdFho1LxxUFfrWwNeMQnBZSPjRMEe4Op+OKewQ4HVfcS7T4PO0AMzZ2bFYvkuTApeNqYOCgx+m4got7nQmFl+E6fPioHXKHx45521Ms2YT7IDhdkLe4gr/iWoHh/mrCdUAvHaPcn8HpuIJLfZ/5K71v41vg0jEa830rVq51/Jngfzhf1fdR7LqjMhYoAA1Ox1XdXzFGwRw6pP7qjOfSepD4CHC0w6TuY+L+6qy3Pb7ABP8PV5Pv4+EYGOYVJowr2jgmXFxncFpwm76F/U24xmDoPyb0K7gocG1C/wOn46ok8GhZpyTwsF5S/i0WmEcWYDL+8sJFlSfxOAjeLOibkR07dzkSXJjwdgKMPsm8fv26nzCos7569brHUUTUZMfOHrdzZ+BqPR2uct2+fdtz3ZRJsHHpW5b169+sTCz4Dr3Amty6dcdz6YIQxwWOc5t0d+92tNMEnetctI1JkToybABO39gwwe3a0W1UvhgzGF388RaBiZFOeNCxzrWrZ5/r7ApcXJcYF3pVuW54HG8FTMhO1dm10/7rKLoJF38m6AWXFobFOYNRLrIMrlwVJhatp+lVLt4WwTV58ozRu5mZ1psrfZPEQoZJME++Tep6GZdmLbS3YMq1/0C/YxGlT0rrXLQD2zPpNDEufSvV2zfgubQ4aYyLNuokpfVG7WplXPUPDD3mCiUq6lz0IbhGZNJ48+Ztb3sdVz09e92y5asrRb7bcWkbGe/glIssj5xTx1Wdi+/ADA6FiZ5x8a/J8MhYkotxhe67esLCDn04p3IdHjviuXRc1fXibRDXmomXiXHp5JykG+jfxMW4gutA74BR+evHOZWLSTh9R8dCXS/6C/2ZRaBJ660hb8vCwv7EiVNeryauhw/f8Vx79x0wKv8WlnPSZ01OnT7juXQsmF46rniIskUerIEHx7g04S0C9opx6bjivsT9yYR2wHX9eniLR3FvuHRcmV46rjzXrvDgIM512dteuWL+igcf+qCF697SK7x5i/kr46JfmXh/lfB99A/aqOPK/JX6vvUbNjr+TILvU3/V8n26UDUuHaP4Y3Qzifk+9EGvqu+b62Na/kp931wfAxf9Xh/uxXwfDyty/ZVy0We4RjoWetr4K/W/9AXaqLs0YlwrV63z+pu9nrV/y5uxZ+2KlvY8VxYoMWPP1eUujS0WKBYoFigWKBYoFnjGLFAWY8/YBS3Neb4sUBZjz9f1Lq0tFigWKBYoFigWKBZ4tixQFmPP1vUsrXnOLEA8wiuLFidbPT5xohJzFfsBSS10D3gMw7GJiclkgVxwcKUSeLCXnliylMCVSrrBvv/xieMpKq+XbuGM/eDE5MlKbEgMwzFiRnQrUAxHHM2x8Ty9UlwnT52pxJnEzscx7MVW0SY5cvSY01iwdli4iMdpktNnzjq2kqUErlRtmjNnp5JFkzkPtteYgti5iU1JFWDmd+ilW2diXGwhPXIkr42Xpi/HKGaPnTx12vX3h615s1/UPqAX28SaBBuASwm6X7gYYgZj+EuXLmdxofvkyVMxitljJMDI0uvouI+ZnP1h5APbvHK5NH42QuWmL1/2fSf2nR6jP+tWX/3OPrPNMEevo8cm3KnTZ+1n0X9JrpLDRYyVbqmNkRFjlsNFzFrqOr719ttZXMRwacxgTC+29TFuUwKXxgjH8Gy3zGkj8YLEgDYJfiqH6xD+ajjPX6V8HzppLGM7/dBLt5bGcN73ZfgYbH/v3r0YxewxrqHGRc5+UfuAXrolsfa1/y/xqBoXGcNwDK47idqf+KqcvtPuHPP9eFmMzfcrVPQrFmiwADEaLy1c1IBofbW9s7sSMxb7ATd8AmlTQrB9146w170dHq5UFqjVa9Y79oKnBK6UQypFn4MVsdf0dPMkfvOWDkdQdErg0v38MTxxXlu2hoD7GIZjcJ0+M9Xua3+8t2+wEnDfDlyKPrcsU4o+hx5CUoRS9LmVPZexlpJS9LlloVL0OfSUXbv2um3bdoQDbT7Rv1IP1ohxJulUSuC6cjXEPcfwJYFHyyolgUesd5RjxQJ/wxYgKJcEHikhCcDo4ZCJKoYnSLxfshzFMBwbHjlcySDYDgdXajG2b3+v27M3BLY3cWkQewxH+3KeWqKXJv6IcZFBTLMRxjAc27FjV/INFJmhNKNjOy70Sr/NGnckbEgJXKm03Dxh1yD5dpxwaQbMGI43f4NDIdtWDMMxuAjybhISfGjmrnZYbK+Z1GI43nBq1soYhmPopZkmY7jJk6ez3iTClUrfzVtJDd6Pnc/0OnM2ZJ6L4bAB50wJT5Z5g9kkZDbL4UL3sSMhS16M8/yFi1lcXB+uU5Pwxi5HL/pN6i0I2UbpOymhP6fetJMdL0uvoWFH5tAmoTxEDteuXXvcwEDISBrj5CFdDhf3pdQbId6yZXEdGqlkTozpBVeO7Q8eGk36K3Y35Ojl/ZVk6ovphZ/K4SIJiyZiiXFxDK6U7yN7ILqlBK7UTg58HzZLSctfNZfKICtitr9KlPDgDW6uv9JkX7F24Kty+k7st0/DsfJm7Gm4SkXHYoE2FigxY20MUw4XCxQLFAsUCxQLFAsUCzwFFiiLsafgIhUViwXaWaAsxtpZphwvFigWKBYoFigWKBYoFpj/FiiLsfl/jYqGxQJtLcB2FLYpai0UAsF55a/b+g709jticUzY9gDm9p2wZYFkILv37HdvS00x49J4Ler49PYK18OHc7jYBggXi0WTGBe1fLZtD3vKOY/XS5JPGBf6maA3uAcPH9ohH9xL7JKJcXFeE9qGXjduhlpBs1wPQm0a4k60xtDDd97x56tzUfj2qux1j3FR4FK5uC7ozp8J1w+9rly9Zod8QDOY+6LX4OBwpTjxO+++O5frwQPPdUlixgiO9lxybXt273XUGjMhQcocvR5zaSHaGBeFSvfu7a0kWalz0edooxaPvXvvnj+n9jkKqCa5Hj70RYdJTGMS42IrENtgdSzU9aKfoNdJqaVGkDs4kheYsN00l+vEZEgYcO+tt+ZwsTVv46atjn5lUteLvo1e2sZZLhlXx8YnPE7HaJ3L2gjWhLEJDk4TtvhxzhQXug8Mhq1yMS4SASS53nnH25RtwSbY3OsliQZOnz6T5OIac32olWbCvQMu+obJ8ROTvu80tREu+uCh4bAlmD5a5yKWkjbqfQgMfyaMK7iGDoaC8bNckrSARC2eS8a7cWnyImIzqVNnwr0DnCZAoN4WXHrviHHt29db2XoLvs5Fzad2XDquuMdRi89klkvu29Q75J6p/sr0Ui7u45qs4Yn9lYyrOb7PfIzoRf+ljXofauev8FkmXHf0Vz9q/kpr4rH9HJz2OfwxupnwHZi6j0GvPN8XauI1+SutIRfzV1zDmL9Svcxfaf0zdER/7XMDg4eq/irm+x77BfWjsz5GxgK+SgvNm92elX/LYuxZuZKlHc+lBSyBB/EsJsRh9ezeVykUSYDsps1h4k0GNjCaTY/YAXAnToT4DZwFOF0kbNpc5SKeA0x/f3DExBDBpVkEKcAL7vLlK6aqL+K4ZOnK2f9PT1/xGHXEZJyC6+jRkMmOxRJcmrWO9oEzQWcw6vDIOgWGpAcmLJbAaQFLbvzKRcwUGHVSTDZJIqGTLGJWwGn8EUkFlOv6zIzHUCjZhOx6YJSLvfZwaSHoOhfZ3MDgsE0oHguXToyIpQOnC6EVK9e6115fZj/zhXHrXMQYwdUrhXSJcwBH1kOTLVs7PU6LpoLhz+Ts1DmPURuOjo55zGnJNLe1o8WlhXrrXMT9YHuKw5oQNwHu1KlQoJrgcfSfkeK6dS5im8CorowF/q/Z4SgoDE4nIHUushWC0YLI9FtwOq7eeHOz++vXllZi8epcly5Ney4t1s54AqeFs0mowzk1G2SdizEHRhPvsMgDp3FRFHMHNy3ZIOtcnAfdN7yx2Uzv9QGn4727e4/noh0mdS7GFefDtibEj4HTLJgUjwWn46rOxbgCQwFZE+6L4FhImxDvRt/hupvUuegvcNEXTehX4HThSF8GpzGCdS7u0WAYIyaMK3A8LDBhjIHTbJDGpeOKwr1r1r5hP/PjEJzGH3EfgktjBLlHgNNxBYZ7igntAKPxssQigdNxxaIXnI6rOhcLVTB6T0NHbM/9zoT7IDhNBtHiCv6K6w6GdpkcHjvq9ToxGbJ6sogDd/VaKMKMX6j4vkvTHqMxYmS75Jws1E146AiXjivumfyZ4H/AaNIYMhHCpWMBfwYO/2ZS14vso2C0aDkPR+DS7Jnc18HpuKr7BdoPRh9OMq6w/YjEqeH/wWlW2joX9zswzCtMGFfopX2O6wxOkz3VuViMg6H/mNCv4Kr2uZbv03FVEni0LFYSeFjPKf8WC8wjC1C9Pie1PUkA9MYWawIBx6ROTwmThbNT51Mwz/WDSu+LXqmAaNqnC4R2CsKlT2FjOCb7qeQQ/A4nyZPQJsE55XCh19tv32+i8hNInWC1A8OVSmHMoo1JSErgIvC+SVjI8vYiJXDpxDKGZ5KBbinB9qnEIiwqcrjQi4Vtk5B4RCek7bBw6cQyhuNNo06wYhiOwZVq47Vr17LGLbqTcKJJmHhxzpSgu066YngSUuRwcX10khrjYgGRy6UPaGImRqw/AAAgAElEQVRcTAhzbE9/TpUV4P6boxcPG1JlBXh7l8NFqvBTspiJtZH7SA4XqftT15G3UnlcU5UHRzG94MqxPffLlL/ibWGOXvgrfQgV0ws/lcM1cfyE4y8lcKV8HzrpwrsdJ1z6ZjSG874vkaWW32H7+/fDDpAYFw//cv1Viuv8+YuVBwKx83GMNqZ8H74qp++0O8d8P17ejM33K1T0KxZosADbKz66+KUGRPmqWKBYoFigWKBYoFigWKBYYL5aoCzG5uuVKXoVC2RYoCzGMoxUIMUCxQLFAsUCxQLFAsUC89QCZTE2Ty9MUatYIMcCFjOWwpaiz8FC7E9Pbbujpsm27SH2JPy6+ok9+KltZD09+ypxLFWG8D/0SnGx1z63iGYp+ux8TKQmKQnWrn7C9hqHVf229T9i+DT2JIbhGFwa7xTD7dm738ddxb7TY3ARG9MkpehzsA4xKhq/E74Jn44eG/exM+FI/BOJMjTeNIZiOzPXKCXEi2msZAxPwp0criVLVrhNm7bGKGaPsR01h6sUfW6ZjC3wOfZatXqd4y8lcKW21RO72NnVnaLyeqW2wu/sxl+FuMt2pPgrjXmN4UrR55hVPvhjZTH2wdu4nKFY4AOzQFmMBdOS6EAzXYVvqp9wlGUx5tzmLR2OoOiUYK9UXAmB4kxeUwLX6URsA1nGmFSnhImFJlOI4QlQL4uxlmVYSGrCiJi9jhwZz5qUksCDbJxNQoIQrndKuD6aSCiGn5xsJQyIfafHymKsZY2yGAu9ggVPqsB6WYwFe5XFWLDFh/mpLMY+TGuXcxUL/IAtULYp/oANWuiKBYoFigWKBYoFigWKBT5EC5TF2Ido7HKqYoEftAXKYuwHbdHCVyxQLFAsUCxQLFAsUCzw4VmgLMY+PFuXMxUL/MAtwHa7nGyK7BMnpXOTkIo3lfqa35O2O8UFDq5Hjx41ndLXHNO6Y+3AcKVSBaNTaj+86ZVKFUxa7hwu6rOk0uSTMj2Hi9owSa6bt9y16zPtzDR7HC7SSDcJ8Wlaq6YdFq5UCmOKfabi3eCHK5XCmK23OVzY/u7dUMw3pj/FVnO40IsHG01CSv5cLi0yHOO8efNmMm06v0OvVBu5B4BLCbqTir1JOFcOFynfU6UAKCadw4VeqXIHFNDN5aL/NMm9e29V6iq1w6LXLSneHMNR/DZXL63vFeNivOZwMWYpZ9AkFP3N4eK+lLqO3Cuz/EIml9a0atcG9Er5GLYWZuk1k+bCT+Vw4aty/VXK93l/NZNxL796LRl/luv7fqD+6uo1984777a7hP44fSvXXz18+E4jF/0+p+80kszjL8tibB5fnKJasUDKAhYzpjVZKJ5IDIY6f+IytOgohSzBaHIAK4h8Vor5Do+Mepw6RuIyND4IJwYXRXdNrJDjSSlGPTJ62OOuXQ8Tx2XLV7ulUvSZCRBcGttCjR5iT7S4J+cCd1UmJbRP44PQGQxtMKEOGVwU5jTBBuC0uCdcmqwBpwLm0PCI/cxNTZ3ziQAoXGwydqTFpQ6bhBvKxXWBS4uhWiIAbTdJIMBp3aQ6F4sNMINDoRgq8V20kWKtJtQmAqd1k1atXu9el6LPd+7cecx10H7m65rBpfzYDi6tm0ShXXC6cADDnwmOFIwmWKBmDxgtwLt9e4sLfUzqXNiEmDHiG0xIwAHu3PkLdsgHyHNOnaDXuaYfF0Tef6Bv9ncUSAXHNTahYDJcOq7qXBRuBaNFTSdPnvJcOq4onE7clU6E61yMK7h2S+FsxhU4rTVHshlwuuCvczHmwIA1YVyB0zpsnAsc49CkzkVxZXTfKEkk0AecFvPFBnDpJLfORfvBaPFuioODw24m+/f3e5yOqzoX1wUuimCbcF8EpwW3KTpL3+G6m9S56C9waQwq/QochXhNKBwMTh9q1LlYAIPZJsWo6e/giKsz4X4ATiecxqXjiqLPa9e9aT/z49BzyT1tZGTMc+m4GhxqjcfbMq64L2lCINoBF0lOTCiAjl46rtAVnI4ruNTHUOMPzJGjoeA2XNie+52JcfFAx6TOxXWHi/urCfcO9KK/mFDcHhwP00xa/ioU3L7y2F8dHgv+iuLucGmdSgoaw0V/N6kXfcb/gBk9HHwA4wkurVvGfR2cjquWvwqxsYxfMFpImXpfcGkx6lnfJzUD6/6K9sOFPUy4/2B7rS2Z4/vMX2lRZsYVelHQ3oTrzDm1YHzdX9FfwFR832N/pfG/9D9wOq5K0eeWpUvRZ+tx5d9igXlkAW5uLy9c5JiUm3Az5CbGU1sTJhU7doRJCk+HwVy9etUgfjHCTV2fBuMEwWk2JwKidfLEGwUwupjhyT9cuogzLp5ym6xes8GxKDDhu7lctzwXTtSEc4HTtxm0TydP6AxGJ3C0Db0uXbpsVN4G4LCJCQHfLApMsCUYdTTY/ntLllcmA0w8W1zhjQ2JRTQzI2+Z6lxcP/TSiQVPv8HpRKx7195KZkaepoPhz4S3DHDpQphJQIsrvBlhMr18+Sr7mXvw4OEcLhZEcLE4Mbl+vcWlb1l2797vOrZ1uYcPHxoswnXXc42Ph0LTTEDQSxdeex9njEQfk3obeRuE7Q8eHDaIm5lpcelbFjLYMSHQt4R1Lopj00adDNBvwelk80DvgNva0VkZV3O53vJcOqFiwdHiCpNN+sSSpSsauejb6EUWRxPGFVy6IBwcPORxOkbrejGu4GKCYwJHiysUuz50aMTjdFzVuTgPuu/YGe4nxqWLS2zAOZu4GFdcHxLAmGBzznlDJtRMGuHSQuZ1vRhXcO3b12tU/r4ITu9Dhw6N+r7TxEV/gYuslyb0qxZXmJyPT0x6vTQhUF0vxgQPK1gEmtDfwekCmodNtFHHlXHpuFq+Yk0lmyL4FldYQPMQocUVHmgYl44r7kv0RRPaAU4XDRcuXvRcOq7Mx+i4gksTZXDfgksX4zzAYdzG/VV4k9/yVz2mlr/udS58AG3UMWo+Rt++d3btTPorFlwtrjBGA1fwV2vWvuH4M6Fvo1fK9wV/Fbjwoehm0uSv1IaBS/zVjp6a72v5q6rva/krCs6b4P/RX33fzp09NX811/eZvzp/4ZJR+esMV8Vf+SyPwY+av1I/av5KHyjH/NXy5at935k94TP2obwZe8YuaGnO82UBnEHONsXnyyqltcUCxQLFAsUCxQLFAsUCT4cFymLs6bhORctigagFymIsapZysFigWKBYoFigWKBYoFjgqbBAWYw9FZepKFksELcA211eWbQ4/qUcJR5Mt63JV7MfCdQmtiglbKdhj31K4Eol3WBrmMZJteOEK5V0g/bRzpTApdtrYnhiXzQ2JIbhGLFUut0phiPOJ1VQmN+hV4qL2JyJiRCzEjufcenWvxiO7YIaBxDDGJduXY3hzp4958YnQhxeDGNcMzfCtrgYbmrqfCWmL4bhGLbX7S4xHHEuGh8Yw3AM2+tWoBjuwoVL7pjE5cQwxqXbg2I4ruOQxPnFMMaVaiNbbtE/JejONqImQe8cLnTXWLMYJ9uKc7i4PhqPFOO6dm0mm2vqXIgZjHFdvnKlEgMZw3CM/qzbhmM4tmdmtXHiRCUeKcZFLFcOF1tJUzi2iqUw6MC9JHUd2T6Xw8X9kntdk8Cl8aftsMePp/0VyY5y9GKLtcYfxs6Jn8rhIjZM48NiXByDK+X70Em3fzdxpRI7ed93PO37Wv4qbG+MnZNrmOP7aOM9CTmIcRGXmuuvdKtvjAtfldN3Yr99Go6VxdjTcJWKjsUCbSzAfvmXFi5q8204vL2zuxIbEL4Jn4hLICg3JQTIk8wgJXCR8apJVq9Z71auWtcE8d/BpXETsR+Uos/BKthrerp54l2KPlftlVowE7uliVjCr6ufsD3JV5qEWCSSYKQELk2yE8OPjh7JGrfonnrwUYo+BwuTpOhAb4hlC9+ET5Z4JxyJfyIeifjFJrk0PZ11HZcsWVGJGYtx8mCBvpOSjo6uSixbDH/jZivJSuw7PUbMmCbU0e/sMzGPJJFIybbtO5P+ioVdThtL0edgbWyvcYrhm/CpFH0OtvgwP5XF2Idp7XKuYoEfsAUIfiWBR0qYSGpSgRiep2+9fYOxryrHyNJHEHxK4Eotxvbs2ZecDHAeuFJPB2mfZmlqpx9cOPImYdKa8+Zie+eOSgB5jJPJcs4TPfTSYPQY19gYGatC5sQYhmNwkdCiSfr7BytJXdph4Uq9NSJDV//AUDuK2eNwaRa72S/kA29w+vvTXNieJ69NwgIrhwu9zp8Pge0xTt4IaybIGIZjcPGmsEnGxo66zs4QvN8OC5dmTozhTp06mzVu0T315gK9OWdK0D31hoC3XTlcXJ/UQvjixelsLs1QGGsHb7voOymhP6felpAAIauNA2QVbF6gM15zuEhU1Nc30Kg+b+xyuEj+ollwY6R37t7N4uJ+qZllY1y8/cix/dDQcNJfsbshp428UdGsgjG98FM5XLv37HP8pQSulO9Dp5ydCXCldnIMj+CvQjKjdvphe03EEsNxDXN8H3ppZs4Y1+HDZBfO81cs1JuklaArPW6bOObzd2UxNp+vTtGtWCBhgRIzljBQ+bpYoFigWKBYoFigWKBYYB5boCzG5vHFKaoVC6QsUBZjKQuV74sFigWKBYoFigWKBYoF5q8FymJs/l6bolmxQNIC1Ptgm6JuYyBxA3+a8KKvf7BSY4j4KzCaMILPe/f1VrjYVgJOtwiy3am/P9QrMi4NwKV+EFxa7yXGxdaDrh3ds+3kPJwvxqW6xriooUQ7TWJc2Am9dDsgvJxTY9LYWtHbG7YCteOiyLTW5IlxsXWSGlUmXBfOx5+J6ZXiYlvLAanJFOOiHbRxejoUtTW9tJ9Qz4vaYCZNXJr4gQcA6K5cFJmlVpRuzam30fTSZA0xLrZ1wqX9t87F9cD2Wsw3xsW2TmJ1UlzYS7c8so2Vc2qtviNHJ7K5NGFAjOvgwRG3Zcv2yriqt9HspW2McREgj/7YxKTOxXdgdAufcfGvCVsxc7jQfehg2H6EnTincpEEJ4eL60MxYJMY15mz55JcXGO42BplYlz0DROSD9F3muwFF32Qfm1Cf6eNykVSF9qo94667Y1Lt4nHuChk3o5LxxWxWYxdkxgX95F2XDoWuJdoHTvj0nstteOyuHoH3KBslcMm2KLKdcPbnvOYmL1UL7bAaU28GBdJStBLuWJ+wfurgbn+SvWi3+Zw4a/4M6EPoX/MX6V8HwXDddtzjIu2oZfW7rI2ap/z/kq2rrbjot9r/T7zC8rFNcz1Vyku7nO5/irm+/Ta4qvQ/1mVshh7Vq9saddzYQFL4MEkymTP3gOue9eeyiKBQGdNPkDhRzDqDEgUAE4zKe3b3+txWtSyznXx0rTH9IozIIYI3NFjIU6CyQ3n1OxwS5etckuWrjTVHRMSMBo4TwwRXDph41zgdJFA+8CZoDMY2mBCbAoYnWSxgANHQVKTOhcxU2D27guTICbJBEQPSiFd4kzAafwRDkT1IoAazO49oaAsk3cwOgEhzgwc2QVNNm/ZXuGauXHDY3p27zWIYxIMly5MWRDCpbFMK1auda+9vmz2d8SZgNnVE7jItAbX/gNhMUm8IDiNZWJyDk4XuWD4MzlzdspjmFyYMEEFo7FMJDuAC31M6lzYBNt3dYWJEXF+4DRrKIV74dKiv3UuFodgeqTdjAVwuhCicC84nTTUuc5fuOgxWkiXfgtOx9WGNzb5BB4ai1fnunjxkufSQrqMK3CauZKEOuilGRzrXIw5MGBNGFfgNC5qx87dHqdF0etcl69c9bpveGOzUflFHrijEhe1s3uP56IdJnUuSzSBbU2On5j0eul47+nZ57l0XNW5GFe0UR8wcF8Ep3FRFNul7+hDgToX/QUu+qIJ/QqcJkFh8QdOsy7WuW7eujWHi3EFbnj4sNH7CTBcZ85MzR4zLo3zWbZsVaXwMOMQnMbxch+BSzMlMq7BkZDDBIxOcGkHGI0/YrEGTscVBazB6bgCoz6G5CZg9J6GjtheH1ZwHwSniSXqXFx3MBqXaolrNIMu9xZwOq7qXPRHMHp/PHLkmG/jxMQJM41f2IPTccU9kz8T/A8YXbwE3xcynOLPwOHfTOo+hvOA2X8gJHpBH/TXJD4sVMERR2lS5wr+Ktxruf9ge42fw//DpYWg61zc78AwrzBhXKFXvc+B47qb1H0f/QWMxt3Rr+DSeG/6HzgdV99bssLrb9zP2r9lMfasXdHSnufKAnfu3M1Kbc9kV518zEg8fdXJZwzDsVOnz1beIrTDwZVK78tEUCdwTVz6dDiGo306qY9hOIZe+iQwhmPhcOrU6dhXlWMjo4crT8orXz7+DwsgFkgpQa+3EqmCp86dr0yK2nHCpU9rY7jJyZOO0gIpgYt+1iRMlnSC1Q4Lly7YYjjeNuSUTsD2OumKcfGgIIcLvXRiGeNiQaMPPWIYjsGlC7YYjglLKtmBcaXayEMHzpkSdNeJZQx/9er1LC5014lSjIvJdY5eXB99qBLj4u1MLpc+VIlxcW3oOymhP7O4bhIWSVl6nTxVWfzFOBmvOVyM2RSO+0gKgw5MhFPX8f6DB1lc3C/1YU+sjbzpyLF9jr/iTVpOG1mQ6oOjmF74qRwuHi7qA8YYF8fgSvk+dNLFchOXvjWM4XJ9H7bXt/0xLq5hju+jjSkuHprpIj52Po7BlfJ9rTI46XHb7hzz/XhZjM33K1T0KxZosABbZj66+KUGRPmqWKBYoFigWKBYoFigWKBYYL5aoCzG5uuVKXoVC2RYoCzGMoxUIMUCxQLFAsUCxQLFAsUC89QCZTE2Ty9MUatYIMcCFjOWwpaiz8FC7E9PbeFjvzqB8ilhD35qSxrxLhoT044TvVJc7NsnDiolcJWiz87Hq2hMTDu7Ya9UratS9DlYj4LVGqcYvgmfSBaCXVPC9dG4ohh+crIVVxL7To8RU6lxsPqdfWabGeM2JaXoc8tCpehz6CmrVq9z/KWEfp/aVk8sKAWpUwKXJsaJ4YnPpFB2Suj3GpsXw5eizzGrfPDHymLsg7dxOUOxwAdmgbIYC6YlacL2jEK6OLeyGHNu85YOR1B0SrDX+fMXGmEkZ2HymhK4TkuCghieAHUm1SlhYpGKeWOSXxZjLUsSmK/JJ2L2PXJkPGsBVRZjLesR+0efTgmJQEj20SSXpqezuJYsWeE2bdraROVjKXP06ujociTjaJKyGAvWKYuxYAv61/WZG+FA5NPu3fuzHx5euXo1whAOlQQeLVv8rWCSuZ92dHW5r37lN+Z+UY4UCxQLfKAWKNsUP1DzFvJigWKBYoFigWKBYoFigQ/UAuXN2Adq3kJeLPDBWqAsxj5Y+xb2YoFigWKBYoFigWKBYoEP0gJlMfZBWrdwFwt8wBagGGRONkVqNqVSipOKN5Xem+bARe2clMD16NGjRtj169eTcVIQwJVKFUz7tDZVuxPDldrPn8tFqvB33nm33an8cbhuSM2sdmD00kK0MRyptEnznZIcLgp2ptKmcx5qmaVKAVD4NEuvGzfcgwcPG9UnjX4OFyndU+mQ2Y6aw0UbU2maGWu5XKkYD66j1u5rZxD0uicFi2O4e/fe8tco9p0eQ3ewTYI9OWdK0F1rX8Xw2CCHC71S24YpoJvLlSrDgF45tkcv+nWTkKo9V6/bCS7GGOM2JYxZLbYbw3MfyeGijbdu345RzB4jrXoOV46PgStVXoET53BxD8/Xq9lf4adyuK7hr65fn7VNuw9wpXzfrVu3/kb8VSpNfq7vo40p3/eD9Ff0+5xx2+6azPfjZTE2369Q0e+5twCTh3/9L/9P98+/9rU5f7/91d90ixa8WKl/FCv6TKHKlatC4HGs6PPY2FFHEWYtThsr+lwvfNmu6DNcFJY1iRV9/t6S5e717y03SNuiz3AdkYKysaLPtG/FyjWzXNy4ScRRL/oMl8YaxYo+w7V8ReDCEcAVK/qsxSpjRZ9XrV5f4SKAGq560Wf0Uq5Y0efVa6pcTATh0mQK1DSDa2BwaNYWsaLPy5av8sV7DcQECK560We4+qSgd6zo85q1G9yy5asrEzu4+DOhdhtc+yV2Jlb0ed36jZ5LF9Z1Liv6rAWRY0WfKUyMXjrRqnNR/Be91Iaxos/ESMClSVbqXNSlgmtnd4812xcrB6fjav2GjT6JhC6G61wUp4Wra0cI8o8Vfd62rcvjdJJb56JGGrprUppY0efOzm7PlSr6TLwehatNSNbBObVmINcG/VNFn9Fr0+YQdxUr+kyfhCtV9BmuNzeGYtSxos/ohf6pos9wcZ1MqJdEGzXujr6MXlqrq257HlzBtXbtG0bl60uB06LPjDG4tB6kcenCl3g9cCaxos/ch8BoHatY0WfucdyfTGgH56wWfR72XFovKlb02XOJj4kVfT54cNjbXmsSxoo+w6X+Klr0+fCY1ytV9Lnl+0Kh5mjR56PjnitV9BlfVfFXbYo+Y3stph4r+rxyVbWANOMX29eLPsM1duSoXSIXK/rc3l/NLfrMNTCJFX1eVfN93O/Qq170Gb20gDTxueC06HPd93EfBlMv+gzX0NAhU8v3P3A6ruj3jNtnVcpi7Fm9sqVdz5QFtm7Z4ja++eacv1XLV7jFH1noeMNkcoZikqdOV56CMyndKEHft2/f9hi9cV66dMmtWfuGu3btmlG5s4+LH+uT6zfe3OL4M2GiwPmmps7ZIf8EC64rV67MHpuaahVS1ifXOF0mKiY8ia5zXb161eul2QE5FzidpNA+nSCiMxjaYELb0EsTUmCDFld4QszEe/2GMNm8d++ex2BbE5wUDoLfmpw/3+Li6aLJ5s3bKlxsLeU3p0+fMYjPcIVeegwdwd28Gd6EkSSDxYoJC/U618zMjG8jRZ1NWHyD40m4ydp1b1QmFsYFzgTniV5Mtk2YzLS4wlP8jm1dbu26Nytvl8AoF+eGSxfV9Dkw6GzS2bXLc6GPSZ0Lm2D7/oFBg/jCweA0WxgTb9qpb9DqXDyhRi+dWLB4AacLr109+zxO3y7N5brtMSykTZhktbjCuNreucPrT78yqXMxRtFLswMynsAxJkwOHOj3OB2jdS7GHFxMCk14WAFOnzb39w95nL4RqnNxntdeX1pZ2LGobHGF8T508JDnoh0mdS7az/XRBwCMUXCXL1+2nzkW7eiv46rOxbiiD5LIx4T7Ijiup8ng4EFve667yVyutz1X146QoY5+BU4LVB87Nu710jFa5+KNK3ppRlXGFThdqE4cP+G59K2Xcd2//8BU9Ul3ePhhAr7OxdjHXvoQwrh0XK1fv7GS4IZ2gON+YcI9Dy4dV9ynwOm44n65SZKZ8DAFjN5r+R3jNs4V3trCpf6K697iOm9qeR3RS8do8H1hXL3x5mb35kb1V3N9H/0DLn04EvN9+Cr1V02+Tx+OmL/ScYVO6GYS81fog17aT86di/m+HH91zdteF+gx38c1rPq+lr9S38e4Qi8tph38VRhXJGJSf9Xk+3iIaGL+SscVi2D6zrMqZTH2rF7Z0q7nwgIlZuy5uMylkcUCxQLFAsUCxQLFAs+oBcpi7Bm9sKVZz4cFymLs+bjOpZXFAsUCxQLFAsUCxQLPpgXKYuzZvK6lVc+JBdj28MqixcnWTp48XYkfiP2AwF7dMx/DcIzYgZOnwha7dji4Ukk3jhw55ohVSwlcqcBjtl9oLEI7TrgIvG+S06fPusnJU00Q/92hQyOV7aCxHxADQuxKStBLt8DF8GfPnnMnToTthzEMx+DSLTEx3PHjJ9zIyOHYV5VjcOn2sMqXj/8zde68I9YnJXDpVskYnlgeja+KYTiG7XUrUAzHdpccLvTS7U4xrosXp5OFofkdXLr1L8bFFijdFhnDGFeqjdPTV7LGLUWtdbte7Jzojf4pQXfdthTDX712PYuL66Pb4mJc16/fyObSuLIYF/WM6DspoT/rNu4Ynq2OOfYirok4xyZhvOZwMWZTOLZ/pjDowr1EY9Ri+rGtMYeL+yX3zSaBK8f2cOl2uhgnSUpy9MJfnUr4K/xUDhexWxq/FdOLY3ClfB86aRxeE1cqsdOpJ/BXPMBtklzfRxt1m2qM0/u+TH91V7Zsx7jo9zl9J/bbp+FYWYw9DVep6Fgs0MYCTJJfWriozbfh8PbO7kosRfgmfCKbV06hUGJ6unaEBAWBofoJrlTWQhJSaKB2lSH8D65URr9S9LlqL42xC9+ET6Xoc7AF/YvFSpMMHRxxFE5OCVwaFxfD79m7Pyv+AS6SiTTJ6OiRrHFbij63rHj02HhWIgDiMzXGLnYNWKxxjVJSij63LEQMUE4Shm3bdyb9FQu7HNt3dnU7TfQTu1b4qRyuUvQ5WA97laLPwR7f76eyGPt+LVh+XyzwN2gBAohfzliMDQwecgcTT4N5+kbGw5QMDg07JqYpgSu1GNvVs8d1S8B9O064Uk8HaR8ZnVICF468SXjyPzCQ5tra0ek0EUCMc2RkzPVncKFXimv08JFKQofY+TgGlybFiOF6e/vd9s6QoCCGMS5NGBHDjR055shwmRL0uiTJFGJ4Mgb29qa5sD1B/U0yPnE8iwu9ps5daKLyb9gOZOgF1+kzIWlMjHT08Jgj6UlK4Eq9IeDpOriUoDtvyJvk9OmpLC50T71V5U1Qjl5ca65Tk1y4cCmb69ixZi6yetJ3UkJ/PnL0WCOMN4lZbewbdGNjzVzXZ2ayuDo7d7oDB/oa9SJ5Ro5eJGzh/tQkd+7ezeLifqnZIWOcJKnIsT1cKX/F7oacNpJM52DCX+Gncri6d+12/KUErpTvQydN9NOOE67UTo6Dh57EX4WEOrFzcg1zfB963brdXPqBvqUJiGLn4xhcNyRRVQyHr8rpO7HfPg3HymLsabhKRcdigTYWKDFjbQxTDhcLFAsUCxQLFAsUCxQLPAUWKIuxp+AiFRWLBdpZoCngksYAACAASURBVCzG2lmmHC8WKBYoFigWKBYoFigWmP8WKIux+X+NiobFAm0tYNsUNZ6K4G3+NOEF2w60oDBb/sBoMC+f2S6gXBybwzV4sLK9IsYFB1zU2DGJcbHlQ+sCNXHVdUUv3brI1kndXkH76200vbTWmemlXGwhoXCqiXHBZwIX2yZ0O2CMiyLJulUjxsW5sZdysZWS8+n1oN4SRT9N2AoDRvUyritXQl2rGBfFsHWbYhOXJn6IcR0+fNRvB9StOe30YsuZSYyL7VxsXUtxYfvJybDtjr5WtxexW2zPS3Fhe7avmRiXbg8aHz/uuXRctWujJriJcY2MjPptijlcsTaqXicmT/q+08TFd8Q/aZIVONBfudjGiC10LNTbCBfbFDWY3rh0vJMIIIeL66MFcmNctuUxpRdcJAUyiXFR64q+02Qv+gt9UOP1GIfYQttIUpdUG41Li0UbF/3fZPpya8tjrI3af9mmqIXsY1zcR9rppVzclzSRTIyLotU5XNwvdTsg7cBe2ka2YWP7WBv1erCtW7fCG5f6gLv35vor66vKhU9ga71JjIs6brSR9pvYvVy52FKv2+pjXHDApbXhjEvbjU65/koTO8W4sJVuhUdns4W1B72w/Y2boQ5YjMv7vv6076ONbIc1sXu5tpG+1dcf/FVML/BwpXxf2abYsvTfMoPH/t3R1eW++pXfiH1VjhULFAt8gBawBB46yerZvc8HLGt2OIJtNfkAGccIatbYnNHRMR/ErAV+9+w94HGa0a3OdeHiJY/hhmpCrAU4nRjt3dfrcRoztGTpSsefCQVV0Wvf/hATQQwRXDox2n+gz+O0GCbtA2eCznDRBhNiU8AMD4/aIT/BBndeCp3Wua5cvea5du/ZN/s7ssARjK6LNhZKcJER0KTOxXUBo4VumVCjl3LxGRwZFE3qXBR1BaNxDGSUhKu3NzhBYhPAaea0FSvXuNdeX2bUPsshGF0cU4gTrv1yPVjUg9NYJtNLsy6C4c+EAqFw7dnba4ccC1UwmlWMZAfgNOtinQubYPvOzu7ANdzi0iyYTD7gIh7HpM5FJkgw3bv2GsQxFsBpJsatHV0ep+OqzkXhU7h27AxxJfRbcDquKKpKAVP6lUmdi0UrXJosh/EEThcvJCgAR1ZFkzoXYw4MyXdMSGQBTpON7Nixy+MuXpo2mMeAM2FcofsGKYp+bHzC44gdNNnZ3eO5dPFd14v2o5fGz5GlDdzhw0eMyo8VcDqu6lxcFzBcJxPui+B0IdTV1e37DtfdpM5Ff4GLvmhCvwKncVF79x7wOF3I17mYsMJFAVwTxhU4jYvingZOMxIal44rig6vWROKPjMOwenDNibAcGkhXcY1OB1XYBi7JrQDjMbeDg0Ney4dV9279nicjqs6FwtouIhLM2Giz7jlfmfCfRDctevX7ZA/n+rFdQejD6JGHieuoVi2ye49+z1Os5nW9SJzJ1yanIUxCo4HLiZcW3DTl8O4WrFyrePPBP8DhmtnwniCS+MN8WfgtGC43TPtdzzwArN3X/BXx8Zb/mr0cEjig58Fh981qXPRfjDYw4Rxhe21z+H/wWkG0jqX+SvmFSaMK9qoC2auM1yaNbTORbFvMMSKm9Cv4NL4OfofOB1X31uywutvv3vW/i1vxp61K1ra81xZIDe1PZNddfIxI/HUKpVRjt/x1D+VKhgcXKn0vjgsncDF9DIufUIZw9E+ndTHMMalT0BjOBYOOWnyefLH08UmYQGkE5l2WOyVShV8dupcXpr845MulSoYh6qT1Ca9bt9pDtQ+d+5CXsr945OOJ+1NwsSAVOApwfakKW8SJiz6oKIdFtszUWgSJlK6OGuHhYu07k0yNXWu8kCgHRYunVjGcCyOwKUE3XViGcNfvXoti4uHGTpRinExuc7S68Sk04cqMS4WEHlcJysPVWJcTC71bVAMwzHSvuviL4a7dft2ll5w6eIvxkWijJw28qCAshRNwn0kh4v7Uuo63n/wII/r5KnKw56YfrypzLE9b2hT/oo3KjltZEGqD45ievnU9hljiIch+oAxxsUx9Er5PnTSxXITl75tiuGwVSo5D7/D9vpmN8b1JP5K3/7FuHwplpyyLhm+D1+V03diejwNx8pi7Gm4SkXHYoE2FmAh8NHFL7X5thwuFigWKBYoFigWKBYoFigWmM8WKIux+Xx1im7FAgkLlMVYwkDl62KBYoFigWKBYoFigWKBeWyBshibxxenqFYskLKAxYylcKXoc7AQ+9Opd9MkxERs276jCeK/Yw++xhDFftDTs891bEtzoVeKi/g3jYmJnY9jcJWiz87HvmzeEmJimuyV2vJEfAQxECnB9hqHFcOXos/BKlwfjVEK34RPJDHBrikhLkuT5cTwpehzsEpHR5fTWKDwTfhE/acc23O/3CVxl4EhfCpFn4MtiIki3jMl2F6ToMTwO7vxV+makfir1HZsruG2TH9Vij7HrsZ/37GyGPvvs1v5VbHAvLBAWYyFy0CAumYHDN9UP+HcymLMuc1bOhxB0SnBXiSmaBKCyrdsDQkK2mHhShVEJkhfkx2042JioUkeYjgm+WUx1rIMC8lUjOCRI63kAzFb6jESePTsDglP9Dv7TMISrndKymKsZaFL09NZ9lqyZIXbtGlro1mJ/cuxfVmMtcxIhskce61avc7xlxK4NGtlDF8WY8Eq2CsV/1sSeLTsVbIphn5TPhULzBsL3L17LytmjIxeqcQJBBynnnTRcM8lKW3bGQOuR48etfvaH+dNUOptEEC4UgHRtI8nrymBK+UoWeTyRDglJE9IBVd7rhtpLjIjprgoZaDZ0NrpB1cqScnMjRtJBwg/XATeNwkJPnL1SgV9U3ZgJsNel69cdZryOaYfSRFoZ0poY+rpM2MNXErApJK63L59O5mYg/PAlWoj3+fqRbrrJkHvHC6SitCvm+Stt9/O4uL6cJ2a5O2372dy3XRatiLGSRvpOymhP5MgqUkYFzn2goux2ySM1xyuq1evJnHcR3K40Ct1HUmclOMXuF/mcE1fvtxkBv8dXCl/xT08R68cf4WfyuF6En+V8n05emGMHH9182/AX6HXO++823gtn8T3PXznnUYuFms547aRZB5/Wd6MzeOLU1QrFkhZoMSMpSxUvi8WKBYoFigWKBYoFigWmL8WKIux+XttimbFAkkLlMVY0kQFUCxQLFAsUCxQLFAsUCwwby1QFmPz9tIUxYoF0hZgG8BLCxdVauuMHj7i63HolhFicLSAKXWQqNmhxWOp0cXebWpGmVAME5xuQatzXbs+4zFHj47bz3ztGri0yDD1xODS7TMUMF26bNXs7ygiCkYLZlJbC67Jk2dmcSRIAKfByFu3dlZijdAZjBaLPve4wO/x46GOFUWlwel2SYoFa6wRW0rAYFsT6mERtzQ2FgrdUqQTHDEbJhS01cQP1CYCo/E7FCKljWNjobgnMTfgdGsGgdXKxTYqMMMjh+10vmYTXCNyjBpT4LTO1Oo1G9zr31s++zvi6MDwZ0JtLbgOHgrHqJkERot3b9++0+ulW+rqXBQ1hUuTNVDnCJwWGaaQ86bN1bi+OhfbQ7G9FuGmLhw4LYba9biIsdZJq3Ox/QW9DvQOWLN9XSJwWgy1u3u3x+m4qnNdvdaK1aHAuQk168DpuKJvEXdFvzKpc9Ef0Wv3nlAElppQ4LSwKgkYwOl2zDoXYw6MJmtgXIHTouIkiAGn46rOxbhCd66RCTW0wGnNKgrdwqXjqs5F+8HslCLZ1PYCp3WmevsGPE7HVZ2LcQUX19yEQu7gqI1oQvIU+o7GqNS56C+MMxIfmdCvPNfJ03bIDT4uiEx/NKlzsb0VLk2wwLgCd0JqMFEAHf0ZJybGpeOK++W69W8axI9DzyW1+Q4fbhUx1iLDxqVbQtFLC27TDnBaSJmC3uil42pk9LDH6biiT2tyIbaywqXFzuHC9tzvTKx+FNfPBB/DPdiE6w4X91cTKxasteAOj7V8n46rOf7qse/jvm9y6nSrIL3Wghs7Mtf3rVy11vFnwjhBL03Yc/bslLeX+j78GTgtko0/RjcTxi8YrbuJPthe65GRgAacFslu+avAZf4Ke5hgJ2xfuR6PfZ/WReQabpZERdzvOF/F9z32V8eOheth/krrItZ9H1t14ar4vout4vbEq5rQ/8DpuCoxYy3rlJgx6yXl32KBeWQBW4zpYolkCyw6NAaGG6xOBph4g1FnfWn6ir/x35AYG5wmON7AmXCD1eyATDbqXDgpnIhOnijsCk7jVlasXOuWL19t1P47MFoEdmamxaWxBpcutbg4twnt08kAOsOljt8mpXoMG4DTpB5MwnTxShHVOhc2x7lpQVEyGILTuJXOrl0Vp8t1AaNJMYh1w15aTJtJGTiNNena0VPhooAnGP5MbIKrC06cWosrTHjWb9hYWYwRy1XnunWrNVkeHw8TlytXWly6KOnu3uMnnBpbVuciToo26uIVxw1OJ0+7evZ6Lo0tm8t1x9u+v3/Qmu2Ipalz7d6z/zHX/VlcnYsFLXrh/E2uXbvmuXRcscACp+NqLtddjxkcHDYqvxgBp+Oqs2unX9Boke86F/2R8/UPDM1yMa7AMSZMensHPU4n7HUuxhxcB3qDveAApwuv/oFDj7nCuKpzMa5YjOn9hHHV4grFrocODnsuHVdzud72izoWgSbYCZwu4njYgP46rupcXBcWF7rg5PqB0/vQ4OCQ7zsaD1bnYlzBRVZVE/ponevYsVbCE/q2SZ2LMcFChYx3JowrcDpxHZ+Y9G3UcWVcDx48tJ+6pUtXug0bNs3+H3yLKywIuY9gL85jYlw6rrZs2e64P5nQDnA6CbaHYTpGzcdoAWHul7p4xb5w6eKS/3PP1Nhe49JxxeJCkzFx3Vtc06aq56WNOq5i/qrl+0I225jvo3/ApQ8KL15s+T4dVytXrXP8mZjvU3816/uk8HvM95F9Uv0V56GNymX+ano6XNvgr8IYxe66eI35PuyE7bmeJoErxGzWfV/MXzGusJc+FDJ/peOqq+b7zF9VfV/Lx5w+Ex6YBH8V4izLYqx11cpizHpv+bdYYB5ZgJtuKfo8jy5IUaVYoFigWKBYoFigWKBY4AksULYpPoGxCrRYYL5ZoCzG5tsVKfoUCxQLFAsUCxQLFAsUC+RboCzG8m1VkMUC884CbN94ZdHipF5sW9E97LEfkCqYeKCUsL9e4zna4eFKpaMnZk1jzZq4UunoaZ9u82viSqV9J/bl1KkQG9KOi9gJFsRNQkyO7vlvh8VeKS5iCIjtSwlcuj0shp+cPJms08Xv4NKtkjEuYquI2UoJXLrdKYa/cOGSIx4kJdhet3nF8MSi5XChl27Xi3ERI6cxPjEMx+DSbXExHNdxdHQs9lXlGFypNl6+fDVr3KK7bj+rnOjxf9Cbc6YE3XW7UwxPLGkOF9dHYwZjXDMzN7O5NLYpxkVcH30nJfRnYs6ahG19WW08ecppbFOMk/Gaw0VtvRSOLW8pDDpwL0ldx7fv38/i4n6p8YexNrJNLcf2Of6K9P05bWQbOXGbTYKfyuEiXou/lMCV8n3opFvc23HClSp5kuv7Wv7q7Xan8se5hjm+D70oX9EkbGPM9VcavhDjpN/n9J3Yb5+GY2Ux9jRcpaJjsUAbC1jMWJuvZw+zD5yiyE3CAoV94CkhxoDYpZTAlVpArV6zvrIHvx0nXKkFVCn6HKyHvYhfa5JS9DlYB3tNHJ8MByKfhg6O+DiiyFeVQ3BpQH/ly8f/IYkEcVcpgUsT0MTwo6NHssYtMVAaOB/jKkWfg1UoYn6gtz8ciHwixodrlBLiqUho0iSl6HOwDvGIKX9FLFOO7Tu7uh0FlpsEP5XDVYo+Bytir1Rttt2791fi4sKvq5/g0oQ61W9b/ysxYy07lJixWO8ox4oF/oYtwJPZlxcuSmrR1z/khoZCUoHYD3j6plngYhiO9Q8cdAODh9p9PXscrtRibGd3TyX72eyPax/gSj0dpH20MyVwpd5AkXygry8kO2jHuXlzR/JND1nSejO40Cv11ohEBpr1r51ecF2/HpIpxHD79/e6jo6u2FeVY3Cl3s6QvW3/gebJJqRwpd6CkE1sf2LiChe2P5l4G8eb1xwu9Do7FZKgVAzw+D9kC0tNqK2NvD1uEq6jZutsh0Wv1FtV3iyBSwm6p97snTp1NosL3Q8NjzSekifsOXpxfTSra4yUN6+5XKmFMG8k6DspoT+nFsK8aczS60B/JRtd7Nxkx8vhYszu2xcSnsS4SLCQw9XbO1BJXBPjImNiDhf3y4MHm/sEyR1ybN/Xl/ZXJEbJ0YsEOINDzf4KP5XDtWPnLsdfSuBK+T500uQ87Tjh0sRIMZz3fX1p34ftNUFMjItrmOP70EszYMa4hofz/ZUmYolx0e9z+k7st0/DsfJm7Gm4SkXHYoE2FigxY20MUw4XCxQLFAsUCxQLFAsUCzwFFiiLsafgIhUViwXaWaAsxtpZphwvFigWKBYoFigWKBYoFpj/FiiLsfl/jYqGxQJtLUBiBbYp6hY+9tLzp9sk2MbAdjmTd99912O0Tgy/YTtdjAu8CbEzBw+F7SgxLjjg0u0VnItzKBdFe6krZdLEpbrGuGifbsU0Ls5pYnrdkfpkMa7hkdHK1hZsCU+da3vnjkpB7BgXcTq6rTPGha7YS+taGZdeD+KD2CZq0sR19WrYpsh1QHflopDuDimQ28RFkgiTGBdbC/v7hypB63V7WRsvXQpFbWNcBMjDhT4mMS5srwlbYlwUiWXraooL22vBV+PSOEViynK5tPgxHOivXKOHx1xn584svbSNMS62aqI/9jWJ2auvf7CSZCXGRWKeHC501/izGBfbFFNcXBdsqoVojYtrYMI2xRwu+o1ueYxxnT171tF3muyFXnBp8XnGDnZVvdimmKuX1teLcZE8pR2XJoNgzPZKLFuMa+bGzbZcOha4L+l1NC7uPSa3bt/J4mLbnRafx77YS7nwV+1sr3rBpXX/YlzU6MNe6Gxi/V652HKuRetjXNRxa8el/YQadlrHLsaFPnDR90zsXq5c6IRuJsZFG0yM6623w/WIcWEr3YpJ+80WyoXtb90KtbtiXFzDQQlDaMdFG+kbJjEuEv0MDOb5qxs3bxqV7zPor9eWfo/+z6qUxdizemVLu54LC1gCDyrWm1ColKBlzehGgCwB/CZk9gKjcT7chMExgTXB8YCbvhyKTra4QswFhTbB7JO4lbGxo56Lf01IWgBOC00vWbrSEZhrQsFLMFoElgkR52QCa8J+dXBk3jOhfeBM0BmMOs9j4xMec0gWk8SsgNNClHUuYqbA6MJxYuKEL6LJJNeEgH9wOrGvc129dt1jNED9+PFWwVfdq89nuHRiX+e6PjPjMRqgfmLypG+jJh8gNgEuzYK5fMUa99rry0x1vxAE0yULNDLKYdN9+0NMEo4anMYymV43pcgsGP5MyBwGF/3AhMkIGM14uHnLdo/ThWmdi+xhFDDVwrA8IACnWdFIwsA5NVNincuK2mqBX8YCOK6xCQVa4dJxVeeyhA47doZkOUxIwOm4Wrd+o0/gobF4dS4y+XE+vR7EMIHTDKRMUMCR7dGkzsWYA0OxaZMjR455LhbSJiTnAaeFZ+tcFHcl+QhFw03QB5zGWJHkBy7NSFjnov1gtPjt+Phxz6WLBMYKOB1XdS7GVZ2L+yK4YSnoTZ+pF7+tc1nhXvqPCf0KnD6I2r3ngD+nZuurczHJRC/GiAnjCpw+PGKMgdPFt3Fp8eZly1e71Ws2GJUfh+B0As1EGS7NcEo/Ajdz48bsb+t60Q4wGnvLJB+cjivuN+B0XNW5WIyD4aGPCVzYnvudCdcWnBb5rnNx3cHoPc381fhE8Ffcn8FdvhIeHtW5WNiD0fjP0cOtJDhHj4Xi9jwoBKdFq1esXOv4M8H/gNkrMXxjR2K+74DH6biye6ZxMX7holC9Cfqg/8joETvk78XgdFzVuWg/GPVX3H+wvfY5/D84zfRZ5+J+B0bvj4wr9BqSWDyuMziuu0mdi/4CRn0f/QoufchI/wN3RrJglgQeLauWBB7Wu8q/xQLzyAIEROektueGl0oxy5M5nTC2ayZJAHTy3A4Hlz7RjeFIV5uT4hsufaoY46J9OmGIYTgGlz61jOFYaBw/ESYMMQzHcEapZCBMrnTy0Y4LvVJcp89MJbP+wQ/Xnbt3253KH2cSo4vSdmC4UoHaLGh04dLEpU9AYzgmXvqmJIbhGLZPpWpnga2TtXZctFEngzEcEy8WCimB68qVa40wFpP6VLwdGK5UG5ksgksJuutbyRiexVEOF7qn0nKTQj6Hi+vDBLlJZmZuZHKdcOfOXWii8tdGJ5HtwPTnqakwsYzheBiW00a4zsgkNcZFoowcLsbs+HhYNMS4eGuUw8V9KXUdeeORxXVisrKQjOkFV47tj2f4K96a5OjFwyldlMb0wk/lcPFAUB8Kxrg4BlfK96ETuqUELn1DFMPj+7BZSrD92/KWLYZ/En9F2YMm4eFfKkstv6eNKd9Hv8/pO036zOfvypux+Xx1im7FAgkLlJixhIHK18UCxQLFAsUCxQLFAsUC89gCZTE2jy9OUa1YIGWBshhLWah8XyxQLFAsUCxQLFAsUCwwfy1QFmPz99oUzYoFkhZgm0xOnTHiN3T/eIyYrXvE66SEeJid3XtSMM+lgdSxH6xb94ZbszbEP8QwHEOv1NZC2qfxNU1cdxNb+CxWrh2HHX/9e8uT29v27DngKLqdEtqY2ipHnAMFUVMCV6ro89aO7Y74k5TApfF0MTzxAh3b0jXL4Ept1yJeQGOIYufjGLbXmMQYjhiVrR2dsa8qx9Artc2HgHuK96YELo09ieGJD9JYyRiGY3BpTFcMR403cClBd2JjmuTo0YksLnTX2L8YJ9uTcvTi+mjygRjXyZNnMrm6KrEnMS7iRuk7KaE/90m8Uwx//vz5LL06tu2oxDvFuCj6nGOv5ctXuy1bQvxZjIs4nxyu7dt3VuJzY1xsK87hIsaHIr9NcvPmzSzbE7uY8lckeMjRi/g2jXeK6YefyuFau26D4y8lcKV8HzpprG87Trg0qUcMt6uH+LZ0/TP6vcb5xbi4hp2Z/ipV9Hnv3t5sf5Uq+oyvyhm3sTY9DcfKYuxpuEpFx2KBNhawBB5tvp49zGJAg2Znv5APLHYIpE0JN30WdymBK+WQVq9Z71auWpei8nqlFmO0TxM6tCNFr9RiDEe5bXs6cxMB0akFVE/PPsdkLCXoleIisUnOQgWu1GJs85aOrAUBXKnF2P4D/U6THbRrK1zEvTUJyQdyJkbYnpjDJiGTV05xZfRKxTaQRZSA9JTAlSo8zEKGJBgpgUuTYsTwZNgElxJ016QYMfyRI+NZXOjesztkQY1xEfeXoxfXRzOuxbgmJ09ncm2vJJ+IcZGtk76TEvqzJoyI4S1hS+w7PcZCWBNG6Hf2mcVYjr2WLFnhNm3aaj+L/stiLIeLQrqa4ChGZglIYt/pMe6Xu3Y19wkWYzm254FTyl+xQMlpI4vE1KIHP5XDtWr1OsdfSuBK+T5LgpLDlVqM8XA05yEdtk8txriG2zL9VWoxxsIu11+lFmMlgUerp5QEHqkRU74vFvgbsACLio8ufil5Zm7ABME3CQHHmimuHRau1E2Y38L16NGjdjT+OMkJNFNjOzBcqYBo2pdyNKZXKhlILteFi5eSb+zICnjt+ky7ps0ep42pBScTo9SCzdqoKbhnTyIfrl27VslsKV9VPqIXgfdNcvPmrWy9UgHkPGDIaSOZyVKLahKP5HDRxnv33mpqoiMtNxn7UgLXXSmdEMNzHTWzWgzDsRZXcyKWO3fuZo1bdAfbJOjNOVOC7prtMobHnjlcXJ9UghgSUmRz3bodU2f22N1797Jsj16aHXSWQD4wLnL1Yow0CeM1h4vMmCkc95EUBl1oY+o6kjwih6vlY0J68lhb4eKemZIcf8ViJ1+vZt+Hn8rhwl+lEurQNrhSvi/Xx8CVWtjlcrX8VSgFELsOMzM3s/3oQykrEOPyvi/znpnyffT7nHtmTI+n4Vh5M/Y0XKWiY7FAGwuUmLE2himHiwWKBYoFigWKBYoFigWeAguUxdhTcJGKisUC7SxQFmPtLFOOFwsUCxQLFAsUCxQLFAvMfwuUxdj8v0ZFw2KBthawmDHd+kHRSWJDdOsPMTiafODa9eseo/WcrCivFpMk9gUu3WJT56LwMBit0zI1dd7vwdcCkCQ1AKfbYgjKXbps1Wz72G7huaT4psVlnDx1ZhbHucDpdkn2pmusETqD0fgd6hmxn//EiVOzXNjAc8lWwjoXdgajyRSwOXvw9RjFMMHp1jjixTRuie1uYDQW6OLFVrwIhXhNqHMGTvfSExegcUtsOwOjiRmswK/Ww6E2HDgthkrhWA2IZosaGP5MqGGFvQ4dGrVDvmYPGN1eSkwiet17K2z1q3OxvQeuoYOHZrmo5wauXrAYLt3qV+eiHha21yQS1McBd/HS9Cw/cRmcU7fn1bnYBgSmtzcUp6X4LTgdV93dezxOx1Wdi+sOl8YHUbQbnI4r+ilxV/QrkzoXW7Xg0gLo1HMDp0Vae3bv9zgdV3UuvoNLEyxQzw2cFlIm4B4c49BkDtfNm1537dPoAw79TCgoC5duHa5z0X4wGh+EncBpsXMKq4PTcVXnYlyB2SHxrFw/cFqUee/eA77v6La0Ohf9hT5IvJEJ/Qqc1uWigC7n1OLdda579+55LpJlmDCuwGnh9OGRUc+l2+CMi4duJtwvKRpuwjgEp7W0rPCwFiw2Lh1Xmzdvq8Sz0g5wWq+R+nS0UccVsZrgdFzRpzWJD/YFo/UaqbfGuOV+Z8J9EBzXzwQuTbzDdQfD/dWE2lrodeFCqFHH/ROcbi+FS30f/RGM1h+kzAMUNQAAIABJREFU7h9cOq7M97Gl2GTlqrWOPxP8D1wp33fsse/TcYVO6GbCGIWLmEYT9EEvLQTO9QCn46rur2g/GPUnjCtsr/UgzfcxHzDhGqpe3O/gok+ZMK7QS+cP5q90XOH7qv4q4vseF6TXdtP/OKeOqxIz1rJ+iRmzXlj+LRaYRxawxZje5Fm8sAgizsIEx6YJKXCiYHQPNgVhucFevx4mYiRuAKfxNNz4NSGFcVEU18QmpbqQYCEEl04GVqxcU8nox3dg1MFeu9aalGrBWs7V4goxMLRPHTg6g9HkEzbBVadrXDqxIBGIOnAmQ3BpQVlsjnMj05sJkwxwOrFgQqfOjWBsMCxYTWyyrIW5WVSB0wk7iVOqXPc9BpyJcenEhUlZnWv9ho2VxRjxL2CUiwUtfUKzA05PX/EYXaAzmcbpapxancsm3ofHwoKTiSc4dDYhixpcGqcW48L2fX2D9jN3+fLVOVwkJ4BL49TqXDaJ1wLYFG0Gp+Nq774D3hY6rupcFGHHXgODYcHJ5AScjqvOzp1+QaOT7Llcdz0X2SVNGFctrhCDyCKSczLpN6lzMa7AHJAFJ+MKnC5w+gcOepyO0ToX44qFpN5PGFd1LhbdnFPHVZ2L9oPZveeAqe5tDk4ndcMjhz1Ox1Wdi3HFtdaEFFw/cDqpGxgc8uO2meu+59IsfPRRuOhnJkeOHvN66Rit63X//gPPpQtOxk6L64pR+cUBttBxZVw6rpYuXek2bNg0+zvjYlyanDx5yusV49Jxxb1EF5y0g3Pqvfbs2dZCRcco9y5wOq64X2rWWOzb4goLLxbrjNs4V9VfaTIm49JFHItD7KVjlPsz59Rxhb/SvhrzV/QPuHSBY/5KxxXJpjThFDGrnK/qr1oPZLT/8j04HVctfxUy0HIeMFoA3fwVyV1M2vkr9X1N/opzmOD/+b+OUa5h1fe1/BXzChNsjr304Yv5Kx1XJPuK+auY79MFJ/0PvXRclcVYy/plMWa9sPxbLDCPLMBNNyeBxzxSuahSLFAsUCxQLFAsUCxQLFAs8NgCZZti6QrFAk+xBcpi7Cm+eEX1YoFigWKBYoFigWKB594CZTH23HeBYoCn2QJsL3hl0eJkE3jlr9sMYj8gfa5uFYhhOMbWBN1m0A4HVyodPfvMdTtdE1cqva9tz2zHYcfRK5VGl+0uGrNiv63/y578VA0Ytp0Qk5AS9Epxsd0lVaeL88Cl22ti5z59+owjliElcOk2lhie7UOnT5+NfVU5BpduPal8+fg/bFHJ4cL2usUuxkU8De1MCXrNyFbJGJ54O40XimE4Bpdud4rhuI4ayxjDGFeqjVevXs8at+iuW6di50Rv9E8Juuv23xierUw5XFwfjT+McbHdLo/rbCX+MMZFGzWWJobhGH1Q46RiOLal5uqlW8JjXIzXHC7G7KlTp2MUs8fYSpvDxX1Jt8XNEsgHtjVmcZ2dqmzjForZj3Dl2J7C8Cl/RZr8HL28v5ItdrPKyAf8VA7X8eMnHH8pgSvl+4jV1G1+7Tjhoq1N0vJXYfthO2zLXzWXKfFcuf4qUfKEvpXrr3RraUx/+n1O34n99mk4VhZjT8NVKjp+oBa4f3qL+09f+Tn34y99xH30Yz/pvvS//5Xru/puxjnfc5N//gX38gsL3ML63+LfdG+GEA7n3H13Zss33Vc//2n3Qy++5D7x2V9yv/tXvS7rNA2aMLF9aeGiBkTrq1L0OZiIve6p+lSl6HPVXqmJdyn6XLVXaqFVij4He5Wizy1blKLPoU+Uos/BFvir1EO6UvQ52Otp/VQWY0/rlSt6/0As8P70Bvdbn1jgfvSLf+hW9fS53q1/6b7+dxe7xT/971xfyA3R5lxvuY6vf8wt/tSvut//f77l/uRb8vftTW7iof3sfTe94avuUy983P3yH650u3sPuI6/+N/c5xZ9xP2P/67PJU9jNJF/WYy9nLEY4+la6m0WT/J279kfOUv1EE+6ct4aEUifKnw5MXHcHT2afjuDXsknjVPns55u7t3X61JFn0nwQRB8SphIpt6y8RZEsze242RBk+LiDdTx45PtKGaP9/YNVBJgzH4hH85OTbmDB0fkSPxjX99QcjJAIo5jx47HCeQoCSI046J8NfuRYPojGX1iZ3dP8i0bhY412+XsSWofhoZGHG85moQEHGSRS8nBQyOVTKYx/JUrVyoZF2MYjpG4QpMwxHAkQxgZORz7qnJsZKSaybTy5eP/cD/RzJkxDMcOHOhLvs26feeOG8roX1yf1Ns/Eh8MDoWkKO30OnJk3JF8pUm4zl07djVB/HdHjx13l6+EpBixHzBJ1gQrMQzHyNynCTZiuLfv33e9kpAmhuEYiWZSb9ofPHjoDvT2t6OYPU7WugsXQzbC2S/kA29lNDuofFX5SDbH1Fs2uDZt7qj8LvYf3vxpls8Yhp0Smk01huHYqdNnk2+g8FOa+KUdF1kTNXNiO1yO75uaOud1a8dhx8mmmtoVMnXuQiUzp/22/i+2f/iw+S0b13ByMu376BOpos+8DT5+/GRdjTn/p69qkpo5AOfc0MFh1yXZTWOYp/lYWYw9zVev6P59WuC+6/s3P+YWfvxrriMkc3PvTr3mfm3xR9wX/vK0e7/pDO8ecd/6/CL3sd98wzVO4+73ut//9AL3ya9tdeE077qp177sPvriP3T/7XTjWZo08FmjSgKPRhOVL4sFigWKBYoFigWKBYoF5q0FymJs3l6aotgHboF3+t0ffHKB+8S/2OlCUl3n3KPrbt0/XuQW/v2/dI3rpNvr3W+9vMj9wn8Zd+81KPtO3++7H3vhY+53d1bO4h5dX+v+ycIF7gt/kX4K1Y6+JPBoZ5lyvFigWKBYoFigWKBYoFhg/lugLMbm/zUqGn5AFnj/0vfcryx40b36/56pvQF7zw3/h7/jFi7+mtseam3O0eKdg3/kPveRH3H/7M+Wu3//v/yM++Til9yPfvYX3T//1g537oHB33eXvvclt2jBF9x3ztTegL037P74MwvcR7+2zcBt/719+7a7dvXqnD+C39mmqMVp2dLX2bWzUgOGQqdszzOhkCMYXv2bUCeErXJXr4VtPvsP9Hqcbi2DBz4Ttv3ANTB40A656cuX/TYZLTLM1jlwWmuF2Kzu7t2zvyOWC0x/f7V+FHppAVNqBYHTrWV1vdAZDG0wIYEBXBpMjw3AaX0Uz7UvtJHtSGD27gvbOEkEQFFhDTQ/NDzicZqkgvpUai+C2OGinpYJXPv39zm2rphQtBmc1uTZt7+3ch3Z2gGme1eP/czX3YHr7NmQUGNs7JjHUaDbhK00bPUzefDwocfs2Bm2cN24ccPrdepU4KI4J+fUrWWmlwaag+HP5NatWw6cFqdl+xYYrUfHlhXsr1s261xcd2x/9GgokEoiGHC6tYxiwXCxbcukzsV1Ry/dfsQWVXCMCZOBgUOei7pRJnUuEp3AxXY5E8YoOB2j9G/015pPdS7GCbrr1khqPoHTOnnDw4c9Tuuf1bl4aAMXWBO2gYGbOid9bnTM6691Betc1JZC9/6BUP+MmEJw6GdCMV9scVfqn9W5aD96DQyG+xBjE9yp0yFJBcH7cGkimTlcDx54LtVrenrac01Ohq1S1AZD/yYu+gt6cc8yoV9xTt0mTDF1xpqO97pebAtj/LO104T7ELjx8bBFmwLQcOm2VOPSccWY7dkd7h2MQ3BaNJdkLXAxfk0Y1+B0LLT8QrjPkXQFzOGxsB2XexL3zBm5d3Tv2u1xOhb8fU58DMWS4RoZDX2OfovtVS/ug+B0LLT0Cvdt7AuG+6vJxYsXvV56H0IHcJoMoqVXaCPjHYwWnydejzZeuaq+r8/jNBESvkr91azvk7GA74NLi3cz3jmnxirX9eI8YA70hn6CPnDpfWhw8KDHNfk+2g8X5zC59thf6bZU831ayJ5+r/6K8Q6XhjBcv37d96/z50PtMa4zOC2SXeeiv4DZ1bPH1HL4pJa/Cvch+h84rSFHv+HvWZWyGHtWr2xpV9IC7x39z+5zLyxyv7EubB5s/eh9d+Yv/oFb+OKvuhVXHrXheeSuL/9199EXPuI++plfc3+0pMP17NzovvONf+R+7MWF7rO/vd5d8Guv99yx//zTbuHCf+o2zDnNafdf//4Ct/hXlrc5R+swC4Gf/Ds/4T79o5+c8/epT/yoW7TgxUo8xarVa92SJSvc+QshFoAirfyZMKEAs3HjVjvk2JsOpl+KzK5du8HjdJJV52JyDdcbb26e5WLiBI6CtCbr1r/pcZrdjgKg/JkQKwDXeilqeuBAv+fSuIUNb2z2OI3rquuFznDRBhOcIjh1Nm9u3OJxxE+YvPZ61V5kmIJr9Zp1BnGDQwe97upY2JMPbmIiZNx67fVl/pz2Q4p2glm5co0dcgcPDnuMOvotW7d7nE6y6lwsUOFatnzVLNfw8Kjn2iFxMR3bujxu7MjRWVzd9kwe4KKorAkOFntpYViKsYJjsWhiemm2PjD8mYyNHfVcWoCV2B0wwyOjBnMU9+ScOpmpc7EIQ/9Nm0L/xVGD0wnb0mUrPZdOZupc4+PHPUZjWZggguMamyxfscbjdFzVuRhX6E6fMtmzZ7/n0nEFF/rTr0zqXCcmT3quDW+EAr/79vV6Lh1Xa9e+4XFnzoQFc52LMYdejEETJnngmAiZrFu/0eNYGJjUuYgXRfcVK9caxPX1DXguJl8m6M05aYdJnYv2g1m5KnANDAx5rt2799nP3MZNWz1Ox1Wdi3EF17Llq2d/NzR0yHPt2hUmf3ChP9fdpM5Ff4GL/mNCvwKnDzA6Oro8jgWeSZ2LGEi46NcmjCtwGgPDuACnCyHj0gUHuvNnwjgEp0WSrai4LoQY1+B0XHE+xq4J7QCjBYRpLzgdV8tXrPY4HVctruBjjo1PeMyWLduN3vHwDd2535lwH+Sc+rACLv5MuO5gdIyyOACjDwFXr1nvcRpvVueiP8KlY5R+C06LyK9d94bHaXxe3fb4H7gqY3R/n+difJngz8BpFsy6XqfPnPWYdevesJ/5cQWOcW+Cn4VL47rqXLQfDPYwYVyhvy7k8f/g9AFD3fdxvwPDvMKEccU5e2RRxXUGx3U3Mb9g/yfmGcwK8X30K7h0XNH/wGkipLrtjfNZ+bcsxp6VK1na8cQWeG/km+5/eGGR++1N9RQa77vz3/2iW7TgVffX52tvs2bP8q478mdfcj/xyV92f340PCl37p4b+qOfdS8v+HH3f+0ineJ7bvSbn3ULF/6m2zLnNOfda6++6Ba9+t1Z1if9ULYpPqnFCr5YoFigWKBYoFigWKBYYP5YoCzG5s+1KJp8yBZ4/9i33M/yZmz9rdqZ7c3Yl92y6XZvxmo/kf++N/Ft94WFH3Gf+7/ZxvO+G//W51pvxuac5vGbsS+HJ4BCk/WxLMayzFRAxQLFAsUCxQLFAsUCxQLz0gJlMTYvL0tR6sOwwKPLy9z//OKL7h99ZyoeM7bon7ltDTFj7z247a7fuDcnecejK0vdP178ovuxf00s1CN3eemvusULXnXfnaq9ZXscM/bKb6dT/bazR+5ijK1FuiUqxkf63PHxsL0uhuFYbtFnuFLp6H3RZ9nS1+6ccKXS+9K+nJT7cGkMRuycxMDotq8YhmNst9G4iRjOF2rOKIiMXiku4mlyipPClapNg61022JMd46NT5xwGkMUw7Fd8uTJsLUthjGuO3frr4iraLZRTWZwkeJb4+mqLK3/sUVMt/PEMBybmJisxP3EcBRX1i13MYznOj5ZiZuI4YhRyUlHf/zESTcjcT8xLuIqwKUEzPWZEEMUw2PPiYzSCWx/SxVEvnnrdhYX14fr1CTE+XCNUgLX5cvNXMRk0XdSQn/WONUYnjgfxkdK2PZJMfMmeevtt7PuvxS+Td2biL/iHpASCltzf2oSYkmzuM6cTaa2Jw5Utyi2Oy9bAzUuMoajPEmOXmfPnkumycdP5XAxNnLGB1wp38dWQnRLCVw5pVh0O2U7TmyfSiHvCzVn+qsUF1uHiV9MCW3UmMEYnm3ulA15VqUsxp7VK1valbbAu4Pu339qgfvE7+52utHQZ1P89UVu4ef/1E3W1k+zpO8ec3/y9xa6l37mm264Vh/63eFvuv/pI4vcL/5Za/Lw7uAfus+88HH3r3oqZ5nNpvjzf5qeZMyet/YhdzFGPFiqhg03fApMpoTYLd0P3w4PV8ohsTd88+Z0AhO4Ug6J9tHOlMCVuvGTBEBjVtpxso9dE3/EcIODhyrJOmIYjqFXigtnRIHPlMClQfIxPDV61kg8XQzDsU2bt1WSdcRwo6NHsmo3wTV9ubl2E3WnOrtCEpHY+ThGPAKTySY5emyiEkvTDrt5y/bk5I/FgMa7tePasrUz+VCAxczSZSHOrx3X1o6u5GSGRQO4lIBJLXKZ0KF/SohRPDQc4vxieGofEfeYEmKdSNDRJMSacI1S0tnZXUmeEsOTkELjpGIYjhHPOJqoK0eMJH06JcQzUuetSVh0M25TQoxg6t5Ewoscrl279lbijWPnJgFLDhcJgQYGQoxljIvFK/fMlBAPRvKdJmFhl6MX8WAHJHY5xomfyuGiP+f0abhSvg+dNMYyphfH4NJkRjEcte40wUYMwzFsr4lrYjiuYU9PiNeMYTiGXqkHa0NDwz5OsB2HHYeLBE9NsnrNBh9b1oR5mr8ri7Gn+eoV3b9PCzxwff/2027hj3zdbbsZtiO+N/W6+7XFC9zf+y8Tc956hRM+dAf/w0+7xS/+Xff7e2672V8/uu46/4+fcIsXf9H9t5OPE94/6HN/8KkF7m9/vcOF07znpl7/svvoC593355oSowfzhj7lLsYI7MZE9Mm4c1TymnxeybLGljbjhOulENi0UPwf0rgSr0Zo320MyVwpZwbWf5GR5snT5yHxBipt0ZM4lMTMbjQK8XFm5lDkhGvXVvh0mxbMRyJAnbvSTtdMspptrgYF2/rcgpIw5V600Mge06xYCbxqbcNPHnOKRZM4L5mUou1kTevmiwghuEYE6PUgpM3JZq1sh0XRbI1SUIMx9tScCkBo0kSYngKE+cUMd65c1fyjSPFl1MTanTg+qTeEFy7NlNJrhDTnWNM/lJvCCi4rcku2nHRn1NP9XnLphkX23IdGkm+OaZINuM2JSSESd2bWPTkcHFfSr3p4Q17FtfoWCVxUawdcHHPTAmLYE0EEcOzuyFHL96oHE0UkcdP5XDRn3P6NFwp34dO6JYSuFI7OcgEm3pwwHmwvWZdjZ2bZCm5/oq3uU1CYhAK16eENtJnm4TFfs7DsCaO+fxdWYzN56tTdPvALfD+pbXuf/34AveJX/g3bnl3v+vb9lfud35qsVv02W+4vbfl9Hc3uN9avMC98qXvOsvp8f6Vre53P7vILf7EF93vfWez27XzDfdf/8XPu0+8+HH3K39+2N2f/fn77tKar7hPvvAx9+o3lrldfb1u+1993X1u0Yvup76xx+lpZn+S+SF3MZZJV2DFAsUCxQLFAsUCxQLFAsUCH6IFymLsQzR2OdX8tMDbJze6//iVn3M//tKLbtHLn3Ff/Pqfur3Ttb2HkcUYrXnnQo/789/5JfczP/KSe3nxx91P/oOvuv+4ftzdmX1VZm1+253c+Mfuq5//tPuhBS+6H/7xX3S/8+09rn4aQ+f+WxZjuZYquGKBYoFigWKBYoFigWKB+WeBshibf9ekaFQskG0BW4zxrwmFJfnTGCviO3QbA9sewOjWALYvEA+mQbl8D063SbCFYUS28MW44MjhooaY1lBp4tKEFDG9Dh8+WoljaeK6ezfYK8ZFkWTddoctza5mZ7Y6Ej9AQW4TrgM43QZJwH0OF/bS7YAxLrZiDg6FGj3t9IJr5kYobBfjIv5M65qxDTTWRrgoSm0S42JrC7EGupW0zsX1INZQtwNyTcFpn6PeWw5XR0dnpZZejIsaeGy707EQ0+vAgYHKdsAYF1sx2c6Yw6W1yIhP5Jwap3icAtWdO9NcvQOVxDsxLmKg6luZYm1kO90ZSRgQ4yJpArbgWpnEuNCdrbwmMS6C91Nc2JLro8lf6AucU8c72yfpO016wcVWTE3YEuNiWyd9J8VFH9T6SzEu6n/tP9DXyMWYGBg8VKlrFuO6fv2Gv2fG9NJx1dOzt3I/4V6DvRiXJtxHGLd6H7LrqFzcl7RGWoyLuKB2XDoW4OK+adKOi61yMb0qXIdGKvXWYly0t66X3cuVi21yI6OhiDX2xRZgTUicBBfXxcS49Hrgr/gziXHBkcOFTrqFr4lLx0JML7bna3IL2l9vIzbE9hozFuPK9X20UbfCx/wC9SApLG1ieqGbCXrBpfHSMS5q1Gn9O/v9s/JvWYw9K1eytOO5tAA3rVcWLXbdu8jc2BICeXf+/+y9h3tdV5X3P3+KZUtyYtIISSipOCQhzYQW2kteCITyJvAOP6YwDAPMDBB4B+I0khBIIa6Je29ykZtky7bce42DLdty77bs9Xs+53rfs87RPndvE9vRldZ6Hj2Szl33e/b+7rrO2WutWY2ZoAsTJ03NOMCzWURHB/VgQseRdv2GNAoXDsbotaloZzjSa2d6NjfoLGxKFykmYbC0nxoTLno6QhlJKd9+J01MiX8MOjpACM79YGHUOOFe6OmIbiSdpJ5OKDM62kkaowEsbZiySUVPRxXDyNKBRXDUR4egF06IBEmySh3IAH8C9IjG6ISACNrJf1/7/kSHM/BO2EBSLm204Z8EFtErneSxiKSHjk48zcYWrMWLl7mvJb406OlokyT4JfmwkwMHDyZYLHpOMEDA0n5EpSAijZngGSyS1FEbk9yPHyf48oClfWzgDh2dZHjK1IYEi/I4yWPByV/fGppxWmdjgx4GmJOp02Ym94QnJ3ksfMEo17x5aWJV+gd6tLETgkOgpxPw5rGIRIbOnMa0n+AXgp4eV7TjoMHDRSfJzmPh3wUWCaid4KuJHj4iTvgfPe2nlsdizKGjg78wrtDTY5R7oaf91PJYSXLwwcMzGyMSKKOnfUnp32BpP7U8FvVHRwdswYcJPe3/OW/+wkRPj6s8FuMKrGnTZzlqBMMePe1j1di4IAngoaPL5rHoL/TnqVMbylj0K/T0BhojmHtqn7c8Fn5lYGlfKcYVetm5Y0mChc+kE4elx9W4cZMy8xxBbNDTm3E2wJSL+zhhXKOnI5BSLh2whXqgo/0s8VEFS48r+gl6elwx92osogWio/0ZeYg3ZuzEjMFMP0FPP/BhfdGBMmh3dLS/lluvtMFMACf09AOf/HpFf0RHz0P0W+qoI2OW1z4VcAgdfpyw/oClDTS39umgNKxn6OlxlS8X4xed+QvSeYgHHtwvu/aV1ivWXSfwrtdk6g+WDmjFuIL7lSooDes/evrhUYKlgtIw36GjA4QwriiXfihLO6OnE26DRR9z0r7frX3pnEa/AqtVBQSi/4GlxxUBPJjzu6uYMdZdW9bq1SMYwBjrV983WNcdO3ZmJlzfF3hiqjefPh2usYkJhR1GD6yQEzNGCBN7SMDST3R9+iwo1DMkYOknpz59Fmy9EPh0uMbGTD9N9ekRCU4bQT4drlGuU6dOF32cXN+1u022bttRUcdh6Tcxvi/wRkVvGHw6XKN9Qo7ahBMPBTtwWKEgJWwk9CayqFxsBEIRuPbua88YekVYBEbRT2Z9emwW9Rscnw7X6NN68+zTI4iENjZ8Og6LzXwlYXOt3wYV6aITCp7CvWKwMDC18ee7J2+MN20Kj20McW3g+rB4mh+TVoB+ow1cHxbl0ptInw7X6M/6IZRPj/k3Zv7CYMKIrSQnTp6Mmn8Zs6G5ibcNzCch4QGJfqDl0+eNTQwWZdIGQhGWNmZ9OlzjYYt+OObTi12vMA54SFJJWKdi6kh/junTYIXWPsqkDZei8oEVWvt4C60f2hVhwb1+0+fTow1D/YvvUa4QFsZnKKCOw6LPVhIeGsWkA6mE0ZU/M2OsK7eOlc0YCDAQa4wFYOxjY8AYMAaMAWPAGDAGjIEPgAEzxj4A0u2WxsClYsCMsUvFpOEYA8aAMWAMGAPGgDFw5RkwY+zKc253NAYuGQOxxpglfU4p53x66AifJX1O+eLMf+gYmSV9TvnCTyJ0LNWSPqd8WdLnEheW9DntE5b0OeWC9Sp0hA+fXu3TlX47+5clfc7y0ZX+M2OsK7WGlcUYuEgGzBhLCcMZWTssp59k/zJjrMQHwUhGjByTJcfznxljJVJI3h2TdNSMsRJfO959LxOEwdO1kktmjJWYMWMs7SFmjKVcmDFW4oIAHgTM6q5ixlh3bVmrV49gINYYIwStDifrI+f8+fNBB3++hzO9Do/rw+IamwswKwkBAw6qqHlFujFY1E+H2q2EFXKuPnr0WDCgA/h79uwNOlfHYhGIIeSoTfCLUKAJygVWKEgJXOloaEV8gRVy1KYfhoJWuHKdVmHTffckxUIM1t59+4LBUwgJHYNFPzwVcCA/ceKkHDxUOZgG9UmwVIhsfx2PB982OqyTASzCcnPPkKCDbiUhGE0M1r72dgkFYiEYTQwW7aNDd/vKx5uBWCz6TyWhjvSdkFAu+nUlYVwwPkJy6HAYi/Eag8WYDc0BZ892RGGBc1SFePfVgzmJ+TckCdbRNFy8Tx8s5syQHI5Yr5jDY8qVrFcqlLrv3rFrH30wph/GrFekDIhdR6PWqyNHfFXLXLvy61XcOhqzXtHvQ8F5MpWtsn/MGKuyBrPiGgOagVhjTH/H/jYGjAFjwBgwBowBY8AY6BoMmDHWNdrBSmEM/F0MmDH2d9FmXzIGjAFjwBgwBowBY6BLMGDGWJdoBiuEMfD3MYAxRtJnncSYHDokANU5mEiki2+GE173o7Nm7Tp3KcntxPl0nfsEXPT08Rn8Zkim64TgDuisXpMmZXYJfnUgA/IqodeuEvCOGj1WsMe8AAAgAElEQVRORowc66CSxJ/orFIJnsl5Qrm2bEmToZIEEz2OSzmhftTTCWVGR3ND3cDauClNDEySTvTISeVk+oxZMmXKDPdvcjQFHZ2fiFxrOEST8NYJuVDQ00lHSWg7WWFx/AkdnW+HHGmUS+f9Ahc9nZ9oRsOcTGJVjvOgo5PHumTBmkMSDqOnE26PnzBZhg0f6YouHJtBhx8n5CCiXCtXrnGXkvwy6OgEpg0zG5NyHVNHnvJY5EgDS9eb3FHo6fxEJKcl4SvlcZLHghMSgC5a1OJUkvxY6On8RLPnzE+SoepjXXksju5QrpaW1jIWua/Q0/n08LEjsaoeV3ksxhU+dgSAcUK+KvT0uJo5c06S9FkfecpjMa7A0onZt23bnmDpnEIklEVPHznNYzHm0NHJ1Ldv35Fg6THa1NSS6OkEvHksjmANHjJcGmbOcVVMchyhpxMWE1SAe+rgL3ks6g+nc+emSbLffXdnUi6dt65lSSmJsR5XeSzGFVg6mTrJgtHT+eEWL16SJH3Wx+XyWPQXfP90AnT6FXo6+THzAX1H51zLY3FMGayZM9ME6Iwr9HSOMsYYWIwTJw5LHwklca9OIM04RE/nyWIeAUvnEHNY+mgc89KMhtnudkk90NPJj0kWDJYeV4xh9PS4okzMm07I0YaOTlC+YeNmwfdHJxl2WLSfk9J6lWLR7mDpBOWMUcqlk3eX1yt19J31Sq996XqVrn3kgQOL3ItOVq4qrX36KOSEiVOEHyesP5RLz7WMJ7AYX074HD09riiT9kFl/KKj8w9SHrD0WCBBNXp6XJHoPLP2HfSvfXCv8wiy/oOlj//l1z7mO3T02se4oly6/9LO6OncfPStyVOmOxqS/oKOXgPoV2CtX7+xrEf/Q0+PK0v6XKLnH8osef5omDFDnnj8W55P7JIxYAxcTgbcm7HdbekCzkLHJlL7YbBxmj0nzXqPfxU6euHfs7e0KdWGFxt79LiPk5mzGjObFHwOSli7nYq079+fTLB68WFjgJ7eWIwbN0nGjJlQ/h6beXT0JoJFislaLxhsQNDT/g7UT28QKTM61MHJ/gMHE6zdu9MErHCQYCl/BzZ0M2akmxSSHuexDhw8mBhjLExOMHbQ04YEzujTp6cbC3yP0NEbEjal1FFvLFiI0MPgcjJvXlNmY0FUSHT4cYJfE1g6cScLZIJ1OMWaNr1B3n57lPua4JuUx2KDBJbeDLCJRQ8/GCds8qdObcgkrc5jkWwXLG0Is8lC76DaiDU1L042FtpXqhPWkSPJhprkw07oHyWs1H8Ko4gNp46emcdic4rRoDeNbHTQo42dLFnSmmyq9bjqhHX0qEycNDWzOdvXvr+EpXyL4AuDRifTzmOxice40A8TGFfoacOLjQ16x9QYzWMx5jBwW5evctVJMNDTD0cwCBIsZVTnsRhXg4e8LQsWNqdYBw4k5dLjnU0jvFIPJ52wTpxINmuLW5Y5leTBD3r6Qcu6dRsTLD2u8liMK9oaI9AJ7YeeftDCQ6M3/zok46+Tx6K/sLld2LTYQSX+giWs1N9s8+YtSZ/WRkkeCx81Nt0LFiwqYzGu0NPGJYYs40OPK4el/RlHjx6fmZvQT7CULxbzSIKlxpXD0uOKeUlH4aMe6LXtSefHv+3alWBpf0m3xuhxxUOnxsb55ToyrsDSG2rm7SFD38n4XTks2s8Jm3i9XtHuCZYyVN1DFP96lfoN8qBo1my99rn1Kl0z6WvwpQ0vHhBxTz2u6M/8OHFrn16vymvf/v1OLVnPEiw1rigTZXPCfdCBbyeUh3Jl1j63XiksHjppoxq/SbD02gdPcK/X/HTtSx980Ya0pRPmO7D0esW4oly63m690sb+3LkLveuVxnLrlTb26X/cU699GGOM2+4q9masu7as1atHMOCMsR5RWaukMWAMGAPGgDFgDBgD3YwBM8a6WYNadXoWA2aM9az2ttoaA8aAMWAMGAPGQPdiwIyx7tWeVpsexkCsMbZjx87MMQMfTYQd3rBhk++jzDWOwHCEICRghULycn5dnzsvwgQrFPadow/UMyRghcK+c7xDH/MrwmxtXREMr85xF+2XU4RFuTjSVEk45rN1W+qLUKQLlj5O59PDH0H7DPp0uIafB/2skuDDpY8yFumCpY+t+fQ4frRlyzbfR5lry5evzPgyZj688A/He/AtCQl9UB8P8+nv27c/43vk0+EaxzC1L5hPj2PFK1eu9n2Uucb40MewMh9e+Icji9oPxKfDNXT08UafHuXWx0h9OlzDn0Yfd/LpcRQPn8CQ0D76GJZPn6NPMfME/WbPnvQYoQ8LHxj6Tkjoz9pf06fP8U/6dEjwSdJHo336jFfGbUjwBwvNTaQwiMHCt1cfi/Pdm7QCMViUSft+FmExZ4YEn0h9bM2nzxweUy58NXfu/JsPonyNdSoGi/4c06fBCq19lEn7kZYLk/sDrOB69d6uxG8z99VO/5bWq9OdrusLtGGof6FPufTxWY3h/ma9oo+FBCx95NWnj2+39jXz6VTzNTPGqrn1rOw9noFYY4xkyDoQgI84JnzOgYdk/oLmTCCAIn2wQgsSzr0T1Rn8SlihBcmSPqfswf2BQG4gS/qc8oWfVOgBgyV9TvkaMvTtTNCY9JP0L0v6nHKBL+ty5a+XfpL+5fyD0iv+v0aOHJvxzfJpOV9P32f62uzZ86RlSeqvpz9zf+MXFbMu4Ge7ePFS9zXvb3yCCXoUEkv6nDIE9xjElQQ/Se37V6QL99qny6dHG86Zk/r++XS4Rrm0D6dPDz9bHQTHp+OwdGAknx4+Y5b0WcQCePh6h10zBj5gBmKNMSIh4VBfSTB2MLRCgpO/jvhUpA9WyBgjWMOCiHuCFTLGqJ+O+FSpXKE3UETtam0NPz2fROCEY5XfGhEVUUc7rFSuEBaRzZYsTaMdVsIKJcBevmKlzJ49twiifJ32Cb3pIVpdaFMHIFg6YET5JuoP3kjogA7qo8yfGPJ/+1saNCbz4YV/eCqrIxv6dLhGQA0dBcynx1tXHRzCp8M1gj6E3hpt2rw549hehMUDhtDbBt4ghB60gI+Odpz33XPXrrZM0AqfDtemz5gZfCPU1rZXFjalQSuKsGif0NNzAqroSJBFWGwkeQtVSdra2jIR3op06c86CqNPj4T1MfMXm9LQ20uCFcTMv4zZ0NzE2+cYrGXLVsi69Wk0WF8dCTITg0WZdDRYHxZv/5gzQ8IbEN6EVBISbseUiwA4OtqhD5N1KgaL/hzTp8EKrX2USQfn8ZWLa2BR10qyZs36qLdGcB865UAbhvqXK1cIiwiJREUMCXUkqFglcVF2K+lU82f2ZqyaW8/K3uMZiDXGejxRRoAxYAwYA8aAMWAMGANdkAEzxrpgo1iRjIFYBswYi2XK9IwBY8AYMAaMAWPAGOh6DJgx1vXaxEpkDEQz4Iwx7fzKNX50wIsVK1Zljmpw7AEdHeQBDI5Y6SMRDksfEeRohT6myGd5LM64g6XPunMv9DRW86IWWbgwPcpUCQundCc+LI596GOKDot7OqFulOvYsTQPjcPS9ebIo3YWLsKaOnVGJheKD2vt2uwxRdrF8ZovF7m4nNAe6OlyceyDo0VOKmHpo4U+LI4pNjam+XcqYenADz4sgitwFEv3uXwd4ZCjcjp/lMPS/WTThSOPISySpuojfD4sjjy2tCwLlot+qAMscIyV8utyEYRlccvSili0FVg6/44PiyAA+BHBiRMfX4sWLckEMnBY+pgtvm7oBbEWLxH8uJz4sN57b1eSSDuERdJqnO6d+LA48ggXISzaRx8thHO40HUkqAt9pxIW/QUsHbDFh0VQAfpOEGtJayaYicOinzkhrxpHrUNYHC3WfPmwDhw4lMxNPiw9FkiQrQOQ0OfgS5eLfGFFc7nGYi5hfnLiw8LPKwYrOVq4dr2DSuYtysWc6AQsuNdzmuv3ulylY/Vr3de8WNS3qFyaw2TtW5Vi8Vm+XLRHHsvN5RqL/syPk0pYYDrxYa1atVYomxMfFjxRLt22Pqz8EX2HRT2dgAX3tIETh6XbI39En3ZxbeS+58ql83z6sJK1L3K90sfqqS/31OUi/5lOku3K0l1+mzHWXVrS6tEjGWDCuqquPpPwkWSZJIDcuy+NKkaiSoIUOCFRMTr6/PuKFasTp1x8nJzgFIyejiqWx2IDh44+c49hhIOv9lObN29hosdmyMnb74yWt99JEw+ziQVr3vwmp5L4DoClE/xyL/R0UkvqpxNyUmZ0tGMzdQNLO9Pji4KejriVx2IziA5O6k7Wb9iYOBQvXdrqLklT0+JE791306iOeSz8X8DSjs1EZKNc2u8K/yT0tm9Po1FNmjw9U0eMJHRIxO0E3xSwFilneowI9Egs62TkqHFJElD3P1H70NGJs/GZAau5Od2AUEb0dMRDVy7thI0OP07YcIOlfX/wJ0Bn0+YtTk2mTJ0hEyYSgCRNuJzHwjD661tDZY4yJtlYoqejnU2dNiO5p05GnMfCF4xyEdDECZtB9GhjJ9Omz0r09LjKY2EYgaUd4Hl4gZ4eV/huDBo8XOhXTvJY+IKBpRPWMq7QY8PkhPZCj4TjTvJYjDl0dD9hbKK3enW6UaVPoqeN3DwWyV0pO0mknVAe9PQYZR4CS0fFy2NRf3TwQXOybv3GBEv70zCG0dPjKo/FuEJn6rQUCwMIPf1ghT5D8lgdeTWPRX9hLqEvOqFfoaf9P0nkzD21z1seC78ysBgjThhX6C1RcwdjDCwdldRhEZDDybjxkzNzAOMQPT13YJSCpX3e6Cfo6XFVKlfajtQDHe1nyRgFS48r+hF6elyBpdcYIiKio40XfJHGjJ2Y8Tekz6FH+znJY9Hu6DC/OnHrFQ+onDA/o6fHFUnYdbnwm0RHz0P0W+q4dl06rpgP0NPjCh1+nLD+oDN/QbpeMZ7QWb069XljPUNPP6ShTJTNCfdBh2BbTvDfAmulMibxUURPj6v8GuNbr/ANhPvlK9Iorqz/YLEfcJLHYr5DRyfhZlxRLu1bRjujR7s7YY6gLZ3QX9DRax/9CiztW0b/Q0+PKwJ4MOd3VzFjrLu2rNWrRzCAMdavvm+wrmxeCUlfSXgCtm5durAV6TLZ6o1MkR5YISfmDRs3iV5MK2HpJ6c+PeoXE0KecumnnT4sFqdtynDx6XANQ0w/wffpsWjqJ/8+Ha5RrhAWm2RtBFXC0k9TfXpwtWr1Gt9HmWtsjo8fT59uZz688A8bCb3x8+lwDSz9NNWnhxHN27GQLFu2PBhYhE1JKHAC9yFSIm8TKgmbRb0hLdIlyMrBQ4eKPk6uw5d+u1GkjJGuN88+PQzymPDq6Og3nD4s3qZS/pDwVlU/VPHpkyogBov2iQltTxuFBKxQIBYMG/pOSOjPeiPu02f+pU+HhLd1vCmsJLxZiJl/2eyH5ibmkRgs5iW9qfeV7/SZM3FY27ZnHmj5sHjToR9e+XS4xiY8FN00er3a/m4whDzrVAxf9OeYPg1WaO0jrH1MCHmwgmtfsl6lD+2KeIX706crBwPhoWTsekXfqCQ8qNUPF4p0qWNo7cNg1gZbEVa1XjdjrFpbzsptDIgkr/JjjDEjyxgwBowBY8AYMAaMAWOg6zFgxljXaxMrkTEQzUDsm7FoQFM0BowBY8AYMAaMAWPAGLhiDJgxdsWothsZA5eegVhjjDProRxJHN3T57uLSstZe5yKQwJW6KgGPhkxeWfACh0tpH7a16yofGCFjvDhY4WjfEjwPQkdbyOwhfY1K8KkXCEs/FW0D1ElrFDS53nzF8rIUWOLIMrX8SHQ/hzlD9Qf5J7Tvmbqo8yfYOFzVElWr8Evak4lleSztwYNCx6nwZdp+oxZQSz8eULHojgmhwN8SCZPmRE8Lrti5SoZOmxECEqmTG0IHvPhOB16IUEndPyT42GUPyTDho/I+GH59AkWQi64kNA+ofxU5JPTPldFmDNmzA7mp9qx412h74SE/qwDFfn0OV5Jnw4JPlb4OFUSkj4zB4Rk1KhxwbmJo5gxWPg2ar813705VhyDhV8fvmqVhOARzJkhwW9K+6359AmQEVMu/ItDefhYp2Kw6M8xfRqs0NpHmbSfta+OXANLBwPx6eEfrH3NfDpcg/tQ0mfasLExvPZRrlDS56VLl2d8zYrKBZb2N/bpkezcfMYs6bOvb9g1Y+ADZyDWGGOiDi1IGDs40oaEBUQ7PxfpgxVakFjYJkZsQMAKGWPUL2ZBAitkjLERIHpTSF5/Y1DQgGJx087PRZiUK2SMcWZ+5qxwomawQsYYDuojRo4pKk75OgtlyBhjo4nDdUjAChljBKmYPiOMxcYi5NuAMRZjQLGhjjHGYqJ5YTSEfBfxuRo85O0QXYlhFPK5wBiLMaDQiTHGYoyeIUPfzgSy8FUEY0wH+fDpcI32iTHGYoye6dNnZQIn+O6JMRZjENCfdRARHxbGGH06JBh2OmiQTx9jjHEbEjalobkJYywGa/bseZnAH757Y4zFYPHAiaTblQRjjDkzJBh2OvCHTx8DJaZcPKALPTxknYrBoj/H9GmwQmsfZYp5eAhWyBjjQaQOVOXji2twHzLGaEMdgKgIi3KFjDEeROpgHZWwQsYYATzeeHNwEUTVX7c3Y1XfhFaBnsxArDGGYz4O9ZWExSO06eb7LPT8hASs8+fPV1QjupKOyFWkDFZocaN+Opx7JayQQzRGUQwW0bFCRiJYBw6mkQErlSuExUIaCugAPnzpsMC+e1K/PXvTaH4+nQSrfX/Q6fvo0WPCZjIk+9r3yykV8tmnz+YvFGiC7xFc4cSJNMy4D+vYseNRWPRBnTrBh8VYiykXWCdU+HMf1tGjRzMRSn06XEuwVGhwnx6BH2LGEDrHg1gno7AIshLa1MFnTLnglHaqJDj3x2Olobt9mDyICQXm4Hv0Z/p1JWGTTJ8OCWOWNq8kjNeY+RcDMDQ3MY/EYFGuw0cqB64529ERhUWZQg+TmHd1RMEiPkpYldeY2PWKYDqh9Yp1KoYv+mBMPwQrtPZRplCgH/gBK7T2Xer1KtS/XLnC69WR6PUqhEUwpl0qYmxR36nW62aMVWvLWbmNAQvgYX3AGDAGjAFjwBgwBoyBqmbAjLGqbj4rfE9nIPbNWE/nyepvDBgDxoAxYAwYA8ZAV2TAjLGu2CpWJmMgkgGMsavr6jOJW3E6J8mpPpqBrwtJa51w9AGdtSrBM74pnAPXvjP476Cnj9mRVFX74XBsAx2diJZcZGDpPCokmUVPH2cbNXqcjBiZBpHgyFIJK02YST4WsLR/EPdCTx8ZIRCA9umhzOhQByfUDazNm7e5SwkH6O1rT5OOgqUTvnKcBB3t0E/yUM7g6zxpJNZEL58YeIoKinD48OFER/ujkDyUcvF9J+SzAUsnMMX3RDuQc1QMHZIUO+EYEFhr1qQckmMKPZ28G51hw0e6ryVHstDhxwnHQtDT9d64aUuio496EaAAXyN93CyPha8YWLqs+DChp3NW4V8Hlj4ilscilxTO3ARacUIuJ/QI9uAEPxZ8jY6oo1h5LI59US4dyIC+hh5t7ISk5WDpcZXHYlzhQ6TLRVAM9PS4gi8SJ+tjSp2wLiQe1gm3GU/oMSac4HvCPfXx1TwWYw4d7TtDrkD0dJJWfE/Qa9+fHjnNY3GfwUOGZxJIk5Q3wdqeJnyFA7D0Mb48FvWH07lz00S35DlCTycoJxAAbaTHVR6LcQXWHBV8gBxa6Gm/u5aWpYnPGO3uJI9Ff6EP6mA59Cv06GdOSKBLuXRuszwWx27B0r6ejCv0dLJzxhhY2qfSYR07nh7jJHGvnpsYh+gxLp0wr4Olj3U5LH1cEj9C7etJPdAj/6MT5g6w9LgiAA16elxRJgKoONmzd1+ioxOnkwcO3x/mOyfMg2DpI44Em9GBd2h3dPT8SL5FyqXHKHkT0dPH7ErrlVr7LqxXeu3DxxMsnYuTfG5g6XFFMnp+nFRc+1Ty4zVrL6x9alyxHusE5dyH+xHAyAnloVw6rxyJqdHLrn2zM0F8qD86Oo8kuTPhXueDhAP0mLec0IZ6vWK+Q0evAYwryqX7HO2MHu3uhEBM2p+VI7Ho6LWPfgWWzt9G/0NPjytL+lxi9R8cub7fDTNmyBOPf8v3kV0zBoyBy8iAezOmN7NMumy08CVxwqSoNxZs4tHRCywbdSZF7RfDxgg9vclumNmY2Viwac5j7du3P8HSkzwJIEtYqR/G2HETZfSYCa6YyQYcHXSdsOhQLj0xk/wYPb1hxxldR+GjzOhQByfUDaxdu9MNOxygp31gMAj0ZoCkx3ksFk+MMQIVOKEd8lhsDrUhTLugoxd+sCjXjnfTzSybLPT0JoUAJdoQxv8FHX6csBCDpRfw3bv3JDrakMBwHf72KPe1xGeqCEsv4PQT9DTW/AWLks2ATtyZx0Kfcm3cuLl8TwxN9PTmqalpcbLZ1D5ceSw4IQjDqlVphDovVnNLshnQvmU+LIwGbbyyUUdPb8QIxMKmWo+rPBZ9CCwSlDphDKCnx9WCBc2JQaOTaeex2DRjXKxQhjbjCj29EWttXZHo6TGaxyJwAljLWlNDG4w8FoFY0NPjqjPW8ST4yPwFTa6K0t5+IMHS452NIFzozX8ei/rzcEEHfoAn9PbuTTeIbBrB0mM0j0W7sPHTxivtV8JKN4irV69J+o4eV52xTib9eWHTonId6aPo7dmTYm3aVDJUMASd5LEYE4w1HTnPYbW1pT6bzrjQ48phnTp12sHL6NHjZYaKEIo+evpBi3uApceVw9LjinlJB36gHugxXzhhLmbcaizmLvT0uGK+1FFj4RcdneyaeXvI0Hcy4yrF0uvV7EzQI7de6XWu0nrFuuiEB1g6iAT9kXLptQ9jjzrqMYrBgZ4eV/RBfpyka1/n9UqPBbf26XFFmSibE7de6bXPrVf6gZxbrzQW65U2qqk/Zc+vfXCv6+2w9LiiDQmE48StV+wrnLj1ivZ0QjtzTz2u6Ft6vaK/oKPXPvoV3OuHVW690lgYYzGBd1x5qu23vRmrthaz8hoDigFnjKlL9qcxYAwYA8aAMWAMGAPGQJUwYMZYlTSUFdMY8DFgxpiPFbtmDBgDxoAxYAwYA8ZAdTBgxlh1tJOV0hjwMhBrjHFcIRRSmPC5+jia94YiyRFCfea/SA+sUHjfrVu3yRblg1EJKxTel/rpYxmVsEJhdPG10McyirA4jqaPEPn0OG6IT01I4CuE5Y4IxmCFcqlRvw0bNoagEh8ZfZzO9wWO9Wn/QJ8O1/C30cd+fHoc79mmfI98OlzDp0Mf6fLpcRQPn62QcEQsFOKbI0Paj6kIE/+kUBoJUgpoH8siLHzXtF+ZT49jPtqf0qfDNXQOHDxU9HFyHT61f1WRMnnB9LFhnx5HjGKwaB997NKHxZEs2igkYOnjYT59juLRd0JCf9Z+ZT595l/tQ+bT4Rp+efp4o0+PdAgx8++GDZuCcxNHI2OwmJd2t7X5ilO+dvrMmTisne8FUwYQvl8f4S3fJPcHc5M+kpj7OPmXMPkxdcSnTB/N82GxTsVg0Z9j+jRYobWPMml/N1+5uAZWKBULRwRj16tQzrLSepUeSaxUrhBWsl5Fr32nim6VXMcnTfvAVVSuwg/NGKvCRrMiGwOOgVhjzJI+O8YkOZ8eMlQs6XPKFz4SoQ2uJX1O+cKvzJI+S+JLGZMg15I+l/oOQVbwnQmJJX0uMYQhEMOXJX1Oe5QlfU656Gp/mTHW1VrEymMMXAQDscbYstYVmWhIvlvwtkg7c/t0uLZ8+SohilhIwAq9zcKpnSh1IQEr9DaLaE/UMyRg6UATPn2enBPBLSTjxk/KBDvw6RMYYsmSVt9HmWuUSztlZz688M+6dRtkccsy30eZa2DpoAKZDy/8s6x1uTQ0pNHPfDpcw5A/GEhaTVAOIvGFBCwdXc+nT4TF5uYwFlHNtLO7D4un2E3Ni30fZa6xYdNR7DIfXvhn27Z3RQd08Olwbf785uBbaKKF6aiYhVgLmoNPz3kiroNDVMLSTvI+PZ7WU/6QTJk6Xdatr/xWFSf8+fPTIB9FmLQPb8grCW+oaKOQELxDR0r16e/evTsTEc+nwzX688ZNabAZnx6BDOjTIeHhDm+0KglvUxm3IWlomBOcmwhSEYPFvESkv0pCovAorKXLZfXqylgEg2DODMnSZcuDb0F4yxZTrnz0Pt+9WadisOjPMX0arNDa56JI+sqjr4FFXSsJEYPhLCRwHzqZQBsuWRLGolw6yqfv3rxBb1kSt17pQD8+LAKUjJ8w2fdRt7hmxli3aEarRE9lINYY66n8WL2NAWPAGDAGjAFjwBjoygyYMdaVW8fKZgwEGDBjLECQfWwMGAPGgDFgDBgDxkAXZsCMsS7cOFY0Y8AxcODAAWlra+v0s23btiTps/aBwkDjRzv9JscUV6ZHCzn2gI7OmcTfHHfSTrkOSx8RXJ5LMsxneSyOAYKlywU+ehqL/ELNi1pcNZPPirDyZc1jrVy5OnNM0ZULPSfUjXLpoxquXPooCEce9TFFHxb6HJ3QOVp8WKtWrc0kFKZdKJOvXPpoIdyho8vFkceWlvTIYyUsfbTQh0Xi1nnz0yNWRVjkxKL/OfFhkfiaJL+6z+XrSD3A0v5nDkv3OY6G0S8qYdEeM2fOyeQw8mGRVJcjYpWwknItXJQ5pkj/pfy6XFu27kj6agiLxMo6WI4Pa/PmLTJ79tzMWMjzRR05wrfzvdSZ3mHx2wl5e9BD30kRls7v48MitxLlD2GR14gcW058WAQV4FhnCIv20ccU4Zzy6zqSj2vBwkWZsZCvI+2yePGSTCAGP1abNMycXbFcCVbL0szRQodFP3NCfjX6tB6j3nK1LBOOGDvxYZGknrnJh6X73Pz5CzO559Dnnrpchw4dKpzLNRbHFDni5sSHRWLnolzHUU8AACAASURBVHVBYzFfMtc5cVh63qaczJmhOnLkbqXKIViEVVQu3efyxxT5jHLocsFdHsvN5RqLvsqPEx8W/RYs3R4+rPwxRR8W/QQsHUDJh5WsV+qYosOink7gEO5Dax9tqNc+2hgcjeXKpZN+u3LptuXIY4s6ol8Jiz7rBO64n8biODDjtruKGWPdtWWtXt2GASY5BupHb7q5088tH7lJ6mp6y9BhI8r1HTFybPI/Gysnf31rqLw1aJj7N0m8y3cmTkoTWJLE9Y03ByebaqdIQmb0iAbmBCx+nBDtCR3tTM0mDCxtaJHgGT0dkY4kjm/+dbCDSiJVoaP9CvADAUv763B2HD0dyYz66XJRZnR0UmkMBrAWqIS1cIDepk1byuXIY+GXg87IUePKOkuWtiZJnxvnzi9fI2ABeto/JI9Fokx0SGLpBGOZcs2ZM89dkqlTGxI9zt07yWMR+QosnbwZYxksneiUhKzorV6T+nTAFXpOSCyKzrDhI90lYcNAG+lFkAUdPTYATgYNHpboaUMLHX6c4IcHlk4COmtWY6KzXCU2JjEpejrRaR4LTnBGnzx5moNPjBv02Hw54X+wiI7pJI+FIYmODjaBPwR6tLGTt98ZnejpcZXHwncOLPzZnOBjgh59z8nb74xKyq8joOWxMCTB0mNh4cJFCZYeV6PHjE/0dNCQPBZjDiw9FjDg0CPJthPGKHo6cmEeiyiDcP/OiNHua7Jo0ZIEa8HC1N9s3PjJCRb1cJLHov7cT48FfEzQ076kjFH09LjKYzGu0NFjgU0leo2N6RgFi/LT7k7yWPQXsIYOe8epJP0KPQxRJ9OmNyR6OmF4Hgt/N8ba4CFvu68l4wq9mbMay9dmzJidjEdtHDksPa4Ys3qeYxyix7h0QjJh9Bi/ThjX6Onk0OAwpzihHuhMmzbTXUrGFVh6XDEW0NPjKo+1bv2GRGfK1BllLNoB7rVvL20Plk4gnMei3dHRY5QHSZRrifJJGjV6fKKno9eWsNL1inkeLJ28mX4Llja0xoy9sPapyK70CX6csP6ApX2Z3NrH+HLCGEZPR2J8a1B2HSUSKDpjxk50X0vKQ7kWqnHF3IKejv6YXxeoPzrw4YSk9XCvfS/d2se85SSPxXwHFvsKJ4wrysU86YR2Ro92d5LHIkImOnruoF+BlRlX02YmejriLDp6r+Du0V1+mzHWXVrS6tEjGeDpUb/6vsG6M6ltVMaG7ws4HOsFyqfDNRz31wec0dHDOAuF921tXREV3IJyhRyiWWT15F1UfqLd6Se6Pj0W2Zjw14MGD8+8PfFhEVJ85crUcPHpcG3qtJlBLDbC2nApwsL40m8WfHoEkZirFlOfDtdmNMyREyfStwE+PVIK6KepPh2uzZw1N+j0zaZMP00twsIICYW2Z7O4aHFqBBVhNTYS8ORI0cfJdUKT82AgJEnAE/WU16fPpkRvUn06XOOpOEEiKglh4Xk7ExLeLLXvT99w+vR5mzpvXjhQxrRpDRJKbxEbkIL20QaCr1w49+vNmk+Ha2w4eSNXSXj7rB+qFOkuWbo8GDyFB2UYPiHB+NBvJX36vA2YPiM1qHw6XMNI1YakT48UGfqhh0+Ha5wm0A/HfHq8nYjpqxiR2ogvwsIICQlGoTbiffrM4RgTIVm7boNsUMaGT591Sj9M9OlwjTd2MYEyYtY+DCDKFpKJk6YF1yuCHukHbUWYGEf6bZNPjzbUbzh9OlybMrVBSHtQSTAwibQbEvpqaL3ioeeIkekDzBBmtX1uxli1tZiV1xhQDJgxlpJxMcYYxzgqycUYY6FF5GKMsRDWxRhjbBQrycUYY/poiw/zYoyxI0eP+iDK1y7GGCP3VyW5GGOMfF2VhKNyscYYYcorCU+bYza4GGOhHFy8NYk1xvbua69ULIHPWGMsFJmRnGb6yXnRjTHGeMNbSTCUY42xUE4pDM5LZYwdO3bskhljRC28VMbYyZOnLpkxxpG0mL4aY4yBZcZYqad/UMZYKJflxRhjp06frjRskxyPscaYPtbpAzVjrMTKP/jIcdcaZsyQJx7/lvvXfhsDxsAVYsCMsZRoM8ZSLngzZsaYJMeoYt+MmTEmZoylQ0hi3oyZMZYSZsZYykVXfjNmxljaTl3pL3sz1pVaw8piDFwkA2aMpYSZMZZyYcZYiQt7M5b2CY4p2psxSXLm2ZuxUr+IOaZob8bSMdQdjimaMZa2Z1f6y4yxrtQaVhZj4CIZMGMsJcyMsZQLM8ZKXJgxlvYJM8ZKXNgxxbRPmDFW4qIn+YyZMZb2/670lxljXak1rCzGwEUyEGuMXSSsqRsDxoAxYAwYA8aAMWAMXAEGzBi7AiTbLYyBy8WAGWOXi1nDNQaMAWPAGDAGjAFj4PIzYMbY5efY7mAMXDYGYo0xEooSarqScFSDBLIhIdDBwUOVscAAKxTankhxOodO0b1jsAhZTT1DQojpUJh8oreFQopzH45GhsLkkxgzFPUPLCIShrGOSvv+/aEqCtH6QhEjCQsfimLHjd57b1cQi0AGMe1IpLszgUiWRG4M+TZRLsImh47ckCyVPE8hIRw6vjGVhPD+OvdZkS6chqKMUUedY6wIi5DvoQibRM4LhYYHn2iQ6FYS7rV7955KKslnlD0UYRMOOCYaEtonFGzm9OkzQjqAkIClE+T69GnnUDh3vkd/pl9XEsZYKMR/gtW+X44ejcB6b1el2yWf0b9CwWaYR3aqPJNFoMxLOnGvT4+5Mqav7j9wMJgeAiySuoeEuZf5vJKAtePduPUqlAIjdu2jT8TMczHrFWUKtSP1p46Xar2C+46Oc5VoTdpw//7wOkqf6DhXGevIkaNxa9974bWPuUQnh69YiSr80IyxKmw0K7Ix4BjAGLu6rj6TyJEEloSU1iGxyeOBH5ETNsXokGDVCTlPiAKl85GREBY9vaGdNn2W8OOESRIdHbWOXGRg6SStJKpFj02hE3KV6LDJu9v2lLAWLXEqSU4zsMB0wr3A0sYE9dO5dSgzOjqpLYsRWDof2eKWZYne39RmDyzyfjlhAQYLvxsn5HYhia5O+Ep+LPT0Bo1w1RqLDRA6hC13QjhhcqmtUomUcRZHT4cQJ7Hr1GkN7muJwYgOua2cEEofrBUqkXJr68oES29eaEOdRPXgoVIoco2FwQOWTvhKnjPuSZh9J+Qioy11ri50+HHCBoWcOTrhK0lp0dGb41mzG5M+QXmc5LHghESqS5akSZlJfovelq3b3deSxNeTp8zIGNZ5LAzXSZOmZZIyk7MHPdrYCbnIwNLjKo9FWH7y2OnksfQ19PS4Ir8byVv1xi6PhYEIVlNTmtuMhKro6XFFP0JPG4p5LMYcOrr/kisQPZ2zauHCxYke49BJHmvP3n1Jn5ir8pGRJgG9dSpvUlNzS9K/dN6vPBb1h1OuO+EBB//rMcp4p+/ocZXHYlxNmTJD5jSmSZlJUYGeTqTMnDd23KTkgYW7Zx4LY4D+TF48J/Qr9HSyc8Youa50kuE8FptusBpmpgmeGVfo6aTMjAvGGsnqnTisw0fSHHi0o55/GYfo6fyDy5evSrC4jxPGNXraAGAu0eH0qQc6eoySI5G+qscViYPR0w+smOM0Fg+X0NH5B2kH5kydj4z+i55+YEXSab1e0e7o6PyDa9asT+ZynY9s4YX1So8r1gTNF0Y9WMz7Tui3ydqn8pHRf9HT46q0XqXzL+sPOnq8u7VP5+IkKTp6elxNT9bRdI3hPuhwXyfkR0vWPjWuSB6Pnn7QUbRewYcTxlWyXq1d7y4l6z9YOh1Efr1ivkNHJ3RnXNFXdS5O2hk92t0Jicz1eoXBjo5OPE2/Akvn4qT/oadz87FWjRo9zkF3u99mjHW7JrUK9SQG3Juxw0fS3E28tSLHj07IuHrNelm/flOZGp6Ao3NIJbrlKTCbD53gt4yl3hqsXbde2BQ64e1EHoun02Dpp9RsStDTbw2Wr1gpy5atdFDJZyWs9Kko+XeSZMHHjpf1KHeCdSp9m0H9qKcTnoCjo9/iUTfyFZFE1kmKlb41YHOpN3A8mfdhsUnh6Z+T5I3awUNy8lSKxSZcLzQk3QSLHycnTp5MFh9tzNCm6Oi3GZs3b81s4M6cOdsJC/184mGHxX2c0IZ6o88bq3y5yP3CwnngQFpW6ouexmJBxeDTb+N8WGy8dA6uI0ePlbBUUmk2l0uXrcy8QeuMdSrZrJGI2YnDOq6wMD7ZJOhEp52wTp1KeNi7N83BdfRYqVy6/7LJWLJkWWZcebGaW6RtT/rA4eix40kdNRaG6ZzG+UK/cpLHYlxhhOxuS98u8TYKvWPH07HA5nLx4qWZN3udsE6fToxNvYEDI8FS46qtrU2am5dk3jjmsRhXc+fOz7yV8GLt2Zfwqt9edsY6k7TPzp3pGw54Qo82cMLmemHTosy4ymPRxkuXrci83WfuSLDUWyke0rBB12PUh7WsdaVsVcYM/Qo9+pmTAwcOJONDj9E8FmOCeU4bIMxDJax07uCtPgaur1x6XJHrbt26dJ5jHCZYah46ePBwktDdVy79ZpoAHvohAfpg6fWEN2f01RPqraqrox5XzJfkznKSYqWGJHPH+AmTM3OHD2v16nXJQ7gy1oX1Ss+PvGmcNbtovUrHFUa9fpDnX6+Ol9YrNXf41j4eSukHU34sz9qXnNrIrn08BNEPHHzrFX2OOuq3qul6pda+DaxX6xxdybwCr/m1D8NOr1cpllqvNm7OJH1mH9EJ6+TJpE/ofsIDA/R0n8MApI858a99p5K+qt9euvVKY/FQVT+4dZjd5bcZY92lJa0ePZIBZ4z1yMpbpY0BY8AYMAaMAWPAGKhyBswYq/IGtOL3bAbMGOvZ7W+1NwaMAWPAGDAGjIHqZsCMsepuPyt9D2cg1hgjCEPIMR8nYe0rUEQtvlUxzvT4U4QCeGzfvkPwcQoJ5Qo5MVM/6hkSjpmEAmW07dkT5bQ+f35T5gic794cpdNn3306XMN/RB/78elxXEv7lPh0uIZfC8deKsmu3btlvTpuWqTL8SN9XMSnh7/Htm3hduQYqT7e6MPCD0X7p/h0uNbSsjRzfMenh3/M5i3bfB9lruEzEgpIwTEajt2EhONH+oidTx++tI+PT4dr+IbpY0U+PY6RaR8yn06CtXGzaN8jnx7HofRxZp8O1zh6FAokA5/6OHMRFu2j/Zh8egT4WKt8XXw6XOMooPZj8ulxHFv7t/p0uIYfo/Zj8ulxjFf7zfh0uLZt+46Mr6FPj+PbK1et9X2UuUb/Cs2/HH/Vx8MyAOoffMTwAawkpWOWqyqpJJ/hx6n9q3xfAGve/NS/1afDNfw4tX+VT4/1oLV1he+jzDX8zfTx3MyHF/5hnWK9CglzXMw8F7P24W+mfSCL7s3x7+Da17YnKmAL3HO0vZLQhjHr1fIVqzNHyX2YHAnmSHZI6Kuh9Yq5ZNGi1J8uhFltn5sxVm0tZuU1BhQDscYYZ9O1b4CCKP/JhI8jbUg4f6+dk4v0OZ8eMsZYTHUQhiIsyhVakNgo6zP4RVg4wGsfDJ8eDsoxm6xBg4cHo91hbGqfMd/9uIYDfChyHv5UMZt4HLpDEerwiyOQREgIzhEyVPCn0o76RZj4/h1R/no+PYJgaEd9nw7XRo8ZH9wsswmL2XgTnCNkEBAEA3+dkOCvp/3ifPpsNmP8H/Cx0wFDfFgY6AtUMBifDtcs6XOJGUv6nPYQNsE6eE76SfoXm+SYvspDG+0XlyKkf4H11qCh6YWCvwiKpANz+NR4oEbwlJAQmIpAGJWEdYr1KiQYWTFGW8zah38dZQsJgWtCDw8JNETQoZC8NWhYxh/Up08brop4KEAwE+3/7cMigMyKFanPmE+Ha4kPp/Jn9uk1zp0vI0aO8X3ULa6ZMdYtmtEq0VMZiDXGeJulgwr4+MLYidnos8ENvWUDn4heIWOMp2a8HQsJ5QoZYzzR0xERizAxjEKL2569e6PesuFUHHqbRWAIHWGqqFxsZkJYbMx1dMUiLDYzoSeNPHmOeaOCgRsyEgmFrKMrFpWLzQdvEyoJm2XeJISETVEo9DgO7DFvXuGBsVRJCB4Q2mzyfTZ+oXLx9kZHziy6Lw8YtPO+T483ZzFv7Niwhd6yUW4dhMF3P67xoCL01oigHjH9i/bRzvu+exLwQkd99Olwjc1fyKimnZcsTaNwFmHRn4n+VkkYFzFv7JjnQnyxsSVCYEhoHx1F1qfPPLJ6TfgtG+HJQ2kkeHAV01c5laCj7vrKBdbCpjSKrE+HazyQCb1lYz1YsTL8xo63iKG3bKxTrFch4VRCzMmEmLWPdBShN5yUhxMTMWtfzFs2guCE3ozRhjEnTDDYdDAYH3c8KIpJi0BfDa19zCU6+rPvftV8zYyxam49K3uPZyDWGOvxRBkBxoAxYAwYA8aAMWAMdEEGzBjrgo1iRTIGYhkwYyyWKdMzBowBY8AYMAaMAWOg6zFgxljXaxMrkTEQzYAzxsh344RjBhzx0EfLCICxYuUap5Lk/0JH+6NwvAe/JQICOOGYAXr6aFnr8lWZ44z4JuWxDh8+LFNzSYB9WORH0k65HEcCC10nHA+jXPooU3t7qVzaL4rjhzoACWXOY1E3EoDqvFlwgJ7GWrV6jSxTDt1wiY4+hsORL5Jo7t+/3xU14RM9nVOK44faL86HRd6zhplzhHo54VgTWNpfi2NM+qgGRxHR4ccJWDNnNWaOH9E/8lgc8dE+Y36sYzJr1lzR+bw4YlfCSvMtrVu3UUhsqo+a5MvFEbhZs+dljgw5LH0UD182EoTrY5adsY4nCYU5zuSE443o6RxyHBkk8WklLMYQCUb1MR/GAlj6WN/mzdtk4cJFmXGVLxftjs/YzvfSxKf02xJWOq44VkgCbz1G81j0R3K86YTCDkvnW+KYL4Fk9BjNY/EZ/mfbVKJuxih6/HaC4/68eQszuQZ9WA0zZ2d8UCkPenqMcjwJXvW4ymNRf9qH/HlOGKMlrDS3HUlpyXWlx5UPC58+7RtL+6Gnjy7Szvjh0O5O8lj0F/qz9o2lX+WxOGpGHig9RjtjnUn8FrV/EP0dPR1shEAajFt9xNVh6XFF++gjdejnsZinmE/0uHJYeiwwLzE/OaEe6OkjlcyP9FU9rnxYHBvWWPCbx2KuJHGvxvKuV8uWZ5Jr0+5gZderg4mvkV6vHJYOOES+OJ1cm/6Yx6LfxqxXJHfWCZ5TrHTedmvfITWu3NrH+uaEMlE2J771inHFeqX7r2+9ImCTXq+oP3XMrldHZNTorJ+tw9LjijbU/r++9YpxRZ/QQXzceqXHFfnitP8vedlK5cquV/RVveY7LD2u8Bkjr2d3FTPGumvLWr16BANMfFfX1ScbB1dhDBx8mfRCTxCGhpmNTiXx+UJn+fJ0MWDjiuOx9rFhsUZPL4JMnPw4YXJFR0e2YrMJlt5kMcGjpxcIFppp02Y6qOQzdPTCAgZY2i9m2bIVCRb3djJzZqNQTyeUGSxtCG3dui3B0r4scIAeGysnbIpYbJywOKDT0rLMXUr8U1jctC8LmyT0tE8Hxsz0GSkW7YLO4sVLylj4pxCkRPuf4FyPnjY42PgRnMMJmwh0dGAJ/FNwbNcO3ZzvR4/AEU5ow8lTprt/hYU/j4UhwMZVO3SzwKKnfQFIpI0TtjZe0OHHCX5zBE/RGyPqi442OBob5yfGtzY48lhwMnbcpCTRtMN3WDt2vOsuJYYRhrzezOSx8NuYPHl6kjDYfZE2RQ8fJCfzFyxKNmx6XOWxaPfJU2ZkfJLoa+jpcUXADdpbb3rzWAQMAWtxy1JXhGQMoKfHFYbrlCkzMpuZPBZjjiAMGBhOwEBPjyvmDu6pje88Fpsmyo7/iZMtW0pY2t+Mhwb0L+rhJI9F/Wkfgos4gSf09BglmTN9R4+rPBbtAta8eU0OKmk/9PQY5YENfUf76+Sx6C/0Z4xJJ/Qr9Ii86WTFilXJ+NA+Nnks9wBozpz57mtJf0cP304nbKgZa9q/1GFp44X20fMv4xA9xqUTNtS0kR5XzBHoaeObuYQ5xQn1QEf7iOEzCpYeV/Qj9PS4Yr5k3nQCv+joAA5wx5yp/UuZB9HT4yqPRbujo41Q+kd+vWJ+Rk+vV/m1j3keHaIUOqHfgqV9Qt3ap40E+gQ/Ttzax3rkxK19+Gg6YT3jnnrtYz3W6xX3QWep8mekPJRr46Y0AAnrLHqZtS+3Xrm1T69XjKvSerXJFStZ/8HSPuDJ2uddr9J5iHmRPqGTadPOYOlxlV+v6C/o6HmIfgWWDr5F/0NPr33MJRjy3VXMGOuuLWv16hEMYIz1q+8brCubdrLaVxKcmPVmvUiXJ356o1ykx9uBUAAP3tjoDWkRFuUKYWEI6CfzhVh/2xV0iCbin95oFGGxwIWCgfB0OgaL4CMhLJ6C601LUbkIshLCog31gl6ExUYoFH2SfhjTjjjSh7FOSPv+9E1vUbnYaOqn/D49nlzva0/fXPp0uAYP+u2DT48n13pj5tNxWKFy8SSatz0hYfPG0+RKwpNrvckr0kXn5KlTRR8n1ym3NsSKlNlw6afpPj3Cq8f0L9pHvzHwYdE2+mGJT4drbEL1mzifHlg73g2H26Y/66f8Piz6sjYQfTpcI7qmfsrv0zvb0REMwc734FQbVD4sxr7eFPt0uMbbZP32zKdH8IiYvsocp43GIiweiIXk0KFDmQc7Pn3KFbVesfYdTt9K+7BYW/TbbJ8O1+gTMfNczNpHmaLWq/ci1qsjR+XgofRNclH54b6j41zRx8l12jBqvfrbbuk4F8KKXK8i1j76vX4gULESVfihGWNV2GhWZGPAMRBrjDl9+20MGAPGgDFgDBgDxoAx0HUYMGOs67SFlcQYuGgGzBi7aMrsC8aAMWAMGAPGgDFgDHQZBswY6zJNYQUxBi6egVhjjPPY2rHddyeOfXB2OySW9DllyJI+l7iwpM9pn7CkzyUuDhw8lPG5ShnK/kVS7tBRP4504ZcYEnxkQkfqLOlzyqIlfS5xwTFFfLNCYkmfU4Ys6XPKxaX4y4yxS8GiYRgDHxADZoylxOM4rZ2A00+yfxEIIOS3tHnL1iSxbfabnf8zY6zEiRljad8wY6zEhRljaZ8gaAiRKivJ8RMnMoF+inSJpqgDkvj0iKanA034dLhmxliJGTPG0h5C0BAdsCn9JPuXGWNZPt7vf2aMvV8G7fvGwAfIQKwx9gEW0W5tDBgDxoAxYAwYA8aAMVDAgBljBcTYZWOgGhgwY6waWsnKaAwYA8aAMWAMGAPGgJ8BM8b8vNhVY6AqGIg1xkqh7S9NeN/o0PY7w+HoCROsc8IUkR4TKph8Ppc0VPDB2FDBHUXFTq4TKlgnmS5SjgltTxjqqND2EaGCY0PbEyY/dKyTfhgT8pl8NmGsE1F94lKGticX1pUPbZ8mrC7qEyQC1omhfXqXMrR9KSnrPt9tMtdiQ9u3qTyAGQD1zwcS2n5HOLQ96RXo15UkOrT9/sjQ9rvaKt0u+exShrZnLokJR6/zPRUVkHDoOs+gTw+/5C3Roe0rr1eXPLT9zjQHo6/sXIsObR+x9n0Qoe3hPhTanjbsiqHt2/bssdD2IvIPRZ2T6w0zZsgTj3+rkop9ZgwYA5eBATYLJH1eqJLrkixx3vymzOaY5J46iTGbKXSWLF1eLhWBOXBi1skqmxctSfT27msv65HAWCcxJncUWC1LWss66y8k5NTJKkkoi57OPUSS1qlTG8rfY/OGzmKVXNkl5NRJYEkoix73dkL9dEJkyowOdXBC3aijTtwKB+hhdDghGScJqZ1gMKLT1NziLiUJQkePmSBr16ZJYHHwRg/DyklDgpUmCmVBR0e3GfnKCJ6iE7e2Ll+Z6On8NyR7hTMnLJpgzV/Q7C4liW7BIomsk+UrViV67+5M/VbgC/85JxiyeSySs5KIVidq5m/0SC7thEShU6c1CAaxE3T4cYLxBJZOtopvAjrbtqeJmmfPmSv4I2jDOo+Fj9q48ZMEvp2Q6DbBUoma5zTOT7AOHDzo1BIdXa73/rYr4UEnB8f3EB2dBBZfMJIra6MzXy7GFZzS153Q19DT42re/IUyYeKUjNGZxyKoBYlOdf9lXKGnx9XChYsTPZ1rLI/FmCNZsO5zJHlHT48r+jfl1zm98ljch/6l+xzBgdBbv2Gjq7Y0L1qaYOngHHksxhVtzXUnJKPm/7UquTLjfdLkaZlxlceiXcDSiZrZfKKnfUlpZ5I+0+5O8lj0F/qzDhpColv0MmO0deWFRM3puMpjselmzJL83QnjCr38GIVXnQPNYWkjh/bR8y/jEL3MGF2xOmkjnVyZ9kJPjyv8yvIJpNFpXb7KFVVKCaSnZBKgk6QbPT2umC91EmMSSKODv5wTklwzZzLfOaFPokcuNifTE6zZ7t+k3dHR451xxVyOf68TEqCjt69dr1fZtY/+iM4SlVyZfpusfZu2OChZtPjC2rc3fThBn+DHSbr2LXOXkvEEFuPLCesZ99QPJ/LrFQ9e0CGgjROXQFr7CLLOoqcTNefXK+qPDnw4YVzl16vy2qfWqzyWW6/YVzhhXNFX9biinbmnToBO35qm1iuMf3R0kneXQFr7qdH/0NMJ0On3lvTZjDHXB+23MdClGHBvxvQCu//AwSRprk48y6K/RhkNOHjz5Fc/AWPBZ4E4dvxEuY4OSyeeZXFevWZdWYdEsmDhsO/k6LHjJaxj6ZNlPkdPP+lftmy56E2wD4tkqZRLJyd1WDqJLUaR3txQZu5HHZxQt5kzG+WwMhrgAD04cbJu/QZZuTLdkMBlHoukt2zqSFDq5OChw4neiZMn3aXE2X652tyQDDfBUomNcd6fNXueH+tEirVx4yZZ1rqyjM3bHLD4cULSW4wQosY54W0mOtzHCW24QBlxPizqOKdxQcYAOXT4SCesTZu2ypIly+XMvPlH6QAAIABJREFU2bMOvlO5uDcGjTbs2agm5VJ9jsSk9An9pqpzHU8mG+89e1JjnDZF75h6m7F12w5Z3LJUTp85U1gu2goeslhHS1iq/7LpZYOmx1W+XCSGZqOhHxKQQBw9xoQTNiAzZ80NYJ2ShU0tmeS9R44eu4B1zEEliW+bmloyyaHz5WLMYWjtfC81QBhPSbmOpli7drUJxp0eV52xTsvs2XMFbp0cPVbConxOdu3ek/Cqx1UeCy5pH53MlfGOnjZAMCbZnOlx1RnrjCxZsixjNDgsnfCedsYwrYh1BqzlsnlLmqCYfsU99dzR3t6eGH86aXW+XGfOnE2MiI0b040+4wo9xpITjBHGmh6jDkuPq4ULF2WCC6Gfx8JIwpDUCbDLWGosMC9pA5p6JFiHDrtiJXMSfdVXLj2uVqxcJTzQcwK/YDEnOmGuHDN2YgaLzT56zItOVq5anTHGfVg8+GmYOTuTfLy8Xp1OE6WzyV+9Zr2DTuZ57pdZr44eu7D2pWMUwwE9vfZhvOgHmJXWq2PH0rHgW6/WrFmfCZTh1it98oE+h0Gjx0IZS61XPLiAMyenPOsVax/c672Cf+3bKCtWhNc++kRo7eNBT2urwvKsV/Qr+qpOWk0Z4V6PqwULmmTS5HC0Z8dBtf22Y4rV1mJWXmNAMeCMMXXJ/jQGjAFjwBgwBowBY8AYqBIGzBirkoayYhoDPgbMGPOxYteMAWPAGDAGjAFjwBioDgbMGKuOdrJSGgNeBmKNMRKhEqSgkuAQjW9RSPCt0n4gRfr4PJG/pZJwPIkjWyGhXJSvklC/UMJXvo9vRUdH5aAbe/buTY5/Vbofny1sWpQ5TufT37u3PXP23afDNY5/6qN5Pj18bEL5ivgeRxD1cTof1u62toy/kE+Ha/gF6KOlPr39+w+K9k/x6XCN4zQc5askHK+M6RNLl7Vmjq76MDn6skX5p/h0uMZxGsZSJTl06EjGh6xIF18Rju1VEo4i6SO1Rbr4YoUCLHCECd+SkGzavCVz3Mmnz9FFfDRDsnr12szRVZ8+R6y0P5pPh2u0jz7u5NPjuJI+AufT4Rr9Rh+99unRzvpotE8nwdr+buaIs0+PcbF2bXoEzqfDNeY57Wvo0+NomT7+7dPhGu0Tmn+ZR2ijkOzc+V7m2LBPnyAlMX31vff+JtpvsQhr4cLUv9WnwzUChmj/Kp8e64E+TufTSbB27c4cG/bpsU6xXoVk+453hZ+QxKx9+GVq3+IizBUrVofXvj17Mz6QRVgcceXYbCWhDWnLkKxctTZzLN2nv29fe9x6FbH2bdiwUfAd7a5ixlh3bVmrV49gINYYY0PNxq6SsLjhlBsSNkUEEggJTswhY6y1dUXUxohyhYwxS/qctgiBTLS/SPpJ+teGjZtk7twF6YWCv3DoxvemkljS55QdS/pc4gLfFh1MI2Uo+xcBC0LGBb6FOphGFiH9r6VlWfCBDMb+yFHj0i8V/IVvkA6e41PDL0gHwPDpcM2SPpeY4QHRW4OGFtFUvk6gDx4eVBIeqE2cFF6veACkg2n4MC3pc8qKJX1OubiSf5kxdiXZtnsZA5eYgVhjjAhHOqiArxgYOzrylU+HazzNw9E/JMuWrQgaY9u378hE1irCpFwhY4wnjTqSUxEWkZpCb8Z4KstT45DMX9AUfJvFk8aYt1krVq4JYvGkUUcxLCrfqlVrgm/GeMOpo3QVYq1eG/Fm7EDU2yyc1nXgBN89eWsU8zaLp6Q6qIsPi7ckOgiDT4dr69ZtDBqcOJVvDmwQwYLT0Jsx3pLEPNVnE6md933lJ5BBzNssdHTwCR8WfK5fH37QsnLlamnfv98HUb6GAR/zNov2Cb3N4sFCzBsoNpI6AEK5MOoPDCgd7VJ9lPmTACXBt1mnTsnqNeE3UNu278hEzszc6MI/vBnTEeV8OlyjfxG1s5IQDCPmbRYRTmPeZsX0VeZLHSnXVz7eshFJNCS8mdERPX36rAc8zAsJUTN1pFyfPsYY61VIePMa89Y+Zu3jAYSO6Fl0b6LPhte+vcEHB+ATBCf0Zow2jFn7eGOnA8v4yk/filmv6KuhkxwE1SKAUncVM8a6a8tavXoEA7HGWI8gwyppDBgDxoAxYAwYA8ZAlTFgxliVNZgV1xjQDJgxptmwv40BY8AYMAaMAWPAGKguBswYq672stIaAxkGnDGmj/kQ5IHjbPq1/6rV2TxjOMSjo4/0cNyJ5L06P4rD0gEccDLnTL8TAjKApY/0EHQALH2MjM/R03mHOGayVCXf9GMdS7D0ca0UKw0GQZ4x6umEMnM/6uCEupHPSycnhgP0dE4TjletXKmxTnuwjieJQnXelhQrzeeFf93yFWkOGNolXy7asZQbTOUsO1gqFzmJnHDUTDuacxwJLH6coI+vjs6vRv9Ah/s4WbN2XRKAxP2P078PK/GBUkfSfFjkGSNnnA5AksfiqNn8+c2ZssIdetonjYSwJGQNYeEXp48ypVhp8AyOmpEkVY8FX7lwbNdYhw+XyqX7L8dtON5WGetkklhZ+0Dh78Q9dSAOjjrhA6VzGOXLxVggaas+kka/RU+PBY50LVpEnrE0T15nrFOyaNGSTJ4xMPJY3IvkrjrISh6L+zQ2zs/kGUux0rxZcECAm8pYp5P20XnG4Jx7wpuTPXv2JUmmtR9kvly0C4E59DGyFCvNdUU7k4S5UrnAIsGwPuLK3ME99XhnbuHYnZ478uWiH3PMWgdZob+XsNLxzpzGuPXVUY8F2kfPv4xpsPQaQECdxrnzMzm4XLk0FoGRtP8vc0ceC1z6qp47HJYeCxyz1seeqQd6eo2Bu/ETJmew3BqjsThmrZN++7AYC7OS9Sqd0xyWHgsERtLJiWn3UrnS3IzkAsyvfW6N0VjLWpcLP04cFrpO6HNg6Zx7Dkv3OcpE2ZywLlIujZWsV7PmZtYrH9badRszx1IpM1j5tQ8/bt1/0/UqXUdpwxUr0rWPdumMdVxmz5mfySGXYqXrFQF8sjk2S1jgOaFf0Vd1P0nXmBSLuWTK1Onua93utxlj3a5JrUI9iQEmsqvr6pMNlKt3c3NLkmxVT+rTZ8wWAjE4YaNEolt9Tp7kn0zWW7ZsdWrJ5hM9PXmSgJkfJ2xu0NFGFUYDWHoDgnM9etpHYdq0mTJ1WoODSnwO0NHRzsAASzthcy/09Aa6oWGOUE8nlBkd7R+yefPWBEtvGjAi0NMbaJzy2ew7YVFDhw2tE5ITjx4zQdat2+AuJT4M6OkNdMPMRpk2PcVi0UGHdnLCBpIgJXqTxSKGno5sxSI/bfpM97VkA4YOxoQTohqCpf1P8PFBT/sC0IaTJqeLG4t0HotN8sRJ04TvO2GjhB7+Jk5mzZqbbHC1kYAOP064N1jamCTiGzo6EuOcxnlJn9CbhjwWnIwbPynTf+GuhJVG5ySJ7pSpDZmNah6LCJzwsHRpusmiTdGjjZ3gbzFl6ozMZimPhS8lWItb0qhf9DX09LjC13DCxCmZzVIei75NcmICXDhhc4OeHldsztHT4yqPxWfokPjZyaZNmxMs7W/WvGiJTJ48PeP7k8diXNG/5qu2pTzo6eiJlBsu9BjNYzGuaB+MdCf4faGnxyjG+aTJ0zLjKo/FuJo6tUHmzkuD0mDYo6f9zWhnkrXryKt5LDaDGGw8IHGCfyt6eozSl+nTBLBxksfCqASLh0BOGFfo6YiH+ODAq/YvdVh6XNE+ev5lHKLHuHTCgySwtJHLHIGeHlfMS8xPTqgHOtpHjIdv9FXq74Q+h542AJkvdTATIiKis1xFKcQAGT1mfMZgduuV3oznsZhPwdI+YjwwK61X6RhdvHhJoqeNkM5rX2m9Yt53Qr8Fi/XBSUvL0gSLaLhOaEd+nLi1T69Xbu3buCmNSsrnlF/71LEe6/WKMYoO66QTt17pcUX/RU+Pq6L1Cj6cMK6S9Uol5mb9B6vT2qfWK/YR6Oj1inFF/9LjinZGj3Z3MjO39hE8Bx36jxP6FVjZsdB57WMuGTU6HHjH4VbbbzPGqq3FrLzGgGIAY6xffV91xf8nC51ehH1aODHHONuyABMyPCSEAA5FU2xvz77VKcKkXCEs6qcX9EKsd3cGHaLZQB04kD7tLMJiwQ0FA+EJrjaMi7DYCIWxjmY28IVY7/1NcJavJIQT14twkS5BUUJY7q1BEYa7zgZYP5l31/Vv3hrsVU9O9Wf6723btmfeLOnP3N+Mjz1797l/C39jROkn8z5Fns7rzZRPh2twSjCGSkId340IEEPQHf1k3ofJ03a9MfPpcA0d/WTep8e9du/e4/socw3DWr/NzHx44R84CAVOQJX20W9/fVi8AY4JA86GljavJLQzm8mQYHTSrysJ4yImCMO+dt6MhrFC0RspC/1LG0G+8jGPaAPRp8M15iV9SsCnR/CImL66/8CBzNvMIixt/Pt0uJasV4fTt5k+PcoVs14R1TNm7YsJWU+f4CckMWtfsl4dDK+j1DEUwONQsl4dDBUrCfTT0VE5RQxrX8x6RZ/oCKSb4SFCe3t4HY1Z+3bt3p15OBasbJUpmDFWZQ1mxb30DJzcOkl+9/h98tG+faTftbfJF3/0qjTvrbyRLZfi5FaZ/PS35P6brpL6+uvkzs/9SP7StFc6f/ukbJv0tDxx783yod595YZbPy8/frVJYm9Tvl/uj1hjLPc1+9cYMAaMAWPAGDAGjAFjoAswYMZYF2gEK8IHx8C53WPkuzfUyIc/+0t5e06zNE1+WZ66o17q7/pPaT4aKNe53TL2iQ9L7bWfk/8aPkeaF06WV75/p1zd+5Py3036y+dk95gn5KZe18kXfjlcGpsWypSX/o/0r+sjd/9ns2jNwB07fWzGWCdK7IIxYAwYA8aAMWAMGANVw4AZY1XTVFbQS8/ASWn+91uk9ronZYp6w392x5vylfo+MuDlrVLphf7Jpp/Jx3tdLz+YnPmyvPVoX6l/8BXZ5r58skl+fnON3PjkZEk1z8qONx+Vfr0fkj9tdYoXX8NYY8ySPqfccvY8dOxu85atmTPs6bezfw0aPDx4jIwjUToYSBYh/Q9fhNCRNHyrcLoPCT4XOhCAT9+SPqesNDYuCB79amvbm/GbSL+d/cuSPpf4sKTPab+wpM8lLjgiakmfS1xwXFMHKUl7S/YvfBJDx9c3bd4q+PaF5K1Bw4JHuy3pc4jFy/O5GWOXh1dDrQYGziySX9xYIzf840xJY/aIyPl2GfVYndQ+8LIU20lnZNF/fERqr/mRzMp+WdpHPCZX9XpQXtlSMrLONP9cbul1rfx4ZkZRzrePlG/U1siAl7b83WyZMZZSRxABHTUr/ST7lxljJT7MGEv7hRljJS7wFZk3ryklpuCvadMagn5EZoyl5JkxVuLCjLG0T5gxlnJBUKqQPysRF0eMHJN+qZv9ZcZYN2tQq048A+d2vSVfquktj/x5W+4NWIe0/urjUlv/pEwr8gU/t0sGfaG31D38Z9mee7HVsezXcluvvvKDqXz5nOx664tSVzNAXiu/KrtQxo5W+c3HaqTfk1PjC53TjDXGcl+zf40BY8AYMAaMAWPAGDAGugADZox1gUawInwwDHSs+b3071Un3xqVHh4sleScbHvpQant/WUZtue8v3Ada+WZO2vkqm+MVkcPL3x768syoFcf+eoQopJ1yNrf3yW1td+UMZ1us1VeeaBG6r801H+PiKtmjEWQZCrGgDFgDBgDxoAxYAx0UQbMGOuiDWPFuvwMdCx/Wm7vVSffm5APoXFOdr7+WamreUTe2Jl77eWK1bFcfveJGrnqiYmdAnCc2/mGfKGmt3z+NfIwdciKp2+V2trvyKROt9kpbz7SW+oeed2hXvTvWGOMcLWh0MqEjifEd0gIV6vz3hTpkxsmFI6eEM0x4egpVwiL+lHPkBAaOhQq+OgxsCqHVuY+MWGHCQEeCq0MFqHHQ74BtHdMWoG2PXuDWCQ6jQnTTDj3kI8doclj2pEw5mcCIffxdYvBIqQ4Ic8ryYmTJ6PCNMNDCIukrDEhn0tYlUPbU0fC1oeEfEk6MbRPHz9DnVfJp8O1ElaaGNqnxzGymD5BXw35JMJnDBacho4okQ5B51HzlZ1r9BudgNmnB5bO3efTcVjHT2SPlud1GRcx6Q6Y50Lh+892dAjjNiRwGpp/mUdi0h0wL4VSFDBXxvTVQ4fBqhy+H6yYEPLR69Xu8Hp1+MgRYa6rJKW1b3clleSzAwcPCj8hiVn7SAJP2UJCeohLtfaRdy609tGGMesVfSIU2v5Srn30+5jUDyE+u+rnZox11Zaxcl12Bs6tHSj38GZsdD7Xh3sz9qgM2V3wZuzcWnmuf+nNWKdvX3gz9pXBTO7nZN3A/qU3Y50VS2/GHh1csa5sep54/FvytS9/pdPP5x/5rNT2qpG7br+j/Nldt98pd9x6u3zuM4+Ur91x623Cj8P4zEMPJzp33/XJ8rVP33Ov3P6J2+SB++4vX/vkHSWszw74TPlaHuuRhwckWP3v1Fj3JVj33/fp8vc+ecddiZ7GuuUjN8ktN95U1kmx7ipfu//eT5ew7r2vfI17UUf0XZ3y5eI+6FAHp/PAfSUs6uquwQF6n3moGAsu0YFb970HP32/XH/NtXLfp+4pX7v7rv4XsB4uX8uXizYrYaVt9uCnH0jqqLE+9ckS1oAHHwpi3XlbivXQ/SWse+/+VPl79/S/O7nnww+kWB+7+Ra56YYbyzpf+OznEp07b7u9fO2h+x9MypXF+tQFrAfLetSRvvPFz31eXbs90XN8PfxACYuyuGvgwgVldte4P1iUx11Dhx/3P5zccO11Qp9y1+69+55CLDh3ep2xHk7uB99Oh3ZAjzZ21xhjlCs7rrLlYlyhkx9XYOlxddvHb5Ubr7+hIhZ9G6z8uAIrP67Q0+MqX0c+K2GlfDGuEqzMuLor0cuOq2wdwbrxuhvk9k/cWuaG8oD16XuyY5R7VsKCS3T0uIInsO77lB6j/RM9+HXtka8jbVzCSscC7VfCSsco88GHr71eBjwYxsqOhQcSLPqZKwN9mXtmx2iWL/oxOpTDfY9xxf/ZcVXCYpw4PVdHPa4Ys4xdp4M+evf01+P9U8k9uY/Toy7oZcdVdl2gHuh86pN6jN5zAUuP0TsSvey4KsJKxxX1Zc5kvnPlYlxxz0pY6XqVYrn1KjtGw2sf/ZH7Zcdoab1ifXDl8q5XNxatV+nad/+9F9a+e1Os/neW1r7sWMjyla5X6RhN16vsuKL8lbB86xXjqvN65dY+PRay5fJhwTl9+tKuV+m4ov9RRz2uPnrTLTLgoQEV90rV/KEZY9Xcelb298XA+bYh8tXeveVzr+3w+4zVfV8Sty/fXc63ydAv9ZG6z7wmO3Ivz0o+Y/Xy5BR8xs5L2+AvS33NI/J6J8WSz9jV35viu0PmWnNTs8yfN6/Tz8yGBqnv3Uf+/Oqfy5+9+MKL8tyzz8mkiRPL1wY+M1AGPvNs+f8xo0cnOn965U/la2/99S155g/PyNAhQ8rX/vjiHxO9CePGl6+VsAaW/x87Zmyi88rLr5SvDXprUII1ZHCK9fJLLyd648aOK+t95Utfli9/8dHy/w4LXVffwYMGJ1hgumsOC313LV8uygwP1MHpUB7qSF3dNThAb8zoMeVrcAWe05k4YUKiA7fu2rChw5KE25rDV//0aqI3etSost6zOSzahfu98PwLZZ3hQ4cl5XrzjTfK12hT9EaNHFm+lseaPGlSovP8c8+Xdd4ePjzBeuP1FOsvf/5LojfinRFlve9864nE2HD1mTJ5Sgnr2efKOu+8/XaC9fprr5evvfaX1xK9d95+p3ztuYElvqZOmZpee/a5RM/hj3jnnQTrtT//pawDLnV8e/jb5WvPP/ucDPzDQKE87rvo8OP+HzlipNz84RvlN7/6Tfka9UVn+LDh5WsvPPe8DPzDMwJP7rt5rFEjRyU6tJ3TefONNxMs2thdo+3B0uMqjzV61OgSVm5coafH1T//+J+FzTH9yuHnscaOGZNgvfKSHldvJeXKjyv69Phx6bjKYzHmKHt+XKE3eFB2XIGlx1Uei3GFQfPPP/5xueyUBz09rpgPSljpuMpjUX/G2R/VuBo6ZOgFrL+W8WkbsPS4ymPRLmC9mBtX6NGejuenf/0buemGDwvt7q7lsegvYNF/nA79Cr38uKJcI0ek4yqPxZgAi37tsBhX6OXHFViZcXWh30+bmo6rh+9/QJ54/NsK650Ei3Hp8F9/7bWEL+7jrnF/7jll8uTyNcrFnOJ0qAc6f/lzup5QX8qVGVfPP5/o6XGVx4JfsPS4Yq68qrZOmO/cPZkH0Zs0MR2jeSzaPY+VrldDy1h/fLG09k0Yn1+v0joyrsDS65XD0uPqpT++lOiNV2vflx/9kvDjyu5br9zax7rl9GLWK8Yv5eK+7ntuvRr0VrpeUW70qIfTgy9+3P/UHx34cNeYf66uq5dX1dyUrn2jy3r5NcatV3rtc+vVX99Mx5Vb+/S46oxVWq8ya98w33pVWvuY5135eSD97W8+ntkXdad/zBjrTq1pdbk4Bs62yH/dVCM3/LhRMod3iKb49TqpvfcF2ZQztNIbnJUlv7xZaq/9J5mb/bK0j/i6XNXrPvnjhS+fbfmlfKzXdfIvczKK5WiK97+wKYW9yL94a9avvu9FfqvrqLOJf+b3v+86BbrIkvB25tCh/CvPiwT5gNTZqLGhrlb59KfukfXrwuGcu2L95jbOla9/9WtdsWhRZfrGY4/JnNmzo3S7mtLGjRvlnv79u1qxosvzk3/+l8SYif5CF1I8cuSIXHt1vy5UoosryrPPPCP8VKtc/6Froo7fd8X6vT1smPzrP/1zVyzaJSmTGWOXhEYDqU4GTknzz26W2uufkqkH0+OIHTv+Kl+pr5FPP7teOipU7FTTf8jHet0gP5xyUMrf7tghgx7tK7X3PCcb3JdPNcsvbqqRjzw1RdLbdMiOvz4q/XrdK8+vd4oVblbwkRljBcRcoctmjF0hoj23MWPMQ8oVumTG2BUi2nMbM8Y8pFyhS2aMXSGiPbcxY6xEyj94uClfapgxI/FpKV+wP4yBKmHg3K6R8u3rauSGh/9dhs5aJM1TX5Uf3lkvdbf+VObp+A1Hx8h362vk6i++LuWYHud2yahvXi+11wyQ/xg8SxY1TZW/PHWXXF1zm/xsrv7yOdk14nG5sde18shPh8js5iaZ9upT0r+ut9z507miNS+WNjPGLpaxS6tvxtil5fNi0MwYuxi2Lq2uGWOXls+LQTNj7GLYurS6ZoxdWj4vBs2MsRJbZoxdTK8x3api4MTm8fLbx++Tj/btLXVXfUw++9QLMm/32WwdfMYYGic2y4TffEvuv+kqqau5Wm4d8JS8OHe35L6Nomwe/xt54t6b5UM1veWaj35Gfvj8XMnfJnvT8H9mjIU5upwaZoxdTnYrY5sxVpmfy/mpGWOXk93K2GaMVebncn5qxtjlZLcythljJX7MGKvcT+xTY+ADYcCMsQ+E9vJNzRgrU3HF/zBj7IpTXr6hGWNlKq74H2aMXXHKyzc0Y6xMxRX/w4yxEuVmjF3xrmc3NAbCDJCfp5oDeJQi5/0hXNEuqvHha6+rWodoohv+y4//qYsyGy4Woa03rF8fVuyCGvPmzpXHvva/umDJ4or0zcf+tzTOmROn3MW0Nm3aJPf2v7uLlSq+OP/2L/8qbEyrUcitdV2/D1Vj0ZMyPzdwoPBTrXLDNdfKkYj8mV2xfkQJ5kFEdxUL4NFdW9bq1WMYWN7aWrV1bWtrk127dlVt+auZe5Jab92ypWq5X716tZDAtxqF5Mpr1qypxqInZSYiYSjBb1etHAl0Vyxf3lWLFyzX9u3b5cCBA0G9rqpQzXOmrVcfXK+q9vUqxJwZYyGG7HNjwBgwBowBY8AYMAaMAWPAGDAGLgMDZoxdBlIN0hgwBowBY8AYMAaMAWPAGDAGjIEQA2aMhRiyz40BY8AYMAaMAWPAGDAGjAFjwBi4DAyYMXYZSDVIY8AYMAaMAWPAGDAGjAFjwBgwBkIMmDEWYsg+NwaMAWPAGDAGjAFjwBgwBowBY+AyMGDG2GUg1SCNAWPAGDAGjAFjwBgwBowBY8AYCDFgxliIIfvcGDAGjAFjwBgwBowBY8AYMAaMgcvAgBljl4FUgzQGjAFjwBgwBowBY8AYMAaMAWMgxIAZYyGG7HNj4LIwcE72TP5Hue2qb8vow54bnNwqk5/+ltx/01VSX3+d3Pm5H8lfmvbKWY+q79LJrZPkd4/fJx/t20f6XXubfPFHr0rz3s7fjtXz3aN6rwW4P/WuzHr+/8qX7vqIXFtXL9d8+C754g+ek4Ydp8JV7tgkLz9cJ7W9ajr99HtirBzTCO+zjTVU9fxdmfuOTX+UR2o7c1fbq698b2yGPW+Vo/tzj+Re5NyeyfL/ffxq+c5IPel0yOaXPiNXefqs68d9P/U/Xr7Tix2y6Y8D/Bj135Fxuul6EvcXMZdE992U9PSvaE5PyrZJT8sT994sH+rdV2649fPy41ebxLM0pNjV+lc096fk3ZkvyI++8Em55ep6ufqqG6X/534oz8/YIeEZ/yL6vfQg7iWS04tZL739MJbTWD3vTa7IRTPGrgjNdhNjQDNwSrZP+pk81K9Gaus9xti53TL2iQ9L7bWfk/8aPkeaF06WV75/p1zd+5Py301HNZD373O7x8h3b6iRD3/2l/L2nGZpmvyyPHVHvdTf9Z/SrL4eq+e9SdVeDHHfJpN++AnpW3erfPO3w2TanEaZNuRp+cYn6qXvx56SCbvOVa758cnyw2v6yMe+9DN5duBAeU79vDh+nZx2336fbexgqut3gHsROT75Kbmh983y1X9/JsPdcwNfkInryux5qx3dn3sk9yKntk+Sn9//IcGwzRpj52X/4mHyguqrrt/+9jtK6qchAAAZYElEQVR3S79etXLHP83wcp5ePC5TnrpW6m/6svz8mWy/f+75CbLeNV1P4v5c/FwS3XdTwtO/ojk9J7vHPCE39bpOvvDL4dLYtFCmvPR/pH9dH7n7P5tFLQ0pdrX+Fc39OWmb8H/ltj71csdjv5XhUxtl7tSh8ruv3ypX9/m4/HD8Lqk840f2e+lB3MtFcBq7Xnr7YSynsXrem1yxi2aMXTGq7UbGgMiJdxvlLz+6X26oqZG6mt5eY+xk08/k472ulx9MPphSdnaHvPVoX6l/8BXZVnF1OCnN/36L1F73pEzJfP1N+Up9Hxnw8tYLi0usXlqEav8rhvuzK/6f3NenXgYMXJt5Knpq1R/kodpaufe3yyvScHb1H+T+2n7y/bH6zUPnr7y/Nu6M19WvxHAvclZW/+E+uerq78q4yvR5qhvfn3sa93LiXZn76o/koWt7S21Nb6nrZIx56BSR84fmyi/618uH7n9aWo6c9yu5q2dXy8B76+Ta74yVI+6a53dP4j5+Lonvux5KJZrTk03y85tr5MYnJ0u6NJyVHW8+Kv16PyR/2lpxYfHdustei+b+7Ar5n7tr5eoHn5W1+jXYqVUy8P466dv/d7Ki84GStN6R/V56EPdyEZzGrpcp4eqvWE5j9RT0B/GnGWMfBOt2z57JwPmDMvIbfZMn03d++0/y15/cJfWd3oydkUX/8RGpveZHMuuEpum8tI94TK7q9aC8sqXConlmkfzixhq54R9nSvbr7TLqsTqpfeBlSdbcWD1dhGr+O4r787J31FNy+4cfkoGrcivw6bny05t6C0cNK8nh0U/INbUPyPPrOiqovc82roDcJT+K4p6SH5YxT1wtV93/nKyvRJ+vktH9uYdxL+fl4IhvSr9eNdLv1m/Lq2/8RPr3zr8Z8xF6ROb/++1SX3uP/HZJZibxKYscHi3fvapOHn52nRQ3XU/i/iLmkui+66M+ntMzzT+XW3pdKz+emW3P8+0j5Ru1NTLgpS2+G1ThtXjuz+8dLT/8xI0y4A+rci4Ap2XuT26WuvwR2zwbUf1epOdwL3IxnMatl3nSS//Hchqr57/LlbtqxtiV49ru1NMZOH9IJv3scfnVyDVy+PwZWfabT3Y2xs7tkkFf6C11D/9Ztudsro5lv5bbevWVH0w9XsjkuV1vyZdqessjf96WO17RIa2/+rjU1j8p046LxOoV3qjaPojhvkKdOja/JJ+t7SO3/6K5gtYZWfbru6Tvdd+Vl4b8Uh6763rpV3+d3DHgSXmu4d30Tdv7bOMKBeiaH8Vyf2apPH1nrdz4nRdl2C//l9x9XV/pd+2t8tknB8rMd/Vj687VjO7PPY17OS+HJvyHfPs/R8maw+flzLLfyN0RxtipVQNlQH0fufPfGuVw4KUYrXFm6a+lf5/r5fsvDpX/+ton5cb6vvLhWz8jPxjYIOWm63Hcd+6nXMnPJdF91wcXzek52fXWF6WuZoC8lj9a0dEqv/lYjfR7cqrvDt3qWp77wsp1bJaXB9RJ/Sd+Ic1nCrXi+r0Y9wmDnTiNXC+99MdyGqvnvckVvWjG2BWl225mDDgGCoyxjrXyzJ01ctU3RqujJKXvnNv6sgzo1Ue+OmSPA+n0u2PN76V/rzr51qj0IMqFb8u2lx6U2t5flmF7zkusXqcbdIsLBdwX1a3jPRn5xE1SV3ef/L61glFwfp8M/3pfqe3dV2778q9k8JTZMmv8X+Rnn/2I1Pf5mDw56r2Sgfw+27iomNVxvZj78/uGyTfqa6S+/uPytf8eJFNnz5QJf/mpfOHGPtL3o9+XMTtzTydUhaP7c4/mXuKMsfN7ZfQT10vdNY/JsPeKOU/pPy/tQ78u/Xr1kX4f+4r8etAUmTNzvLz208/JLb1r5dbvjZYEpodzn/DlmUui+25KePpXNKcdsvb3d0lt7TdlTKelYau88kCN1H9paIrbHf/ycO+vZoe8N+IJuaWmXu7/f63pQ7ROypH9Xox7EQ+nsetlJ965EMtprJ73Jlf0ohljV5Ruu5kx4Bgo2JR2LJfffaJGrnpiYieH6nM735Av1PSWz7+204F0+t2x/Gm5vVedfG9C3h37nOx8/bNSV/OIvLHznMTqdbpBt7hQwL2vbuf2yuyf3y/X1Fwjnx/Ymo2GmNc/u0pe+sJH5ZbPvyBrtM12rEWe/lSd1N3yE5lDVLn32cb521bX/8Xcn131onzplo/Ioy+syWyAjrX8Wj5d21s+8a+zC6sa3Z97NPdxxljHhhfkM3V95PafzpPid/C6Kc7K6he/KJ+48Qvyx2zHlyW/vkeuqvmo/NvsYz2834tIwVwS3Xc15e7v6P7cISuevlVqa78jkzotDTvlzUd6S90jrzvU7ve7gPvOFT0ne2f9Qh68qrdc/8iz0qqjgHZSjuz30sO5lwJOY9fLTrxzIZbTWD3vTa7oRTPGrijddjNjwDFQsCk9t1ae6196M3bIqV747d6MfWXw7twn6b/n1g6Ue3gzNrrTty+8GXtUhuw+L7F6KXJ3+quA+3wVT22TcT++Wz5Uc6088uu50h7zkiCPkfzfIRuee1Cu6n2n/HrJGZH32cbeW1TNxUjudX061ssLD9RJ/R2/0lczf0f35x7NfYwxdkaWP91f+va5V/6Q95vMMB73T8f652VAbR/p/99Lena/rzCXRPddH+XR/fmcrBvYv/RmrNPScOHN2KODfXeo/msVuM9W7pRsH/tjubdvb7nh4V/LvH1/94QvmX4vPZh7+Xs4za2X2Ua68F8sp7F63ptc0YtmjF1Ruu1mxoBjoGBTer5Nhn6pj9R95jXZkVsLSj5j9fLklOLn1efbhshXe/eWz722w+8zVvd9weUsVs+Vtnv9LuBeVfL8gUXy4ldulvo+t8g3Xl4W5TfD07pTh9vlwLF8CIPzsmfw/5J+NTfJv805Dfnvq41VMavwzwrcd5ySI+0HpDN9e2TI1/pK3Ud+Uljf6P7co7mPMMbOLpf/6V970UFUOk4dlvYDxzoF7zi/Z7A8Vt9bbvnXxh7b70NzSXTf9fX+6P58XtoGf1nqax6R1zstLCWfsau/N8V3h6q+FuK+XLnzB2Tx81+Vj/aulY9//RVZFuMoyfuZmH4vPZN7CXIauV6WG0n/EctprJ7G/mD+NmPsg+Hd7trjGSjalJ79/9u7E++oyjuM4/1TMpPZMiQhQkDBsGqAFAmgrCrWBRRryiLYowiiIotFpWFVK+DSStGyNCiLyhYOBQ5UXBBUsIWyVYgVkCXbzNMzWSeTeZOb5QJ35ptzcpLMe+/vvvfzvpmZJ3PnjQ4830WejKkqjr7UTZHVFMcokNJfS47GpLRoy4r9ejHbpawpOxtc6qVwidaM8crTb5Gqdre6XXTthPneZF99gqFz2/TCgKC8gVw9XXS8oWMTBhXfLNDAVI/unHswZmWuiupXGzyDtPRoJKi1cYyb6MPN32Syr9DhBXnyp/bVy5/HrGRZcVAv9/EocNdi8+lZns/JbN98GKte4MCjfi9/GTOHzfSqOKzCAR75+8zVwUZDN1d3pno1ePHRpJz3lu5LLM/deGNgfT5X7H9et6Vk6vc7GjywqHY1xbxFkTFKnA9L9pHTjVzCODNPGa40DXiqSMcb8phBLM97KdnsrZhaf7yMPwRWTa1uF/8o1+9Wwtj1s+ZICEQJmJ6USqV7Zui2lCxN2PSz6hYyqzyh90b45ckt1HexL7xEVZVKtXd6F3k6Fmjzz3V7q/LEOxrtc2nAH7+t+eu11e0aFE+QH8z2Kj2sN4ZlyBu8S7OLz8e8utjM6Zcd0JxeqfL1mK5dUX9ZDZds0dRuqQoOeV3HasaubWPcTD9u6mazfdmB2errTlWfZ4tV/2+twirZ8qRy3H4NW3asiTOzPp+T1765MBbWhTVjle7qrKe3W31GGhmSMv3zpd7yuXvqueKL9fdZ4RJ98mR3+XxD9UbNxE8qe8v3JdbnbrxfAMumpXs1M9ulzgWbVP/QUKkT74xQMKWfFrb4/0nE681NclsL7I8sG64sVwflz2rppejW572SyV6lsmTagsfLuLPKqqnV7eIe5PrdSBi7ftYcCYEoAfOTUoXOaM1DHeVJz9eMP2/Tvj2b9VZBb6W5cjS9OPq/4f6i9eP88nhHVC3KUVs8dOZvGpvpUtagZ/X+tn3au/lNTejlk/f2adoVtbvV7WrrJs5Xk31IJ9+7X5kpbmXlT9GrCxaoMOZz8dqv6xh+WTdOwRSfRi0/WRPaQvpx42T18qQqe8izWrlhm7atX6YpAzLkyxiuZV9dq9vX+hjX75IY35nsI3+h/lGbJuco4L5Fw6at0MfbturvSydrYHqqbhm2RF9H8TW2j/y7BmvzPnntmwtjFToYeb+Yd4RWNLFyZVz7Hzdqyu1e+bKGasbyj7R963q9PilPWe5MjVzyleqGzvJ9m9Nne8vuS6zO3Xj21udzSGc+fFidUjI0ZNpftH3vHm15s0B9vW71mlasqIcGh+Nbtw+dfE8PBF3yZgzWU/Mb398XLlyrQ7XvCvhlnR7zuZQ2fIVqfz1CVud9ZHn7pLCXrJu24PEyjr0smzrDnjDm8Lsduu9UgSaelEZO6eoxbZjziPKyA/K60nR7foEWF5+NuXQofhir3r1I8x7ur1v9bnkDt2lowSLtOhtzDVHVYaxt51Tl+P022IfPVS9Nn+KSx/AZfGBVXcm4T4xUrtM7Fmny3T3V2edVMKO78sfN0bojl+pfMaitYGmMazdOlK8G+9rTKz+lnYsmaniPLAU9fmV1u0uPzVmrb+tfKqvaMr595NfG4nxOSvvmwlipPp2YLk+wQJvq0lPtwNR/NdmXn9qhJRPuUZ+OfgV8mcoZOE7z1h6JepWzpkYy2LfwviQiY2XumuytPV5UHUXHiuZoXL8u6uByK/3WwZqwsFhxHhrqB9xp31m2D+t81b9kMN/fe3wPaPX5mitM4gYCyfK819XEt1cLTa0+XhrsZdn05rcnjDntjob+IoAAAggggAACCCCAQEIIEMYSYhg5CQQQQAABBBBAAAEEEHCaAGHMaSNGfxFAAAEEEEAAAQQQQCAhBAhjCTGMnAQCCCCAAAIIIIAAAgg4TYAw5rQRo78IIIAAAggggAACCCCQEAKEsYQYRk4CAQQQQAABBBBAAAEEnCZAGHPaiNFfBBBAAAEEEEAAAQQQSAgBwlhCDCMngQACCCCAAAIIIIAAAk4TIIw5bcToLwIIIIAAAggggAACCCSEAGEsIYaRk0AAAQQQQAABBBBAAAGnCRDGnDZi9BcBBBBAAAEEEEAAAQQSQoAwlhDDyEkggAACCCCAAAIIIICA0wQIY04bMfqLAAIIIIAAAggggAACCSFAGEuIYeQkEEAAAQQQQAABBBBAwGkChDGnjRj9RQABBBBAAAEEEEAAgYQQIIwlxDByEggggAACCCCAAAIIIOA0AcKY00aM/iKAAAIIINDeAle+1CsDx2j1+XB7V273ele+nK/8MavavS4FEUAAgRshQBi7EeocEwEEEEAAgVYKlO+fpd5ulzwpMZ8uj4IZXZV7T4EWbj+tCkv1w7p8bIOeH5gpj2uk5TAWLvlQY1x9VPhdyNJR2mWj8GX9UDRT+RkueUcSxtrFlCIIIHDDBQhjN3wI6AACCCCAAAJWBUI6vXKk0mKDWOzPaSO0/IfK5ouGz2r99KlasWer5vUebTmMXfr4UaV1fUlfWEt8zffDwhbhs+s0c8py7d06R3eMIoxZIGMTBBBwgABhzAGDRBcRQAABBBCoFriqTyd1lMczSEuPxoatkMoundLuPwxVRopP97171jpa5WG90sdqGLumnZOC6vTMHpVZP0K7bVn5zXzdSRhrN08KIYDAjRUgjN1Yf46OAAIIIICAdYGKQ3ot1yN//9d02PCqVOnuGerh9mn0ilPW67YkjJXv08ysgCZ+dtVQP6STK4YqLfs5fXZorWaNyVVXv08dsvP0eOEelZT/pM9XTtWInEwFfR3Vd/QL2njCeqwjjBnYuRkBBBwpQBhz5LDRaQQQQACBZBQIl/xVD/k8yp33Rcx7wsIqu3hKh7Ys1viefnlS79D82msIrxTpt76Y95dFLmv0jtK7p2ve89WCMFb59VzluB9R0QXTCFSHsYA3S9mdcjXxT5u0d99Ovf9kX6WldFDeoFzljJil1Vv/od1F83XfLS4FB7+l4yHpStF4BWMvuUxxKW3k23UHI4zVUfANAggkgABhLAEGkVNAAAEEEEgOgbJd09TNFSdYNQgwacqbuUM/tWRhRMthLKSjhX3lGblK5oUXa8JYilf3LD+uuospL27QY5FQ2PUZ7b5cO14hHVucJ593jD40F6zduOorYawBBz8ggIDDBQhjDh9Auo8AAgggkCwClfph6WAFGgSv2mDmVjAzR4MffFrLNn6vSy0JYhE+q2EsdEorB7mU/9Z/ZF5HsSaMuftpYfRqixX79WIXl4KPb1b0BY7/W/uQgp7BWh55aczCB2HMAhKbIICAYwQIY44ZKjqKAAIIIJDcAhe1YXwHedOf0MaaV5bCFZd1Zt+bejjbr17jV+n7UnuFwudX696U5pa0r71McZRW/TcqFVYc0KyubmU9tavBJZYX1o+tDmP/thbG7D1DqiOAAALXV4Awdn29ORoCCCCAAAKtEyjfr9k9UhUY8rr+VXftX6RUWOfWjVcXV0B3L/lW5a2rbmmvi0VjFeg6W18ZFg+pLlIbxu7XB9GXHhLGLBmzEQIIJJcAYSy5xpuzRQABBBBwqEDo9Nu61+tWt2m7Gi8pX/6NCvO88mY9oY9a9GaxlmBc1bbfBdRpWnNL2hPGWqLKtgggkNwChLHkHn/OHgEEEEDAIQLXPpmszi6/Hnz/nKIu/qvpfUgnV45Sh5SARi8/0cT7udpwsmV7ND0zoElbo9/xFa8eYSyeCrchgAAC8QQIY/FUuA0BBBBAAIGbSqBCh17tL3/0kvUx/QufX6NH013y576iQzZcq1hx8CV1d4/VhosxB270I2GsEQk3IIAAAgYBwpgBhpsRQAABBBC4aQTCJfrgN3550gvqFu9o3LeL+mRSZ3nd3TW9+Erj5jbdEtL3C3pXLWlf0vhluZjKhLEYEH5EAAEEjAKEMSMNDQgggAACCCCAAAIIIICAfQKEMftsqYwAAggggAACCCCAAAIIGAUIY0YaGhBAAAEEEEAAAQQQQAAB+wQIY/bZUhkBBBBAAAEEEEAAAQQQMAoQxow0NCCAAAIIIIAAAggggAAC9gkQxuyzpTICCCCAAAIIIIAAAgggYBQgjBlpaEAAAQQQQAABBBBAAAEE7BMgjNlnS2UEEEAAAQQQQAABBBBAwChAGDPS0IAAAggggAACCCCAAAII2CdAGLPPlsoIIIAAAggggAACCCCAgFGAMGakoQEBBBBAAAEEEEAAAQQQsE+AMGafLZURQAABBBBAAAEEEEAAAaMAYcxIQwMCCCCAAAIIIIAAAgggYJ8AYcw+WyojgAACCCCAAAIIIIAAAkYBwpiRhgYEEEAAAQQQQAABBBBAwD4Bwph9tlRGAAEEEEAAAQQQQAABBIwChDEjDQ0IIIAAAggggAACCCCAgH0ChDH7bKmMAAIIIIAAAggggAACCBgFCGNGGhoQQAABBBBAAAEEEEAAAfsECGP22VIZAQQQQAABBBBAAAEEEDAKEMaMNDQggAACCCCAAAIIIIAAAvYJEMbss6UyAggggAACCCCAAAIIIGAUIIwZaWhAAAEEEEAAAQQQQAABBOwTIIzZZ0tlBBBAAAEEEEAAAQQQQMAoQBgz0tCAAAIIIIAAAggggAACCNgnQBizz5bKCCCAAAIIIIAAAggggIBRgDBmpKEBAQQQQAABBBBAAAEEELBPgDBmny2VEUAAAQQQQAABBBBAAAGjAGHMSEMDAggggAACCCCAAAIIIGCfAGHMPlsqI4AAAggggAACCCCAAAJGAcKYkYYGBBBAAAEEEEAAAQQQQMA+AcKYfbZURgABBBBAAAEEEEAAAQSMAoQxIw0NCCCAAAIIIIAAAggggIB9AoQx+2ypjAACCCCAAAIIIIAAAggYBQhjRhoaEEAAAQQQQAABBBBAAAH7BAhj9tlSGQEEEEAAAQQQQAABBBAwChDGjDQ0IIAAAggggAACCCCAAAL2CRDG7LOlMgIIIIAAAggggAACCCBgFCCMGWloQAABBBBAAAEEEEAAAQTsE2iXMLZv7z7d0bu3ft1/AJ8YMAeYA8wB5gBzgDnAHGAOMAeYA8wBC3OgT89eunDhQrNp71dNbXHt2jUdOXyYTwyYA8wB5gBzgDnAHGAOMAeYA8wB5kAL5kA4HG4qalW1NRnGmt2bDRBAAAEEEEAAAQQQQAABBFolQBhrFRs7IYAAAggggAACCCCAAAJtEyCMtc2PvRFAAAEEEEAAAQQQQACBVgkQxlrFxk4IIIAAAggggAACCCCAQNsECGNt82NvBBBAAAEEEEAAAQQQQKBVAoSxVrGxEwIIIIAAAggggAACCCDQNgHCWNv82BsBBBBAAAEEEEAAAQQQaJUAYaxVbOyEAAIIIIAAAggggAACCLRNgDDWNj/2RgABBBBAAAEEEEAAAQRaJUAYaxUbOyGAAAIIIIAAAggggAACbRMgjLXNj70RQAABBBBAAAEEEEAAgVYJ/B/lqznkbNgDlgAAAABJRU5ErkJggg==\" width=\"788\"/></span></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span class=\"fontstyle0\">Suggest whether the data are consistent with the theoretical prediction.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span class=\"fontstyle0\">Show that the value of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>γ</mi></math></span><span class=\"fontstyle2\">  </span><span class=\"fontstyle0\">is about 0.03.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span class=\"fontstyle0\">Identify the fundamental units of </span><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>γ</mi></math>.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span class=\"fontstyle0\">In order to find the uncertainty for </span><span class=\"fontstyle2\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>γ</mi></math></span><span class=\"fontstyle0\">, a maximum gradient line would be drawn. On the graph, sketch the maximum gradient line for the data.</span></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b(iii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span class=\"fontstyle0\">The percentage uncertainty for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>γ</mi></math></span><span class=\"fontstyle2\"> </span><span class=\"fontstyle0\">is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>15</mn><mo>%</mo></math>. State </span><span class=\"fontstyle2\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>γ</mi></math></span><span class=\"fontstyle0\">, with its absolute uncertainty.</span></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b(iv).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p><span class=\"fontstyle0\">The expected value of </span><span class=\"fontstyle2\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>γ</mi></math> </span><span class=\"fontstyle0\">is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn><mo>.</mo><mn>027</mn></math>. Comment on your result</span>.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b(v).</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">«theory suggests» <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>P</mi><mi mathvariant=\"normal\">i</mi></msub><mo>-</mo><msub><mi>P</mi><mi mathvariant=\"normal\">o</mi></msub></math> </span><span class=\"fontstyle0\">is proportional to <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mn>1</mn><mi>R</mi></mfrac></math> </span><span class=\"fontstyle3\">✓</span></p>\n<p><span class=\"fontstyle3\"><br/></span><span class=\"fontstyle0\">graph/line of best fit is straight/linear «so yes»<br/></span><span class=\"fontstyle4\"><em><strong>OR</strong></em><br/></span><span class=\"fontstyle0\">graph/line of best fit passes through the origin «so yes» </span><span class=\"fontstyle3\">✓</span></p>\n<p> </p>\n<p><em><span class=\"fontstyle2\">MP1: Accept ‘linear’<br/></span></em></p>\n<p><em><span class=\"fontstyle2\">MP2 do not award if there is any contradiction<br/>eg: graph not proportional, does not pass through origin.</span></em></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">gradient <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo></math> «<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>4</mn><mi>γ</mi></math>» <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>0</mn><mo>.</mo><mn>10</mn></math><br/></span><span class=\"fontstyle2\"><em><strong>OR</strong></em><br/></span><span class=\"fontstyle0\">use of equation with coordinates of a point </span><span class=\"fontstyle3\">✓</span></p>\n<p><span class=\"fontstyle3\"><br/></span><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>γ</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>025</mn></math> <span class=\"fontstyle3\">✓</span></p>\n<p> </p>\n<p><em><span class=\"fontstyle5\">MP1 allow gradients in range <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn><mo>.</mo><mn>098</mn></math> to <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn><mo>.</mo><mn>102</mn></math><br/></span></em></p>\n<p><em><span class=\"fontstyle6\">MP2 allow a range <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn><mo>.</mo><mn>024</mn></math> to <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn><mo>.</mo><mn>026</mn></math> for </span><span class=\"fontstyle4\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>γ</mi></math></span></em></p>\n<p> </p>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>kg</mi><mo> </mo><msup><mi mathvariant=\"normal\">s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></math> <span class=\"fontstyle2\">✓</span></p>\n<p> </p>\n<p><em><span class=\"fontstyle3\">Accept <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mi>kg</mi><msup><mi mathvariant=\"normal\">s</mi><mn>2</mn></msup></mfrac></math></span></em></p>\n<p><span class=\"fontstyle3\"> </span></p>\n<div class=\"question_part_label\">b(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">straight line, gradient <strong>g</strong></span><span class=\"fontstyle2\"><strong>reater</strong> </span><span class=\"fontstyle0\">than line of best fit, and within the error bars </span><span class=\"fontstyle3\">✓</span></p>\n<p><span class=\"fontstyle3\"><img src=\"data:image/png;base64,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\"/></span></p>\n<div class=\"question_part_label\">b(iii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>15</mn><mo>%</mo></math> of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn><mo>.</mo><mn>025</mn></math>» = <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn><mo>.</mo><mn>00375</mn></math><br/></span><span class=\"fontstyle2\"><em><strong>OR</strong></em><br/></span><span class=\"fontstyle0\">«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>15</mn><mo>%</mo></math> of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn><mo>.</mo><mn>030</mn></math>» = <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn><mo>.</mo><mn>0045</mn></math> </span><span class=\"fontstyle3\">✓<br/></span></p>\n<p><span class=\"fontstyle0\">rounds uncertainty to 1sf<br/><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>±</mo><mn>0</mn><mo>.</mo><mn>004</mn></math><br/></span><span class=\"fontstyle2\"><em><strong>OR</strong></em><br/></span><span class=\"fontstyle0\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>±</mo><mn>0</mn><mo>.</mo><mn>005</mn></math> </span><span class=\"fontstyle3\">✓</span></p>\n<p> </p>\n<p><em><span class=\"fontstyle4\">Allow ECF from (b)(i)<br/>Award </span><strong><span class=\"fontstyle2\">[2] </span></strong><span class=\"fontstyle4\">marks for a bald correct answer</span></em></p>\n<div class=\"question_part_label\">b(iv).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">Experimental value matches this/correct, as expected value within the range </span><span class=\"fontstyle2\">✓<br/></span><span class=\"fontstyle3\"><em><strong>OR</strong></em><br/></span><span class=\"fontstyle0\">experimental value does not match/incorrect, as it is not within range </span><span class=\"fontstyle2\">✓</span></p>\n<div class=\"question_part_label\">b(v).</div>\n</div>",
    "Examiners report": "",
    "topics": [
      "tools"
    ],
    "subtopics": [
      "tool-3-mathematics"
    ]
  },
  {
    "question_id": "20N.3.SL.TZ0.2",
    "Question": "<div class=\"specification\">\n<p>A student studies the relationship between the centripetal force applied to an object undergoing circular motion and its period <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math>.</p>\n<p>The object (mass <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>m</mi></math>) is attached by a light inextensible string, through a tube, to a weight <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>W</mi></math> which hangs vertically. The string is free to move through the tube. A student swings the mass in a horizontal, circular path, adjusting the period <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math> of the motion until the radius <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>r</mi></math> is constant. The radius of the circle and the mass of the object are measured and remain constant for the entire experiment.</p>\n<p><img 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\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p style=\"text-align: center;\">© International Baccalaureate Organization 2020.</p>\n<p>The student collects the measurements of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math> five times, for weight <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>W</mi></math>. The weight is then doubled (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>2</mn><mi>W</mi></math>) and the data collection repeated. Then it is repeated with <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>3</mn><mi>W</mi></math> and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>4</mn><mi>W</mi></math>. The results are expected to support the relationship</p>\n<p style=\"text-align: center;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>W</mi><mo>=</mo><mfrac><mrow><mn>4</mn><msup><mi mathvariant=\"normal\">π</mi><mn>2</mn></msup><mi>m</mi><mi>r</mi></mrow><msup><mi>T</mi><mn>2</mn></msup></mfrac><mo>.</mo></math></p>\n</div><div class=\"specification\">\n<p>In reality, there is friction in the system, so in this case <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>W</mi></math> is less than the total centripetal force in the system. A suitable graph is plotted to determine the value of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>m</mi><mi>r</mi></math> experimentally. The value of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>m</mi><mi>r</mi></math> was also calculated directly from the measured values of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>m</mi></math> and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>r</mi></math>.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>State why the experiment is repeated with different values of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>W</mi></math>.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Predict from the equation whether the value of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>m</mi><mi>r</mi></math> found experimentally will be larger, the same or smaller than the value of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>m</mi><mi>r</mi></math> calculated directly.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The measurements of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math> were collected five times. Explain how repeated measurements of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math> reduced the random error in the final experimental value of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>m</mi><mi>r</mi></math>.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline why repeated measurements of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math> would not reduce any systematic error in <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math>.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">c(ii).</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">In order to draw a graph « of </span><span class=\"fontstyle2\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>W</mi></math> </span><span class=\"fontstyle0\">versus <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mn>1</mn><msup><mi mathvariant=\"normal\">T</mi><mn>2</mn></msup></mfrac></math> »<br/></span><span class=\"fontstyle3\"><em><strong>OR</strong></em><br/></span></p>\n<p><span class=\"fontstyle0\">to confirm proportionality between «<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>W</mi></math></span><span class=\"fontstyle2\"> </span><span class=\"fontstyle0\">and </span><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi>T</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></math> <span class=\"fontstyle2\">»<br/></span></p>\n<p><span class=\"fontstyle3\"><em><strong>OR</strong></em><br/></span></p>\n<p><span class=\"fontstyle0\">to confirm relationship between «<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>W</mi></math></span><span class=\"fontstyle2\"> </span><span class=\"fontstyle0\">and </span><span class=\"fontstyle2\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math> »<br/></span></p>\n<p><em><span class=\"fontstyle3\"><strong>OR</strong></span></em><span class=\"fontstyle3\"><br/></span></p>\n<p><span class=\"fontstyle0\">because </span><span class=\"fontstyle2\">W </span><span class=\"fontstyle0\">is the independent variable in the experiment </span><span class=\"fontstyle4\">✓</span></p>\n<p> </p>\n<p><em><span class=\"fontstyle2\">OWTTE</span></em></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\"><strong>ALTERNATIVE 1</strong></span></p>\n<p><span class=\"fontstyle2\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>W</mi><mo>+</mo><mpadded lspace=\"-1px\"><mi>friction</mi></mpadded><mo>=</mo><mfrac><mrow><mn>4</mn><msup><mi mathvariant=\"normal\">π</mi><mn>2</mn></msup><mi>m</mi><mi>r</mi></mrow><msup><mi>T</mi><mn>2</mn></msup></mfrac></math></span></p>\n<p><span class=\"fontstyle3\"><em><strong>OR</strong></em></span></p>\n<p><span class=\"fontstyle2\">centripetal force is larger «than <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>W</mi></math>» / <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>W</mi></math> is smaller «than centripetal» </span><span class=\"fontstyle4\">✓</span></p>\n<p><span class=\"fontstyle2\">«so» experimental </span><span class=\"fontstyle5\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>m</mi><mi>r</mi></math> </span><span class=\"fontstyle2\">is smaller «than calculated value» </span><span class=\"fontstyle4\">✓</span></p>\n<p> </p>\n<p><strong><span class=\"fontstyle0\">ALTERNATIVE 2 </span></strong><span class=\"fontstyle2\"><strong>(refers to graph)</strong><br/></span></p>\n<p><span class=\"fontstyle2\">reference to «friction force is» a systematic error «and does not affect gradient» </span><span class=\"fontstyle4\">✓</span></p>\n<p><span class=\"fontstyle2\">«so» </span><span class=\"fontstyle5\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>m</mi><mi>r</mi></math> </span><span class=\"fontstyle2\">is the same </span><span class=\"fontstyle4\">✓</span></p>\n<p> </p>\n<p><em><span class=\"fontstyle5\">MP2 awarded only with correct justification.<br/>Candidates can gain zero, MP1 alone or full marks.</span></em></p>\n<p><em><span class=\"fontstyle5\">OWTTE</span></em></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">mention of mean/average value «of </span><span class=\"fontstyle2\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math></span><span class=\"fontstyle0\">» </span><span class=\"fontstyle3\">✓</span></p>\n<p><span class=\"fontstyle0\">this reduces uncertainty in </span><span class=\"fontstyle2\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math> </span><span class=\"fontstyle0\">/ result<br/></span><span class=\"fontstyle4\"><em><strong>OR</strong></em><br/></span><span class=\"fontstyle0\">more accurate/precise </span><span class=\"fontstyle3\">✓</span></p>\n<p> </p>\n<p><em><span class=\"fontstyle2\">Reference to “random errors average out” scores MP1</span></em></p>\n<p><em><span class=\"fontstyle2\">Accept “closer to true value”, “more reliable value” OWTTE for MP2</span></em></p>\n<p> </p>\n<div class=\"question_part_label\">c(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">systematic errors «usually» constant/always present/ not influenced by repetition </span><span class=\"fontstyle2\">✓</span></p>\n<p> </p>\n<p><em><span class=\"fontstyle3\">OWTTE</span></em></p>\n<div class=\"question_part_label\">c(ii).</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>Most candidates scored. Different wording was used to express the aim of confirming the relationship.</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Most successful candidates chose to consider a single point then concluding that the calculated <em>mr</em> would be smaller than the real value as <em>W</em> &lt; centripetal force, or even went into analysing the dependence of the frictional force with <em>W</em>. Many were able to deduce this. Some candidates thought that a graph would still have the same gradient (if friction was constant) and mentioned systematic error, so <em>mr</em> was not changed which was also accepted.</p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Most candidates stated that the mean of 5 values of <em>T</em> was used to obtain an answer closer to the true value if there were no systematic errors. Some just repeated the question.</p>\n<div class=\"question_part_label\">c(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Usually very well answered acknowledging that systematic errors are constant and present throughout all  measurements.</p>\n<div class=\"question_part_label\">c(ii).</div>\n</div>",
    "topics": [
      "inquiry"
    ],
    "subtopics": [
      "i-1-2-designing",
      "i-2-3-interpreting-results",
      "inquiry-1-exploring-and-designing",
      "inquiry-2-collecting-and-processing-data"
    ]
  },
  {
    "question_id": "20N.2.HL.TZ0.10",
    "Question": "<div class=\"specification\">\n<p>The de Broglie wavelength <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>λ</mi></math> of a particle accelerated close to the speed of light is approximately</p>\n<p style=\"text-align: center;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>λ</mi><mo>≈</mo><mfrac><mrow><mi>h</mi><mi>c</mi></mrow><mi>E</mi></mfrac></math></p>\n<p>where <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>E</mi></math> is the energy of the particle.<br/>A beam of electrons of energy <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>4</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup><mo> </mo><mi>eV</mi></math> is produced in an accelerator.</p>\n</div><div class=\"specification\">\n<p>The electron beam is used to study the nuclear radius of carbon-12. The beam is directed from the left at a thin sample of carbon-12. A detector is placed at an angle <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>θ</mi></math> relative to the direction of the incident beam.</p>\n<p><img height=\"137\" src=\"data:image/png;base64,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\" style=\"display: block; margin-left: auto; margin-right: auto;\" width=\"378\"/></p>\n<p>The graph shows the variation of the intensity of electrons with <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>θ</mi></math>. There is a minimum of intensity for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>θ</mi><mo>=</mo><msub><mi>θ</mi><mn>0</mn></msub></math>.</p>\n<p><img height=\"235\" 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\" style=\"display: block; margin-left: auto; margin-right: auto;\" width=\"365\"/></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Show that the wavelength of an electron in the beam is about <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>15</mn></mrow></msup><mo> </mo><mi mathvariant=\"normal\">m</mi></math>.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Discuss how the results of the experiment provide evidence for matter waves.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The accepted value of the diameter of the carbon-12 nucleus is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>4</mn><mo>.</mo><mn>94</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>15</mn></mrow></msup><mo> </mo><mi mathvariant=\"normal\">m</mi></math>. Estimate the angle <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>θ</mi><mn>0</mn></msub></math> at which the minimum of the intensity is formed.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline why electrons with energy of approximately <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mn>10</mn><mn>7</mn></msup><mo> </mo><mi>eV</mi></math> would be unsuitable for the investigation of nuclear radii.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b(iii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Experiments with many nuclides suggest that the radius of a nucleus is proportional to <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi>A</mi><mstyle displaystyle=\"false\"><mfrac><mn>1</mn><mn>3</mn></mfrac></mstyle></msup></math>, where <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>A</mi></math> is the number of nucleons in the nucleus. Show that the density of a nucleus remains approximately the same for all nuclei.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>λ</mi><mo>=</mo><mfrac><mrow><mn>6</mn><mo>.</mo><mn>63</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>34</mn></mrow></msup><mo>×</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup></mrow><mrow><mn>1</mn><mo>.</mo><mn>60</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup><mo>×</mo><mn>4</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup></mrow></mfrac></math> <em><strong>OR <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>2</mn><mo>.</mo><mn>96</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>15</mn></mrow></msup><mo>«</mo><mi mathvariant=\"normal\">m</mi><mo>»</mo></math></strong></em> ✓ </span></p>\n<p><em><span class=\"fontstyle2\"><br/>Answer to at least <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn mathvariant=\"italic\">2</mn></math> s.f. (i.e. 3.0)</span></em></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">«</span><span class=\"fontstyle1\">the shape of the graph suggests that</span><span class=\"fontstyle0\">» </span><span class=\"fontstyle1\">electrons undergo diffraction </span><span class=\"fontstyle0\">«</span><span class=\"fontstyle1\">with carbon nuclei</span><span class=\"fontstyle0\">» </span><span class=\"fontstyle3\">✓</span></p>\n<p><span class=\"fontstyle1\">only waves diffract </span><span class=\"fontstyle3\">✓</span></p>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>sin</mi><msub><mi>θ</mi><mn>0</mn></msub><mo>=</mo><mfrac><mrow><mn>2</mn><mo>.</mo><mn>96</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>15</mn></mrow></msup></mrow><mrow><mn>4</mn><mo>.</mo><mn>94</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>15</mn></mrow></msup></mrow></mfrac><mo>«</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>599</mn><mo>»</mo></math> </span><span class=\"fontstyle3\">✓</span></p>\n<p><span class=\"fontstyle0\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>37</mn><mo> </mo><mo>«</mo><mpadded lspace=\"-1px\"><mi>degrees</mi></mpadded><mo>»</mo></math> <em><strong>OR </strong></em><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn><mo>.</mo><mn>64</mn><mo>/</mo><mn>0</mn><mo>.</mo><mn>65</mn><mo> </mo><mo>«</mo><mi>rad</mi><mo>»</mo></math> </span><span class=\"fontstyle3\">✓</span></p>\n<div class=\"question_part_label\">b(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">the de Broglie wavelength of electrons is </span><span class=\"fontstyle2\">«</span><span class=\"fontstyle0\">much</span><span class=\"fontstyle2\">» </span><span class=\"fontstyle0\">longer than the size of a nucleus </span><span class=\"fontstyle3\">✓</span></p>\n<p><span class=\"fontstyle3\"><br/></span><span class=\"fontstyle0\">hence electrons would not undergo diffraction<br/></span><span class=\"fontstyle4\"><em><strong>OR</strong></em><br/></span><span class=\"fontstyle0\">no diffraction pattern would be observed </span><span class=\"fontstyle3\">✓</span></p>\n<div class=\"question_part_label\">b(iii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">volume of a nucleus proportional to <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mfenced><msup><mi>A</mi><mstyle displaystyle=\"false\"><mfrac><mn>1</mn><mn>3</mn></mfrac></mstyle></msup></mfenced><mn>3</mn></msup><mo>=</mo><mi>A</mi></math> </span><em><strong><span class=\"fontstyle2\">AND </span></strong></em><span class=\"fontstyle0\">mass proportional to <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>A</mi></math> </span><span class=\"fontstyle3\">✓</span></p>\n<p><span class=\"fontstyle0\">the ratio <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mi>mass</mi><mpadded lspace=\"+1px\"><mi>volume</mi></mpadded></mfrac></math> independent of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>A</mi></math> </span><span class=\"fontstyle4\">«</span><span class=\"fontstyle0\">hence density the same for all nuclei</span><span class=\"fontstyle4\">» </span><span class=\"fontstyle3\">✓</span></p>\n<p> </p>\n<p><em><span class=\"fontstyle5\">Both needed for MP1</span></em></p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>An easy calculation with only one energy conversion to consider and a 'show' answer to help. </p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This question was challenging for candidates many of whom seemed to have little idea of the experiment. Many answers discussed deflection, with the idea that forces between the electron and the nucleus causing it to deflect at a particular angle. This was often combined with the word interference to suggest evidence of matter waves. A number of answers described a demonstration the candidates remembered seeing so answers talked about fuzzy green rings.</p>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was answered reasonably well with only the odd omission of the sine in the equation.</p>\n<div class=\"question_part_label\">b(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Candidates generally scored poorly on this question. There was confusion between this experiment and another diffraction one, so often the new wavelength was compared to the spacing between atoms. Also, in line with answers to b(i) there were suggestions that the electrons did not have sufficient energy to reach the nucleus or would be deflected by too great an angle to be seen.</p>\n<div class=\"question_part_label\">b(iii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This question proved challenging and it wasn't common to find answers that scored both marks. Of those that had the right approach some missed out on both marks by describing A as the mass of the nucleus rather than proportional to the mass of the nucleus.</p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "topics": [
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "e-1-structure-of-the-atom",
      "e-2-quantum-physics"
    ]
  },
  {
    "question_id": "20N.2.HL.TZ0.6",
    "Question": "<div class=\"specification\">\n<p>One possible fission reaction of uranium-235 (U-235) is</p>\n<p style=\"text-align: center;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mmultiscripts><mi mathvariant=\"normal\">U</mi><mprescripts></mprescripts><mn>92</mn><mn>235</mn></mmultiscripts><mo>+</mo><mmultiscripts><mi mathvariant=\"normal\">n</mi><mprescripts></mprescripts><mn>0</mn><mn>1</mn></mmultiscripts><mo>→</mo><mmultiscripts><mi>Xe</mi><mprescripts></mprescripts><mn>54</mn><mn>140</mn></mmultiscripts><mo>+</mo><mmultiscripts><mi>Sr</mi><mprescripts></mprescripts><mn>38</mn><mn>94</mn></mmultiscripts><mo>+</mo><mn>2</mn><mmultiscripts><mi mathvariant=\"normal\">n</mi><mprescripts></mprescripts><mn>0</mn><mn>1</mn></mmultiscripts></math></p>\n<p style=\"text-align: left;\">Mass of one atom of U-235 <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>235</mn><mo> </mo><mi mathvariant=\"normal\">u</mi></math><br/>Binding energy per nucleon for U-235 <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>7</mn><mo>.</mo><mn>59</mn><mo> </mo><mi>MeV</mi></math><br/>Binding energy per nucleon for Xe-140 <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>8</mn><mo>.</mo><mn>29</mn><mo> </mo><mi>MeV</mi></math><br/>Binding energy per nucleon for Sr-94 <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>8</mn><mo>.</mo><mn>59</mn><mo> </mo><mi>MeV</mi></math></p>\n</div><div class=\"specification\">\n<p>A nuclear power station uses U-235 as fuel. Assume that every fission reaction of U-235 gives rise to <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>180</mn><mo> </mo><mi>MeV</mi></math> of energy.</p>\n</div><div class=\"specification\">\n<p>A sample of waste produced by the reactor contains <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>1</mn><mo>.</mo><mn>0</mn><mo> </mo><mi>kg</mi></math> of strontium-94 (Sr-94). Sr-94 is radioactive and undergoes beta-minus (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi mathvariant=\"normal\">β</mi><mo>-</mo></msup></math>) decay into a daughter nuclide X. The reaction for this decay is</p>\n<p style=\"text-align: center;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mmultiscripts><mi>Sr</mi><mprescripts></mprescripts><mn>38</mn><mn>94</mn></mmultiscripts><mo>→</mo><mi mathvariant=\"normal\">X</mi><mo>+</mo><msub><mover><mi mathvariant=\"normal\">v</mi><mo>¯</mo></mover><mi>e</mi></msub><mo>+</mo><mi>e</mi></math>.</p>\n<p> </p>\n</div><div class=\"specification\">\n<p>The graph shows the variation with time of the mass of Sr-94 remaining in the sample.</p>\n<p><img height=\"367\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAl4AAAGCCAYAAAAxNc1PAAAgAElEQVR4Ae2d72scSZrn9z8pQb2SQGDjZdErN8POHGq9EF6/aBrM/kItsAcMTTOw0KVVv2kOem4pMaZpw+zuyLS6j9uF3dTCHjPY7isGFnPnJaEPzCGKm2Ebt6gXxvhEQRshiud4siqkrKzMjMyqiCfzqfwWCGVlZEZ84xNPhr7KjIz4A8IHBEAABEAABEAABEBAhMAfiJSCQkAABEAABEAABEAABAjGC0EAAiAAAiAAAiAAAkIEYLyEQKMYEAABEAABEAABEIDxQgyAAAiAAAiAAAiAgBABGC8h0CgGBEAABEAABEAABGC8EAMgAAIgAAIgAAIgIEQAxksItNZi+v0+/fDDD1rlQzcIgAAIgAAI1IoAjFetmqNeYthwtVsrdBwE9RIGNSAAAiAAAiCglACMl9KGk5DNhouN14/eeQd3vSSAowwQAAEQAIGlJwDjtfRNPF8F+W4XGy42Xg+/eIi7XvNhxFkgAAIgAAIgMEUAxmsKB74YAny3iw0XG6/Xr1/jrpcBg98gAAIgAAIgsAABGK8F4C3rqeZuFxsuNl78wV2vZW1t1AsEQAAEQECSAIyXJG0lZZm7XSzXGC/c9VLSeJAJAiAAAiBQawIwXrVuHnlx8btdXLoxXryNu17y7YESQQAEQAAElosAjNdytefCtYnf7eLM4sYLd70WxosMQAAEQAAEGk4AxqvhAZCs/pMnT6LB9GZ/3HjxvmS6OQ6/QQAEQAAEQAAE7ARgvOyMGn1E0ng1GgYqDwIgAAIgAAILEoDxWhDgsp8O47XsLYz6gQAIgAAISBKA8ZKkrbAsGC+FjQbJIAACIAACtSUA41XbpqmHMBiverQDVIAACIAACCwHARiv5WhHb7WA8fKGFhmDAAiAAAg0kACMVwMbvUyVYbzK0MKxIAACIAACIJBPAMYrn0/jU2G8Gh8CAAACIAACIOCQAIyXQ5jLmBWM1zK2KuoEAiAAAiBQFQEYr6rIKykXxktJQ0EmCIAACICACgIwXiqaqTqRMF7VsUfJIAACIAACy0cAxmv52tRpjWC8nOJEZiAAAiAAAg0nAOPV8ACwVR/Gy0YI6SAAAiAAAiBQnACMV3FWjTwSxquRzY5KgwAIgAAIeCIA4+UJ7LJkC+O1LC2JeoAACIAACNSBAIxXHVqhqIbhczrY3KDd4KXljHMahF/T3uYasXHin/WdLh2HAxpZzkwmw3glieA7CIAACIAACMxPAMZrfnayZw5f0KOdDWq3rtuN11mP9lbXaKsTUH84IhqdUm9/m9qtO/So/7aUbhivUrhwMAiAAAiAAAjkEoDxysVTh8TJ3avt+/TLv/8rumE1XiM66+3TesJkjfqHdMt67mx9YbxmmWAPCIAACIAACMxLAMZrXnJS5w0C2m1t0ye9UzoPuwWM15DC7rvUXt2n3lnsweJFSAfXVmi906OzEtphvErAwqEgAAIgAAIgYCEA42UBVHny8HcU9sdW6aKQ8XpFvc5Nal/rUngRUz86oUfba9TeCWgQ223bZOP1+vVr22FIBwEQAAEQAAEQKEAAxqsApLocUsx4vaTjneuzxosm+1OMF5urvJ+f/PFP6Ne/eUzf/I/f4gcMEAOIAcQAYkAsBury99elDhgvlzQ95+XLeOXJNobs5599lndY7dLYJGr9aNUO3bIRB96yvLk0MJdlrpW3jRKMl41QjdKLGS/3jxq/OjqK7oh9++23NaKRL0XzBatVO3Tnx6TrVPB2TdSeH5jbGbk8QitvGwMYLxuhGqUXM17uB9f/8MMP9NN79+hH77yjZryX5gtWq3bolu0swFuWN5cG5rLMtfK2UYLxshGqUXox45U3ncQa3To8KTWJKj9q5M/3338f3fXqfPxxjYhkS9F8wWrVDt3Z8egjBbx9UM3PE8zz+bhO1crbxgHGy0aoRunFjBcRRROo8mz1R3TCE6gOT+i4s03t1Q/p+PS8VI2M8eKTjoMgMl/8u+4fzResVu3QLXtVgLcsby4NzGWZa+VtowTjZSNUo/Qs4zW7f3bJoPZmh44cLBnEd7zYjPEdsDp/NF+wWrVDt+wVAd6yvLk0MJdlrpW3jRKMl41Qw9Pjd7wYBc/pxWO93n/vPeKxX3X9aL5gtWqHbtmrAbxleXNpYC7LXCtvGyUYLxuhhqcnjRfj4LcbeX+dp5jQfMFq1Q7dsp0FeMvy5tLAXJa5Vt42SjBeNkINT08zXozETDHx7NmzWhLSfMFq1Q7dspcCeMvy5tLAXJa5Vt42SjBeNkINT88yXnWfYkLzBatVO3TLdhbgLcubSwNzWeZaedsowXjZCDU8Pct4MRYzxQTP8VW3j+YLVqt26Ja9CsBbljeXBuayzLXytlGC8bIRanh6nvFiNE+ePInGe/Gjxzp9NF+wWrVDt+wVAN6yvLk0MJdlrpW3jRKMl41Qw9Ntxovx8CB7Pq5OSwppvmC1aodu2c4CvGV5c2lgLstcK28bJRgvG6GGpxcxXjzei6eXqNOSQpovWK3aoVu2swBvWd5cGpjLMtfK20YJxstGqOHpRYwXIzLjveqypJDmC1arduiW7SzAW5Y3lwbmssy18rZRgvGyEWp4elHjxZjqtKSQ5gtWq3bolu0swFuWN5cG5rLMtfK2UYLxshFqeHoZ48WozJJC/X6/UnKaL1it2qFbNuTBW5Y3lwbmssy18rZRgvGyEWp4elnjxeO9eKwX/1S5pJDmC1arduiW7SzAW5Y3lwbmssy18rZRgvGyEWp4elnjxbj4bhefV+V4L80XrFbt0C3bWYC3LG8uDcxlmWvlbaME42Uj1PD0eYwXI6t6vJfmC1arduiW7SzAW5Y3lwbmssy18rZRgvGyEWp4+rzGi7GZ8V5VzO+l+YLVqh26ZTsL8JblzaWBuSxzrbxtlGC8bIQanr6I8apyfi/NF6xW7dAt21mAtyxvLg3MZZlr5W2jBONlI1R1+mhA4Zcd2mqtROOm2q0N2u0GFA7Oc5SNaNh/TAc7G5Nz1mir87XlnPTsFjFenKOZ30t6PUfNF6xW7dCdfg352gvevshm5wvm2Wx8pGjlbWMB42UjVGn6iM56+7Te2qa94ISGRDQaPKVPNteovX1I/VG6uNFpQPdW12hr/ykNomPOqB/s09bmAwqHGSelZxUZt4ykwrurWM9R8wWrVTt0F74knBwI3k4wlsoEzEvhWvhgrbxtFYfxshGqNP0V9To3EybrLfUP71C7dZ+OBxcp6kz6HXrUf3uVPjqhR9vX6dbhCZWxXove8TICzHqOz549M7u8/tZ8wWrVDt1eQ3omc/CeQeJ9B5h7RzxVgFbeU5VI+QLjlQKlNrsuQjq4tkLrnR6dxURdhF260bpJe71Xsb1m8yUd71yn9rUuhVO+bLJ/J6CBObTAb1fGi8d78eNGnt+LHz/6/mi+YLVqh27fUT2dP3hP85D4BuYSlK/K0Mr7qgbpWzBe6VzqsfesR3urK3SjG1LcQ436h3SrdZ12g5cpOi3Ga8aQpWQR2+XKeHGWbLjYeLEB8z25quYLVqt26I5dOAKb4C0AOVEEmCeAeP6qlbcNC4yXjVCV6YOAdluzxoui/VnGa/KocXWfemexh4oTEzd7J4wmA/DN4P3Z3xz8rn4+//yLqLy7d+85y9OVNuTjrp3BEiwRA4gBFzFQ5Z9gX2XDePki6yLfuYwX0Xhw/Qbt/uLZeHD96JR6+9tjg1XhHS+D5Kujo0gLD7r39eELXutHq3bolo048JblzaWBuSxzrbxtlGC8bISqTJ/rUSMLTkwnsfoBHTx9TI947FfO25BpVXX5qDGePz9u5Lx9Laat+YLVqh264xHufxu8/TNOlgDmSSJ+v2vlbaMC42UjVGX6XIPrMwRn5JVx9OVuX8aLx3iZxbRfv359WZ6rDc0XrFbt0O0qeovlA97FOLk8Csxd0rTnpZW3rWYwXjZClabnTSeRmC7iUmfGdBLRY8usNyEvT57Z8GW8uKD45KquB9trvmC1aofumcvH6w7w9oo3NXMwT8XibadW3jYgMF42QpWmmwlUN2j38AUNo0eIAe1trtH63YBOY2Pn4zJnJlAd9umb7gd0I+ec+PnxbZ/Gi8sxk6s+/OJhvNiFtzVfsFq1Q/fCYVsqA/AuhcvJwWDuBGPhTLTytlUQxstGqOr0mSWDZpf/Gc/rFX/Lkcd4jQ0aG6fxMkOPqV9y1nquum/jxWWw6eJyXE6uqvmC1aodumU7C/CW5c2lgbksc628bZRgvGyEGp4uYbzM5KpclqvJVTVfsFq1Q7dsZwHesry5NDCXZa6Vt40SjJeNUMPTJYwXI+YB9i4H22u+YLVqh27ZzgK8ZXlzaWAuy1wrbxslGC8boYanSxkvxuxysL3mC1arduiW7SzAW5Y3lwbmssy18rZRgvGyEWp4uqTxYtQ8zovLXHSwveYLVqt26JbtLMBbljeXBuayzLXytlGC8bIRani6tPFi3Gaw/SIz22u+YLVqh27ZzgK8ZXlzaWAuy1wrbxslGC8boYanV2G8GLmZ2f7bb7+dqwU0X7BatUP3XKE690ngPTe6uU8E87nRzXWiVt62ysJ42Qg1PL0q48VvOr7/3nvRgPt53nTUfMFq1Q7dsp0FeMvy5tLAXJa5Vt42SjBeNkINT6/KeDF2Nlz8piPf/So7s73mC1arduiW7SzAW5Y3lwbmssy18rZRgvGyEWp4epXGi9Gbwfadjz8u1RKaL1it2qG7VIgufDB4L4ywdAZgXhrZQido5W2rNIyXjVDD06s2Xoz/OAhKv+mo+YLVqh26ZTsL8JblzaWBuSxzrbxtlGC8bIQanl4H48VNYN50LLqskOYLVqt26JbtLMBbljeXBuayzLXytlGC8bIRanh6XYxXfFmhIm86ar5gtWqHbtnOArxleXNpYC7LXCtvGyUYLxuhhqfXxXhxM7D5MssK2d501HzBatUO3bKdBXjL8ubSwFyWuVbeNkowXjZCDU+vk/HipjBvOvJUE3lvOmq+YLVqh27ZzgK8ZXlzaWAuy1wrbxslGC8boYan1814cXPwo0bWlTfNhOYLVqt26JbtLMBbljeXBuayzLXytlGC8bIRanh6HY0XNwkvJ8TastZ01HzBatUO3bKdBXjL8ubSwFyWuVbeNkowXjZCDU+vq/HiZjFvOn51dDTTSpovWK3aoXsmDL3uAG+veFMzB/NULN52auVtAwLjZSNUdfpoQOGXHdpqrUR3eNqtDdrtBhQOznOVjQbP6aizPTlnhdZ3HtA3/bPcc9IS62y8WC9PrMoak9NMaL5gtWqH7rQryN8+8PbHNitnMM8i42e/Vt42GjBeNkKVpo/orLdP661t2gtOaEhEo8FT+mRzjdrbh9QfZYgbPqeDzTVavxvQaXTMGwq7t6m9uk+9s6yT0vOqu/GKTzPR7/cvK6H5gtWqHbovw09kA7xFME8VAuZTOLx/0crbBgbGy0ao0vRX1OvcTJist9Q/vEPt1n06HlykqrsIu3SjdZ12g5eX6Wn7LhNzNupuvFh62jQTmi9YrdqhO+dC8pAE3h6gWrIEcwsgx8laedswwHjZCFWZfhHSwbUVWu/0KP6QcGyibtJe71WqujSTlbYv9eTETg3GiyWbaSZ4ni82YpovWK3aoTtx8Xj+Ct6eAadkD+YpUDzu0srbhgTGy0aoyvSzHu2trtCNbkjxe1uj/iHdStzRmpKZ+ajxQzo+zR8bNpUPUTR+Krmvrt/5USMbRZ5m4te/eVxXmVZdWjsb6LY2rdMDwNspzkKZgXkhTM4O0srbBgDGy0aoyvRBQLutWeNF0f7pR4lJmWNzZgbk8+/sO2RsVvJ+OPi1/Hz++RdRXf7sT/9cjWYtbKFTz3WAtkJbLUsMJP+2LcN3GK86t+Kcxmt0GtC91Q3aPXwRDcgnOqdB71Paat2mg/BNqRpredQYr9RxEETmK2uOr/ixddzmDlPjB7plWw28ZXlzaWAuy1wrbxslGC8boSrT53rUOBmQn3yDcXRCj7bXqL0T0KBEnTQaL67eRx/9LDJfaXN8lah+JYdq7WygWzZcwFuWN5cG5rLMtfK2UYLxshGqMn2uwfUv6XjnOrWvdSmMDwyjrP35FdRqvPiC/flnn0XmKznHV36Nq0/V2tlAt2zsgLcsby4NzGWZa+VtowTjZSNUaXredBJ36FH/bYq6IYXdd2eNV8PuePEFG5/jS5P50trZQHfK5ehxF3h7hJuRNZhngPG0WytvGw4YLxuhStPNBKpmvNaIhv2A9qYmR50VOB7jtU17Xz6nQTRfarPGeDERc8HGzRdPOaHhY7Rr0BrXCN1xGv63wds/42QJYJ4k4ve7Vt42KjBeNkJVp88sGbRGW52vp5YMmp2jiw3aYzrY2YgetUVvLG526CgcULl563VNJxFvqvgFG5/jS4P5imuP16nu29At20LgLcubSwNzWeZaedsowXjZCDU8XfMYr3jTaTJfWjsb6I5HnP9t8PbPOFkCmCeJ+P2ulbeNCoyXjVDD05fFeHEzsvni+vAEq/wIsq4frZ0NdMtGFHjL8ubSwFyWuVbeNkowXjZCDU9fJuPFTcmD7OtuvrR2NtAt21mAtyxvLg3MZZlr5W2jBONlI9Tw9GUzXtycdTdfWjsb6JbtLMBbljeXBuayzLXytlGC8bIRanj6MhovbtInT55Ed77qOLu91s4GumU7C/CW5c2lgbksc628bZRgvGyEGp6+rMaLm5VNF9evbuZLa2cD3bKdBXjL8ubSwFyWuVbeNkowXjZCDU9fZuPFTVtH86W1s4Fu2c4CvGV5c2lgLstcK28bJRgvG6GGpy+78eLmNearLus6au1soFu2swBvWd5cGpjLMtfK20YJxstGqOHpTTBe3MSdjz+OHjvWYWkhrZ0NdMt2FuAty5tLA3NZ5lp52yjBeNkINTy9KcYrvrRQ1eZLa2cD3bKdBXjL8ubSwFyWuVbeNkowXjZCDU9vivHiZq6L+dLa2UC3bGcB3rK8uTQwl2WulbeNEoyXjVDD05tkvLip62C+tHY20C3bWYC3LG8uDcxlmWvlbaME42Uj1PD0phkvbu6qzZfWzga6ZTsL8JblzaWBuSxzrbxtlGC8bIQant5E48VNHjdf3377rWgUaO1soFs0TGACZHFHpSHGZaFr5W2jBONlI9Tw9KYaL252XlT7R++8E/3wttRHa2cD3VIRMi4HvGV5c2lgLstcK28bJRgvG6GGpzfZeHHTV2G+tHY20C3bWYC3LG8uDcxlmWvlbaME42UjVHX6aEDhlx3aaq1E80y1Wxu02w0oHJxnKHtJxzvXJ8eac2K/r3UpvMg4NWV3040XI5E2X1o7G+hOuYA87gJvj3AzsgbzDDCedmvlbcMB42UjVGn6iM56+7Te2qa94ISGRDQaPKVPNteovX1I/VFRcW8o7N6mdmubPumdUuHTiCIDV7SUOh3n+oKVNF+utUu1C3RLkR6XA96yvLk0MJdlrpW3jRKMl41QpemvqNe5mTBZb6l/eIfarft0PCh262p0GtC91RVa7/TorGR9cMfrCpiU+dLa2UD3VaxIbIG3BOXpMsB8mofvb1p527jAeNkIVZl+EdLBtVnDdBF26UbrJu31XhVQNzFvqx/S8WnW48nsbGC8ptlImC+tnQ10T8eK72/g7ZvwbP5gPsvE5x6tvG1MYLxshKpMP+vR3uoK3eiGFL+3Neof0q3WddoNXlrVjY9do63u8+hRpfWExAEwXgkgAmO+tHY20D0bKz73gLdPuul5g3k6F197tfK28YDxshGqMn0Q0G5r1nhRtL+I8TJju+7Qo/7bzJqwucr74eDHzzSDf/jHf6I/uvGH0Q9vg880H/AAD8QAYsBFDGT+4VKcAONV58Zb1HhN7piVG4g/DQR3vKZ5xL/5euzInZXGD3TLthp4y/Lm0sBclrlW3jZKMF42QlWmL/iocTwWbI1uHZ6UepMxXmUYrziN2W0f5ktrZwPds/Hhcw94+6SbnjeYp3PxtVcrbxsPGC8boSrTFxpcb95+zH/MaKsejJeNkPt5vrR2NtBtjxWXR4C3S5rF8gLzYpxcHaWVt63+MF42QpWm500nYTNUk4lUS06YmqwujFeSSPr3+J2vRdd21NrZQHd6bPjaC96+yGbnC+bZbHykaOVtYwHjZSNUabqZQHWDdg9f0JBGNOwHtLe5Rut3AzrNmwl1cresvRPQYIE6wHgVh2fMFzN79uxZ8RMTR2rtbKA70ZCev4K3Z8Ap2YN5ChSPu7TytiGB8bIRqjp9ZsmgNdrqfD21ZNB4LFfiLceMx5RlqwPjVY4Ym6+f3rsXvSU6r/nS2tlAd7lYWfRo8F6UYPnzwbw8s0XO0MrbVmcYLxuhhqfDeJUPgB9++GEh86W1s4Hu8rGyyBngvQi9+c4F8/m4zXuWVt62+sJ42Qg1PB3Ga74AWMR8ae1soHu+WJn3LPCel9z854H5/OzmOVMrb1tdYbxshBqeDuM1fwDMa760djbQPX+szHMmeM9DbbFzwHwxfmXP1srbVk8YLxuhhqfDeC0WAHHz9dXRUaHMtHY20F2oeZ0dBN7OUBbOCMwLo3JyoFbetsrDeNkINTwdxmvxAGDz9fPPPosG3D/84qE1Q62dDXRbm9bpAeDtFGehzMC8ECZnB2nlbQMA42Uj1PB0GC93AcCmi3nazJfWzga63cVKkZzAuwglt8eAuVuetty08rbVC8bLRqjh6TBebgMgbr74TljaR2tnA91prelvH3j7Y5uVM5hnkfGzXytvGw0YLxuhhqfDeLkPAGO+eL6vNPOltbOBbvexkpcjeOfR8ZMG5n64ZuWqlXdWfcx+GC9DAr9TCcB4pWJZeCdPrsps08yX1s4GuhcOi1IZgHcpXE4OBnMnGAtnopW3rYIwXjZCDU+H8fIXAHHzxTPem4/Wzga6TQvK/AZvGc7xUsA8TsP/tlbeNjIwXjZCDU+H8fIbAGy+fvTOO9GPMV9aOxvo9hsrydzBO0nE/3cw9884XoJW3vE6pG3DeKVRwb5LAjBelyi8bZjFtdmA9ft90trZQLe3EEnNGLxTsXjdCeZe8c5krpX3TEUSO2C8EkDwdZoAjNc0D1/fjPli3p9//oWvYrzmq7WThG6vYTGTuVbeXBGt2qF7Jgwr3QHjVSn++hcO4yXXRq9fv15ocW05pekloXNP5+JrL3j7IpudL5hns/GRopW3jQWMl41Qw9NhvGQDgKeXuP0ntwtNtCqrzF6a1k4Suu1t6/IIrbyZgVbt0O0yghfPC8ZrcYZLnQOMl3zz/vo3j6PZ7Zk9z/mVNteXvCp7iejc7YxcHgHeLmkWywvMi3FydZRW3rb6w3jZCDU8HcZLPgBMZ2ObaFVeWX6JRnf+UfVLhW7ZNtHKmylp1Q7dsjFuKw3Gy0ao6vTRgMIvO7TVWokeP7VbG7TbDSgcnOcrS563+gE9eD6gUf5ZM6kwXjNIvO+Id5JZc315FzFHAXHdc5xe2SnQLYteK2+mpFU7dMvGuK00GC8boUrTR3TW26f11jbtBSc0JKLR4Cl9srlG7e1D6me6qDcUdm/T+s4RnQxHRKNT6u1vU7t1mw7CN6VqBONVCpeTg5OdZNpcX04KcpxJUrfj7L1lB93e0KZmrJU3V0arduhODcXKdsJ4VYa+SMGvqNe5mTBZb6l/eIfarft0PLhIzWTUP6RbrZu013t1lX7Wo73VFbrRDSn9rKtD41swXnEaMttpnaSZboLn+mIjVsdPmu466kxqgu4kEb/ftfJmKlq1Q7ffmC6bO4xXWWKSx1+EdHBthdY7PTqLlXsRdulG0lhdpk+M2eo+9c4yb4ldHm3bgPGyEXKfntVJsvnitR25TZ48eeK+4AVzzNK9YLbeT4du74inCtDKmyuhVTt0T4Vg5V9gvCpvghwBGXepxne0rtNu8DLl5CGF3Xepfe1TOn72kHZXJ2PDNjt0FKaP8eI/5Hk/fNHipx4M+I1HM93ERx/9DO2C2EQMIAaWOgZS/sip3wXjVecmHAS020p5PBjtzzJeL+l453pkpNZ3HtK/R4Pwz2nQ+5S2MMarzq19qa3If6d1fOOxiO7LStZoA7plG0Mrb6akVTt0y8a4rTQYLxuhKtMXMV6rH9LxaezNx9EJPdpem3lsaaseHjXaCLlPL9pJHgdBZLD58SM/hqz6U1R31TqT5UN3kojf71p5MxWt2qHbb0yXzR3GqywxyePnetQ4GZB/rUvh1Cj6yZ2wmf35FYLxyufjI7VMJxl/45EX2K7yU0Z3lTqTZUN3kojf71p5MxWt2qHbb0yXzR3GqywxyeMXGVw/Y7Amxit3GorZysF4zTLxvadsJ2neeOS2qvKNx7K6fXMsmj90FyXl5jitvLn2WrVDt5vYdZULjJcrkl7yyZtO4g496r9NKdXM/ZVIx6PGFFb13DVPJ8nLCpk3Hnn8VxWfeXRXoTNZJnQnifj9rpU3U9GqHbr9xnTZ3GG8yhITPd6YqA3aPXxBQxrRsB/Q3uYard8N6DRrtojRd3R8dyN2zBn1g33aSo77KlAX3PEqAMnxIfN2kmy+zKD7zscfi6/xOK9ux/hKZwfdpZEtdIJW3lxprdqhe6GQdX4yjJdzpI4zTC7901qjrc7XU0sGjef1SrzlOOzTN90PaH0yVcT6zgP6ph+fDayYThivYpxcHrVoJ2kG3b//3nuig+4X1e2SYZm8oLsMrcWP1cqba65VO3QvHrcuc2is8YrmwkqdZHS+QeguG6VOecF4ybeGi07y22+/JZ7lnn94W+LjQreEzmQZ0J0k4ve7Vt5MRat26PYb02Vzb6jxGs/unpwRfgwPxiseRDBecRoy2646SR50z3e9uA35LpjvjyvdvnUm84fuJBG/37XyZipatUO335gum3tDjRcPWv8x3To8odlhUjBe8SCC8YrTkNl22UnyuC8e78Xt+PPPPqBQfocAACAASURBVPM67sulbhnS41KgW5K2XvPClBAriBUXBNwZr2iyTx5/9Dkd7GxEHX27tUG7v/g36p88ju3bpr3ghIZG/bBPvcMObV0uW5MYwzQzxmmDdruPqT+cWCZbuikn/juaHyvx1t9letJ4mVnf12hr/ykNomLPqP/0wdRyPL+KxlO9SwfhZc0uc9S8AeMl33o+Ovevjo68T7bqQ7cEfeiWoHxVhlbeXAOt2qH7Kv7qsOXYePGaf9v0Se+URvSGwu7tsQFb/YAePB/QaHRKvf1tarcmpmfy9l1781PqmaVtno/XFxw/Bpws+Hy51M2IhidHkeEplp6GePKmYOZ8VnHjZcqLm65zOg0+pPWWMZDGmHHdYbzSiFexT2tHw6x8aY9Ptupj3Jcv3b7jB7p9E57OXytvn9fmNCH337Qy16rb1oLOjVd83NR4MeeVqWVq4m/gjdPXph/5TeabakcTgE5MUOogeK6aLT2t+nnju2J5Xvsv1HvBJi9uuogodT6syXxbMF5pwCvZp/mC9ak9Pu6L74K5/PjU7VJnMi/oThLx+10rb6aiVTt0+43psrk7N143uiFdrlSTsphz3HiNxfLcVL+NBv8eB//t6pFkZLzM3aUVWt/p0j8Hv716xBidbEtPwREZpx/TXu9VSiLvmpg58+gzYfrGZjExdQOZ+bZwxysDqvhurR0Ng/Ktncd98Xgvfozscr4v37p9BRF0+yKbnq9W3hLXZjqxxfdqZa5Vt63FqjVel48ejbEK6Lj3mB7tXKfxHS+Wf0b9XkCPOvyIkh/njY89DgeTgfG29GkE2dNImOOujNf65rv0n3jerO7zyzFps8ZxfN54P4yXoVj1b80XrJR2M98XTznhYpFtKd2uYwu6XRPNz08rb66VVu3QnR+T0qkVGq//oLPePq23Nuhe8N3V24VTjxqTONhkHUYzt7cTd6LGR9rSbeO7OJf448vXk3FqVwPxUx+P4o5XsqEq/661o2Fwktp5YW02XvwPzZMnTxZqN0ndCwlNnAzdCSCev2rlzVi0aoduz0FdMvsKjdfvaRDcvxpob4RHbxyuxO54mQTz+yL9PJNMeel500iYDCbGa7LI9Og0oHurK1fL76SO8TIvEuCOl6FY9W+tHQ1zk9b++vXrqXUe+VHkPB9p3fNoTDsHutOo+NunlTcT0aoduv3F8zw5V2i8/oOG4QPaij3KGw2e05F5pMh3tN78PlpzsL25T8dmuZvhC3rE01VsPqDwzJJuppwwZHKnkTAHTRsvIjOOzNyZM9/xVqMhVsffWjsaZlmVdrPOIy+2Pc+jx6p0Lxp/0L0owXLna+Vd5bVZjvDs0VqZa9U92wLTeyo0Xi/H47d48WYzkJ2naDj873Tcff/yTthoENJxbM3BdmKtQlt6vLr28V18dNJ4EdHwOR1sro3NXmTmkvN4/RUdRIYRd7zivKvc1nzBVqk9PuUEb5f5VKm7jM7ksdCdJOL3u1beTEWrduj2G9Nlc3dnvMqWvFTHm8eb9+l4cPlO51LUkMf+aPxo7WiYddXa+W4X3/Xitue7YEUfPVate944he55yc13nlbedbg25yNefZ/SNN22+sJ42Qgl0ydj0NZ3jugkuvvF02EE0YD/9bsBnc6uQZTMQdV3GC/55qrDHyY2W2UfPdZB9zytBd3zUJv/HK28ucZatUP3/PHq40wYr9JUz2kQBlfzjUWPSfkRaS8xx1jpjGt5AoyXfLPUqZMs8+ixTrrLtBp0l6G1+LFaeXPNtWqH7sXj1mUOMF4uaS5hXjBe8o1at04y/ugxb6Htuuku2nLQXZSUm+O08ubaa9UO3W5i11UuMF6uSPrKJ3UR8IDCaG3LrELNmLPxhLNsnsY/5Qf/w3hlMfa3v46dJD96NAttv//ee6lvPdZRd5FWgu4ilNwdo5U3E9CqHbrdxa+LnGC8XFD0lodZishMXUE0GjylT/gNy8xFvlnMZO3I3GOKiYbxKsbJ5VF17iR5cW0z4SrPfB//1Fl3XGdyG7qTRPx+18qbqWjVDt1+Y7ps7jBeZYmJHp9moMaLfLdbOW9Qpk7yOp9wGK/5uC1yVt07SZ5wldd45NiIr/VYd91ZbQLdWWT87NfKm2lo1Q7dfmJ53lxhvOYlJ3HeRUgH11ZovdOjs1h543Uhb2Yv9B29eZlcyDuWQYlNGK8SsBwdqqWTjK/1yHfCtOhONhN0J4n4/a6VN1PRqh26/cZ02dxhvMoSkzx+MnXFjW5I8dnBxutFZhursTHboL/ceZ/WzfiuzQ4dXS4sXrwSMF7FWbk6UlMnyWs98piv6O5X568Lz/nlipWLfDTxjtcXuuM0ZLbBXIazKUUrb6M/6zeMVxaZOuwfBLTbWqGk8aJof5bxMo8iN2j38AUNo3qMaHhyRLurt+kgfDNTM/6jmffDwY8fMMiKgV//5jHdvTuecPX2n9ymf/jHf0K84JpBDCAGnMTAzB+sJdgB41XnRpzLeGVVaLIUUskB97jjlcXT336t/+X97d/9KnPgvT9ai+eslTd0L972ZXMA87LEFjteK29brWG8bISqTJ/zUWO65JQ1KNMPnNoL4zWFQ+SL1s6GdScH3vP3un8086472zR9WnlzXbRqh+60SKxuH4xXdeztJc87uD41ZxivVCw13LkMnWR84P2TJ09qSPlK0jLwvqpN/be08mayWrVDd72uCxiverVHQk3edBJ36FH/beJ4/jo5Z3WfemexhSPnnGICd7xSEHvetSydZHzG+/i0E57xlc5+WXiXrnhFJ2jlzbi0aofuioI9o1gYrwww9dhtJlA1A+WLLMg9omH4gLZa5hyuyTkNep/S1uqHdHx6XqpqMF6lcDk5eNk6yfjdL552om6fZeNdN75JPVp5cz20aofuZBRW+x3Gq1r+9tJnlgxao63O11NLBo2nj4i/5Ti7kPf6zgP6ph+fDcxeNB8B41WMk8ujlrGTjE87kbfeo0uORfNaRt5F617FcVp5Myut2qG7ikjPLhPGK5sNUmC8KomBZe0k4+s98rJDdbn7tay8KwneAoVq5c1V06odugsEpuAhMF6CsDUWhTte8q227J1k3e5+LTtv+QjOL1Erb66VVu3QnR+T0qkwXtLElZUH4yXfYE3oJOt096sJvOWjOLtErby5Rlq1Q3d2PFaRAuNVBXVFZcJ4yTdWkzrJOtz9ahJv+WieLVErb66JVu3QPRuHVe6B8aqSvoKyYbzkG6lpnWTy7tezZ89EoTeNtyjclMK08uaqaNUO3SmBWOEuGK8K4WsoGsZLvpWa2knG737xvF9Ss943lbd8ZI9L1Mqb1WvVDt1VRXt6uTBe6Vywd0IAxks+FJreScbn/ZKY9b7pvKUjXCtv5qRVO3RLR3l+eTBe+XwanwrjJR8C6CSJ4rPe//Tevei7r5YAb19k0/PVyptro1U7dKfHYlV7YbyqIq+kXBgv+YZCJ3nFnO948ZxfHIdfHR0Rjwdz/QFv10Tz89PKm2ulVTt058ekdCqMlzRxZeXBeMk3GDrJaeY81otnu+dYfP+994jHgrn8gLdLmva8tPLmmmnVDt32uJQ8AsZLkrbCsmC85BsNnWQ6c57p3tz9YiPmavA9eKfz9rVXK2/moVU7dPuK5vnyhfGaj1tjzoLxkm9qdJLZzJNTT7gYfA/e2bx9pGjlzSy0aoduH5E8f54wXvOza8SZMF7yzYxO0s48Ofh+kceP4G3n7fIIrbyZgVbt0O0yghfPC8ZrcYZLnQOMl3zzopMszjw++P7hFw/nGnwP3sV5uzhSK2+uu1bt0O0ict3lAePljuVS5gTjJd+s6CTLMefHj2y6OFZ5DFjZx4/gXY73okdr5c311qoduheNWrfnw3i55bl0ucF4yTcpOsn5mPPjRp7zi2OWfxd9/Aje8/Ge9yytvLm+WrVD97zR6uc8GC8/XJcmVxgv+aZEJ7kY87KPH8F7Md5lz9bKm+upVTt0l41Sv8fDePnlu3juowGFX3Zoq7US/Sffbm3QbjegcHBeMO8RDcMHtNW6TrvBy4LnXB0G43XFQmoLneTipJOPH3kZoqwPeGeR8bNfK2+moVU7dPuJ5XlzhfGal5zIeSM66+3Temub9oITGhLRaPCUPtlco/b2IfVHBUQMn9MBHw/jVQBWPQ5BJ+muHfhxIy+4zf9A8OSrPBdY8gPeSSJ+v2vlzVS0aoduvzFdNncYr7LERI9/Rb3OzYTJekv9wzvUbt2n48GFRc0bCru3J3fKcMfLAqs2yegk3TfFs2fPLidfZSMWn3wVvN3zzstRK2+uk1bt0J0XkfJpMF7yzIuXeBHSwbUVWu/06Cx21kXYpRutm7TXexXbm9w0jxhv02fdn9EN3PFKAqrtd3SSfpqGHz/yI0e++8U/Zu1H8PbDOytXrby5Plq1Q3dWNFazH8arGu7FSj3r0d7qCt3ohhS/tzXqH9Itm5GKHjFep63uc/p/kVHLvuNl/hBl/eaLFj9gsCwxcPwv/0p3747ffvyjG39In376nxHfuMYRAzWNgWJ/LHUdBeNV5/YaBLTbmjVeFO3PNlJEk0eMmw8oHI5ofIcs7/hsCGzGNH60/ofHrLVq16Y7Of6LH0dq+mjjbdhq1Y1r07Sg3G/NsZJHCcYrj07VaXMZr6tHjAfhm6gGMF5VN2S58rV2Nlp1f/75F9HAe/4ng8d/FZ3/q1yruj9aK2+turkFtWqHbvfX3yI5wngtQs/3ufM8aow9YuS3IPkD4zUBoeQXOknZhmLeZvwXz3zPBuznn302NQBfVlGx0hAnxTi5PArMXdK056WVt61mMF42QlWmzzG4fmyyzJxfKb93AhqUqBMeNZaA5ehQrZ3NMuiOz//FsT/v+o+OQiE3m2XgnVvBGiaCuWyjaOVtowTjZSNUaXredBJ36FH/bSF1uONVCFNtDtLa2SyTbp5ugu96sfniu2D8NiSbsjp9lol3nbjmaQHzPDru07TytpGA8bIRqjTdTKC6QbuHL2hIIxr2A9rbXKP1uwGdFplAFY8aK23BeQrX2tkso+74APx5FuCep/2LnrOMvIvWvarjwFyWvFbeNkowXjZCVafPLBm0Rludr6eWDLLd0bKl51URjxrz6PhJ09rZLLNuNmA88z1fD/y7Dm9ALjNvP1fW4rmC+eIMy+SglbetjjBeNkINT4fxkg8ArZ1NE3Sz4aqLAWsCb/mrL79EMM/n4zpVK28bBxgvG6GGp8N4yQeA1s6mSbrjBqyqKSiaxFv+KkwvEczTufjaq5W3jQeMl41Qw9NhvOQDQGtn0zTdySkopA1Y03jLX4mzJYL5LBOfe7TytjGB8bIRang6jJd8AGjtbJqquyoD1lTe8lfkVYlgfsVCYksrbxsbGC8boYanw3jJB4DWzqbpuqUNWNN5y1+ZmLlemrnWGLdxgvGyEWp4OoyXfABo7WygexwrUgYMvHFtFiWAWClKSuY4GC8ZzmpLgfGSbzp0krLMffH2bcB86fZNX6tu5qJVO3T7jupy+cN4lePVuKNhvOSbHJ2kLHPfvH0ZMN+6fbWCVt3MQ6t26PYVzfPlC+M1H7fGnAXjJd/U6CRlmUvxTjNgi0zEKqXbdWto1c0ctGqHbtdRvFh+MF6L8Vv6s2G85JsYnaQsc2neSQM270z40rpdtYpW3Vx/rdqh21X0uskHxssNx6XNBcZLvmnRScoyr4o3G7D4RKxlDVhVuhdtHa26ud5atUP3olHr9nwYL7c8ly43GC/5JkUnKcu8DrzjBowX4z4OAmJjlvepg+48fVlpWnVzfbRqh+6saKxmP4xXNdzVlArjJd9U6CRlmdeJNxswngGfrzs2YF8dHdHr169TgdRJd6rAjJ1adXN1tGqH7oxgrGg3jFdF4LUUC+Ml31LoJGWZ15F3v9+/NGB8DT784uGMAauj7iItp1U3102rduguEplyx8B4ybFWWRKMl3yzoZOUZV5n3t9//31kuvg65J/4epB11p3Xglp1c520aofuvIiUT4PxkmeuqkQYL/nmQicpy1wDb37cyI8d+fEjX5M8EP/zz7+QBeWoNA28s6qqVTt0Z7VoNfthvKrhXrzU0YDCLzu0NfmPt93aoN1uQOHgPCePEQ37j+lgZyPqpIudk54djFc6F5970Un6pDubtybePOD+yZMnkfHia7PoQPzZWle3RxPvJCWt2qE72ZLVfofxqpa/pfQRnfX2ab21TXvBCQ2JaDR4Sp9srlF7+5D6o/TTR6cB3Vtdo61OQP3h6OqczQcUDjNOSs8qMm4ZSbXerbWjYahatUO37CXBd7zMQHw2YTwOjB9N1v2jNU5wbcpHluZYyaMF45VHp/K0V9Tr3EyYrLfUP7xD7dZ9Oh5cpCg06XfoUf/tJP2CBsF9arfepYOQ7VvxD+54FWfl6kitnQ10u4qAYvkY3jwQn00XX6v8w2bs22+/LZZJBUcZ3RUUvXCRWrVD98JN7zQDGC+nOB1ndhHSwbUVWu/06CyW9UXYpRutm7TXexXbm7cJ45VHp25p6CRlW2RZePM4MJ7/Kz4OjB9L2uYDk6Wt944uc1qWWJFu83nL08rbVl8YLxuhKtPPerS3ukI3uiHF722N+od0q3WddoOXBdTxeK+A9jbXaP1uQKflnjTiUWMBwq4P0drZQLfrSMjPL4t3ckb8uj2GzNKdX9t6pGrVDt31iB+jAsbLkKjj70FAu61Z40XR/gLGa3RCj7bXxo8gVj+gB88HlOa7zCOKrN980eIHDBAD+mLgy6P/Sh999LPLx5B/9qd/Hr0NibbU15ZNbbM6/mleVBOM16IEfZ6/qPG61HZOg96ntNXaoHvBd6nm6/LQxAabMY0f7qS0frRqh27ZiCvDO/kY0jYrvs+alNHtU8c8eWvVDt3ztLa/c2C8/LFdPGcnjxonMszdr5y3IdMEw3ilUfG7D52kX77J3JvGO74sEV/fP//sM9HB+Fp5c9xo1Q7dyau+2u8wXtXyzy/d2eB6LuYlHe9cp/a1LoXxAWP5CjDGy8LHRzI6SR9Us/NsKu+0SVl5cD7v9/nRypuZaNUO3T4junzeMF7lmQmekTedRHy6iLikyTmr+9Q7i43omtzxKjvAHne84mxlttFJynA2pTSdtxmM/9N79y7Hgvm8C6aVN8eLVu3Qba72evyG8apHO2SoMBOobtDu4QsaUpE3FEc0DB9E47nG53DWZ9QP9mmrdZsOwjcZZaXvhvFK5+JzLzpJn3Rn8wbvKyZmbcj4lBS8VJHLu2BaeTMlrdqh+yrG67AF41WHVsjTMLNkEM9I//XUkkHjeb3ibzme0yAMYksGrdD6zgP6ph+fDSyv0Ks0GK8rFlJb6CSlSI/LAe9Z3uYuWHxmfN7m8WGLzgumlTdT0qodumdjvMo9MF5V0ldQNoyXfCOhk5RlDt75vJNjwfhu2CLLE2nlzZS0aofu/BiXToXxkiaurDwYL/kGQycpyxy8i/PmpYh4/Bf3C/zz/nvvRYt2l3kUqZU3U9KqHbqLx7jEkTBeEpQVlwHjJd946CRlmYN3ed5stHg5IjZexoSxIeNHkbaPVt5cL63aodsWlbLpMF6yvNWVBuMl32ToJGWZg/divJMD8s2jSF68O+2jlTfXRat26E6LxOr2wXhVx15FyTBe8s2ETlKWOXi74532KDL5VqRW3kxJq3bodhfjLnKC8XJBcYnzgPGSb1x0krLMwds9b37zkR9FxucG423ed/wv/+q+QKEcEStCoCfFaOVtowTjZSPU8HQYL/kA0NrZQLdsrGjhzePBeEb8tPFgi05NIUscd7zA2w0BGC83HJc2Fxgv+abV8gc1SQa6k0T8ftfIm8eDdTp/TWaCVu5fzKB8DSZMI3OOQuj2ey2WzR3Gqyyxhh0P4yXf4OgkZZmDdzW8eTwYzwdmTJgZlM/76/pBrMi2jFbeNkowXjZCDU+H8ZIPAK2dDXTLxsoy8dZiwpaJuWy0zleaVt622sJ42Qg1PB3GSz4AtHY20C0bK8vImx838lxg8Ula63QnbBmZy0ZtudK08rbVEsbLRqjh6TBe8gGgtbOBbtlYWXbedTRhy85cNoLtpWnlbasZjJeNUMPTYbzkA0BrZwPdsrHSJN5ZJkx6YH6TmMtGc3ppWnmn1+ZqL4zXFQtspRCA8UqB4nmX1s4Guj0HRiL7JvNOjgnjfkrChDWZeSL8RL5q5W2DA+NlI9TwdBgv+QDQ2tlAt2ysgPeYd5oJM5O1llm8u0jrgXkRSu6O0crbRgDGy0ao4ekwXvIBoLWzgW7ZWAHvWd68PiQvURSfrJVNGO/jOcQW/YD5ogTLna+Vt62WMF42QlWnjwYUftmhrdYKsQlqtzZotxtQODjPUXZOg/Br2ttcm5yzQus7XToOBzTKOSstCcYrjYrffVo7G+j2GxfJ3ME7SWT6OxstnjE/vmwRGzKeO2zeucLAfJqx729aedu4wHjZCFWaPqKz3j6tt7ZpLzihIRGNBk/pEzZU24fUT3VRIxqGD2iLDdovntGAjxme0HFnm9qt23QQvilVIxivUricHKy1s4FuJ81fOBPwLoyK+JEjrxMZn6aC+zYzLqzoI0kwL87cxZFaedvqDuNlI1Rp+ivqdW4mTNZb6h/eoXbrPh0PLlLUTc651qUwnnzWo73VFVrv9Ogs5aysXTBeWWT87dfa2UC3v5hIyxm806jY95k3JOOz5nM/x3fG+A5Z3iNJMLfzdXmEVt42BjBeNkJVpl+EdHBt1ixdhF260bpJe71XxdVN8mrvBDQoflb0qLLE4bU5VPMFq1U7dMuGP3i74W3GhcUfScYnbWWjZj5gbkjI/NbK20YHxstGqMr0yV2qG92Q4jevRv1DutW6TrvBy8LqxuesUDIvWwa442Uj5D5da2cD3e5jIS9H8M6jM19a1iPJzscfR48q/+Ef/2m+jCs+C7FScQMkiofxSgCp1ddBQLutFLMU7S9jvN5Q2L1N7dYdetR/O1NFNld5P3zR4gcMEAOIgabFwN/+3a+o0/lr+skf/+Syj+Ttjz76GXHar3/zGH2j578PM3+wlmAHjFedG9GJ8boabH8v+A5vNda5vSfa+I+bxg90y7YaeMvy5rthf/M33ZkB+kXGhskqnS0NsTLLpMo9MF5V0reVvfCjxhENT45od3WNtrrPo7cibUUm0/GoMUnE/3d0kv4Zx0sA7zgN/9taeTOZuHaekiI5ZxiPDSv7pqR/4tO6JcpzVUact6s865APjFcdWiFLw0KD689p8Pzh2HTtPx1PK5FVTs5+GK8cOJ6StHY20O0pIDKyBe8MMB53ZzHnu2HPnj2LTBebLzN0g+cNY3PGJi0+SN+jxNSss3SnHlyjnVp12xDCeNkIVZqeN51E+nitsdwzOjm8S+utNdpawHRxXjBe8gGgtbOBbtlYAW9Z3lxaUeZm8lYelG9MGP82jyX5TUrJT1HdkpqKlKVVt61uMF42QpWmmwlUN2j38AUNaUTDfhDNSL9+N6DT1AlUz+k0+JDWWyuUfUzxSsF4FWfl6kitnQ10u4qAYvmAdzFOLo+ahznf6TKPJeNTVnDfyo8leWLXvLnDXOifR7eLchfNQ6tuW71hvGyEqk6fWTJojbY6X08tGTSe12vylqOZryvrTcXkxKqW+sF4WQB5SNba2UC3h2DIyRK8c+B4SnLB3DyW5Alc42tKmvFhPoyYC92ekOZmq1V3bqWICMbLRqjh6TBe8gGgtbOBbtlYAW9Z3lyaD+bxucPi48N4m80Zjx3jYxb5+NC9iJ6i52rVbasfjJeNUMPTYbzkA0BrZwPdsrEC3rK8uTQJ5vzY0awrGTdiZoHveYyYhG4fraFVt40FjJeNUMPTYbzkA0BrZwPdsrEC3rK8ubQqmLswYlXodtE6WnXb6g7jZSPU8HQYL/kA0NrZQLdsrIC3LG8urQ7Ms4xY3hixOuiep7W06rbVFcbLRqjh6TBe8gGgtbOBbtlYAW9Z3lxaHZkXMWJYY1I+VvJKhPHKo4M0zONVQQzUsXMvggG6i1Bydwx4u2NZNCcNzLOMGP8TzfOKHQcBSc8jVpRv8jgNvJOai3yH8SpCqcHH4I6XfONr7WygWzZWwFuWN5emkTm/Efn5519Eb0jGp68wRqwOM+tntaRG3ll1ie+H8YrTwPYMARivGSTed2jtbKDbe2hMFQDeUzhEviwDczZiWRO68gSvrqawcNEgWnnb6g7jZSPU8HQYL/kA0NrZQLdsrIC3LG8ubRmZ88z6/OiRH0EmlziKD9iv4vGkVt62yITxshFqeDqMl3wAaO1soFs2VsBbljeX1hTmbLLS5hIzjyfZpEks/K2Vty0yYbxshBqeDuMlHwBaOxvolo0V8JblzaU1lTk/nuSJW3k8WHK9STOxq4/W0MrbxgLGy0ao4ekwXvIBoLWzgW7ZWAFvWd5cGpiPmScfT7IZW3RZo7TW1Mo7rS7xfTBecRrYniEA4zWDxPsOrZ0NdHsPjakCwHsKh8gXMBfBfFmIVt6XFcjYgPHKAIPdYwIwXvKRoLWzgW7ZWAFvWd5cGpjLMtfK20YJxstGqOHpMF7yAaC1s4Fu2VgBb1neXBqYyzLXyttGCcbLRqjh6TBe8gGgtbOBbtlYAW9Z3lwamMsy18rbRgnGy0ao4ekwXvIBoLWzgW7ZWAFvWd5cGpjLMtfK20YJxstGqOr00YDCLzu01VqJ1k1stzZotxtQODgvqOwNhd3b1N4JaFDwjPhhMF5xGjLbWjsb6JaJD1MKeBsScr/BXI41l6SVt40SjJeNUKXpIzrr7dN6a5v2ghMaEtFo8JQ+2Vyj9vYh9Uc2cWd0cniX1tm0wXjZYNUmXWtnA92yIQTesry5NDCXZa6Vt40SjJeNUKXpr6jXuZkwWW+pf3iH2q37dDy4yFQ3Gjyno84d2v3lQ9q7BuOVCaqGCVo7G+iWDSbwluXNpYG5LHOtVA/DeQAAFXlJREFUvG2UYLxshKpMvwjp4NoKrXd6dBbTcRF26UbrJu31XsX2xjdf0vHOBm3tP6XB+TgP3PGK86n3ttbOBrpl4wq8ZXlzaWAuy1wrbxslGC8boSrTz3q0t7pCN7ohxe9tjfqHdKt1nXaDlxnqzqgf/i56NEkT85ZnvHgcV94PBz9+wAAxgBhADCAGpGMg44+c6t0wXnVuvkFAu61Z40XR/jzjFatUAeMVO3pmE4PrZ5B438Edm8YPdMu2GnjL8ubSwFyWuVbeNkowXjZCVabDeM1NX/MFq1U7dM8drnOdCN5zYVvoJDBfCF/pk7XytlUUxstGqMr0uR81xkTjjlcMho5NrZ0NdMvGF3jL8ubSwFyWuVbeNkowXjZCVabPPbg+JhrGKwZDx6bWzga6ZeMLvGV5c2lgLstcK28bJRgvG6FK0/Omk7hDj/pv7epgvOyManaE1s4GumUDCbxleXNpYC7LXCtvGyUYLxuhStPNBKobtHv4goY0omE/oL3NNVq/G9CpdQJVoiJvNeZVEYPr8+j4SdPa2UC3n3jIyhW8s8j42w/m/tim5ayVd1pd4vtgvOI06rg9s2TQGm11vp5aMmg8r1fGW46441XHVs3VpLWzge7cZnWeCN7OkVozBHMrIqcHaOVtgwDjZSPU8HTc8ZIPAK2dDXTLxgp4y/Lm0sBclrlW3jZKMF42Qg1Ph/GSDwCtnQ10y8YKeMvy5tLAXJa5Vt42SjBeNkINT4fxkg8ArZ0NdMvGCnjL8ubSwFyWuVbeNkowXjZCDU+H8ZIPAK2dDXTLxgp4y/Lm0sBclrlW3jZKMF42Qg1Ph/GSDwCtnQ10y8YKeMvy5tLAXJa5Vt42SjBeNkINT4fxkg8ArZ0NdMvGCnjL8ubSwFyWuVbeNkowXjZCDU+H8ZIPAK2dDXTLxgp4y/Lm0sBclrlW3jZKMF42Qg1Ph/GSDwCtnQ10y8YKeMvy5tLAXJa5Vt42SjBeNkINT4fxkg8ArZ0NdMvGCnjL8ubSwFyWuVbeNkowXjZCDU+H8ZIPAK2dDXTLxgp4y/Lm0sBclrlW3jZKMF42Qg1Ph/GSDwCtnQ10y8YKeMvy5tLAXJa5Vt42SjBeNkINT4fxkg8ArZ0NdMvGCnjL8ubSwFyWuVbeNkowXjZCDU+H8ZIPAK2dDXTLxgp4y/Lm0sBclrlW3jZKMF42Qg1Ph/GSDwCtnQ10y8YKeMvy5tLAXJa5Vt42SjBeNkINT4fxkg8ArZ0NdMvGCnjL8ubSwFyWuVbeNkowXjZCDU+H8ZIPAK2dDXTLxgp4y/Lm0sBclrlW3jZKMF42QlWnjwYUftmhrdYKsQlqtzZotxtQODjPUXZOg/Br2ttcm5yzQus7XToOBzTKOSstCcYrjYrffVo7G+j2GxfJ3ME7ScT/dzD3zzheglbe8TqkbcN4pVGpzb4RnfX2ab21TXvBCQ2JaDR4Sp+wodo+pH6Wizrr0d7qGm11AuoPR0SjU+rtb1O7dYce9d+Wqh2MVylcTg7W2tlAt5PmL5wJeBdG5exAMHeGslBGi/B++MVDev+99+jZs2eFypI8CMZLknbpsl5Rr3MzYbLeUv/wDrVb9+l4cJGSozFr0yZr1D+kW63rtBu8TDknexeMVzYbXymLdDa+NBXJF7qLUHJ3DHi7Y1k0JzAvSsrNcYvyZtPF5qtuBgzGy018+MnlIqSDayu03unRWayEi7BLN1o3aa/3KrbXbA4p7L5L7dV96p3Fboll5GXOyvoN45VFxt/+RTsbf8ryc4bufD6uU8HbNVF7fmBuZ+TyCFe862bAYLxcRonrvKJHhit0oxtS/N5W/t2ryV2ya10Kp046oUfba9TeCWhQQieMVwlYjg511dk4klM4G+gujMrJgeDtBGOpTMC8FK6FD3bNuy4GDMZr4dDwmMEgoN3WrPGiaH/WY8OXdLxzndpJ40WT/SnGi80VfsAAMYAYQAwgBpoUA99//73HP+DZWcN4ZbOpPkXIeOVVlC9CjR+tupm1Vu3QLXulgLcsb1ybunn/8MMPdBwE9KN33iEeeP/69Wv5Ck1KhPGqDH2BgvGosQCk9EO0/lHi2mjVDt3psehrL3j7IpudL5hns/GR4oJ3nQyXYQTjZUjU8XfGgHgMrrc3losL1l6KnyO0aoduP/GQlSt4Z5Hxtx/M/bFNy3kR3nU0XKaOMF6GRC1/500nMT1dxJX8vOkk1ujW4UmpSVQXCfwrTfJbWnUzKa3aoVs2zsFbljeuTV28vzo6qvyRYhYxGK8sMrXYb0zUBu0evqAhjWjYD6IZ6dfvBnQamy1iSu7kEeX6zhGd8ASqwxM67mxTe/VDOj7Nm/F+KpfoCzr3WSa+94C5b8LT+YP3NA/f37TyZi5atUO376gulz+MVzle8kfPLBnEM9J/PbVk0PjRY/wtx9klg9qbHTpq0JJBWjsaDjCt2qFbtnsAb1neuDbB2xUBGC9XJJc0H3Tu8g0L5rLMwRu8ixJArBQl5eY4rbxttYfxshFCOgiAAAiAAAiAAAg4IgDj5QgksgEBEAABEAABEAABGwEYLxshpIMACIAACIAACICAIwIwXo5AIhsQAAEQAAEQAAEQsBGA8bIRQjoIgAAIgAAIgAAIOCIA4+UI5FJlMzOFxQbtdoOpKSxqUd8iOifrXfLbMfGfG92QLiqrxGTB8oSm+MLmo8FzOuK518wxqx/QQRDSIGvuNu91ydBs9F0uyp5x3GW6d6HTBQyf08HmBu0GL6f3F4idatvgDYXd29ROLmpfQDdVGvMjGoYPaKt1n44H8SvsggbB/at4NnHTepcOwuG4bYrUbboVHX5L050Ry0b7ZUwXqJtDpVFWBVjZ43d22qH1nS4dzzHtUPHqFSizQN2qjfHitc06EsYri0xj95tJW7dpLzgh7hJHg6f0yeYatbcPqV/ZH/5kg0z+MK1+QA+eD2gUm1y2vfmAQp44lkxdsmb5T+Yp9D2a4DZvFYHJigWb+3TcPyOicxr0PqWtVt45Qtqnipm0QWubPumdjldEsNZtKgO/X4Yv6NHOBrVb8TnuuEgTF3kxXmUbnNHJ4V1a5z/wU8ar7jE/ouHJEe2u8j85SeOVtgpHvPmLtEn8eJfbebqT5aTEPNnqlsxj0e9F4qBA/E6u1a1OQH3uL0en1Nvnf/Z89ZfG3G7Q7i+ejf+JNJN7t27TQfiGiIrUzcSKL52Lto/9fBgvO6OGHZHWibyl/uGdlM60QjST2fmn71yZC/Im7fVeEdFE9+o+9c5q4xhp1D+kWy2jMYVhmnkZndCj7bXEH+KUcwV3jU4Dure6QuudHrE95I+1bpPj/P6a/Fe9fZ9++fd/RTdmjFeBGK+oDcZ3Ke7Q7i8f0t61hPGqc8xP7lLc2nlAv+r8eLavmMRvPFamY6BAm0yf4OabTXeilLSYJ2vdEpks+rVIHFjj1/SV0+ZlfP0m/1FZVLA5f9LGl3cKJ/sn9Ylio0jdatqvm1oW+Q3jVYRSk46Za2Hu+gCansV/cqFP3TWoWqvp8JJ3BK50pS+CPqSw+y61a2MiJ2ynlqGy1+2qlh63okdt47tw52F31ngViPFq2oAfbW3Q1v5TGpyHdJA0XhnIqo/5yaO2zU+pN3g9jtPkHa/oD2rOH/QCbZJR/QV2F9A9lXtazBORrW5Tefj7Eo8De/yepfcnGe3gTzURTcqcvrs7XWK8bmTuMNaqX5/Wa/sG42Uj1LT01P84zJ2MnI6zFpzMnbnJuBHTifzFB/SX0eMPfgSyTXtfPq9wrJQxUO/T7l/wYzDWFF8GypiX2NiXiK2pW7Zhk2yC8X/Ga7TVfR49jh6XbaubkMLh7yiMHtFyn55ivKwx/h901tun9fj4I5E2OKN++LsxzwJ/jMY0TVxUGfO8huz/Hj+uokkMJIzXuB026C933h8/QuW4jy9jZm2TxBg9J6Fk1x0vJj3mTYzl1C2eibfteBycFYjfAfU6Nyk+rjSSVsGd9THXFZp+ehEHFa/b8NKordeqX4/rtW/DeNkZNeuIycDcmYsg2l9z4xUNpL4ai2Yu6MvFwrklo3E/NxOGQbCJTce2epcenZgHdJMxPdHYtPPJIOSk8TIDeOtgvMw4l+nHFOaRSzuzbvKPe1ONlzXGf199GxQ1XrWL+TTjZf5wbtDu4YuJUTfjqiZje6xt4sN4xa/7NN3x9IyYN4+9Wjl1i2fja3sqDkxfkdeH/J6Od67PGi+avFAgdjcpi2sM1FTdzE2AFapVvx6TW2QTxqsIpSYdU3kHOC9sMyjzQzo+Pc/JxHRKCdOQc4ZIUsSdB8+/oNPo7a+8TjP+tpiIuulCJncnCr9scVm3k/EA/OncvH5bbuNVx5i3GZh4c0/+yPNLO98HtNtKuesRxY7EP3wW3WVj3hgYkReSknFg+ri8PqQOxutqsP294LuMviFZt3j8xLdNnWvWr8clxrZhvGIwsGnGK8x2gOO7RxId4DytYN4CM2/G5OVhLtBkp5R3jkDapeF9Tq8recxVvI5jM1PiDcvLuslP4ZFqvKyPtap61BhrA+sdr7rGvMXAxKpIxpzwYOvXPdpbrbLfydddOubjdfP6f1JaHBQZrlD1o0ZzxzM5XCEeIGl1i6fHt2var8clxrZhvGIwsHk10DH59tG448l5E68qeKMB/fsvPqD1+JQGuVpqeoHGzMnbaFxSkvXkD0Plg+vNY6MS/1nG6ub1b1BKu6caLzP2L/Y2Jp8aj/H49lW2gm2QZ7xqHfP5BuaKJW9N7nix8Xo7fpmgun4nT/ccMR+vm6+gz4kDe/xWObj+nAbPH9Lu6tr4RZK0EQg5dZuOIfOtpv26kZf4DeOVAIKvkzd3pm6Rz9PxCJC8nKcpNo/UZbHmv76kgZnUpSoDM7nbkvwDM76jONEaHZO4o2TGhk21y2VlBTdifyyTf1CK1E1QKReVarzMW1FTLBMxXnUbZBmv2sd8moExbwMmpnWZmoah6n4nTbcJ1pyYN7GU7E+m6mbycfg7Nw7Mk4u8PsT0j9P/QI37ocR5DmUTmbtYOaYrt25Gd8369ZKMYLxKAlv+w01gm8Gi/OZPQHuba7R+N6DTtP9OqoAy+o6O7/JbgRuUOT5gMigzPghzPBnszexzvNfFjFmIDa6fTFx4xdf8oTLHnFE/2KetvLp61z0pIMsQRMlF6iYldFxOuvEqEuMVt0EaZxUxn2ZgrsbyXA2un0wKfDkdSZE28Rk7abon5aW1xaWUInW7PNjNRpE4uDSEOX2I+Udp54hOeAJVM5npZZu4kXuVyzmdBh9Gb7Ve9XVXqdFWkbrVsl9P1MPyFcbLAqiRyTNLNsSnO6gHkfEf1OllgC6X14kN0h0NQjru8qPIybG89M7TfmwKhArqw3yD7mSGb9bFSzI9nryOP9Yzs9xH5dNgTDhN/ggl79hdUixQt8tjBTbSjVe0HAOFX3Zoy8TF1JQeY2GVtkHKH3sdMZ9lYHhS24AOopUExtfi+s4D+mYy7UdEvNJ+J0t39vCLq/AtULergxfeKh4HiWXHZvqQ2eV7pqb4WFhpIgMT05fXXKL/vtal//U/efqXxP7Yd/O2fS379UR1877CeOXRQRoIgAAIgAAIgAAIOCQA4+UQJrICARAAARAAARAAgTwCMF55dJAGAiAAAiAAAiAAAg4JwHg5hImsQAAEQAAEQAAEQCCPAIxXHh2kgQAIgAAIgAAIgIBDAjBeDmEiKxAAARAAARAAARDIIwDjlUcHaSAAAiAAAiAAAiDgkACMl0OYyAoEQAAEQAAEQAAE8gjAeOXRQRoIgAAIgAAIgAAIOCQA4+UQJrICARBYZgK8fNZjOuj+mgZRNfPW8BPgEK0H+GPa670SKAxFgAAIuCIA4+WKJPIBARBYcgITo7UTTIxXtdWNFjROLs5crSSUDgIgUIAAjFcBSDgEBEAABIjqZLwmi0pvH1K/LgvXI0RAAAQKEYDxKoQJB4EACDSawMwCv+/SQfh/6HjnOrWvdSm8IKJBQLvRYtufxxaD3qDdX/wb9U8ex/Zt015wcrVQe3Jx6EILub+iXufHdOvwhFJ9VzLPlIXYG92eqDwIVEgAxqtC+CgaBEBAE4HkHa/EGK/IeK1Qu7VNn/ROaURvKOzepnZrhdqrH9CD5wMajU6pt79N7dYdetR/S2SOMel0ToPep7TV2qB7wXfppoqRnfVob9XkkWT4lvqHd6jduk0H4RsiGtHw5Ih2V1dovdOjs+Th+A4CICBKAMZLFDcKAwEQ0EugmPGKm5toHFZr2vBchF260bpOu8FLGqevJe5c8d2sm9TOGb+VP75rojPnfL1tAOUgoJ8AjJf+NkQNQAAERAgUM143uiHxk8foE90FG5sss+vKeP2eBsF9arf4seXQJBPRRcZ+c8j4jlbc4JmU8e9zOg0+pHU2fDtd+ufgt9Qfpj6QnD4N30AABEQIwHiJYEYhIAAC+gm4Nl79ySNBfjyZ9pM0ZBOChaaROKN+L6BHHX6sOc6bTdhxOMh+fKm/gVADEFBBAMZLRTNBJAiAQPUEXBsvc8cra6xWRo1zx3elncMm7JD2NtdyH1+mnYl9IAAC7gnAeLlnihxBAASWkoBr45U1xssMjk8zZPNOI2EeX6bluZSNhUqBQG0JwHjVtmkgDARAoF4EJsaLp4948x31B/83ZTqJFSo+xusl0eg7Or67cfXWI7/V+Pwh7a6u0Vb3+dWUE5cgLNNI8HEmz819Ou5P3mEcvqBHOxvU3nxAIcZ7XdLEBghUQQDGqwrqKBMEQEAhAWOKeMzUTdrrhYsbL6YwM+fWNu19+ZwGaePhC43v4ixDOu5+EA2wH4/xWqOtztcUDs4VcodkEFguAjBey9WeqA0IgAAIgAAIgECNCcB41bhxIA0EQAAEQAAEQGC5CMB4LVd7ojYgAAIgAAIgAAI1JgDjVePGgTQQAAEQAAEQAIHlIgDjtVztidqAAAiAAAiAAAjUmACMV40bB9JAAARAAARAAASWiwCM13K1J2oDAiAAAiAAAiBQYwIwXjVuHEgDARAAARAAARBYLgIwXsvVnqgNCIAACIAACIBAjQnAeNW4cSANBEAABEAABEBguQjAeC1Xe6I2IAACIAACIAACNSYA41XjxoE0EAABEAABEACB5SIA47Vc7YnagAAIgAAIgAAI1JgAjFeNGwfSQAAEQAAEQAAElosAjNdytSdqAwIgAAIgAAIgUGMCMF41bhxIAwEQAAEQAAEQWC4CMF7L1Z6oDQiAAAiAAAiAQI0JwHjVuHEgDQRAAARAAARAYLkIwHgtV3uiNiAAAiAAAiAAAjUmAONV48aBNBAAARAAARAAgeUi8P8BZTvAc/VevBYAAAAASUVORK5CYII=\" style=\"display: block; margin-left: auto; margin-right: auto;\" width=\"576\"/></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>State what is meant by binding energy of a nucleus.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline why quantities such as atomic mass and nuclear binding energy are often expressed in non-SI units.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Show that the energy released in the reaction is about <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>180</mn><mo> </mo><mi>MeV</mi></math>.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a(iii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Estimate, in <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi mathvariant=\"normal\">J</mi><mo> </mo><msup><mi>kg</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, the specific energy of U-235.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The power station has a useful power output of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>1</mn><mo>.</mo><mn>2</mn><mo> </mo><mi>GW</mi></math> and an efficiency of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>36</mn><mo> </mo><mo>%</mo></math>. Determine the mass of U-235 that undergoes fission in one day.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The specific energy of fossil fuel is typically <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>30</mn><mo> </mo><mtext>MJ</mtext><mo> </mo><msup><mtext>kg</mtext><mrow><mo>–</mo><mn>1</mn></mrow></msup></math>. Suggest, with reference to your answer to (b)(i), <strong>one</strong> advantage of U-235 compared with fossil fuels in a power station.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b(iii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Write down the proton number of nuclide X.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">c(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>State the half-life of Sr-94.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">c(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Calculate the mass of Sr-94 remaining in the sample after <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>10</mn></math> minutes.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c(iii).</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">energy required to </span><span class=\"fontstyle2\">«</span><span class=\"fontstyle0\">completely</span><span class=\"fontstyle2\">» </span><span class=\"fontstyle0\">separate the nucleons<br/></span><span class=\"fontstyle3\"><em><strong>OR</strong></em><br/></span><span class=\"fontstyle0\">energy released when a nucleus is formed from its constituent nucleons </span><span class=\"fontstyle4\">✓</span></p>\n<p><em><span class=\"fontstyle5\"><br/>Allow protons </span><span class=\"fontstyle3\"><strong>AND</strong> </span><span class=\"fontstyle5\">neutrons.</span></em></p>\n<div class=\"question_part_label\">a(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">the values </span><span class=\"fontstyle2\">«</span><span class=\"fontstyle0\">in SI units</span><span class=\"fontstyle2\">» </span><span class=\"fontstyle0\">would be very small </span><span class=\"fontstyle3\">✓</span></p>\n<div class=\"question_part_label\">a(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle3\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>140</mn><mo>×</mo><mn>8</mn><mo>.</mo><mn>29</mn><mo>+</mo><mn>94</mn><mo>×</mo><mn>8</mn><mo>.</mo><mn>59</mn><mo>-</mo><mn>235</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>59</mn></math> <em><strong>OR </strong></em><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>184</mn><mo> </mo><mo>«</mo><mi>MeV</mi><mo>»</mo></math> ✓</span></p>\n<div class=\"question_part_label\">a(iii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle3\">see <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>«</mo><mi>energy</mi><mo>=</mo><mo>»</mo><mo> </mo><mn>180</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mo>×</mo><mn>1</mn><mo>.</mo><mn>60</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup></math> <em><strong>AND</strong></em> <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>«</mo><mi>mass</mi><mo>=</mo><mo>»</mo><mo> </mo><mn>235</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>66</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>27</mn></mrow></msup></math> ✓</span></p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>7</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>13</mn></msup><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">J</mi><mo> </mo><msup><mi>kg</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> ✓</p>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">energy produced in one day<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo> </mo><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup><mo>×</mo><mn>24</mn><mo>×</mo><mn>3600</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>36</mn></mrow></mfrac><mo>=</mo><mn>2</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>14</mn></msup><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">J</mi><mo>»</mo></math> ✓</span></p>\n<p><span class=\"fontstyle0\">mass<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo> </mo><mo>=</mo><mfrac><mrow><mn>2</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>14</mn></msup></mrow><mrow><mn>7</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>13</mn></msup></mrow></mfrac><mo>=</mo><mn>3</mn><mo>.</mo><mn>9</mn><mo> </mo><mo>«</mo><mi>kg</mi><mo>»</mo></math> ✓</span></p>\n<div class=\"question_part_label\">b(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>«specific energy of uranium is much greater than that of coal, hence» more energy can be produced from the same mass of fuel / per <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mtext>kg</mtext></math><br/><em><strong>OR</strong></em><br/>less fuel can be used to create the same amount of energy ✓</p>\n<div class=\"question_part_label\">b(iii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>39</mn></math> </span><span class=\"fontstyle2\">✓</span></p>\n<p><em><span class=\"fontstyle3\"><br/>Do not allow <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mmultiscripts><mi mathvariant=\"normal\">X</mi><mprescripts></mprescripts><mn>39</mn><mn>94</mn></mmultiscripts></math> unless the proton number is indicated.</span></em></p>\n<div class=\"question_part_label\">c(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>75</mn><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">s</mi><mo>»</mo></math> <span class=\"fontstyle3\">✓</span></p>\n<div class=\"question_part_label\">c(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><em><strong>ALTERNATIVE 1</strong></em></p>\n<p><span class=\"fontstyle0\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>10</mn><mo> </mo><mi>min</mi></math><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>8</mn><mo> </mo><msub><mi>t</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></math> ✓</span></p>\n<p><span class=\"fontstyle0\">mass remaining<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>8</mn></msup><mo>=</mo><mn>3</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>«</mo><mi>kg</mi><mo>»</mo></math> ✓</span></p>\n<p> </p>\n<p><em><strong>ALTERNATIVE 2</strong></em></p>\n<p><span class=\"fontstyle0\">decay constant<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo> </mo><mo>=</mo><mo>«</mo><mfrac><mrow><mi>ln</mi><mn>2</mn></mrow><mn>75</mn></mfrac><mo>=</mo><mo>»</mo><mn>9</mn><mo>.</mo><mn>24</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mo>«</mo><msup><mi mathvariant=\"normal\">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> ✓</span></p>\n<p><span class=\"fontstyle0\">mass remaining<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo> </mo><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mi>e</mi><mrow><mo>-</mo><mn>9</mn><mo>.</mo><mn>24</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>×</mo><mn>600</mn></mrow></msup><mo>=</mo><mn>3</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mo>«</mo><mi>kg</mi><mo>»</mo></math> ✓</span></p>\n<div class=\"question_part_label\">c(iii).</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>Generally, well answered but candidates did miss the mark by discussing the constituents of a nucleus rather than the nucleons, or protons and neutrons. There seemed to be fewer comments than usual about 'the energy required to bind the nucleus together'. </p>\n<div class=\"question_part_label\">a(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Well answered with some candidates describing the values as too large or small.</p>\n<div class=\"question_part_label\">a(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Well answered.</p>\n<div class=\"question_part_label\">a(iii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This caused problems for some with mass often correctly calculated but energy causing more difficulty with the eV conversion either being inaccurate or omitted. Candidates were allowed error carried forward for the second mark as long as they were dividing an energy by a mass.</p>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Most candidates had the right idea, but common problems included forgetting the efficiency or not converting to days.</p>\n<div class=\"question_part_label\">b(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>HL only. This was well answered.</p>\n<div class=\"question_part_label\">b(iii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Most candidates answered this correctly.</p>\n<div class=\"question_part_label\">c(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Most candidates answered this correctly.</p>\n<div class=\"question_part_label\">c(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was answered well with most candidates (even at HL) going down the number of half-lives route rather than the exponential calculation route.</p>\n<div class=\"question_part_label\">c(iii).</div>\n</div>",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-4-rigid-body-mechanics"
    ]
  },
  {
    "question_id": "20N.2.HL.TZ0.7",
    "Question": "<div class=\"specification\">\n<p>A vertical solid cylinder of uniform cross-sectional area <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>A</mi></math> floats in water. The cylinder is partially submerged. When the cylinder floats at rest, a mark is aligned with the water surface. The cylinder is pushed vertically downwards so that the mark is a distance <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>x</mi></math> below the water surface.</p>\n<p style=\"text-align: center;\"><img height=\"210\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAjcAAADqCAYAAABeF2R2AAAgAElEQVR4Ae2dz4skR5bn5z/JgtyFzWITRpfd3EuJBh2y85AUOgyCuqg3K6Gq2V50GNAymaQuOsyMIAsVYmsWthSJanXRUIpA0Bd1DoFAFD0lgumDGJIAHYpWkjSiEUlQLQoRvMXczTzcPdwjPH54hJu9T4EUkeFuZu993nOzr5ubu/+V8A8CEIAABCAAAQgEROCvAvIFVyAAAQhAAAIQgIAgbkgCCEAAAhCAAASCIoC4CSqcOAMBCEAAAhCAAOKGHIAABCAAAQhAICgCiJugwokzEIAABCAAAQggbsgBCEAAAhCAAASCIoC4CSqcOAMBCEAAAhCAAOKGHIAABCAAAQhAICgCiJugwokzEIAABCAAAQggbsgBCEAAAhCAAASCIoC4CSqcOAMBCEAAAhCAAOKGHIAABCAAAQhAICgCiJugwokzEIAABCAAAQggbsgBCEAAAhCAAASCIoC4CSqcOAMBCEAAAhCAAOKGHIAABCAAAQhAICgCiJugwqnMmeGFnO2/JrdbFzIUkWG/Jbc3bslx94cFQfwg3aNbsrnfkr6peOn/hjLot+V496ZsbtyQzf2PpPN/79TU3rX0zz+S9z6JGRlXlsdp6WCocOUEfpJ+K5V70TF1U7aPunK9qC3XXTneupkcn4tWt77yltHWiXSv6+gQhnLdPZHtjTty1v9pfW4G1jLiJrCAqnInJ26W53vN4sYNIPfachn1lbkBZnmOiAQzwCwTCnWNCJB7IxZl3xA3ZWSa/DvipsnRwbbJBHwXN8nZMQPM5ECztT4C5N50toib6YyatwfipnkxUWXR8Oq5PDnajy/PbOzI4emX0h8MZXjZlvtbRZeY4lmVaNo8J26yl1vc7Msj6T7/dHQJaOuuPDjvyyBFeXjVk87pXdk2l4giG1ry4GAnd5nolVz1UvVs7MtxqxvZGldl29s9ko9dXQXT2LGNph33n/Hxj9lLA1GF19LvtkZ2j7VndjI2tWNbXX27R3LWtf5FszaunRuyae2Zl5MM+vIvzreI06dyZmJX4GcKL1/rJjC8kt4nR7Jnc2D74KH8S/9aZPhCOvd2Ci4x2csgUdxeZnPPzSo64e1m/h6fyzdFbSS+5XLRHGefncph/rJUztbNdL6aumx7e0cfJXldeIksZde/fuiO3Zuyd/Sp9K5eWavsMZnPT3tcjOo1l4m7cS4XHUfixI3zyR5TBX2JTPPPWGb2aRs2cT3bB6fyz9FxxWWpJJ2W8AVxswSIVDEfgVjAmA6pHYuEwbdydrAj29HlGitikks3to2oY7Kip4q42UjVb8RA933Z23hTHvR+jCscPJcHu6+NbJBr6bdP4oEiWXPzSi7b78j21l15+PwqWt8jGVtNVbYjNYN+61sZmLb6LzIiKqGUH0Bc55m0dy0XrXuZ9oZXz+ShEVy7D6U3iFYYyaD3UPbSNhX55wYBuy7J2FAobqZxcgPlwRO5iNq3NprBID94JI7ypXYCNi6buyfSMYJGXO68I53Ln+K1HFvmuxvwjUX22IoETG7mJp+bVghsGnHdvojzeXgp3ZP98VxM7zO4kE500pJac5Pk0CP5JhIgQxlcPJHDrR25334RH1euva17cnZhBNqfpP9dweoft5853j58JlfmkHBtJsdIRXET9QG37HFr+Lh+wokNy6jyMTLBP/lReqdvyihe6fV3rr3as0ZFA4gbFWFuopPubCi9SC+9sO5lPHhnFtmlzziHIlXETX7gzQz2ufoSTLZTdGIjUybZyZ5lutmlko40tXvyNT+A5MVN1F6qw3cFM3akByi3g1Eu2UXW7kzYLbo2exaKm0qcigdJxE2K/4q/ZmNpG0/niRXv6fjHOeHytpq4Gc1yRBmUWwBbkotpOyR9bKcXzeaOwajMjYLZphxYt9+kkx93wlGY26M2YoaThEVRX5U/1mbxz7F3PpWVddv5nIcA4mYeapRZnIAd4CfekZQfqDNnnPnOpeKgnREWORGTeJXu8F3Hk++QXPvuzpJliRvXXkFnm7HdGWsuX30hnXZbOu3H9jJW6mw5M8DEZbIDYondmbamcMoPHs40PmsmYPM0cwKQbzKdy2abza8kZrntmbi7y0QjIeBqz+RQQY5F+0V1ubsZS/LMWJS+y9GJFndZzDWY/5zY5pRjMt9GJABNmafyTfe30o1mwNINWkYJM7stw6qKf3/KicJRG9MF1mhfvlUjgLipxom9lk3AdgwTxY24y0F2difqlFKXlDKdZ66TLDtrS3dIpTakO3wnNlJrV9x1ebfGIeqIyzu3MXRpG6KN6fbs96IBK2Ovm9I3dpn1P0+l0/5Cuhe/l7N917m7wSkldvKDSRVObh83k5U4VNLpJ9v5Ui+BCbmSaji7fs3k6Ruyd/rcXjJN515esLv8mSxu4oE5m2NR81G+5sRN7tjJrj37wc6GjreXcif+OkXcxP1KyTGZFzemxkFfusnJgTum3Jq6kjzPHMe2rYn+2bV1Bcc24mYswgv/gLhZGCEVzEUgM1BPqCHqiMysiT3rSQ+wmc5zDnEzbdCO2nLipmAmJWN2SUea2cf+kekUzW/pAWZCe+ly7nvhtHxqcCgYBDJnyo5BlbPSNPvIlZJOv8hnfquBgOVfMFhmG4tzM7q0FOVDOpfTuTefuCm69Bm1nzk+7fExlkNZS+O6Uvmb25z8WZDXozaduC85JqOyE9pILfiNL8eV5Lk7BtMnNxP9Kz+2ETdJZJf2BXGzNJRUNBuB4g5j/CwwXoC3fe8j+fjdN7IPBMt0nvOIG9vZ5Ad2N+C7jirqDAvWwGTWM5R0pEVQMp2i2SE3wJS1l+7Q099TbcRn6amOu2C/2cXNFE5j/FIG8bVWAtlY2qZsfo1mRYd28flv5OPHfyvbLq+j3XO5l8/NKH9S+eSaSF9KssdLdl2Om/VxMzouh/LrtqxtTqCVtDcGsWy/6Hd3Cbm4j6kmoNJirKSeDKtZ/HP2Oa9sWcfA/cznQgQQNwvho/AiBIZX5/KeuVPp5Dy+22HsLoy49rgDN1PF6TNOd5bppr3nETemDnu7bOouoGp3S9m7QabdmVEEKNMpmh1yA0xyx8v43Vmju6Vs57v7vnTtra/JHVUbqcEoassyejkQc6NTdkAsEWV5GyNOt4rvKkPcFEV5Nb8lx4zLA3enT+ryrbHExnNzw4kNZ14u9/JxLxER2RwS++gGd6dg6s6ldHvJsZa6myh6Uvdro8tkJe05a5NPu1/mLq6xOxhdrhfZNTpGYl9Sd4OJu4Pplr2Lq4q4SfclE/xLLrXbu8GStszTynP9W+IsX+YhgLiZhxpllkYg+5yb/HMqbDO2Uxydibrfs3cGZTvcioO2qSrz/JbYhs7pW7nn3OSfO2OeydOe/kyNIlL5AWRM3JhC+fbyz9Uxj8tIPyPohpjnZXze/Vo6R7dSd5u4wW4kDpfDKfY/4oS4KYry6n4reLbKk559ZEFihV2/NjaALkfcmIXKg/6XybNpItHx9DN5kHo9SmSKWdvSGj2TZ9M8K6bdi09uzA4ziRtzrD6WzzPPXoqfk5W4bY6j84fJM2XMc3WePD+Xj9Pr0syt3/nnRWXsqihuTKPT/IsMy9t0Ip+3P5DbY7EZecG32QkgbmZnRolVE4jEgDuLWnXjtFdOIO70xy5HlBdgy9oI2Fjl12itzZ4FG45EUH4WasE6KR4UAcRNUOEM0Rk785Bc/gnRx6b75NYTuKl0Y+8ruXr+SA63cpc/mu6KUvviS8BvjR5e6TsHxI3vEazdfsRN7YhpYF4C8eWTG6mnec5bE+UWJpC6g8Tdvmsug3XGLn8s3BIVLJNAstYmvaZkmQ2sqS7EzZrA+9Ms4safWGEpBCAAAQhAAAIVCCBuKkBiFwhAAAIQgAAE/CGAuPEnVlgKAQhAAAIQgEAFAoibCpDYBQIQgAAEIAABfwggbvyJFZZCAAIQgAAEIFCBAOKmAiR2gUBMwDx86yN575MLGa4LSfTAwb+XJ/2f1mUB7QZPgNcBZELMnVkZHL78gbjxJVLYuX4Ca+/kGHTWnwQaLCDPMlFe+3GfsYY/KhJA3FQExW4QKH378crQMOisDLXqhsizTPgRNxkcvvyBuPElUthZM4GC98vsHslZty8D03LUwZn3M9n/yt6nZDvCvaOPkvfsuNcTZN8FZd6L05Ju/zrll3k/T1fOjvZH7SQ2uAFnZIOrN1UBXyEwO4HcAxrNwxn/OXpfU/pFjvnczOZv9n1l1gR7zGTzNH7n2/bRufyxeyLbG3fk4+5X8iTJefPOMvt+qLF3sJl6i94ZZ4+N5JicciyLO5b25fjxB/a9U+5N3bmy5h1Tn53K4Vb6VQ/5975lWcweAErUQQBxUwdV6vSMwFAGvYeyt5V6C7d5vUD3fdnbSL1eoMoZnBNBW/ZVBcM/Sf+769Fbkz98Zl8SeC0XrXuyvfWOdC5fxbwGz+XB7i05bH0bC6rEBjfIuE7Z/e0ZZsxtIIEfpXf6Zuop4O6N2Om3VA9lcPFEDrd25NDl7/BKvvnwrmy742NMiLhcvZF9AW10fBgh8Se5jsRN9gnk8Wsi3FvCC15Y6Y6vzEsmnWDqyrV5gefUY3lk2/bBE7kYDGV49Z18N/g5LruReprz4EI6kfBy4sbVn3oViXsz+35L+mtbjNfA1FqzSYibNQeA5ptAIN05puyJOuzX5HbLLiCeQdwUna2OvdXcnoW6feOz30nCxXXKk/ZJ2c9XCEwjkIiNH1J75vPMHh9jL920syjRoG6FSDLA2xd1vn1XfrXl8tXWG82w/GzFjZsxcc2n6xTJHxPR31tvyeHbt3LHpaunyrHs/HNlsm2749H9mr0cnfcz2YsvDSOAuGlYQDBnnQTMdPMX0mm3pdN+LMe75uzVnbG5S1Opv4tMtWeWmQ6y6LeobO7MNJq5uSnbR0/lm+5vc5esTAHXKbvBosgAfoNAVQLl+ZQRFaWiPpu/mTLRicEbcnz+lZztvyHHXSOe0sLDtZ0XGNk6JXOCEW/bPvqtfNO6I/ExZutJLkk53ycdyyVtl/mZscHO3GzckuP219JtfyX9AdM1jnqTPhE3TYoGtqyJgJt2N+tZ9uW49VQ67S+ke/F7Ods3YsNMdy8ubpL1Om7djvtMd8yDvnQTYeXs6doO1HXKiJs1JUpgzVohkbnEE7uYFirx9yJRnyufFgFGKPz1iXSvX0rfCREneCKh43J5irgR20Y0I2TE0ZuRUIpsio6bVP2R6VWO5eK2S/1M++Xa6H8lndaR7LljOFkbF1iKeOwO4sbj4GH6kghEnddN2c5Pu+dnXMrO7NJm5MuYbVXKpetw31MLPTNnqQWDkSvCJwSqE3CD/LhYToub8vy1wiMR5/HfyWLhSJDYNvZbcnHRktvJvq7taeLGXpoy5f54LsfuEld0TN2Rs4t/S80MmcnNi/iEZOKxXNJ22XE6Jm6yhIdXPelEC7DzvmT346/VEkDcrJY3rTWRQEmnNrxsy/2tG4vP3Ljp+HyHK3YxZ7JOoQhOeg2C65THB6OikvwGgakEotzPD8r5PLOXk8byN52bpiVbrnBNzC/l8OCXo2PJ7Wsu70QzOc7SvGByJwc78quDt2Q7OVZM22/I3sHbspcIJrfv+CxT9lh2/uXbtn66mVpnUkn/4DZHn1X2yRTgj7oJIG7qJkz9HhCwnfTu+9K9iu9cGl49k4cHO9Et2cllqfQZ3MuBFF5qjzq5lCCy3seda+puE7mWfvskczdWfLaculPD3PnRb8vx7i25334RPRV5dEb9Ul4OXq7vSckeRBUTqxB4JZftd2Tb3d2X5NyUu6XE3u3n7pZyTdn830yLFjubkvltFnHjbv/eSB9XVgRlfjNGVDmWy8SNjO5qdHcsjt0tZdvdPZFO8hgHeyyn73x0PPhcGwHEzdrQ03CTCGSfQXNDzLM+Pu9+LZ2jW6mzTXd7uFkLUzJ7UiJuzFlt/hk2po1O7yolUHLP2DDX881zNto9e/u4OTm+lO6JfQ5OchbbJJLY4h8B81qRh/Z5L/Gt2Z+3P5DbmRzP52/Zs12suEjPprh1M7n64lvB87MnBTM3JUKobI3M9GO5XNzEx+mXyTOqojV4Tz+TB/upuyZTl4vdOrrxY9m/LAjNYsRNaBHFHwhAAAIQgIByAogb5QmA+xCAAAQgAIHQCCBuQoso/kAAAhCAAASUE0DcKE8A3IcABCAAAQiERgBxE1pE8QcCEIAABCCgnADiRnkC4D4EIAABCEAgNAKIm9Aiij8QgAAEIAAB5QQQN8oTAPchAAEIQAACoRFA3IQWUfyBAAQgAAEIKCeAuFGeALgPAQhAAAIQCI0A4ia0iOIPBCAAAQhAQDkBxI3yBMB9CEAAAhCAQGgEEDehRRR/IAABCEAAAsoJIG6UJwDuQwACEIAABEIjgLgJLaL4AwEIQAACEFBOAHGjPAFwHwIQgAAEIBAaAcRNaBHFHwhAAAIQgIByAogb5QmA+xCAAAQgAIHQCCBuQoso/kAAAhCAAASUE0DcKE8A3IcABCAAAQiERgBxE1pE8QcCEIAABCCgnADiRnkC4D4EIAABCEAgNAKIm9Aiij8QgAAEIAAB5QQQN8oTAPchAAEIQAACoRFA3IQWUfyBAAQgAAEIKCeAuFGeALgPAQhAAAIQCI0A4ia0iOLPGIHNjRui9b8xGPwAAQhAQAEBxI2CIGt30Qgbjf+0+q0x1vgMAQhkCSBusjz4K0ACWgd5rX4HmMK4BAEIzEgAcTMjMHb3j4DWQV6r3/5lKBZDAALLJoC4WTZR6mscAa2DvFa/G5eAGAQBCKycAOJm5chpcNUEtA7yWv1edX7RHgQg0DwCiJvmxQSLlkxA6yCv1e8lpw/VQQACHhJA3HgYNEyejYDWQT5Iv4cXcrZ/U7aPunI9WxqwNwQgoIgA4kZRsLW6GuQgXyGYQfqNuKkQeXaBAAQQN+RA8ASCHOQrRC1IvxE3FSLPLhCAAOKGHAieQJCDfIWo1e73dVeOt27K7dOn8uXpXdmOngR9U/aOPpXe1Q/SP38oh1vx06G3Dx7JN1evRlYPr6TXPk22b26Yci3p9t3Fph+ke3RLNneP5GNX99aJdH/899xlqaEMLp7I4daOHH74TK6Goyb4BgEI6CWAuNEbezWe1z7IN5Rk7X5H4saIl305bl/IQESGV+fy3u5N2dxIiY3Bt3J2sCPb99pyGYmPH6V3+qZkBM/wUron+7K5+1B6A7OTFTemnta3MpBXctV/IYPMzE1K2ET7NDQQmAUBCKycAOJm5chpcNUEah/kV+1QxfZq99uKm+ziXitK9lvST2ZRfpJ+645smpmX66FIVO6WHHd/yHgy7Lfk9sYdOev/NBI3rozbMxE353LpZmwQNo4OnxCAgCWAuCEVgidQ+yDfUIK1+z2vuHG8Bn3pttvSMf+1jmQvuqxVUdwcvCv/y8wQZUSUq5hPCEBAOwHEjfYMUOB/7YN8QxnW7nckbm7K7daFJJM07nJSRnTkZm7kWi5a9+I1OrtHchYJnK/kovdYbm+4GR07A1QycxOt0Xn33Witzf32i1T7DQ0GZkEAAislgLhZKW4aWweB2gf5dThVoc3a/Z5T3MSXn3YkK0qGct09ke2K4ia+FOZE0zvSuUwtVq7Ahl0gAIGwCSBuwo4v3olI7YN8QynX4fdf/vKXkbdziZufrYhxl59cda/ksv3OjOJGRAbP5cEuD/VzFPmEAARiAogbMiF4AnUM8j5AW6bf33//vfzi9dfFfCb/5hI3bkHxTdk7Obe3br+Sq+eP7G3h1S5LjRYxD2XQeyh7G2/Kg96PiWl8gQAEdBNA3OiOvwrvlznI+wRsWX6b2Zpf378vj/73o6z784obc1t371M5jm4ZN7eS78jh6WfSff5UjrdmFTfm/vMX0rm3k7qNPGsmf0EAAvoIIG70xVydx8sa5H0Dtwy/S4WNbzCwFwIQUEUAcaMq3DqdXcYg7yO5ZfhtZmz+8R/+wUf3sRkCEFBMAHGjOPhaXF/GIO8jq0X9NpehjLjJLCL2EQQ2QwAC6gggbtSFXJ/Diw7yvhJbxG+Eja9Rx24IQMAQQNyQB8ETWGSQ9xnOvH7/7ne/i+6MYsbG5+hjOwR0E0Dc6I6/Cu/nHeR9hzOP38+ePRu/5dt3ENgPAQioI4C4URdyfQ7PM8iHQGlWvxE2IUS9Ph9MPmn9rz6q1FwXAcRNXWSptzEEZh3kG2P4gobM4rd7SJ8ROPyDQBGBWfKpqLyvv2n129d4ObsRN44En8ES0No5VfUbYRNs6i/Vsar5tNRGG1CZVr8bgH4hExA3C+GjsA8EtHZOVfz+85//HK2xMYuI+QeBSQSq5NOk8r5u0+q3r/FydiNuHAk+gyWgtXOa5jdPHw425WtxbFo+1dJoAyrV6ncD0C9kAuJmIXwU9oGA1s5pkt8IGx8yt1k2TsqnZlm6XGu0+r1ciquvDXGzeua0uGICWjunSX6bVyoc/d3frTgSNOczgUn55LNf02zX6vc0Lk3fjrhpeoSwb2ECWjunMr95+vDCKaWygrJ8Ch2GVr99jyvixvcIYv9UAlo7pyK/ETZT04UdSggU5VPJrkH9rNVv34OIuPE9gtg/lYDWzinvt3tIn7lDin8QmJVAPp9mLe/r/lr99jVezm7EjSPBZ7AEtHZOab+dsDHPtOEfBOYhkM6necr7Wkar377Gy9mNuHEk+AyWgNbOyfn9hz/8IXpsPsIm2BRfiWMun1bSWIMa0ep3g0IwlymIm7mwUcgnAlo7J+M3Tx/2KVObbavm46jZkcG6IgKImyIq/BYUAc2d8i9ef114X1RQ6bw2ZzQfR2uDTsNzE0DczI2Ogr4Q0Ngpm4f0Gb877bYvYcLOhhPQeByZkGj1u+HpONU8xM1UROzgOwFtnZN7+rA2v33P06bbrzWftPrd9HycZh/iZhohtntPQFPn5ISNeZ6NJr+9T1IPHNCaT1r99iAlJ5qIuJmIh40hENDUObmH9Jm4afI7hDxtug9a80mr303Px2n2IW6mEWK79wS0dE5O2JjZG/NPi9/eJ6gnDmjNJ61+e5KWpWYibkrRsCEUAho6p//35Im89Td/I07YmNhp8DuUHPXBD635pNVvH3Jyko2Im0l02BYEgdA7p7KnD4fudxDJ6ZETWvNJq98epWahqYibQiz8GBKBkDunMmFj4hey3yHlpy++aM0nrX77kpdldiJuysjwezAEQu2c+v1+JGDMZ9G/UP0u8pXf6iegNZ+0+l1/RtXbAuKmXr7U3gACIXZOVV6rEKLfDUgntSZozSetfvue6Igb3yOI/VMJhNY5VRE2Bkpofk8NNDvUSkBrPmn1u9ZkWkHliJsVQKaJ9RIIqXNyD+kzd0dN+xeS39N8ZXv9BLTmk1a/68+oeltQKm6upX/+kbz3yYUM6+VbU+3X0m+fyN7GDdncuCm3W776UROeXLWhdE5O2Jjn2VT5F4rfVXxln/oJaM0nrX7Xn1H1tqBT3Fx35XjLX1Ew7Lfk9saO3G+/8FSc1ZvU+dpD6Zx+ff++VBU2hkEofufjyd/rIaA1n7T6vZ4sW16riJvlsVxZTbG4uSXH3R9W1qbPDYXQOeWfPlwlHiH4XcVP9lkNAa35pNXv1WRVfa00V9wML+Rs/6ZsH3XlOvH/B+ke3ZLNrRPpXrsLSkO57p7IdvLbK7nqteXBwU505moSc3P3SM66fRmYeqJZG3M5x/6XlBMZXj2XJ0f7dttN2TtqSbfvWrftbOzL8eMP5HDLlC8TGNfS77bkePdmSV1Ffoxsi30uai9ld97+4ZX02qfWLrNf3v4YYtbHHTk8/VL6A8dSDATpfXJkL3nl2CVx8OuL753TPMLGRMh3v/3KsvCt1ZpPWv32PaObK27kJ+m37mSFTCJM7shZ/yfLPhYKThAMeg9lb+uuPHx+ZS/ZvJKr7vuyt/GmPOj9GJcpuCw1vGzL/a0dOfzwmVxFY/21XLTuyfbWO9K5fGVG/VhEbdyQ7YMncjEYyvDqO/kuLQyi2ocS23BPzi6sMBpeSvdkXzb3W9KP6p5F3Iy3Nz5z86P0Tt+U7YNH8s2VsdWYa9vcfSg9a2PsoxE97VjQDL6Vs4Md2b7Xlktj1/CFdO7tpOoZyuDiiRxu+X0JzOfOqdNuyy9efz3zWoU4wNP/77Pf071jj1UT0JpPWv1edX4tu70GixuReBAfCZno76235PDtW6NFtJFQcTMoaaGTQhXNAr2WK5Nec2PFRiI+XNl0fU7cuLbcPvlPK8rG6krvN4u4GW9vTNxkGIzayfIrEIuJYDOMX1rxNuId12T9Ts1wjVrw45vpnLT+50eEsNIHAloHea1++5CTk2xstLiRjCiJB+fto9/KN6079nJV2cBrLgt9Ieast9N+bC8PpcRMfuYm+vtG7hKYwZYWBD/bwX9cbGQB25kbc8mq/bV0219lL/tEOy9Z3DgDBn3pRj63pdNyl5asWLGX+UazR66Q+yyxyUzoRAuYp/nt6mnep1ZhQ6fcvFz02SKt+aTVb59z1djebHHjxEU0C2IG3zejRbTxDI5Zd/MyunQ1WpfjLqOYM/V9OW49lU77C+le/D67fqdE3JQOgtGsRVVxY7AOZdD/KiUw8mtXSoRERmSVzxSNiw17Cc2tL4oEzldy0Xsst926oKripnSWo1zclHIrrUvvTAqslhN73zvevP2+5EXebg1/+xKbWe0MPXYNFzd21sCIiz+ey/GWnYWIRMAdObv4Nznbf2N015AdwJM1JC56GdHgFu5OmMlx5TKf5WIjs1vBH8OrnnRO78q2ExqyXHETi538upicvVXFzcTLaQXOefDTrAd9SPt7EB5M9ISAOS40/qvid5V9NLJbp8+NFzfx3U078quDt2Q7GXiNOHhD9g7elr30WpD8jIwlGy+kTV12GtsvFhtjokjihbrxpZycWJg1apk205e7UqsPTC8AAAxeSURBVHcqZURYeXvZmRu3X36tzCu5bL+TElTFbcZ1GaH37/JjdNeZW0DtHHSX2fL1u+3N/wxJrMzqS/Ojg4W+ENA6gFfxu8o+vsQ5FDubL27cLIe5Sym5LdwO1JnfTEjsjMju+9K1dw0Nr57JQ3tbeFI+msWwC4xfDsTcTFR0t1T8FGB3l5UTEeWXZ+KksLbtnkgnuY3cPlE4ufPKrWPZkcPWt/Et6oML6djb0N2dX9Et7slszyjlsuJmNBO1d3Ju7/R6JVfPH43drj68Opf3dl+TZL/8HVVFd0v123Jsypw+j+0cmeHNN60dj1a/vUlMzwzVmk9V/K6yj2fh9t5cD8RNsagYzThkXz2QfY6LuY36VD7vfi2do1spceRuDzfX/92MhFkn05Wz5Dk3cdlOz91SXmxHYQaMPXMmX5cpZV4B8XD0XJrdI3ny/Fw+Tp7tU97emLgR82yfT1PP1THPr/lMus+fyvFWVoxl+Zjbwj+Vnrt93JhlFiUni5FvyObWXXnQ7lnRVOht43/U2vFo9bvxCempgVrzqYrfVfbxNOzemu2BuPGWLYY3hIDWjker3w1Ju+DM0JpPVfyusk9wCdFwhxA3DQ8Q5i1OQGvHo9XvxTOGGooIaM2nKn5P3+dnuWr/ZvTE+ugyf2r5wF+fSu/nIur8Ni8BxM285CjnDYHpHY83rsxkqFa/Z4LEzpUJaM2nKn5X2ScCbdc1bm4dSef8kRy7NZeVo8COVQkgbqqSYj9vCVTueLz1sNhwrX4X0+DXRQlozacqflfZJ+bv1lLeGL32ZtHAUL6QAOKmEAs/hkSgescTkte8ODOsaK7fG46j8hjMxCbzWJDyOtmyGAHEzWL8KO0BgZk6Hg/8qWqiVr+r8mG/2QhozacqflfZx9F2z10rfxWO25PPRQggbhahR1kvCMzS8XjhUEUjtfpdEQ+7zUhAaz5V8bvKPhFus+bmf/xGjt/dl830A2hnjAW7TyeAuJnOiD08J1C54/Hcz7z5Wv3Oc+Dv5RDQmk9V/K6yj4h5avyR/M/2C/k5eRlxX3offiCdy1fLCRK1JAQQNwkKvoRKoFrHE573Wv0OL5LN8EhrPlXxe/I+A+md/jJ+mXP7wj6R/rk82L0pm5kn2TcjzqFYgbgJJZL4UUpgcsdTWsz7DVr99j5wDXVAaz5V8bvKPg0Na7BmIW6CDS2OOQJaOx6tfru487lcAlrzqcjv//Zf/qt9IJ95hU/xf59//vlyA0BtMxFA3MyEi519JFDUOfnox6w2a/V7Vk7sX42A1nwq8vvX939dKmrM/v/pP/xH6ff71cCyVy0EEDe1YKXSJhEo6pyaZF9dtmj1uy6e2uvVmk9Ffhvh8p+3tkoFzn9/+1fa02Xt/iNu1h4CDKibQFHnVHebTahfq99NYB+iDVrzqczvstkbZm2akf2Im2bEAStqJFDWOdXYZCOq1up3I+AHaITWfCrzu2z2hlmbZiQ/4qYZccCKGgmUdU41NtmIqrX63Qj4ARqhNZ8m+Z2fvWHWpjmJj7hpTiywpCYCkzqnmppsRLVa/W4E/ACN0JpPk/zOz94wa9OcxEfcNCcWWFITgUmdU01NNqJarX43An6ARph80vrfpHC62RtmbSZRWv02xM3qmdPiigloHeS1+r3i9FLTnFZhM+04MrM3Zh9mbZp1KCBumhUPrKmBwLTOqYYmG1GlVr8bAT9AI0w+af1vWjj/zz/9k3z//ffTdmP7CgkgblYIm6bWQ0DrIK/V7/VkWfitahU2ab9dlNO/pY+zZf/u2uNzdgKIm9mZUcIzAunOxzPTFzJXq98LQaNwKYH8wK3p71IobGgsAcRNY0ODYcsioHWQ1+r3svKGerIENImZvK9ZEvzlAwHEjQ9RwsaFCGgd5LX6vVCyULiUgNZ80up3aSJ4sgFx40mgMHN+Alo7J61+z58plJxEQGs+afV7Ui74sA1x40OUsHEhAlo7J61+L5QsFC4loDWftPpdmgiebEDceBIozJyfgNbOSavf82cKJScR0JpPWv2elAs+bEPc+BAlbFyIgNbOSavfCyULhUsJaM0nrX6XJoInGxA3ngQKM+cnoLVz0ur3/JlCyUkEtOaTVr8n5YIP2xA3PkQJGxcioLVz0ur3QslC4VICWvNJq9+lieDJBsSNJ4HCzPkJaO2ctPo9f6ZQchIBrfmk1e9JueDDNsSND1HCxoUIaO2ctPq9ULJQuJSA1nzS6ndpIniyAXHjSaAwc34CWjsnrX7PnymUnERAaz5p9XtSLviwDXHjQ5SwcSECWjsnrX4vlCwULiWgNZ+0+l2aCJ5sQNx4EijMnJ+A1s5Jq9/zZwolJxHQmk9a/Z6UCz5sQ9z4ECVsXIiA1s5Jq98LJQuFSwlozSetfpcmgicbEDeeBAoz5yegtXPS6vf8mULJSQS05pNWvyflgg/bEDc+RAkbFyKgtXPS6vdCyULhUgJa80mr36WJ4MkGxI0ngcLM+Qlo7Zy0+j1/plByEgGt+aTV70m54MM2xI0PUcLGhQho7Zy0+r1QslC4lIDWfNLqd2kieLIBceNJoDBzfgJaOyetfs+fKZScREBrPmn1e1Iu+LANceNDlLBxIQJaOyetfi+ULBQuJaA1n7T6XZoInmxA3HgSKMycn4DWzkmr3/NnCiUnEdCaT1r9npQLPmxD3PgQJWxciIDWzkmr3wslC4VLCWjNJ61+lyaCJxsQN54ECjPnJ6C1c9Lq9/yZQslJBLTmk1a/J+WCD9sQNz5ECRsXIqC1c9Lq90LJQuFSAlrzSavfpYngyQbEjSeBwsz5CWjtnLT6PX+mUHISAa35pNXvSbngwzbEjQ9RwsaFCGjtnLT6vVCyULiUgNZ80up3aSJ4sgFx40mgMHN+Alo7J61+z58plJxEQGs+afV7Ui74sA1x40OUsHEhAlo7J61+L5QsFC4loDWftPpdmgiebEDceBIozJyfgNbOSavf82cKJScR0JpPWv2elAs+bEPc+BAlbFyIgNbOSavfCyULhUsJaM0nrX6XJoInGxA3ngQKM+cnoLVz0ur3/JlCyUkEtOaTVr8n5YIP2xA3PkQJGxciYDonrf8tBI7CEEgR0DrIa/U7FXovvyJuvAwbRkMAAhBYLQGtg7xWv1ebXctvDXGzfKbUCAEIQCA4AloHea1++57AiBvfI4j9EIAABFZAQOsgr9XvFaRUrU0gbmrFS+UQgAAEwiCgdZDX6rfvWYu48T2C2A8BCEBgBQS0DvJa/V5BStXaBOKmVrxUDgEIQCAMAloHea1++561iBvfI4j9EIAABFZAQOsgr9XvFaRUrU0gbmrFS+UQgAAEwiCgdZDX6rfvWYu48T2C2A8BCEBgBQS0DvJa/V5BStXaBOKmVrxUDgEIQCAMAloHea1++561iBvfI4j9EIAABFZAQOsgr9XvFaRUrU0gbmrFS+UQgAAEwiCgdZDX6rfvWYu48T2C2A8BCEBgBQS0DvJa/V5BStXaBOKmVrxUDgEIQCAMAloHea1++561iBvfI4j9EIAABFZAQOsgr9XvFaRUrU0gbmrFS+UQgAAEwiCgdZDX6rfvWYu48T2C2A8BCEBgBQS0DvJa/V5BStXaBOKmVrxUDgEIQCAMAloHea1++561iBvfI4j9EIAABFZAQOsgr9XvFaRUrU0gbmrFS+UQgAAEwiCgdZDX6rfvWYu48T2C2A8BCEBgBQS0DvJa/V5BStXaBOKmVrxUDgEIQCAMAloHea1++561iBvfI4j9EIAABFZAQOsgr9XvFaRUrU0gbmrFS+UQgAAEwiCgdZDX6rfvWYu48T2C2A8BCEBgBQTMIK/1vxXgpYklE0DcLBko1UEAAhCAAAQgsF4CiJv18qd1CEAAAhCAAASWTABxs2SgVAcBCEAAAhCAwHoJIG7Wy5/WIQABCEAAAhBYMgHEzZKBUh0EIAABCEAAAuslgLhZL39ahwAEIAABCEBgyQQQN0sGSnUQgAAEIAABCKyXAOJmvfxpHQIQgAAEIACBJRNA3CwZKNVBAAIQgAAEILBeAoib9fKndQhAAAIQgAAElkwAcbNkoFQHAQhAAAIQgMB6CSBu1suf1iEAAQhAAAIQWDIBxM2SgVIdBCAAAQhAAALrJYC4WS9/WocABCAAAQhAYMkEEDdLBkp1EIAABCAAAQislwDiZr38aR0CEIAABCAAgSUTQNwsGSjVQQACEIAABCCwXgL/H2foTnVuPGrOAAAAAElFTkSuQmCC\" width=\"509\"/></p>\n<p style=\"text-align: left;\">At time <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>t</mi><mo>=</mo><mn>0</mn></math> the cylinder is released. The resultant vertical force <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>F</mi></math> on the cylinder is related to the displacement <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>x</mi></math> of the mark by</p>\n<p style=\"text-align: center;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>F</mi><mo>=</mo><mo>-</mo><mi>ρ</mi><mi>A</mi><mi>g</mi><mi>x</mi></math></p>\n<p style=\"text-align: left;\">where <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>ρ</mi></math> is the density of water.</p>\n</div><div class=\"specification\">\n<p>The cylinder was initially pushed down a distance <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>x</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>250</mn><mo> </mo><mi mathvariant=\"normal\">m</mi></math>.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline why the cylinder performs simple harmonic motion when released.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The mass of the cylinder is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>118</mn><mo> </mo><mi>kg</mi></math> and the cross-sectional area of the cylinder is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>2</mn><mo>.</mo><mn>29</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo> </mo><msup><mi mathvariant=\"normal\">m</mi><mn>2</mn></msup></math>. The density of water is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>1</mn><mo>.</mo><mn>03</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo> </mo><mi>kg</mi><mo> </mo><msup><mi mathvariant=\"normal\">m</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></math>. Show that the angular frequency of oscillation of the cylinder is about <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>4</mn><mo>.</mo><mn>4</mn><mo> </mo><mo> </mo><mi>rad</mi><mo> </mo><msup><mi mathvariant=\"normal\">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Determine the maximum kinetic energy <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>E</mi><mi>kmax</mi></msub></math> of the cylinder.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Draw, on the axes, the graph to show how the kinetic energy of the cylinder varies with time during <strong>one</strong> period of oscillation <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math>.</p>\n<p><img height=\"371\" 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\" style=\"display: block;margin-left:auto;margin-right:auto;\" width=\"610\"/></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c(ii).</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">the </span><span class=\"fontstyle2\">«</span><span class=\"fontstyle0\">restoring</span><span class=\"fontstyle2\">» </span><span class=\"fontstyle0\">force/acceleration is proportional to displacement </span><span class=\"fontstyle3\">✓ </span></p>\n<p><em><span class=\"fontstyle4\"><br/>Allow use of symbols i.e. </span><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>F</mi><mo>∝</mo><mo>-</mo><mi>x</mi></math><span class=\"fontstyle4\"> or </span><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>a</mi><mo>∝</mo><mo>-</mo><mi>x</mi></math></em></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">Evidence of equating <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>m</mi><msup><mi>ω</mi><mn>2</mn></msup><mi>x</mi><mo>=</mo><mi>ρ</mi><mi>A</mi><mi>g</mi><mi>x</mi></math> «to obtain <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mi>ρ</mi><mi>A</mi><mi>g</mi></mrow><mi>m</mi></mfrac><mo>=</mo><msup><mi>ω</mi><mn>2</mn></msup></math>» ✓</span></p>\n<p> </p>\n<p><span class=\"fontstyle0\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>ω</mi><mo>=</mo><msqrt><mfrac><mrow><mn>1</mn><mo>.</mo><mn>03</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo>×</mo><mn>2</mn><mo>.</mo><mn>29</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>×</mo><mn>9</mn><mo>.</mo><mn>81</mn></mrow><mn>118</mn></mfrac></msqrt></math> <em><strong>OR </strong></em><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>4</mn><mo>.</mo><mn>43</mn><mo>«</mo><mi>rad</mi><mo> </mo><msup><mi mathvariant=\"normal\">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> ✓</span></p>\n<p> </p>\n<p><em><span class=\"fontstyle0\">Answer to at least <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn mathvariant=\"italic\">3</mn></math> s.f.</span></em></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>E</mi><mi mathvariant=\"normal\">K</mi></msub></math> </span><span class=\"fontstyle1\">is a maximum when <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>x</mi><mo>=</mo><mn>0</mn></math> hence</span><span class=\"fontstyle0\">» <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>E</mi><mrow><mi mathvariant=\"normal\">K</mi><mo>,</mo><mo> </mo><mi>max</mi></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>118</mn><mo>×</mo><mn>4</mn><mo>.</mo><msup><mn>4</mn><mn>2</mn></msup><mfenced><mrow><mn>0</mn><mo>.</mo><msup><mn>250</mn><mn>2</mn></msup><mo>-</mo><msup><mn>0</mn><mn>2</mn></msup></mrow></mfenced></math> </span><span class=\"fontstyle3\">✓</span></p>\n<p><br/><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>71</mn><mo>.</mo><mn>4</mn><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">J</mi><mo>»</mo></math> <span class=\"fontstyle3\">✓</span></p>\n<div class=\"question_part_label\">c(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">energy never negative </span><span class=\"fontstyle2\">✓</span></p>\n<p><span class=\"fontstyle0\">correct shape with two maxima </span><span class=\"fontstyle2\">✓</span></p>\n<p><img src=\"data:image/png;base64,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\"/></p>\n<div class=\"question_part_label\">c(ii).</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was well answered with candidates gaining credit for answers in words or symbols.</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Again, very well answered.</p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>A straightforward calculation with the most common mistake being missing the squared on the omega.</p>\n<div class=\"question_part_label\">c(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Most candidates answered with a graph that was only positive so scored the first mark.</p>\n<div class=\"question_part_label\">c(ii).</div>\n</div>",
    "topics": [
      "a--space-time-and-motion",
      "c-wave-behaviour"
    ],
    "subtopics": [
      "a-4-rigid-body-mechanics",
      "c-1-simple-harmonic-motion"
    ]
  },
  {
    "question_id": "20N.2.HL.TZ0.8",
    "Question": "<div class=\"specification\">\n<p>The diagram shows the electric field lines of a positively charged conducting sphere of radius <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>R</mi></math> and charge <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>Q</mi></math>.</p>\n<p><img height=\"213\" src=\"data:image/png;base64,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\" style=\"display: block; margin-left: auto; margin-right: auto;\" width=\"352\"/></p>\n<p>Points A and B are located on the same field line.</p>\n</div><div class=\"specification\">\n<p>A proton is placed at A and released from rest. The magnitude of the work done by the electric field in moving the proton from A to B is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>1</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>16</mn></mrow></msup><mo> </mo><mi mathvariant=\"normal\">J</mi></math>. Point A is at a distance of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>5</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo> </mo><mi mathvariant=\"normal\">m</mi></math> from the centre of the sphere. Point B is at a distance of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>1</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo> </mo><mi mathvariant=\"normal\">m</mi></math> from the centre of the sphere.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Explain why the electric potential decreases from A to B.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Draw, on the axes, the variation of electric potential <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>V</mi></math> with distance <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>r</mi></math> from the centre of the sphere.</p>\n<p><img height=\"236\" src=\"data:image/png;base64,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\" style=\"display: block;margin-left:auto;margin-right:auto;\" width=\"336\"/></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Calculate the electric potential difference between points A and B.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">c(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Determine the charge <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>Q</mi></math> of the sphere.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The concept of potential is also used in the context of gravitational fields. Suggest why scientists developed a common terminology to describe different types of fields.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">d.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\"><em><strong>ALTERNATIVE 1</strong></em><br/></span><span class=\"fontstyle2\">work done on moving a positive test charge in any outward direction is negative </span><span class=\"fontstyle3\">✓<br/></span><span class=\"fontstyle2\">potential difference is proportional to this work </span><span class=\"fontstyle4\">«</span><span class=\"fontstyle2\">so </span><span class=\"fontstyle5\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>V</mi></math> </span><span class=\"fontstyle2\">decreases from A to B</span><span class=\"fontstyle4\">» </span><span class=\"fontstyle3\">✓</span></p>\n<p> </p>\n<p><span class=\"fontstyle0\"><em><strong>ALTERNATIVE 2</strong></em><br/></span><span class=\"fontstyle2\">potential gradient is directed opposite to the field so inwards </span><span class=\"fontstyle3\">✓<br/></span><span class=\"fontstyle2\">the gradient indicates the direction of increase of </span><span class=\"fontstyle4\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>V</mi></math> </span><span class=\"fontstyle5\">«</span><span class=\"fontstyle2\">hence </span><span class=\"fontstyle4\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>V</mi></math> </span><span class=\"fontstyle2\">increases towards the centre/decreases from A to B</span><span class=\"fontstyle5\">» </span><span class=\"fontstyle3\">✓</span></p>\n<p> </p>\n<p><span class=\"fontstyle0\"><em><strong>ALTERNATIVE 3</strong></em><br/></span><span class=\"fontstyle2\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>V</mi><mo>=</mo><mfrac><mrow><mi>k</mi><mi>Q</mi></mrow><mi>R</mi></mfrac></math> </span><span class=\"fontstyle3\">so as </span><span class=\"fontstyle2\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>r</mi></math> </span><span class=\"fontstyle3\">increases </span><span class=\"fontstyle2\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>V</mi></math> </span><span class=\"fontstyle3\">decreases </span><span class=\"fontstyle4\">✓<br/></span><span class=\"fontstyle2\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>V</mi></math> </span><span class=\"fontstyle3\">is positive as </span><span class=\"fontstyle2\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>Q</mi></math> </span><span class=\"fontstyle3\">is positive </span><span class=\"fontstyle4\">✓</span></p>\n<p><span class=\"fontstyle2\"> </span></p>\n<p><span class=\"fontstyle0\"><em><strong>ALTERNATIVE 4</strong></em><br/></span><span class=\"fontstyle2\">the work done per unit charge in bringing a positive charge from infinity </span><span class=\"fontstyle3\">✓<br/></span><span class=\"fontstyle2\">to point B is less than point A </span><span class=\"fontstyle3\">✓</span></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">curve decreasing asymptotically for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>r</mi><mo>&gt;</mo><mi>R</mi></math> </span><span class=\"fontstyle2\">✓</span></p>\n<p><span class=\"fontstyle0\">non <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>-</mo></math> zero constant between <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn></math> and </span><span class=\"fontstyle3\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>R</mi></math> </span><span class=\"fontstyle2\">✓</span></p>\n<p><img src=\"data:image/png;base64,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\"/></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>«</mo><mfrac><mi>W</mi><mi>q</mi></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>16</mn></mrow></msup></mrow><mrow><mn>1</mn><mo>.</mo><mn>60</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup></mrow></mfrac><mo>=</mo><mo>»</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">V</mi><mo>»</mo></math> <span class=\"fontstyle0\">✓</span></p>\n<div class=\"question_part_label\">c(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>8</mn><mo>.</mo><mn>99</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup><mo>×</mo><mi>Q</mi><mo>×</mo><mfenced><mrow><mfrac><mn>1</mn><mrow><mn>5</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup></mrow></mfrac><mo>-</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></mfrac></mrow></mfenced><mo>=</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></math> ✓</span></p>\n<p><span class=\"fontstyle0\"><br/><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>Q</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>8</mn></mrow></msup><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">C</mi><mo>»</mo></math> ✓</span></p>\n<div class=\"question_part_label\">c(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">to highlight similarities between </span><span class=\"fontstyle2\">«</span><span class=\"fontstyle0\">different</span><span class=\"fontstyle2\">» </span><span class=\"fontstyle0\">fields </span><span class=\"fontstyle3\">✓</span></p>\n<div class=\"question_part_label\">d.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>The majority who answered in terms of potential gained one mark. Often the answers were in terms of work done rather than work done per unit charge or missed the fact that the potential is positive.</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was well answered.</p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Most didn't realise that the key to the answer is the definition of potential or potential difference and tried to answer using one of the formulae in the data booklet, but incorrectly.</p>\n<div class=\"question_part_label\">c(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Even though many were able to choose the appropriate formula from the data booklet they were often hampered in their use of the formula by incorrect techniques when using fractions.</p>\n<div class=\"question_part_label\">c(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was generally well answered with only a small number of answers suggesting greater international cooperation.</p>\n<div class=\"question_part_label\">d.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion",
      "d-fields",
      "nature-of-science"
    ],
    "subtopics": [
      "a-4-rigid-body-mechanics",
      "d-2-electric-and-magnetic-fields"
    ]
  },
  {
    "question_id": "20N.2.HL.TZ0.9",
    "Question": "<div class=\"specification\">\n<p>The diagram shows an alternating current generator with a rectangular coil rotating at a constant frequency in a uniform magnetic field.</p>\n<p><img height=\"199\" 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\" style=\"display: block; margin-left: auto; margin-right: auto;\" width=\"506\"/></p>\n</div><div class=\"specification\">\n<p>The graph shows how the generator output voltage <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>V</mi></math> varies with time <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>t</mi></math>.</p>\n<p><img height=\"382\" src=\"data:image/png;base64,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\" style=\"display: block; margin-left: auto; margin-right: auto;\" width=\"520\"/></p>\n<p>Electrical power produced by the generator is delivered to a consumer some distance away.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Explain, by reference to Faraday’s law of induction, how an electromotive force (emf) is induced in the coil.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The average power output of the generator is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>8</mn><mo>.</mo><mn>5</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup><mo> </mo><mi mathvariant=\"normal\">W</mi></math>. Calculate the root mean square (rms) value of the generator output current.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The voltage output from the generator is stepped up before transmission to the consumer. Estimate the factor by which voltage has to be stepped up in order to reduce power loss in the transmission line by a factor of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>2</mn><mo>.</mo><mn>5</mn><mo>×</mo><msup><mn>10</mn><mn>2</mn></msup></math>.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The frequency of the generator is doubled with no other changes being made. Draw, on the axes, the variation with time of the voltage output of the generator.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b(iii).</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">there is a magnetic flux </span><span class=\"fontstyle2\">«</span><span class=\"fontstyle0\">linkage</span><span class=\"fontstyle2\">» </span><span class=\"fontstyle0\">in the coil / coil cuts magnetic field </span><span class=\"fontstyle3\">✓</span></p>\n<p><span class=\"fontstyle0\">this flux </span><span class=\"fontstyle2\">«</span><span class=\"fontstyle0\">linkage</span><span class=\"fontstyle2\">» </span><span class=\"fontstyle0\">changes as the angle varies/coil rotates </span><span class=\"fontstyle3\">✓</span></p>\n<p><span class=\"fontstyle2\">«</span><span class=\"fontstyle0\">Faraday’s law</span><span class=\"fontstyle2\">» </span><span class=\"fontstyle0\">connects induced emf with rate of change of flux </span><span class=\"fontstyle2\">«</span><span class=\"fontstyle0\">linkage</span><span class=\"fontstyle2\">» </span><span class=\"fontstyle0\">with time </span><span class=\"fontstyle3\">✓</span></p>\n<p><em><span class=\"fontstyle4\"><br/>Do not award MP2 or 3 for answers that don’t discuss flux.</span></em></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>V</mi><mi>rms</mi></msub><mo>=</mo><mfrac><mrow><mn>25</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow><msqrt><mn>2</mn></msqrt></mfrac><mo>«</mo><mo>=</mo><mn>17</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo> </mo><mo> </mo><mi mathvariant=\"normal\">V</mi><mo>»</mo></math> ✓</span></p>\n<p> </p>\n<p><span class=\"fontstyle0\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>I</mi><mi>rms</mi></msub><mo>=</mo><mfrac><mrow><mn>8</mn><mo>.</mo><mn>5</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup></mrow><mrow><mn>17</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow></mfrac><mo>=</mo><mn>48</mn><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">A</mi><mo>»</mo></math> ✓</span></p>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">«</span><span class=\"fontstyle1\">power loss proportional to <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi>I</mi><mn>2</mn></msup></math> hence the step-up factor is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msqrt><mn>2</mn><mo>.</mo><mn>5</mn><mo>×</mo><msup><mn>10</mn><mn>2</mn></msup></msqrt><mo>»</mo><mo> </mo><mn>16</mn></math> </span><span class=\"fontstyle3\">✓</span></p>\n<div class=\"question_part_label\">b(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">peak emf doubles </span><span class=\"fontstyle2\">✓</span></p>\n<p><span class=\"fontstyle3\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math> </span><span class=\"fontstyle0\">halves </span><span class=\"fontstyle2\">✓</span></p>\n<p><em><span class=\"fontstyle3\"><br/>Must show at least 1 cycle.</span></em></p>\n<div class=\"question_part_label\">b(iii).</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>This question was well answered with the majority discussing changes in flux rather than wires cutting field lines, which was good to see.</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Generally well answered.</p>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was well answered by many, but some candidates left the answer as a surd. The most common guess here involved the use of root 2.</p>\n<div class=\"question_part_label\">b(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Well answered, with the majority of candidates scoring at least 1 mark.</p>\n<div class=\"question_part_label\">b(iii).</div>\n</div>",
    "topics": [
      "b-the-particulate-nature-of-matter",
      "d-fields"
    ],
    "subtopics": [
      "b-4-thermodynamics",
      "d-4-induction"
    ]
  },
  {
    "question_id": "20N.2.SL.TZ0.1",
    "Question": "<div class=\"specification\">\n<p>A company delivers packages to customers using a small unmanned aircraft. Rotating horizontal blades exert a force on the surrounding air. The air above the aircraft is initially stationary.</p>\n<p><img height=\"179\" 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\" style=\"display: block; margin-left: auto; margin-right: auto;\" width=\"319\"/></p>\n<p>The air is propelled vertically downwards with speed <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>v</mi></math>. The aircraft hovers motionless above the ground. A package is suspended from the aircraft on a string. The mass of the aircraft is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn><mo>.</mo><mn>95</mn><mtext> kg</mtext></math> and the combined mass of the package and string is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn><mo>.</mo><mn>45</mn><mo> </mo><mi>kg</mi></math>. The mass of air pushed downwards by the blades in one second is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>1</mn><mo>.</mo><mn>7</mn><mo> </mo><mi>kg</mi></math>.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>State the value of the resultant force on the aircraft when hovering.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline, by reference to Newton’s third law, how the upward lift force on the aircraft is achieved.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Determine <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>v</mi></math>. State your answer to an appropriate number of significant figures.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">a(iii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The package and string are now released and fall to the ground. The lift force on the aircraft remains unchanged. Calculate the initial acceleration of the aircraft.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">zero </span><span class=\"fontstyle2\">✓</span></p>\n<div class=\"question_part_label\">a(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">Blades exert a downward force on the air </span><span class=\"fontstyle2\">✓</span></p>\n<p><span class=\"fontstyle0\"><br/>air exerts an equal and opposite force on the blades </span><span class=\"fontstyle3\">«</span><span class=\"fontstyle0\">by Newton’s third law</span><span class=\"fontstyle3\">»<br/></span><span class=\"fontstyle4\"><em><strong>OR</strong></em><br/></span><span class=\"fontstyle0\">air exerts a reaction force on the blades </span><span class=\"fontstyle3\">«</span><span class=\"fontstyle0\">by Newton’s third law</span><span class=\"fontstyle3\">» </span><span class=\"fontstyle2\">✓</span></p>\n<p><em><span class=\"fontstyle5\"><br/>Downward direction required for </span><strong><span class=\"fontstyle4\">MP1</span></strong></em><span class=\"fontstyle4\">.</span></p>\n<div class=\"question_part_label\">a(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">«</span><span class=\"fontstyle1\">lift force/change of momentum in one second</span><span class=\"fontstyle0\">» <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>1</mn><mo>.</mo><mn>7</mn><mi>v</mi></math> </span><span class=\"fontstyle3\">✓</span></p>\n<p><span class=\"fontstyle3\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>1</mn><mo>.</mo><mn>7</mn><mi>v</mi><mo>=</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>95</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>45</mn></mrow></mfenced><mo>×</mo><mn>9</mn><mo>.</mo><mn>81</mn></math> ✓</span></p>\n<p><span class=\"fontstyle4\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>v</mi><mo>=</mo><mn>8</mn><mo>.</mo><mn>1</mn><mo>«</mo><msup><mi>ms</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> <em><strong>AND </strong></em></span><span class=\"fontstyle1\">answer expressed to <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>2</mn></math> sf only </span><span class=\"fontstyle3\">✓</span></p>\n<p><span class=\"fontstyle5\">Allow <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn mathvariant=\"italic\">8</mn><mo mathvariant=\"italic\">.</mo><mn mathvariant=\"italic\">2</mn></math> from </span><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>g</mi><mo mathvariant=\"italic\">=</mo><mn mathvariant=\"italic\">10</mn><mo mathvariant=\"italic\"> </mo><mi>m</mi><msup><mi>s</mi><mrow><mo mathvariant=\"italic\">-</mo><mn mathvariant=\"italic\">2</mn></mrow></msup></math>.</p>\n<div class=\"question_part_label\">a(iii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">vertical force = lift force – weight </span><span class=\"fontstyle2\"><em><strong>OR</strong></em> <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>0</mn><mo>.</mo><mn>45</mn><mo>×</mo><mn>9</mn><mo>.</mo><mn>81</mn></math> <em><strong>OR</strong></em> <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>4</mn><mo>.</mo><mn>4</mn><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">N</mi><mo>»</mo><mo> </mo></math></span><span class=\"fontstyle4\">✓</span></p>\n<p><span class=\"fontstyle0\">acceleration<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>45</mn><mo>×</mo><mn>9</mn><mo>.</mo><mn>81</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>95</mn></mrow></mfrac><mo>=</mo><mn>4</mn><mo>.</mo><mn>6</mn><mo> </mo><mo>«</mo><msup><mi>ms</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>»</mo><mo> </mo></math></span><span class=\"fontstyle4\">✓</span></p>\n<div class=\"question_part_label\">b.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a(iii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-1-kinematics",
      "a-2-forces-and-momentum",
      "a-3-work-energy-and-power"
    ]
  },
  {
    "question_id": "20N.2.SL.TZ0.12",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the terminal velocity of the sphere.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c(i))\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the force exerted by the spring on the sphere when the sphere is at rest.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  radius of sphere\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    012\n   </mn>\n   <mo>\n   </mo>\n   <mo>\n    «\n   </mo>\n   <mi mathvariant=\"normal\">\n    m\n   </mi>\n   <mo>\n    »\n   </mo>\n  </math>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  weight of sphere\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    6\n   </mn>\n   <mi>\n    π\n   </mi>\n   <mi>\n    η\n   </mi>\n   <mi>\n    r\n   </mi>\n   <mi>\n    v\n   </mi>\n   <mo>\n    +\n   </mo>\n   <mi>\n    ρ\n   </mi>\n   <mi>\n    V\n   </mi>\n   <mi>\n    g\n   </mi>\n  </math>\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    v\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mfenced>\n      <mrow>\n       <mn>\n        1\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        26\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mrow>\n         <mo>\n          -\n         </mo>\n         <mn>\n          2\n         </mn>\n        </mrow>\n       </msup>\n       <mo>\n        -\n       </mo>\n       <mn>\n        915\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <mn>\n        7\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        24\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mrow>\n         <mo>\n          -\n         </mo>\n         <mn>\n          6\n         </mn>\n        </mrow>\n       </msup>\n      </mrow>\n     </mfenced>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      9\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      81\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      6\n     </mn>\n     <mi mathvariant=\"normal\">\n      π\n     </mi>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      37\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      9\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        3\n       </mn>\n      </mrow>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      2\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        2\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    v\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    6\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    84\n   </mn>\n   <mo>\n   </mo>\n   <mo>\n    «\n   </mo>\n   <mi mathvariant=\"normal\">\n    m\n   </mi>\n   <mo>\n   </mo>\n   <msup>\n    <mi mathvariant=\"normal\">\n     s\n    </mi>\n    <mrow>\n     <mo>\n      –\n     </mo>\n     <mn>\n      1\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n    »\n   </mo>\n   <mo>\n   </mo>\n  </math>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <span class=\"fontstyle0\">\n    Accept use of\n    <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mi>\n      g\n     </mi>\n     <mo mathvariant=\"italic\">\n      =\n     </mo>\n     <mn mathvariant=\"italic\">\n      10\n     </mn>\n    </math>\n    leading to\n    <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mi>\n      v\n     </mi>\n     <mo mathvariant=\"italic\">\n      =\n     </mo>\n     <mn mathvariant=\"italic\">\n      7\n     </mn>\n     <mo mathvariant=\"italic\">\n      .\n     </mo>\n     <mn mathvariant=\"italic\">\n      0\n     </mn>\n     <mo mathvariant=\"italic\">\n     </mo>\n     <mo>\n      «\n     </mo>\n     <mi mathvariant=\"normal\">\n      m\n     </mi>\n     <mo>\n     </mo>\n     <msup>\n      <mi mathvariant=\"normal\">\n       s\n      </mi>\n      <mrow>\n       <mo>\n        –\n       </mo>\n       <mn>\n        1\n       </mn>\n      </mrow>\n     </msup>\n     <mo>\n      »\n     </mo>\n    </math>\n   </span>\n  </em>\n </p>\n <p>\n  <em>\n   <span class=\"fontstyle0\">\n    Allow implicit calculation of radius for MP1\n   </span>\n  </em>\n </p>\n <p>\n  <em>\n   <span class=\"fontstyle0\">\n    Do not allow ECF for MP3 if buoyant force omitted.\n   </span>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c(i))\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    F\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mi>\n    m\n   </mi>\n   <mi>\n    g\n   </mi>\n   <mo>\n    -\n   </mo>\n   <mi>\n    ρ\n   </mi>\n   <mi>\n    V\n   </mi>\n   <mi>\n    g\n   </mi>\n  </math>\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  <em>\n   <strong>\n    <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mi>\n      F\n     </mi>\n     <mo>\n      =\n     </mo>\n     <mfenced>\n      <mrow>\n       <mn>\n        0\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        0126\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <mn>\n        9\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        81\n       </mn>\n      </mrow>\n     </mfenced>\n     <mo>\n      -\n     </mo>\n     <mfenced>\n      <mrow>\n       <mn>\n        915\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <mn>\n        7\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        24\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mrow>\n         <mo>\n          -\n         </mo>\n         <mn>\n          6\n         </mn>\n        </mrow>\n       </msup>\n       <mo>\n        ×\n       </mo>\n       <mn>\n        9\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        81\n       </mn>\n      </mrow>\n     </mfenced>\n    </math>\n   </strong>\n  </em>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <span class=\"fontstyle0\">\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     F\n    </mi>\n    <mo>\n     =\n    </mo>\n    <mn>\n     5\n    </mn>\n    <mo>\n     .\n    </mo>\n    <mn>\n     86\n    </mn>\n    <mo>\n     ×\n    </mo>\n    <msup>\n     <mn>\n      10\n     </mn>\n     <mrow>\n      <mo>\n       -\n      </mo>\n      <mn>\n       2\n      </mn>\n     </mrow>\n    </msup>\n    <mo>\n    </mo>\n    <mo>\n     «\n    </mo>\n    <mi mathvariant=\"normal\">\n     N\n    </mi>\n    <mo>\n     »\n    </mo>\n   </math>\n   ✓\n  </span>\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <span class=\"fontstyle0\">\n    Accept use of\n    <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mi>\n      g\n     </mi>\n     <mo mathvariant=\"italic\">\n      =\n     </mo>\n     <mn mathvariant=\"italic\">\n      10\n     </mn>\n    </math>\n    leading to\n    <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mi>\n      F\n     </mi>\n     <mo>\n      =\n     </mo>\n     <mn mathvariant=\"italic\">\n      6\n     </mn>\n     <mo mathvariant=\"italic\">\n      .\n     </mo>\n     <mn mathvariant=\"italic\">\n      0\n     </mn>\n     <mo mathvariant=\"italic\">\n      ×\n     </mo>\n     <msup>\n      <mn mathvariant=\"italic\">\n       10\n      </mn>\n      <mrow>\n       <mo mathvariant=\"italic\">\n        -\n       </mo>\n       <mn mathvariant=\"italic\">\n        2\n       </mn>\n      </mrow>\n     </msup>\n     <mo mathvariant=\"italic\">\n     </mo>\n     <mi>\n      N\n     </mi>\n    </math>\n   </span>\n  </em>\n </p>\n</div>\n",
    "Examiners report": "<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  Only those candidates who forgot to include the buoyant force missed marks here.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c(i))\n </div><div class=\"card-body\">\n <p>\n  Continuing from b, most candidates scored full marks.\n </p>\n</div>\n",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-2-forces-and-momentum"
    ]
  },
  {
    "question_id": "20N.2.SL.TZ0.15",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the apparent brightness\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     b\n    </mi>\n    <mo>\n     ∝\n    </mo>\n    <mfrac>\n     <mrow>\n      <mi>\n       A\n      </mi>\n      <msup>\n       <mi>\n        T\n       </mi>\n       <mn>\n        4\n       </mn>\n      </msup>\n     </mrow>\n     <msup>\n      <mi>\n       d\n      </mi>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </mfrac>\n   </math>\n   , where\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     d\n    </mi>\n   </math>\n   is the distance of the object from Earth,\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     T\n    </mi>\n   </math>\n   is the surface temperature of the object and\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     A\n    </mi>\n   </math>\n   is the surface area of the object.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Two of the brightest objects in the night sky seen from Earth are the planet Venus and the star Sirius. Explain why the equation\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     b\n    </mi>\n    <mo>\n     ∝\n    </mo>\n    <mfrac>\n     <mrow>\n      <mi>\n       A\n      </mi>\n      <msup>\n       <mi>\n        T\n       </mi>\n       <mn>\n        4\n       </mn>\n      </msup>\n     </mrow>\n     <msup>\n      <mi>\n       d\n      </mi>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </mfrac>\n   </math>\n   is applicable to Sirius but not to Venus.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  substitution of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    L\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mi>\n    σ\n   </mi>\n   <mi>\n    A\n   </mi>\n   <msup>\n    <mi>\n     T\n    </mi>\n    <mn>\n     4\n    </mn>\n   </msup>\n  </math>\n  into\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    b\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mi>\n     L\n    </mi>\n    <mrow>\n     <mn>\n      4\n     </mn>\n     <msup>\n      <mi>\n       πd\n      </mi>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </mrow>\n   </mfrac>\n  </math>\n  giving\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    b\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi>\n      σ\n     </mi>\n     <mi>\n      A\n     </mi>\n     <msup>\n      <mi>\n       T\n      </mi>\n      <mn>\n       4\n      </mn>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      4\n     </mn>\n     <msup>\n      <mi>\n       πd\n      </mi>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </mrow>\n   </mfrac>\n  </math>\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <span class=\"fontstyle0\">\n    Removal of constants\n    <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mi>\n      σ\n     </mi>\n    </math>\n    and\n    <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mn>\n      4\n     </mn>\n     <mi mathvariant=\"normal\">\n      π\n     </mi>\n    </math>\n    is optional\n   </span>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  <span class=\"fontstyle0\">\n   equation applies to Sirius/stars that are luminous/emit light «from fusion»\n  </span>\n  <span class=\"fontstyle2\">\n   ✓\n  </span>\n </p>\n <p>\n  <span class=\"fontstyle0\">\n   but Venus reflects the Sun’s light/does not emit light\n  </span>\n  <span class=\"fontstyle3\">\n   «\n  </span>\n  <span class=\"fontstyle0\">\n   from fusion\n  </span>\n  <span class=\"fontstyle3\">\n   »\n  </span>\n  <span class=\"fontstyle2\">\n   ✓\n  </span>\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <span class=\"fontstyle0\">\n    OWTTE\n   </span>\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "e-5-fusion-and-stars"
    ]
  },
  {
    "question_id": "20N.2.SL.TZ0.3",
    "Question": "<div class=\"specification\">\n<p>A sample of vegetable oil, initially in the liquid state, is placed in a freezer that transfers thermal energy from the sample at a constant rate. The graph shows how temperature <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math> of the sample varies with time <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>t</mi></math>.</p>\n<p><img height=\"299\" 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\" style=\"display: block; margin-left: auto; margin-right: auto;\" width=\"515\"/></p>\n<p>The following data are available.</p>\n<p style=\"padding-left: 30px;\">Mass of the sample <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>0</mn><mo>.</mo><mn>32</mn><mo> </mo><mi>kg</mi></math><br/>Specific latent heat of fusion of the oil <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>130</mn><mo> </mo><mi>kJ</mi><mo> </mo><msup><mi>kg</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><br/>Rate of thermal energy transfer <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>15</mn><mo> </mo><mi mathvariant=\"normal\">W</mi></math></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Calculate the thermal energy transferred from the sample during the first <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>30</mn></math> minutes.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Estimate the specific heat capacity of the oil in its liquid phase. State an appropriate unit for your answer.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The sample begins to freeze during the thermal energy transfer. Explain, in terms of the molecular model of matter, why the temperature of the sample remains constant during freezing.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Calculate the mass of the oil that remains unfrozen after <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>60</mn></math> minutes.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>«</mo><mn>15</mn><mo>×</mo><mn>30</mn><mo>×</mo><mn>60</mn><mo>»</mo><mo>=</mo><mn>27000</mn><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">J</mi><mo>»</mo></math> ✓</span></p>\n<p> </p>\n<div class=\"question_part_label\">a(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>27</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo>=</mo><mn>0</mn><mo>.</mo><mn>32</mn><mo>×</mo><mi>c</mi><mo>×</mo><mfenced><mrow><mn>290</mn><mo>-</mo><mn>250</mn></mrow></mfenced></math> <em><strong>OR </strong></em><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>2100</mn></math> ✓</p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi mathvariant=\"normal\">J</mi><mo> </mo><msup><mi>kg</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo> </mo><msup><mi mathvariant=\"normal\">K</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> <em><strong>OR</strong></em> <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi mathvariant=\"normal\">J</mi><mo> </mo><msup><mi>kg</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo> </mo><msup><mo> </mo><mn>0</mn></msup><msup><mi mathvariant=\"normal\">C</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> ✓</p>\n<p><span class=\"fontstyle0\"><em><br/>Allow any appropriate unit that is</em> <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>g</mi><mi>y</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>×</mo><mi>t</mi><mi>e</mi><mi>r</mi><mi>m</mi><mi>p</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>u</mi><mi>r</mi><mi>e</mi></mrow></mfrac></math></span></p>\n<div class=\"question_part_label\">a(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">«intermolecular» bonds are formed during freezing </span><span class=\"fontstyle2\">✓</span></p>\n<p><span class=\"fontstyle0\"><br/>bond-forming process releases energy<br/></span><span class=\"fontstyle3\"><em><strong>OR</strong></em><br/></span><span class=\"fontstyle4\">«</span><span class=\"fontstyle0\">intermolecular</span><span class=\"fontstyle4\">» </span><span class=\"fontstyle0\">PE decreases </span><span class=\"fontstyle4\">«</span><span class=\"fontstyle0\">and the difference is transferred as heat</span><span class=\"fontstyle4\">» </span><span class=\"fontstyle2\">✓</span></p>\n<p><span class=\"fontstyle2\"><br/></span><span class=\"fontstyle4\">«</span><span class=\"fontstyle0\">average random</span><span class=\"fontstyle4\">» </span><span class=\"fontstyle0\">KE of the molecules does not decrease/change </span><span class=\"fontstyle2\">✓</span></p>\n<p><span class=\"fontstyle2\"><br/></span><span class=\"fontstyle0\">temperature is related to «average» KE of the molecules «hence unchanged» </span><span class=\"fontstyle2\">✓</span></p>\n<p> </p>\n<p><em><span class=\"fontstyle5\">To award MP3 or MP4 molecules/particles/atoms must be mentioned.</span></em></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">mass of frozen oil <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>«</mo><mo>=</mo><mfrac><mrow><mn>27</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow><mrow><mn>130</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow></mfrac><mo>»</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>21</mn><mo> </mo><mo>«</mo><mi>kg</mi><mo>»</mo></math> </span><span class=\"fontstyle2\">✓</span></p>\n<p><span class=\"fontstyle0\">unfrozen mass <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>«</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>32</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>21</mn><mo>»</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>11</mn><mo> </mo><mo>«</mo><mi>kg</mi><mo>»</mo></math> </span><span class=\"fontstyle2\">✓</span></p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.</div>\n</div>",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-1-thermal-energy-transfers"
    ]
  },
  {
    "question_id": "20N.2.SL.TZ0.5",
    "Question": "<div class=\"specification\">\n<p>The graph shows how current <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>I</mi></math> varies with potential difference <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>V</mi></math> across a component X.</p>\n<p><img height=\"357\" src=\"data:image/png;base64,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\" style=\"display: block; margin-left: auto; margin-right: auto;\" width=\"532\"/></p>\n</div><div class=\"specification\">\n<p>Component X and a cell of negligible internal resistance are placed in a circuit.</p>\n<p>A variable resistor R is connected in series with component X. The ammeter reads <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>20</mn><mo> </mo><mi>mA</mi></math>.</p>\n<p style=\"text-align: center;\"><img height=\"157\" src=\"data:image/png;base64,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\" width=\"187\"/></p>\n</div><div class=\"specification\">\n<p>Component X and the cell are now placed in a potential divider circuit.</p>\n<p><img height=\"131\" src=\"data:image/png;base64,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\" style=\"display: block; margin-left: auto; margin-right: auto;\" width=\"241\"/></p>\n<p> </p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline why component X is considered non-ohmic.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Determine the resistance of the variable resistor.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Calculate the power dissipated in the circuit.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>State the range of current that the ammeter can measure as the slider S of the potential divider is moved from Q to P.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">c(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Describe, by reference to your answer for (c)(i), the advantage of the potential divider arrangement over the arrangement in (b).</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c(ii).</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">current is not «directly» proportional to the potential difference<br/></span><span class=\"fontstyle2\"><em><strong>OR</strong></em><br/></span><span class=\"fontstyle0\">resistance of X is not constant<br/></span><span class=\"fontstyle2\"><em><strong>OR</strong></em><br/></span><span class=\"fontstyle0\">resistance of X changes «with current/voltage» </span><span class=\"fontstyle3\">✓</span></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><em><strong>ALTERNATIVE 1</strong></em></p>\n<p><span class=\"fontstyle0\">voltage across X<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>2</mn><mo>.</mo><mn>3</mn><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">V</mi><mo>»</mo></math> ✓</span></p>\n<p><span class=\"fontstyle0\">voltage across R<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>«</mo><mo>=</mo><mn>4</mn><mo>.</mo><mn>0</mn><mo>-</mo><mn>2</mn><mo>.</mo><mn>3</mn><mo>»</mo><mo>=</mo><mn>1</mn><mo>.</mo><mn>7</mn><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">V</mi><mo>»</mo></math> ✓</span></p>\n<p><span class=\"fontstyle0\">resistance of variable resistor <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>«</mo><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>7</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>020</mn></mrow></mfrac><mo>»</mo><mo>=</mo><mn>85</mn><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">Ω</mi><mo>»</mo></math> ✓</span></p>\n<p> </p>\n<p><em><strong>ALTERNATIVE 2</strong></em></p>\n<p>overall resistance <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>«</mo><mo>=</mo><mfrac><mrow><mn>4</mn><mo>.</mo><mn>0</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>020</mn></mrow></mfrac><mo>»</mo><mo>=</mo><mn>200</mn><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">Ω</mi><mo>»</mo></math> ✓</p>\n<p>resistance of X <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>«</mo><mo>=</mo><mfrac><mrow><mn>2</mn><mo>.</mo><mn>3</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>020</mn></mrow></mfrac><mo>»</mo><mo>=</mo><mn>115</mn><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">Ω</mi><mo>»</mo></math> ✓</p>\n<p>resistance of variable resistor <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>«</mo><mo>=</mo><mn>200</mn><mo>-</mo><mn>115</mn><mo>»</mo><mo>=</mo><mn>85</mn><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">Ω</mi><mo>»</mo></math> ✓</p>\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>power <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>«</mo><mo>=</mo><mn>4</mn><mo>.</mo><mn>0</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>020</mn><mo>»</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>080</mn><mo> </mo><mo>«</mo><mi mathvariant=\"normal\">W</mi><mo>»</mo></math> <span class=\"fontstyle0\">✓</span></p>\n<div class=\"question_part_label\">b(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">from <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn></math> to <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>60</mn><mo> </mo><mi>mA</mi></math> </span><span class=\"fontstyle2\">✓</span></p>\n<div class=\"question_part_label\">c(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><span class=\"fontstyle0\">allows zero current through component X / potential divider arrangement </span><span class=\"fontstyle2\">✓</span></p>\n<p><span class=\"fontstyle0\">provides greater range </span><span class=\"fontstyle3\">«</span><span class=\"fontstyle0\">of current through component X</span><span class=\"fontstyle3\">» </span><span class=\"fontstyle2\">✓</span></p>\n<div class=\"question_part_label\">c(ii).</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b(ii).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c(i).</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c(ii).</div>\n</div>",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-5-current-and-circuits"
    ]
  },
  {
    "question_id": "20N.2.SL.TZ0.7",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline why the cylinder performs simple harmonic motion when released.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The mass of the cylinder is\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mn>\n     118\n    </mn>\n    <mo>\n    </mo>\n    <mi>\n     kg\n    </mi>\n   </math>\n   and the cross-sectional area of the cylinder is\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mn>\n     2\n    </mn>\n    <mo>\n     .\n    </mo>\n    <mn>\n     29\n    </mn>\n    <mo>\n     ×\n    </mo>\n    <msup>\n     <mn>\n      10\n     </mn>\n     <mrow>\n      <mo>\n       -\n      </mo>\n      <mn>\n       1\n      </mn>\n     </mrow>\n    </msup>\n    <mo>\n    </mo>\n    <msup>\n     <mi mathvariant=\"normal\">\n      m\n     </mi>\n     <mn>\n      2\n     </mn>\n    </msup>\n   </math>\n   . The density of water is\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mn>\n     1\n    </mn>\n    <mo>\n     .\n    </mo>\n    <mn>\n     03\n    </mn>\n    <mo>\n     ×\n    </mo>\n    <msup>\n     <mn>\n      10\n     </mn>\n     <mn>\n      3\n     </mn>\n    </msup>\n    <mo>\n    </mo>\n    <mi>\n     kg\n    </mi>\n    <mo>\n    </mo>\n    <msup>\n     <mi mathvariant=\"normal\">\n      m\n     </mi>\n     <mrow>\n      <mo>\n       -\n      </mo>\n      <mn>\n       3\n      </mn>\n     </mrow>\n    </msup>\n   </math>\n   . Show that the angular frequency of oscillation of the cylinder is about\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mn>\n     4\n    </mn>\n    <mo>\n     .\n    </mo>\n    <mn>\n     4\n    </mn>\n    <mo>\n    </mo>\n    <mo>\n    </mo>\n    <mi>\n     rad\n    </mi>\n    <mo>\n    </mo>\n    <msup>\n     <mi mathvariant=\"normal\">\n      s\n     </mi>\n     <mrow>\n      <mo>\n       -\n      </mo>\n      <mn>\n       1\n      </mn>\n     </mrow>\n    </msup>\n   </math>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c(ii))\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Draw, on the axes, the graph to show how the kinetic energy of the cylinder varies with time during\n   <strong>\n    one\n   </strong>\n   period of oscillation\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     T\n    </mi>\n   </math>\n   .\n  </p>\n  <p>\n   <img height=\"371\" src=\"data:image/png;base64,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\" style=\"display:block;margin-left:auto;margin-right:auto;\" width=\"610\"/>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <span class=\"fontstyle0\">\n   the\n  </span>\n  <span class=\"fontstyle2\">\n   «\n  </span>\n  <span class=\"fontstyle0\">\n   restoring\n  </span>\n  <span class=\"fontstyle2\">\n   »\n  </span>\n  <span class=\"fontstyle0\">\n   force/acceleration is proportional to displacement\n  </span>\n  <span class=\"fontstyle3\">\n   ✓\n  </span>\n </p>\n <p>\n  <em>\n   <span class=\"fontstyle4\">\n    <br/>\n    Allow use of symbols i.e.\n   </span>\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     F\n    </mi>\n    <mo>\n     ∝\n    </mo>\n    <mo>\n     -\n    </mo>\n    <mi>\n     x\n    </mi>\n   </math>\n   <span class=\"fontstyle4\">\n    or\n   </span>\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     a\n    </mi>\n    <mo>\n     ∝\n    </mo>\n    <mo>\n     -\n    </mo>\n    <mi>\n     x\n    </mi>\n   </math>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  <span class=\"fontstyle0\">\n   Evidence of equating\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     m\n    </mi>\n    <msup>\n     <mi>\n      ω\n     </mi>\n     <mn>\n      2\n     </mn>\n    </msup>\n    <mi>\n     x\n    </mi>\n    <mo>\n     =\n    </mo>\n    <mi>\n     ρ\n    </mi>\n    <mi>\n     A\n    </mi>\n    <mi>\n     g\n    </mi>\n    <mi>\n     x\n    </mi>\n   </math>\n   «to obtain\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mfrac>\n     <mrow>\n      <mi>\n       ρ\n      </mi>\n      <mi>\n       A\n      </mi>\n      <mi>\n       g\n      </mi>\n     </mrow>\n     <mi>\n      m\n     </mi>\n    </mfrac>\n    <mo>\n     =\n    </mo>\n    <msup>\n     <mi>\n      ω\n     </mi>\n     <mn>\n      2\n     </mn>\n    </msup>\n   </math>\n   » ✓\n  </span>\n </p>\n <p>\n </p>\n <p>\n  <span class=\"fontstyle0\">\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     ω\n    </mi>\n    <mo>\n     =\n    </mo>\n    <msqrt>\n     <mfrac>\n      <mrow>\n       <mn>\n        1\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        03\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mn>\n         3\n        </mn>\n       </msup>\n       <mo>\n        ×\n       </mo>\n       <mn>\n        2\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        29\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mrow>\n         <mo>\n          -\n         </mo>\n         <mn>\n          1\n         </mn>\n        </mrow>\n       </msup>\n       <mo>\n        ×\n       </mo>\n       <mn>\n        9\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        81\n       </mn>\n      </mrow>\n      <mn>\n       118\n      </mn>\n     </mfrac>\n    </msqrt>\n   </math>\n   <em>\n    <strong>\n     OR\n    </strong>\n   </em>\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mn>\n     4\n    </mn>\n    <mo>\n     .\n    </mo>\n    <mn>\n     43\n    </mn>\n    <mo>\n     «\n    </mo>\n    <mi>\n     rad\n    </mi>\n    <mo>\n    </mo>\n    <msup>\n     <mi mathvariant=\"normal\">\n      s\n     </mi>\n     <mrow>\n      <mo>\n       -\n      </mo>\n      <mn>\n       1\n      </mn>\n     </mrow>\n    </msup>\n    <mo>\n     »\n    </mo>\n   </math>\n   ✓\n  </span>\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <span class=\"fontstyle0\">\n    Answer to at least\n    <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mn mathvariant=\"italic\">\n      3\n     </mn>\n    </math>\n    s.f.\n   </span>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c(ii))\n </div><div class=\"card-body\">\n <p>\n  <span class=\"fontstyle0\">\n   energy never negative\n  </span>\n  <span class=\"fontstyle2\">\n   ✓\n  </span>\n </p>\n <p>\n  <span class=\"fontstyle0\">\n   correct shape with two maxima\n  </span>\n  <span class=\"fontstyle2\">\n   ✓\n  </span>\n </p>\n <p>\n  <img src=\"data:image/png;base64,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\"/>\n </p>\n</div>\n",
    "Examiners report": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  This was well answered with candidates gaining credit for answers in words or symbols.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  Again, very well answered.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c(ii))\n </div><div class=\"card-body\">\n <p>\n  Most candidates answered with a graph that was only positive so scored the first mark.\n </p>\n</div>\n",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-1-simple-harmonic-motion"
    ]
  },
  {
    "question_id": "21M.2.HL.TZ1.10",
    "Question": "<div class=\"specification\">\n<p>In an electric circuit used to investigate the photoelectric effect, the voltage is varied until the reading in the ammeter is zero. The stopping voltage that produces this reading is 1.40 V.</p>\n<p style=\"text-align: center;\"><img 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\"/></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Describe the photoelectric effect.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Show that the maximum velocity of the photoelectrons is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>700</mn><mo> </mo><msup><mtext>km  s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The photoelectrons are emitted from a sodium surface. Sodium has a work function of 2.3 eV.</p>\n<p>Calculate the wavelength of the radiation incident on the sodium. State an appropriate unit for your answer.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>electrons are ejected from the surface of a metal <strong>✓</strong></p>\n<p>after gaining energy from photons/electromagnetic radiation <strong>✓</strong></p>\n<p>there is a minimum «threshold» energy/frequency<br/><em><strong>OR</strong></em><br/>maximum «threshold» wavelength <strong>✓</strong></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>e</mi><mi>V</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo> </mo><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup></math>» and manipulation to get <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>v</mi></math> <strong>✓</strong></p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>v</mi><mo>=</mo><msqrt><mfrac><mrow><mn>2</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup><mo>×</mo><mn>1</mn><mo>.</mo><mn>4</mn></mrow><mrow><mn>9</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>31</mn></mrow></msup></mrow></mfrac></msqrt></math>  <em><strong>OR  </strong></em><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>702</mn><mo>«</mo><msup><mtext>km s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math><strong>✓</strong></p>\n<p><em>Must see either complete substitution or calculation to at least 3 s.f. for <strong>MP2</strong></em></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><strong><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>E</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>.</mo><mn>4</mn></math> ✓</strong></p>\n<p><strong><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>λ</mi><mo>=</mo><mfrac><mrow><mn>6</mn><mo>.</mo><mn>63</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>34</mn></mrow></msup><mo>×</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup></mrow><mrow><mn>3</mn><mo>.</mo><mn>7</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup></mrow></mfrac></math> ✓</strong></p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>3</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>7</mn></mrow></msup><mo> </mo><mtext>m </mtext><mtext mathvariant=\"bold-italic\">OR</mtext><mtext> 340 nm</mtext></math> <strong>✓</strong></p>\n<p><em><br/>Must see an appropriate unit to award<strong> MP3.</strong></em></p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.</div>\n</div>",
    "topics": [
      "b-the-particulate-nature-of-matter",
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "b-5-current-and-circuits",
      "e-2-quantum-physics"
    ]
  },
  {
    "question_id": "21M.2.HL.TZ1.2",
    "Question": "<div class=\"specification\">\n<p>A planet is in a circular orbit around a star. The speed of the planet is constant. The following data are given:</p>\n<p style=\"padding-left: 120px;\">Mass of planet                                      <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>8</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>24</mn></msup><mo> </mo></math>kg<br/>Mass of star                                          <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>3</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>30</mn></msup><mo> </mo></math>kg<br/>Distance from the star to the planet <em>R</em>  <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>4</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>10</mn></msup><mo> </mo></math>m.</p>\n</div><div class=\"specification\">\n<p>A spacecraft is to be launched from the surface of the planet to escape from the star system. The radius of the planet is 9.1 × 10<sup>3</sup> km.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Explain why a centripetal force is needed for the planet to be in a circular orbit.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Calculate the value of the centripetal force.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Show that the gravitational potential due to the planet and the star at the surface of the planet is about −5 × 10<sup>9 </sup>J kg<sup>−1</sup>.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Estimate the escape speed of the spacecraft from the planet–star system.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.ii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>«circular motion» involves a changing velocity <strong>✓</strong></p>\n<p>«Tangential velocity» is «always» perpendicular to centripetal force/acceleration <strong>✓</strong></p>\n<p>there must be a force/acceleration towards centre/star <strong>✓</strong></p>\n<p>without a centripetal force the planet will move in a straight line <strong>✓</strong></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>F</mi><mo>=</mo><mfrac><mrow><mo>(</mo><mn>6</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>)</mo><mo>(</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>24</mn></msup><mo>)</mo><mo>(</mo><mn>3</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>30</mn></msup><mo>)</mo></mrow><mrow><mo>(</mo><mn>4</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>10</mn></msup><msup><mo>)</mo><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mn>8</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup></math> «N» <strong>✓</strong></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><em>V</em><sub>planet</sub> = «−»<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mo>(</mo><mn>6</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>)</mo><mo>(</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>24</mn></msup><mo>)</mo></mrow><mrow><mn>9</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfrac><mo>=</mo></math>«−» 5.9 × 10<sup>7 </sup>«J kg<sup>−1</sup>» <strong>✓</strong></p>\n<p><em>V</em><sub>star</sub> = «−»<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mo>(</mo><mn>6</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>)</mo><mo>(</mo><mn>3</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>30</mn></msup><mo>)</mo></mrow><mrow><mn>4</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>10</mn></msup></mrow></mfrac><mo>=</mo></math>«−» 4.9 × 10<sup>9 </sup>«J kg<sup>−1</sup>» <strong>✓</strong></p>\n<p><em>V</em><sub>planet</sub> + <em>V</em><sub>star </sub>= «−» 4.9 «09» × 10<sup>9 </sup>«J kg<sup>−1</sup>» <strong>✓</strong></p>\n<p><em><br/></em><em>Must see substitutions and not just equations.</em></p>\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>use of <em>v</em><sub>esc</sub> = <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msqrt><mn>2</mn><mi>V</mi></msqrt></math> <strong>✓</strong></p>\n<p><em>v = </em>9.91 × 10<sup>4</sup> «m s<sup>−1</sup>» <strong>✓</strong></p>\n<p> </p>\n<p> </p>\n<div class=\"question_part_label\">c.ii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.ii.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion",
      "d-fields"
    ],
    "subtopics": [
      "a-2-forces-and-momentum",
      "d-1-gravitational-fields"
    ]
  },
  {
    "question_id": "21M.2.HL.TZ1.8",
    "Question": "<div class=\"specification\">\n<p>On a guitar, the strings played vibrate between two fixed points. The frequency of vibration is modified by changing the string length using a finger. The different strings have different wave speeds. When a string is plucked, a standing wave forms between the bridge and the finger.</p>\n<p>                                                       <img src=\"data:image/png;base64,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\"/></p>\n</div><div class=\"specification\">\n<p>The string is displaced 0.4 cm at point P to sound the guitar. Point P on the string vibrates with simple harmonic motion (shm) in its first harmonic with a frequency of 195 Hz. The sounding length of the string is 62 cm.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline how a standing wave is produced on the string.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Show that the speed of the wave on the string is about 240 m s<sup>−1</sup>.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Sketch a graph to show how the acceleration of point P varies with its displacement from the rest position.</p>\n<p>                 <img src=\"data:image/png;base64,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\"/></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Calculate, in m s<sup>−1</sup>, the maximum velocity of vibration of point P when it is vibrating with a frequency of 195 Hz.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Calculate, in terms of <em>g</em>, the maximum acceleration of P.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.iv.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Estimate the displacement needed to double the energy of the string.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.v.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The string is made to vibrate in its third harmonic. State the distance between consecutive nodes. </p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>«travelling» wave moves along the length of the string and reflects «at fixed end» <strong>✓</strong></p>\n<p>superposition/interference of incident and reflected waves <strong>✓</strong></p>\n<p>the superposition of the reflections is reinforced only for certain wavelengths <strong>✓</strong> </p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>λ</mi><mo>=</mo><mn>2</mn><mi>l</mi><mo>=</mo><mn>2</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>62</mn><mo>=</mo><mo>«</mo><mn>1</mn><mo>.</mo><mn>24</mn><mo> </mo><mtext>m</mtext><mo>»</mo></math> ✓</p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>v</mi><mo>=</mo><mi>f</mi><mi>λ</mi><mo>=</mo><mn>195</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>24</mn><mo>=</mo><mn>242</mn><mo> </mo><mo>«</mo><msup><mtext>m s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> ✓</p>\n<p><em>Answer must be to 3 or more sf or working shown for<strong> MP2.</strong></em></p>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>straight line through origin with negative gradient <strong>✓</strong></p>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>max velocity occurs at x = 0 <strong>✓</strong></p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>v</mi><mo>=</mo><mo>«</mo><mo>(</mo><mn>2</mn><mi>π</mi><mo>)</mo><mo>(</mo><mn>195</mn><mo>)</mo><msqrt><mn>0</mn><mo>.</mo><msup><mn>004</mn><mn>2</mn></msup></msqrt><mo>»</mo><mo>=</mo><mn>4</mn><mo>.</mo><mn>9</mn><mo> </mo><mo>«</mo><msup><mtext>m s</mtext><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong></p>\n<div class=\"question_part_label\">b.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>a</mi><mo>=</mo><msup><mfenced><mrow><msub><mn>2</mn><mi mathvariant=\"normal\">π</mi></msub><mo> </mo><mn>195</mn></mrow></mfenced><mn>2</mn></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>004</mn><mo>=</mo><mn>6005</mn><mo> </mo><mo>«</mo><msup><mtext>m s</mtext><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong></p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>600</mn><mo> </mo><mtext>g</mtext></math> <strong>✓</strong></p>\n<div class=\"question_part_label\">b.iv.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>use of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>E</mi><mo>∝</mo><msup><mi>A</mi><mn>2</mn></msup><mtext mathvariant=\"bold-italic\"> OR  </mtext><msup><msub><mi>x</mi><mtext>o</mtext></msub><mn>2</mn></msup></math> <strong>✓</strong></p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>A</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>4</mn><msqrt><mn>2</mn></msqrt><mo>=</mo><mn>0</mn><mo>.</mo><mn>57</mn><mo> </mo><mo>«</mo><mtext>cm</mtext><mo>»</mo><mo> </mo><mo>≅</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>6</mn><mo> </mo><mo>«</mo><mtext>cm</mtext><mo>»</mo></math> <strong>✓</strong></p>\n<div class=\"question_part_label\">b.v.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mn>62</mn><mn>3</mn></mfrac><mo>=</mo><mn>21</mn><mo> </mo><mo>«</mo><mtext>cm</mtext><mo>»</mo></math> <strong>✓</strong></p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.iv.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.v.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.</div>\n</div>",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-1-simple-harmonic-motion",
      "c-2-wave-model",
      "c-4-standing-waves-and-resonance"
    ]
  },
  {
    "question_id": "21M.2.HL.TZ2.10",
    "Question": "<div class=\"specification\">\n<p>The table gives data for Jupiter and three of its moons, including the radius <em>r</em> of each object.</p>\n<p style=\"text-align: center;\"><img src=\"data:image/png;base64,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\"/></p>\n</div><div class=\"specification\">\n<p>A spacecraft is to be sent from <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mtext>Io</mtext></math> to infinity.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Calculate, for the surface of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mtext>Io</mtext></math>, the gravitational field strength <em>g</em><sub>Io</sub> due to the mass of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mtext>Io</mtext></math>. State an appropriate unit for your answer.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Show that the <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mi>gravitational</mi><mo> </mo><mi>potential</mi><mo> </mo><mi>due</mi><mo> </mo><mi>to</mi><mo> </mo><mi>Jupiter</mi><mo> </mo><mi>at</mi><mo> </mo><mi>the</mi><mo> </mo><mi>orbit</mi><mo> </mo><mi>of</mi><mo> </mo><mi>Io</mi></mrow><mrow><mo> </mo><mi>gravitational</mi><mo> </mo><mi>potential</mi><mo> </mo><mi>due</mi><mo> </mo><mi>to</mi><mo> </mo><mi>Io</mi><mo> </mo><mi>at</mi><mo> </mo><mi>the</mi><mo> </mo><mi>surface</mi><mo> </mo><mi>of</mi><mo> </mo><mi>Io</mi></mrow></mfrac></math> is about 80.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline, using (b)(i), why it is not correct to use the equation <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msqrt><mfrac><mrow><mn>2</mn><mi>G</mi><mo>×</mo><mtext>mass of Io</mtext></mrow><mtext>radius of Io</mtext></mfrac></msqrt></math> to calculate the speed required for the spacecraft to reach infinity from the surface of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mtext>Io</mtext></math>.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>An engineer needs to move a space probe of mass 3600 kg from Ganymede to Callisto. Calculate the energy required to move the probe from the orbital radius of Ganymede to the orbital radius of Callisto. Ignore the mass of the moons in your calculation. </p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>«</mo><mfrac><mrow><mi>G</mi><mi>M</mi></mrow><msup><mi>r</mi><mn>2</mn></msup></mfrac><mo>=</mo><mfrac><mrow><mn>6</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>×</mo><mn>8</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>22</mn></msup></mrow><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>»</mo><mn>1</mn><mo>.</mo><mn>8</mn></math><strong> ✓</strong></p>\n<p>N kg<sup>−1  </sup><em><strong>OR</strong>  </em>m s<sup>−2</sup><strong>  ✓</strong></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mn>1</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>27</mn></msup></mrow><mrow><mn>4</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup></mrow></mfrac></math><strong>  <em>AND </em> </strong><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mn>8</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>22</mn></msup></mrow><mrow><mn>1</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfrac></math><strong> </strong>seen<strong> ✓</strong></p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>«</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>27</mn></msup><mo>×</mo><mn>1</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow><mrow><mn>4</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup><mo>×</mo><mn>8</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>22</mn></msup></mrow></mfrac><mo>=</mo><mo>»</mo><mn>78</mn></math><strong>  ✓</strong></p>\n<p><em><br/>For <strong>MP1</strong>, potentials can be seen individually or as a ratio.</em></p>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>«this is the escape speed for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mtext>Io</mtext></math> alone but» gravitational potential / field of Jupiter must be taken into account<strong>  ✓</strong></p>\n<p><em><strong><br/>OWTTE</strong></em></p>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>-</mo><mi>G</mi><msub><mi>M</mi><mtext>Jupiter</mtext></msub><mfenced><mrow><mfrac><mn>1</mn><mrow><mn>1</mn><mo>.</mo><mn>88</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfrac><mo>-</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>.</mo><mn>06</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfrac></mrow></mfenced><mo>=</mo><mo>«</mo><mn>5</mn><mo>.</mo><mn>21</mn><mo>×</mo><msup><mn>10</mn><mn>7</mn></msup><mo> </mo><msup><mtext>J kg</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math><strong>  ✓</strong></p>\n<p>« multiplies by 3600 kg to get » 1.9 × 10<sup>11 </sup>«J» <strong>✓</strong></p>\n<p><em><br/>Award <strong>[2]</strong> marks if factor of ½ used, taking into account orbital kinetic energies, leading to a final answer of 9.4 x 10<sup>10 </sup>«J».</em></p>\n<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong></em></p>\n<p><em>Award <strong>[2] marks</strong> for a bald correct answer.</em></p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.</div>\n</div>",
    "topics": [
      "d-fields"
    ],
    "subtopics": [
      "d-1-gravitational-fields"
    ]
  },
  {
    "question_id": "21M.2.HL.TZ2.8",
    "Question": "<div class=\"specification\">\n<p>Monochromatic light of wavelength <em>λ</em> is normally incident on a diffraction grating. The diagram shows adjacent slits of the diffraction grating labelled V, W and X. Light waves are diffracted through an angle <em>θ</em> to form a <strong>second-order</strong> diffraction maximum. Points Z and Y are labelled.</p>\n<p style=\"text-align: center;\">  <img src=\"data:image/png;base64,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\"/></p>\n</div><div class=\"specification\">\n<p>State the effect on the graph of the variation of sin <em>θ</em> with <em>n</em> of:</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>State the phase difference between the waves at V and Y.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>State, in terms of <em>λ</em>, the path length between points X and Z.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The separation of adjacent slits is <em>d</em>. Show that for the second-order diffraction maximum <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>2</mn><mi>λ</mi><mo>=</mo><mi>d</mi><mi>sin</mi><mo> </mo><mi>θ</mi></math>.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Monochromatic light of wavelength 633 nm is normally incident on a diffraction grating. The diffraction maxima incident on a screen are detected and their angle <em>θ</em> to the central beam is determined. The graph shows the variation of sin<em>θ</em> with the order <em>n</em> of the maximum. The central order corresponds to <em>n</em> = 0.</p>\n<p><img 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U0/L3jI7RSvhZ3Y2WLGM1xZ3n3zyy725+vWv/3G/1qp8L9WebbDae4KO2/aSlj+ya4O1PI72M2rQkI18URCt6pytpwMmu/6kfKJV322ZHY1ds7PBiubsQ+NW663u3v3x7vr1l3ZffvnlvgiZrJqxKvv0+ZztUPkt5yF6olXdqJ6O2xY+pzrGBitI1gYrCG7jJiE72dDye9bTRN1z2zVaaf0z+dG6n0qv9VavvPKDnRauj/93oPYXQzV81v6526nq31KPzLJVPxp3LW081TE2WAGyCjgNGD37YQaOAceAY2B7MfD3P/vZ7sqVF3Y/fOut6veAlqC8/tprz5ksvdd+x8u8eAl8Ta9CYoMV7AbPYAXBLfAXiZIT2TL1tGz61xwtv2e92bFxk8lvbXE3XG/Vkovu3L7dctjkMZntzyxbQGjcTUI9wwc2WEHINlhBcAsMmOwBT8onWhGnyYaW37Pe7GywolmrxH1tvVXLOXuOvdL2lnbWjqF6yq5Wp3Pts8EKkrbBCoLbuEnITja0/J71NFH33HaNVlr/TH607kvoD623OpYNM9nRvl+C3TE+hz6n7A6d+9Sf2WAFCdtgBcHZYMXBbZydwJFkTxM1KZvWfQ36TH7Z7LXeSve3eu+9n4bGbyY7GjvZ7Cm7UIctJLLBCoK0wQqC27hJoMmKJhtafs96s/MlwkjW0norLWafe2uFYVk9x172mKfshv1w7tc2WEHiNlhBcDZYcXAbZydwJNnTRE3KpnVfgz6TXwb74Xqrf/jgg82O2wz2Q9g07obnOvdrG6wgcRusILiNmwSarGiyoeX3rDc7z2C1Zq3xeisa9z3HHm071VN2rX1+iuNssAJUFTAyWHr2wwwcA44Bx8DliYFj97dyX5+/rwNf06uQ2GAFu8EzWEFwnsGKg9s4O4HTl1t0o38Jk7Jp3degz+R3LvZT97ei5Weyo7FD2071lF00Xyyhs8EKUrTBCoLbuEnITja0/J71NFH33HaNVlr/TH607sf0w/VW5fcEhxnumH54bO11Jjva97TtVE/Z1frjXPtssIKkbbCC4Gyw4uA2zk7gSLKmiZqUTeu+Bn0mv1OyH6+3qg1QWn4mOxo7tO1UT9nV+vNc+2ywgqRtsILgNm4SspMNLb9nPU3UPbddo5XWP5MfrfuU/tGjR033t5rSt2bBTHa072nbqZ6ya+2jUxxngxWkaoMVBGeDFQe3cXYCR5I1TdSkbFr3Negz+Z2C/Ycf/nxvrlrub0XLz2RHY4e2neopO7U/a7PBCpK3wQqC27hJyE42tPye9TRR99x2jVZa/0x+tO5DvdZb3blze3f9+ku72nqrWmYb6mufH9uXyY72PW071VN2x/rmlJ/bYAXp2mAFwdlgxcFtnJ3AkWRNEzUpm9Z9DfpMfkuxl6F65ZUf7N544/WdjFbrRsvPZEdjh7ad6im71j4+xXE2WAGqChgZLD37YQaOAceAY2D9MfB3P/nJ/idvfvjWW87bnX13Bb6mVyGxwQp2g2ewguA2PgujL2Ky0b/maPk9682u39ijcXfn9u3m9Va18UnL7zn2aNupnrKr9ee59tlgBUnbYAXB2WDFwW2cncCRZE0TNSmb1n0N+kx+UfZlvdV3v/v7zeutagM0Wn45VyY7Gju07VRP2ZU+yHi2wQpSt8EKgtu4SchONrT8nvU0Uffcdo1WWv9MfpG6D9dbffzxL+IJq3N2tO8j7IewqZ7G3bAu535tgxUkboMVBGeDFQe3cXYCR5I1TdSkbFr3Negz+c1l/5vf/NNz97eaqx8PUqrPZEdjh7ad6im7cV+e870NVpC2DVYQ3MZNQnayoeX3rKeJuue2a7TS+mfym1P32v2t5uhrmY3qM9nRvqdtp3rKrtaf59pngxUkbYMVBGeDFQe3cXYCR5I1TdSkbFr3Negz+bWwL+utave3atEfGphUn8mOxg5tO9VTdof69dSf2WAFCdtgBcFt3CRkJxtafs96mqh7brtGK61/Jr9jdR+ut6rd3+qY/lg2o/pMdrTvadupnrI71ren/NwGK0BXASODpWc/zMAx4BhwDOTFQLm/lW7F4H7I64dTsg98Ta9CYoMV7AbPYAXBeQYrDm7j7AROSTy60b+ESdm07mvQZ/KbYl/WW2lR+6FtSn9IM/yM6jPZqR2k/kRLy5aeshv247lf22AFidtgBcEtMGCyBzwpn2hFnCYbWn7PerOLm9Ps2BvHXVlvpZ+9afk9wbF+bvai+p5jj7ad6im7uX295PGrNli6d4mMTHncu/fu0bbfv//+s+Nv3Xpz9/jxF89pxufUua9du/rcMS1vbLBaKNWPoQOGDthMPS17y+wUTYSf2V0Og1XWW+kHm2vrrWpZh8QNjTvpe4693tnV4uFc+1ZrsB48+GxvfD799Fd7FjJKMkKHbhinz27ceHn35MmTvebtt3+0fz+EKZMm40U3G6w4wZ6TjVpNEg7Rquwts6Psza5/g1Xub6VLg3M2Ou6ovufYo22nespuTpwsfexqDVbNCNX2DYHIXA0NmIyWjFAxaTpWx2iWi242WHGCdMDQAZupp2VvmZ0ijvAzu74NVut6q1pmInFD4076nmOvd3a1eDjXvtUaLM0yjY2QzNOcy3k1gyX90HBFQdtgRcn1nWzUapJwiFZl95yoKTuqN7s+DZYuA968+equdb2V4mS80XFH9T3HHm071VN241g45/vVGqzaTJMuG8rYPH36tImRTJoGZtkePvx8r9d+nUcPvS6XFMtxLc82WC2U6sfQAUMHbKaelr1ldoomws/s+jNYZb2V8njreqta1iFxQ+NO+p5jr3d2tXg4177VGizNNI1nsFoNlma6ioEaXjLUzJX26zxl0+cyc8OtaI89a9D4YQaOAceAY2D5GLj15pu7b3/7W7tXX/0z59mNf9cMv597er1ag7XEDJZmpmrnGXdQ5LKhzBfZyF8FRKs6Z+v1ZUS27PqT8olWzLbMjsau2fUzgzVeb0XHTba+59jrnR35rqHa1RosXbob35ZBM1Bz1mAJTsu6LZ1zONPVAtUGq4VS/Ziek41aRBIO0arsLbOj7M1u/QZr6v5WdNxk63uOvd7Z1b+FzrN3tQar9j8GZYJkvGpbbUG7jtNlxnIJUOcsr8s5tJ5LZknrs+ZsNlhzaD1/bM/JRi0hCYdoVfaW2VH2Zrdug1XWW9Xub0XHTba+59jrnd3z3z7nfbdag1UWpJf/8af7YMkcHZpp0n2vhovayyXCotE5ZIzGa7CGmlb8NlitpC4e13OyUWtIwiFalb1ldpS92a3XYB27vxUdN9n6nmOvd3YXv4HOt2e1BksINPskI1MeMlDDTe/Hlww1S1WOlyErBq3oZK5kqMoxOkfr/0os59Cz9GQjQUu0qnO2vudkQ/lR9ltmR9mb3ToN1ni9VS2v0nGTre859npnV4unc+1btcE6F4RIOTZYEWpfa3pONmoBSThEq7K3zI6yN7t1Gayp9VZfZ4nn/6XjJlvfc+z1zu75SDrvOxusIG8brCC4jZsEmqx6TtSKGNp+oje79RisQ+utapmF9Ht23Kn8nmMvmz1lV4unc+2zwQqQVsDJYOnZDzNwDDgGHAPtMfB3P/nJ7sqVF3Z3bt92/vR3SFMMBL6mVyGxwQp2g2ewguA6/2tOrdaXaXQjWpVJ/5qj5fesN7t43C4Vey3rrWpjq+e4W4pdjUvrPsKPaFU/qqfjtpXRKY6zwQpStcEKgtu4SchONrT8nvU0Uffcdo1WWn/Cj/6eIK17tp6wW6LvSPuJdom6U3bxbyqutMEKMrTBCoKzwYqD2zg7gSPJniZqUjat+xr0UX5lvRX5PcHe2UfZlWSR2f7MstV+yq4wzHi2wQpSt8EKgltgwGQPeFI+0Yo4TTa0/J71Znf+S4TD+1uR2CFajZtsfc+x1zu7+DcVV9pgBRnaYAXBbdwk0GTVc6JWxND2E73Znddgjddbkb4j2uy4U/k9x142e8ou/k3FlTZYQYY2WEFwnScbtZokHKJV2TTZ0PJ71pvdeQzW1P2tSOwQLR2zS+h7jr1s9pSd+i9rs8EKkrfBCoLbuEmgyYomG1p+z3qzO73BKuutlv49wZ7jTpmy59jLZk/Zxb+puNIGK8BQASeDpWc/zMAx4Bi4zDGg+1bpnlV6/P3PfjaZ83x/K4+DU42DwNf0KiQ2WMFu8AxWEFznf82p1Uoi0Y1oVSb9a46W37Pe7ObFrS71vfLKD579bqtynh537/74QviP11tdOCB53GTHbc+x1zu7Wiyea58NVpC0DVYQ3MZNAk1WPSdqRQxtP9Gb3TyDJSNVTNX4WYZK29R6q1p2IH1HtNlxp/J7jr1s9pRdLRbPtc8GK0jaBisIrvNko1aThEO0KpsmG1p+z3qzazdYMk5jUzV8f/36S7tD661q2YHEDtHSMbuEvufYy2ZP2dVi8Vz7bLCCpG2wguA2bhJosqLJhpbfs97s2g3Wo0ePDhos5b+rV1/clZmslmxAYodoVbdsfc+x1zu7ltg81TE2WEGyNlhBcDZYcXAbZydwJNn3/CVH2z5Xf2wG6/d+75/vdBPRORvpO6Kd2/Zam2j5PccebTvVU3a1/jzXPhusIGkbrCC4jZuE7GRDy+9ZTxN1z23XaJ1b/zfeeH1yFuu//td7sxPA3PKHBRBtpO3DspfQ9xx72ewpu3FfnvO9DVaQtg1WEJwNVhzcxtkJHEn2NFGTsmndM/RT/4vwP/7H/3u/uH1uIBN+RJvBbsym59jLZk/ZjfvinO9tsAK0FXAyWHr2wwwcA46ByxoDH3/8i91bt27tvvWt/333b//t/7X727t3nfOc988eA4Gv6VVIbLCC3eAZrCC4jc/C6IuYbPSvOVp+z3qzmx97w/tbZfLrOe403jPZqXzCj2hp2Uuw0zmyNhusIHkbrCC4zpONWk0SDtGq7J4TNWVH9WbXbrBq97fK5EfHTbY+kx0dN72zU/uzNhusIHkbrCC4jZsEmqx6TtSKGNp+oje7NoM1dX+rTH6k37PjTuVnsqPtz2ZP2an9WZsNVpC8DVYQXOfJRq0mCYdoVTZNNrT8nvVmd9xg/frX/zh5f6tMfj3HXe/jNps9jbv4NxVX2mAFGdpgBcFt3CTQZEWTDS2/Z73ZHTZY77330725mrq/VSa/nuNOmTKTncon/IiWlr0EO50ja7PBCpK3wQqC6zzZqNUk4RCtyu45UVN2VG92dYOl9Va655V+2FmXB6e2TH503GTrM9nRcdM7u6l4Psd+G6wgZRusILiNmwSarHpO1IoY2n6iN7uLBkuGSr8reOfO7aP3tsrkR/o9O+5UfiY72v5s9pSd2p+12WAFyCvgZLD07IcZOAYcAz3GgO5pdeXKC7s7t287jzmXrzoGAl/Tq5DYYAW7wTNYQXCd/zWnVuvLNLoRrcqkf83R8nvWm903cXtsvVUtvjP59Rx3vY/bbPY07mqxfK59XRusJ0+e7G7devPZ72XdvPnq7sGDzw6ye/z4i52Ok0HSQ3cqjmw2WBFqX2vogMke8KR8ohW9LbNT+wk/s/tkfxmwZb1VbXRn8iP9TuNmCX0mO1r/bPaUXS2Wz7Wva4MloySD9fTp0z2vt9/+0e7atauT7HTcjRsv7+7ff39/jMyWjo+YLBusScxHP6ADJnvAk/KJVmC3zE7tJ/y2zu4fPvigeb1VbRBn8iP9TuNmCX0mO1r/bPaUXS2Wz7WvW4Ol2SuZnIcPP3/Gqrbv2Ye73e7TT391wYDdu/fu3nQNj2t5bYPVQql+DB0w2QOelE+0orlldmo/4bdldrq/ldZb6advolsmP9LvNG6W0Geyo/XPZk/ZReN9CV23BkvGSianzF4VGHNnpGywCrn2Zzrg6ICh5WfqadlbZqcIJfy2yq6st/q7n/ykfZBXjszkR/qdxs0S+kx2tP7Z7Cm7SiifbVe3BkuzUTWDpcuG5RLgMYparyVDpnPN3TyDNZfYN8fTAZM94En5RCuCW2an9hN+W2M3vpEztRMAACAASURBVL8VYZcde7Tu2fqeY693dt9885z/VbcGS+umiMGSsZJea7i0Fmu4aX/LQ4PGDzNwDDgG1hYDuvXCiy9+Z/e97/3J7q/fecd5yrm66xgYfj/39Lpbg7XEDJY6SrNdMlvjS43HOlEGjGzkrwKiVZ2z9foyIlt2/Un5RCtmW2ZHY3cr7MrvCX7yyS+fG2Y9xx6te7a+59jrnd1zg+DMb7o1WGUNlha2Dzf9L8G5/ytw7rotlWeDNaQ+73XPyUYtJQmHaFX2ltlR9ltgV9ZbPXr06MKg7Dn2aN2z9T3HXu/sLgyEM+7o1mBN/Y9BmaXh/ywcsqwtaNfMlczS3HVYNlhDsvNe95xs1FKScIhWZW+ZHWV/mdkN11t99dVvqwOy59ijdc/W9xx7vbOrDoYz7ezWYImP1k8N74MlAyWDNbVprdXYTOkSoWa95m42WHOJfXN8z8lGrSAJh2hV9pbZUfaXlV35PcG7d3988PcEe449Wvdsfc+x1zu7b755zv+qa4M1viu7jNLwTu7FUA0vGerz4Z3cdXPSueuv1E02WPFg7TnZqNUk4RCtyt4yO8r+MrKbWm9VG509xx6te7a+59jrnV1tLJxrX9cG61yQauXYYNWotO3rOdmohSThEK3K3jI7yv6ysTu03qo2EnuOPVr3bH3Psdc7u9pYONc+G6wgaRusILiNmwSarHpO1IoY2n6ivyzsWtZb1UYnYafzZfKjdc/WZ7Kj4653drWxcK59NlgB0go4GSw9+2EGjgHHwLliQL8n+N3v/v7u9dde2/9v6XOV63Ic45kxEPiaXoXEBivYDZ7BCoJL/ktYtVaiIBvRE63q3PNfwtnse2f3t3fv7q5efXE3vr9Vayz3HHu07tn6nmOvd3at4+MUx9lgBanaYAXBbdwk0GTVc6JWxND2E33P7LTeSj/WXLu/VetIJOxURiY/WvdsfSY7Ou56Z9c6Pk5xnA1WkKoNVhBccqJWrTMTBi2750Sdzb5HdsP1Vh999GF80C0Q95n86LjJ1meyo+Oud3Zo0ECxDVYQoA1WEJwNVhzcxtkJHEn2vX3Jje9vRdpO2UmfyS+77bT8THa072nbqZ6yU/uzNhusIHkbrCC45EStWtMBT/REq7rTZEPL71nfE7va/a2y2Wfyy247LT+THc15tO1UT9nFv6m40gYryNAGKwhu4yYhO9nQ8nvW00R9rrZP3d/qXOVPjexMftltp+VnslN/kvoTLS1bespuKp7Psd8GK0jZBisIboEBkz3gSflEK+I02dDye9avnd1wvVXt9wSz2Wfyy247LT+TnfIGqT/R0rKXyHk6R9ZmgxUgr4CTwdKzH2bgGHAM0Bjw/a0cQzSGLrM+8DW9CokNVrAbPIMVBLfxWRglQbL1/Jew2k3bT/RrZVdbb1WLEdL2Jdhn8stuOy0/kx3te9p2qqfsamPpXPtssIKkbbCC4Gyw4uA2zk7gSLKmiZqUPVX3qfVWtSA5Rfm1cqb2ZfLLbjstP5PdVOxN9fN4P2071VN24/ac870NVpC2DVYQ3MZNQnayoeX3rKeJesm2H1tvVRtdS5ZfO/+xfZn8sttOy89kp34l9SdaWrb0lN2xuD7l5zZYQbo2WEFwCwyY7AFPyidaEafJhpbfs34t7Mb3t2odSdnsM/llt52Wn8lO8UXqT7S07CVyXuv4OsVxNlhBqjZYQXAbNwk0WfWcqBUxtP1EvwZ2reutaqOLtH0J9pn8sttOy89kR/uetp3qKbvaWDrXPhusIGkbrCA4G6w4uI2zEziSrGmiJmWr7j986639jzVHf0+Qlk/1mfxo3bP1mezouOmdHUq4UGyDFQRogxUEt3GTQJNVz4laEUPbT/RZ7Mp6q+vXX9rV7m/VOpJI25dgn8VvibpvmR3l1zu71vF1iuNssAJUFXAyWHr2wwwcA46BqRjw/a0cG1Ox4f3tsRH4ml6FxAYr2A2ewQqC8wxWHNzG2QmcvpSi27lnYMbrrUjdaduX0J+b37CfzS4e97Tvs9nTuBvG0blf22AFidtgBcFt3CTQZEWTDS2/Z/052dXub9UzO432c/IbZxezs8Eax0QP722wgr1kgxUEl5yoVevMZE3LzvySy2ZHyz8Hu7Le6pVXfnBhvRXt+2z9OfhNZZXsttPyM9nRcUPbTvWU3VRMnWO/DVaQsg1WEJwNVhzcxtkJHEnWNFEfK/vY/a2O6Y8FRrb+1PwOtT+77bT8THZ03NC2Uz1ldyiuTv2ZDVaQsA1WENzGTUJ2sqHl96ynifpQ28frrWqj45C+dvx4X7b+lPzGbR2/z247LT+TnViS+hMtLVt6ym4cS+d8b4MVpG2DFQS3wIDJHvCkfKIVcZpsaPk960/FrrbeqjY6emaXHXtm5zVYtTG19n02WMEessEKgtu4SaBfFKcyCa29SeufqV+a3aH1VjWemW1XfWj5S/OrMZraR+uerc9kR/u+d3ZTMXWO/TZYAcoKOBksPfthBo6B7cWA72+1vT73OM/r88DX9CokNljBbvAMVhCcZ7Di4DbOTuD0JRfdlppFaFlvVasjqTtt+xL6pfjV2BzbZ3bxuKd9n82ext2x2Drl5zZYQbo2WEFwGzcJNFnRZEPL71m/BLvW9Va10dEzO7VnCX41Li37zM4GqyVO1nbMqg3Wxx//Yn8pTmZGj3v33j3I7+nTp7u33/7RM821a1d3n376q+c043PqvDpu7maDNZfYN8dnJmrVIjNZ07K3zI72HWGn9Vbf//6f7mr3t/omsg+/on2frSf8aN9lt52Wn8mud/aU3eFRedpPV2uwHjz4bG98ikF6/PiL/XsZpKnt1q03dzdvvrqT0dImrYyQzlU2mTQdRzcbrDhBOmBossvU07K3zE4RR/hF2en+Vlevvrh7/bXXdjJa0Y3UnbZ9CX2UX+FF2k+0S7Sdlp/Jjraftp3qKbsSfxnPqzVYNSNU21egPXny5IKZ0mcyU0NDdePGy7v7998vsvCzDVYYXeqlBtWaDniiJ1rVnSYbWn7P+gg7rbfSWP/kk1+mxk123GbHXs9xl82Oxk42+8i4VZvXsK3WYMkUjY2QZq/mXs4bG6zaZcNIR9hgRah9raEDJnvAk/KJVvS2zE7tJ/zmsrt798f7matHjx7tA5eUTeu+Bv1cfntog38IP6LdOjva/mz2NO4GIXj2l6s1WLWZJl3qk7EplwCP0dJxMlTlsuLDh5/v9TJdOo8eeq3Zr7mbDdZcYt8cTwdM9oAn5ROtCG6ZndpP+LWy02VArbUar7ciZdO6r0Hfyk91rW2EH9GqLtn6THa0/b2zq8Xiufat1mDJGI1nsOYaLF1S1JqsstXWZMl8ycwNt2K+jj1r0PhhBo6ByxMDd27f3n3729/afe97f7L763fe8fh2jnMMrCAGht/PPb1ercGiM1jlcmLL7FTksqFnsOJh3vNfc2o1+YuOaFX2ltlR9sfYDddb1aKb9l3v+mP8asyG+0j7iZbGzRL6THa0/tnsKbthDJ779WoNli7daQZquGkGSmbo2FbMlf7nYcs2vIzYcryOscFqJXXxODpgsgc8KZ9oRXLL7NT+KD/9T8BXX/2z/WL1r7767YWgHK+3unAAKLucK1r3tegzY8/sfB+sMg56el6twar9j0EZJxmvqU1rrvS5DFPNXOmc48uB0sgsaX3WnM0Gaw6t54/NTNSqSWaypmVvmV2k78rvBWq8Dh+6Yai2qfVW+w9H/9C+612fGXtmZ4M1Go5dvF2twSoL0of3wZI5ksma2rTeSuZq6rKgTJeS7PC+WDrfcJ3W1LnH+22wxkTa32cmatUyM1nTsrfMLtJ3mpkaGqvh6//+3//b/n8J6piW+1vRvutdnxl7ZmeD1f4Ns54jV2uwhEiL3IcJUXdpH256Xy4ZlgXsw+PL63KMtDJXMlTlM52j9X8lDsuWnmwkYRCt6pytz0zU2e2n7LfMbm7fyTSVcT71rPtbtW6073rXZ8ae2dlgtY7TNR23aoO1JlDjuthgjYm0v89M1KplZrKmZW+Z3dy+0/2rpoxV2d8etblxM7fttXb1HHu07tn6nsdt7+xqY+Fc+2ywgqRtsILgNr5QmyarnhO1Ioa2f45ei9mLkao96+dv5mxzyq6dt3d9ZuyZnWewamNq7ftssAI9pMGuhK1nP8zAMbDeGNAPNNfMlfbptwXdd+vtO/eN+6bEQOBrehUSG6xgNyhBk02BE92IVmVm6zP/Es5uP2W/ZXaRvtPtGa5c+fYFk6W7tLcsbB+OUdp3veszY8/s4t8XkXGzprincTdsy7lf22AFidtgBcH5EmEc3MbZCdzcL1r9D8F/9a9e3Ol/DP7RH/2b3RtvvL6/F1akE+aWPS6jdz39oiPtJ9pI3Czdd5nsaPuz2VN2474853sbrCBtG6wguI2bBJqsaLKh5feiH97fqsxUmR2bBcnk10vcTWXFTHaqE+FHtLRs6Sm7qT45x34brCBlG6wguAUGTPaAJ+UTrYjTZEPL70Gvy4JawK7Zq+FmdjZYw3iY85rGfc+xR9tO9ZTdnH5e+lgbrCBRG6wguI2bhOxkQ8tfu778nqCexxtN1Gtv+7i94/e0/pn8aN2z9ZnsFAek/URLy5aeshuPg3O+t8EK0rbBCoJbYMBkD3hSPtGKOE02tPw16zVjpZkrzWDVNrPzDFYtLlr20bjvOfZo26mesmvp31MdY4MVJGuDFQS3cZOQnWxo+WvU19Zb1aKTJuo1tr3Wzql9tP6Z/Gjds/WZ7BQPpP1ES8uWnrKbGg/n2H92g6Xf/pM50UM/WRP5mZpzgDlUhgJO9dezH2bgGMiLgX/44IPdlSsv+J5WzkXOxZc4Bg59H6/5s2aDJTM0/i3AuQ2T/tatN/cy/fCyfiPw0I83zz3/OY/3DFacNv2LRIaGbJl6WvaW2anPh/wOrbeqxYfZsXGTyW/Y77W+PbYvW5/JbjxujrEaf947u3F7zvm+2WDRSslI3bjx8nOnkeGScetxs8GK91rPyUatJgmHaFX2ltkN2R9bb1WLTrOzwarFRcu+LY9b2naqp+O2pX9PdcxZDJYuA9Zmq2SwxqbrVA1d+rw2WHGidMDQAZupp2VvmZ0iTn+o6S7skTuxb51dz7FH656t7zn2emcX/6biymcG68mTJ/vLdzIOemhm6cGDz56VMLxEeP/++/vP791799l6Kl360zlqW1l3NV5vpXPaYNWIHd6XHfC0/J6TjXqGtJ9oVfaW2X39szcvXLi/1eHR8s2nW2ZH4zY79ui4ydb3HHu9s/smA5z/1TODJYNU1kepGjJPmnUq29hgyYTpGG0yVjJK5X3RlGfNVBXjNn7WZz1uagfZSNASreqcre852VB+lP1W2ZX1Vn9792542G2VXQHWc+zRumfre4693tmV+M94fmawZJCGBmtcmbHBGpovHStzpWNqm47VrNdw0+yYTMp4//CYNb+2wYr3Ts/JRq0mCYdoVfYW2Q3XWxF+W2Q3HKWEXXbs0bpn63uOvd7ZDcfAuV8/M1jF8Mg4yGiNjc/YYI3NVLlsOG6AZrd0zvH/FpQh0379b8IeNxuseK/1nGzUapJwiFZlb4ld7f5WhN+W2NVGJ2GXHXu07tn6nmOvd3a1sXCufc8MVilQRkhmSQZCM09lXVXUYD18+Pn+XJ9++qtSxP7eVzr3oRmzZwev8IUCTnz07IcZOAaWjwHf32p5po5TM+01BlZoA5qqdMFgDVXDS3tRg6UZKpmRocEqi957nb0SI89gDSNl3uue/5pTS5WkohvRqswtsCvrrWq/J0j4bYHdobgk7LJjj9Y9W99z7PXO7tCYOPVnzwyW1mANF5yXS4blfxJGDZYaIG2ZrZLRGhuuUzfyFOe3wYpT7TnZqNUk4RCtyr7s7IbrrWoRRvhddnY1XsN9hF127NG6Z+t7jr3e2Q3HwLlfPzNYmk2SCZJx0EOGa7huihgsnVvnK+cdzmadu8FLlWeDFSfZc7JRq0nCIVqVfVnZ1dZb1SKM8Lus7GqcavsIu+zYo3XP1vcce72zq42Fc+17ZrDOVeBlKccGK96TPScbtZokHKJV2ZeRne5vdfXqi033tyL8LiO7OaOQsMuOPVr3bH3Psdc7uzljZOljbbCCRG2wguAuqUlopUGTVc+JWozG7T+03qrGdKyvHTO177Kxm2rn1H7CTufM5Efrnq3PZKe+I+0nWlr2EnGnc2RtNlhB8jZYQXDJiVq1zkwYtOyeE/WY/bH1VrUII/wuE7sam2P7CDudO5MfrXu2PpOd+o60n2hp2UvEnc6RtdlgBcnbYAXBJSdq1TozYdCye07UhX3reqtahBF+l4FdjUnrPsJOZWTyo3XP1meyU9+R9hMtLXuJuNM5sjYbrAB5BZwMlp79MAPHQHsM+P5W7awcV2blGPg6BgJf06uQ2GAFu8EzWEFwyX8Jq9ZKWmQjeqJVnXv+S3jueqtaHxF+PbMTC9L2JfSZ/LLbTsvPZEf7nrad6im7Wh451z4brCBpG6wguM5NglpNEgbRqmyabGj5UX1Zb6UZLLJFy++ZXeFF2q5zUH1m7NG6Z+sz2dG+751dGT8Zz10bLP2Mz/DeXbpXV7kx6hRM3YOr3JNLJkn6p0+fTh0+ud8GaxLN0Q96TjZqHEk4RKuye2M3Xm9F20/0vbEbDyTSdhq32bGX3XZafs+xR9tO9ZTdeByd833XBqvcIb4YJN2JXj/vM7WV30UsN1CVTgZL55m72WDNJfbN8XTA0AGbqadl98Sudn8r2n6i74ndN6Plm1ek7ToL1Wfyo3XP1meyo33fO7tvRtD5X3VrsDR7JZMj01S22r7ymZ7v3Xv3gpkqpmt4nqFm6rUN1hSZ4/t7TjZqHUk4RKuye2E3td6Ktp/oe2E3NYJI22ncZsdedttp+T3HHm071VN2U+PpHPu7NVjFGJXZqwJLM1hlhqrsO/RczmODdYjS859lDxhafqaelk2TDS2/RV/WW2kGa7y16Mea4Xui74HdsK3j16TtOhfVZ/Kjdc/WZ7Kjfd87u/E4Ouf7bg1W+dHoscHS5b77999vZqhjD11WnDqRZ7CmyBzf33OyUetIwiFalb1mduP1VrVIoO0n+jWzq7Ea7yNt17moPpMfrXu2PpMd7fve2Y3H0Tnfd2uwNEslk0MMli4pylyNf3xa5215aND4YQaOgb/Z3bl9e/ftb39r973v/YnHhPOCY8AxsGgMnNMULVlWtwaLzmDJmOl/E2pdVmTzDFaE2teanv+aUwvIX3REq7LXyG5qvVUtQmj7iX6N7GqMpvaRtuucVJ/Jj9Y9W5/JjvZ97+ymxtM59ndrsMraKc1CDTeZpmNrsKTRpUT9r8PoZoMVJbdOkzCnNSThEK3quLZEfWi9VY0pbT/Rr41djc+hfaTtOi/VZ/Kjdc/WZ7Kjfd87u0Nj6tSfdWuwpv7HoC75HVqwrpkvHUPMlTrFBisemj0nG7WaJByiVdlrYffVV7/dvfLKD/YPrb1q3Wj7iX4t7FpZjY8jbde5qD6TH617tj6THe373tmNx9E533drsARJ97Aa3ihUl/sOLVgvlxWjlwWHHWODNaQx73XPyUYtJQmHaFX2Gtg9evRod/XqizvNXs3daPuJfg3s5vIaHk/arvNQfSY/WvdsfSY72ve9sxuOoXO/7tpgPX78xf5Sn8yOHro8OLyTuz7X/nLJcHgH96Ipz+WY1g6QjmwkaIlWdc7W95xsKD/KPpvdO3/1V/sxpXVXkY22n+iz2ZG607hbQp/Jz+z6/f1U2nc07iJ5ailN1wZrKQiR89hgRah9raEDhg7YTD0tO4udLgNqxurKlRd2tftbtUYDbT/RZ7ErbEjddY5sfSa/7LbT8jPZ0dihbad6yq6Mv4xnG6wgdRusILiVXOaK15590WUnm0j5w/VWc2d6x5wj5Q/PQfQ0UZOy1Ybe9Zn8zM4zWMM80MtrG6xAT2mwy2Dp2Q8zuMwx8Pc/+9l+1ur1115zrHu8OwYcAykxEPiaXoXEBivYDZ7BCoLzDFYc3JnZffLJLy+st5KZJFumPnMGRswy275E+Zn8zC5v3GWzp3FH8hXV2mAFCdpgBcGd2STUapmZMGjZNNm0lF/WW+l/Co7XW7Xoa8zLvkz9OdiVdtaeM9uu+tDyM/nRumfrM9nRvu+dXW0snmufDVaQtA1WEJwNVhzcGdgN11vV7m+VnWxJ+T1/ySloSNuX0Gfyy247LT+THe172naqp+xQwoViG6wgQBusILgzmIRjNaMDnuiJVu2iyeZQ+S33tzqkP8Zdn2fqT8lu7W1fgn0mv8y46Z0drX82exp3LWPzVMfYYAXJ2mAFwZ3YJLTUKjNh0LJpspkqv7beqsZySl87trYvU38qdrV21vZltl31oeVn8qN1z9ZnsqN93zu72lg81z4brCBpG6wgOBusOLgTsCvrra5ff+nCeqtaRbOTLSm/5y859QVp+xL6TH7ZbaflZ7KjfU/bTvWUXS2PnWufDVaQtA1WENwJTMLcmtABT/REq3bSZDMsv6y3euON13e19VY1rkN97fNj+zL1S7I71s7a55ltV31o+Zn8aN2z9ZnsaN/3zq42Fs+1zwYrQFoBJ4OlZz/MoMcYKPe3+uFbbzmGPY4dA46BVcdA4Gt6FRIbrGA3eAYrCG7hWZhILWSIyEb0RKs6L/GXsNZb6RYMkd8TpPXP1C/BLituVG4mu6ViL8ovu+20/J5jj7ad6im7aMwtobPBClK0wQqCW8gkxEvP/aLKTDa6DKg7sreut6oxpvXP1NNEnVl39UV2+Zn8sttOy89kR2OHtp3qKbtaHjvXPhusIGkbrCA4G6w4OMCurLf6/vf/tHm9Va2iNFlm6mmizqy7+iK7/Ex+2W2n5Weyo7FD2071lF0tj51rnw1WkLQNVhAcMAmlRDpgM/W07EiyKfe3eu+9n6Z/SdP2E32EXYk5PZOyL4M+k1/v7DPZ0djLZk/ZDcfwuV/bYAWJ22AFwdlgxcEF2I3XW2Uny8zyaaLOrLuCJrv8TH7ZbaflZ7KjsUPbTvWUHUq4UGyDFQRogxUEFzAJ45LogM3U07Jbk83U/a1o+T3rW9mN462877ntagOtfyY/WvdsfSY72ve9syvjN+PZBitAXQEng6VnP8xgbTHw0Ucf7heya73Vxx//wjHqceoYcAx0HQOBr+lVSGywgt3gGawgOM9gxcE1sBuut6oVJDNItp71Pc8iqM+y2Wfyy247LT+THY0d2naqp+xIvqNaG6wgQRusILgGk3DszHTAZupp2YeSzXi9VY0jLb9n/SF2NVbjfT23XW2h9c/kR+uerc9kR/u+d3bjcXzO9zZYQdo2WEFwNlhxcBPsptZb1QrKTpaZ5ff8Jae+zGSn8jP5Zbedlp/JjsYObTvVU3a1PHiufTZYQdI2WEFwyYlataYDnuiJVnUfJ5tyf6vW3xOk5fesH7ObG8E9t32JuM/k1zv7THa077PZU3Zzx/mSx9tgBWnaYAXBVUzC3DNlD3hSPtGK0zDZHFtvVeNKy+9ZP2RXY3NsX89tV9to/TP50bpn6zPZ0b7vnd2xcX3Kz22wgnRtsILgRiYhcpbsAU/KJ1qxKom6Zb1VjS0tv2d9YVfj0rKv57arfbT+mfxo3bP1mexo3/fOrmVsn+oYG6wgWRusILiBSYieIXvAk/KJVrz++p13dnfv/jj8e4K0/J71PX/Jqe+z2Wfyy247LT+THY0d2naqp+yi3zNL6GywAhQVMDJYevbDDM4RA7qf1e2//MvdlSsv7K5d+z92/+9/+S+OPY8/x4BjYBMxEPiaXoXEBivYDZ7BCoLzDNZscF9++eXuX/7LK3tTr7grD81kzd1kBsnWs57+Jdxz29XntP6Z/Gjds/WZ7Gjf986O5DuqtcEKErTBCoKzwZoN7o/+6N88M1XFXJXnDz/8+azzZSfLzPJ7/pJTJ2eyU/mZ/LLbTsvPZEdjh7ad6im7WQly4YNXbbB0WaR8kej53r13m5v/6ae/2l27dvXC8eNz6ry14y4IRzukIxsJOqJVnbP1dMBk15+UP0er+1v95V/+P8+NgeF40OtXXvnBrDCcU37txD3rtxx3S4z7TH49x53YZ7KjfZ/NnrKr5bFz7VutwXrw4LO98ZFR0vb48Rf79zJIxzZpp4yTTNqtW28eO8XRz22wjiKaPIAOmOwBT8pv1Zb7W8lAjU3V+P0k6MoHreVXpPtdPeu3HHfqPNp3mfxo3bP1mexo3/fObiqXnWP/ag1WzQjV9g0hPX36dPf22z/aGyg912ambtx4eXf//vtDWei1DVYI217Uc7JRA0jCadEO728lozU2VMP3usHonK2l/EPn61m/5bijcSt9Jr+e4y6bHe37bPY07tT+rG21BkuzTGMjpNmrmmkq8DTLJWOlTdrasdpXZsWKLvJsgxWh9rWGDpjsAU/KP6at3d9KJmpoqoavf/3rf5zVEcfKP3aynvVbjjv1K+27TH607tn6THa073tndyynnfLz1Rqs2kxTufSnmapjW81gPXz4+f6LSuatfEnp9ZMnT46d7sLnNlgXkDTv6DnZqJEk4UxpD/2eoD6rXSr0/yJsDrn9gVuOOxq30mfymxo3rRGQrc9kR/u+d3atMXKK41ZrsDTTNJ7BogZLM1cyRjpP2TQrJjM33Ir5OvasQeOHGdAY+NF//s+7P/iDazv9b0HdSHTqfH/++uu7V1/9s/3jzu3bk8dN6b3fseoYcAz0GAPD7+eeXq/WYJ1iBmuqYyKXDT2DNUXz+H4NcLJl/0VFyh9rh+utWphsmZ34jPm1MCvHmB27B1omP9LvNG6W0Geyo/XPZk/ZlfGf8bxag6VLd+PbMkzdeqEGrnaJsHac9slgtfzvxKHeBmtIY95rOmCyBzwpf6itrbc6RnLL7MRmyO8Yq/HnZmeDNY6J1vck7lRGZwpieAAAIABJREFUz7FH2071lF1rH5/iuNUarNr/GJQJkvFq2WoGS+ccXw7Uei6ZJa3PmrPZYM2h9fyxdMDQAZupV9mH1ls9T+riuy2zEw3Sd2Zng3VxRLXtIXGnEnqOPdp2qqfs2nr4NEet1mCVBenlf/zpfwjKHLXONNUMls4hYzReg3Xz5quz6dpgzUb2TEAHDB2wmfqPPvpwv2Bd/zNQRmvutmV2YkX6zuxssOaOt3I8iTudo+fYo22nesqu9GHG82oNlmDIJMnIlEe5BUMBNXWvq6LVpb/xJnMlQzU8Z8v/ShyfxwZrTKT9PR0wdMBm6bXeSj/W/N57P22HNTpyq+wKBtJ3ZmeDVeJo7jOJO5XVc+zRtlM9ZTe3r5c8ftUGa8mGLn0uG6w4UTpg6IDN0Jf1Vn97924cXOeJWg3PYF+AbzHuStuXYJ/JLzNuemdH65/NnsbdcAyc+7UNVpC4DVYQ3MZMwni9FU1WNNnQ8nvWm51nsKJZi8Z9z7FH2071lF20z5fQ2WAFKCpgZLD07IcZTMWA1ltdv/7S7vvf/9P92sGp47zfMeQYcAw4BqZjIPA1vQqJDVawGzyDFQS3kRmsqftbKYmSjf41R8vvWW92/cZez3Gn8d5z7GWzp+xIvqVaG6wgQRusILjOk41afSzhlPVWtd8JPKY9RpUmG1p+z3qzs8E6Nr6mPqdx33Ps0bZTPWU31afn2G+DFaRsgxUEd4kNltZb3blze39Z8Msvv6wCyk42tPye9TRR99x2BSOtfyY/WvdsfSY72ve9s6sm4jPttMEKgrbBCoK7pAZLhko/yHzs/lY0WfWcqBUxtP1Eb3aewYpmLRJ3KrPn2KNtp3rKLtrnS+hssIIUbbCC4DpPNmr1OGH85jf/tLt69cWm+1uNtXMp0mRDy+9Zb3Y2WHPHWzmexn3PsUfbTvWUXenDjGcbrCB1G6wguEtmsD788Od7c1Vbb1UjlJ1saPk962mi7rntikVa/0x+tO7Z+kx2tO97Z1fLw+faZ4MVJG2DFQR3SQxWy3qrGiGarHpO1OJB20/0ZucZrNqYbNlH4k7n7zn2aNupnrJr6d9THWODFSCrgJHB0rMf22PwDx984PtbOfY99h0DjoEzxUDga3oVEhusYDd4BisIrvO/5rTeivyeYPZfc7T8nvX0L+Ge267RSuufyY/WPVufyY72fe/s4t9UXGmDFWRogxUE17HBKuutyO8J0mTVc6JWxND2E73Z+RJhNGuRuFOZPccebTvVU3bRPl9CZ4MVpGiDFQTXYbIZr7ciCYNoRZwmG1p+z3qzs8GKZi0a9z3HHm071VN20T5fQmeDFaRogxUE15lJqN3fiiQMohVxmmxo+T3rzc4GK5q1aNz3HHu07VRP2UX7fAmdDVaQog1WEFxHJmHq/lYkYRCtiNNkQ8vvWW92NljRrEXjvufYo22nesou2udL6GywghRtsILgOjEJZb2VTNZ4IwmDaFUPmmxo+T3rzc4GazyWW9/TuO859mjbqZ6ya+3jUxxngxWkaoMVBLdyk1DWW+lnb07xe4LZyYaW37OeJuqe267RSuufyY/WPVufyY72fe/s4t9UXGmDFWCogJPB0rMfl4dBub/VzZuv7j7++BfuW8e3Y8Ax4BhYQQwEvqZXIbHBCnaDZ7CC4FY6g1XWW+nS4LGN/EVHtKpXz38Jq/60/URvdr5EeGxsT31O4q73cUvbTvV03E716Tn222AFKdtgBcGt0CQcWm9VayVJGESrutBkQ8vvWW92Nli18dyyj8Z9z7FH2071lF1L/57qGBusIFkbrCC4FZmElvVWtVaShEG0qgtNNrT8nvVmZ4NVG88t+2jc9xx7tO1UT9m19O+pjrHBCpK1wQqCW4lJKPe3unPn9k5Ga85GEgbRqo402dDye9abnQ3WnHE+PJbGfc+xR9tO9ZTdsB/P/doGK0jcBisIbgUm4e9+8pPd1asv7lrWW9VaSRIG0aouNNnQ8nvWm50NVm08t+yjcd9z7NG2Uz1l19K/pzrGBitI1gYrCC7ZJMhU6ceaa/e3am0RSRhEq/rRZEPL71lvdjZYrWN8fByN+55jj7ad6im7cV+e870NVpC2DVYQXJJJGK630u0YyEYSBtGqzjTZ0PJ71pudDVZ03NO47zn2aNupnrKL9vkSOhusAEUFjAyWnv1YPwPf32r9feRx5D5yDDgGpmIg8DW9CokNVrAbPIMVBHfmWZja/a00iMlG9ESrOtO/5mj5PevNjsV9Jr+e4673cZvNnsYdyfVUa4MVJGiDFQR3RpMwdX+rzIRBy6bJhpbfs97sbLCiWYvGfc+xR9tO9ZRdtM+X0HVtsJ48ebK7devN/eU6GR79xMmDB581cyk/idIsGBxogzWAMfMlHTDHBuxwvVXt9wSP6Y81h+iJVvU6NbtTtl3npu0nerOzwToW31Ofk7jTOXuOPdp2qqfspvr0HPu7NlgySDJYT58+3bN6++0f7a5du9rErRgz/eZcZLPBilD7WkMHzKEB23J/q0P6llYRPdGqbqdkd+q26/y0/URvdjZYLTFeO4bEnc7Xc+zRtlM9ZVfrz3Pt69ZgafZKJufhw8+fsarte/bh/3rx6ae/2t248fL+x3ylt8EaEzr+PnvATJVfW29Va82UvnZsbR/RE63qQpMNLb9nvdnZYNXGc8s+Gvc9xx5tO9VTdi39e6pjujVYMlYySGX2qgDSDNYh03Tv3ru7x4+/2OtssAq1ec/ZA6ZW/tR6q1rLavracVP7iJ5oVR+abGj5PevNzgZrakwf20/jvufYo22nesruWN+e8vNuDZZmomoGS5cN799//ygzGTMbrKOYqgdkD5hh+cfWW9UaMNTXPj+2j+iJVvWiyYaW37Pe7Gywjo3tqc9p3Pcce7TtVE/ZTfXpOfZ3a7A0S3Uqg6XztjzU8X7kMbhz+/buD/7g2u6P//j67q/fecd94Xh0DDgGHAOXMAbOYYZOUUa3BsszWPFwoH9RUD39i0Tlt663qlGi9Sd6olVblmBXY9K6j9Y/U292nsFqjfPxcTRue4492naqp+zGfXnO990arLIGSwvbh1tZwD7cV3vtS4Q1Km37sgeMZq70Y83R3xOk9Sd6olXv0GRDy+9Zb3Y2WG0Z7uJRNO57jj3adqqn7C725vn2dGuwpv7HoBa5D/9n4RRKG6wpMsf3Zw2Yst7q+vWXdrX7Wx2v+ddH0PoTPdGq9jTZ0PJ71pudDVZrjhgfR+O+59ijbad6ym7cl+d8363BEiTdy2p4Hyz9D8HW+2DZYMXDLGPADO9vdeh/iba0itaf6IlWbaPJhpbfs97sbLBa8kPtGBr3PccebTvVU3a1/jzXvq4Nlm63oP81WBak6/Lg8E7u+lyf1b6QbbDiIXbuATNeb0XLz9TTsmmyoeX3rDc7G6xo1qNx33Ps0bZTPWUX7fMldF0brCUARM8h40Y2EnREqzpn6r/66re7//QXf9GMrnZ/q8z6U3607jTZ0PJ71pudDVZz4hkdSOO+59ijbad6ym7UlWd9a4MVxG2DNQ+cLvFp7VSZbdTze+/9dPIkZb3VK6/84MJ6KzpgM/W0bJpsaPk9683OBmsy4Rz5gMZ9z7FH2071lN2Rrj3pxzZYAbwKGBkEPftxnMFHH324u3LlhefMVTFaP3zrrQsM/+GDD/ZmrPwYtxkfZ2xGZuQYcAxc1hgIfE2vQmKDFewGGQSyaSBEN6JVmefW373746q5KiZLlw3LNl5vVfYPn89d/2HZek3KJ1qVTf+ao+X3rDe7eM7Jjr2e4y6bXXbOon1Hx63an7XZYAXJ22C1g3vjjdcPGqxHjx7tT1Zbb1UrhQ7YTD0tmyYbWn7PerOzwarlk5Z9NO57jj3adqqn7Fr691TH2GAFydpgtYM7ZrD+5//8/3Z37tze1dZb1UqhAzZTT8umyYaW37Pe7GywavmkZR+N+55jj7ad6im7lv491TE2WEGyNljt4LSYvVwOHD+/+OJ3dv/u331/b7C0sL1lowM2U0/LpsmGlt+z3uxssFryS+0YGvc9xx5tO9VTdrX+PNc+G6wgaRusdnAyTvppm7G50vsrV76906XBORsdsJl6WjZNNrT8nvVmZ4M1J88Mj6Vx33Ps0bZTPWU37Mdzv7bBChK3wZoHTiZLi92L0frDP/zXu+9854XQ7wnSAZupp2XTZEPL71lvdjZY87LWN0fTuO859mjbqZ6y+6YXz//KBivI3AYrBk5G64//+HrzeqtaKXTAZupp2TTZ0PJ71pudDVYtn7Tso3Hfc+zRtlM9ZdfSv6c6xgYrQFYBI4OlZz/aGfj+Vu2sHFdm5RhwDDgGvo6BwNf0KiQ2WMFu8AzWPHDD+1vRv0iUdMiWqadlb5md+pzwMzs2bjL5kX6ncbOEPpMdrX82e8pO7c/abLCC5G2w2sHpfxFq7ZVMljY6YLIHPCmfaLfOTu0n/LYcd5RdduyRfl+i7bT8nmOPtp3qKTv1f9ZmgxUkb4N1HJzWW+keWOP7W9EBQwdspp6WvWV2ijjCz+w8g3U8a9WPIHGnM/Yce7TtVE/Z1Xv0PHttsIKcbbAOgys/7qwbiMpoDTc6YOiAzdTTsrfMTjFE+JmdDdYwD815TeJO5fQce7TtVE/ZzennpY+1wQoStcGaBvfrX//j/pLg1P2t6IChAzZTT8veMjtFHOFndjZY01nr8Cck7nTmnmOPtp3qKbvDPXvaT22wgnxtsOrgxuutakfRAUMHbKaelr1ldoolws/sbLBq+ahlH4k7nb/n2KNtp3rKrqV/T3WMDVaQrA3W8+Cm1ls9f9TX7+iAoQM2U0/L3jI7RQ/hZ3Y2WLV81LKPxJ3O33Ps0bZTPWXX0r+nOsYGK0BWASODpWc/Ptnp/lbf/e7v727efHX38ce/MBPHhWPAMeAYcAwsFgOBr+lVSGywgt3gGayvwR1bb1XDS/8ioX8RZepp2Vtmp1gi/MzOM1i1fNSyj8Sdzt9z7NG2Uz1l19K/pzrGBitI1gZrt2tZb1XDSwcMHbCZelr2ltkplgg/s7PBquWjln0k7nT+nmOPtp3qKbuW/j3VMTZYQbJbNli6DFi7v1UrSjpg6IDN1NOyt8xO8UX4mZ0NVmuOGh9H4k7n6jn2aNupnrIb9+U539tgBWlv1WDp/lZab1W7v1UrSjpg6IDN1NOyt8xO8UX4mZ0NVmuOGh9H4k7n6jn2aNupnrIb9+U539tgBWlv0WCV9Vbv/NVfBal9LaMDhg7YTD0te8vsFD2En9nZYEUTF4k7ldlz7NG2Uz1lF+3zJXQ2WEGKWzNYZb3Vo0eP0Jdc78lG9ScJg2i3zo6yp4ma9l3v+kx+ZsfMMeFHtHTMLpHzdI6szQYrSH4rBmt4f6uvvvrtnhYdcJmJWg2g9Sd6olXdt8yO9p3ZsS/pTH503GTrM9nRcdM7O7U/a7PBCpBXwMlg6fkyP8r9rV5/7TXf3+qS9/VljmO37XLnKffv5e/fwNf0KiQ2WMFuuOwzWGW91Sef/PICISU0svX815zaTdpPtCp7y+woe7Prd9zScZOt7zn2emdHvquodtUGS7cDkJEpj3v33j3a3rff/tGz469du7qfeRmKxufUuXXc3O0yG6zheqsaFzrgek424kHaT7Qqe8vsKHuzs8Gq5bOWfVset7TtVE/HbUv/nuqY1RqsBw8+2xufTz/91b7tjx9/sX8vgzS13b///v7nWnSstmKmHj78/JlEJu3WrTefvY++uIwGq7beqsYne8DQ8jP1tGyabGj5PevNzgarls9a9tG47zn2aNupnrJr6d9THbNag1UzQrV9QzA3brx8YcZqvE/vZcTodtkMlu5vdf36S7u7d3+8k9E6tGUPGFp+pp6WTZMNLb9nvdnZYB3Ka4c+o3Hfc+zRtlM9ZXeoX0/92WoNlmaZxkZIM1KHLufpM818DTddMhzOWOmYMis2PG7u68tksA6tt6pxyR4wtPxMPS2bJhtafs96s7PBquWzln007nuOPdp2qqfsWvr3VMes1mDVZppknmRsnj59eoHHkydP9p+NDVa5bCiBLhVKL8Ol5/Ja2rmbtGQjQUe0qvNQf2y9Va2NQ33t82P76ICh5WfqadlbZjeO3WNxNv7c7GywxjHR+n7L45a2nerpuG3t41Mct1qDpZmm8QzWIYOldVcyPYcMlmauxsdoVkxmbu7Wu8FqXW9V45I9YGj5mXpaNk02tPye9WZng1XLZy37aNz3HHu07VRP2bX076mOWa3BOsUM1hTE8WVDmaeWhzq+x8ed27d3L774nd33vvcnu79+550u29Ajd9e5z/HifnO/OQZyY2Dqu3vt+1drsHQZb3xbBs1AyQxNbWOjpOOOLYzXMdId+t+JtfJ6ncHSeqsrV17Y1e5vVWtnbV/2XyS0/Ew9LVuJnmy0/J71ZucZrOjYoXHfc+zRtlM9ZRft8yV0qzVYNWMkEzRcsD4GoFmvsVHS8WWfzjm+HKj1XDJLw1s5jM9be9+jwSrrrf7+Zz+rNal5X/aAoeVn6mnZNNnQ8nvWm50NVnOSGx1I477n2KNtp3rKbtSVZ327WoNVFqSX//GnNVY1AzWkJSOlY8p9sMqaq2Keauu0pLl589XhaZpe92SwxuutaMBTPR0wtPxMPS17y+w0MAk/s7PBakrulYNI3Ol0PccebTvVU3aV7jzbrtUaLBHQIncZmfLQLReGm94PLxlqNmr4PwSlK7NXRadF8DJUw3PW/ldiOX7qWXqykaCbo63d32qOvtZGqqcDhpafqadlb5mdYpHwMzsbrFo+a9lH4k7n7zn2aNupnrJr6d9THbNqg3WqRi9x3h4M1tT9rWjAUz0dMLT8TD0te8vsNG4JP7OzwYrmfhJ3KrPn2KNtp3rKLtrnS+hssIIU126wynqrR48eXWghDXiqpwOGlp+pp2VvmZ0CmfAzOxusC8mwcQeJOxXRc+zRtlM9ZdfYxSc5zAYrgFUBI4Ol57U9dEn0+9//0/3P3nz00Yerq9/aeLk+64th94n7xDHgGBjGQOBrehUSG6xgN6xxBqu23qrWPAUu2aie/kVCy8/U07K3zE4xS/iZHRv3mfxIv9O4WUKfyY7WP5s9Zaf2Z202WEHyazNYU+utas3rfcBk15+UT7TqS5psaPk9683OBquWD1v20bjvOfZo26mesmvp31MdY4MVJLsmg3VovVWteTTgqZ4OGFp+pp6WvWV2imXCz+xssGr5sGUfiTudv+fYo22nesqupX9PdYwNVpDsGgzW+P5WrU2hAU/1dMDQ8jP1tOwts1N8E35mZ4PVmiPHx5G407l6jj3adqqn7MZ9ec73NlhB2tkGq3W9Va15NOCpng4YWn6mnpa9ZXaKZcLP7GywavmwZR+JO52/59ijbad6yq6lf091jA1WkGymwfrbu3d3V6++GP49QRrwVE8HDC0/U0/L3jI7DVXCz+xssILpHsWdyuw59siYo2N2CXbRPl9CZ4MVpJhlsLTeSj/WXLu/VWtTeh8w2fUn5ROt+rfnRK360/YTvdnZYLXmyPFxJO56H7e07VRPx+24L8/53gYrQFsBI4Ol53M9fH+r87E+V5+6HPepY8Ax4Bg4HgOBr+lVSGywgt1wzhms8XorDUiyZevpXyTZ9SflE636fMvs1H7Cz+xY3sjkR/qdxs0S+kx2tP7Z7Ck7tT9rs8EKkj+Xward3yo74Gn5dMDQ8jP1tOwts9NQJfzMzgYrmO5R3KnMnmOPjDk6ZpdgF+3zJXQ2WEGK5zBYU/e3yg54Wn7PyUbhQtpPtCp7y+woe7OzwQqmezTmex+3NGdRPR230T5fQmeDFaR4SoN17P5WNGCz9XTAZNeflE+0vSdq1Z+2n+i3HHdLsM/kR/p9ibbT8jPZ0fbTtlM9Zaf2Z202WEHypzJY4/VWterRgM3W0wGTXX9SPtEqFrbMTu0n/MzOM1i1fNqyj8Rd7+OWtp3q6bht6d9THWODFSR7CoNVW29Vqx4N2Gw9HTDZ9SflE61iYcvs1H7Cz+xssGr5tGUfibvexy1tO9XTcdvSv6c6xgYrSHZpgzW13qpWPRqw2Xo6YLLrT8onWsXCltmp/YSf2dlg1fJpyz4Sd72PW9p2qqfjtqV/T3WMDVaArAJGBkvP9OH7W3GGtA+sdx84BhwDjoH1xkDga3oVEhusYDcsMYPVst6qVj0lArJl6+lfJNn1J+UTrfp8y+zUfsLP7FjeyORH+p3GzRL6THa0/tnsKTu1P2uzwQqSpwaL/J5gdsDT8umAoeVn6mnZW2anoUr4mZ0NVjDdo7hTmT3HHhlzdMwuwS7a50vobLCCFInBunv3x+j3BLMDnpbfc7JRuJD2E63K3jI7yt7sbLCC6R6N+d7HLc1ZVE/HbbTPl9DZYAUpRgyW7m/1yis/2D8++ujDYMnsC16F0oCnejpgaPmZelr2ltnR2DU7G6xo0t3yuKVtp3o6bqN9voTOBitIca7B0nqrq1df3Gn2SkaLBB3RqrnZejpgsutPyida9d2W2dHYNTsbrGC6xzmz59ijOYvqKbtony+hs8EKUpxjsHR/Kx3/ySe/fFYaCTqiVQWy9XTAZNeflE+06rsts6Oxa3Y2WM8S8MwXWx63tO1UT8ftzK5e9HAbrCDOVoOlGSvNXD169Oi5kkjQEa0qka2nAya7/qR8olXfbZkdjV2zs8F6LgnPeLPlcUvbTvV03M7o5sUPtcEKIFXAyGDpeeqh+1tdv/7S/qH1VlPHef80Q7MxG8eAY8Ax4BgIfE2vQmKDFeyGQzNY4/VWtSKUNKIb0arMbD39iyS7/qR8olXfbZkdjV2zi+ec7Nij4yZb33Ps9c5OsZu12WAFyU8ZrNp6q1oRJGiJVnXJ1vecbCg/yn7L7Ch7s7PBquXiln1bHre07VRPx21L/57qmM0ZrAcPPtvduPHy/hKfTNKtW2/unjx5MptvzWBNrbeqnZwEHdGqLtl6OmCy60/KJ1r13ZbZ0dg1OxusWi5u2bflcUvbTvV03Lb076mO2ZTBevr06e7atau7+/ff3/PU+5s3X92brFbAmqF6443X9wZNhuqrr367v+1Cub+V3rdsJOiIVnXL1tMBk11/Uj7Rqu+2zI7GrtnZYLXk5toxWx63tO1UT8dtrT/PtW9TBuvTT3+1N1hDuLV9w8+Hr2WiNHM1fLz44nd23/nOC8/ubzU8/tBrEnREqzpl6+mAya4/KZ9o1XdbZkdj1+xssA7l5EOfbXnc0rZTPR23h/p1zme6zZImV1onUXTuTRks/c8+zVgNt8ePv9gbpocPPx/uvvBacIfGavj6ypVvXzj+2A4SdESremXr6YDJrj8pn2jVd1tmR2PX7GywjuXlqc+3PG5p26mejtupPo3s//DDn+9vu6Tnlm1TBuvevXcvGCxdJpRZ0tqsQ1u5LDg0VsPX4/tcHTqXPiNBR7S07CX0dMD03H5a9y2zo7FndjZYiqHItuVxS9tO9XTcRvr7kEYzWPIDuqJ17Ht/Uwbr7bd/1GSwhsbJr5+/JGoe5uEYcAw4BhwDjoGvY0C3ZZraNmWwyAzWnTu3Jy8RKtAOQZ6Cv9X94uUtRsDsYtykMrs4O/MzO0Ygrl7juNWSIf1Ciy4V6reFp7ZNGSytwdItGoabbtGgDjy2BktTgTqu9tB0obd2AmscMO21zz3S7OL8zS7OTkrzi/Mzu8vBThMp5Y4BLZMqmzJYtf8xKGOlWze0bLpFg1yrBkt5yFwdcrAt593aMU428R43O7OLE2BKx16cn9n1z+43v/mn/fe/Zq9at00ZLEGRmdKlQm1a4K4bjerRuslMlbu1tzjY1vNu6Tgnm3hvm53ZxQkwpWMvzs/s+menxe1zbtGgFm/OYJVZLAW8HkveyT0eQttSOtnE+9vszC5OgCkde3F+ZrdNdpszWPFufl7pAfM8jznvzG4OreePNbvnecx5Z3ZzaF081vwuMmndY3atpC4e1zM7G6yL/dm0p+dOb2rgCQ8yuzhcszO7OAGmdOzF+ZndNtnZYAX73QMmCM7/GykOzuzMDhFgYue8OD+z2yY7G6x4v1tpAiZgAiZgAiZgAlUCNlhVLN5pAiZgAiZgAiZgAnECNlhxdlaagAmYgAmYgAmYQJWADVYVS32n7vqu2zroeroeN2++evRHoutn2vbecquMbVOY13r9CkGJOz3fv//+vBNs+OjHj7/Yj9XCTyy9zSegmzKL4YMHn80Xb1Sh+y6WuCvPjr+2YFCc6TtW3MRR3xu9bTZYM3pMnS2DpRuUatOPR7feBX5GMZf6UA2aMmAudUMXbJwSsuJMRkGbnvWTTzZZxyFrrA5ZiZ1Y+kvuOLvhEYWjxq4N1pDM9OvWn2GbPsN2PynjtOS88r3RW+zZYDXGcG2w1PY1nm5zhylBy5DKoNqYzuv+oUEoymK6yns/1wnUZkv1Sw7j3yStq723ENC4FTMbrELk+LNiT7zKH+THFT6iECjfFeW9nhWD5VdYhvvX/NoGq7F3yvT4eLD4r+E2gPpLRINGm2ZePPPXxm3qKBusKTLH99tgHWc0PEJGQeaq5MDeZhGGbTnna41RG/kYcX0/9HhJcNxaG6wxkYn3U3+N6LKhL9VMQJvYbYM1AWbG7nK5eobEh+52+8tblyV5n6NDNUsvXjJX+iPJM1jt1DXjonFaZv7E0Zemj/PTJIbiTKzEUK/L++PqdR1hg9XYH+psdfJ4BssGqxHg4DAbrAGMwEuZfSVrffl5aycgZhrDStplbUe7eptHDvObDda8GJCxUqyVTd8d4mmTVYjUn0uciV8Zp8p1et8bOxuseh9f2OsZrAtIwjtssMLonl2muQzT53EKTFnib/zHEjvr5VPrUqoMQdnKF58vERYi859lEGQUvE0TKGubxzlO43ZoWKfPsJ5PbLAa+6KsPxjPGvToqhubfLLDyhfcyQqjmTblAAADIklEQVS4pCfWF5svMyzTueZ4nGOZ8SuXaIbPGsPe5hOQwRJXb4cJiJG+c4dbj+xssIY9eOB1cdXjTq8FwoHT+CMvcg/FgL7Q9AXX2xR5qLELimoL2ssaj/FfyAsWeylP5Rms9m4t3xfjGOtxFqa91csdqZmqca7TWPYM1nKMV3cmda4e5dKCOtx/jczvJs9gzWOmOJO5GifreWfZ5tHFFAzZKf58mWZ+PBSWvkTYxm58q4GyBsv8jvMTI43R8l0rw6r3vbHzDNbxvn52hBKM1iSUqfIeO/xZYxJf2GC1wy9/CZeYGz8rJr0dJqCkPBy3+uIrifuw0p8OCdhgDWm0vS5/HGnc6vtiaPTbzrDdo8RKzMROExk9srPB2m78uuUmYAImYAImYAInImCDdSKwPq0JmIAJmIAJmMB2Cdhgbbfv3XITMAETMAETMIETEbDBOhFYn9YETMAETMAETGC7BGywttv3brkJmIAJmIAJmMCJCNhgnQisT2sCJmACJmACJrBdAjZY2+17t9wETMAETMAETOBEBGywTgTWpzUBEzABEzABE9guARus7fa9W24CJmACJmACJnAiAjZYJwLr05qACZiACZiACWyXgA3WdvveLTcBEzABEzABEzgRARusE4H1aU3ABNZBQL9hpt8ye/jw8/2PtZffhfPvOK6jf1wLE7isBGywLmvPul0mYAJ7AuXHxW/denOnH8/Wph9/1o8+ezMBEzCBUxGwwToVWZ/XBExgFQRkrDSD9fTp02f1scF6hsIvTMAETkTAButEYH1aEzCBdRCQubp3793nKqN9H3/8i+f2+Y0JmIAJLEnABmtJmj6XCZjAqgjokqDWXGkdVtm09kr7Hjz4rOzyswmYgAksTsAGa3GkPqEJmMBaCMhEyUyVtVeql8zWeN9a6ut6mIAJXB4CNliXpy/dEhMwgREBXQbU5cDhpkXvN268PNzl1yZgAiawOAEbrMWR+oQmYAJrIaD/KahF7sNN78f7hp/7tQmYgAksQcAGawmKPocJmIAJmIAJmIAJDAjYYA1g+KUJmIAJmIAJmIAJLEHg/wfkzsj9xp/THwAAAABJRU5ErkJggg==\" style=\"display:block;margin-left:auto;margin-right:auto;\"/></p>\n<p>Determine a mean value for the number of slits per millimetre of the grating.</p>\n<div class=\"marks\">[4]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>using a light source with a smaller wavelength.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>increasing the distance between the diffraction grating and the screen.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">c.ii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>0 <em><strong>OR</strong> </em>2<em>π</em> <em><strong>OR</strong> </em>360° <strong>✓</strong></p>\n<p> </p>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>4<em>λ</em> <strong>✓</strong></p>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>sin</mi><mo> </mo><mi>θ</mi><mo>«</mo><mo>=</mo><mfrac><mtext>XZ</mtext><mtext>VX</mtext></mfrac><mo>»</mo><mo>=</mo><mfrac><mrow><mn>4</mn><mi>λ</mi></mrow><mrow><mn>2</mn><mi>d</mi></mrow></mfrac></math><strong>✓</strong></p>\n<p><em><br/>Do <strong>not</strong> award <strong>ECF</strong> from(a)(ii).</em></p>\n<div class=\"question_part_label\">a.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>identifies gradient with <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mi>λ</mi><mi>d</mi></mfrac></math> <em><strong>OR</strong> </em>use of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>d</mi><mo> </mo><mi>sin</mi><mo> </mo><mi>θ</mi><mo>=</mo><mi>n</mi><mi>λ</mi></math><strong> ✓</strong></p>\n<p>gradient = 0.08 <em><strong>OR</strong> </em>correct replacement in equation with coordinates of a point <strong>✓</strong></p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>d</mi><mo>=</mo><mfrac><mrow><mn>633</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>9</mn></mrow></msup></mrow><mrow><mn>0</mn><mo>.</mo><mn>080</mn></mrow></mfrac><mo>=</mo><mo>«</mo><mn>7</mn><mo>.</mo><mn>91</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo> </mo><mtext>m</mtext><mo>»</mo></math> <strong>✓</strong></p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>1</mn><mo>.</mo><mn>26</mn><mo>×</mo><msup><mn>10</mn><mn>2</mn></msup><mo> </mo><mtext mathvariant=\"bold-italic\">OR</mtext><mo> </mo><mn>1</mn><mo>.</mo><mn>27</mn><mo>×</mo><mn>102</mn><mo>«</mo><msup><mtext>mm</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong></p>\n<p><em><br/>Allow <strong>ECF</strong> from <strong>MP3</strong></em></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>gradient smaller <strong>✓</strong></p>\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>no change <strong>✓</strong></p>\n<div class=\"question_part_label\">c.ii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.ii.</div>\n</div>",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-3-wave-phenomena"
    ]
  },
  {
    "question_id": "21M.2.HL.TZ2.9",
    "Question": "<div class=\"specification\">\n<p>In an experiment to demonstrate the photoelectric effect, monochromatic electromagnetic radiation from source A is incident on the surfaces of metal P and metal Q. Observations of the emission of electrons from P and Q are made.</p>\n<p>The experiment is then repeated with two other sources of electromagnetic radiation: B and C. The table gives the results for the experiment and the wavelengths of the radiation sources.</p>\n<p><img src=\"data:image/png;base64,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\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline the cause of the electron emission for radiation A.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline why electrons are never emitted for radiation C.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline why radiation B gives different results.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Explain why there is no effect on the table of results when the intensity of source B is doubled.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Photons with energy 1.1 × 10<sup>−18 </sup>J are incident on a third metal surface. The maximum energy of electrons emitted from the surface of the metal is 5.1 × 10<sup>−19 </sup>J.</p>\n<p>Calculate, in eV, the work function of the metal.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>photon transfers «all» energy to electron <strong>✓</strong></p>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>photon energy is less than both work functions<br/><em><strong>OR</strong></em><br/>photon energy is insufficient «to remove an electron» <strong>✓</strong></p>\n<p><em><br/>Answer must be in terms of photon energy.</em></p>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Identifies P work function lower than Q work function<strong> ✓</strong></p>\n<div class=\"question_part_label\">a.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>changing/doubling intensity «changes/doubles number of photons arriving but» does not change energy of photon<strong> ✓</strong></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><strong><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>5</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup><mo>=</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>18</mn></mrow></msup><mo>-</mo><mi mathvariant=\"normal\">ϕ</mi></math> ✓</strong></p>\n<p>work function <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mtext>= «</mtext><mfrac><mrow><mo>(</mo><mn>11</mn><mo>.</mo><mn>0</mn><mo>-</mo><mn>5</mn><mo>.</mo><mn>1</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup></mrow><mrow><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup></mrow></mfrac><mtext>= » 3.7 «eV»</mtext></math> <strong> ✓</strong></p>\n<p><em><br/>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.</div>\n</div>",
    "topics": [
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "e-2-quantum-physics"
    ]
  },
  {
    "question_id": "21M.2.SL.TZ1.1",
    "Question": "<div class=\"specification\">\n<p>Two players are playing table tennis. Player A hits the ball at a height of 0.24 m above the edge of the table, measured from the top of the table to the bottom of the ball. The initial speed of the ball is 12.0 m s<sup>−1</sup> horizontally. Assume that air resistance is negligible.</p>\n<p><img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAmQAAADbCAYAAADDEo01AAAgAElEQVR4Ae2dv88cx32H/X8E7g2CbSIKLGNbEBsHkQmITmUSjthZasTCgViJTUS6EhurcSAWUUoxEBunEAH1FvwPMPYfQP8FFzynfOjhau995/Z2b3/MM8D73t3u7OzMs9+de2721w92JglIQAISkIAEJCCBWQn8YNa1u3IJSEACEpCABCQggZ1CZhBIQAISkIAEJCCBmQkoZDNvAFcvAQlIQAISkIAEmhWyv/71r7svvvjP3aNHD3c3b76zu337l/v3z559ZVRIQAISkIAEJCCBsxJoTsgQsYcPP9ldufKj3Q9/+He7f/rZz3bv//rXu3/91a92P/7xP+6nMe+zz3531g3hyiQgAQlIQAISaJdAU0KGjL311k/2MvZvv/nN7n/+8IfdN99889rffz99uhc0ZO2DD97fsYxJAhKQgAQkIAEJTEmgGSGLjDEK9l9ffPGahHWljM//8fvf78UNKTNJQAISkIAEJCCBKQk0I2T373+0FyxGwPoErG8aUsZIGeeamSQgAQlIQAISkMBUBJoQsj//+X/3YvXb3z6qlrEIGueWXbv2D1Pxt1wJSEACEpCABCTQxn3IOEGfE/UjWce8MqLGKJlXX7q3SEACEpCABCQwFYEmRsh+/vN/3l9FeYyIlXk574zbY5gkIAEJSKAtAo8ff7r/UX7jxtv7hufz3bvvtQWi4dayrRmYYdtPmZoQMu4zxlWVpWQd855bY3AOmkkCEpCABNoiEAFTyOq3O8wuE9anT7/c3br17u7ly5f1Bc+UUyEbEfypQvYvv/jF7v33fz1ijSxKAhKQgATWQKArZGuo85x1rOH17bd/3I84MeqkkP1tazUzQsbNX48ZFSvzMkLmIcu/BY3vJCABCWyVwJMnn++uXr3y6jDlvXsfvnpPmyMc5QgQ07IMknH9+ps7yinTgwcfv5IQ8mfUhekkRuBYNtMpD1l58eLFfiSJefkjT0Qm+XllxIk8LIv08EddmEb5lHUoZf3UJ+WwHHUtE+1KXuaTN+Uy6sW08o86lIl6l/N5n3UwL7yZTjsyryyjfM86y/qU5SVfN093ZK47v1tGGJd1KeOkmz/rPfa1CSFDpt544+8HCRk3jwW2J/UfG1rH5edKWNPpBOjQ6JyeP//69MIsQQKNEeBLlv6+74/9isSXMvP5kib1SUiWj6iUMpZ5EbiukJXzKb8rG5mPuJAiC5meV0Qs68g0RORQOrQelk1/cogP66GtfSyOEbJDdUhbu3Wnv+u2MW2NPFH3TCtfsz0vKoP2ksI4ZR7ikG3ZrWft5yaE7JTbXnDuGVdomqYlgDRfu/bGXpqnWhMdBjtvt4Pgc/mLkB21m6dbp3TK2cEPdRjd5ab8TJ3ToaUDnXJ9li2BrRFIPxBx4cs60/IFnn0/QtZlQD+TfiH9SKQhX9hM707Lvpt1Z9lu+RlByvojCwgY9WW5rD95UmfWeShl/bxSDn8ZXYuI5HP6O/Jkue66mH4olXWkDFLqyDrS9kyjPZlWltlXTjmf99l+qV/ZrkP9ZNqZdodxPmd+hC3fLRfx7dar73MTQkbDueM+o2R9j0sqD0+W77mjP4Hg4cq+0Bl3GozTiXDO39gjZuww2YnKHTs7Z3ZWWkVnw46VjqLbUn4FMj87I+XxOTtrN/+5PlMPOhjaeaijOVddXI8E1kiA/Zh+iH08KaMhEYxIQtlnkBfZ4i/9TCTikDRErCJpEZv0K1k/r9SHfBEDys76My3l0G+lL007eGUa7TuUsv6yH4vMMC3t6JYRPrSbFD7h1be+lEWd0s+mHeX6WTY8+7gwP3VMm+FQltG3TfvqxDIsW5aXcsq6lXyzzvL1lL63GSHj0UmMdHELixopQ8bIz7MvTdMTKIUswc20MZ4lyk5F58DORtl0BknpTNIpZDo7cXbGTMsrHSk7bZn6ppXzz/leITsnbde1JQJ9X97pIyIY9Av0IxGiyA59AvPKL2z6mj75gNkhIYtEhWsEgf6LstKPZf2RBaaTuutnWurYlamsg9c+IUvZtCvt6JYRPnMJGXWnDrQ/rNg+8CX1bdP9jP//lx/r1J8y4NdlUXIo+ea7qnztbr9yXZe9b0bIAPGnP/1pf9d9ROvQXfuRtQcff/xKxsYQgss2gvN3+1HIMqjznm116qOr2EnZidIp0bFcltiJDwkZ5aXzSznk7XZUzGPHZmcuOwry0oGkoyAPnUI3Ud90DPCgDPLxCyx88prOhzIUsi5JP0ugjkD2U15J5Zcz+yKJ/Zf9jv2alGXSJ2Q+edLXZF9PHqZ3p2VfL7/Qs6+Tl7qU9cn6IwspmzzpF7L+9H2Ucyhl/dQ/KWVnWuqc/qasT6ZlXeGVssrXso68J4Ub/VfqnWm0p6+PLMvM+whi2prt07dNyZt1pL7ltkm7uxyoI3XK/Kz71NemhAxYCBaHL4HJIUwejcR5YvxxewsEgHkPH35yKluXP4JA3wgZ2yF/jFRyOPmUlI4iO/uhspLv0NBzfkmVy2eZdC6Zl06O+SQ6TdpE50Be/siTzjXL8UqHkk6Wz+RLp1Lm675XyLpE/CyBOgLZj9PvlK/5ws4XePZZRKTMx/uIS/qQ7PdlvuTJPt7tK6gxElIuU5adviCykHLoU7JM+rq0K5LSRyPrLyUjZWda2p7y80q5EaasK/PCoFxnWUfyUS7TIjpZNq+RvbIM3kdYk698zfY5lId1kSJw5bLZNml3LYeU2a1n7efmhCxgOEeJRyrdvv3L3U9/+tO9iEXGyg3j+79J0RJY3Llze/D5Zeko0kklFrqvdEyHOgDysrOm88uyKZtOpUyUlY6T6ekcyJ/EushXpnTE6RDKeZe9V8guI+R8CRwm0B29jnBlH42U5AuffZ59PP0j8yNg5f6bL3XysY58Tl9C+cwr+wZqWQoD66H/Il/kqltOKTvp69I/ZZm+1mf9fXUup1Gf5KUe1CkylnJLHqlD5uU1jCgj5VP38E4bMy/LdV9pW7k+lgvT5CXPRXUu1wnP8KJcUhiXdeF9xO0Qh6y/9rVZIQsgRsyA6d96GCDOQ84vy052qIMgJtgB2XEvSghP3w5PDPUJWZk3nWlZB+b3rZPpiUs6jLIzuKh+zpOABJZFIF/c2c/pJ+hH2L/dr5e1reasTfNCxiOR8qXn63qkjMPOx57fd5mQRca6UtXdQcmHIJUpv6rLabynAx4qZCmL5fMLLR165vkqAQksn0D2377vmPLH2fJbYg2nJNC0kOX+ZH07idOWKWfcEmPouWSHhIwOEdHh7zIZY2dExjKUnZ2TX7ndacwbQ8iyjr7DnZnnqwQksGwC5WExvl/oG+iTTBIIgaaFjC93xWuZ4tXdLtw09tSrLfuEjHMfOJxA51ibIkaMipEQOg4/9B16GCpklAmDskxGyqhrjTTWtsV8EpCABCSwDALNChmjLN0v/Xwe+6aky9jU39WCR0AhovyVFzHwuZvgACduFzJ1OnSV5dDzxfrq2ydk3V+tiQFeOcxAQor4XB5aKM/vKvN21ztUyCgH4ct5JqyDETh/UXcJ+1kCEpDANgg0K2SMuPAl1/fHlXwtJYSrT0K7I4gwY9qpI1V9bPuE7JQrKvvW4TQJSEACEpDAUgk0KWTc7qJPxMppQ89TWuqGPqVeCBs84IY49T1oHXlC1jjZnjzHjqyVQjbGPcdOaa/LSkACEpCABM5NoDkh48q88lBdKWHlex+ZdFwoImlIFVIGu7BE4roJweteIcmybJcpRt+66/ezBCQgAQlIYGkEmhQyRm/KP+Sh/Jz3XWlY2sZben04DNplyOfIGgKGwHHrkU8++ffdX/7y56U3yfpJQAISkIAEJiHQnJD1UUQQTOcjgJQhvYyeIWNIGXLGtDKRj5G37vQyj+8lIAEJSEACWyCgkO12+xGbLWzMrbUBESsPL3MolHPV+g6Dbq3ttkcCEpCABNoioJApZIuP+Nx+g/PMcvFA96pQPjOado5bdCwemBWUgAQkIIHVEVDIFLLVBW1fhbkYIOem8Zpz0/quCO1b3mkSkIAEJCCBOQkoZArZnPE3+roZIUPOcm4aYtZNjKY5ktal4mcJSEACEpiTgEKmkM0Zf7OsO7flyFWeHAplJK17RegslXOlEpCABCTQJAGFTCFrMvC7I2kc5uSmtiYJSEACEpDAHAQUMoVsjrhbxTo5tMkoGiNqHALlUGj3YoJVNMRKSkACEpDA4gkoZArZ4oN0zgpy6408gSAXDfTdM23OOrpuCUhAAhJYPwGFTCFbfxSfsQUc6uQ+aN3zzZjuuWhn3BCuSgISkMDGCChkCtnGQnqe5jCSlosFGEnLYU5vuzHP9nCtEpCABNZGQCFTyNYWs4uvb3mY89q1NxZfXysoAQlIQALzE1DIFLL5o7CxGvC0AUSNqzq9UKCxjW9zJSABCRwgoJApZAdCw8lTEeBKTc5DQ8zyrE4EDTkzSUACEpBAmwQUMoWszchfUKtzoUDf+WYc/uxeQLCgqlsVCUhAAhIYiYBCppCNFEoWMzYBRtJyq43yIgEFbWzSlicBCUhgfgIKmUI2fxRagwsJMErGjWnLqzi9Qe2FyJwpAQlIYHUEFDKFbHVB23KFGR1D0LqJaV4g0KXiZwlIQALrIaCQKWTriVZrepAAMlZeIMCImg9MP4jLGRKQgAQWR0AhU8gWF5RWaDiBPDEghze5ktMkAQlIQALLJ6CQKWTLj1JrOIgAhzf7LgDglhuOng1C6kISkIAEJiOgkClkkwWXBS+TAKNmuXrz5s139vdE8yKBZW4rayUBCbRDQCFTyNqJdlv6igAjZ4yS8bSAnHvWd7HAqwV8IwEJSEACkxJQyBSySQPMwtdBgHPPuolRMy4W6Dvs2c3rZwlIQAISOI2AQqaQnRZBLr1ZAoygZfSMiwQ496xP3DYLwIZJQAISOCMBhUwhO2O4uao1EkDMuI0Gz9vk3DOv3FzjVrTOEpDA0gkoZArZ0mPU+i2IACNkfaNkTPPQ5oI2lFWRgARWR0AhU8hWF7RWeHkEcmiT0TPPO1ve9rFGEpDA8gkoZArZ8qPUGi6eAKNjiBhCFjnjvDNHzRa/6aygBCSwEAIKmUK2kFC0GlsiwHlnjx493Hl/sy1tVdsiAQlMSUAhU8imjC/LlsBrBLhSk5EzLhLoOxfttcx+kIAEJNAQAYVMIWso3G3q3AQYMSuv2OTKTT47kjb3lnH9EpDA3AQUMoVs7hh0/Y0SYIQscsarSQISkEDLBBQyhazl+LftCyXAxQDeiHahG8dqSUACkxBQyBSySQLLQiVwCgGELDeizWFNzzk7hajLSkACSyegkClkS49R69cwgfKwJk8JuHnznYZp2HQJSGDLBBQyhWzL8W3bNkQAOeMwpkkCEpDAFgkoZArZFuPaNjVEgFEz/nxCQEMb3aZKYIMEFDKFbINhbZNaIvDNN9/sPvjg/VdPCMjjm1piYFslIIH1E1DIFLL1R7EtkMBut39MUx7fxPlmvDdJQAISWAsBhUwhW0usWk8JnESAKze9UvMkhC4sAQlMSEAhU8gmDC+LlsByCHBBACNn3EaD9z4dYDnbxppIQAK7nUKmkLkfSKAZArmNxpUrP9rLGRcDcA6aSQISkMDcBBQyhWzuGHT9EpiFwLNnX+0vBnj06OEs63elEpCABEoCCplCVsaD7yXQPAHONUPSPKTZfCgIQAJnJaCQKWRnDThXJoGlE0DE8timt976ifc3W/oGs34S2AgBhUwh20go2wwJjEuge3+z+/c/GncFliYBCUigIKCQKWRFOPhWAhLoEuAQJvc04+azJglIQAJTEVDIFLKpYstyJbB5Apxr5g1oN7+ZbaAEzkJAIVPIzhJorkQCWyTAqBn3NuM2GhzS9MazW9zKtkkC5yGgkClk54k01yKBjRLgkCY3mi0vBGCaSQISkMAxBBQyheyYeDGvBCRwAQEuBOAwpkJ2ASRnSUACvQQUMoWsNzCcKAEJjEeA88wYRVPUxmNqSRLYGgGFTCHbWkzbHgksjgCjZnlcE+ed+bimxW0iKySB2QkoZArZ7EFoBSTQAgFGxxgp42azeci5TwNoYcvbRgnUEVDIFLK6SDGXBCQwGgGuxmTUzKsyR0NqQRJYPQGFTCFbfRDbAAlshQCHMhlF81yzrWxR2yGBegIKmUJWHy3mlIAEJiXAif/lfc08pDkpbguXwKIIKGQK2aIC0spIoHUCjI6V9zW7efMdD222HhS2vwkCCplC1kSg20gJrJEAhzDv3Lm9e/bsqzVW3zpLQAJHEFDIFLIjwsWsEpDAEghwKNMLApawJayDBMYjoJApZONFkyVJQAJnIZBzzbiFhhcBnAW5K5HA5AQUMoVs8iBzBRKQwPgEGCHrPtzciwDG52yJEjgXAYVMITtXrLkeCUhgAgJcBMA9zXi4Oa8mCUhgnQSOErLHjz/dX5LNZdn83bv34YWt/vbbP+5u3Xr31TI3bry9Y1pfevny5e769Td3Dx583Dd70mm0xSQBCUhAAhKQgATmIlAtZE+ffrm7evXK7smTz/d1Raz4jKT1pQjW3bvvvZqNwLEM87op4qaQdcn4WQISkMAwApxfxjM079//aOfhzGEMXUoC5yJQLWTIFNJUpr5pmY+4MfLUla8+iUPqGB1jnkIWgr5KQAISOI1AeTiT/tgHm5/G06UlMCWBaiFDxrqyhEghUcekrpC9ePFiX8bz519fKGQc7mS0LSNpdC6sH/GjTD6Th/KOTSxrkoAEJLBlAoyWcZNZ+jvPNdvylrZtayVQLWR953dxGJOduzsKdghG8iNfSUhUDnteNEJGPtZFGSTkkM8IGuvnL9KWsmtfKcckAQlIoAUCXJ3p4csWtrRtXBuBaiHrk6UIVq2QIUzlhQC8Z1pS3zoyj3zlIVOkrhQ08nXLy7KXvSpklxFyvgQksGUCPBGAUTNFbctb2bYtnUC1kJ06QoZMlfKVQ43lIcbLhKw8ZMpFBYhUedUm88t11MJXyGpJmU8CEtgiAUbNuG0GfSGPakLQTBKQwHkJVAsZQlWOblHNSNVlVY6MlSNpnA/Gzt/31ydVTFPILiPtfAlIQALDCfDMzJxnxlMAFLPhLF1SAscSqBYyZKw8ZMiKOPerO62sAKNXiBR/pYyVecr3jpCVNHwvAQlIYB4CiBhXZHry/zz8XWubBKqFLOdsMSpGQrY4jJkT8rv4cvVk32hXN28+K2Qh4asEJCABCUhAAi0RqBYyoOTKxhxmLG/6ynyEKtMYUUu+7mvydEErZF0ifpaABCSwHAJ5qDmjZ14AsJztYk22QeAoIdtGk7/fCoTRJAEJSEAClxPgfma5AIDzzTzP7HJm5pBADQGFzIeL18SJeSQgAQm8RgARywUAnmv2Gho/NEyA/YIfLUOSQqaQDYkbl5GABCSwJ+CNZg0ECXxHIIf0eXbskKSQKWRD4sZlJCABCRwkgKTx5cSzNE0SaIEAEsbpT6eMFitkClkL+4ptlIAEzkiA+5ldufKj/R9fUIrZGeG7qlkIcJjy1PMpFTKFbJbgdaUSkMC2CSBhyBhixsgBV2YqZtve5rbuNAIKmUJ2WgS5tAQkIIFLCOTKTA5jmiSwBQIclh87KWQK2dgxZXkSkIAEJCCBTRJglJfnvU5xuyyFTCHb5E5joyQggeUTYMTMh5kvfztZw+8IMCrGM145DH/q+WJ9TBUyhawvLpwmAQlIYHICfMHlXmbeZHZy3K7gBAIIGCKGkE31lAqFTCE7IURdVAISkMDpBPiyK8Vsqi+802tqCS0S4IfDOS5MUcgUshb3L9ssAQkskABixtWYUxwOWmBzrdJKCHDe2DliUiFTyFayS1hNCUhAAhKQwHYJKGQK2Xaj25ZJQAKbIMDhTB5oPvQZgZuAYCPORoBD5nMcNlfIFLKzBbkrkoAEJDCEAF+OHMrkPB7FbAhBl6klgPRz8v4pj0CqXVc3n0KmkHVjws8SkIAEFkmgK2ZzjGIsEoyVGoVAHg6O/M+RFDKFbI64c50SWBwBRl9q/xZX+cYqhIj5jMzGNvrEzc0I7JxPk1DIFLKJw9ziJbAOAshYTarNV1OWecYl4IjZuDxbKQ0Z4zDls2dfzdpkhUwhmzUAXbkElkKgVrRq8y2lXS3Vg/PLPMespS0+Tlu5z9gSZF4hU8jGiWhLkcDKCdSKVm2+leNYZfX5Us2hJ8VslZuw6UorZApZ0zuAjZdACNSKVm2+lOvr+QmUYsajbkwSKAlwo9clJoVMIVtiXFonCZydQK1o1eY7ewNc4fcIIGbeu+x7WJqewMUg7MPnuPP+saAVMoXs2JgxvwQ2SaBWtGrzbRLSRhrFOUOm9gjkcPZSJV0hU8ja2yttsQR6CNSKVm2+nlU4aQEEGDVjG3Ioc4mjJAtAtLkqcIiSpz0s4UrKi+AqZArZRfHhPAk0Q6BWtGrzNQNuhQ1Fyu7cub0XM76oFbMVbsQjqox8I2NLHxlVyBSyI8LarBLYLoFa0arNt11S22kZIoaQsU3v3/9oOw2zJa8R4LwxJHzpSSFTyJYeo9ZPAmchUCtatfnOUmlXMgoBxMxRslFQWsgJBBQyheyE8HFRCWyHQK1o1ebbDpl2W7KGUZV2t872Wq6QKWTbi2pbJIEBBGpFqzbfgCq4yIIIlA+aVswWtGEuqQpXUHJT4DUmhUwhW2PcWmcJjE6gVrRq841eQQs8O4F8ubPNfZj52fEfvcLc1mLOB4QfXeliAYVMISvCwbcSaJdArWjV5muX5PZazhc8V+nx57lmy9y+kbGl3mOshppCppDVxIl5JLB5ArWiVZtv88AaayD3skLMln7rhMY2y765a7jHWM12UcgUspo4MY8ENk+gVrRq820emA2UwEIIIGRbEGWFTCFbyC5lNSQwL4Fa0arNN29rXPu5CCAD3vX/XLS3vR6FTCHbdoTbOglUEqgVrdp8las128oJcAVmbi7Lq+eYrXyDzlh9hUwhmzH8XLUElkOgVrRq8y2nZdbkHAQQsYgZJ5ibpiHAock1n7h/ERWFTCG7KD6cJ4FNEHjx4sXu6dMvL2xLrWjV5rtwZc7cLIFnz77aPyeTiwBM4xJAernSdavCq5ApZOPuMZYmgQUSuHHj7d2DBx9fWLNa0arNd+HKnCkBCRxFgFEx9r2tyhgwFDKF7KidwswSWCMBhWyNW207dWa0jMOZWz3UNvWWakHGYKiQKWRT70uWL4GTCCBTd+++t7t16939L2R+Jd+79+FrZT558vnu+vU3e+ezPMvwd/XqldeWKz8wvybV5qspyzztEMiNS3msjyf+1293zhljn9vyyFhoKGQKWWLBVwkskkCECukicS4YHXT5GdHKOWKcLxaJS4P47CHL0PB1LgJckXnnzu19/DJitoV7Z03NktHFVgRWIVPIpt6fLF8CJxFAphgdKxOjYREs5nVHzJ4//3r/pYeckRSykp7v5yaQKzJbGPWZm/Wa1q+QKWRrilfr2iCBPpkqpzE6xohZ3x9iRirzH0LI8jWpNl9NWeaRgAQkEAIKmUKWWPBVAosk0CdT5TSE7PHjTy+se5n/UMZa0arNd2g9TpfAIQJbvsfWoTZ3pzNqyOHcFpNCppC1GPe2eUUE+mSqnMb77iHNbvPK/N15+VwrWrX5Uq6vEqglkKsJWz3xHxnjPmOtXo2qkClktX2F+SQwC4E+mSqncXI/klSOknFVJueZJZG/e55Z5uW1VrRq86VcXyVwDIHuif98biFFxlq+0EEhU8ha2Ndt44oJlPKVZnSndW97wYhZTuhnmUgbMvXy5csU89prrWjV5nutcD9I4EgCnPjPQ8uJt61LCocoGRnbejsvCwGFTCG7LEacL4EmCNSKVm2+JqDZyMkJIGZbfwyTtwD5LowUMoVs8g7FFUhgDQRqRas23xrabB0lIIHlEFDIFLLlRKM1kcCMBGpFqzbfjE1x1RsnQAw6qrS9jayQKWTbi2pbJIEBBGpFqzbfgCq4iASqCOTGssQiJ8Ov6ZBmS3fer9qYRSaFTCErwsG3EmiXQK1o1eZrl6QtPxcBbg/ByfBruVUEMsaFCtTX9H0CCplC9v2ocIoEGiRQK1q1+RpEaJNnIIDkPHr0cP83w+qrV1nKWOtXUx6CppApZIdiw+kSaIpArWjV5msKno2VwAUElLEL4BSzFDKFrAgH30qgXQK1olWbr12StnwJBDjPjJEzZGjudOfObe8zVrERFDKFrCJMzCKB7ROoFa3afNsnZguXTODZs68Wc34Z57p5mPLyaFHIFLLLo8QcEmiAQK1o1eZrAJlNXDgBRsfu3/9of7d/bpPBqJlpuQQUMoVsudFpzSRwRgK1olWb74xVd1USuJAAo1MIGbHrSNWFqGad2ZyQ8aBWgvKyv2vX3ljEsfdZo8OVS6AhArWiVZuvIXQ2dSUEziFjjMpx7lorD0Ufc9M3J2TAyxDuRVLGMW+TBCTQDoFa0arN1w45WyqB7wiUV1MqZMdHRZNCRtBwY7pDQsbQrkkCEmiLQK1o1eZri56tXSMBvguJZ66CHEOgvJrytChoUshAxgjYISHzxMfTgsqlJbBGArWiVZtvjQysc3sE+L7jFB0GKTjUODTxCCfKOMdh0aF1XPpyzQoZG4ZHOHSljKAySUAC7RGoFa3afO0RtMVrJoCMIVTI2bFS9dlnv1PGRtj4TQsZvwxKISMYGcI1SUAC7RGoFa3afO0RtMVrJ8BhSwYljh0pY7kxDnmund+p9W9ayIDHMe9I2bFBeCp8l5eABJZDoFa0avMtp2XWRAISWAOB5oUMq88w7Ro2mHWUgASmIVArWrX5pqmlpUrg/AQ4muS51dNzb17IQEwH658MjAFjwBgwBowBY2CMGBiibwqZQqaMKuTGgDFgDBgDxsCIMaCQDSGgkLkTjrgTjvHLyjL8hW4MGAPGwLpjYIiOOEKmkClkCpkxYAwYA8aAMTBiDK/ZKYMAAATKSURBVChkQwgoZO6EI+6E/qpd969at5/bzxgwBsaIgSE64giZQqaQKWTGgDFgDBgDxsCIMaCQDSGgkLkTjrgTjvHLyjL8hW4MGAPGwLpjYIiOOEKmkClkCpkxYAwYA8aAMTBiDChkQwgoZO6EI+6E/qpd969at5/bzxgwBsaIgSE64giZQqaQKWTGgDFgDBgDxsCIMaCQDSGgkLkTjrgTjvHLyjL8hW4MGAPGwLpjYIiOOEKmkClkCpkxYAwYA8aAMTBiDChkQwgoZO6EI+6E/qpd969at5/bzxgwBsaIgSE64giZQqaQKWTGgDFgDBgDxsCIMaCQDSGgkLkTjrgTjvHLyjL8hW4MGAPGwLpjYIiOOEKmkClkCpkxYAwYA8aAMTBiDChkQwgoZO6EI+6E/qpd969at5/bzxgwBsaIgSE64giZQqaQKWTGgDFgDBgDxsCIMaCQDSGgkLkTjrgTjvHLyjL8hW4MGAPGwLpjYIiOOEKmkClkCpkxYAwYA8aAMTBiDChkQwgoZO6EI+6E/qpd969at5/bzxgwBsaIgSE64giZQqaQKWTGgDFgDBgDxsCIMaCQDSGgkLkTjrgTjvHLyjL8hW4MGAPGwLpjYIiOOEI2hJrLSEACEpCABCQggREJKGQjwrQoCUhAAhKQgAQkMISAQjaEmstIQAISkIAEJCCBEQkoZCPCtCgJSEACEpCABCQwhIBCNoSay0hAAqsi8Pjxp9X1ffny5f5Cl6dPvzy4zI0bb+8ePPj44HxnSEACEjiWgEJ2LDHzS0ACqyKAWHHFGqJVkxSyGkrmkYAExiagkI1N1PIkIIFFEVDIFrU5rIwEJHCAgEJ2AIyTJSCB9ROIjOWeTjl0yev162++ugff1atXdk+efL5vcEbI7t378FUe8paHMLuHLL/99o+7W7fefVUe71+8eLF+gLZAAhI4GwGF7GyoXZEEJDAHgUhZDlnm8/PnX7+qDgKFlJEiZEgYokXifDGkLp9LISM/y0b2yE95LG+SgAQkUEtAIaslZT4JSGCVBCJgEbK+RiBTCBejWhGyUrBYBsFi1IxUCllG27rllqNu3Xl+loAEJNAloJB1ifhZAhLYFIE+IUO6GPXirzzUyAhYhKwcQQPI3bvv7fPyvhQypueQaPe1K3WbAmtjJCCBUQkoZKPitDAJSGBpBLpChmghTogYQoY08ce0oUJGWSYJSEACpxBQyE6h57ISkMDiCXSFrBzpSuXLc8QyQpaT/JOHQ5bkI5UjZEzL+WfJ66sEJCCBYwkoZMcSM78EJLAqAhGyXPWYqycRLxLihVB1R8gQsHIZ8uRzKWRMY145SlaOuK0KlpWVgARmI6CQzYbeFUtAAucigEAhXIxmIWLleWO8j0AhZxkhQ9wiaiyfKyypcylkfGZeWSbzEUGTBCQggVoCClktKfNJQAISkIAEJCCBiQgoZBOBtVgJSEACEpCABCRQS0AhqyVlPglIQAISkIAEJDARAYVsIrAWKwEJSEACEpCABGoJKGS1pMwnAQlIQAISkIAEJiKgkE0E1mIlIAEJSEACEpBALQGFrJaU+SQgAQlIQAISkMBEBBSyicBarAQkIAEJSEACEqgloJDVkjKfBCQgAQlIQAISmIjA/wELo5jbjNTQ5wAAAABJRU5ErkJggg==\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n</div><div class=\"specification\">\n<p>The ball bounces and then reaches a peak height of 0.18 m above the table with a horizontal speed of 10.5 m s<sup>−1</sup>. The mass of the ball is 2.7 g.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Show that the time taken for the ball to reach the surface of the table is about 0.2 s.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Sketch, on the axes, a graph showing the variation with time of the vertical component of velocity <em>v</em><sub>v</sub> of the ball until it reaches the table surface. Take <em>g</em> to be +10 m s<sup>−2</sup>.</p>\n<p><img src=\"data:image/png;base64,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\" style=\"display:block;margin-left:auto;margin-right:auto;\"/></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The net is stretched across the middle of the table. The table has a length of 2.74 m and the net has a height of 15.0 cm.</p>\n<p>Show that the ball will go over the net.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Determine the kinetic energy of the ball immediately after the bounce.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">d.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Player B intercepts the ball when it is at its peak height. Player B holds a paddle (racket) stationary and vertical. The ball is in contact with the paddle for 0.010 s. Assume the collision is elastic.</p>\n<p><img src=\"data:image/png;base64,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\" style=\"display:block;margin-left:auto;margin-right:auto;\"/></p>\n<p>Calculate the average force exerted by the ball on the paddle. State your answer to an appropriate number of significant figures.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">d.ii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><em>t</em> = «<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msqrt><mfrac><mrow><mn>2</mn><mi>d</mi></mrow><mi>g</mi></mfrac></msqrt></math>=» 0.22 «s»<br/><strong><em>OR</em></strong></p>\n<p><em>t</em> = <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msqrt><mfrac><mrow><mn>2</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>24</mn></mrow><mrow><mn>9</mn><mo>.</mo><mn>8</mn></mrow></mfrac></msqrt></math>  <strong>✓</strong> </p>\n<p><em>Answer to 2 or more significant figures or formula with variables replaced by correct values.</em></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>increasing straight line from zero up to 0.2 s in <em>x</em>-axis <strong>✓</strong></p>\n<p>with gradient = 10 <strong>✓</strong></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><em><strong>ALTERNATIVE 1 </strong></em></p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>t</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>37</mn></mrow><mn>12</mn></mfrac><mo>=</mo></math>«0.114 s» ✓</p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>10</mn><mo>×</mo><mn>0</mn><mo>.</mo><msup><mn>114</mn><mn>2</mn></msup><mo>=</mo><mn>0</mn><mo>.</mo><mn>065</mn></math> m ✓</p>\n<p>so (0.24 − 0.065) = 0.175 &gt; 0.15  <em><strong>OR</strong>  </em>0.065 &lt; (0.24 − 0.15) «so it goes over the net» <strong>✓</strong></p>\n<p> </p>\n<p><em><strong>ALTERNATIVE 2</strong></em></p>\n<p>«0.24 − 0.15 = 0.09 = <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>10</mn><mo>×</mo><msup><mi>t</mi><mn>2</mn></msup></math> so» <em>t </em>= 0.134 s <strong>✓</strong></p>\n<p>0.134 × 12 = 1.6 m <strong>✓</strong></p>\n<p>1.6 &gt; 1.37 «so ball passed the net already»  <strong>✓</strong></p>\n<p> </p>\n<p><em>Allow use of g = 9.8.</em></p>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><em><strong>ALTERNATIVE 1 </strong></em></p>\n<p>KE = <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mn>1</mn><mn>2</mn></mfrac></math><em>mv</em><sup>2</sup> + <em>mgh</em> = <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mn>1</mn><mn>2</mn></mfrac></math>0.0027 ×10.5<sup>2</sup> + 0.0027 × 9.8 × 0.18 <strong>✓</strong></p>\n<p>0.15 «J» <strong>✓</strong></p>\n<p> </p>\n<p><em><strong>ALTERNATIVE 2</strong></em></p>\n<p>Use of <em>v</em><sub>x</sub> = 10.5 <em><strong>AND</strong></em> <em>v</em><sub>y </sub><em>= </em>1.88 to get <em>v</em> = «<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msqrt><mn>10</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mo>.</mo><msup><mn>88</mn><mn>2</mn></msup></msqrt></math>» = 10.67 «m s<sup>−1</sup>» <strong>✓</strong></p>\n<p>KE = <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mn>1</mn><mn>2</mn></mfrac></math> × 0.0027 × 10.67<sup>2</sup> = 0.15 «J»  <strong>✓</strong></p>\n<div class=\"question_part_label\">d.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mtext>Δ</mtext><mi>v</mi><mo> </mo><mo>=</mo><mo> </mo><mn>21</mn></math> «m s<sup>−1</sup>» <strong>✓</strong></p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>F</mi><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>0027</mn><mo> </mo><mo>×</mo><mn>21</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>01</mn></mrow></mfrac></math></p>\n<p><em><strong>OR</strong></em></p>\n<p>5.67 «N» <strong>✓</strong></p>\n<p>any answer to 2 significant figures «N» <strong>✓</strong></p>\n<div class=\"question_part_label\">d.ii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">d.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">d.ii.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-1-kinematics",
      "a-2-forces-and-momentum",
      "a-3-work-energy-and-power"
    ]
  },
  {
    "question_id": "21M.2.SL.TZ1.2",
    "Question": "<div class=\"specification\">\n<p>A planet is in a circular orbit around a star. The speed of the planet is constant.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Explain why a centripetal force is needed for the planet to be in a circular orbit.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>State the nature of this centripetal force.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Determine the gravitational field of the planet.</p>\n<p>The following data are given:</p>\n<p style=\"padding-left:180px;\">Mass of planet            <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>8</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>24</mn></msup></math> kg<br/>Radius of the planet    <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>9</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></math> m.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>«circular motion» involves a changing velocity <strong>✓</strong></p>\n<p>«Tangential velocity» is «always» perpendicular to centripetal force/acceleration <strong>✓</strong></p>\n<p>there must be a force/acceleration towards centre/star <strong>✓</strong></p>\n<p>without a centripetal force the planet will move in a straight line <strong>✓</strong></p>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>gravitational force/force of gravity ✓</p>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>use of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mi>G</mi><mi>M</mi></mrow><msup><mi>R</mi><mn>2</mn></msup></mfrac></math> ✓</p>\n<p>6.4 «Nkg<sup>−1</sup> or ms<sup>−2</sup>» ✓</p>\n<div class=\"question_part_label\">b.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-2-forces-and-momentum"
    ]
  },
  {
    "question_id": "21M.2.SL.TZ1.3",
    "Question": "<div class=\"specification\">\n<p>A mass of 1.0 kg of water is brought to its boiling point of 100 °C using an electric heater of power 1.6 kW.</p>\n</div><div class=\"specification\">\n<p>A mass of 0.86 kg of water remains after it has boiled for 200 s.</p>\n</div><div class=\"specification\">\n<p>The electric heater has two identical resistors connected in parallel.</p>\n<p><img src=\"data:image/png;base64,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\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>The circuit transfers 1.6 kW when switch A only is closed. The external voltage is 220 V.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The molar mass of water is 18 g mol<sup>−1</sup>. Estimate the average speed of the water molecules in the vapor produced. Assume the vapor behaves as an ideal gas.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>State <strong>one</strong> assumption of the kinetic model of an ideal gas.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Estimate the specific latent heat of vaporization of water. State an appropriate unit for your answer.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Explain why the temperature of water remains at 100 °C during this time.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The heater is removed and a mass of 0.30 kg of pasta at −10 °C is added to the boiling water.</p>\n<p>Determine the equilibrium temperature of the pasta and water after the pasta is added. Other heat transfers are negligible.</p>\n<p style=\"padding-left:180px;\">Specific heat capacity of pasta = 1.8 kJ kg<sup>−1</sup> K<sup>−1</sup><br/>Specific heat capacity of water = 4.2 kJ kg<sup>−1</sup> K<sup>−1</sup></p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Show that each resistor has a resistance of about 30 Ω.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">d.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Calculate the power transferred by the heater when both switches are closed.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">d.ii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><em>E</em><sub>k</sub> = « <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>(</mo><mn>1</mn><mo>.</mo><mn>38</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>23</mn></mrow></msup><mo>)</mo><mo>(</mo><mn>373</mn><mo>)</mo></math>» = <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>7</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>21</mn></mrow></msup></math> «J» <strong>✓</strong></p>\n<p><em>v = </em>«<em><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msqrt><mfrac><mrow><mn>3</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>38</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>23</mn></mrow></msup><mo>×</mo><mn>6</mn><mo>.</mo><mn>02</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup><mo>×</mo><mn>373</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>018</mn></mrow></mfrac></msqrt></math></em>»<em> = </em>720 «m s<sup>−1</sup>» <strong>✓</strong></p>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>particles can be considered points «without dimensions» <strong>✓</strong></p>\n<p>no intermolecular forces/no forces between particles «except during collisions»<strong>✓</strong></p>\n<p>the volume of a particle is negligible compared to volume of gas <strong>✓</strong></p>\n<p>collisions between particles are elastic <strong>✓</strong></p>\n<p>time between particle collisions are greater than time of collision <strong>✓</strong></p>\n<p>no intermolecular PE/no PE between particles  <strong>✓</strong></p>\n<p> </p>\n<p><em>Accept reference to atoms/molecules for “particle”</em></p>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>«<em>mL = P</em> t» so «<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>L</mi><mo>=</mo><mfrac><mrow><mn>1600</mn><mo>×</mo><mn>200</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>14</mn></mrow></mfrac></math>» = 2.3 x 10<sup>6</sup> «J kg<sup>-1</sup>» <strong>✓</strong></p>\n<p>J kg<sup>−1 </sup><strong>✓</strong></p>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>«all» of the energy added is used to increase the «intermolecular» potential energy of the particles/break «intermolecular» bonds/<strong>OWTTE</strong> <strong>✓</strong></p>\n<p><em>Accept reference to atoms/molecules for “particle”</em> </p>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>use of mcΔT <strong>✓</strong></p>\n<p>0.86 × 4200 × (100 – <em>T</em>) = 0.3 × 1800 × (<em>T</em> +10) <strong>✓</strong></p>\n<p><em>T</em><sub>eq</sub> = 85.69«°C» ≅ 86«°C» <strong>✓</strong></p>\n<p><em>Accept T<sub>eq</sub> in Kelvin (359 K).</em></p>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>P</mi><mo>=</mo><mfrac><msup><mi>v</mi><mn>2</mn></msup><mi>R</mi></mfrac><mo> </mo><mi>so</mi><mo> </mo><mfrac><msup><mn>220</mn><mn>2</mn></msup><mn>1600</mn></mfrac><mo> </mo><mi>so</mi><mo> </mo><mi>R</mi><mo>=</mo><mn>30</mn><mo>.</mo><mn>25</mn></math> «Ω» <strong>✓</strong></p>\n<p><em>Must see either the substituted values <strong>OR</strong> a value for R to at least three s.f.</em></p>\n<p> </p>\n<div class=\"question_part_label\">d.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>use of parallel resistors addition so <em>R</em><sub>eq</sub> = 15 «Ω» <strong>✓</strong></p>\n<p><em>P</em> = 3200 «W» <strong>✓</strong></p>\n<div class=\"question_part_label\">d.ii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">d.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">d.ii.</div>\n</div>",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-1-thermal-energy-transfers",
      "b-3-gas-laws",
      "b-5-current-and-circuits"
    ]
  },
  {
    "question_id": "21M.2.SL.TZ1.6",
    "Question": "<div class=\"specification\">\n<p>On a guitar, the strings played vibrate between two fixed points. The frequency of vibration is modified by changing the string length using a finger. The different strings have different wave speeds. When a string is plucked, a standing wave forms between the bridge and the finger.</p>\n<p>                                                       <img 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\"/></p>\n</div><div class=\"specification\">\n<p>The string is displaced 0.4 cm at point P to sound the guitar. Point P on the string vibrates with simple harmonic motion (shm) in its first harmonic with a frequency of 195 Hz. The sounding length of the string is 62 cm.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline how a standing wave is produced on the string.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Show that the speed of the wave on the string is about 240 m s<sup>−1</sup>.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Sketch a graph to show how the acceleration of point P varies with its displacement from the rest position.</p>\n<p>                 <img src=\"data:image/png;base64,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\"/></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b.ii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>«travelling» wave moves along the length of the string and reflects «at fixed end» <strong>✓</strong></p>\n<p>superposition/interference of incident and reflected waves <strong>✓</strong></p>\n<p>the superposition of the reflections is reinforced only for certain wavelengths <strong>✓</strong> </p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>λ</mi><mo>=</mo><mn>2</mn><mi>l</mi><mo>=</mo><mn>2</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>62</mn><mo>=</mo><mo>«</mo><mn>1</mn><mo>.</mo><mn>24</mn><mo> </mo><mtext>m</mtext><mo>»</mo></math> <strong>✓</strong></p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>v</mi><mo>=</mo><mi>f</mi><mi>λ</mi><mo>=</mo><mn>195</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>24</mn><mo>=</mo><mn>242</mn><mo> </mo><mo>«</mo><msup><mtext>m s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong></p>\n<p><em>Answer must be to 3 or more sf <strong>or</strong> working shown for<strong> MP2.</strong></em></p>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>straight line through origin with negative gradient <strong>✓</strong></p>\n<div class=\"question_part_label\">b.ii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.ii.</div>\n</div>",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-1-simple-harmonic-motion",
      "c-2-wave-model",
      "c-4-standing-waves-and-resonance"
    ]
  },
  {
    "question_id": "21M.2.SL.TZ1.7",
    "Question": "<div class=\"specification\">\n<p>Conservation of energy and conservation of momentum are two examples of conservation laws.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline the significance of conservation laws for physics.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>When a pi meson π- (du̅) and a proton (uud) collide, a possible outcome is a sigma baryon Σ<sup>0</sup> (uds) and a kaon meson Κ<sup>0</sup> (ds̅).</p>\n<p><br/>Apply <strong>three</strong> conservation laws to show that this interaction is possible.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">b.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>they express fundamental principles of nature <strong>✓</strong></p>\n<p>allow to model situations <strong>✓</strong></p>\n<p>allow to calculate unknown variables <strong>✓</strong></p>\n<p>allow to predict possible outcomes <strong>✓</strong></p>\n<p>allow to predict missing quantities/particles <strong>✓</strong></p>\n<p>allow comparison of different system states <strong>✓</strong></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>three correct conservation laws listed <strong>✓</strong></p>\n<p>at least one conservation law correctly demonstrated <strong>✓</strong></p>\n<p>all three conservation laws correctly demonstrated <strong>✓</strong></p>\n<div class=\"question_part_label\">b.</div>\n</div>",
    "Examiners report": "",
    "topics": [
      "nature-of-science"
    ],
    "subtopics": []
  },
  {
    "question_id": "21M.2.SL.TZ1.8",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline how a standing wave is produced on the string.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the speed of the wave on the string is about 240 m s\n   <sup>\n    −1\n   </sup>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Sketch a graph to show how the acceleration of point P varies with its displacement from the rest position.\n  </p>\n  <p>\n   <img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAjgAAAEeCAYAAACHaG9AAAAdUUlEQVR4Ae3dv24kx7UHYL+H4dxYKL82FF8YVmoIsFIrsMLrRMquIyuzMiuxQymwUusJLEC5Bb3AWi+wegJeHF4eurbZze3Z/ld/vgaoIXuqq059Z7jz0wyX+5M7BwECBAgQIECgM4GfdLYf2yFwk8BHH/3+7p13Xtx0zZbBL1++vPvgg9/efffdvx6nifWjDgcBAgQI7Ccg4OxnaaYGBc4OOJ9//pe7n/3sp68FnAbZlEyAAIHqBQSc6lukwCMFBJwjdc1NgACB6wQEnOvsh1053qaJYBGvZORHvG0T58vj66//cf92Tjnm1atXj0Om87z33q+fvDISr5i8++4vH9eJdcs55gLOm66JdaLe+Ija4i2mnPPTT//0uFbcF2NjH3FM74u145i+RRVzffLJx6/NE9fmEffH3HGuHFeulWPdEiBAYFQBAWfUzl+47wgcEQ7yiKAST87xkcc33/zz/kk8x8WYuC7HxJN8fB0fGYxibBk28u2guI1jbp1pwFlzTdSQASPmzQATc5X1xH1LNT33Mzgxf8yTY2L+2FdaZMApa4hz07XuN+0/BAgQGFRAwBm08Vdt+8svv7gPB/nknXXkqxvxRB1HPFnHE3iGlziX4SPCT34e8+WRoSjui+vi+nyVJMfEunE+xsRRBpy112TAKWvLa3PeXC/CSayXISjrLvdfvoKT9+f4nKc8nwEnQlB5pO302nKMzwkQIDCKgIAzSqcr22c8wUeoiY8MMxEEMuDEk/70CbzcQl5Thozy/nyyLwNQ3l++GlIGnLXXRMCJOeaOqD/3Vb59lKEjg8pSwCnrKefPABVzZsCZhrdYowxT5fU+J0CAwGgCAs5oHa9gvxlOIihEGIgn/bjNgJNP4HH/0pGvomQgmo7LIBFzzn3k3GWgWHtNXDsXcHIPcV+GnAxNawPO0txpEvWWn5f7FnBKDZ8TIDC6gIAz+iPg5P1niMgn/Fw+X+3IwBIhYY9XcKbr5Hp5WwacaRjJMdPbuRCSb49FsCmP6Zy5/7d9BSfmF3BKYZ8TIEBgXkDAmXdx9iCBCBT5Sk25RISG8ny+ylO+BZVhIUJCBoU4l0e+jRPX5ufTwBHhIF9hievKgLP2mrmAk/VMA1WsH/vK8zluKeDk/Tk+95bnY78CTqq4JUCAwLKAgLNs454DBPKJugweGXoiCGSgyVdEIqzEEU/qESziVZ34PD7i8ziX1+Q8cW0c+apQrJlzxHw5R5wrA87aa+YCTgSWqD/rjblyr3E+g1iGtAgwWXcErqgjj9xnhqAYG2NybgEnpdwSIEBgWUDAWbZxz0EC+apGPPHHRwSRDAPlKxfxeTyp57j4PENBlBafZ6iJMREMyutjTMwbgWZpjmnAWXPNXMCJ6yK8RBAp18p9ZaCLcJJ7innimAacGJPhLOfK62O8gHPP5j8ECBB4VkDAeZbHnQTGFvj222/v4sNBgACB1gQEnNY6pl4CJwq8//5v7n71q/8+cUVLESBAYB8BAWcfR7MQ6E7gq6/+/vh229/+9tfu9mdDBAj0LSDg9N1fuyPwVgI//vjj3YsXP38MOPF5nHMQIECgFQEBp5VOqZPAiQKfffbnx3CTP+j8xz/+74kVWIoAAQLbBAScbX6uJtCdwA8//PtJuMmQE/c5CBAg0IKAgNNCl9RI4ESBDz/83WLAiR86dhAgQKAFAQGnhS6pkcBJAvFXwvPVmqVbf238pGZYhgCBTQICziY+FxPoSyD+5lT8/E1+ZMjJr+M2xjgIECBQu4CAU3uH1EfgQoEMOBeWYGkCBAi8lYCA81ZsLiIwhoCAM0af7ZJAjwICTo9dtScCOwkIODtBmoYAgdMFBJzTyS1IoB0BAaedXqmUAIHXBQSc1z18RYBAISDgFBg+JUCgKQEBp6l2KZbAuQICzrneViNAYD8BAWc/SzMR6E5AwOmupTZEYBgBAWeYVtsogdsFBJzbzVxBgEAdAgJOHX1QBYEqBQScKtuiKAIEVggIOCuQDCEwqoCAM2rn7ZtA+wICTvs9tAMChwkIOIfRmpgAgYMFBJyDgU1PoGUBAafl7qmdwNgCAs7Y/bd7As8KCDjP8riTAIGKBQScipujNAJXCwg4V3fA+gQIvK2AgPO2cq4jMICAgDNAk22RQKcCAk6njbUtAnsICDh7KJqDAIErBAScK9StSaARAQGnkUYpkwCBJwICzhMSJwgQSAEBJyXcEiDQmoCA01rH1EvgRAEB50RsSxEgsKuAgLMrp8kI9CUg4PTVT7shMJKAgDNSt+2VwI0CAs6NYIYTIFCNgIBTTSsUQqA+AQGnvp6oiACBdQICzjonowgMKSDgDNl2mybQhYCA00UbbYLAMQICzjGuZiVA4HgBAed4YysQaFZAwGm2dQonMLyAgDP8QwAAgWUBAWfZxj0ECNQtIODU3R/VEbhUQMC5lN/iBAhsEBBwNuC5lEDvAgJO7x22PwL9Cgg4/fbWzghsFhBwNhOagACBiwQEnIvgLUugBQEBp4UuqZEAgTkBAWdOxTkCBO4FBBwPBAIEWhUQcFrtnLoJnCAg4JyAbAkCBA4REHAOYTUpgT4EBJw++mgXBEYUEHBG7Lo9E1gpIOCshDKMAIHqBASc6lqiIAL1CAg49fRCJQQI3CYg4NzmZTSBoQQEnKHabbMEuhIQcLpqp80Q2FdAwNnX02wECJwnIOCcZ20lAs0JCDjNtUzBBAg8CAg4HgoECCwKCDiLNO4gQKByAQGn8gYpj8CVAgLOlfrWJkBgi4CAs0XPtQQ6FxBwOm+w7RHoWEDA6bi5tkZgq4CAs1XQ9QQIXCUg4Fwlb10CDQgIOA00SYkECMwKCDizLE4SIBACAo7HAQECrQoIOK12Tt0EThAQcE5AtgQBAocICDiHsJqUQB8CAk4ffbQLAiMKCDgjdt2eCawUEHBWQhlGgEB1AgJOdS1REIF6BAScenqhEgIEbhMQcG7zMprAUAICzlDttlkCXQkIOF2102YI7Csg4OzraTYCBM4TEHDOs7YSgeYEBJzmWqZgAgQeBAQcDwUCBBYFBJxFGncQIFC5gIBTeYOUR+BKAQHnSn1rEyCwRUDA2aLnWgKdCwg4nTfY9gh0LCDgdNxcWyOwVUDA2SroegIErhIQcK6Sty6BBgQEnAaapEQCBGYFBJxZFicJEAgBAcfjgACBVgUEnFY7p24CJwgIOCcgW4IAgUMEBJxDWE1KoA8BAaePPtoFgREFBJwRu27PBFYKCDgroQwjQKA6AQGnupYoiEA9AgJOPb1QCQECtwkIOLd5GU1gKAEBZ6h22yyBrgQEnK7aaTME9hUQcPb1NBsBAucJCDjnWVuJQHMCAk5zLVMwAQIPAgKOhwIBAosCAs4ijTsIEKhcQMCpvEHKI3ClgIBzpb61CRDYIiDgbNFzLYHOBQSczhtsewQ6FhBwOm6urRHYKiDgbBV0PQECVwkIOFfJW5dAAwICTgNNUiIBArMCAs4si5MECISAgONxQIBAqwICTqudUzeBEwQEnBOQLUGAwCECAs4hrCYl0IeAgNNHH+2CwIgCAs6IXbdnAisFBJyVUIYRIFCdgIBTXUsURKAeAQGnnl6ohACB2wQEnNu8jCYwlICAM1S7bZZAVwICTlfttBkC+woIOPt6mo0AgfMEBJzzrK1EoDkBAae5limYAIEHAQHHQ4EAgUUBAWeRxh0ECFQuIOBU3iDlEbhSQMC5Ut/aBAhsERBwtui5lkDnAgJO5w22PQIdCwg4HTfX1ghsFRBwtgq6ngCBqwQEnKvkrUugAQEBp4EmKZEAgVkBAWeWxUkCBEJAwPE4IECgVQEBp9XOqZvACQICzgnIliBA4BABAecQVpMS6ENAwOmjj3ZBYEQBAWfErtszgZUCAs5KKMMIEKhOQMCpriUKIlCPgIBTTy9UQoDAbQICzm1eRhMYSkDAGardNkugKwEBp6t22gyBfQUEnH09zUaAwHkCAs551lYi0JyAgNNcyxRMgMCDgIDjoUCAwKKAgLNI4w4CBCoXEHAqb5DyCFwpIOBcqW9tAgS2CAg4W/RcS6BzAQGn8wbbHoGOBQScjptrawS2Cgg4WwVdT4DAVQICzlXy1iXQgICA00CTlEiAwKyAgDPL4iQBAiEg4HgcECDQqoCA02rn1E3gBAEB5wRkSxAgcIiAgHMIq0kJ9CEg4PTRR7sgMKKAgDNi1+2ZwEoBAWcllGEECFQnIOBU1xIFEahHQMCppxcqIUDgNgEB5zYvowkMJSDgDNVumyXQlYCA01U7bYbAvgICzr6eZiNA4DwBAec8aysRaE5AwGmuZQomQOBBQMDxUCBAYFFAwFmkcQcBApULCDiVN0h5BK4UEHCu1Lc2AQJbBAScLXquJdC5gIDTeYNtj0DHAgJOx821NQJbBQScrYKuJ0DgKgEB5yp56xJoQEDAaaBJSiRAYFZAwJllcZIAgRAQcDwOCBBoVUDAabVz6iZwgoCAcwKyJQgQOERAwDmE1aQE+hAQcProo10QGFFAwBmx6/ZMYKWAgLMSyjACBKoTEHCqa4mCCNQjIODU0wuVECBwm4CAc5uX0QSaEfj887/cvfPOi8cfFP7gg9/eff31P26qX8C5ictgAgQqEhBwKmqGUgjsJRBBJsLJp5/+6XHKCDhx7uXLl4/n3vSJgPMmIfcTIFCrgIBTa2fURWCDwCeffHz37ru/fG2GCDYRWL788ovXzj/3hYDznI77CBCoWUDAqbk7aiPwlgIRbj766PdPrl46/2TgwwkBZ0nGeQIEahcQcGrvkPoI3Cjw6tWrJ29P5RTvvffru/hYewg4a6WMI0CgNgEBp7aOqIfARoE3BZz4weO1h4CzVso4AgRqExBwauuIeghsFBBwNgK6nACBLgQEnC7aaBME/iPwpoDjLar/WPmMAIF+BQScfntrZwMLLP0w8dL5JSpvUS3JOE+AQO0CAk7tHVIfgbcQeO6viccvAFx7CDhrpYwjcJzADz/8++7bb789boFOZxZwOm2sbY0tkL/oL4JOHvGL/uIHjOMtrLWHgLNWyjgCxwlEuInvxQ8//N1dhB3HOgEBZ52TUQSaE5j+Uw3xszf+qYbm2qhgAvev3uT/bMTtZ5/9+e7HH38k8wYBAecNQO4mMLJA/qE6soG9E7haIF/Bye/HuP3FL/7r7quv/n51aVWvf2nAKZvl85/evwTJgYPHgMeAx4DHwNrHwPvv/8bP5yzELAHnZ76R1n4jGeex4jHgMeAxUNdj4MWLn9+/ZbXwHD/06UsDztDyNk+gAYF8MmugVCUS6FZg7i2q+N78wx/+xw8dP9N1AecZHHcRGF1AwBn9EWD/NQhMA463pdZ1RcBZ52QUgSEFBJwh227TlQlkwIm3o/xg8frmCDjrrYwkMJyAgDNcy224QoHvv//eXw1/i74IOG+B5hICowgIOKN02j4J9Ccg4PTXUzsisJuAgLMbpYkIEDhZQMA5GdxyBFoSEHBa6pZaCRAoBQScUsPnBAi8JiDgvMbhCwIEGhIQcBpqllIJnC0g4Jwtbj0CBPYSEHD2kjQPgQ4F5gLO9B/xjH+l/NZ/xLNDKlsiQKAyAQGnsoYoh0BNAtOAE0Emzn366Z8ey4yAE+devnz5eM4nBAgQuFpAwLm6A9YnULHANOB88snHd++++8vXKo5gE+O+/PKL1877ggABAlcKCDhX6lubQOUC04AT4eajj37/pOql808GOkGAAIGTBASck6AtQ6BFgTLgvHr16snbU7mn99779V18OAgQIFCLgIBTSyfUQaBCgVsCzjvvvKhwB0oiQGBUAQFn1M7bN4EVAgLOCiRDCBCoUkDAqbItiiJQh8AtAcdbVHX0TBUECPy/gIDjkUCAwKJAGXBi0NIPEy+dX5zYHQQIEDhYQMA5GNj0BFoWmAac5/6aePwCQAcBAgRqERBwaumEOghUKDANOPmL/iLo5BG/6C9+wDj+lpWDAIH/COT3S/6m7/gVC3v/MP533/3r/m83jvo/GPF7uOLPoHCYHgLOVMTXBAg8CkwDTtwx/aca4mdv8g/wxwt9QoDA/fdFfA8d+f0xesCJP4/CWMDxDUeAwE0CcwHnpgkMJjCwwPQVnCMoBBwB54jHlTkJdC8g4HTfYhvcUSD+jbb8nolXNuOt3Pg6X8GZvkUV5/Pfcotx8fZV+VZTvjoRt/GD/Dl3OWYu4EznjevKt5Vzy2W9sfb0n1uZzjN9K+i5+qKucm/lv18X68dbS+GRe4r9leuXv1g0HWNs+YpxWX/cN/0t696iyk67JUDgiUD+4fPkDicIEHhNIMNLhpm4jdAQ30N5LsfEhfEEHveXwSMDQz7R59cxLueI+2LODDnTgJNfl4EiaynPZfjIeTMs5NfffPPP+3ViXB7xedSS/7Bu1hehI89lGClrznG5r9h7BJryurkx+edP1h3XZQ3xeRx5Xex7egg4UxFfEyDwKJB/wDye8AkBAk8EMlTEk215TENDGXAiSMT3Vz7pl9fl5/nkPZ23nGe6dgSMCA/TI8JEfMSR4aUMV3E+QkkGmphjbp44F+vHkfWVe8i5pzXH3LlehqBpKIl5c80IMOGTX98veHd37xXnM4hlDdO5YryAk2puCRB4IiDgPCFxgsATgXySjSf38sgn+3wyLoNJvooRgSKuzzHl9TlvvjqS9+X5mH8acHJMhI4IWPERwSa+lzPg5PVlMMnr4jbWi/EZSMr7yj3kPGW4WKonAk4Gowgt0+ASa+R8sa8MOHlN1pDBML3ymrKGHCvgpIRbAgSeCAg4T0icIPBEYOlJNp/s88m4DAcxSQSJCCDx5J/fazEmA03Om2/H5MLlk3yuEWNzzggPMV+Ep5g/gkz5Ck6ci/uzrpw3b3POrGnuNmrK+spwkddmPTlnGXDK/c7NHXUJOCnnlgCBQwTyD59DJjcpgU4E8on+lldwpluPJ/QMHtNXWqYBp1xvGiimP6OS60Tomc77pldwop7njqzj1oBT1rI0v4CzJOM8AQK7CAg4uzCapHOBfEtnGggyAOQrJdNXcOZYyjHT63N8OWYacOLVkQwyOT7CQnk+3zqbvgUVwSPGxbEUQspXgrK+WwNOrBvrTINb+OV5ASe755YAgUMEBJxDWE3aoUA+aWeYidt4so7voTxXBpM4F/dFSMgjr8ngkQEiwkaGiDyX100DTqxRrhnhK17ViXMxTx75Sk/WNp03Xt2Ja2K+PKKuOJevVOU1WVuMm9aT14ZFzhU1xddRQ74dl+vlvtYGnLwu9pFz5Zp+Bicl3BIg8EQg/jCLDwcBAm8WyCf8+J6JMJFfZ4goA07MFk/O8YpIfp/FbT7Bx/15fb6ykfPGdXlMA0UEgww0MT6CRFyfAax81STO59oxrlw75o+6y7mi1txLWd+tASeujTCSYSzrLNdfG3DK/U5fuRJw8lHilgCBJwL5h9+TO5wgQOBwgQw4ZYA4fNGOFhBwOmqmrRDYW0DA2VvUfATWCwg4663mRgo4cyrOESBwLyDgeCAQuE5AwNlmL+Bs83M1ga4FBJyu22tzBLoWEHC6bq/NEdgmIOBs83M1AQLXCQg419lbmUD1AgJO9S1SIAECCwICzgKM0wQI3D3+FVIWBAgQaE1AwGmtY+olcKKAV3BOxLYUAQK7Cgg4u3KajEBfAgJOX/20GwIjCQg4I3XbXgncKCDg3AhmOAEC1QgIONW0QiEE6hMQcOrriYoIEFgnIOCsczKKwJACAs6QbbdpAl0ICDhdtNEmCBwjIOAc42pWAgSOFxBwjje2AoFmBQScZluncALDCwg4wz8EABBYFhBwlm3cQ4BA3QICTt39UR2BSwUEnEv5LU6AwAYBAWcDnksJ9C4g4PTeYfsj0K+AgNNvb+2MwGYBAWczoQkIELhIQMC5CN6yBFoQEHBa6JIaCRCYExBw5lScI0DgXkDA8UAgQKBVAQGn1c6pm8AJAgLOCciWIEDgEAEB5xBWkxLoQ0DA6aOPdkFgRAEBZ8Su2zOBlQICzkoowwgQqE5AwKmuJQoiUI+AgFNPL1RCgMBtAgLObV5GExhKQMAZqt02S6ArAQGnq3baDIF9BQScfT3NRoDAeQICznnWViLQnICA01zLFEyAwIOAgOOhQIDAooCAs0jjDgIEKhcQcCpvkPIIXCkg4Fypb20CBLYICDhb9FxLoHMBAafzBtsegY4FBJyOm2trBLYKCDhbBV1PgMBVAgLOVfLWJdCAgIDTQJOUSIDArICAM8viJAECISDgeBwQINCqgIDTaufUTeAEAQHnBGRLECBwiICAcwirSQn0ISDg9NFHuyAwooCAM2LX7ZnASgEBZyWUYQQIVCcg4FTXEgURqEdAwKmnFyohQOA2AQHnNi+jCQwlIOAM1W6bJdCVgIDTVTtthsC+AgLOvp5mI0DgPAEB5zxrKxFoTkDAaa5lCiZA4EFAwPFQIEBgUUDAWaRxBwEClQsIOJU3SHkErhQQcK7UtzYBAlsEBJwteq4l0LmAgNN5g22PQMcCAk7HzbU1AlsFBJytgq4nQOAqAQHnKnnrEmhAQMBpoElKJEBgVkDAmWVxkgCBEBBwPA4IEGhVQMBptXPqJnCCgIBzArIlCBA4REDAOYTVpAT6EBBw+uijXRAYUUDAGbHr9kxgpYCAsxLKMAIEqhMQcKpriYII1CMg4NTTC5UQIHCbgIBzm5fRBIYSEHCGarfNEuhKQMDpqp02Q2BfAQFnX0+zESBwnoCAc561lQg0JyDgNNcyBRMg8CAg4HgoECCwKCDgLNK4gwCBygUEnMobpDwCVwoIOFfqW5sAgS0CAs4WPdcS6FxAwOm8wbZHoGMBAafj5toaga0CAs5WQdcTIHCVgIBzlbx1CTQgIOA00CQlEiAwKyDgzLI4SYBACAg4HgcECLQqIOC02jl1EzhBQMA5AdkSBAgcIiDgHMJqUgJ9CAg4ffTRLgiMKCDgjNh1eyawUkDAWQllGAEC1QkIONW1REEE6hEQcOrphUoIELhNQMC5zctoAkMJCDhDtdtmCXQlIOB01U6bIbCvgICzr6fZCBA4T0DAOc/aSgSaExBwmmuZggkQeBAQcDwUCBBYFBBwFmncQYBA5QICTuUNUh6BKwUEnCv1rU2AwBYBAWeLnmsJdC4g4HTeYNsj0LGAgNNxc22NwFYBAWeroOsJELhKQMC5St66BBoQEHAaaJISCRCYFRBwZlmcJEAgBAQcjwMCBFoVEHBa7Zy6CZwgIOCcgGwJAgQOERBwDmE1KYE+BAScPvpoFwRGFBBwRuy6PRNYKSDgrIQyjACB6gQEnOpaoiAC9QgIOPX0QiUECNwmIODc5mU0gaEEBJyh2m2zBLoSEHC6aqfNENhXQMDZ19NsBAicJyDgnGdtJQLNCQg4zbVMwQQIPAgIOB4KBAgsCgg4izTuIECgcgEBp/IGKY/AlQICzpX61iZAYIuAgLNFz7UEOhcQcDpvsO0R6FhAwOm4ubZGYKuAgLNV0PUECFwlIOBcJW9dAg0ICDgNNEmJBAjMCgg4syxOEiAQAgKOxwEBAq0KCDitdk7dBE4QEHBOQLYEAQKHCAg4h7CalEAfAgJOH320CwIjCgg4I3bdngmsFBBwVkIZRoBAdQICTnUtURCBegQEnHp6oRICBG4TEHBu8zKawFACAs5Q7bZZAl0JCDhdtdNmCOwrIODs62k2AgTOExBwzrO2EoHmBASc5lqmYAIEHgQEHA8FAgQWBQScRRp3ECBQuYCAU3mDlEfgSgEB50p9axMgsEVAwNmi51oCnQsIOJ032PYIdCwg4HTcXFsjsFVAwNkq6HoCBK4SEHCukrcugQYEBJwGmqREAgRmBQScWRYnCRAIAQHH44AAgVYFBJxWO6duAicICDgnIFuCAIFDBAScQ1hNSqAPAQGnjz7aBYERBQScEbtuzwRWCgg4K6EMI0CgOgEBp7qWKIhAPQICTj29UAkBArcJCDi3eRlNgAABAgQINCAg4DTQJCUSIECAAAECtwkIOLd5GU2AAAECBAg0IPB/OXmSBHonHjkAAAAASUVORK5CYII=\"/>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The string is made to vibrate in its third harmonic. State the distance between consecutive nodes.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  «travelling» wave moves along the length of the string and reflects «at fixed end»\n  <strong>\n   ✓\n  </strong>\n </p>\n <p>\n  superposition/interference of incident and reflected waves\n  <strong>\n   ✓\n  </strong>\n </p>\n <p>\n  the superposition of the reflections is reinforced only for certain wavelengths\n  <strong>\n   ✓\n  </strong>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.i)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    λ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    2\n   </mn>\n   <mi>\n    l\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    2\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    62\n   </mn>\n   <mo>\n    =\n   </mo>\n   <mo>\n    «\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    24\n   </mn>\n   <mo>\n   </mo>\n   <mtext>\n    m\n   </mtext>\n   <mo>\n    »\n   </mo>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    v\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mi>\n    f\n   </mi>\n   <mi>\n    λ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    195\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    24\n   </mn>\n   <mo>\n    =\n   </mo>\n   <mn>\n    242\n   </mn>\n   <mo>\n   </mo>\n   <mo>\n    «\n   </mo>\n   <msup>\n    <mtext>\n     m s\n    </mtext>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      1\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n    »\n   </mo>\n  </math>\n  ✓\n </p>\n <p>\n  <em>\n   Answer must be to 3 or more sf or working shown for\n   <strong>\n    MP2.\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.ii)\n </div><div class=\"card-body\">\n <p>\n  straight line through origin with negative gradient\n  <strong>\n   ✓\n  </strong>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     62\n    </mn>\n    <mn>\n     3\n    </mn>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    21\n   </mn>\n   <mo>\n   </mo>\n   <mo>\n    «\n   </mo>\n   <mtext>\n    cm\n   </mtext>\n   <mo>\n    »\n   </mo>\n  </math>\n  <strong>\n   ✓\n  </strong>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-1-simple-harmonic-motion",
      "c-2-wave-model",
      "c-4-standing-waves-and-resonance"
    ]
  },
  {
    "question_id": "21M.2.SL.TZ2.1",
    "Question": "<div class=\"specification\">\n<p>A football player kicks a stationary ball of mass 0.45 kg towards a wall. The initial speed of the ball after the kick is 19 m s<sup>−1</sup> and the ball does not rotate. Air resistance is negligible and there is no wind.</p>\n<p style=\"text-align: center;\"><img src=\"data:image/png;base64,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\"/></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The player’s foot is in contact with the ball for 55 ms. Calculate the average force that acts on the ball due to the football player.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The ball leaves the ground at an angle of 22°. The horizontal distance from the initial position of the edge of the ball to the wall is 11 m. Calculate the time taken for the ball to reach the wall.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The top of the wall is 2.4 m above the ground. Deduce whether the ball will hit the wall.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>In practice, air resistance affects the ball. Outline the effect that air resistance has on the vertical acceleration of the ball. Take the direction of the acceleration due to gravity to be positive.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The player kicks the ball again. It rolls along the ground without sliding with a horizontal velocity of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>1</mn><mo>.</mo><mn>40</mn><mo> </mo><msup><mtext>m s</mtext><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The radius of the ball is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn><mo>.</mo><mn>11</mn><mo> </mo><mtext>m</mtext></math>. Calculate the angular velocity of the ball. State an appropriate SI unit for your answer.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">d.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mtext>Δ</mtext><mi>p</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>45</mn><mo>×</mo><mn>19</mn><mo> </mo><mtext mathvariant=\"bold-italic\">OR  </mtext><mi>a</mi><mo> </mo><mo>=</mo><mfrac><mn>19</mn><mrow><mn>0</mn><mo>.</mo><mn>055</mn></mrow></mfrac></math> <strong>✓</strong> </p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>«</mo><mo>=</mo><mi>F</mi><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>45</mn><mo>×</mo><mn>19</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>055</mn></mrow></mfrac><mo>»</mo><mn>160</mn><mo> </mo><mo>«</mo><mtext>N</mtext><mo>»</mo></math> <strong>✓</strong></p>\n<p><em>Allow <strong>[2]</strong> marks for a bald correct answer.</em></p>\n<p><em>Allow <strong>ECF</strong> for <strong>MP2</strong> if 19 sin22 <strong>OR</strong> 19 cos22 used.</em></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mtext>horizontal speed =</mtext><mo> </mo><mn>19</mn><mo>×</mo><mi>cos</mi><mo> </mo><mn>22</mn><mo> </mo><mo>«</mo><mo>=</mo><mn>17</mn><mo>.</mo><mn>6</mn><msup><mtext> m s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong> </p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mtext>time</mtext><mo>=</mo><mo>«</mo><mfrac><mtext>distance</mtext><mtext>speed</mtext></mfrac><mo>=</mo><mfrac><mn>11</mn><mrow><mn>19</mn><mo> </mo><mi>cos</mi><mo> </mo><mn>22</mn></mrow></mfrac><mo>=</mo><mo>»</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>62</mn><mo> </mo><mo>«</mo><mtext>s</mtext><mo>»</mo></math> <strong>✓</strong></p>\n<p><em>Allow <strong>ECF</strong> for <strong>MP2</strong></em></p>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mtext>initial vertical speed</mtext><mo>=</mo><mn>19</mn><mo>×</mo><mi>sin</mi><mo> </mo><mn>22</mn><mo> </mo><mo>«</mo><mo>=</mo><mo> </mo><mn>7</mn><mo>.</mo><mn>1</mn><mo> </mo><msup><mtext>m s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong> </p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>«</mo><mn>7</mn><mo>.</mo><mn>12</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>624</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>9</mn><mo>.</mo><mn>81</mn><mo>×</mo><mn>0</mn><mo>.</mo><msup><mn>624</mn><mn>2</mn></msup><mo>=</mo><mo>»</mo><mo> </mo><mn>2</mn><mo>.</mo><mn>5</mn><mo> </mo><mo>«</mo><mtext>m</mtext><mo>»</mo></math> <strong>✓</strong></p>\n<p>ball does not hit wall <em><strong>OR</strong> </em>2.5 «m» &gt; 2.4 «m» <strong>✓</strong></p>\n<p><em><br/>Allow <strong>ECF</strong> from (b)(i) and from <strong>MP1</strong> </em></p>\n<p><em>Allow g = 10 m s<sup>−2</sup></em></p>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>air resistance opposes «direction of» motion<br/><em><strong>OR</strong></em><br/>air resistance opposes velocity <strong>✓</strong></p>\n<p>on the way up «vertical» acceleration is increased <em><strong>OR</strong> </em>greater than g <strong>✓</strong></p>\n<p>on the way down «vertical» acceleration is decreased <em><strong>OR</strong> </em>smaller than g <strong>✓</strong></p>\n<p><em><br/>Allow deceleration/acceleration but meaning must be clear</em></p>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>13</mn><mo> </mo><mo>«</mo><mtext>rad</mtext><mo>»</mo><mo> </mo><msup><mtext>s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><strong>✓</strong></p>\n<p><em><br/>Unit must be seen for mark</em></p>\n<p><em>Accept Hz</em></p>\n<p><em>Accept <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>4</mn><mo> </mo><mi>π</mi><mo> </mo><mo>«</mo><mtext>rad</mtext><mo>»</mo><mo> </mo><msup><mtext>s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></em></p>\n<div class=\"question_part_label\">d.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">d.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-1-kinematics",
      "a-2-forces-and-momentum"
    ]
  },
  {
    "question_id": "21M.2.SL.TZ2.5",
    "Question": "<div class=\"specification\">\n<p>A vertical tube, open at both ends, is completely immersed in a container of water. A loudspeaker above the container connected to a signal generator emits sound. As the tube is raised the loudness of the sound heard reaches a maximum because a standing wave has formed in the tube.</p>\n<p style=\"text-align: center;\"><img src=\"data:image/png;base64,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\"/></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Describe <strong>two</strong> ways in which standing waves differ from travelling waves.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline how a standing wave forms in the tube.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The tube is raised until the loudness of the sound reaches a maximum for a <strong>second time</strong>.</p>\n<p>Draw, on the following diagram, the position of the nodes in the tube when the second maximum is heard.</p>\n<p><img src=\"data:image/png;base64,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\" style=\"display:block;margin-left:auto;margin-right:auto;\"/></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Between the first and second positions of maximum loudness, the tube is raised through 0.37 m. The speed of sound in the air in the tube is 320 m s<sup>−1</sup>. Determine the frequency of the sound emitted by the loudspeaker.</p>\n<p> </p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.iii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>energy is not propagated by standing waves <strong>✓</strong></p>\n<p>amplitude constant for travelling waves <em><strong>OR</strong> </em>amplitude varies with position for standing waves <em><strong>OR</strong> </em>standing waves have nodes/antinodes <strong>✓</strong></p>\n<p>phase varies with position for travelling waves <em><strong>OR</strong> </em>phase constant inter-node for standing waves <strong>✓</strong></p>\n<p>travelling waves can have any wavelength <em><strong>OR</strong> </em>standing waves have discrete wavelengths<strong> ✓</strong></p>\n<p><strong><em><br/>OWTTE</em></strong></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>«sound» wave «travels down tube and» is reflected <strong>✓</strong></p>\n<p>incident and reflected wave superpose/combine/interfere <strong>✓</strong></p>\n<p><strong><em><br/>OWTTE</em></strong></p>\n<p><em>Do not award <strong>MP1</strong> if the reflection is quoted at the walls/container</em></p>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>nodes shown at water surface <em><strong>AND </strong></em><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mn>2</mn><mn>3</mn></mfrac></math>way up tube (by eye) <strong>✓</strong></p>\n<p><em><br/>Accept drawing of displacement diagram for correct harmonic without nodes specifically identified. </em></p>\n<p><em>Award <strong>[0]</strong> if waveform is shown below the water surface</em></p>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>λ</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>74</mn><mo> </mo><mo>«</mo><mtext>m</mtext><mo>»</mo></math> <strong>✓</strong></p>\n<p><strong><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>f</mi><mo>=</mo><mo>«</mo><mfrac><mi>c</mi><mi>λ</mi></mfrac><mo>=</mo><mfrac><mn>320</mn><mrow><mn>0</mn><mo>.</mo><mn>74</mn></mrow></mfrac><mo>=</mo><mo>»</mo><mo> </mo><mn>430</mn><mo> </mo><mo>«</mo><mtext>Hz</mtext><mo>»</mo></math> ✓</strong></p>\n<p><em><br/>Allow <strong>ECF</strong> from <strong>MP1</strong></em></p>\n<div class=\"question_part_label\">b.iii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.iii.</div>\n</div>",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-4-standing-waves-and-resonance"
    ]
  },
  {
    "question_id": "21M.2.SL.TZ2.6",
    "Question": "<div class=\"specification\">\n<p>A photovoltaic cell is supplying energy to an external circuit. The photovoltaic cell can be modelled as a practical electrical cell with internal resistance.</p>\n<p>The intensity of solar radiation incident on the photovoltaic cell at a particular time is at a maximum for the place where the cell is positioned.</p>\n<p>The following data are available for this particular time:</p>\n<p style=\"text-align: left; padding-left: 150px;\">                                          Operating current = 0.90 A<br/>Output potential difference to external circuit = 14.5 V<br/>                      Output emf of photovoltaic cell = 21.0 V<br/>                                                 Area of panel = 350 mm × 450 mm</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Explain why the output potential difference to the external circuit and the output emf of the photovoltaic cell are different.</p>\n<p> </p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Calculate the internal resistance of the photovoltaic cell for the maximum intensity condition using the model for the cell.</p>\n<p> </p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The maximum intensity of sunlight incident on the photovoltaic cell at the place on the Earth’s surface is 680 W m<sup>−2</sup>.</p>\n<p>A measure of the efficiency of a photovoltaic cell is the ratio</p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mtext>energy available every second to the external circuit</mtext><mtext>energy arriving every second at the photovoltaic cell surface</mtext></mfrac><mo>.</mo></math></p>\n<p>Determine the efficiency of this photovoltaic cell when the intensity incident upon it is at a maximum.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>State <strong>two</strong> reasons why future energy demands will be increasingly reliant on sources such as photovoltaic cells.</p>\n<p><img src=\"data:image/png;base64,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\" style=\"display:block;margin-left:auto;margin-right:auto;\"/></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">d.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>there is a potential difference across the internal resistance<br/><em><strong>OR</strong></em><br/>there is energy/power dissipated in the internal resistance <strong>✓</strong></p>\n<p>when there is current «in the cell»/as charge flows «through the cell»<strong> ✓</strong></p>\n<p><em><br/>Allow full credit for answer based on <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>V</mi><mo>=</mo><mi>ε</mi><mo>-</mo><mi>I</mi><mi>r</mi></math></em></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><em><strong>ALTERNATIVE 1</strong></em><br/>pd dropped across cell <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>6</mn><mo>.</mo><mn>5</mn><mo> </mo><mo>«</mo><mtext>V</mtext><mo>»</mo></math>✓</p>\n<p>internal resistance <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi mathvariant=\"normal\">=</mi><mfrac><mrow><mn>6</mn><mo>.</mo><mn>5</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>9</mn></mrow></mfrac></math> ✓</p>\n<p><strong><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>7</mn><mo>.</mo><mn>2</mn><mo> </mo><mo>«</mo><mtext>Ω</mtext><mo>»</mo></math>✓</strong></p>\n<p><em><strong><br/>ALTERNATIVE 2</strong></em></p>\n<p><em><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>ε</mi><mo>=</mo><mi>I</mi><mo>(</mo><mi>R</mi><mo>+</mo><mi>r</mi><mo>)</mo></math> so <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>ε</mi><mo>=</mo><mi>V</mi><mo>+</mo><mi>I</mi><mi>r</mi></math> <strong>✓</strong></em></p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>21</mn><mo>.</mo><mn>0</mn><mo>=</mo><mn>14</mn><mo>.</mo><mn>5</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>9</mn><mo>×</mo><mi>r</mi></math> <strong>✓</strong></p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>7</mn><mo>.</mo><mn>2</mn><mo> </mo><mo>«</mo><mtext>Ω</mtext><mo>»</mo></math> <strong>✓</strong></p>\n<p><em><br/>Alternative solutions are possible</em></p>\n<p><em>Award <strong>[3]</strong> marks for a bald correct answer</em></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>power arriving at cell = 680 x 0.35 x 0.45 = «107 W» <strong>✓</strong></p>\n<p>power in external circuit = 14.5 x 0.9 = «13.1 W» <strong>✓</strong></p>\n<p>efficiency = 0.12 <em><strong>OR</strong></em> 12 % <strong>✓</strong></p>\n<p><em><br/>Award <strong>[3] marks</strong> for a bald correct answer</em></p>\n<p><em>Allow <strong>ECF</strong> for <strong>MP3</strong></em></p>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>«energy from Sun/photovoltaic cells» is renewable<br/><em><strong>OR</strong></em><br/>non-renewable are running out <strong>✓</strong></p>\n<p>non-polluting/clean <strong>✓</strong></p>\n<p>no greenhouse gases<br/><em><strong>OR</strong></em><br/>does not contribute to global warming/climate change <strong>✓</strong></p>\n<p><em><strong><br/>OWTTE </strong></em></p>\n<p><em>Do not allow economic aspects (e.g. free energy)</em></p>\n<div class=\"question_part_label\">d.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">d.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion",
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "a-3-work-energy-and-power",
      "b-5-current-and-circuits"
    ]
  },
  {
    "question_id": "21N.2.HL.TZ0.5",
    "Question": "<div class=\"specification\">\n<p>A square loop of side 5.0 cm enters a region of uniform magnetic field at <em>t</em> = 0. The loop exits the region of magnetic field at <em>t</em> = 3.5 s. The magnetic field strength is 0.94 T and is directed into the plane of the paper. The magnetic field extends over a length 65 cm. The speed of the loop is constant.</p>\n<p><img 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\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Show that the speed of the loop is 20 cm s<sup>−1</sup>.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Sketch, on the axes, a graph to show the variation with time of the magnetic flux linkage <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>Φ</mi></math> in the loop.</p>\n<p><img src=\"data:image/png;base64,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\"/></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Sketch, on the axes, a graph to show the variation with time of the magnitude of the emf induced in the loop.</p>\n<p><img src=\"data:image/png;base64,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\"/></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>There are 85 turns of wire in the loop. Calculate the maximum induced emf in the loop.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The resistance of the loop is 2.4 Ω. Calculate the magnitude of the magnetic force on the loop as it enters the region of magnetic field.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Show that the energy dissipated in the loop from <em>t </em>= 0 to <em>t </em>= 3.5 s is 0.13 J.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">d.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The mass of the wire is 18 g. The specific heat capacity of copper is 385 J kg<sup>−1</sup> K<sup>−1</sup>. Estimate the increase in temperature of the wire.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">d.ii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mn>70</mn><mrow><mn>3</mn><mo>.</mo><mn>5</mn></mrow></mfrac></math> ✓</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><img src=\"data:image/png;base64,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\"/></p>\n<p>shape as above ✓</p>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><img src=\"data:image/png;base64,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\"/></p>\n<p>shape as above ✓</p>\n<p> </p>\n<p><em>Vertical lines not necessary to score.</em></p>\n<p><em>Allow <strong>ECF</strong> from <strong>(b)(i)</strong>.</em></p>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><em><strong>ALTERNATIVE 1</strong></em></p>\n<p>maximum flux at «<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>5</mn><mo>.</mo><mn>0</mn><mo>×</mo><mn>5</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>4</mn></mrow></msup><mo>×</mo><mn>85</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>94</mn></math>» <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>0</mn><mo>.</mo><mn>19975</mn><mo>≈</mo><mn>0</mn><mo>.</mo><mn>20</mn><mo> </mo></math>«Wb» ✓</p>\n<p>emf = «<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mn>0</mn><mo>.</mo><mn>20</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>25</mn></mrow></mfrac><mo>=</mo></math>» <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn><mo>.</mo><mn>80</mn><mo> </mo></math>«V» ✓</p>\n<p><em><strong><br/>ALTERNATIVE 2</strong></em></p>\n<p>emf induced in one turn = <em>BvL</em> = <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn><mo>.</mo><mn>94</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>20</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>05</mn><mo>=</mo><mn>0</mn><mo>.</mo><mn>0094</mn><mo> </mo></math>«V» ✓</p>\n<p>emf <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>85</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>0094</mn><mo>=</mo><mn>0</mn><mo>.</mo><mn>80</mn><mo> </mo></math>«V» ✓</p>\n<p> </p>\n<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>\n<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong>.</em></p>\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>I</mi><mo>=</mo><mo>«</mo><mfrac><mi>V</mi><mi>R</mi></mfrac><mo>=</mo><mo>»</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>8</mn></mrow><mrow><mn>2</mn><mo>.</mo><mn>4</mn></mrow></mfrac></math>  <em><strong>OR  </strong></em><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn><mo>.</mo><mn>33</mn></math> «A» ✓</p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>F</mi><mo>=</mo><mo>«</mo><mi>N</mi><mi>B</mi><mi>I</mi><mi>L</mi><mo>=</mo><mn>85</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>94</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>33</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>05</mn><mo>=</mo><mo>»</mo><mo>=</mo><mn>1</mn><mo>.</mo><mn>3</mn></math> «N» ✓</p>\n<p> </p>\n<p><em>Allow <strong>ECF</strong> from <strong>(c)(i)</strong>.</em></p>\n<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>\n<div class=\"question_part_label\">c.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Energy is being dissipated for 0.50 s ✓</p>\n<p><br/><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>E</mi><mo>=</mo><mi>F</mi><mi>v</mi><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>3</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>20</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>50</mn><mo>=</mo></math>«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn><mo>.</mo><mn>13</mn></math> J»</p>\n<p><em><strong>OR</strong></em></p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>E</mi><mo>=</mo><mi>V</mi><mi>l</mi><mi>t</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>80</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>33</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>50</mn><mo>=</mo></math>«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn><mo>.</mo><mn>13</mn></math> J» ✓</p>\n<p> </p>\n<p><em>Allow <strong>ECF</strong> from <strong>(b)</strong> and <strong>(c)</strong>. </em></p>\n<p><em>Watch for candidates who do not justify somehow the use of 0.5 s and just divide by 2 their answer.</em></p>\n<div class=\"question_part_label\">d.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>∆</mo><mi>T</mi><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>13</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>018</mn><mo>×</mo><mn>385</mn></mrow></mfrac></math> ✓</p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>∆</mo><mi>T</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup></math> «K» ✓</p>\n<p> </p>\n<p><em>Allow <strong>[2]</strong> marks for a bald correct answer.</em></p>\n<p><em>Award <strong>[1]</strong> for a <strong>POT</strong> error in <strong>MP1</strong>.</em></p>\n<div class=\"question_part_label\">d.ii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">d.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">d.ii.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion",
      "b-the-particulate-nature-of-matter",
      "d-fields"
    ],
    "subtopics": [
      "a-3-work-energy-and-power",
      "b-1-thermal-energy-transfers",
      "b-5-current-and-circuits",
      "d-3-motion-in-electromagnetic-fields",
      "d-4-induction"
    ]
  },
  {
    "question_id": "21N.2.HL.TZ0.7",
    "Question": "<div class=\"specification\">\n<p>A conducting sphere has radius 48 cm. The electric potential on the surface of the sphere is 3.4 × 10<sup>5</sup> V.</p>\n</div><div class=\"specification\">\n<p>The sphere is connected by a long conducting wire to a second conducting sphere of radius 24 cm. The second sphere is initially uncharged.</p>\n<p style=\"text-align: center;\"> <img src=\"data:image/png;base64,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\"/></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Show that the charge on the surface of the sphere is +18 μC.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Describe, in terms of electron flow, how the smaller sphere becomes charged.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Predict the charge on each sphere.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">b.ii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>Q</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mi>V</mi><mi>R</mi></mrow><mi>k</mi></mfrac><mo>=</mo><mo>»</mo><mfrac><mrow><mn>3</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>48</mn></mrow><mrow><mn>8</mn><mo>.</mo><mn>99</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfrac></math></p>\n<p><em><strong>OR</strong></em></p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>Q</mi><mo>=</mo><mn>18</mn><mo>.</mo><mn>2</mn></math> «μC» ✓</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>electrons leave the small sphere «making it positively charged» ✓</p>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>k</mi><mfrac><msub><mi>q</mi><mn>1</mn></msub><mn>48</mn></mfrac><mo>=</mo><mi>k</mi><mfrac><msub><mi>q</mi><mn>2</mn></msub><mn>24</mn></mfrac><mo>⇒</mo><msub><mi>q</mi><mn>1</mn></msub><mo>=</mo><mn>2</mn><msub><mi>q</mi><mn>2</mn></msub></math> ✓</p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>q</mi><mn>1</mn></msub><mo>+</mo><msub><mi>q</mi><mn>2</mn></msub><mo>=</mo><mn>18</mn></math> ✓</p>\n<p>so <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>q</mi><mn>1</mn></msub><mo>=</mo><mn>12</mn></math> «μC», <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>q</mi><mn>2</mn></msub><mo>=</mo><mn>6</mn><mo>.</mo><mn>0</mn></math> «μC» ✓</p>\n<p> </p>\n<p><em>Award <strong>[3]</strong> marks for a bald correct answer.</em></p>\n<div class=\"question_part_label\">b.ii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.ii.</div>\n</div>",
    "topics": [
      "b-the-particulate-nature-of-matter",
      "d-fields"
    ],
    "subtopics": [
      "b-5-current-and-circuits",
      "d-2-electric-and-magnetic-fields"
    ]
  },
  {
    "question_id": "21N.2.HL.TZ0.8",
    "Question": "<div class=\"specification\">\n<p>The graph shows the variation with diffraction angle of the intensity of light after it has passed through four parallel slits.</p>\n<p><img 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\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>The number of slits is increased but their separation and width stay the same. All slits are illuminated.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>State what is meant by the Doppler effect.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>A plate performs simple harmonic oscillations with a frequency of 39 Hz and an amplitude of 8.0 cm.</p>\n<p>Show that the maximum speed of the oscillating plate is about 20 m s<sup>−1</sup>.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Sound of frequency 2400 Hz is emitted from a stationary source towards the oscillating plate in (b). The speed of sound is 340 m s<sup>−1</sup>.</p>\n<p><img src=\"data:image/png;base64,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\" style=\"display:block;margin-left:auto;margin-right:auto;\"/></p>\n<p>Determine the maximum frequency of the sound that is received back at the source after reflection at the plate.</p>\n<p> </p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>State what will happen to the angular position of the primary maxima.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">d.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>State what will happen to the width of the primary maxima.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">d.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>State what will happen to the intensity of the secondary maxima.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">d.iii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>the change in the observed frequency ✓</p>\n<p>when there is relative motion between the source and the observer ✓</p>\n<p> </p>\n<p><em>Do not award<strong> MP1</strong> if they refer to wavelength.</em></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>use of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>2</mn><mi mathvariant=\"normal\">π</mi><mi>f</mi><mi>A</mi></math> ✓</p>\n<p>maximum speed is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>2</mn><mi mathvariant=\"normal\">π</mi><mo>×</mo><mn>39</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>080</mn><mo>=</mo><mn>19</mn><mo>.</mo><mn>6</mn></math> «m s<sup>−1</sup>» ✓</p>\n<p> </p>\n<p><em>Award <strong>[2]</strong> for a bald correct answer.</em></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>frequency at plate <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>2400</mn><mo>×</mo><mfrac><mrow><mn>340</mn><mo>+</mo><mn>19</mn><mo>.</mo><mn>6</mn></mrow><mn>340</mn></mfrac></math>«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>=</mo><mn>2538</mn><mo> </mo></math>Hz»</p>\n<p>at source <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>2538</mn><mo>×</mo><mfrac><mn>340</mn><mrow><mn>340</mn><mo>-</mo><mn>19</mn><mo>.</mo><mn>6</mn></mrow></mfrac><mo>=</mo><mn>2694</mn><mo>≈</mo><mn>2700</mn></math> «Hz» ✓</p>\n<p> </p>\n<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>\n<p><em>Award <strong>[1]</strong> mark when the effect is only applied once.</em></p>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>stays the same ✓</p>\n<div class=\"question_part_label\">d.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>decreases ✓</p>\n<div class=\"question_part_label\">d.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>decreases ✓</p>\n<div class=\"question_part_label\">d.iii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">d.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">d.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">d.iii.</div>\n</div>",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-1-simple-harmonic-motion",
      "c-3-wave-phenomena",
      "c-5-doppler-effect"
    ]
  },
  {
    "question_id": "21N.2.SL.TZ0.3",
    "Question": "<div class=\"specification\">\n<p>A longitudinal wave travels in a medium with speed 340 m s<sup>−1</sup>. The graph shows the variation with time <em>t</em> of the displacement <em>x</em> of a particle P in the medium. Positive displacements on the graph correspond to displacements to the right for particle P.</p>\n<p style=\"text-align: center;\"><img 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\"/></p>\n</div><div class=\"specification\">\n<p>Another wave travels in the medium. The graph shows the variation with time <em>t</em> of the displacement of each wave at the position of P.</p>\n<p><img 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\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n</div><div class=\"specification\">\n<p>A standing sound wave is established in a tube that is closed at one end and open at the other end. The period of the wave is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math>. The diagram represents the standing wave at <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>t</mi><mo>=</mo><mn>0</mn></math> and at <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>t</mi><mo>=</mo><mfrac><mi>T</mi><mn>8</mn></mfrac></math>. The wavelength of the wave is 1.20 m. Positive displacements mean displacements to the right.</p>\n<p style=\"text-align: left;\"><img 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\"/></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Calculate the wavelength of the wave.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>State the phase difference between the two waves.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Identify a time at which the displacement of P is zero.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Estimate the amplitude of the resultant wave.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">b.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Calculate the length of the tube.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>A particle in the tube has its equilibrium position at the open end of the tube.<br/>State and explain the direction of the velocity of this particle at time <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>t</mi><mo>=</mo><mfrac><mi>T</mi><mn>8</mn></mfrac></math>.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Draw on the diagram the standing wave at time <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>t</mi><mo>=</mo><mfrac><mi>T</mi><mn>4</mn></mfrac></math>.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">c.iii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi><mo>=</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo></math>«s» or <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>f</mi><mo>=</mo><mn>250</mn><mo> </mo></math>«Hz» ✓</p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>λ</mi><mo>=</mo><mn>340</mn><mo>×</mo><mn>4</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>=</mo><mn>1</mn><mo>.</mo><mn>36</mn><mo>≈</mo><mn>1</mn><mo>.</mo><mn>4</mn><mo> </mo></math>«m» ✓</p>\n<p> </p>\n<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong>.<br/>Award <strong>[2]</strong> for a bald correct answer.</em></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>«±» <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mi mathvariant=\"normal\">π</mi><mn>2</mn></mfrac><mo>/</mo><mn>90</mn><mo>°</mo></math>  <em><strong>OR</strong></em>  <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mn>3</mn><mi mathvariant=\"normal\">π</mi></mrow><mn>2</mn></mfrac><mo>/</mo><mn>270</mn><mo>°</mo></math> ✓</p>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>1.5 «ms» ✓</p>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>8.0 <em><strong>OR</strong> </em>8.5 «μm» ✓</p>\n<p><em><br/>From the graph on the paper, value is 8.0. From the calculated correct trig functions, value is 8.49.</em></p>\n<div class=\"question_part_label\">b.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><em>L</em> = «<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle displaystyle=\"false\"><mfrac><mn>3</mn><mn>4</mn></mfrac><mi>λ</mi><mo>=</mo></mstyle></math>» 0.90 «m» ✓</p>\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>to the right ✓<br/><br/></p>\n<p>displacement is getting less negative</p>\n<p><em><strong>OR</strong></em></p>\n<p>change of displacement is positive ✓</p>\n<div class=\"question_part_label\">c.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>horizontal line drawn at the equilibrium position ✓</p>\n<div class=\"question_part_label\">c.iii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.iii.</div>\n</div>",
    "topics": [
      "c-wave-behaviour",
      "d-fields"
    ],
    "subtopics": [
      "c-1-simple-harmonic-motion",
      "d-2-electric-and-magnetic-fields"
    ]
  },
  {
    "question_id": "21N.2.SL.TZ0.4",
    "Question": "<div class=\"specification\">\n<p>A charged particle, P, of charge +68 μC is fixed in space. A second particle, Q, of charge +0.25 μC is held at a distance of 48 cm from P and is then released.</p>\n<p style=\"text-align: center;\"><img src=\"data:image/png;base64,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\"/></p>\n</div><div class=\"specification\">\n<p>The diagram shows two parallel wires X and Y that carry equal currents into the page.</p>\n<p><img src=\"data:image/png;base64,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\"/></p>\n<p>Point Q is equidistant from the two wires. The magnetic field at Q due to wire X <strong>alone </strong>is 15 mT.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The work done to move a particle of charge 0.25 μC from one point in an electric field to another is 4.5 μJ. Calculate the magnitude of the potential difference between the two points.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Determine the force on Q at the instant it is released.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Describe the motion of Q after release.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>On the diagram draw an arrow to show the direction of the magnetic field at Q due to wire X <strong>alone</strong>.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Determine the magnitude and direction of the resultant magnetic field at Q.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.ii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>V</mi><mo>=</mo><mfrac><mrow><mn>4</mn><mo>.</mo><mn>5</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>25</mn></mrow></mfrac><mo>=</mo></math>» 18 «V» ✓</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>F</mi><mo>=</mo><mfrac><mrow><mn>8</mn><mo>.</mo><mn>99</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup><mo>×</mo><mn>68</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>25</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow><mrow><mn>0</mn><mo>.</mo><msup><mn>48</mn><mn>2</mn></msup></mrow></mfrac></math> ✓</p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>F</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>66</mn></math> «N» ✓</p>\n<p> </p>\n<p><em>Award <strong>[2]</strong> marks for a bald correct answer. </em></p>\n<p><em>Allow symbolic k in substitutions for <strong>MP1</strong>. </em></p>\n<p><em>Do <strong>not</strong> allow <strong>ECF</strong> from incorrect or not squared distance.</em></p>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Q moves to the right/away from P «along a straight line»</p>\n<p><em><strong>OR</strong></em></p>\n<p>Q is repelled from P ✓</p>\n<p><br/>with increasing speed/Q accelerates ✓</p>\n<p>acceleration decreases ✓</p>\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p> </p>\n<p><img src=\"data:image/png;base64,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\"/></p>\n<p>arrow of any length as shown ✓</p>\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>«using components or Pythagoras to get» <em>B</em> = 21 «mT» ✓</p>\n<p>directed «horizontally» to the right ✓</p>\n<p> </p>\n<p><em>If no unit seen, assume</em> mT.</p>\n<div class=\"question_part_label\">c.ii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">c.ii.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion",
      "b-the-particulate-nature-of-matter",
      "d-fields"
    ],
    "subtopics": [
      "a-2-forces-and-momentum",
      "b-5-current-and-circuits",
      "d-2-electric-and-magnetic-fields",
      "d-3-motion-in-electromagnetic-fields"
    ]
  },
  {
    "question_id": "21N.2.SL.TZ0.5",
    "Question": "<div class=\"specification\">\n<p>Plutonium-238 (Pu) decays by alpha (α) decay into uranium (U).</p>\n<p>The following data are available for binding energies per nucleon:</p>\n<p style=\"padding-left: 30px;\">plutonium          7.568 MeV</p>\n<p style=\"padding-left: 30px;\">uranium             7.600 MeV</p>\n<p style=\"padding-left: 30px;\">alpha particle     7.074 MeV</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>State what is meant by the binding energy of a nucleus.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Draw, on the axes, a graph to show the variation with nucleon number <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>A</mi></math> of the binding energy per nucleon, <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mtext>BE</mtext><mi>A</mi></mfrac></math>. Numbers are not required on the vertical axis.</p>\n<p><img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAuUAAAFBCAYAAADQX9GbAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABUVSURBVHhe7d1/mFX1feDxj1NWkSFTQk3xB0yJMoJaE0JMsxvypJi2QhQtxeZHk5qi+NgkZjcaNTFYfbrJbhtXhcg+abLGRAqSGmuEGkyiMaJ9Sn+IQ9ioqGBaGEEgEhyHwSjivXvvzBkcYNDJPuJnzvh6+Vy59zvnjzlzvjP3Pd8599xDqjUBAACkaSj+BQAAkohyAABIttfpK83No4t7AADA66GtbeP+UV4fBAAADr6e/nb6CgAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPllM/u1rh23H+KIUP2vR0Tp37+W3Hv2o5iw5rNt8ef7bdd79upcW1rZ7ExAEAOUU55few78eTuF2N3cdv15K1x1pavxGmnfjnu7agUG3Ub++V/jed7bfvybXlc+s7hxVYAADlEOYNGw1H/JWb/2fQYtfXuuOvB7cUoAMDAJ8oZhI6N8aOtfgMA5SHKGTQqm/8lvvm3/xK/f8NV8aHjhxajAAADnyinvBZ/OMb0etHmoWOmxGWLfxHx7LOxY+9TymP95f85hvbads9t3LXRurvYCAAgiSinvPZ5oefu9ofi1kuOisWXfTKuXLohenf5AV/o+cSl8c4hxUYAAElEOYPH8Akx84rPxyWjHo0F/9AaW4thAICBTpQzuDS1xLt//7eKBwAA5SDKGVw61sW/3bMhRh05IhqLIQCAgU6UM3hUNsW9X746rtv6R/Gl2e+JpmIYAGCgE+WU1z5XXxly6Ng4Z9O0+MGaG+O8fS6JeMCrr9Ru465tDRdgAQAyHVKtKe5Hc/PoaGvbWDwCAAAOpp7+tlIOAADJRDkAACQT5QAAkEyUAwBAMlEOAADJRDml0tclDV+rGwBAFlFOqeze/eJBux3I3XffXdwDADg4RDm8gu3bt8fpp58RK1asKEYAAF57ohxewbe//e2uf6+55pqufwEADgZRDgdQXyW/6KKLu+4vW3an1XIA4KAR5QxqlU23x/nH1F/I+aH41trni9H+6Vkl72G1HAA4WEQ5g1h7/OTvvhU/mPLR+PCoYqif1q5du2eVvIfVcgDgYBHlDFqVTffG1+YNiy995oMxOv49Ht/YWXzk1d14443Fvb1ZLQcADgZRziC1Le6b/1fxgz/9RPzxKeNi/G+3x+r126JSfPSV1FfJ586dVzzam9VyAOBgEOUMSpW1d8TV1x0bX5r9nmhqOCLGThwRDz/+VPRnrfy2224r7vXNajkA8FoT5QxC2+K+b/5NPHzJJ+KPjx9aezw8Ro8/NrauXh9b+rFUPmfOnD1vKLRmzSNdY/V/e8aWLl3aNQYA8FoR5Qw6e62Sd40cGkeOHRejHn4iNnb25wQWAIDXlyhncKlsiKX/6yu9Vsl72fpErN+yq3gAADBwiHIGkUp0/uT2+N8LHo2t102NkUPq1yev3w6LkaddE1t/xSuwAAC8XkQ5g0flybj7azfF2kvuiu3F+d97btvvikt+xWuVAwC8XkQ5g0TPKvmEXueS9zL86F/psogAAK8nUc7gsGeVvI9zyet+xcsiAgC8ng6p1hT3o7l5dLS1bSweAfU3EjrxxJO6Lol4/PHHF6MAAK+Nnv62Ug4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAEAyUQ4AAMlEOQAAJBPlAACQTJQDAKWycOHCWLFiRfEIBgdRDgCUysMPPxy/+7tTYsaMGeKcQUOUAwCltGzZneKcQeOQak1xP5qbR0db28biEbB27do48cST4vvfvzPGjh1bjAKQ6ZprrombblpQPHrZ9OlnxGWXXRaTJ08uRmDg6+lvUQ6vYOPGjfHpT//XWLZsWTECwEB37rmzYv78+XH44YcXIzBwiXLop+3bt8e2bduKRwBkO9BK+aRJ74jLL788PvCBDwhySkOUAwCl9LnPfS7mzp1XPBLjlFtPf3uhJwBQSvUYv/XW78T9998fM2fOFOSUmigHAEplxIgRYpxBR5RDXypbYtWiK2Ja8+iuPys1N/9OnD9vaazasqvYoKx2x5alny72qfdtasxb1Vlssyu2rFocV0wbv+fjJ5w/N5au2hKVYotS6FwZ86bVjtvSJ4uBbpUtK2PRFWe+vO8nzI55S1fFll47159tBqb2WDXvj6L5/KWxpRjp1o/jXtI5/9ocz5LP+f4cuy1L4/w9H3/5NnHeqtrs6FameT9nzhwxzuBTP6e8x5gxxxT34I3speqzy6+sThgzvTpnyWPVHfWRzfdUr5x6fHXMmTdV177UvVU5PV1dPmfyK+/Hs8urcyYcX506Z0l17Y7aRi9tqi6/cnrt58NHqzet/WWx0QC34+HqTbPfVfucT67OXtJWDNYV+z/1yuqStc/WHr9Q3bz8S9WpY46vnnnTY7Uj399tBqJnq4/d9Oe1eXtMdczsJdXNxWi3VzvuJZ3zOx6ozq19jhNmf636wOYXagPPVtcuubLrWE2d+0DXfvTreJZ6zj9TbZ07ozpmwnnV6x/YXNufl6o71i6pzqkfu6nXV1vr+7Pn+L7S/pR13kP59fS3lXLYz/ZY9aN7Y+fEs2PWWeNjeG2k4cjJcc5HTolY/WA88vOedaUSqvwi1j/0dDSePDZG9fndX4mOVffG7TtPiY/MmhYtw2sbNRwd7zvn7JgYD8U/PfJ0sd1AVax4fvRrses9p8bIYnSPjofjR7c/HRM/8rE4q6WpNnBoHPm+D8ZHJtYO7T89Gj/v7zYDTPcK5yfjml0TY+Z+O13zqse9jHO+Nlcf/F7csGZsXPCpP413HXlobawpWmb8t7j8nLfEmhu+Fw92VPpxPEs+5ztWx3dvWBkjL7gwPvWuI6Oh9t/wlrPi85d/OBrX3BrffXB7baNdsXX9z2Jn43ExdlT969SHEs77vu2Kp5Z+Jk6or/SftSDWleJPHdBNlMO+drfFT+5cv0/ADI23vu2dtchbHSsfay/GSqhzc6xbd1hMftdxtXzpy3PxxE/+bb8n74a3vi1OHbk9Vqz8WXQUYwPSlu/HX8y4JX7ts3Ni1sRRxeDLdj+xKu7c+ZY4eexvvPzDr+GYeNupYyNWrIrHahHXn20Glifjjr+4MBb/2nnxP2b9ThxRjO7l1Y57Ked8QzRN+WI82nZXXDyp/mtEj6HRdERjxM7t0f5cf45nZ7nnfNOU+J+PbozVF0+KIcVQ/WszrGlEHFb7zLe2/7L2uDM2rdsQMXlSTGja81XYS/nm/QF0/t/4ztdb492nTY7aLIBS6fu7E97InuuIbS9EHHZEUwwrhuoa3jQymvc8yZVT9xPv0Ni97NLulaT6bdoVsWjPubPPR8e2nbWdHxFNw3r9eGhojDc3N8bOre21bB/Ahp8cn/rx4vjilKP7+OFWqR3a9nih9lR9RNPQYqxuSLzpzbWU7Yq43f3YZqDFya/HSZ/6u7jti78XRx7gJ/qrHvfBNOcrm+Kny9dHjDw2mo9o6MfxfK7cc75Pz8d//LQ1tsdRcVLzm1/+pWv39+LyE4rj33xmXLFoZXG+eH++N8oQ5bviqXtujhsOPTcu/JPxEev+PTZ1luHzhm6iHPb1XHtsrT1H76vhTSPiN4v75dTzRF17qn3vVbGybWO0tbXFmusnxP0f+2Rcv6q+GvrLaN/ax7pgw7AY8ZuHFQ8GsOHHxaSuP733pRYe7dtj/0NbC48RtXDp0p9tBpqmaJl0XNcpJ33rx3EfNHO+Ep2r74pbVkdMvOiMmDikP8ez5HO+L50PxbJbHqx9Ef4kpk8cHpX/+Gks75oAU+ILK9u6rofctubL0XL/xTHr+pXRWcp534eOf46vfqE1Zn72D+OdzcdGy86fxfqtZX9xPm8kohzeMIZGy6zFtSfkB+LGWScVEdcQw8dPiemTfxbz/nKp8y8HpX4c95e6BsuvszW+MeerseH0q+PrHx//Bn2Ca49V3/irmLdhWsz/+kejpfZFaGiZFXfUQvzRG8+J8fVz5uuGj49p0yfGmnlfidvWPd89VmrPx7rbvxGLWs6PWe87IhpGjY2TGzfEuk09V5WCgU+Uw76GjYhRfZyMWNnRXqIXO/1/aNseOyqHx4hRfaw0V56L9p+/UDwoq4baoR3Zx3mmu2NH+zPF/f5sM8jUj/vhg2DOdz4SCy66MObFhbH42rPi6K5nt/4cz8E05zvi8QWXx8fmRVy8+L/HjKMP8KLOvWyLZ3ZUyj/vO/41Fly9Ic757PSuX0Ri+FHR0tIRD63/RVhroCxEOexrWFMccVjEC9s69jqXtLJje7RFU4waMZivi1u8SO6F9ujofQ5pZWc807YzGkeN2Ouc43LpefHbztjW0XtlsBYez2yLaBwZI4YN6cc2g/DHZsnnfGXLP8f8i86NqzaeFQsXfCIm9awG9+uYDxscc76yJVbOvzhmXLUpPrjwq/GZSSOKD/RHf75OA3ne771K3qXhN2LsyU2xbt3msFZOWYhy2NeQ5njHGWNj50PrY+ue5+ie83J/K1qOOfDZuwPbtrjvivdG8wlXxX29r6RQrAg2njEpxg0ZFuPe8e5o3OdczO5zUhujpeWoVzh3eeAbMm5SnNH49N6rZz0vDGw5No6pxVx/timXfhz3oWWd85XofHxRXHDqh+LariD/XEzpujTiy179eA4v/5yv/5XggrPi7Gt/Xgvy/xN/udcLnSvRcd9VcULze+OK+2qBvUexCt747njHuGGlnveVp34Y1/VeJe9l7zkNA5soh/2MjEl/8P5oXP03cfXCR7peBNW57oex4JYHo/H0D8Zpx/W+OkGZjIxTzv5QnLjzh3Hz7Y8Wq0e7Yss//n3csm5a/PWF74mm2o+Epknvj5mN98fVV/99PF6/ckHn43HHgu/G6sZpcd5pby33D42m344/mPmWWH31vFj4eP3FfR2x7o7FccvqX4/Tz3t/HFffuf5sUyr9Oe7lnPOVp+6IS2d8Ie6Os2P+t/YP8i6vejxLPucrbbH00nPjqrsjTp//1X2CvK62f6ecGRec+HTcfvMPuvevprJlRSy6ZUOc/tfnx/vql0ks7bxvj9Xf+dv4/s71sejjE4sry9RvE+Pji2q/ULgCC2XS9RZCBe/oCYWXNldbF86pTq2/O2LXrf5ufzdXW7veNbDMXqhubl1Sndv1bpfd+zZh9vXVe7rewa9HfZubu98RsGf/p86pLmytv1tgebzYel317fu9o2f90D5QXTin/m6NPcd2enXOwgeqm3vtXH+2GZBebK3OfXvt893vHT37cdxLN+d3VFvnnrZnf/a/nVad29r9np6vfjzLO+e753nPfu1/e/vc1uqLte1e2txaXTL3vO53fK3fJpxXnXvP2uJdT7uVcd6/tGlJ9c8nTK7OWf50MdKjeBfTCVdWlz870I8ib3T177e6Q+r/K/q867fL+qWSAAAGtvZYNe/cmLH8D+PHS2ftd+pKZd2CmPF7P4qZP/5mzGop6184eSPo6e8B/Vc5AIC+VJ66L2644ek+zyWvc1lEysZKOQAAJLFSDgAAA4QoBwCAZKIcAACSiXIAAEgmygEAIJkoBwCAZKIcAACSiXIAAEgmygEAIJkoBwCAZKIcAACSiXIAAEgmygEAIJkoBwCAZKIcAACSiXIAAEgmygEAIJkoBwCAZKIcAACSiXIAAEgmygEAIJkoBwCAZKIcAACSiXIAAEgmygEAIJkoBwCAZKIcAACSiXIAAEgmygEAIJkoBwCAZKIcAACSiXIAAEgmygEAIJkoBwCAZKIcAACSiXIAAEgmygEAINkh1ZrifjQ3jy7uAQAAr4e2to17RzkAAPD6c/oKAACkivh/VJCzmuZ+zWMAAAAASUVORK5CYII=\"/></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Identify, with a cross, on the graph in (a)(ii), the region of greatest stability.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Show that the energy released in this decay is about 6 MeV.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The plutonium nucleus is at rest when it decays.</p>\n<p>Calculate the ratio <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mtext>kinetic energy of alpha particle</mtext><mtext>kinetic energy of uranium</mtext></mfrac></math>.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.ii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>the energy needed to «completely» separate the nucleons of a nucleus</p>\n<p><em><strong>OR</strong></em></p>\n<p>the energy released when a nucleus is assembled from its constituent nucleons ✓</p>\n<p> </p>\n<p><em>Accept reference to protons <strong>AND</strong> neutrons.</em></p>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>curve rising to a maximum between 50 and 100 ✓</p>\n<p>curve continued and decreasing ✓</p>\n<p> </p>\n<p><em>Ignore starting point.<br/></em></p>\n<p><em>Ignore maximum at alpha particle</em></p>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>At a point on the peak of their graph ✓</p>\n<div class=\"question_part_label\">a.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>correct mass numbers for uranium (234) and alpha (4) ✓</p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>234</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>600</mn><mo>+</mo><mn>4</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>074</mn><mo>-</mo><mn>238</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>568</mn></math> «MeV» ✓</p>\n<p>energy released 5.51 «MeV» ✓</p>\n<p> </p>\n<p><em>Ignore any negative sign.</em></p>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mi>K</mi><msub><mi>E</mi><mi>α</mi></msub></mrow><mrow><mi>K</mi><msub><mi>E</mi><mi>U</mi></msub></mrow></mfrac><mo>=</mo></math>»<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle displaystyle=\"false\"><mfrac><mfrac><msup><mi>p</mi><mn>2</mn></msup><mrow><mn>2</mn><msub><mi>m</mi><mi>α</mi></msub></mrow></mfrac><mfrac><msup><mi>p</mi><mn>2</mn></msup><mrow><mn>2</mn><msub><mi>m</mi><mi>U</mi></msub></mrow></mfrac></mfrac></mstyle></math>  <em><strong>OR  </strong></em><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><msub><mi>m</mi><mi>U</mi></msub><msub><mi>m</mi><mi>α</mi></msub></mfrac></math> ✓</p>\n<p>«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mn>234</mn><mn>4</mn></mfrac><mo>=</mo></math>» <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>58</mn><mo>.</mo><mn>5</mn></math> ✓</p>\n<p> </p>\n<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>\n<p><em>Accept <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mn>117</mn><mn>2</mn></mfrac></math> for <strong>MP2</strong>.</em></p>\n<div class=\"question_part_label\">b.ii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.ii.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion",
      "b-the-particulate-nature-of-matter",
      "d-fields"
    ],
    "subtopics": [
      "a-3-work-energy-and-power",
      "b-1-thermal-energy-transfers",
      "b-5-current-and-circuits",
      "d-3-motion-in-electromagnetic-fields"
    ]
  },
  {
    "question_id": "21N.2.SL.TZ0.6",
    "Question": "<div class=\"specification\">\n<p>Titan is a moon of Saturn. The Titan-Sun distance is 9.3 times greater than the Earth-Sun distance.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Show that the intensity of the solar radiation at the location of Titan is 16 W m<sup>−2</sup></p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Titan has an atmosphere of nitrogen. The albedo of the atmosphere is 0.22. The surface of Titan may be assumed to be a black body. Explain why the <strong>average </strong>intensity of solar radiation <strong>absorbed</strong> by the whole surface of Titan is 3.1 W m<sup>−2</sup></p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Show that the equilibrium surface temperature of Titan is about 90 K.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">a.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The orbital radius of Titan around Saturn is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>R</mi></math> and the period of revolution is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math>.</p>\n<p>Show that <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi>T</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><mn>4</mn><msup><mi mathvariant=\"normal\">π</mi><mn>2</mn></msup><msup><mi>R</mi><mrow><mo> </mo><mn>3</mn></mrow></msup></mrow><mrow><mi>G</mi><mi>M</mi></mrow></mfrac></math> where <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>M</mi></math> is the mass of Saturn.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The orbital radius of Titan around Saturn is 1.2 × 10<sup>9 </sup>m and the orbital period is 15.9 days. Estimate the mass of Saturn.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.ii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>incident intensity <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mn>1360</mn><mrow><mn>9</mn><mo>.</mo><msup><mn>3</mn><mn>2</mn></msup></mrow></mfrac></math> <em><strong>OR </strong></em><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>15</mn><mo>.</mo><mn>7</mn><mo>≈</mo><mn>16</mn></math> «W m<sup>−2</sup>» ✓</p>\n<p> </p>\n<p><em>Allow the use of 1400 for the solar constant.</em></p>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>exposed surface is ¼ of the total surface ✓</p>\n<p>absorbed intensity = (1−0.22) × incident intensity ✓</p>\n<p>0.78 × 0.25 × 15.7  <em><strong>OR </strong> </em>3.07 «W m<sup>−2</sup>» ✓</p>\n<p> </p>\n<p><em>Allow 3.06 from rounding and 3.12 if they use 16</em> W m<sup>−2</sup>.</p>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><em>σT </em><sup>4</sup> = 3.07</p>\n<p><em><strong>OR</strong></em></p>\n<p><em>T</em> = 86 «K» ✓</p>\n<div class=\"question_part_label\">a.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>correct equating of gravitational force / acceleration to centripetal force / acceleration ✓</p>\n<p>correct rearrangement to reach the expression given ✓</p>\n<p> </p>\n<p><em>Allow use of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msqrt><mfrac><mrow><mi>G</mi><mi>M</mi></mrow><mi>R</mi></mfrac></msqrt><mo>=</mo><mfrac><mrow><mn>2</mn><mi mathvariant=\"normal\">π</mi><mi>R</mi></mrow><mi>T</mi></mfrac></math> for <strong>MP1</strong>.</em></p>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi><mo>=</mo><mn>15</mn><mo>.</mo><mn>9</mn><mo>×</mo><mn>24</mn><mo>×</mo><mn>3600</mn></math> «s» ✓</p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>M</mi><mo>=</mo><mfrac><mrow><mn>4</mn><msup><mi mathvariant=\"normal\">π</mi><mn>2</mn></msup><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfenced><mn>3</mn></msup></mrow><mrow><mn>6</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>×</mo><msup><mfenced><mrow><mn>15</mn><mo>.</mo><mn>9</mn><mo>×</mo><mn>24</mn><mo>×</mo><mn>3600</mn></mrow></mfenced><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mn>5</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>26</mn></msup><mo> </mo></math>«kg» ✓</p>\n<p> </p>\n<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>\n<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong>.</em></p>\n<div class=\"question_part_label\">b.ii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.iii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.ii.</div>\n</div>",
    "topics": [
      "b-the-particulate-nature-of-matter",
      "d-fields"
    ],
    "subtopics": [
      "b-2-greenhouse-effect",
      "d-1-gravitational-fields"
    ]
  },
  {
    "question_id": "22M.2.HL.TZ1.3",
    "Question": "<div class=\"specification\">\n<p>Two loudspeakers A and B are initially equidistant from a microphone M. The frequency and intensity emitted by A and B are the same. A and B emit sound in phase. A is fixed in position.</p>\n<p><img src=\"data:image/png;base64,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\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>B is moved slowly away from M along the line MP. The graph shows the variation with distance travelled by B of the received intensity at M.</p>\n<p><img src=\"data:image/png;base64,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\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Explain why the received intensity varies between maximum and minimum values.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>State and explain the wavelength of the sound measured at M.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>B is placed at the first minimum. The frequency is then changed until the received intensity is again at a maximum.</p>\n<p>Show that the lowest frequency at which the intensity maximum can occur is about 3 kHz.</p>\n<p style=\"text-align:center;\">Speed of sound = 340 m s<sup>−1</sup></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Loudspeaker A is switched off. Loudspeaker B moves away from M at a speed of 1.5 m s<sup>−1</sup> while emitting a frequency of 3.0 kHz.</p>\n<p>Determine the difference between the frequency detected at M and that emitted by B.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">d.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>movement of B means that path distance is different « between BM and AM »<br/><em><strong>OR</strong></em><br/>movement of B creates a path difference «between BM and AM» ✓</p>\n<p>interference<br/><em><strong>OR</strong></em><br/>superposition «of waves» ✓</p>\n<p>maximum when waves arrive in phase / path difference = n x lambda<br/><em><strong>OR</strong></em><br/>minimum when waves arrive «180° or <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>π</mi></math> » out of phase / path difference = (n+½) x lambda ✓</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>wavelength = 26 cm ✓</p>\n<p><br/>peak to peak distance is the path difference which is one wavelength</p>\n<p><em><strong>OR</strong></em></p>\n<p>this is the distance B moves to be back in phase «with A» ✓</p>\n<p> </p>\n<p><em>Allow 25 – 27 cm for <strong>MP1</strong>.</em></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mi>λ</mi><mn>2</mn></mfrac></math>» = 13 cm ✓</p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>f</mi><mo>=</mo></math>«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mi>c</mi><mi>λ</mi></mfrac><mo>=</mo><mfrac><mn>340</mn><mrow><mn>0</mn><mo>.</mo><mn>13</mn></mrow></mfrac><mo>=</mo></math>» 2.6 «kHz» ✓</p>\n<p> </p>\n<p><em>Allow ½ of wavelength from (b) or data from graph for <strong>MP1</strong>.</em></p>\n<p><em>Allow ECF from <strong>MP1</strong>.</em></p>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><em><strong>ALTERNATIVE 1</strong></em><br/>use of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>f</mi><mo>'</mo><mo>=</mo><mi>f</mi><mfrac><mi>v</mi><mrow><mi>v</mi><mo>+</mo><msub><mi>u</mi><mn>0</mn></msub></mrow></mfrac></math> (+ sign must be seen) <strong><em>OR</em> </strong><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>f</mi><mo>'</mo></math>= 2987 «Hz» ✓<br/>« <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>Δ</mi><mi>f</mi></math>» = 13 «Hz» ✓</p>\n<p> </p>\n<p><em><strong>ALTERNATIVE 2</strong></em><br/>Attempted use of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mi>Δ</mi><mi>f</mi></mrow><mi>f</mi></mfrac></math>≈ <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mi>v</mi><mi>c</mi></mfrac></math><br/><br/>« Δf » = 13 «Hz» ✓</p>\n<div class=\"question_part_label\">d.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was an \"explain\" questions, so examiners were looking for a clear discussion of the movement of speaker B creating a changing path difference between B and the microphone and A and the microphone. This path difference would lead to interference, and the examiners were looking for a connection between specific phase differences or path differences for maxima or minima. Some candidates were able to discuss basic concepts of interference (e.g. \"there is constructive and destructive interference\"), but failed to make clear connections between the physical situation and the given graph. A very common mistake candidates made was to think the question was about intensity and to therefore describe the decrease in peak height of the maxima on the graph. Another common mistake was to approach this as a Doppler question and to attempt to answer it based on the frequency difference of B.</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Many candidates recognized that the wavelength was 26 cm, but the explanations were lacking the details about what information the graph was actually providing. Examiners were looking for a connection back to path difference, and not simply a description of peak-to-peak distance on the graph. Some candidates did not state a wavelength at all, and instead simply discussed the concept of wavelength or suggested that the wavelength was constant.</p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was a \"show that\" question that had enough information for backwards working. Examiners were looking for evidence of using the wavelength from (b) or information from the graph to determine wavelength followed by a correct substitution and an answer to more significant digits than the given result.</p>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Many candidates were successful in setting up a Doppler calculation and determining the new frequency, although some missed the second step of finding the difference in frequencies.</p>\n<div class=\"question_part_label\">d.</div>\n</div>",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-3-wave-phenomena",
      "c-5-doppler-effect"
    ]
  },
  {
    "question_id": "22M.2.SL.TZ1.1",
    "Question": "<div class=\"specification\">\n<p>A student uses a load to pull a box up a ramp inclined at 30°. A string of constant length and negligible mass connects the box to the load that falls vertically. The string passes over a pulley that runs on a frictionless axle. Friction acts between the base of the box and the ramp. Air resistance is negligible.</p>\n<p><img src=\"data:image/png;base64,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\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>The load has a mass of 3.5 kg and is initially 0.95 m above the floor. The mass of the box is 1.5 kg.</p>\n<p>The load is released and accelerates downwards.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline <strong>two</strong> differences between the momentum of the box and the momentum of the load at the same instant.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The vertical acceleration of the load downwards is 2.4 m s<sup>−2</sup>.</p>\n<p>Calculate the tension in the string.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Show that the speed of the load when it hits the floor is about 2.1 m s<sup>−1</sup>.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The radius of the pulley is 2.5 cm. Calculate the angular speed of rotation of the pulley as the load hits the floor. State your answer to an appropriate number of significant figures.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>After the load has hit the floor, the box travels a further 0.35 m along the ramp before coming to rest. Determine the average frictional force between the box and the surface of the ramp.</p>\n<div class=\"marks\">[4]</div>\n<div class=\"question_part_label\">d.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The student then makes the ramp horizontal and applies a constant horizontal force to the box. The force is just large enough to start the box moving. The force continues to be applied after the box begins to move.</p>\n<p><img src=\"data:image/png;base64,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\" style=\"display:block;margin-left:auto;margin-right:auto;\"/></p>\n<p>Explain, with reference to the frictional force acting, why the box accelerates once it has started to move. </p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">e.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>direction of motion is different / <em><strong>OWTTE</strong> </em>✓</p>\n<p><em>mv</em> / magnitude of momentum is different «even though <em>v</em> the same» ✓</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>use of <em>ma = mg − T</em> «3.5 x 2.4 = 3.5<em>g − T</em> »</p>\n<p><em><strong>OR</strong></em></p>\n<p><em>T </em>= 3.5(<em>g − </em>2.4) ✓</p>\n<p>26 «N» ✓</p>\n<p> </p>\n<p><em>Accept 27 N from g = 10 m s<sup>−2</sup></em></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>proper use of kinematic equation ✓</p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msqrt><mfenced><mrow><mn>2</mn><mo>×</mo><mn>2</mn><mo>.</mo><mn>4</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>95</mn></mrow></mfenced></msqrt><mo>=</mo><mn>2</mn><mo>.</mo><mn>14</mn></math> «m s<sup>−1</sup>» ✓</p>\n<p> </p>\n<p><em>Must see either the substituted values <strong>OR</strong> a value for v to at least three s.f. for <strong>MP2</strong>.</em></p>\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>use of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>ω</mi><mo>=</mo><mfrac><mi>v</mi><mi>r</mi></mfrac></math> to give 84 «rad s<sup>−1</sup>»</p>\n<p><em><strong>OR</strong></em></p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>ω</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>1</mn><mo>/</mo><mn>0</mn><mo>.</mo><mn>025</mn></math> to give 84 «rad s<sup>−1</sup>» ✓</p>\n<p> </p>\n<p>quoted to 2sf only✓</p>\n<p> </p>\n<div class=\"question_part_label\">c.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p><em><strong>ALTERNATIVE 1</strong></em></p>\n<p>«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi>v</mi><mn>2</mn></msup><mo>=</mo><msup><mi>u</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>a</mi><mi>s</mi><mo>⇒</mo><mn>0</mn><mo>=</mo><mn>2</mn><mo>.</mo><msup><mn>1</mn><mn>2</mn></msup><mo>-</mo><mn>2</mn><mi>a</mi><mo>×</mo><mn>0</mn><mo>.</mo><mn>35</mn></math>» leading to <em>a </em>= 6.3 «m s<sup>-2</sup>»</p>\n<p><em><strong>OR</strong></em></p>\n<p>« <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>x</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn><mfenced><mrow><mi>u</mi><mo>+</mo><mi>v</mi></mrow></mfenced><mi>t</mi></math> » leading to <em>t</em> = 0.33 « s » ✓</p>\n<p><em><br/></em><em>F</em><sub>net</sub> = « <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>m</mi><mi>a</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>6</mn><mo>.</mo><mn>3</mn></math> = » 9.45 «N» ✓</p>\n<p>Weight down ramp = 1.5 x 9.8 x sin(30) = 7.4 «N» ✓</p>\n<p>friction force = net force – weight down ramp = 2.1 «N» ✓</p>\n<p> </p>\n<p><em><strong>ALTERNATIVE 2</strong></em></p>\n<p>kinetic energy initial = work done to stop 0.5 x 1.5 x (2.1)<sup>2</sup> = <em>F</em><sub>NET</sub> x 0.35 ✓</p>\n<p><em>F</em><sub>net</sub> = 9.45 «N» ✓</p>\n<p>Weight down ramp = 1.5 x 9.8 x sin(30) = 7.4 «N» ✓</p>\n<p>friction force = net force – weight down ramp = 2.1 «N» ✓</p>\n<p> </p>\n<p><em>Accept 1.95 N from g = 10 </em>m s<sup>-2</sup><em>.</em><br/><em>Accept 2.42 N from u = 2.14 </em>m s<sup>-1</sup><em>.</em></p>\n<div class=\"question_part_label\">d.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>static coefficient of friction &gt; dynamic/kinetic coefficient of friction / μ<sub>s</sub> &gt; μ<sub>k</sub> ✓</p>\n<p>«therefore» force of dynamic/kinetic friction will be less than the force of static friction ✓</p>\n<p><br/>there will be a net / unbalanced forward force once in motion «which results in acceleration»</p>\n<p><em><strong>OR</strong></em></p>\n<p>reference to net F = ma ✓</p>\n<div class=\"question_part_label\">e.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>Many students recognized the vector nature of momentum implied in the question, although some focused on the forces acting on each object rather than discussing the momentum.</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Some students simply calculated the net force acting on the load and did not recognize that this was not the tension force. Many set up a net force equation but had the direction of the forces backwards. This generally resulted from sloppy problem solving.</p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was a \"show that\" questions, so examiners were looking for a clear equation leading to a clear substitution of values leading to an answer that had more significant digits than the given answer. Most candidates successfully selected the correct equation and showed a proper substitution. Some candidates started with an energy approach that needed modification as it clearly led to an incorrect solution. These responses did not receive full marks.</p>\n<div class=\"question_part_label\">c.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This SL only question was generally well done. Despite some power of 10 errors, many candidates correctly reported final answer to 2 sf.</p>\n<div class=\"question_part_label\">c.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Candidates struggled with this question. Very few drew a clear free-body diagram and many simply calculated the acceleration of the box from the given information and used this to calculate the net force on the box, confusing this with the frictional force.</p>\n<div class=\"question_part_label\">d.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was an \"explain\" question, so examiners were looking for a clear line of discussion starting with a comparison of the coefficients of friction, leading to a comparison of the relative magnitudes of the forces of friction and ultimately the rise of a net force leading to an acceleration. Many candidates recognized that this was a question about the comparison between static and kinetic/dynamic friction but did not clearly specify which they were referring to in their responses. Some candidates clearly did not read the stem carefully as they referred to the mass being on an incline.</p>\n<div class=\"question_part_label\">e.</div>\n</div>",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-1-kinematics",
      "a-2-forces-and-momentum"
    ]
  },
  {
    "question_id": "22M.2.SL.TZ1.2",
    "Question": "<div class=\"specification\">\n<p>Cold milk enters a small sterilizing unit and flows over an electrical heating element.</p>\n<p><img src=\"data:image/png;base64,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\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>The temperature of the milk is raised from 11 °C to 84 °C. A mass of 55 g of milk enters the sterilizing unit every second.</p>\n<p style=\"padding-left: 210px;\">Specific heat capacity of milk = 3.9 kJ kg<sup>−1 </sup>K<sup>−1</sup></p>\n</div><div class=\"specification\">\n<p>The milk flows out through an insulated metal pipe. The pipe is at a temperature of 84 °C. A small section of the insulation has been removed from around the pipe.</p>\n<p style=\"text-align: center;\"><img src=\"data:image/png;base64,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\"/></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Estimate the power input to the heating element. State an appropriate unit for your answer.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Outline whether your answer to (a) is likely to overestimate or underestimate the power input.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Discuss, with reference to the molecules in the liquid, the difference between milk at 11 °C and milk at 84 °C.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>State how energy is transferred from the inside of the metal pipe to the outside of the metal pipe.</p>\n<div class=\"marks\">[1]</div>\n<div class=\"question_part_label\">d.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The missing section of insulation is 0.56 m long and the external radius of the pipe is 0.067 m. The emissivity of the pipe surface is 0.40. Determine the energy lost every second from the pipe surface. Ignore any absorption of radiation by the pipe surface.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">d.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Describe <strong>one</strong> other method by which significant amounts of energy can be transferred from the pipe to the surroundings.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">d.iii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>energy required for milk entering in 1 s = mass x specific heat x 73 ✓</p>\n<p>16 kW <em><strong>OR</strong> </em>16000 W ✓</p>\n<p> </p>\n<p><em><strong>MP1</strong> is for substitution into mcΔT regardless of power of ten.</em></p>\n<p><em>Allow any correct unit of power (such as </em>J s<sup>-1</sup><em> OR </em>kJ s<sup>-1</sup><em>) if paired with an answer to the correct power of 10 for <strong>MP2</strong>.</em></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Underestimate / more energy or power required ✓</p>\n<p>because energy transferred as heat / thermal energy is lost «to surroundings or electrical components» ✓</p>\n<p> </p>\n<p><em>Do not allow general term “energy” or “power” for <strong>MP2</strong>.</em></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>the temperature has increased so the internal energy / « average » KE «of the molecules» has increased <em><strong>OR</strong></em> temperature is proportional to average KE «of the molecules». ✓</p>\n<p>«therefore» the «average» speed of the molecules or particles is higher <em><strong>OR</strong> </em>more frequent collisions « between molecules » <em><strong>OR</strong> </em>spacing between molecules has increased <em><strong>OR</strong> </em>average force of collisions is higher <em><strong>OR</strong> </em>intermolecular forces are less <em><strong>OR</strong> </em>intermolecular bonds break and reform at a higher rate <em><strong>OR</strong> </em>molecules are vibrating faster. ✓</p>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>conduction/conducting/conductor «through metal» ✓</p>\n<div class=\"question_part_label\">d.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>use of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>P</mi><mo>=</mo><mi>e</mi><mi>σ</mi><mi>A</mi><msup><mi>T</mi><mn>4</mn></msup></math> where <em>T</em> = 357 K ✓</p>\n<p>use of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>A</mi><mo>=</mo><mn>2</mn><mi>π</mi><mo> </mo><mi>r</mi><mo> </mo><mi>l</mi></math> « = 0.236 m<sup>2</sup>» ✓</p>\n<p><em>P</em> = 87 «W» ✓</p>\n<p> </p>\n<p><em>Allow 85 – 89 W for <strong>MP3</strong>.</em></p>\n<p><em>Allow ECF for <strong>MP3</strong>.</em></p>\n<div class=\"question_part_label\">d.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>convection «is likely to be a significant loss» ✓</p>\n<p><br/>«due to reduction in density of air near pipe surface» hot air rises «and is replaced by cooler air from elsewhere»</p>\n<p><em><strong>OR</strong></em></p>\n<p>«due to» conduction «of heat or thermal energy» from pipe to air ✓</p>\n<div class=\"question_part_label\">d.iii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>Most candidates recognized that this was a specific heat question and set up a proper calculation, but many struggled to match their answer to an appropriate unit. A common mistake was to leave the answer in some form of an energy unit and others did not match the power of ten of the unit to their answer (e.g. 16 W).</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Many candidates recognized that this was an underestimate of the total energy but failed to provide an adequate reason. Many gave generic responses (such as \"some power will be lost\"/not 100% efficient) without discussing the specific form of energy lost (e.g. heat energy).</p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was generally well answered. Most HL candidates linked the increase in temperature to the increase in the kinetic energy of the molecules and were able to come up with a consequence of this change (such as the molecules moving faster). SL candidates tended to focus more on consequences, often neglecting to mention the change in KE.</p>\n<div class=\"question_part_label\">c.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Many candidates recognized that heat transfer by conduction was the correct response. This was a \"state\" question, so candidates were not required to go beyond this.</p>\n<div class=\"question_part_label\">d.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Candidates at both levels were able to recognize that this was a blackbody radiation question. One common mistake candidates made was not calculating the area of a cylinder properly. It is important to remind candidates that they are expected to know how to calculate areas and volumes for basic geometric shapes. Other common errors included the use of T in Celsius and neglecting to raise T ^4. Examiners awarded a large number of ECF marks for candidates who clearly showed work but made these fundamental errors.</p>\n<div class=\"question_part_label\">d.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>A few candidates recognized that convection was the third source of heat loss, although few managed to describe the mechanism of convection properly for MP2. Some candidates did not read the question carefully and instead wrote about methods to increase the rate of heat loss (such as removing more insulation or decreasing the temperature of the environment).</p>\n<div class=\"question_part_label\">d.iii.</div>\n</div>",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-1-thermal-energy-transfers",
      "b-2-greenhouse-effect"
    ]
  },
  {
    "question_id": "22M.2.SL.TZ1.3",
    "Question": "<div class=\"specification\">\n<p>Two loudspeakers A and B are initially equidistant from a microphone M. The frequency and intensity emitted by A and B are the same. A and B emit sound in phase. A is fixed in position.</p>\n<p><img src=\"data:image/png;base64,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\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>B is moved slowly away from M along the line MP. The graph shows the variation with distance travelled by B of the received intensity at M.</p>\n<p><img src=\"data:image/png;base64,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\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Explain why the received intensity varies between maximum and minimum values.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>State and explain the wavelength of the sound measured at M.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>B is placed at the first minimum. The frequency is then changed until the received intensity is again at a maximum.</p>\n<p>Show that the lowest frequency at which the intensity maximum can occur is about 3 kHz.</p>\n<p style=\"text-align:center;\">Speed of sound = 340 m s<sup>−1</sup></p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>movement of B means that path distance is different « between BM and AM »<br/><em><strong>OR</strong></em><br/>movement of B creates a path difference «between BM and AM» ✓</p>\n<p>interference<br/><em><strong>OR</strong></em><br/>superposition «of waves» ✓</p>\n<p>maximum when waves arrive in phase / path difference = n x lambda<br/><em><strong>OR</strong></em><br/>minimum when waves arrive «180° or <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>π</mi></math> » out of phase / path difference = (n+½) x lambda ✓</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>wavelength = 26 cm ✓</p>\n<p><br/>peak to peak distance is the path difference which is one wavelength</p>\n<p><em><strong>OR</strong></em></p>\n<p>this is the distance B moves to be back in phase «with A» ✓</p>\n<p> </p>\n<p><em>Allow 25 − 27 </em>cm<em> for <strong>MP1</strong>.</em></p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mi>λ</mi><mn>2</mn></mfrac></math>» = 13 cm ✓</p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>f</mi><mo>=</mo></math>«<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mi>c</mi><mi>λ</mi></mfrac><mo>=</mo><mfrac><mn>340</mn><mrow><mn>0</mn><mo>.</mo><mn>13</mn></mrow></mfrac><mo>=</mo></math>» 2.6 «kHz» ✓</p>\n<p> </p>\n<p><em>Allow ½ of wavelength from <strong>(b)</strong> or data from graph.</em></p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was an \"explain\" questions, so examiners were looking for a clear discussion of the movement of speaker B creating a changing path difference between B and the microphone and A and the microphone. This path difference would lead to interference, and the examiners were looking for a connection between specific phase differences or path differences for maxima or minima. Some candidates were able to discuss basic concepts of interference (e.g. \"there is constructive and destructive interference\"), but failed to make clear connections between the physical situation and the given graph. A very common mistake candidates made was to think the question was about intensity and to therefore describe the decrease in peak height of the maxima on the graph. Another common mistake was to approach this as a Doppler question and to attempt to answer it based on the frequency difference of B.</p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>Many candidates recognized that the wavelength was 26 cm, but the explanations were lacking the details about what information the graph was actually providing. Examiners were looking for a connection back to path difference, and not simply a description of peak-to-peak distance on the graph. Some candidates did not state a wavelength at all, and instead simply discussed the concept of wavelength or suggested that the wavelength was constant.</p>\n<div class=\"question_part_label\">b.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>This was a \"show that\" question that had enough information for backwards working. Examiners were looking for evidence of using the wavelength from (b) or information from the graph to determine wavelength followed by a correct substitution and an answer to more significant digits than the given result.</p>\n<div class=\"question_part_label\">c.</div>\n</div>",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-2-wave-model",
      "c-3-wave-phenomena"
    ]
  },
  {
    "question_id": "22M.2.SL.TZ1.6",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline\n   <strong>\n    two\n   </strong>\n   reasons why both models predict that the motion is simple harmonic when\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     a\n    </mi>\n   </math>\n   is small.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the time period of the system when\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     a\n    </mi>\n   </math>\n   is small.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [4]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline, without calculation, the change to the time period of the system for the model represented by graph B when\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     a\n    </mi>\n   </math>\n   is large.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (d)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The graph shows for model A the variation with\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     x\n    </mi>\n   </math>\n   of elastic potential energy\n   <em>\n    E\n   </em>\n   <sub>\n    p\n   </sub>\n   stored in the spring.\n  </p>\n  <p>\n   <img 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\"/>\n  </p>\n  <p>\n   Describe the graph for model B.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    For both models:\n   </strong>\n  </em>\n  <br/>\n  displacement is ∝ to acceleration/force «because graph is straight and through origin» ✓\n </p>\n <p>\n  displacement and acceleration / force in opposite directions «because gradient is negative»\n  <br/>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <br/>\n  acceleration/«restoring» force is always directed to equilibrium ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  attempted use of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msup>\n    <mi>\n     ω\n    </mi>\n    <mn>\n     2\n    </mn>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <mfenced>\n    <mo>\n     -\n    </mo>\n   </mfenced>\n   <mfrac>\n    <mi>\n     a\n    </mi>\n    <mi>\n     x\n    </mi>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  suitable read-offs leading to gradient of line = 28 « s\n  <sup>\n   -2\n  </sup>\n  » ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    T\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mi>\n      π\n     </mi>\n    </mrow>\n    <mi>\n     ω\n    </mi>\n   </mfrac>\n  </math>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mi>\n      π\n     </mi>\n    </mrow>\n    <msqrt>\n     <mn>\n      28\n     </mn>\n    </msqrt>\n   </mfrac>\n  </math>\n  » ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    T\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    2\n   </mn>\n  </math>\n  s ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  time period increases ✓\n </p>\n <p>\n </p>\n <p>\n  because average ω «for whole cycle» is smaller\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  slope / acceleration / force at large x is smaller\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  area under graph B is smaller so average speed is smaller. ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  same curve\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  shape for small amplitudes «to about 0.05 m» ✓\n </p>\n <p>\n  for large amplitudes «outside of 0.05 m»\n  <em>\n   E\n  </em>\n  <sub>\n   p\n  </sub>\n  smaller for model B / values are lower than original / spread will be wider ✓\n  <em>\n   <strong>\n    OWTTE\n   </strong>\n  </em>\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept answers drawn on graph – e.g.\n  </em>\n </p>\n <p>\n  <em>\n   <img 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gqObuKLjujZFkTO5QdM08vk8r7322qTos7Vr1zI0NMSsWbMmxSkGFGmUyWR8a9N9waRYQQT3REqJEoZKz9Uz9Qn7wwfTV4oTEf6vDFp0XaehoYGTTz6Z//qv/yKfz/sKr2DZlT6V0uytzr29C8+C8dq4v63QNA1E8FwHxAaxWfvses4+69N88KQTOf8L57L+1S3YlDK4AriMDg9y/Q++z6pVH+MjZ3yUb19xFf1DQ7jise6p5zjrrDM59YMnccV3vk8665bOQfzgl2W4KgFfqe3h9o/Xr+pdsO/C9NwbhNNrmkZNTQ2u65bFqxgPv0q47u1ZpbywJ36DqteyLO69916WLVvGwoULy2I/7I1nwmWOx2P7okMwRkSQj9RKOGx0Nx5UVUAoohmGwfz588saHwxsEf5dKVhI0KpQPRuvrEqBSMJlLlu2jFNPPZVNmzaxadMmX3iMlyd8rKb+Bzt1b8yhrO7Ub6VkC6abO28umlFaM5Sq1jQBzWF0aDdX/MdPOH3Vx7l9za9Yvnghv7ztlzgCngbg4CE89Oc/076tnRtuvJ6f3XorHR07uO+PfyCXzfAft9zBh8/4OGvuuI30cD/r121E14r5i2qIvTP1ePQIP69Eg3FPZgLMHv4drF9NNMlkkoMOOmiM09h4gkGVF+yr4KBSz4P1qi2nShfue03T6Ozs5KmnnuLjH/84S5YsKXPoCqYL4hOsW2131fMwncL0CJYb/K/0DkG+r6+vZ+7cuWNoXQmqKiAUATzPI5/PA+VHn6pBYc/I8MAZz5lLpVHMoggXzB8ksHqnaRqFQoFFixaxcOFC7rnnnooMppaxIjLG21B1SniQhDsy6Kkadn4KHtN5nkfBzuOJlFYQpUFR2mKMDPfR7Rn88+kfYu6cOZzxwQ+yY+s2CraACUIGwWDpYe/gwtVfYdGiRcyePZN3v+twXtu4npHBPnYOCStP/ygzZ7Vy3JHvZPP6DeAVDahsxg5qNVDCjk1BYafaHGzn3qCSkA8Oikr0DA40EfFtDsKrnEoRp4KCIegdqeqotPJUptzB/gzipWkav/vd75g9ezaHH364H/ciWG8YHwXBY+xwGxWuwbERFCKVygumMwzDDyqjAt7sCyaFDgKgvb0dy7J8IliWhW3bWJblE90rBWFRwTY0TcNxHH8LENwG2Lbtf9Qz13XL8itCqyhCihFUkA/XdfnQhz7EI488QmdnJ47j+Diq+oIfxUz5fN6PfBX071D5Yc/MpXBUW5tgm4MDxbZtNrdvIZvP+WXm8xae6+JaBYaH+rEbWnAiBo5l0RCLM7x7gNHRHHnHwSZPwRXmL1jIvPkHggaWXeC5Z57iyHe/i+H+3Wh107E0E9fO05ww6N3ejmdD1nbIWbYfqCSXy5FOpzEMA8uyyhjecRy/PeqZoq9t22XCpVAo+M9UWtV+lU7lD64uFL0LhQKWZfnvvVLQmU2bNvnRvxQvKdyC9au6guls2yabzeI4jj8BqD5S/KXyOo6D4zj+6ZfK09HRwR133MHHPvYxYrEY69atq9jHKk+wnfl83i8HKGtfcPviuq6fVqUTEZ+3VXpFU5VX13WGhobo7u6e0Bitvmq1BKOjowwODjJt2jQymYw/IOPxOHPmzMEwDLq6ukilUsRiMaZPn05tbS29vb0MDg5imibNzc1MmzaNdDpNd3c3hUKBtrY2pk+fTiqVoqenB9u2x+QfGhqitbWVqVOnkslk6Orqoru7m9bWVv7pn/6JZDLJHXfcwSmnnEJNTQ2zZ88mFovR3d3tG8E0Nzczc+ZM8vk8O3fupFAo0NzczPTp07Ftmx07dlAoFIjH48ydO5doNEpPTw/9/f1EIhFmz55NPB6nr6+vrMy2tjYcx2Hnzp10d/bR2jJMLFqL5zjs2N6OZ2eJRYShVJZ63aJ71yD68G4G+/pJp4epMVwGBvrIDfXg2D00Nk+hbep0+vqHuOrKK2lsbmHpwYsZTQ2Bm2fLaztIRkfY2dWFGHls2+Lxx5+gb3cXRuDsxDAMXnzxRbZt21aKSFVHf38/fX19RCIRZs2a5T/r7e31o3jNmjULy7J8GrW1tTF16lSy2Szd3d3kcjmi0SgzZ84syx+LxZg2bRoNDQ0MDQ35oeWam5sBmDZtGo7j0N3dTU9PD21tbcyaNQvbtuns7CSXy2EYBrNmzfLLUC7PM2fOpKmpicHBQQYHB3Ecx++7fD5Pb28vuVyO2tpa5syZw8DAgJ+urq6OWbNmoes6mzdvxvM8HnjgAQzD4IgjjmDbtm309PTQ3t5OW1sbdXV1dHR0UCgU0HXdb+fg4CC7d+/GdV0aGxuZMWMGg4ODDAwM4DgOyWSSAw44ANu2fYtaTdOYPXs2NTU17Ny5k3w+j67rfht3795NX1+fH1lt9uzZDA8Ps3PnzokrTaXKoCLfdHd3+xGdvEDUJxUtSP0ORiVSz1SaYBSgYISjcDSecASf4DsVeWfbtm1+2ltuuUWOOuooGRkZ8d8Ho14FI0J5oSg+Xiiyj2pjsG6Fr3oe/K3abtu27OzaJXnLEU9EXNcWTyzx3Kx4XkZe3fS8HHfKh2XUcWXEcmRbz245duUHpH9kRPKOLXnbEs8aFtvKSGdvr3zjyu/Kv13yTekbHBDPzUn7xuflxJPOlFTOlnTBkj888Hv5wQ3XFSMpFTxx7PJoSLZty4033ujTJNh3wfapSF2KVsG+VM+D6StFVwqmC/ahommQ1plMRjo6OvyoTkEeGa+McB+Eywz3h8IpHM3KcRwZGhqSD3zgA3LTTTf5dNmxY0dZBKhwNKogHwRpGMRTvRMRv6wgnwWjogX5JszvjuNIJpORnp6eCY3Pqp9iQHG5PXXqVH9vJ4H9oFrOS0jxAvh7f7UUVLqF8fanaolYaR+s0qnl3dy5c31cTjnlFAYGBnj44Yd9U+ygziIY2Ui9V+1SoNIoo6swbkG37bAiStUzbVorkYiB63pQvGKr6IClGbS0tGKnR9i5dRtxXWPj+peYNW0GNfFaRHTQDDSgf1cvX//q/6ahLsk3LrmEhsYmHE+jdfpscEfYuW0bEU1n04ZtLF68vOjmbYBo5Xth5S0ZbFeYngp3lTasoFN0DPatol2l/BLQOY0XUSoWizFjxowyU+ugTiFYRlAfpfBT9QX1VMGtsPoORsgK6lyef/55+vr6OPXUU33+VCuMIH+EcVd1Bfk22H4FqkxFq7DuS+EV1NmE08TjcVpbW8eMgUpQ9XgQ6ruzs9N3Z1bPwg0Md3DwWVC5V6n8IDME8ytQnawG8KZNm/zQZVOmTOETn/gEd9xxBytXriQSiVRcooU150ElZiVlmDqpCCqfgowSHBi6rrNzZxczZkwrU8qK5yEI9fVNfOyDp3DheZ9nSmsbA0NDfPFLXyYaMdmyZQe/+93vufCzH+KOX9zGfz/8F7J5l7VrX0DT4Ogj38NZn/g4H/3QiVz4pXNpaZmJYSb41Cc/jeMVnTl1bY8HaLB/1F4XqEjjYFsqtTmYLjxIwmWNp8AMQj6fp6+vz9fSq8ESVvSpd0HhVEkZGg7OEx7UQdwsy+Luu+/myCOPZNq0aX6a7du3M2fOHF9RGMRH0TDY1krvg/wdnADVxBcsN4hvML/qh2w2S39//4RCLEwKHYSIkEqlmD17dtlgCacJEqkSIwUJq95V+g7mV78Nwyg7dVAh8NxSJOqzzjqLO++8kyeeeILjjjuuIo7hWUjVGaw/yARhAVBpZRFs79DQUFFAaBogiICmmUAxhsUXz/sCR7/3vWzbvoPFhyxhwaKFuI7Q1trMe97zT0RjtRx3/PEsOHg5DiaYUVzPY87s2WhmjHPOPpN/eue72LFjgMPfeQTNTQ0lNw0HXSvGilAQ7KcgzkFmrDSIw/ER1e/g/3D/7K1Pw7RXkbWVgKjUT+GVjEoX1PgHVw3hVUol3AE2b97Mc889x8033+xH8zIMg127dnHAAQf4fRwc6EpohPEKT3xBQVJphVFppRDGXQkTy7L8SOH7gqoHjAl3inpeKe2+/lfKt7e6w7/VdsZ1XTo7O7Ft2zcomT59OieddBJ33XUXRx99dFnHjofT3uoNH6mN16by9oGmF4VDMa8R8NYCdGHZYYex7LB3FM9B9WLwl6bGOt531BHoXp7D330kh2MgmlG0b9iTG02iLD/snSw/NKo8vRENjEAciTB+4X6baB9MpD9fD6hBFPSbeT3OWpVw31ucSfWtBrxlWdx2222sWLGCxYsXlwl9dYISjUbL6tgbfpWE2kQmvn3hHZ7A9gVVd/dWyM6bN+91M8X+ANXZV1xxBX/4wx98guq6zumnn86mTZv8eANvNRxwwDwMXccTwddBQHEUi4anG3i6jug6omipSSDeQxTBRNBRxpF66VM0lKwBzQQdNN1F0zx0BF00NKl+30wEkskkixYtKptF9yeo49Wuri4efvhhTj/9dGpra4Eif+dyOW655Rbuu+++twSfiUAikeCAAw6YUNpJoaQM7yurBWpFU1NTw7e//W0uv/xyNm7c6O+bly9fzrJly7j99turYluv6YEFQwVSOZqGq2m4mlDUTOzx09BwEU0Hf4la7HwdMABDA88z8ESn6PhddPVGvJIp5eQXEGpGf6s8OdXkJiKsWbOGQw89lBUrVvgzuOM43HnnnTz33HMcddRR+x2ficDrHWNVFxBqb7V9+/aqCwi1nzQMg2nTpnHkkUdy3XXX+UYx8XicD3/4wzz44INs3bp1zF2e+xu2tbcjroemURr8JSgFgjLUaqAUULIoR7Q9Kwz2hH8otXjPR6S4ciidVqB0Dpqmsk968DyPdDrNpk2bynQD+7M+EWFgYIA777yTs846y79yz/M81q5dy0033cSXv/xl316jmqDokc1m2bZt24TyVF1AQFFxpQxHqglBhY/jOFx22WVs2rSJu+66y1coHnHEESxatMhfRQRPVvY7eMWtglJS+hHilICg+FFULEaC8NcI6EW1RCCPVvoWNE1KwoHSyyhokdIRBlRUQkwyUCtAJaz3d78o/cLPf/5zFi1axJFHHunjkcvluOiiizjjjDM4+OCDq87bUE4PZUG6L6g61qpTW1tbq7KvD+OiFJUzZsxg2rRpXHTRRVxzzTV0dXUBxbsQP//5z3PXXXfR3t4+5hhsf0JjY+OYY6zXA1roe8+/4qfy8+CvyQ2aVvQKbm5urnh6sT9g9+7d3HPPPZx//vkkEglfh/XNb36TxsZGLrjgAqZPn77f8ZgIBE87JrqiqbqAgGLHKmOSakLwqEt5BK5cuZLjjjuO1atX+34Y73nPe1iyZAk333xzmS/C/oaZM2eOOeYtb8BeMgu+snLsJkMFpS3+C2w8Qv8mN3ieRyKR8G0O3oo++e1vf0tdXR3ve9/7gKLe4YEHHuCee+7hmmuuoaamhkWLFlV98oM9px3xeJyZM2dOKE/VnbWgyOy9vb1VJ2JwZlYBbKLRKF//+tfZvHkzt99+u381/OrVq3nggQfYuXPnW3b6EqRR8IjYNzLylLK3GFbOE8ErKR1EpKhwFK9oXFUaPK4nfoxK8Zyi85fr4UogbmUpz2QHXdfJZrPs2rVrv/BScDvpeR69vb3ceeednHvuuf62dNu2bVx66aXceOONLFy4ENM02bFjx6QJGANQKBT86wD3BVU/5lSWeBNFeH/jowZ7V1eX/3vmzJlce+21XH/99bz66qvous6KFStYunQpa9asKTOw2p+we/fushgEYbwdx6Grs5vnn19LX1+/fzOW6xaFh+vYiLhFJad4dHR2ki8UcFxBNI1saoS1zz/Hc8+vZd1L6xnNZBHxcKwCk+AEep8gUvRm7O3t3S8rCFWm8hD+4x//SCwWY+XKlf5pxkUXXcTxxx/PSSed5PPERD0n9zeoiURdvTcRqPoW4/UaOO1PCJr8qhu/1J7/mGOO4eSTT+ZrX/sa+XyeSCTCpz/9aX7/+9+zbdu2t2Q5G7y9OUw313X56yOP8uEPf5TPfOaznH32OTz55LO+LhMPdN+L+1wAACAASURBVPFABM9z2bF9O1/4wnm8smEToml4Ijzx2KN86PTTOefcc/ns587j1de2FC1JI5FiJNtJDuoEKujHsz/q0HWdnp4e7rjjDlavXk0ymUTTNH784x8zMDDAN7/5Td/ALmgGXW0I8uhEt/NV32JoWtH/YdasWZNKUCxYsKDM/No0TVavXs3AwABr1qwhEonwvve9jwMPPJDf/OY3b8kdDLNnzx5jagtFOg4ODnL99Tdw4403snbt8/zrv/4rv7r9V3gi6Ebx+EIzNDzX4a9/+Qvf+MYlPL92LTU1NTiu4LjC+pde5LJLL2XdC2t58snHWbZ8KbppAt7bQkupacVwc0E/jDcTgr4Ov/jFL6irq+Ooo44iEonw+OOP8+Mf/5hrrrmGxsZGX5Douj5prt6DIk2SySQzZsyYUHqd0ta0uAwt/kZcxLMAD9cp7kNdN3DyXtrPem4xOo3rCbYneAKelJa/noctHo7rgZuhIBkKfvY9+zglWWtra8c47IR/q+9g4I9wnvAxVyUFYjAEnUoX3F+KiH99W9DopqWlhe9973t85zvf4eWXXyYajXLhhRdy7733+rEAKpUV/q8+QY9NBeHtQ3BLUZuIIeKhofm6BVwHTQqMDnUxnGjlkHe9A0PLc8Ix72ZnZw+jtofteeiejeMJrq2zq3sXn/zkRzh4yYHkLRdDA50MW9p3UFOb4Laf/YJXXtxAzDDQ0BDNwB3H8bcS/nujfaVj4XD/hfspmC8Y23G8ehobG8ucyMYroxLPjNdX6p2maWzfvp3f/va3fO5zn6O+vp6Ojg5Wr17NhRdeyIoVK8oc0wDq6up8waLqD7elUv0KhyCfVKKpGg/jtSHIl1A8zZjoPTSmlLz1UJVK0TlH0wXHsdGJ4rqg6yUHI10vJsJD10uRbHQT3TRxPA9D93yFt6cDGJhuGktAMxNEA41TM2GhUGDz5s3MmzePZDKJ5xXD4KulWU1N8cIYFSZLRPy7PINRdVRniBRvV/K84n2asVgMx3HI5fZEY6qpqfGPpJSLd01NDY7jkM1meemllzj88MOJRqOYpkkul8N1XQ477DBWrVrFV77yFdasWcNBBx3EgQceyA9/+EOuu+464vE4qVQK0zT9OxA9z/MjHKkgI4AfvUjXdRKJBICPDxQDiyqcCoUCr766nkWLlhCN1KDrBtl0Bihg6gUKgz2kE1PIuS56uo8oFrv7B0hZHhE0XGuUQsQg7iX56EdXkbZ24Go5sjnBc8ApDLBl206yhT9TXz+Fh/70MN+89N9ZuvxgencPoeEhXnkIPNu2GR0dpba2Fsdx/ChPUBT4kUiEfD7vb8kU3TVNY3R0FM/ziMVixOPxMZGoYrEYpmliWRaFQsGnpeIXlVYNxtraWlzXZXh4mC1btrB06VLq6ur8/lTm8uEyXNclkUhgGIbPM2piiMfjiIifXzlgrVmzhgMOOICjjz6a4eFhvvWtbzF37lxWrVrl31hVX1/v9++6detYsmQJNTU1xGIxvx6Fj2maZe0H/H5XYf0MwyASiaDrOqOjo/4WwTRNotEouVzO148EaR/MH41GcRyH3t5e8vn8hFY2Zuk+JRCbfB6GhjNEYy6WlSUaTWBb0NLSjIhWFCRBEDAjJo4Hw8MjNDc24N/OQsAs2HHIWBBLeohevv9xSxeuDg4OMnXqVBKJBJlMht7eXizLIhaL+ZfqpFIpUqkUuq77np+Dg4OMjIygaRotLS0kk0nS6TS7du3CsiyampqYNm0ahUKBXbt2Yds2uq4zZ84c4vE4AwMDjIyMMGXKFF+QdHd309/fT1dXl++CPjg4SCqVwvM8Vq9ezamnnsq3v/1tPvvZz/KRj3yEK664gpdffplDDjmEnp4eRIT6+npmzJhBoVCgq6sL27b9m59isRhDQ0P09/cTjUaZMWMGNTU1DA0NMTQ0hGma1NXVMX36dCzLoru7m127dtHSMpXZs+eRzeTp6OxA9/LEIx7ZgkVC8xgdHiU71Meu3t3YhQKIRyqTId29AycWpTE2hZkzWnGyNvl8gc6uLubPbmXG1FruvOtOent2AxGe+NvT/PG++zngwHm89NJ6+vt6y+75BNi6dSvd3d3EYjEaGxvp6+sjlUoBMGfOHEzTZHR01FdA19XVUVNTQ6FQoLu7G9u2aW5uZurUqViWRUdHB5ZlYRgGs2fPJpFIMDw8TH9/vx99KZFIMDIyQn9/v09jKMaB8DyPzs5ORkdH6e/vp7a2Fs/zGBgY8CeHYBmDg4OICNOmTaOxsdF3g3Zdl4aGBqZOnQrg549Go8TjcX79619z6aWX0tXVxX333ce6dev4wx/+wNDQkG9xG4vF/NO5np4eWltbmT59Orqu09fXRz6fxzAMpk+fTl1dHalUym9TTU0NM2fOZHR0lJ6eHjSteNnN3LlzsW2bgYEBMpkMkUiEadOmoWmaz1+6rjN9+nSf9sH8s2bNYnh4+PUdCLhOXsTLiOeNyDcv+YYsWfIuOebYY+SYY98rxx1/nPzLiafI/zz6dCnCTTFSjXiuiGeLuLbYVkGGRlJy0SWXSs/uAXE8WxzHFnFsyYkt6YIjud6NcuoHT5ZnX+0ti/SjfluWJZs2bSqLqqOi/QQj74QjSqn3IuK/E9kT3ScYScd1XSkUCmMiUgWjBak8juPIyy+/XBbtx7IsHxfbtuWJJ56QZcuWyd/+9jcpFApyySWXyFlnnSWDg4N++mD0qPEiXAXbG0xr2/aY/Nu2viq2bUmhYIvnibiOK55TEK+Qkm0bn5P3fvAcSWXzItao9O7cKitP/bD0ZFzJOCLi2lJw8+JZIlJwZTS1RY77wHvkb2tflbwlkknvlPXrnhe7UBDHcuWJx5+WL3/5IsnmbHE8T2yn1PcB+P73vy/pdLpiBKxwW1TkJpVWRWQK0iJcTrC/C4VCWZkqclIwApfjOJJKpWT9+vVjIikpPML/w7yl+CmMs6rj1ltvlXPOOUds25Z169bJ0qVL5f777/fxVe1XZbmuK6+88kpZe8PtVv8ty/LzKz4OR8FS36q8IG8Fo1aFaaPKd11XRkdHpb29fUx/VgITHMBF7Bxbt27h2utv5Oj3vZOio46OqUWJRk0Qr+RqHBAurothmGxr30ZzSwuNDY0IXpnFnqGBKXvCeQeVayrKrmEYLFiwoOyYMegHHzyyUs9VfvW8krt42BfeNM2y1YuqT9UR3NcedNBBZcrA4Dm2ruscccQRfOITn+CSSy7h17/+NWeffTZnnHEGzz77LO9///v9EweVPlhXEILtUmnV/2DbRIRZs2ZjGiYOHq6UTKPR0SIxWqZMp9bL8cRfH+PoI9/Jw39+hBltbSRjxXaNWhaxGgPxKCorS1sEXS+6R4+OpvnGv3+DK6+4mgPmH8TLr2zg6KPfh2GULunRxhpnVYr+FGxX2KVd9b/qw/ECx4RjYwTThvtX9ZlKo7w5g/gFeaGSq3aYJ4PPg2kty+LBBx/kkksuYWRkhAsvvJAzzjiD448/3nfoU1uHIP4LFizwI26pbZF6r9LDnmjZYQV0mJehuP0Mtj3YN+PlV/UkEokJXwWoa4YBrsdw/wC9Pb0sWLgQ3YwQidcQjcVB0/E8SmfnYQYpuh4//czTHDh/PpFIUT+h1JkCaLqOFonghqLiBDsIYGhoaExjwumDnRZudKXn4fLG87EPl6FpGrt3766YP4jX5z73OUzT5Oabb2bWrFmsWrWKW2+9lUwmUxYSPlxX+Khyb20L5h8aGMHzBE0vXYWnKQtIk0Sykf/nc5/ihh98nyOOeC/3PfgQXzr/C0QENry0nksuuZRsLlfMJ8X+NM0InudgmhotU6bwpS99kW9+8985+uj30dXVwbHHHoNhGuil+sI4hwV6JWYsY7ZAe8JXGVQa/OMJhWBZ4bBr+Xze56WgUVml70o4hPvDC/DtU089RU1NDUuXLuWKK65A0zTOP/98otHoGH4N4q5usVL4VmpHJf4IB+MJ8obKG+TdYNogr4YnH9u2J3zjuIkYiKvRub2Lvl0D3Pl/f0ssaqNpFjhwwvv/hXccdghSYswgiIBj22zevJnjT1yJ4wiGoaGVLPdEB83zEMfBNIyi5r1CQ0WEnTt30tLSMiGk9zfous7WrVuZNWvWXtPV19dz7bXXcvrpp3PMMcdwxhln8NBDD/HAAw+watWqNx2v3p5emltb0XQdDyVkiw5ZerSGD6x8P+86fBl5yyYaidHS3ITmuSxbvJivX3QRsWi0qEfyIJFIcustP6G17SBEwNR1Tvjn41l+6GFk0nnapk6nNlFbXKn4DmKTHzKZDO3t7bS2to4ZWK8X1BG353mMjIxw/fXXs2rVKh588EHuv/9+7rvvPpqbm8vC6IVB0zS2bNnC7Nmz/y5c3kzIZrPs3r2btra2fabVER3NiPPc/zzN1LYZZLJ5Mrkco6Np8oUC0ZgJIoQWD0Cx8Z2dHcRiMVpbWzBNDTQpugZr4Nil4w9dL4uEFAQpHfc0NDRU3ZhEdbBt2/5Jw77SL168mK985St89atfpaamhtNPP52f/vSn9Pb2vun4xWKxUl8EXL71PW7dGjZt06bSOn0GbdPaMDSNiKYR1U1mTp9KNBItXrHpueiGUdyyREozaGmZ2tbWxty586ipLZ42GLqGroUduSYnaFrRWUudhP29EDyuvPvuu+no6GDp0qVceumlXH311SxYsMCvt1J9UtpaT5kypeykrVoQXPFFo9EJ5TFFAE9j/dYdrDrzY/zruZ9G17Sih68G4oArGrpBaTYBPEHXNVzXpn1rO8uWLiUei6HYVNOEV9a9wFNrn+fMT55DQU9iS5yIPvaaMCjO2PPmzau6s5bSk+i6zpIlS/aZ3nEcYrEYZ599No899hhXXnkll19+OQ8++CC33HILl112Wdm++u+d0ebNPwDdLFnlqT1uKbJUcTsXQdMgFjWLfWTqIIIRK+keKEaoRjOBBKZmFJ3BNRCJo2kmaDqGaSBFgxik1NdvF6irq+PAAw8cswV6I6Amr87OTv7zP/+T8847jz/+8Y+sXLmSk08+uWzpXklAKBwWLlw4ZnteDVAnhslk0o96tS/Q0TQGUileam9n0bKDMPGKV8SjIa6GbmiI7qnD0KLmMbDP2rhxA8uWHIJR3BSjo4Pnks+muPfONWSG+9m2a5R0QahPFKVWpX3fRINo7m9Q+KTT6X2mVWf7tbW1XHnllTz88MM8/vjjrF69mvvvv5/169f7Cs43g0Ey+dyeP55gUBLkeqlLtCigF6M/6KAZOphGMRCMSbFv/IARCUwtTlRFrNZqSgLGAA1fz2HoelHovy3WEEU7EnWk+fcKZDXof/azn9HS0sKxxx7Lgw8+yEUXXUQ8Hi/b448X5VzxUrUnP4UPFAWfstfYZx5llDQ4OMg3Lvl3TjrpJP7Xyg9wykmn8ZGPnMH69RvRAM8N3GtQYvbUyAjZTIbpM2aULLzA9Tx0TWPRkqUsWryYVas+zkX/+yJOOP44Zk4v3xeK7LkMtbOzs+pSVnW253ls3rx5n+mDvhoHHnggl156KVdccQVz587l/e9/PzfccAPZbPZNc+bauXPnmMjde2kNf5999NslCkQ5pNNp3xP39fKT4kcFuq7z4osv8uc//5mPf/zjXHzxxZxxxhk0NzdPaAujytuwYcOkEBCKV9PpNB0dHRPKYwK0tbWxZs0aHNdRcxKgE4lEmDFzBi88/wK7dvfiCrzniPfQ2tKEiEdtIsEnzjqLpqZGPPQ9hjSaTrK+ke9cex3btncQTdbTNn1GKYjR2Lj91RYMCoJHbBPdMypnHIDTTjuN+++/nyuvvJLVq1dzzjnn8MADD/DRj360zOrvjYIKZTZ+zEVFx/C78Z5PJH+wb94eAuPv0T8ounqeRy6X49prr+Woo47ilVdeYfv27dx8882vC4/xTnSqAcExN1EamVBUfh188MGBk4ryS14efvjh4t2Ts2fzyH//Nx/90AfRteISe9bs2XhSOrI0dDQp7V81iMVrOGjxYkQzis5CFRBWxzHqopFqgyLcvHnzJpRehVkXEaLRKNdccw0nnHACjz/+OJ/85Cf5yU9+wrHHHutHOYLKdgMTgZkzZ5aFdQ9D0ZW7KOCDSTRNcD0HXYuMEc7BVZOue6j4clLyAhVA0zw8rxRmfxKDUlLOmDHjDW0xFD2Uj8SDDz7Ixo0bOeqoo/jRj37EmjVraG5u9vtvIviIyIQjSL9VUFtbO3FnLWU85J+7lnabekmD7bkuTY1NHLrsUA45eAm9PT2+ZFQziqZrGEbgPFbX0XQD9KI/gqFrfgRllUaBMmCaMmVK1SVtcOAqM9u9QfBMW9Fw+vTp/OAHP+Daa69l+fLlNDQ08B//8R8VnWdeL7S0tOyV6QUHEQ/HdnEdD68UB8LzXHSt/FKbYHt9JybPKd3h4BbzCniei+s6TJJJcK/gui61tbW0tbW9oZWpruv+inDnzp1cd911nHbaafzyl7/kggsu4LDDDhtjS7Gv8nRdn/A1d28FqImsqalpQunHdrsfXaxk3abB0MAAzzz9LOteWFcKxVaSoOPQSNAQTS+GWS+qO9H9cGflyCqJ3dnZ+Za4TO8NXq8OIgyKKY877jjOPvtsvvvd73LmmWdyzz338MILL/iDcaIzUBh27txZ5uE4Bn8fj6IRmx5gZk+cspUDUOZNWGx70TpTpHi06Xml0xcd3g4h5wzDIJ1Os23btjek91F0yGaz3HzzzSSTSTZv3szSpUv5zGc+87onMMcpejtv37696kf4QchmsxPWQeylxYJQnD0a6huYNnUqc2bP4ehjji6uEDQNzxl/QEvom1KwkrI0gf/Dw8NVD8ulBJZhGBOOuBOE4KWqX/ziFykUCrz88succsopXH311YyOjvpp3shqSTlCjRctybYLrH1hLb/5zd289uoOLMtB04qrgKI15J5jOdd1efHFF8lms/7AcGybtS+s5e7f3E1Hxy50vWRJSNGNf7KDMoceGhoal0b7Al3Xefrpp3n00Udpa2tjw4YNXH311W/oJEqtIFSEq2pD0B18eHh4QnkqXHNd+pR+6KbJIcsOYcW738nhhx9KbTxWFA6uh25G8LcZlC8oKtiUjXkatBFQfhnBThjPb0H9VjNy0N+9Uprw73BZQZNcVU40Gh2TP/wd/gRn96amJr7zne/w61//mhUrVjA0NMRtt922V+VnGMdgezzPI2KYiFdc+gvFwes6FuJZiJPn1pvv4OuXXs1jj97P6gs+xW8efJy8aOi4uOKhiYXlOriuxbpnH+dz55/Pum29eHoEyQ9z220/5cpvXsWjDz/A179+EZ09g7hS6jtPG9P2sF9LuF/C/RdcIYb7IugHM9G+rPSJRCJlhkvh2Ajj8YPq/4GBAa666iqam5t58sknueWWW5g6dWqZ70Olfqv0zivFpAjnDfNuuJyJ0DJMw3D9QZqo/MEVlYp4tU+QCUDQM/LNhLB3WtjDLegdOJ7HWjh92PNNeX0Gywh70YXzu64rmUymrO1hOgTzhD01gx6MN9xwgyxatEjuuOMOWbx4sWzevLnMC1W1T5UfzC8ivsehiIiVL4jneuJ6nthuqX47J56dlv6uzfL+Yz4kT73WJeLslkfu+5V8+HOXSn9BROxRyUlWPCslWcuSn/2fH8uHVh4hs+YfIPe/tF0yrojV+7KceNKxsuGFzSKFEbnmu9+RB/7rWcl7BbHcnLiON6adP/jBDySVSo3xGgz3QZBOlfoiSEP1CXtpjpc/6LWo/udyuTE4BctVZQT5SfHjFVdcIe985ztlzpw5cuONN47xllR9FcZL1RXsU1W24qUwTsG04/F7sP4gXYNezEH+DHsnh/MHvWEnAvtc96jl5/64ziw4AwUv8pCQQk/hofIENdRq1g7GIlT5leQMexPCHsWikvJhrbdbusQ36LSj8onsuXU57Fij6lZlff7zn+dd73oXf/rTnzjqqKP41re+5QefCa9+wo47juP4XqGu6+K5rr9n0/XS8Zmmo+k6g4OD6A1TmH/QDASTw99xKD0dW7ELDgi4REGPkLdspk+fztVXXcGCBfPQNQcP6O/rphBpYP7BC/BEY+khi3hx7fMly1ij5D26Z4ui6BqkZ3AVEKZV2HEqmDZIP8VnQXqq/ME+qqRwVVsn27bHnNAE8wTzKQ9Kz/N47rnn+NnPfsbw8DAnnHACX/jCF8p0RqrdwX4LtnW81azisfAqSfFusOxgmWFHxSBtFY+q56qsMH+GeV29n+gx/l5v9w4OkDDjv1mgCLl+/XoOOuggmpub/SvcoUgQdWw1ODhIoVDA8zymTZuGrusMDw+TTqcxDIPa2lqam5vJ5/MMDg7iui7JZNIvs6+vzyfa1KlT0XXdDwZSX19PU1MTlmWxe/duXn75ZZYvX05LSwvRaJT+/n4/MlJLS4sf5EZFuVJ1FwoFBgYG/MhR9fX1fPe73+XYY49l5cqVPProo9x5552cffbZfn7TNKmvr6e2tpahoSFGR0cRKYa9UzgNDAyw5dXXOGTpMpqntODYDrt6uzF0j6ghpFIptGQD3SMOkh0i09lJqr8bO58jZaXZkcvS7OXQautZ+S8ryfRvxbFz7Orrp2+wEWt0kJxRx7aeURr03eRSQ4wM9WM5Dj27BolikIibNDY24rouXV1dDAwM0NHRwYEHHgjAyMgI+XwezytehFRbW0sqlfJ1Aslk0o+0pIL3NDQ0+H02NDTkD7KWlpYx+dva2ohEIqRSKYaHhxERkskkgK+Vb29vp6Ojg2XLljFlyhQ0TaOndPImIv52QZVhGAZNTU309/dz2WWXkc/nqa+v57zzzvMDF3d1dfmCesqUKYyMjJDJZBApRr6aMmUKnufR09OD4zgkEgmampoQEXp6eli/fj2LFy+mtbWVWCzG7t27/UmpoaGBRCLhO1Cpo9rW1lbS6bQfICkSiTBlyhREhL6+PizLQtd1nz/VM03TfNqNjIyMyZ9Op+np6SGTyfCOd7xjn+NzrwIi6Eb7ZgsGBUHho3zmo9Go3/HKMAgoC8+laZofbkuF2FL5I5EIiUTCD2mmacVwYcoBS83WpmlSW1uLYRhFRyiKUluFJVNh7dQz9VsJGRVOTv1WbaipqUFE/LBzra2t3HTTTZx//vmceeaZXHfddRx66KEsXbrUb0sQT3VDUywWG4OnaRqlo+RilCA8G0NziUYi2FIgYuqYZi3JZAO1tRF0vThr1MRrqMXEKe3RNb2om6iJRzEjBrahY8YTROJx4notpmESMU1EPP7854dZ98w6amNFoaXrOv39/fT39/tOdrFYzI8rqnAO9oViUkXDRCKB4zhEo1G/L2tqavyIUpXyqyP5YP8qpyM1S6rQbCo8m+d5fvzF4EpThZTTdR3Hcfj1r3/NCy+84LvvqxvCTdP0+1n1kfqvylFlJJNJ3z9H8ayqW4W1U7ykBJbqY13Xqa+vL+qaSrjH43Fs2/b5Isif0WjUHxuKf9UzRbtwfsWrij4TggltRPYTBPdTHR0db7qO443iZNu2vPrqq393WcH9ZqFQkKuuukpWrFgh55xzjpx22mnS19dXts/eF+xo3yaO7YrteOJ6pfLdgoiTkR2vvSiH//PJssMWcXJ56dj4jBx32kdlIJMVKaQk6xYDgWVdEfEKkhvYKCf+y1Hyp5e3SVpE+rY8LstXnioDaUesbFp+c+ca+clP/q/k3IIUXEvcCvqFH/3oRzI6Ourva6sNnudJOp2W7du3V9SZBXFXdC8UCvKXv/xF5syZI3V1dfLDH/6wok7hjeLjeZ5s3bp10vC24ziSyWSko6NjQnkmRdh7XdcnRdh7Ceg8Fi5c+HeXF9wvRyIRvvSlLzFlyhRyuRxDQ0P89Kc/pVAojDkRGA9mzZ5dMkjbE2G8WIfQ0jqFOY0u9955Lzu3d/CHex9gwZJlROJRnEKW4d5BbNfbY/AkGpqrEzNNPIHmltkcPL2e3935O7q6O/nrE0+z5LDD0XUwNQ9xxp4oKb1RtftNgaZp1NbWMmfOnIo6s7D+CfDvsejv7+fcc8/lnHPO8ffn8gaOSSvBAQccMClopFYcr8uScj/jtFeQwDHMZHHWUsu99vb2N61ctdxMJBLceOONPPvss8ydO5d7772Xhx9+GJgYM/Z0dxcjSoUsUUGjNpnk0q98hmf++hCfPfscXmvv4jOf/wKiabS/uoFbrv8RBcspHpE6LoZmMH3aTDQxcAX0WANfO+8snvjzA3zmU5+kdeYcDjn0QCy7gCYuulZu86KW1xPF/a0AkaKXouKl8fBSCsVsNsu3vvUtXnzxRVasWMHFF1/sRzGfqNDeG6gJcPv27X9XOW8WqC1XLpejp6dnYpne9HXM6wC1BLMsS9auXVv1ZVhwCfrEE0+8KeWJjD3OfeSRR2TRokXysY99TE488UTZtGlT2TFWMG8Q1r3wgji2I67nieOWlvuuLeJaIl5BxNkto9mcpAaGxc7lZcQTyTiOiJ2W9GBabNcTW0TEc0SsEUmPjMiIK1IQEbEtES8lhVRORocGJOdYknNFCm5exM6JuGO3QOqYU7VtMkB/f788++yz4x7LB4PU/uIXv5BkMinz58+Xl19+uexoOXwU+UZALekfeeSRqvO2iPhHtcPDw7J+/foJ5an6FkMt6ZVipZoQPoJ7s8oL+rrous7RRx/NWWedxSuvvIJlWXz7299mZGRkjMFQhQJRF24WYzhoaLoJeqQYC8JoJVkTp665ATMeo16DWsMAM0GiKYGpa0WttGZApJ5EfT31OkQBzAhodUTr4iQbm4kbEeI6RPUYmHEYx1ErHGOx2rC343jHcfy+eOyxx7j88ssxDINrrrmGRYsW+W0JXnH494Kmab7RXbVBten14FJ1+0+1VJ0M+zRFOF3XWbx48ZtevtJc27bNl7/8ZQ477DBisRivvvoqv/rVr4qXEJWWt5092QAAIABJREFUxpVoMX/+/Kqbo09mEBESicS4+iN1leKOHTu49tpr6erq4uKLL+a0004D3ryJIYiP53ksX778TS33jYLiq0Qiwfz58yeUp6oCImi4MRlWEEHJqo4930xQEjwejxOPx7nqqqv8S1Vuu+02/vKXv+xVAFQylvkH7AG1SlPHhJWErGVZfO973+ORRx7hYx/7GF/5ylf8vPsDH3UMWe3JD/bwT1B/tM88+xOhfYGyEITiLU3VZvygtdmGDRv2Sx3K58Q0TWbMmMEvfvELNmzYwMyZM7nsssvYsGFDmSWp+hYR2tvbx1gQ/gP2gOu6ZLNZNm7ciOd5/mmEMr6ybZtf/vKX3H777RxxxBHccMMNZRasb/bqTPXfxo0bq87bsGcFm8vlJqw4rfoKQpmYKoOOaoIEzIcnGrPv9YBqX3CPu3z5cr73ve+xYcMGYrEYX/3qVxkeHvZNZ4Mmu0ET4snAcJMNDMPAsiyfl0zTxLZt3wnwf/7nf/ja175Ga2sr119/Pc3Nzf6dFvvD21L1t7rbs9oQ1KuoO1T3BVUVEEEz7skU9t513bckyIcyt/3whz/MueeeS29vLzt37uTrX/+6b2OghJaikXo2GRhusoHaqqr7VYIWs88//zz/9m//RjQa5Wc/+xnLly9/y4Rsa2vrpBDoQd8MdafpPvPsT4T2BWqLEYlEJkXYe9ijF1HXt+1PULeXRyIRLrjgAo477jgcx+GZZ57hhhtu8G3rlSCZN2/emxYh+/+rUF9f71/2rCafzs5OvvGNb7B161auv/563vve9wJvLCbH6wVN0/z7M6oNamJRxmQTgaobSkFxJh0YGKj6CgL27Pf3x8U3YVBLWyk5Zl133XXMnTuXTCbDT37yE+66666yFcTg7j4/SI8geEpQeKV4PE7Rkc2ldD+O54EU07uAJQ5YHkiOnNhgCbZAAbeUIQMuOJ6LI4Ir4HoOiIPnvD2EknKWU7yVzWY5//zzefTRR7n88ss544wzfF+b/c1vanuobu2uNih8CoXChK/eq/qUrZi/s7Oz6isINRgNw3hTLSnHg7DLeCwW44477qCpqQnDMLj22mt55JFHfH3E7u5eP2aoyJ47UD1X0ATAIzU6yraOLlKZfOmdi207WK7g4IHj4VhZugZ20de1i7ztkfFcxPHATtO1o5eurm46entJ5wU0B8+1eLtcnpNOp+ns7AQgl8tx8cUX89BDD3HBBRfwxS9+sexGqf29TVO8vWXLlkmxJVTjq1Ao+PeF7guqerYYlOLJZLLqe2tVd3C//1aC8ji9++67Oe200xgdHWX16tXceuutvOtd7/K9RBljxFOMOv3Ek89w3Q3/Qd5yaW1t4cILvsg7DjuseMs64KJhZUe44ec389CTfyOZgnf/8wmsOu8cmqJJ/vrXR7j44ltJtJro8QRXfut6Dn/HVAzdKMWnrD6T7wuUp2Mul+OGG27g5z//OWeccQZf+9rXqK2tLevj/c1rqvyJBoh9q0B5zk4IJmRvuR9Bec4VCoWqm6Mqz1LHcSYccefNBGUe7DiObNiwQQ4//HCZMWOGrFixQp577jmxM1mRkhen4xUjSxUfODKye5eccPLp8qeH/1t6d+2Sn9x6q5z/pS9L1rLFcj2xXVdyji0vPvQ7OfPc8+S1He3Su6NTPvv/tnfm8VVVV9//7nPulNzMCYFAyIwgM4ojzlPVqqXV6qMVW/GtE1Zp62MdarXaUm0fh9YBnGod26ptH1qrvlarVdQ6gjKEIQyBJJB5vLnDOWfv94+bfXNyDRAgkLyf5vf5XHI595x99rj22muv9dsXna+eef1d5URtdc+iG9VD//OEau/oUG2hTtUVlipmh5V0wkr140l97733qlAoNChuyYMBnY+Ojg714IMPqqysLHX66aerxsbGPhGz7qjU/Z0fzXA1HJAcXTwQDLkNQmsRoVAocU3/dTPuuL/3547svpbM1qR/18w+Oh33u6B3V0VKSUdHR5/0k+8dSNncHJXuvLj/JudFX58wYQLPPfccGRkZrFy5kmuvvZYVKz/HduyetHtIgJUE4dDaWk9UpHD0sceQn5vNGaeeRHVNLWGrh61KOphCsK7yYwonHUpZYQl540Zz+pyZfPLpBmJWlE1bqikuLWPZu+/Q3NiEzyNQSBCC/gjHtWeiu/6TWZPc7ee+7v7/zurXXX+a4au/tN3PRqNRnn76aW6++WaOPPJInnnmGbKysrAsK+Hnou/tL6+7sku43+VmlEruE+5rjuMQDof7za97K1unmZyn5DrZ2e/Jed9Z39L+IXq87Q5DvsTQ1ODV1dUEAgH8fj+O4ySYiSAeBSmE6HNNE7RYltWHjs7v96OUSrA1+3y+BJFGJBJJrAtTUlISaVqWlSCjUT2OJJ9//jlHHHFEgtBE76cbhpFQzxzHSWxH+ny+hKNNOBxOEHf4/X5s2yYSiSTyqJ+PRqNEo1FM00zkR+/jAxQVFbF06VLmzZvHRx99xJULruCZZ39PcUkFPp83Xh5sDBmlq70ZUnNQQCzciUcoGhqbiNgSjwHSChFzDBrrqwhOPgnDUbRFOsn2xdi0pYlQtJstW7exdOlf6YrVITwmN9+4iIkHj6G1rQvH7gZ6acqEiJ+nqinevF4v0Wg04auhyXZ02bUjksfjwev1JgaN1+tNtFk0Gk3s2GhDomVZiedTU1N7zu2wsSyrj2OT3+/Hsiyee+45brrpJg4//HAWL15Mbm4unZ2deDweotFogtRGt507r7FYrI8g12QukUgkwa6mSW10u2viGXef9Xq9iT4Xi8VYuXIlhxxySKJMkUgkMXDd79ZpuvtxNBpN1J0m5O3q6kpMrtqPw7KsxMSYmpqa6Oe67jR5kW3bNDY20tHRMaClz5D7N2up3tLSQmNjI4WFhYRCIbZs2ZJg56moqMA0Terq6mhvb0/EbgSDQWpra2lpacHj8ZCfn8/YsWMThqpYLMaoUaMoLCykq6uLTZs2JTSESZMmkZKSwo4dO2hpaSE/P5/CwkJs22bTpk20tLRQVVVFeXk5qamp1NTU0NbWRkpKCsXFxQSDQXbs2EFjYyNA4j0dHR1UV1cn3l1UVIRlWWzatAnLsvD5fJSXlxMIBKivr6e+vp5AIJAoj05TU6wVFRXx0ksvcdlll/HPt//BpfMv5ZFHfktZWQUb12/AjnaSmeYhFGrDMgLUN7UTrv6c7nCE7nCUsGXT3dZJpGETNkEaG7dge4PEuqJsqN1I+/YqbHk4voCPXz/wMPU14AuG+Ne77/DqK68ydvz5vPHPt9lR24zH0ysgHMehqqqKyspKpk6disfjYfv27QkquNLSUjIzM2loaKCurg6Px0N6ejqlpaVEIhHWr1+PlJK8vDyKiooS3n1aYJaVlZGamkpjYyM7duxACMGkSZMIBAK0trayZcsW/H5/Yj9/3Lhx/OUvf+FHP/oRs2bN4tZbb6W4uBjLsti2bVvCWWny5MkEAgFaWlqoqanBNE3Gjx9PTk4OjY2NCTq4vLw8xo8fTzgcZvPmzYTDYTIzMykpKaGxsZH6+nqEEKSlpSVOYdP3ZWVlUVxcnJj4GhoaWLt2beI9mzZtSjBnFRcXk5mZmThTVNMklpeXJ/Ko31NeXo5t24nyKKWoqKggNTWVLVu2EAqF+qTZ1NTU5/mysjLa2tqoq6sbuNfogBYi+wnuEOjGxsYEQ6+badgdepvM7KttBW5WJvfv+h3u5/V1N4Oye22q2bXr6uq+xJjsTqO/j5s5OJl9yV3eZMZmXd7ksup3xWIx1dDQoK5ccJny+L3q0COOUp99vlpZMUcpJ6qU3ao2rvyXmnruD1RrzFbK7lA7qivVyWd9Q1V3yTiLlBNSMibV/z7wbXXZw28rFVWqW0XVu7+5XM275S+qM9KhWlpqVSyklGNH1bvv/FNde81NKhoLq6gTjrNYJeX97rvvVp2dncqyLBWNRvvUUX+Mz26mZTeztLtepIsN2s3SrNvIHVbuOI6KRCIqEomoJUuWqJycHHXhhReqjRs3fon52c0k3l/7JDOmu7+73+fOu7t82naV3Ncsy0r0Jb32d/+enAf9f52eu36S2b531p929ry+JxQKqaampgGN0SHf5tTqkz7z0M09KGXvQbVKqT5BL27+Qa0VuD3F3Dsk+v/Jz+s03M5HWg3TnpTu+3Qa+loyq7Wbkdn9Xq3u6fTc92i1W6uBGvo9+npOTg6/uvte7vrFL9hQWcmVl3+XFZ8vx5HgOCZZo4sJdm1l9WfLiViCf39WScGYAnJSBV7hoBwHqSQFk06kfd37tLW3EQ518+aqeo6bnkPDjgbOO+88anfUELMk1Vu2c+ihMzCEgSlEgtvS7a6ruRV1GdwHB+m6cJffzeHorofk+3T7J7Nm6zSUirMyx2IxlixZwpIlS7jpppv41re+xZIlSygqKsJxnARjte5TyUQwyW3ndoF3u19r24e+ptvJfY8uv7uv6XeNHj06saTQS1Z3ud3jQH/X6enyJvc9d3248+HuM8nPa/7TQCBAVlbWwManUmpgVrf9AP1q27apq6tLHE47VHDTiFdWVjJ58uQhy0t/2Lx5M0VFRbz55ptcf/31OI7DQw89xFFHHYVpmjz/xGJeWvoyKVn5tHZFWLjwWk45fg7VGyp589WXmXf5Ndi2zfXXX59gdA4Gg9x1112kp6fzzLOP8fbb7yFtLwVjivjh9ddRMDYXYdiAgaAv0el9993HFVdckbCp7M9tQ22b0G3U0dHBokWLeOqppwBYuHAhCxcuxLZt6uvrE96LQ7ltrvv36tWrmTx58pD7+egJs7u7m5aWlgF5Uw65DQLiUq++vp7i4uIhz4eeEffm6L39jfb2dmzb5tRTT+Uvf/kLd955J+effz433ngj3/3ud7n4O5dy9Amn0NDWRU5+AYWF8eMCRo8p4MRTT0sYCO+99142bNiAbdscfPDBCUPZJZd8m5NOPI2G+jYmTJhEbm4mUtkYGEgVP7dzqKB3TDweDxs2bGDhwoWsXbuWRx99FICzzjoLiIdzd3V1AUMfs6K1F31k4nCANvwONE/DZhcjPT09cbLyUEJbhPUuyXCCViUdx6GsrIzFixfz2GOPceedd7J8+XIeffg3lE2YwDhLYni9SKkwDUFqMJWKCQehelTg1NRUpk6d2kfNdRwHr8dHSUkZhYUKn9cHAgxhALLHf3PooC30L7/8MgsXLqSwsJAXXniBQw89FOgdjNrqPxyg1Xu9ozHUGoR7uTHgvAzIUrEf4TbUDbWzjTYqacPncIM2oCYbTf/xj3+oGTNmqB9e9z21Y3udimjnKO1MJR2lnFgfjsxkw6qUUjkypmKxaA+dvlTx26WS0lL9eUrtD0cpt1HXbViLxWJq0aJFKiUlRc2fP1/V1dV9qSz6E4lEBoW2fl+RbNQcariNnIN29N7+hupZp+nIxaGE20A1UEeSAwm9pw19j7878cQTefrpp9mwaTPz51/Gqi++wIpGMdAOWxKp+p7unWx8FUJgCE8vG5MhEksKIUz6O455MKFczlNaS9KG5ra2Nh5//HGefPJJ7rjjDu6++24KCgq+VBZ9/3DgFoHe/qT9FoYD9DLafdTlLu/fz/nZLVSPB9jGjRv7nP48FHDvflRWVg5pXvrD5s2b+3iCugXalClT+O2Tv+PgyZNZsOBqnn3maUJdXfEz1Q0DOaD++eUT2Huv7f8Bp8PfddmUUmzbto1rr72W5557jnvuuYerr76a3NzcnfaVrq6uBKPUUEP37aqqqiHv2250dHSwbdu2Ad07LFytdccYavuDnrW8Xu+ADzc9kFDqy4eyamFhGAbZOTn8/Oc/5/rrr+fRR5ZwzTULqKuri3fOPZ5RFYmTgg8A9AyrZ/5IJMLSpUs544wzMAyDRx55hDPOOCNhG+qvr+gBqbdJh8OsrT0xhwPnKvTaagYqsIZcg9Az9q5mhQMFrX45B4hRak+RlZXVRyC4tQg9sHw+H3PnzuWFF17AsW3OPPNMfv/73xNxUejpNPR3t3vx/oR+r/644wq0sJNSsmHDBn7wgx/w4x//mBtuuIEHHniAKVOm9FkO9achaMLa3NzcYcHdqcs5bty4YSOsgD4eqLvDkPpBQF/fg+HSoKrHKWu4QZPd6s6fXF96oEG8XkOhEH/729949NFHKS4uZv78+cyZMyfhSONeqmihsyfYEz8Id7yM/r/ePdEaZFNTE3/605/4wx/+QElJCddddx3Tpk1LHDy7uzbRXVmnOdT9ScO27WGRH/dOiu5Lu8OQaxBa3ampqRkW60bdiFVVVUOcky+jtrZ2wNGG+gzGiy66iN/97neUlJRwww03cN1117Fu3bo+Riq3YNlfcBsRdRn0kq69vT0RlPbnP/+Za665hocffphZs2YlPBIHKrC7u7upq6s7YFrRrqDbo7q6esjzAr3aejgcHjBj2pDbIDRaWlqGfJ9YQweGDTfoQKidDebk67pDlJSUcMstt/D4448TDoc566yzuPHGG1mzZk0f3sv9if6WQ93d3SxdupRzzz2X2267jW984xs8//zznHfeeaSmpiaedYdp7wo6UlIHUg31jK37d11d3ZDnBXq1uFgsRltb24CeGXJHqeEg6TX0GlgIkQi3Her8JMdxJC8LdvYc9GXp9nq9TJs2jUceeYQPP/yQp556innz5jF79mzOOeccDj/8cLKzsxPxCLoukkly3YZR6OUw0NfdjlfQuzOhr+loxL///e+88sortLe381//9V+cd955jB07tk/ZdPnd6e8K2tNS53mo7RBuozcM/YFH7r400HoZ8lgMvRYKhUKkpKQMuRahO2hbW9uADTn7C8nr9XA4TCAQSKjbezrruwdxOBxmzZo1vPjii/z73/8mOzubOXPmcMIJJ1BYWMioUaPweDyJTq56gqi0QFdK8cgjjzBv3jzS0tIS6UNvu+rAN8dxqKurY9WqVbz66qt8/vnnjBkzhjPPPJOzzz6bUaNGDcqug55wQqEQaWlpAxIq+xtCCDo7OxN1NNhp7ym0n4gOK98dhlSDUD2EIfrvUAsH94wzXIQV9K7fNTmIHqR7mj/3DJ+SksLs2bOZPn069fX1fPTRR7z++us8//zzZGdnc9RRR3H22WdTUlJCdnZ2op3cM7rmNNB1po1gWoWtqqris88+47333mPt2rXk5ORw+umnM2/ePGbMmEFKSkofY+lg1LcmW3E7hQ0VtADXxDNDDb0hoMl1BoIh1SD0mkhKyfvvv09JScmQr9W0R19lZSUzZswY0rxo6JiVqqoqysrKEiHHe9N0upO469k927e2tvLxxx/zyiuv8P777+M4DlOnTmX06NHk5ORQXl7O2LFjCQaDvPXWWxx22GFIKWlsbGTjxo0JkpONGzcSDoeZOXMmhx9+OMcffzwVFRUEg8HEiVduyrrBOO9DKUUoFGLr1q1MmjRpWNghYrEY69evZ+LEiYmlxlBBC/aOjg5isRgzZ87c7TNDLiD055ZbbqG0tHRIVUJtLVdK8de//jURIXgg3++Ge4mxceNGuru7mTFjRh8fhj1FMi+jOwBMq+h6KaE7lKb1a2pqorm5mUgkQlVVFTU1NRQWFlJUVERaWhoZGRnk5uaSmZnZx18heXmi363vcdtV9hVNTU2sWrWKk08+ecj9aiBe30uXLmXu3LmDnp89bX+Px0MsFqO7u5v09HS+973v7f6Zvc3cYMC99TVx4kQuueSSIZWybgNZc3MzCxYsGLK8AH3W0O+++y7hcJhTTz31gM6K7kGulErM/OFwmCVLljB//nzS0tISxk23JnCgZ2+lFJs3b+bvf/87V1111QF9967Q0tIybPKjlGLLli289957A7p/ePh/0stCNIJeuHcLoHdJdqDhHuiaoDUtLY309HR8Ph9+v7/PfUPt5jzUhkmN5B2ZoV7u6PfvzBO1PwwLAaHV2eHSsMPB+q3zAV/etjyQ2NnWpV7vJ+cpmeZvf2J36Q/1gNRI9v8YKrg9cAealwMqINwdPVmquq3hbsnrLkjy87tyNd7TPLnhDojaW+wNQUh/5dWC071+7c892l03yfv/g7FD4HaJ10jWHKDvrsFgDIhkn4/+ytffM9DrTuzOe/JOTHKf2xO43ceT+6x7qzfZ/8AtRJPbZmd9f6DoLx/uOnO/L9n9vT8MiQahM+s2jkFvJ0yuMOgdtP2pbTqNPV2iuBvB3WF0wFZyA7ljITTc2446n7oR9raB9V/DMLBtO0F02l/ZNRFpso+93sbSgndfGY20w1PywHL7SQzmDNmf4HYLhp3FZui2cP9NFqLud+yrdubuf8nbtboPuH/X+XaHtbv72r4Icz1+NCWA1vTcQsI0TSzLGnB0qXn77bffvle52QckS27TNElLSyMvL69fiZ6sarup6bTV3a0K7wn0ANPv0R1q1KhR5Ofn97nX7Z3nVruTO6ruAHujQbjLq8/RUEoRDAYZM2ZMnzNM9f3ugaOFaHLk494KLA238NZp5uTkMGbMmP22BErWkNyCaGfh3oFAgLy8vETbJWs+us3cdHvu3ZQ9LYPW7LSQdvcl3V/y8/MT0cFuIeVetvX3/J7CXYbk8eWuS6/XS05ODllZWbvtpwd0m9PpOT4tFoslHKN05vtrpO7ubnw+Xx/68q6urj7uu6mpqXs9AHQaoVAIr9ebMJT2p8kAiROdtGqtO0B3dzd+vz/BQ7C3jaxVUvcJU8lqvBaI2kMxFosloil1XYZ7Qrt10waDwUHh23DPyJFIBNu28Xq9iZ2nwTQyJ2tk2gNQa1Q7M2rHYrE+R9oFg8GEENenfOk21qeuwc41kl1Byvgxdt3d3QniX7fjl3b9ht6+o+tKCznLsnb6/J5OMLo/65O7hIhT3PenKevvsVisT9xLMgZ1iaEVb0P17LMLgUIglERIi+r1q7n/4cdYvameg4uL+M63v8OM2VMwpYNterGVQ0AJUIKu9gYee+JFjjnuNGbPnoASUT79eCU/vfNXRLo7EAbMPvJIbrjxRoIpAYRyQIEwdlEkZWMBCAMvYDjdrF6/kTvvugfDCnHaKedw7iUXk2IYCGyi+PAhEU4ImwAfvv0Kb6/sYOFVF+D1mxjtLdz3zP+y7I0XSfXncupZ53DBhd/E6zHxAkKLXkNhAd7dsDIJadLSvJ5f/M9zfLJ2GZNzRnHJ/EVMP6YUL1FQPjAtZCzCW2+/y4PPPEesoY5T55zJOVdeSXFugPot61jw3z+hqTNKUHZTMWkKP75zEQUZfuJnfO8tHEChMKlcWclD99/LttpaJk6fzqVXXkVFWXGf1Pd8NlY99DSa5w6UYxPnzHV4441lPPnss7S31HLCcSdz8bzLGV2QDSLe10wlUNKBrnYWP/oE/3jvQ8aMGsdpXz2Fr59zGsJyePrZP/Lssy/h9wgMIbj0u5dzztfPxhACoSziBDm76D8SHKEwiCJsyfrVa7n/d0+yrnI9x0yZxYVXX0N5+ThQEo/oYfJyJKYJ4a4Wnnn8OQ4/+3xmHJSDJyb5vHIFi5e8RvWGd5kx/QjmXbGAiRVFCNXTd/rM3WK3pF7Ctvj0/U+494WH6VoT5shjp/CNa69jYl4mUnkwAMOIohwvhvDS3LqVxY8+w09uuXWnaQ6q/6dUIJXqaWqJAmypUEjsUCtPPb6EcUUl3HnXXUybNJGnn3qW1pDEQMafMQSOHaOpsZHHF/+aB3/9CK0tEqUclAyxbk0lJSWTWLx4CQ8+8ADfvfJKfKmpOMJACAVOX/dRLYkTSpJysJWDrXoOvbW7uP+eX3LOeedz7TVX8b8v/InlldviWoC0CEuwHAc70sprr73Oz25eyIp1zWCY2EhWvfs2yz5Zza233cCVly/gb0tfZeXqDThC4GhCJhn/K+n/sFn3xxCKZx/6DV0xD3ffew+nnHgY9y96mOYoICwcZYJwaNy2luef/iNnX3Q+9/zPL2nespXn/voutuOwvWoV6VnZ3PvQwzy25GH++4Yb8WWkx+tn31oX6cSIdodZ9Itfcsghh/OrX95NejDIQ4/9loE57u4eiWpTCsMA5cRort/G448/yTcvnMeiRT+ltqaWV159C0uCxEHioJSDoRzefPUVPvzwU267404uOO8Cljz6GFtr6zBkmI8+/IDv/+BH3H/f/Tzw6wc4/vgTEKaJFALDVMSF4C6rAKlAiBgy1MmLTz9L8UEHce9vfkNeaipLHn+B7qhEGfFDjwXgWA5bqjZw3z138dsHH6YpIrCEg4q0suSRh6k4+DB+ff895Odm87tnX6Kz20b1EawDZ/YKN9fz2JLfctgJR3Lf3fcRCbXw2B9fJiYlomfiRXVhGIL1q9axaNGPeeb5Z3eZ5qAKiES5lIoPCtkziyhFdzhMdUMXX/n6RcycOoHz5x5HKNpGQ2cYx/DiEQYeBaZh8rvHH0dKybRpkxFGvGCGEmzdupVjjpmD3+cnJzeHMaNHowBDxIlZhblz6S+lRCqZkMJKQXtjCw0NrZx84lc44sgTOPn4OaxZuQ6kBEPEm8Uw+WzZv/nzX1/h1BNPJmB6cGwbU5isXLGCM886k2mzZnDMicdwzPQpbFr9BVI6OAYog/j7lMCTJP6ThYNSim6rhS0rm/nm/AuZWTSdr158Hj65mc219RjKwMBBKC87ajeQlVLG6accy8TyGZz7zZP44vMPiNkOmzZv5pBZs0jPyCQlmELR+LHx9w2MlHLnUCYCDx31m9hcv52vXXYJB02bzMXnn0PNxo2EovuWfL+vVAphGNRUbyM9PZ3jjzuWg6dM5qyzzmL58uWEIyoxfBSAY/H6Ryv4ygUXM/3ggzn9tEOYXFLC6jU1dHSEUVGLignlZGRmUFAwhuzsDKTuEsLY/Tg0ACFRyqSjJcyqlVXMPfvrHDSxgm9ddhEb16yjraEVjwRDCMyeuJQlSxaTPzqfWbOmoowYpgjS2lxH3TYatzvsAAARC0lEQVSHuV8/jgmlE7ngwrOprtpEZ1s7ylIYwqVJCZADUMZqa9dSE3G45GuXUj6zmHMvOYdV76xkR7eFoeL8H8LwsKOmhieeeIKJEycydcquD4ca1CWGSrSWiusPQsSFhGNjxWJ0qxSCeWMxlEVWhonyxNjW2k55QSYB20IZ8bXagmu/h090smLVrfEEDUWkK0Llmko+XL6Bh359Fylpfi789nzOveCbKE/P8Xm2jTB6PTHd61ch4ic7KBWf0hXQ3t6FHVOkpXlRjmR0bgZrt29DSRuUjekF24aZRx/HvcfP5ZM/PMi/3w6T4vVhSYvt9TsoPz4bYXiRwLi0VNp21GEKiY3CIzx4RLwIpupVEd3bXG6EnUaijT7SR4/CHzNpTXcoyuumpqkFyrIwTQeUh4b6TQS94/GZMUzbS95oD62t2whHY3z+xResqA3z1J9epdjXxQlnfINvXXMt0lGY++Ck6kiBIQyszh1kjBlNKMUk3bEpGJ1FS/12OrshfxCPEjGEiKvnQlFTs43c3FxMU2AKg3HjxrFl85bESeIAQpkoJ8bW9m7mFE/AaxhgtzOhcBzrqtsoKWhg09oqbr/9Nmo3raeivJyrF/6QmYfNwO5ZBrC7JZGQCGyUNGhv7qY75JCRlYOJIj3Di93VTaSjC5NcpOPgKEFKIMCtP7kNRZiVyz7GMGxs26CrqwnDGY0vxYswA6SmgRWO0NUewluQh5IS4REJJVSy+9m8oWEjxuhxpKhULG+MtLwA9Wsb6BI+UCEkPlCKnLw8fnrHHXTZm3ntzU93meagCoi2tna++OILZDSEdByU6ScmFUEPjAoadMckyjSBKMKnkFhEVXzwStsGnwfTG8A0JSLWgWkSVzOlwB9M46oFVzC68CBKigrYvHkjt9zxc2YfdSQVJcUoBIan7whQKu56u3HjRpRSeFSEsBFAmQGyPJAmwziOQjqAFJiGwrai8X4i4o3j8Rj4/KnYXh8Cgc/rIxa1MNMMuru748sN5WCiCHo87GhvSTwvoUeDiH8Uis7OTlasWJE4bdqNrHHdYPmIKhVXZxEYqouucLTn4BoHxzEIhzvxGmkYhh2/z+5CqRi2o7hw3iV8e9QExpSVo5q3ceU1P2LSnNM4bWbZPrWtYQiQoOww3bEolnRwkJjKBtuKL6kGEQowTBNpO4lDc7xegWF4sKwYoHqMkXrYxGn6I0rhGB6UI8G0sCIRbOUjd1wRP7n9dmYccyxBn59XX36ZBx98iMWPL8HjMUE57H6dL3smGIEVjQsKj2FgKwtT2TgxG48QKMfBMI34qDZNAqkpWLaNVDbKUBhALBbGjnnw+wyEYaKwUI7EsSXSIa45Q18NaTdwZIyY6cWLgTIVjrDwKR+d3WHw2UgDvMKDGUgFn0F3u0A5uyZnHlQBEQj4KSwchyEtUBJp+JAIPDJGioqQmeonFrYR6V5iIRuv6SczJQVQmD4/jnRQhsBE4SgHqRxsx+pRs0wmT5lKMDMXJW0Kxhb0HDnfxISSYnAcMD19GlgIQXZ2NiUlJfEdE6J0SQMlvKQZCjoa8fu9OI5CmILuSJiMrPhBqwjlshHFBwcCbOngD3iJyRi5ubmEuyMYPWK+PRwhIycPIXrOrNDCoScJpeKnLBUWFiY0Gze8aW14UiU+ep5zHByRRmZaMN4xVbx8+aPHEXM6caSJkuAoP4FAOqbXx8TJk5GpBVhAenYmhePHUV/fgJT7JiC00dHwpOABfELgFR6iliQlLYNg6pfZrPbxhfE0BGRlZvYc1qtISVHEYhZp6el4vR603cB2bLwKcjNSCLc3I8wKED5ijiIrLUC6z89hRx2JkRIAx+agiRPYsmUL0ZgdP0VsQEfEGCAMBIpgeir+gIdwNErA50E4IDwGhtcLhgAlEaaBtCWm10s0pjAMD46twID01HR8AUk4HEN6PDiOgeEx8fk9GIYWEGqPDh3IyszDiNZhI/ErD8oSBHOCpPn9YIDtgGGCiUDJHi4Wc9flHlQbRMAfoLy8jPLycsorKigtKaa0tISyinKyc3LwOZ3UbviCqCVoaI4SarcYm5GBaVtYSiE93viCS8StzELEjYlCCNqbmrnt1tvZtm07hhEPWTVNk7y87PgYNL1JVt+4Kp+RkUFFRQVlZWUUlZRSVl5CeUUJpWWlFBTkIwyH5pY2FDEqN1RRMH58fPelZ4DH1+4SE5CmQHhNonZ8+VRaXELlqrVxa7sjWbmthvziMsBEOGBq0S/i1m+Is06XlpZSUlJCRUVFn8+ozBJS8m1WfbicWAA8IYvla8NMKi5EGRKpTDAd8vKK2dG6hraQBT7JhjX15OaVIEwvP/7RTVSuWYMpwI6EaWxsYFT+KDy+fQuCi9t5LHLGTyTS0k7H1mawFavXV5OWk4t/kMNoEt5/CMaXlFBXV4dlOVi2xbp16ygqKsLv92IIE0OYmIaB8Pkozwmy8bP3cJTEjqXyaeVaplWMYdXHH3LbbbcSiUQwDEFTUxOlpaV4PWbcfiXE7qdpZQAmQkhy8tPJzkmlsXEHHo+fxppmMkblEcxORxoCG4kje2aVxL9ehPJiGJLsnALwNNBQ3waGTVN9iEB6Grn5ucQchZRxO54gPkgHUr3ZeSXY27dR21qDDCs2rNxCbkUO2V4JBMAApUTPOavufO0cg6pBCCM+oOLGJYEw4utW5dikZqRz1qlH86vb/5tJh55M3aqPOeW0r1KQ5SHU2sCLr73NGefMZUxaEIXCkTagMD0mjm2TmZXNxIkHcdvtt1E4JoeOjnZmzJhBWWlxXP1W8RnfXWDt5dhrg3CFFwP+7ExOOPFYfnTT9YxJcWipb+XSo2bjKPjrSy+RO/U4jpk2Ia492IqYdIhJgTDjo/7QY4/lvjse44db3oRwDp0xhxlHHo3lKHyY8R04BRgKGxXf+nR5Wia7oAT9eZz+zTnc+pvFfPDBSzgbV3P86f+H8flBOjprefHF/8tX586ieNIhjBq3jIXf/zFTgim0rG/m3J/+krQ0H0cedSQ///nPKJk4E2/zeorHF3HYoQcjlcTYh8NvpIzh8Rio9HzmnvoVbrt6ARWl41m9aRMXXrGAwCD75Cq91WcajCssZOzYsSz8/vcZleVQW93E93/4M0yP4tMV8TX01rWbOf+8s/nON77K5T+4metq64i2Rwnm5jNtShGqzcef/u5w8y03k53ip7W5jfnzL8XnM1GJgbxrCaGceH6UsPFn+jj5lDncdvutFBcW0fnFOr76nYWkZaexqaaaN19/lYsvuJj01HRQdnygKy92zI8iTCBrDMeffDA/ve3XzCyNsWFDDadfeAXBzFSUVBimSBj7ExrEbppvfNEUjp9yEN+79RoONWazvuZfzL35F+R4BWvX17LskzV868Kj8Ymek9YAczcaxKA6Skl6PLfoMQyaJlIJDOUgcHBi3XyxZgMr1m5jankpU6cchCfFR6yzg/eXr+SwI48mw+9FKAkizAfvf05J2TTGjElDqhiOBWvWrmftmpWUlZUx/ZDZGKYXjwE4apeGJqUUAoeYUgjDxJQSYYfpVgbL3v8Iu6uVo46Ygz83nxQDPlz2FjlFk6gYX4CpIkiRwvbNX7C+KcjRh5ZimOCNRahqDFO54p8oK4Ujjjue7Nx0BODRHRx26geRXPVCCqRqZuWaVlZs/IDJOflMm3UaKg2scAsfvL+Wo+YcTLo/QFt7iLc+W4HdtJ3Dp84hZ0oZPiXw2p1Ubqjmsy/WML10DJNnHYHl85O6+230vuND6Au9+7VKCRQeVCzG8o8/oXprNWUHT6Z8ylRSvQaefVpW9PWDUEoS96KRIB06Qg7/eu99Otu3M3vWEZSWTcBGUVOzCYCm7Y3MPnQmHmFTU9vA+8tXkZ6SzZFzjiAt1cQnFG1dXXz08XLaW5o49JDZjC8uRhoeTAGm6DmgeBdlUA5IQ2EQQUiwog4frFxJ9eatzK6YRNGMGXhMRXtHKx/9+wNOOu5EUlNSQdnYdpTlHyxn9PTDKchy8NrQZXXw6fJmtlW9x+TJhzJh+nT8vnh+lC3xmO68DKABY1HCIYtlVR/StrKDWYdPIHfKFLKwqa5uZMOmak44fiZC+eI7LFYr773/CSedeNpOkzzghDFu33C3O2h/rtL9ufDu7N7Bypc7kCXZk21nkYp76/m2u7xAX9IY7e3ndrPW+XE7JrnrSP8+sBe7vgtIOHHodZJL0d1f7tW7zF5SuZJ/6y8/yf8f7P7jbvtk/5Zkz8z+gqMGMz/9xZrsrP/o33fnQXpABYS7MtwNOpCKcRv0+vM539f86HT35LnkZ/a1gZOjFHeWXnK+k4VF8vcBCzCXQbX3gnRd/HIQnf4+2AL7S1nbg77Tn4DtL419zbO7vfqb9HaXtjuuZ2/iQPqD269mVwM/uR52hgMezbm3cQq7mxn2JT97Mhv21/kGS8YOJL1kT0x3sJH7nmQMuL6+dJtBrwbx5bzsb8HgRnIg1M7Kuas87Usw1K7gbruBDtD+vu8L9qQ9krXQnd53oJcYwwn7qiZ/yYYwyCrinqjSg5Gf5OfdwUZuHkvTNGlpaSEYDOL3+/uEu+8qcnIw62ug9XCgl0B7W+eDlc89KftA8jv0XNxDiH2d/dyz1WA08EDSG8hve5sf2bNzBL0zoJS9ZDX6Wjgc5sEHH6SpqanfDqkFg45I1dGVyZrPvmCg9XAgsTfvG+x87knZB3LPf7SAGEFfiB5fB8vWLswC23YwDBNBXANwHAfLsmhpaUmcyO4+vsB99mZ/jEsa/8GK6/9XGBaclCMYHnCkw2uvvcYnH3/K1Vd/j9df/wdNjS1cffVVmKaBYcYH+ltvvcWECRMSTFe2bRONRrn77rspLy/njTfeIDMzk4svvph33nmHZcuWMXfuXC666KLEmR4HenYfwd5hRIMYQQICm4qyMpqb2/jXOx9QMLaIiZMmIoTE9Mi4L4vj8MZb/+Kk005HCoFUEq9HYIca+OijZXy4ehOXXT6fPNPmZ7ffQdnU2Vy34DL+9MJLrN64A7xeFAqlbFAy7uCGRCF3n8ERHHCMaBAjSMAUioMOmsB5557PpyvW8LWvfw2hHDymike4SkVLaycSk7FFxSgh4t6ZyiFoxshID3D6ud/kiENK8NWspzlscMzJJ5Fl1/LkE39kR7vNJASmQdwZrsetXvUEuozoFMMPIxrECFwwUFKRnZNFZ1cHpil6KNCI2yEMk61btzJhQgUBX9+5RQoTj9dHqt+LVOBNyyA9PR2PCSJOpBCPWYEerQF64xRGhMNwxYgGMYIEttfUYfpSaGpqoqWlifb2LgJ+L8EUL8j4TsSa1auZMX1awm0qHiMgsJUHYXgwkXgND7YS2NLBo8AQHqRSeJCuGUkkfUYwHDGiQYwggeef+z2LH3qYKVMmk54e5NNPPyESCaOUwJGKzs4uampqKC0pwugJRUbERYUy/fgDqQR6AvYIpJEaTMGLwhA+AimpCKfH7hBn74i/tCdmZUREDE/8RztKjaAv2hp3IAyT1IxMmts6SElJIS01NU5/piSOdKivbyB/9GgM0+yhRYsLCiUtqmtqyRpVQJrXxI5009LWxeixYzFkjC3V28nKH0d6mokpnDjDlYgzSiM079vIfDXcMCIgRtALK4YyDDAMbKUwDBOkwhQCpUAqJxFCn+xG7Mgepyh9MIxlYZgepCPjvBqYcYZz00ZJC4/hA8weL+6eHQwxIiCGG0ZaZAS9MMwePg8ZXzmgA3qI80n0ODzFhUScBp+ef5UwkRAPvVcK5fHGn1EOwjBQCkxDIZTENOI85ongMDVihxiuGNEgRjCCEewU/w/IGFU+hLJ6xAAAAABJRU5ErkJggg==\"/>\n  </em>\n </p>\n</div>\n",
    "Examiners report": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  This item was essentially encouraging candidates to connect concepts about simple harmonic motion to a physical situation described by a graph. The marks were awarded for discussing the physical motion (such as \"the acceleration is in the opposite direction of the displacement\") and not just for describing the graph itself (such as \"the slope of the graph is negative\"). Most candidates were successful in recognizing that the acceleration was proportional to displacement for the first marking point, but many simply described the graph for the second marking point.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  This question was well done by many candidates. A common mistake was to select an incorrect gradient, but candidates who showed their work clearly still earned the majority of the marks.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  Many candidates recognized that the time period would increase for B, and some were able to give a valid reason based on the difference between the motion of B and the motion of A. It should be noted that the prompt specified \"without calculation\", so candidates who simply attempted to calculate the time period of B did not receive marks.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  Candidates were generally successful in describing one of the two aspects of the graph of B compared to A, but few were able to describe both. It should be noted that this is a two mark question, so candidates should have considered the fact that there are two distinct statements to be made about the graphs. Examiners did accept clearly drawn graphs as well for full marks.\n </p>\n</div>\n",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-1-simple-harmonic-motion"
    ]
  },
  {
    "question_id": "22M.2.SL.TZ2.2",
    "Question": "<div class=\"specification\">\n<p>A fixed mass of an ideal gas is contained in a cylinder closed with a frictionless piston. The volume of the gas is 2.5 × 10<sup>−3 </sup>m<sup>3</sup> when the temperature of the gas is 37 °C and the pressure of the gas is 4.0 × 10<sup>5 </sup>Pa.</p>\n</div><div class=\"specification\">\n<p>Energy is now supplied to the gas and the piston moves to allow the gas to expand. The temperature is held constant.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Calculate the number of gas particles in the cylinder.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Discuss, for this process, the changes that occur in the density of the gas.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Discuss, for this process, the changes that occur in the internal energy of the gas.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">b.ii.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>Correct conversion of T «T = 310 K» seen ✓</p>\n<p>« use of = <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>N</mi><mo>=</mo><mfrac><mrow><mi>p</mi><mi>V</mi></mrow><mrow><mi>k</mi><mi>T</mi></mrow></mfrac></math> to get » 2.3 × 10<sup>23</sup> ✓</p>\n<p> </p>\n<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong> i.e., T in Celsius (Result is 2.7 x 10<sup>24</sup>)</em></p>\n<p><em>Allow use of n, R and N<sub>A</sub></em></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>density decreases ✓</p>\n<p>volume is increased <em><strong>AND</strong> </em>mass/number of particles remains constant ✓</p>\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>internal energy is constant ✓</p>\n<p><br/>internal energy depends on kinetic energy/temperature «only»</p>\n<p><em><strong>OR</strong></em></p>\n<p>since temperature/kinetic energy is constant ✓</p>\n<p> </p>\n<p><em>Do not award <strong>MP2</strong> for stating that “temperature is constant” unless linked to the correct conclusion, as that is mentioned in the stem.</em></p>\n<p><em>Award <strong>MP2</strong> for stating that kinetic energy remains constant.</em></p>\n<div class=\"question_part_label\">b.ii.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>a) This was well answered with the majority converting to K. Quite a few found the number of moles but did not then convert to molecules.</p>\n<p>bi) Well answered. It was pleasing to see how many recognised the need to state that the mass/number of molecules stayed the same as well as stating that the volume increased. At SL this recognition was less common so only 1 mark was often awarded.</p>\n<p>bii) This was less successfully answered. A surprising number of candidates said that the internal energy of an ideal gas increases during an isothermal expansion. Many recognised that constant temp meant constant KE but then went on to state that the PE must increase and so the internal energy would increase.<br/><br/></p>\n<div class=\"question_part_label\">a.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.ii.</div>\n</div>",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-3-gas-laws"
    ]
  },
  {
    "question_id": "22M.2.SL.TZ2.3",
    "Question": "<div class=\"specification\">\n<p>A loudspeaker emits sound waves of frequency<em> <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>f</mi></math></em> towards a metal plate that reflects the waves. A small microphone is moved along the line from the metal plate to the loudspeaker. The intensity of sound detected at the microphone as it moves varies regularly between maximum and minimum values.</p>\n<p><img src=\"data:image/png;base64,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\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p>The speed of sound in air is 340 m s<sup>−1</sup>.</p>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Explain the variation in intensity.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>Adjacent minima are separated by a distance of 0.12 m. Calculate <em><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>f</mi></math></em>.</p>\n<div class=\"marks\">[2]</div>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px; padding-right: 20px;\">\n<p>The metal plate is replaced by a wooden plate that reflects a lower intensity sound wave than the metal plate.</p>\n<p>State and explain the differences between the sound intensities detected by the same microphone with the metal plate and the wooden plate.</p>\n<div class=\"marks\">[3]</div>\n<div class=\"question_part_label\">b.</div>\n</div>",
    "Markscheme": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>«incident and reflected» waves superpose/interfere/combine ✓</p>\n<p>«that leads to» standing waves formed <em><strong>OR</strong> </em>nodes and antinodes present ✓</p>\n<p>at antinodes / maxima there is maximum intensity / constructive interference / «displacement» addition / louder sound ✓</p>\n<p>at nodes / minima there is minimum intensity / destructive interference / «displacement» cancellation / quieter sound ✓</p>\n<p> </p>\n<p><strong><em>OWTTE</em></strong></p>\n<p><em>Allow a sketch of a standing wave for <strong>MP2</strong></em></p>\n<p><em>Allow a correct reference to path or phase differences to identify constructive / destructive interference</em></p>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>wavelength = 0.24 «m» ✓</p>\n<p><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>f</mi></math> = «<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mn>340</mn><mrow><mn>0</mn><mo>.</mo><mn>24</mn></mrow></mfrac></math>=» 1.4 «kHz» <em><strong>OR</strong> </em>1400 «Hz» ✓</p>\n<p> </p>\n<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong></em></p>\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n<p>relates intensity to amplitude ✓</p>\n<p>antinodes / maximum intensity will be decreased / quieter ✓</p>\n<p>nodes / minimum will be increased / louder ✓</p>\n<p>difference in intensities will be less ✓</p>\n<p>maxima and minima are at the same positions ✓</p>\n<p> </p>\n<p><em><strong>OWTTE</strong></em></p>\n<div class=\"question_part_label\">b.</div>\n</div>",
    "Examiners report": "<div class=\"question\" style=\"padding-left: 20px;\">\n<p>ai) On most occasions it looked like students knew more than they could successfully communicate. Lots of answers talked about interference between the 2 waves, or standing waves being produced but did not go on to add detail. Candidates should take note of how many marks the question part is worth and attempt a structure of the answer that accounts for that. At SL there were problems recognizing a standard question requiring the typical explanation of how a standing wave is established.</p>\n<p>3aii) By far the most common answer was 2800 Hz, not doubling the value given to get the correct wavelength. That might suggest that some students misinterpreted adjacent minima as two troughs, therefore missing to use the information to correctly determine the wavelength as 0.24 m.</p>\n<p>b) A question that turned out to be a good high level discriminator. Most candidates went for an answer that generally had everything at a lower intensity and didn't pick up on the relative amount of superposition. Those that did answer it very well, with very clear explanations, succeeded in recognizing that the nodes would be louder and the anti-nodes would be quieter than before.</p>\n<div class=\"question_part_label\">a.i.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">a.ii.</div>\n</div><div class=\"question\" style=\"padding-left: 20px;\">\n[N/A]\n<div class=\"question_part_label\">b.</div>\n</div>",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-4-standing-waves-and-resonance"
    ]
  },
  {
    "question_id": "22N.2.HL.TZ0.6",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline, by reference to nuclear binding energy, why the mass of a nucleus is less than the sum of the masses of its constituent nucleons.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate, in MeV, the energy released in this decay.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The polonium nucleus was stationary before the decay.\n  </p>\n  <p>\n   Show, by reference to the momentum of the particles, that the kinetic energy of the alpha particle is much greater than the kinetic energy of the lead nucleus.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   In the decay of polonium−210, alpha emissions can be accompanied by the emissions of gamma photons, all of the same wavelength of 1.54 × 10\n   <sup>\n    −12\n   </sup>\n   m.\n  </p>\n  <p>\n   Discuss how this observation provides evidence for discrete nuclear energy levels.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   A sample contains 5.0 g of pure polonium-210. The decay constant of polonium-210 is 5.8 × 10\n   <sup>\n    −8\n   </sup>\n   s\n   <sup>\n    −1\n   </sup>\n   . Lead-206 is stable.\n  </p>\n  <p>\n   Calculate the mass of lead-206 present in the sample after one year.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  according to Δ\n  <em>\n   E\n  </em>\n  = Δ\n  <em>\n   mc\n  </em>\n  <sup>\n   2\n  </sup>\n  / identifies mass energy equivalence ✓\n </p>\n <p>\n </p>\n <p>\n  energy is released when nucleons come together / a nucleus is formed «so nucleus has less mass than individual nucleons»\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  energy is required to «completely» separate the nucleons / break apart a nucleus «so individual nucleons have more mass than nucleus» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept protons and neutrons.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  according to Δ\n  <em>\n   E\n  </em>\n  = Δ\n  <em>\n   mc\n  </em>\n  <sup>\n   2\n  </sup>\n  / identifies mass energy equivalence ✓\n </p>\n <p>\n </p>\n <p>\n  energy is released when nucleons come together / a nucleus is formed «so nucleus has less mass than individual nucleons»\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  energy is required to «completely» separate the nucleons / break apart a nucleus «so individual nucleons have more mass than nucleus» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept protons and neutrons.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.i)\n </div><div class=\"card-body\">\n <p>\n  (\n  <em>\n   m\n  </em>\n  <sub>\n   polonium\n  </sub>\n  −\n  <em>\n   m\n  </em>\n  <sub>\n   lead\n  </sub>\n  −\n  <em>\n   m\n   <sub>\n    α\n   </sub>\n  </em>\n  )\n  <em>\n   c\n  </em>\n  <sup>\n   2\n  </sup>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  (209.93676 − 205.92945 − 4.00151)\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  mass difference = 5.8 × 10\n  <sup>\n   −3\n  </sup>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  conversion to MeV using 931.5 to give 5.4 «MeV» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    MP1\n   </strong>\n   .\n  </em>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    [2]\n   </strong>\n   for a\n   <strong>\n    BCA\n   </strong>\n   .\n  </em>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    [1]\n   </strong>\n   for 8.6 x 10\n   <sup>\n    −13\n   </sup>\n   J.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.ii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n </p>\n <p>\n  energy ratio expressed in terms of momentum, e.g.\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <msub>\n     <mi>\n      E\n     </mi>\n     <mi>\n      α\n     </mi>\n    </msub>\n    <msub>\n     <mi>\n      E\n     </mi>\n     <mtext>\n      lead\n     </mtext>\n    </msub>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <msubsup>\n      <mi>\n       p\n      </mi>\n      <mi>\n       α\n      </mi>\n      <mn>\n       2\n      </mn>\n     </msubsup>\n     <mo>\n      /\n     </mo>\n     <mn>\n      2\n     </mn>\n     <msub>\n      <mi>\n       m\n      </mi>\n      <mi>\n       α\n      </mi>\n     </msub>\n    </mrow>\n    <mrow>\n     <msubsup>\n      <mi>\n       p\n      </mi>\n      <mtext>\n       lead\n      </mtext>\n      <mn>\n       2\n      </mn>\n     </msubsup>\n     <mo>\n      /\n     </mo>\n     <mn>\n      2\n     </mn>\n     <msub>\n      <mi>\n       m\n      </mi>\n      <mtext>\n       lead\n      </mtext>\n     </msub>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     p\n    </mi>\n    <mi>\n     α\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <msub>\n    <mi>\n     p\n    </mi>\n    <mtext>\n     lead\n    </mtext>\n   </msub>\n  </math>\n  hence\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <msub>\n     <mi>\n      E\n     </mi>\n     <mi>\n      α\n     </mi>\n    </msub>\n    <msub>\n     <mi>\n      E\n     </mi>\n     <mtext>\n      lead\n     </mtext>\n    </msub>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <msub>\n     <mi>\n      m\n     </mi>\n     <mtext>\n      lead\n     </mtext>\n    </msub>\n    <msub>\n     <mi>\n      m\n     </mi>\n     <mi>\n      α\n     </mi>\n    </msub>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <msub>\n     <mi>\n      m\n     </mi>\n     <mtext>\n      lead\n     </mtext>\n    </msub>\n    <msub>\n     <mi>\n      m\n     </mi>\n     <mi>\n      α\n     </mi>\n    </msub>\n   </mfrac>\n   <mo>\n    ≃\n   </mo>\n   <mfrac>\n    <mn>\n     206\n    </mn>\n    <mn>\n     4\n    </mn>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    51\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    5\n   </mn>\n   <mo>\n    ⇒\n   </mo>\n   <msub>\n    <mi>\n     E\n    </mi>\n    <mi>\n     α\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mn>\n    51\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    5\n   </mn>\n   <msub>\n    <mi>\n     E\n    </mi>\n    <mtext>\n     lead\n    </mtext>\n   </msub>\n  </math>\n  «so\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    α\n   </mtext>\n  </math>\n  has a much greater KE»\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mtext>\n     m\n    </mtext>\n    <mtext>\n     lead\n    </mtext>\n   </msub>\n  </math>\n  «much» greater than\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mtext>\n     m\n    </mtext>\n    <mtext>\n     alpha\n    </mtext>\n   </msub>\n  </math>\n  «so\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    α\n   </mtext>\n  </math>\n  has a much greater KE» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n </p>\n <p>\n  alpha particle and lead particle have equal and opposite momenta ✓\n </p>\n <p>\n  so their velocities are inversely proportional to mass ✓\n </p>\n <p>\n  but KE ∝\n  <em>\n   v\n  </em>\n  <sup>\n   2\n  </sup>\n  «so\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    α\n   </mtext>\n  </math>\n  has a much greater KE» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.iii)\n </div><div class=\"card-body\">\n <p>\n  photon energy is determined by its wavelength ✓\n </p>\n <p>\n  <br/>\n  photons are emitted when nucleus undergoes transitions between its «nuclear» energy levels\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  photon energy equals the difference between «nuclear» energy levels ✓\n </p>\n <p>\n  <br/>\n  photons have the same energy / a fixed value\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  energy is quantized / discrete ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  undecayed mass\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    5\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mi>\n     e\n    </mi>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      5\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      8\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        8\n       </mn>\n      </mrow>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      365\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      24\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      60\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      60\n     </mn>\n    </mrow>\n   </msup>\n  </math>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    8\n   </mn>\n  </math>\n  g» ✓\n </p>\n <p>\n  mass of decayed polonium «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    5\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    -\n   </mo>\n  </math>\n  undecayed mass»\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    4\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    2\n   </mn>\n  </math>\n  «g» ✓\n </p>\n <p>\n  mass of lead «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     206\n    </mn>\n    <mn>\n     210\n    </mn>\n   </mfrac>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    4\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    2\n   </mn>\n  </math>\n  »\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    4\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    1\n   </mn>\n  </math>\n  «g» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    [2] max\n   </strong>\n   for answers that ignore mass difference between Pb and Po (4.2 g).\n  </em>\n </p>\n <p>\n  <em>\n   Allow calculations in number of particles or moles for\n   <strong>\n    MP1\n   </strong>\n   and\n   <strong>\n    MP2\n   </strong>\n   .\n  </em>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    MP1\n   </strong>\n   and\n   <strong>\n    MP2\n   </strong>\n   .\n  </em>\n </p>\n</div>\n",
    "Examiners report": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Still several answers that thought that the nucleus needed to gain energy to bind it together. Most candidates scored at least one for recognising some form of mass/energy equivalence, although few candidates managed to consistently express their ideas here.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Still several answers that thought that the nucleus needed to gain energy to bind it together. Most candidates scored at least one for recognising some form of mass/energy equivalence, although few candidates managed to consistently express their ideas here.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.i)\n </div><div class=\"card-body\">\n <p>\n  Generally, well answered. There were quite a few who fell into the trap of multiplying by an unnecessary c\n  <sup>\n   2\n  </sup>\n  as they were not sure of the significance of the unit of u.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.ii)\n </div><div class=\"card-body\">\n <p>\n  Those who answered using the mass often did not get MP3 whereas those who converted to the number of particles or moles before the first calculation did, although that could be considered an unnecessary complication.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.iii)\n </div><div class=\"card-body\">\n <p>\n  Many identified conservation of momentum and consequently the relative velocities but it was common to miss MP3 for correctly relating this to KE.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  Several answers referred incorrectly to electron energy levels. Successful candidates managed to score full marks, although it was also common to miss the relationship between energy and wavelength.\n </p>\n</div>\n",
    "topics": [
      "a--space-time-and-motion",
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "a-2-forces-and-momentum",
      "e-3-radioactive-decay"
    ]
  },
  {
    "question_id": "22N.2.HL.TZ0.7",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The intensity of light at point O is\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <msub>\n     <mi>\n      I\n     </mi>\n     <mn>\n      0\n     </mn>\n    </msub>\n   </math>\n   . The distance OP is\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     x\n    </mi>\n   </math>\n   .\n  </p>\n  <p>\n   Sketch, on the axes, a graph to show the variation of the intensity of light with distance from point O on the screen. Your graph should cover the distance range from 0 to 2\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     x\n    </mi>\n   </math>\n   .\n  </p>\n  <p>\n   <img 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\"/>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a.i)\n </div><div class=\"card-body\">\n <p>\n  smooth curve decreasing from\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     I\n    </mi>\n    <mn>\n     0\n    </mn>\n   </msub>\n  </math>\n  to 0 between 0 and\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    x\n   </mi>\n  </math>\n  ✓\n </p>\n <p>\n  secondary maximum correctly placed\n  <em>\n   <strong>\n    AND\n   </strong>\n  </em>\n  of intensity less than 0.3\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     I\n    </mi>\n    <mn>\n     0\n    </mn>\n   </msub>\n  </math>\n  ✓\n </p>\n <p>\n  <em>\n   E.g.\n  </em>\n  <img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVUAAADyCAYAAAD9YlbMAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAACKVSURBVHhe7d0JlBTV1Qfwy5dEdsEB2ZcBEQYcNS4sKiiMDEuGTTbZE4mIKChqWMQgoOYoEREMoBAhkUEiooAEgoJA2ARBGBxgwiaMwyICIvtiNPPxv101p8EemO5+1VPV/f+dU6e7qnuqe2q5/erVe/cVyL5IiIjIiP+zHomIyAAGVaJc8CLOm/J7vzGoRsD+/ftlypQp8t///tdaYgYOHtPrhP/973/y008/WXNm/fjjj9Yzc7AdnPi+hw8f1m1h2g8//GA9M8uJ9WLbOvV9nTgWcBwcOXLEmssfrFN1WEZGhuzZs0c2btwo8fHxkpycLKVKlbJeDY8dTH75y19aS8ywA8n//Z/531x831/84hfWnBnYDvjOptd79OhRiYuLM74d8EP4q1/9ypozx2vrdeJYwDqPHz8e0jlWsGBB61l4GFQdlpmZqcH0rbfekr59+0pWVpZUrVrVejU82HX4tTd9wCNAYd2mD3jA9zX9I+BUUP3222/l+uuvNx5UUfK75pprrDlznFgvti2CqhPf14ljAUH1u+++kzJlylhLIo+X/w5DQLUVKFDAWEAlIndiUCUiMohBlYjIIAZVIiKDGFSJiAxiUCUiMohBlYjIIAZVIiKDGFSJiAxiUCUiMohBlYjIIAZVIiKDGFSJiAxilqoImThxovTp08eaMwO7jqn/nE39hxRySIRjElP/+TiVpSrU1H+mMnExqEYIUv89+uij1pwZ2HVM/cfUfzam/mPqPyKiqMOgSkRkEIMqEZFBDKpERAYxqBIRGcSgSkRkEIMqEZFBDKpERAYxqBIRGcSgSkRkEIMqEZFBDKpERAYxqBIRGcQsVRHitdR/WHesZ6k6cuSIppAznaXKSyn6sG2dyIQGTmWp+v7776V06dLWkrxj6j+PYeo/Hy8FVab+821bpv4LDi//iYgMYlAlIjKIQZWIyCAGVSIigxhUiYgMYlAlIjKIQZWIyCAG1SCkp6fLF198Yc0REf0cg2oQhg4dKrNnz7bmiIh+jkE1j9BbZcuWLVKvXj1rCRHRzzGo5tGBAwe0+1ujRo2sJUREP8egmkfbtm2Tm2++OV/7FBOR+zGo5tGuXbvkrrvusuZ8iSamT58uqampmhjiSpDk4fDhw5KVlSUnT560lhJRNGKWqjxChql7771XunXrpvMrVqzQQHvhwgUpUKCAPPbYY7o8kIyMDOncubNUqFBBChcuLImJiXLjjTdK3bp1pXjx4ta7gudUdiasE0xnZwKs2/R6sR0wmV7v6dOnpWjRorp/TcKPrBMZwJxYr1PHGDhxLGCdZ8+elWLFillL8q5KlSrWs/AwqOZRkyZNZNq0aVKtWjWd79evnwwfPlxKliwp3bt3lzlz5uR68mETjx07Vrp27SoHDx6UnTt3yvbt2+Xrr7+WGjVqSMeOHaV27drWu/MO62XqP+dOfKb+821bpv4LjvmiSBTCQXX8+PFLfsmQwLhQoUJa8jx16pS1NDAEW5R4UFK98847tbT7wgsvaOLq+Ph4GTFihOZbPX/+vPUXRORVDKp5gF/UYcOGXVISiouLk3PnzumlBoJrKHCJ0rNnT3nqqadk6dKlMnLkSP2VJSLvYlDNA5RGO3XqZM35oGkV2q2uW7dOWwWEU++GG2B/+tOfdBiIQYMGyaFDh6xXiMhrGFRD9OCDD8ry5ctl/vz5GgjDVbNmTRk9erTW4U2YMOGqLQqIyJ0YVEOEinsEwfHjx2tVgAm46TVq1Ci59tpr5Y9//CNLrEQexKDqMqifffLJJ/WOM+pxcQeaiLyDQdWFChYsKIMHD5YiRYrISy+9pC0PiMgbGFRdClUBzz33nDbXeuONN7T9HRG5H4Oqi5UvX17rWJHMZe7cudZSInIzBlWXq1q1qrZfRY8t9MQiIndjUPUAlFiTk5O1BxZyDRCRezGoekRKSoo2sZo5c6b2xyYid2JQ9QgkiOjVq5f885//1LGyiMidmKUqQiZNmiSPPPKINRcaZGKaOnWqdo199dVX5brrrtNWAaYz/eBzwHR2JvBSejrkwC1durTx7YAEPaYzi4HX1uvEsYB1ors39luwTJ1HDKoRgixUyMkaLhzgSDmIfKy9e/dm6r+LnAqqTP3H1H+h4OW/xyCAosS7cuVKOXHihLWUiNyCQdWDqlevLgkJCTJr1ixrCRG5BYOqRzVr1kw++eQTHfeKiNyDQdWjfv3rX0uDBg00S9bVRh4goshhUPUo3JTBOFnHjh2TGTNmsO0qkUswqHoYhmNBsuwlS5ZIZmamtZSI8hODqsclJSVJ5cqVWVolcgkGVY9D+8H+/fvL1q1bdSKi/MWgGgXQEaBt27bahZWI8heDapRo1aqV7NixQ29cEVH+YVCNEhgsEM2s0CGAdatE+YdBNYrcc8898u9//5uDBRLlIyZUiZA333wz7CxVl8Ou889ShQQVQ4cO1exVeAw1wYiTWaq8lFCFWap8nFqvUwlVUAWGRDjBMnX8sKQaQQUKFDA++a8XB37fvn0lLS1N1q5de8n7gp3818vJG5MT+8wW6LVom0xhUI0Q7DSUeJyeatWqJXXr1pWPPvpIPzfQezjlbXJqn0XqWIjVKdTtawqDapTBAdWpUyfZs2eP7N6921pKRJHCoBqFatSooQMFIosVEUUWg2oUQmm1R48esmHDBmawIoowBtUoVaJECa1f/de//mUtIaJIYFCNYsi3+vHHH8uZM2esJUTkNAbVKHbnnXfKyZMntUMAEUUGg2oUQxVA+/bttesqhu0lIucxqEa5du3aaa+VOXPmWEuIyEkMqlGuaNGi0qJFC1m6dKkcP37cWkpETmFQjQEIqugfj2FXiMhZDKoxAGkBGzVqpM2rfvjhB2spETmBQTVGdOzYUbMCffHFF9YSInICU/9FiFOp/xAo85qWbe7cubJ9+3Z59tlnrSWBIY0e1m06lR4w9Z+3UvQFe4wFg6n/yJXQJTWv7r//fk2ykpfOAMGsNxhOrZec4cX9ld/fmSXVCHnrrbfk0UcftebMCKUUMXLkSKlfv760bNnSWvJzLKn6YAQFlHhMl1RRr41RcE1zYr3YtigBO/F9nSqpfvfdd1KmTBlrSeQFdbTg7vHq1autucDOnz/vSA+ezz77LGe00BMnTsiqVav0OQWncePG8v7772tPKyIyL6igesMNN0jVqlWtucA+//xzLQ2ZVqVKFUlISNDnU6dOlfHjx+tzCg5KqSh5MNEKkTOCCqqnT5/OqY9bsGCBppZ75plnZPjw4bJ//35djhLloUOH5IMPPtB5PH/++edlwIABugyXaTB//nzZtWuXTJgwQcdTOnDggC6H9PR0efrpp2X06NFy5MgRXYbPRekKyZfXr18vmZmZWnL1Dw4XLlyQd955R86dO2ctocsVLlxY61aRa5Xbici8oILqwoULZdmyZfr8xRdf1LvZqBRGgEV3SNSRYGwkO6iiPqZnz56yc+dOrZMZMmSIBlAsR2k2JSVFAyTGVOrQoYP+/ddffy1NmjTRaoR58+ZJ69atdfmKFSt0nXv37tVmQVlZWRrUu3XrpnUosHHjRhk7dqwj9T/RBJ0BUIWCH0AiMiusGviBAwfKmDFjdDykzZs3y9GjR7XkivHn33vvPfnyyy+lQoUK+vy1116TdevWyd/+9jd9HyAQT58+XScERHSj3LRpk44G+vrrr2sQRx2gf4N1lLL69esn9957r4waNUpuvPHGnPGYUN/bpUsXR26wRJPy5cvL7bffrmkB7SsHIjIjrKCKYTsAJynuumHyt2bNGg10CIyYMHYSoDQKqN+DkiVLamkUJzjehxM+MTFRnnjiCU20nNvdV5SSEdgRgPH3y5cvl4ceesh6la4EPz4o9eMqgojMCSuoXq2pSZEiRaR79+7aGsCeUEeKPJ8Q6O+RAGTy5MmycuVKTbKM+lrUu+YGPYUwZMi0adO0hFquXDnrFboS3HREaR/VKkRkTlhBNTe4u4x606SkJK1vxQ0mzGdkZGjVANr/5ebtt9+W5s2baxUA2nXedtttegPKH0qo9mcULFhQAyt6CdWrV896B10NtmGzZs20ioZVAETmGA+qqArAjSQE1LJly8rdd98t1apV02CK8ehRJ3qlhrm4LMWlPC77Ub2AqoLf//731qs+aFqFu9cvv/yyzmOQO3RNa9iwoc5T3mAb44eJVQBE5gTVowp35FHCQekQl9xonoMeEVgF7iYjGxJeR3Mn3HS6+eabdf6rr77S0mrFihX18hzL8PeFChXS3kD+f48qAZRC0Ucdl/MIrLibj9IqSlT4TLwf3S3x2fHx8Vqt8Nvf/lb/BlUObuSWHlWXw01EXEGgNYZdHYPtjHWzRxV7VGHbskdVcII6WhAEEVChePHiORsEQRI3m3Dw4TlKprhsx+s40GvWrKn1qCjF4nXA39vBwP/vAcsRkOvUqZOzM/G5CKiA9+OuPz7n8ccf12ZXL7zwgmsDqpshJSDaBW/dutVaQkThMH75H2lowoW7/iipUvDwQ4cfKHSkQKmEiMLDhCoRMmnSJOnTp481ZwZ2HS53wr2EQguAiRMnyrhx47RdsZOX//i+pteL7+rE5T9aqpQqVcr45T8up8OpssmNE+vFtg23iik3Tl3+Y5BLpGwMlqn/kUE1QlCn2rdvX2vODFMHPOrK0TuuadOm0qtXL9apWpyqU/VaUPVanWqo+VTtqslwef7y30uw09w4oa66c+fO2sMKvd0CvYeTucmpY8Gp9XptCnU7mMKgSgptg0uUKCGzZ8+2lhBRKBhUSeHyDm2I0bX47Nmz1lIiChaDKuVAhw20B0Z7XyIKDYMq5cCd7rZt2zoycgNRrGBQpUu0adNGOwOgRQARBY9BlS6Bm1Xo+ssE1kShYVCln7njjjt0mBq0+SOi4MRsUEUSEYyBNWXKlFzHwUfSFgxkaE92cm0bEnAjSUq09Z9ARjEksOYNK6LgxWRQxRDNgwYN0hIZkmJjkMFAMGAhRhXApTAmZN/yh+ZH+HuTDYfdoFKlSprQBhms0FOJiPIu5oIqSpUYtBBZrdAtEyMTIO0gUhEGgkTOTz31lE733XeftdQHmZ3QtjPa4EcC22XLli06KCMR5V3MBVU0bMdor1WqVLGW+G7O7Nu3z5q7FIbexqCFl2dxwnOUXHGpHI0w3AqyV6HrarRVbxA5KeaCKhq34waMf+IJ5IlFZptApk6dqr2NkMXJHrUVkAwCibeROs+GxBOXD/3iVUgi0rJlSy2p4keIiPIm5rJUIXiiFIbRCDAOFvTv31+HZMFAg/4WLVqkIxUg4TYGIsRNKdzgggMHDuQMaggIqIMHD9YMORj+BYPq+Rs7dqxmgDIJu86J7Ex2PSr+J1R7NGnSJGck3HA5lfoPk+lsUhi9wh6NwiQnsjOBUxnAsM+c+L5OHAs4dlGVh6vPYIWSLjCQmAuqGHICIwYgsTVGJAAEx1deeUUqV66s8zZsGvsmFO6E33rrrXqiIatTamqqrFu3TkuwgFIsRh7AOFk9e/aUWbNmXXLAIJ8q0uuZhO+HE8l0ujccmFg3vj/GAps+fbr+nxidIVxOnfhO/LgcPnxYTzSm/vNW6r9Q86ma+i4xd/mPgyMlJUVmzpypB8y5c+d0TBuMnwU7duzQ0ubp06flL3/5S06pbcOGDXpjyx7SZcmSJXqH3LZp0yZN8IzXsWMRvP3hxMRO89qE/xmlNfx/gV6P5glBOtDycCevrddrU6jnmikxF1RhxIgRMn/+fL0cb9WqlXbNtEsjAwYMkKVLl+qYWLjUR1DBOFgTJkzQ0iYgGO/atSunpAv4ezsA24/RANuhRYsWOkIuEV1dzGb+R73L5s2bte4lMTExJ6ii5IpLKPxyITii7hWN/nHp759NHB0GcIPLvuREyRc3rVCXiqQkqA7wvxx162iqgeD/xrrt74/LKbTlxY+KXVIPlZcu/zmaqjcv/z01mmo0wWiuGEn0lltuueSkQdCwdzSWo1kRSquXD8+ARv/+JzFGdEUHAfTSevjhh42f4PkJN/Rq1aolCxcutJYQUW5iNqiahiD93HPPybBhw6Rdu3bW0uiBFgAffPBBrp0kiMiHQZXypE6dOvq4bNkyfSSiwBhUKU+KFSsm9evXl8WLF2sdGxEFxqBKeYL2umglgU4PaF5FRIExqFKeVa9eXVs3IHsVS6tEgTGoUp6htNq1a1fJyspirlWiXDCoUlCQCwF5aNevX28tISJ/DKoUFLtuFfWq0dRzjMgUBtUIQu8U01N+rBfNq9BJAvkQAr1+pelK63Xb5NR39dJ6bYFeC3dy23pNidluqpGGLE9ezFKVG/SuQmrEcePGBdXV0EvdVI8cOSKlSpUy3k3ViWxS4FQ3VSeOMXCqm2qoWapM/Y8MqhHi5b7/gRw8eFATzaAHWd26da2lV+eloMq+/75ty77/weHlP4UEN6xq164tCxYs0BOPiHwYVCkkKL3hhlV6eroO5U1EPgyqFLJ69epplq+///3veilHRAyqFAaUVjF0zLZt25jEmsjCoEphwSCKGKb7ww8/ZLtVoosYVCks6AyA/LGoV92/f7+1lCh2MahS2DAAIpKtbNy40VpCFLsYVClsaB/au3dvHfabN6wo1jGokhHouopE1qtWrbKWEMUmBlUyAnWr6Fk1b9487dVCFKsYVMmYBg0a6HDe69ats5YQxR4GVTIGXVeTk5NlxowZcubMGWspUWxhUI0g9JE3PblpvYDOAKdPn5a5c+cGfA8nd+2zq022QK+5dQr1+5rCLFURMmnSJOnTp481ZwZ2XX5lqbqSmTNn6qir+J+LFCliLfXxUpYqpv5z7hgDJ44Fpv6LIdGW+u9KcFAjLeBjjz0mDRs2tJb6eCmoMvWfb9sy9V9wePlPxl133XXSsmVLWb16tbWEKHYwqJIj2rdvL3v37tWJKJYwqJIjihYtKo0aNZK//vWvTLRCMYVBlRyDoJqRkcGcABRTGFTJMVWqVJHExESmBaSYwqBKjkHX1b59+8q+ffu0+yobmlAsYFAlR1WuXFm6dOki//jHP5hvlWICgyo5rlmzZhIXF6eBlSjaMaiS4woWLCjdu3eXtWvXysGDB62lRNGJQZUi4u6775YaNWrIypUrrSVE0YlBlSIC3REHDBggK1askGPHjllLiaIPgypFDJpY3XLLLdohgC0BKFoxqFJEJSUlad1qWlqatYQoujBLVYRMnDjRkdR/yMpjOtOP3VDfdHYmQMaj0aNHaxXAyy+/rDexwoXt4ESWKq+l/nNivdi2Xkv9d/z4cd1vwTKViYtBNUJiKfXfleD7HjhwQJ5++mlNaN2uXTvrldDhuzoRVJn6z7dtmfovOLz8p4irWrWq9OvXT9utZmZmWkuJogODKuWL+++/XxNYv//++9YSoujAoEr5AnkBevXqJdu2bdMRWImiBYMq5ZsSJUrIPffco/XNqF8jigYMqpSvOnXqpHfZJ0+erDcZiLyOQZXyFcazeuaZZ+TTTz+VhQsXWkuJvItBlfJd7dq1pWPHjpKamipfffWVtZTImxhUyRUQVOPj42X8+PHa3pLIqxhUyRXQs2rgwIFav7p8+XJrKZH3MKiSa1SsWFGeffZZHdOKzazIqxhUyVWQxQodA0aNGiVHjx61lhJ5B4MquU6rVq20H/9rr70m58+ft5YSeQODagQhOQWnq09FihSRQYMGyd69e7VjANqvBnofJ06BplDPNVOYpSpCJk2apMM1m4Rd58UsVXnNTLRr1y559dVXdeBAtA7IDb6rE1mqDh8+LKVLl475LFVOHGPgVJYqpJVEdrFgmTp+GFQjhKn/fII9kQ4dOiRDhgyR3/3ud9K4cWPNGXA5fFem/mPqP2DqP6KrKFeunHTr1k2TfH/++efWUiL3YlAl10tOTtbRWHHjav369Vp6InIrBlVyPVx+9+/fX/Ovoo513bp11itE7sOgSp6AOr3HH39cc7Dipt+8efNYYiVXYlAlz8BNjdatW+uAgfPnz5cpU6YwTwC5Du/+Rwjv/vuYuuO7ZcsWeemll6R69eqaMwBNn6L17j/2B/7mzJkzOiE/wvfffy+nTp2Ss2fP6nT69Gl9Da0jsI2x/7CdcWzgs5BbAe1/CxcuLEWLFpVrr71W4uLipGTJkjqP1/B+/K/+LSywHt79Dw6DaoQwqPqYPJF2796tN6/OnTsngwcPljp16livmBHpoIptjv/lm2++0dwH+/fv1yZlGH0WXXbRuwwBDvsFf49gaAfLYsWK6XFgT4BtbU/4TARhBF+s58KFC7ocn4n3FypUSAMtfpzKly+f84hBGpHzFp9hejuYPBZsDKpRADsQU7Vq1a4Y3BhUfUyfSAgUU6dOlQ0bNuj2xfAspk5+p4MqtgUC5vbt27X3GAIpRpdFyRP7FGPXly1bVqpUqSIVKlTQ74IhaFDCRBDFdsQ+skuWVysBY59i3yLwYMK2Q4kXE8bKx3GMgH7w4EF9jgCM92Gd+Gw0b0OgRYpGTPhuCLahHicMqvQzb7/9tt6JxgG2Zs0aeeWVV+TWW2+1Xr0Ug6qPEycSvu/q1atl9uzZGmCQkAVNsBAIwmEqqKJ0id5ZCJwImgikmMfJjyCJ7FwIApgQtDChdIhgFqizQ26uFlTzyg4JWB96JyHIomrBDsCofsD3RyBGEEOJGQEXQRbf2/4xwLZD9UJu+5tBlS6BE7lDhw4yZ84cPfC//PJLeeedd2Ts2LHWOy7FoOrjxImE74rvjP2AH7d3331XT/o2bdpI+/bt9bI2FKEEVXwXlPAQONPT02Xjxo06mgH+b1xS33TTTXpVg6oK/Bhj3wUTOK/EVFD1h/8nUJ0qlgP+L2wn/I/40cD/jSBsV1dgXyPAVqpUKaeEa/9ooMoBk0kMqh6GSyf05Z85c6bO45ccXSlRWgqEQdXHyaBqf1/UF6LkiuCK5w0aNJAmTZpIrVq1gtpWeQmq+FwcCzt27JC0tDTNV4C6UNSNosSGVIYYLqZmzZpaIkVwciL4QSSD6pXY2wRVCZj27dunE0rpKPnaxywCK4ItSrn2hGoObDd8HvZnsD84wQZVlLzxPUxiUA0RbiAgkxLGVQIc0CgVLViwQOcvx6DqE4mgasOJvXjxYlm2bJmWoHDC1q9fXxISEqRGjRp6aXql/9E/qNrbGuvEunCTDIE0KytLS8X4fAQIBM8bbrhBHytXrhwwGEV7UM0NAh62H4Iegu2ePXv0EdsZVQoomGA74rOKFy+u+wfb365GwITqEgRB1CvbN8+wD+0fvmCD6ieffKKfhx9dUxhUQ4SD4Q9/+IOWhgAHdNu2bWXRokU6f7kRI0YY3XGAXYeDyHSQwoENwVz25hW+r+lgje0QKKja8DoC39atWzUYorSEZXZpCScqmhph3l4HAuiJEyd0G+ByHvWH2Mf4/ig94UYRSlY44XECI6DmtZrBiR8WQPAz/QPr1DEG/scCPgele2xz7B8EX0yYxyP2AbY//kf7+AR8L0xoBYHgiOd4HfvC3p924MWEfYfJPwijmgY3AydMmKDLwsWgGiLs6N69e+dc7mPnP/TQQ1rHGghOJHIXnFCo+0MdIE5au5kR4OS023TichSBEyetqfpPCh9Clz2hxQSCMupxMeE59ieCMPYzHrFv8V4EXf+CA0qrd9xxh57PJjCohgg7JSUlRceqx45Zu3atzJo1S8aNG2e9g4jcDtV1uFpBUzxTGFTDMGzYMH1Ens/hw4dr98mkpCRdRkTud/LkyZBbh+SGQTUMuGREjx7c2fzNb34jDzzwAC8PiWIcg2oEoKrAvoPKoEsU3czf3qVLoEE0qgfuuusubYyO5h5EZAaatQ0dOlTGjBmjLTzcgEHVYa+//rrWvaI7a9OmTbVrKxGFD724kF/3tttuk23btmnhxQ2FFgZVh6GhePPmzfXSHz2wNm/ebL1CROFAaxu0/37wwQe1sIJuwNOnT7dezT8Mqg6y28PZ9ahooIy7jeR+6FKJLow2XFqiPSu5B4bYwfhlgIb96MWGnlmALsMIuvYtoyVLlkRs4EgGVQdhh+IGlQ3BFQ2Syf1WrVolHTt21P2Hy0x0QUZrD3IPu9cU7Ny5U1auXJnTFRx5HpDEHANFYl+iPXm9evX0NacxqDrs8rv9drc8creuXbtq99U333xTXnzxRXnvvfe0JETugysKBNNp06Zpd1NAXgA0d0SSI7QfHzlyZMRa3jCoOsjuX2xDqQdVAOR+6KaKkxKdOrp06aJ9+8l9UL2GH7033nhDR9v1h5Isri5Q54pkLJHCoOog/DKi7ziaVcFnn32muTTJ/ZC8Y/z48Zrw2q6nI3dBn36UQtHFNDEx0Vrqk5GRIX/+85+1Xz9+HP3rx53Gxv8Ow91+jFWP/sXIdIRfVQZWd8OggmgKh+Y6GEEAl5AoCeHuMrkHksJjtI3bb7/dWiL6I4gSK1oDoGUACjVIcoQ8t0OGDLHe5SwG1QjAJsZ0eXUAuQ9uJCL3bffu3XOCKLL34wcRJyy5h926xp9db4pH+3zDuYf3Rep+BoMqEZFBLDoRERnEoEpEZBCDKhGRQQyqREQGMagSERnEoEpEZBCDKhGRQQyqREQGMagSERnEoEpEZBCDKhGRQQyqREQGMahS1NqwYYOMGjVKn6empuqQGlfyn//8Rw4dOmTNEYWGQZWiFpJLb9q0SZ8nJCRIfHy8Ps8NxqRiUKVwMahSVDl37py8++67MmHCBDlx4oS1VOT666/XROGAYDtlyhRNPL1v3z5dlp6erkNv4BF+/PHHnKzxM2bMyBnA8dixY1oCRvJxvIaB5ezsmcjZiVE7x4wZIx9++KGuA/A6BqUbN26cbN26Nef9FJ0YVClqIEDWrVtX1qxZowESw2nYMCjcRx99pCOjYlTN/fv3y5kzZ+SBBx6Qs2fPyrJly3T4cDxiOTL+I7M8kh2j2qBNmza6HgTRpk2bytSpU/Xv2rVrp0EXf9O4cWMN1vgbZJsfOHCgLsffIshjiJYnn3xSM9BfnlyZogiSVBNFg+effz67R48e1lx29sSJE7MvBjR9Pnz48OxJkyZlL1++PLtEiRLZF4Ne9sUgmp2ZmZl9sUSp70lISMhOS0vT+YslVn28WELNXr16dXbp0qX1PYsWLcouU6ZM9oULF3R+0KBB2Q8//HD2p59+mt2wYcPsn376SZfjcd68edmpqanZycnJ2adOndLp8OHD+ve7d+/W91H0YUmVosaePXu07tRmD1fsD4PEoe4UI6RWrFhRqwAwgJw/DLuBEm1KSooOS92iRQvrFR9UI1xzzTX6vFChQlrqvBgs5aabbsoZwgOPbdu21bGRUCVQvHhxnS4GVH3vxWCu76Pow6BKUaNYsWJysTRozflGRL0chp6ePHmyBjvUfX788cc6tr8/1Jn27t1bmjdvrlUAS5cutV7JHYKs/2fDwYMHpXDhwtK6dWsNpP5To0aNrHdRtGFQpajRpEkTrcu0hyO+eNmuj/7QtAolz3Llyskjjzwi/fr1k2+++cZ61XdTCS0G6tSpo/WfCH5paWlaGr28ROuvdu3aWiJFXS2gTrdVq1ZaMl61apUcPXpUb5ah3hafi0eKTgyqFDU6dOigo6A2a9ZMkpKS5Ntvv81pRlW2bFkpVaqUlhrLly+vwxjjPYsXL5YBAwboe1AyxXPciMKleoMGDXRdqFZA0Dxw4IAur1Wrlr4fsN5KlSpptcPIkSOlc+fOGtwx8uoTTzyhQRU3zFDyve+++6RHjx6SnJwscXFx1hoo2nA0VSIig1hSJSIyiEGViMggBlUiIoMYVImIDGJQJSIyiEGViMgYkf8HvWO3s1fsWOkAAAAASUVORK5CYII=\"/>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a.i)\n </div><div class=\"card-body\">\n <p>\n  smooth curve decreasing from\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     I\n    </mi>\n    <mn>\n     0\n    </mn>\n   </msub>\n  </math>\n  to 0 between 0 and\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    x\n   </mi>\n  </math>\n  ✓\n </p>\n <p>\n  secondary maximum correctly placed\n  <em>\n   <strong>\n    AND\n   </strong>\n  </em>\n  of intensity less than 0.3\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     I\n    </mi>\n    <mn>\n     0\n    </mn>\n   </msub>\n  </math>\n  ✓\n </p>\n <p>\n  <em>\n   E.g.\n  </em>\n  <img src=\"data:image/png;base64,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\"/>\n </p>\n</div>\n",
    "Examiners report": "<br><div class=\"qn_code_number\">\n  (a.i)\n </div><div class=\"card-body\">\n <p>\n  Most scored MP1. Many candidates scored full marks but it was common to see a maximum at 2x or a secondary maxima too high.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a.i)\n </div><div class=\"card-body\">\n <p>\n  Most scored MP1. Many candidates scored full marks but it was common to see a maximum at 2x or a secondary maxima too high.\n </p>\n</div>\n",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-3-wave-phenomena"
    ]
  },
  {
    "question_id": "22N.2.HL.TZ0.8",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The diagram shows field lines for an electrostatic field. X and Y are two points on the same field line.\n  </p>\n  <p>\n   <img src=\"data:image/png;base64,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\" style=\"display:block;margin-left:auto;margin-right:auto;\"/>\n  </p>\n  <p>\n   Outline which of the two points has the larger electric potential.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the kinetic energy of the satellite in orbit is about 2 × 10\n   <sup>\n    10\n   </sup>\n   J.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the minimum energy required to launch the satellite. Ignore the original kinetic energy of the satellite due to Earth’s rotation.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  potential greater at Y ✓\n </p>\n <p>\n </p>\n <p>\n  «from\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    E\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mo>\n    -\n   </mo>\n   <mfrac>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <msub>\n      <mi>\n       V\n      </mi>\n      <mi>\n       e\n      </mi>\n     </msub>\n    </mrow>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mi>\n      r\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  » the potential increases in the direction opposite to field strength «so from X to Y»\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  opposite to the direction of the field lines, «so from X to Y»\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  «from\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    W\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mi>\n    q\n   </mi>\n   <mo>\n    ∆\n   </mo>\n   <msub>\n    <mi>\n     V\n    </mi>\n    <mi>\n     e\n    </mi>\n   </msub>\n  </math>\n  » work done to move a positive charge from X to Y is positive «so the potential increases from X to Y» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  potential greater at Y ✓\n </p>\n <p>\n </p>\n <p>\n  «from\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    E\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mo>\n    -\n   </mo>\n   <mfrac>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <msub>\n      <mi>\n       V\n      </mi>\n      <mi>\n       e\n      </mi>\n     </msub>\n    </mrow>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mi>\n      r\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  » the potential increases in the direction opposite to field strength «so from X to Y»\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  opposite to the direction of the field lines, «so from X to Y»\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  «from\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    W\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mi>\n    q\n   </mi>\n   <mo>\n    ∆\n   </mo>\n   <msub>\n    <mi>\n     V\n    </mi>\n    <mi>\n     e\n    </mi>\n   </msub>\n  </math>\n  » work done to move a positive charge from X to Y is positive «so the potential increases from X to Y» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.i)\n </div><div class=\"card-body\">\n <p>\n  orbital radius\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    6\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    4\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     6\n    </mn>\n   </msup>\n   <mo>\n    +\n   </mo>\n   <mn>\n    5\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     5\n    </mn>\n   </msup>\n  </math>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    6\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    9\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     6\n    </mn>\n   </msup>\n  </math>\n  m» ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    KE\n   </mtext>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    8\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     2\n    </mn>\n   </msup>\n   <mo>\n    ×\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      6\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      67\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        11\n       </mn>\n      </mrow>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      6\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       24\n      </mn>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      6\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      9\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       6\n      </mn>\n     </msup>\n    </mrow>\n   </mfrac>\n  </math>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    2\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    3\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     10\n    </mn>\n   </msup>\n  </math>\n  «J» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    [1] max\n   </strong>\n   for answers ignoring orbital height (KE = 2.5 × 10\n  </em>\n  <sup>\n   <em>\n    10\n   </em>\n  </sup>\n  J\n  <em>\n   ).\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.ii)\n </div><div class=\"card-body\">\n <p>\n  change in PE\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    6\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    67\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      11\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    6\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     24\n    </mn>\n   </msup>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    8\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     2\n    </mn>\n   </msup>\n   <mfenced>\n    <mrow>\n     <mfrac>\n      <mn>\n       1\n      </mn>\n      <mrow>\n       <mn>\n        6\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        4\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mn>\n         6\n        </mn>\n       </msup>\n      </mrow>\n     </mfrac>\n     <mo>\n      -\n     </mo>\n     <mfrac>\n      <mn>\n       1\n      </mn>\n      <mrow>\n       <mn>\n        6\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        9\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mn>\n         6\n        </mn>\n       </msup>\n      </mrow>\n     </mfrac>\n    </mrow>\n   </mfenced>\n   <mo>\n    =\n   </mo>\n  </math>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    3\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    6\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     9\n    </mn>\n   </msup>\n  </math>\n  J» ✓\n </p>\n <p>\n  energy needed = KE + ΔPE =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    2\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    7\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     10\n    </mn>\n   </msup>\n  </math>\n  «J» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from 8(b)(i).\n  </em>\n </p>\n</div>\n",
    "Examiners report": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  A significant majority guessed at X, probably because the field lines are closer together. Those that identified Y were generally successful in their explanation.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  A significant majority guessed at X, probably because the field lines are closer together. Those that identified Y were generally successful in their explanation.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.i)\n </div><div class=\"card-body\">\n <p>\n  This question was well done, with only a few missing the height of the satellite.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.ii)\n </div><div class=\"card-body\">\n <p>\n  Generally, this question was not well done. Most carried out a calculation based on the formula for escape velocity. An opportunity to remind candidates of reading back the stem for the sub-question when answering a second or any subsequent part of it.\n </p>\n</div>\n",
    "topics": [
      "d-fields"
    ],
    "subtopics": [
      "d-1-gravitational-fields",
      "d-2-electric-and-magnetic-fields"
    ]
  },
  {
    "question_id": "22N.2.SL.TZ0.1",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the initial acceleration of the raindrop.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Explain, by reference to the vertical forces, how the raindrop reaches a constant speed.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the energy transferred to the air during the first 3.0 s of motion. State your answer to an appropriate number of significant figures.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c.ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Describe the energy change that takes place for\n   <em>\n    t\n   </em>\n   &gt; 3.0 s.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   g\n  </em>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  9.81 «m s\n  <sup>\n   −2\n  </sup>\n  »\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  acceleration of gravity/due to free fall ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept 10 «\n  </em>\n  m s\n  <sup>\n   −2\n  </sup>\n  <em>\n   ».\n  </em>\n </p>\n <p>\n  <em>\n   Ignore sign.\n  </em>\n </p>\n <p>\n  <em>\n   Do\n   <strong>\n    not\n   </strong>\n   accept bald “gravity”.\n  </em>\n </p>\n <p>\n  <em>\n   Accept answer that indicates tangent of the graph at time t=0.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   g\n  </em>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  9.81 «m s\n  <sup>\n   −2\n  </sup>\n  »\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  acceleration of gravity/due to free fall ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept 10 «\n  </em>\n  m s\n  <sup>\n   −2\n  </sup>\n  <em>\n   ».\n  </em>\n </p>\n <p>\n  <em>\n   Ignore sign.\n  </em>\n </p>\n <p>\n  <em>\n   Do\n   <strong>\n    not\n   </strong>\n   accept bald “gravity”.\n  </em>\n </p>\n <p>\n  <em>\n   Accept answer that indicates tangent of the graph at time t=0.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  Identification of air resistance/drag force «acting upwards» ✓\n </p>\n <p>\n  «that» increases with speed ✓\n </p>\n <p>\n  <br/>\n  «until» weight and air resistance cancel out\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  net force/acceleration becomes zero ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   A statement as “air resistance increases with speed” scores\n   <strong>\n    MP1\n   </strong>\n   and\n   <strong>\n    MP2\n   </strong>\n   .\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c.i)\n </div><div class=\"card-body\">\n <p>\n  «loss in» GPE = 3.4 × 10\n  <sup>\n   −5\n  </sup>\n  × 9.81 × 21 «= 7.0 × 10\n  <sup>\n   −3\n  </sup>\n  » «J»\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  «gain in» KE = 0.5 × 3.4 × 10\n  <sup>\n   −5\n  </sup>\n  × 9.0\n  <sup>\n   2\n  </sup>\n  «= 1.4 × 10\n  <sup>\n   −3\n  </sup>\n  » «J» ✓\n </p>\n <p>\n  <br/>\n  energy transferred to air «=7.0 × 10\n  <sup>\n   −3\n  </sup>\n  − 1.4 × 10\n  <sup>\n   −3\n  </sup>\n  » = 5.6 × 10\n  <sup>\n   −3\n  </sup>\n  » «J» ✓\n </p>\n <p>\n </p>\n <p>\n  any calculated answer to 2 sf ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    [1]\n   </strong>\n   through the use of kinematics assuming constant acceleration.\n  </em>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    MP1\n   </strong>\n   .\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c.ii)\n </div><div class=\"card-body\">\n <p>\n  «gravitational» potential energy «of the raindrop» into thermal/internal energy «of the air» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept heat for thermal energy.\n  </em>\n </p>\n <p>\n  <em>\n   Accept into kinetic energy of air particles.\n  </em>\n </p>\n <p>\n  <em>\n   Ignore sound energy.\n  </em>\n </p>\n</div>\n",
    "Examiners report": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  A nice introductory question answered correctly by most candidates. Most answers quoted the data booklet value, with a few 10's or 9.8's, or the answer in words. Very few lost the mark by just stating gravity, or zero.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  A nice introductory question answered correctly by most candidates. Most answers quoted the data booklet value, with a few 10's or 9.8's, or the answer in words. Very few lost the mark by just stating gravity, or zero.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  This was very well answered with most candidates scoring 3. The MP usually missed in candidates scoring 2 marks was MP2, to justify the variation of the magnitude of air resistance, although that rarely happened.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c.i)\n </div><div class=\"card-body\">\n <p>\n  Generally well answered, although several candidates lost a mark, usually as POT (power of ten) by quoting the value in kg leading to an answer of 5.3 J. Most candidates were able to score MP3 by rounding their calculation to two significant figures.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c.ii)\n </div><div class=\"card-body\">\n <p>\n  Of the wrong answers, the most common ones were gravitational potential to kinetic or the idea that because there was no change in velocity there was no energy transfer. A significant number, though, scored by identifying the change into thermal (most of them), kinetic of air particles (a few answers) or internal (very few).\n </p>\n</div>\n",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-1-kinematics",
      "a-2-forces-and-momentum",
      "a-3-work-energy-and-power"
    ]
  },
  {
    "question_id": "22N.2.SL.TZ0.2",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the minimum area of the solar heating panel required to increase the temperature of all the water in the tank to 30°C during a time of 1.0 hour.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a.ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Estimate, in °C, the temperature of the roof tiles.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State\n   <strong>\n    one\n   </strong>\n   way in which a real gas differs from an ideal gas.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The water is heated. Explain why the quantity of air in the storage tank decreases.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a.i)\n </div><div class=\"card-body\">\n <p>\n  energy required = 250 × 4200 × (30 − 15) ✓\n </p>\n <p>\n  energy available = 0.30 × 680 ×\n  <em>\n   t\n  </em>\n  ×\n  <em>\n   A\n  </em>\n  ✓\n </p>\n <p>\n  <em>\n   A\n  </em>\n  = «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      250\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      4200\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      15\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      30\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      680\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      60\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      60\n     </mn>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n  </math>\n  » 21 «m\n  <sup>\n   2\n  </sup>\n  »\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  22 «m\n  <sup>\n   2\n  </sup>\n  » ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    MP1\n   </strong>\n   and\n   <strong>\n    MP2\n   </strong>\n   .\n  </em>\n </p>\n <p>\n  <em>\n   Accept the correct use of 0.30 in either\n   <strong>\n    MP1\n   </strong>\n   or\n   <strong>\n    MP2\n   </strong>\n   .\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a.ii)\n </div><div class=\"card-body\">\n <p>\n  absorbed intensity = (1 − 0.2) × 680 «= 544» «W m\n  <sup>\n   −2\n  </sup>\n  »\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  emitted intensity = 0.97 × 5.67 × 10\n  <sup>\n   −8\n  </sup>\n  × T\n  <sup>\n   4\n  </sup>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   T\n  </em>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mroot>\n    <mfrac>\n     <mn>\n      544\n     </mn>\n     <mrow>\n      <mn>\n       0\n      </mn>\n      <mo>\n       .\n      </mo>\n      <mn>\n       97\n      </mn>\n      <mo>\n       ×\n      </mo>\n      <mn>\n       5\n      </mn>\n      <mo>\n       .\n      </mo>\n      <mn>\n       67\n      </mn>\n      <mo>\n       ×\n      </mo>\n      <msup>\n       <mn>\n        10\n       </mn>\n       <mrow>\n        <mo>\n         -\n        </mo>\n        <mn>\n         8\n        </mn>\n       </mrow>\n      </msup>\n     </mrow>\n    </mfrac>\n    <mn>\n     4\n    </mn>\n   </mroot>\n   <mo>\n    =\n   </mo>\n   <mn>\n    315\n   </mn>\n  </math>\n  «K» ✓\n </p>\n <p>\n  42 «°C» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    MP1\n   </strong>\n   and\n   <strong>\n    MP2\n   </strong>\n   .\n  </em>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    MP1\n   </strong>\n   if absorbed or emitted intensity is multiplied by area.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.i)\n </div><div class=\"card-body\">\n <p>\n  can be liquefied ✓\n </p>\n <p>\n  has intermolecular forces / potential energy ✓\n </p>\n <p>\n  has atoms/molecules that are not point objects / take up volume ✓\n </p>\n <p>\n  does not follow the ideal gas law «for all\n  <em>\n   T\n  </em>\n  and\n  <em>\n   p\n  </em>\n  » ✓\n </p>\n <p>\n  collisions between particles are non-elastic ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept the converse argument.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.ii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n </p>\n <p>\n  «constant\n  <em>\n   p\n  </em>\n  and\n  <em>\n   V\n  </em>\n  imply»\n  <em>\n   nT\n  </em>\n  = const ✓\n </p>\n <p>\n  <em>\n   T\n  </em>\n  increases hence\n  <em>\n   n\n  </em>\n  decreases ✓\n </p>\n <p>\n  <br/>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n </p>\n <p>\n  «constant\n  <em>\n   p\n  </em>\n  and\n  <em>\n   n\n  </em>\n  imply»\n  <em>\n   V\n  </em>\n  is proportional to\n  <em>\n   T\n  </em>\n  / air expands as it is heated ✓\n </p>\n <p>\n  «original» air occupies a greater volume\n  <strong>\n   OR\n  </strong>\n  some air leaves through opening ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    MP2\n   </strong>\n   in\n   <strong>\n    ALT 2\n   </strong>\n   must come from expansion of air, not from expansion of water.\n  </em>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    [0]\n   </strong>\n   for an answer based on expansion of water.\n  </em>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    [1]\n   </strong>\n   <strong>\n    max\n   </strong>\n   for an answer based on convection currents.\n  </em>\n </p>\n</div>\n",
    "Examiners report": "<br><div class=\"qn_code_number\">\n  (a.i)\n </div><div class=\"card-body\">\n <p>\n  Most candidates had a good attempt at this but there were often slight slips. Some missed the efficiency of the process. Some included the albedo of the roof tiles. Some thought that the temperature rise needed to have 273 added to convert to kelvin. However, sometimes scoring through ECF (error carried forward), the average mark was around 2 marks.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a.ii)\n </div><div class=\"card-body\">\n <p>\n  This was a bit more hit and miss than the previous question part. One common mistake was not understanding what albedo meant. Some took it as the amount of energy absorbed rather than reflected. Emissivity was often missed. Several candidates, successfully answering the question or not, were able to score MP3 converting the final temperature into Celsius degrees.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.i)\n </div><div class=\"card-body\">\n <p>\n  This was very well answered. Candidates showed an understanding of the differences between ideal and real gases.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.ii)\n </div><div class=\"card-body\">\n <p>\n  It was surprising to see a large number of answers based on the expansion of water, as the stem of the question clearly states that the level of water remains constant. Most successful candidates scored by quoting\n  <em>\n   pV\n  </em>\n  constant so concluding with the inverse relationship of n and\n  <em>\n   T\n  </em>\n  , others also managed to score by explaining that the volume of air increases and therefore must go out through the opening. Answers based on convection currents were given partial credit.\n </p>\n</div>\n",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-1-thermal-energy-transfers",
      "b-2-greenhouse-effect",
      "b-3-gas-laws"
    ]
  },
  {
    "question_id": "22N.2.SL.TZ0.3",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Draw, on the axes, a graph to show the variation with\n   <em>\n    t\n   </em>\n   of the displacement of particle Q.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a.ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the speed of waves on the string.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the fundamental SI unit for\n   <em>\n    a\n   </em>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The tension force on the string is doubled. Describe the effect, if any, of this change on the frequency of the standing wave.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The standing wave on the string creates a travelling sound wave in the surrounding air.\n  </p>\n  <p>\n   Outline\n   <strong>\n    two\n   </strong>\n   differences between a standing wave and a travelling wave.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline\n   <strong>\n    one\n   </strong>\n   difference between a standing wave and a travelling wave.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c.ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The speed of sound in air is 340 m s\n   <sup>\n    −1\n   </sup>\n   and in water it is 1500 m s\n   <sup>\n    −1\n   </sup>\n   .\n  </p>\n  <p>\n   Discuss whether the sound wave can enter the water.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a.i)\n </div><div class=\"card-body\">\n <p>\n  oscillation in antiphase ✓\n </p>\n <p>\n  smaller amplitude than P ✓\n </p>\n <p>\n  <br/>\n  <img src=\"data:image/png;base64,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\"/>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a.i)\n </div><div class=\"card-body\">\n <p>\n  oscillation in antiphase ✓\n </p>\n <p>\n  smaller amplitude than P ✓\n </p>\n <p>\n  <br/>\n  <img src=\"data:image/png;base64,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\"/>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a.ii)\n </div><div class=\"card-body\">\n <p>\n  wavelength\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     2\n    </mn>\n    <mn>\n     3\n    </mn>\n   </mfrac>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    80\n   </mn>\n   <mo>\n    =\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    53\n   </mn>\n  </math>\n  «m» ✓\n </p>\n <p>\n  speed\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      53\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      8\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        3\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    190\n   </mn>\n  </math>\n  «m s\n  <sup>\n   −1\n  </sup>\n  » ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from incorrect wavelength.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.i)\n </div><div class=\"card-body\">\n <p>\n  kg m s\n  <sup>\n   −2\n  </sup>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  m\n  <sup>\n   2\n  </sup>\n  s\n  <sup>\n   −2\n  </sup>\n  seen ✓\n </p>\n <p>\n  kg m\n  <sup>\n   −1\n  </sup>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    [2]\n   </strong>\n   for a\n   <strong>\n    BCA\n   </strong>\n   .\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.ii)\n </div><div class=\"card-body\">\n <p>\n  speed increases hence frequency increases ✓\n </p>\n <p>\n  by factor\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msqrt>\n    <mn>\n     2\n    </mn>\n   </msqrt>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  travelling waves transfer energy\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  standing waves don’t ✓\n </p>\n <p>\n  amplitude of oscillation varies along a standing wave\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  is constant along a travelling wave ✓\n </p>\n <p>\n  standing waves have nodes and antinodes\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  travelling waves don’t ✓\n </p>\n <p>\n  points in an internodal region have same phase in standing waves\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  different phase in travelling waves ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c.i)\n </div><div class=\"card-body\">\n <p>\n  travelling waves transfer energy\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  standing waves don’t ✓\n </p>\n <p>\n  amplitude of oscillation varies along a standing wave\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  is constant along a travelling wave ✓\n </p>\n <p>\n  standing waves have nodes / antinodes\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  travelling waves don’t ✓\n </p>\n <p>\n  points in an internodal region have same phase in standing waves\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  different phase in travelling waves ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c.ii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n </p>\n <p>\n  critical angle\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    13\n   </mn>\n   <mo>\n    °\n   </mo>\n  </math>\n  «from\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    sin\n   </mi>\n   <mo>\n   </mo>\n   <msub>\n    <mi>\n     θ\n    </mi>\n    <mi>\n     c\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     340\n    </mn>\n    <mn>\n     1500\n    </mn>\n   </mfrac>\n  </math>\n  » ✓\n </p>\n <p>\n  the angle of incidence is greater than\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     θ\n    </mi>\n    <mi>\n     c\n    </mi>\n   </msub>\n  </math>\n  hence the sound can’t enter water ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    sin\n   </mi>\n   <mo>\n   </mo>\n   <msub>\n    <mi>\n     θ\n    </mi>\n    <mi>\n     r\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     1500\n    </mn>\n    <mn>\n     340\n    </mn>\n   </mfrac>\n   <mi>\n    sin\n   </mi>\n   <mo>\n   </mo>\n   <mn>\n    30\n   </mn>\n   <mo>\n    °\n   </mo>\n  </math>\n  ✓\n </p>\n <p>\n  sine value greater than one hence the sound can’t enter water ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Conclusion must be justified, award\n   <strong>\n    [0]\n   </strong>\n   for\n   <strong>\n    BCA\n   </strong>\n   .\n  </em>\n </p>\n</div>\n",
    "Examiners report": "<br><div class=\"qn_code_number\">\n  (a.i)\n </div><div class=\"card-body\">\n <p>\n  Although there were good answers which scored full marks, there were a significant number of wrong answers where the amplitude was the same or not consistent throughout, or the wave drawn was not in antiphase of the original sketch.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a.i)\n </div><div class=\"card-body\">\n <p>\n  Although there were good answers which scored full marks, there were a significant number of wrong answers where the amplitude was the same or not consistent throughout, or the wave drawn was not in antiphase of the original sketch.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a.ii)\n </div><div class=\"card-body\">\n <p>\n  This was well answered, particularly MP1 to determine the wavelength, although several candidates misinterpreted the unit of time and obtained a very small value for the velocity of the wave.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.i)\n </div><div class=\"card-body\">\n <p>\n  Students seem to be well prepared for this sort of question, as it was high-scoring.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.ii)\n </div><div class=\"card-body\">\n <p>\n  This question was answered well, although the numerical aspect was often missing. It is worth highlighting that if there is a term like\n  <em>\n   '\n  </em>\n  doubled\n  <em>\n   '\n  </em>\n  in the question, it makes sense to expect a numerical answer.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  This question was answered well. Students showed to be familiar with the differences between standing and travelling waves. In SL they had to identify two differences, so that proved to be more challenging.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c.i)\n </div><div class=\"card-body\">\n <p>\n  This question was answered well. Students showed to be familiar with the differences between standing and travelling waves.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c.ii)\n </div><div class=\"card-body\">\n <p>\n  Surprisingly well answered as it was sound from air to water, rather than light from air to glass. A mixture of approaches but probably the most common was to calculate a sine value of over 1. Some went about calculating the critical angle but nowhere near as many.\n </p>\n</div>\n",
    "topics": [
      "c-wave-behaviour",
      "tools"
    ],
    "subtopics": [
      "c-2-wave-model",
      "c-3-wave-phenomena",
      "c-4-standing-waves-and-resonance",
      "tool-3-mathematics"
    ]
  },
  {
    "question_id": "22N.2.SL.TZ0.4",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The scale diagram shows the weight\n   <em>\n    W\n   </em>\n   of the mass at an instant when the rod is horizontal.\n  </p>\n  <p>\n   Draw, on the scale diagram, an arrow to represent the force exerted on the mass by the rod.\n  </p>\n  <p>\n   <img src=\"data:image/png;base64,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\"/>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Explain why the magnitude of the force exerted on the mass by the rod is not constant.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  horizontal component of any length to the left ✓\n </p>\n <p>\n  vertical component two squares long upwards ✓\n </p>\n <p>\n  E.g.\n </p>\n <p>\n  <img 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\"/>\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Ignore point of application.\n  </em>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    [1]\n   </strong>\n   <strong>\n    max\n   </strong>\n   if arrowhead not present.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  horizontal component of any length to the left ✓\n </p>\n <p>\n  vertical component two squares long upwards ✓\n </p>\n <p>\n  E.g.\n </p>\n <p>\n  <img src=\"data:image/png;base64,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\"/>\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Ignore point of application.\n  </em>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    [1]\n   </strong>\n   <strong>\n    max\n   </strong>\n   if arrowhead not present.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n </p>\n <p>\n  the net/centripetal force has constant magnitude ✓\n </p>\n <p>\n  the direction of the net/centripetal force constantly changes ✓\n </p>\n <p>\n  this is achieved by vector-adding weight and the force from the rod\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  the force from the rod is vector difference of the centripetal force and weight ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n </p>\n <p>\n  at the top F\n  <sub>\n   rod\n  </sub>\n  = F\n  <sub>\n   c\n  </sub>\n  − W ✓\n </p>\n <p>\n  at the bottom, F\n  <sub>\n   rod\n  </sub>\n  = F\n  <sub>\n   c\n  </sub>\n  + W ✓\n </p>\n <p>\n  net F/F\n  <sub>\n   c\n  </sub>\n  is constant so the force from the rod is different «hence is changing» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept reference to centripetal or net force indistinctly.\n  </em>\n </p>\n <p>\n  <em>\n   Allow reference to centripetal acceleration.\n  </em>\n </p>\n</div>\n",
    "Examiners report": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Most just added the horizontal component. Not many centrifugal forces, but still a few. Very few were able to score both marks, so this question proved to be challenging for the candidates.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Most just added the horizontal component. Not many centrifugal forces, but still a few. Very few were able to score both marks, so this question proved to be challenging for the candidates.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  Many got into a bit of a mess with this one and it was quite difficult to interpret some of the answers. If they started out with the net/centripetal force being constant, then it was often easy to follow the reasoning. Starting with force on the rod varying often led to confusion. Quite a few did not pick up on the constant speed vertical circle so there were complicated energy/speed arguments to pick through.\n </p>\n</div>\n",
    "topics": [
      "a--space-time-and-motion",
      "tools"
    ],
    "subtopics": [
      "a-2-forces-and-momentum",
      "tool-3-mathematics"
    ]
  },
  {
    "question_id": "22N.2.SL.TZ0.5",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State what is meant by an ideal voltmeter.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the internal resistance of the cell is about 0.7 Ω.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the internal resistance of the cell is about 0.7 Ω.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the emf of the cell.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Explain, by reference to charge carriers in the wire, how the magnetic force on the wire arises.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c.ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Identify the direction of the magnetic force on the wire.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  infinite resistance\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  no current is flowing through it ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.i)\n </div><div class=\"card-body\">\n <p>\n  current\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      47\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      50\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      0\n     </mn>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    2\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    94\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      2\n     </mn>\n    </mrow>\n   </msup>\n  </math>\n  «A» ✓\n </p>\n <p>\n  <em>\n   r\n  </em>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      49\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      94\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        2\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n   </mfrac>\n   <mo>\n    -\n   </mo>\n   <mn>\n    50\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n  </math>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    68\n   </mn>\n  </math>\n  «Ω» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   For\n   <strong>\n    MP2\n   </strong>\n   , allow any other correctly substituted expression for r.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.ii)\n </div><div class=\"card-body\">\n <p>\n  29.4 (50.0 +\n  <em>\n   r\n  </em>\n  ) = 139 (10.0 +\n  <em>\n   r\n  </em>\n  ) ✓\n </p>\n <p>\n  <br/>\n  attempt to solve for\n  <em>\n   r\n  </em>\n  , e.g. 29.4 × 50.0 − 139 × 10.0 =\n  <em>\n   r\n  </em>\n  (139 − 29.4)\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  0.73 «Ω» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Do\n   <strong>\n    not\n   </strong>\n   allow working backwards from 0.7 Ω.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.iii)\n </div><div class=\"card-body\">\n <p>\n  139 × 10\n  <sup>\n   −3\n  </sup>\n  (10.0 + 0.73)\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  29.4 × 10\n  <sup>\n   −3\n  </sup>\n  (50.0 + 0.73)  ✓\n </p>\n <p>\n  <br/>\n  1.49 «V» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Watch for\n   <strong>\n    ECF\n   </strong>\n   from 5(b)(i).\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c.i)\n </div><div class=\"card-body\">\n <p>\n  charge/carriers are moving in a magnetic field ✓\n </p>\n <p>\n </p>\n <p>\n  there is a magnetic force on them / quote\n  <em>\n   F = qvB\n  </em>\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  this creates a magnetic field that interacts with the external magnetic field ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept electrons.\n  </em>\n </p>\n <p>\n  <em>\n   For\n   <strong>\n    MP2\n   </strong>\n   , the force must be identified as acting on charge / carriers.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c.ii)\n </div><div class=\"card-body\">\n <p>\n  into the plane «of the paper» ✓\n </p>\n</div>\n",
    "Examiners report": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  A majority of candidates scored a mark by simply stating infinite resistance. Several answers went the other way round, stating a resistance of zero.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.i)\n </div><div class=\"card-body\">\n <p>\n  Many answers here produced a number that did not round to 0.7 but students claimed it did. The simultaneous equation approach was seen in the best candidates, getting the right answer. It is worthy of reminding about the need of showing one more decimal place when calculating a show that value type of question.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.ii)\n </div><div class=\"card-body\">\n <p>\n  Many answers here produced a number that did not round to 0.7 but students claimed it did. The simultaneous equation approach was seen in the best candidates, getting the right answer. It is worthy of reminding about the need of showing one more decimal place when calculating a show that value type of question.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.iii)\n </div><div class=\"card-body\">\n <p>\n  Usually well answered, regardless of b(ii), by utilising the show that value given.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c.i)\n </div><div class=\"card-body\">\n <p>\n  Many scored MP1 here but did not get MP2 as they jumped straight to the wire rather than continuing with the explanation of what was going on with the charge carriers.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c.ii)\n </div><div class=\"card-body\">\n <p>\n  Generally, a well answered question although there was some confusion on how to communicate it, with some contradictory answers indicating into or out, and also North or South at the same time.\n </p>\n</div>\n",
    "topics": [
      "b-the-particulate-nature-of-matter",
      "d-fields"
    ],
    "subtopics": [
      "b-5-current-and-circuits",
      "d-3-motion-in-electromagnetic-fields"
    ]
  },
  {
    "question_id": "22N.2.SL.TZ0.6",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline, by reference to nuclear binding energy, why the mass of a nucleus is less than the sum of the masses of its constituent nucleons.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate, in MeV, the energy released in this decay.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The polonium nucleus was stationary before the decay.\n  </p>\n  <p>\n   Show, by reference to the momentum of the particles, that the kinetic energy of the alpha particle is much greater than the kinetic energy of the lead nucleus.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b.iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   In the decay of polonium-210, alpha emission can be followed by the emission of a gamma photon.\n  </p>\n  <p>\n   State and explain whether the alpha particle or gamma photon will cause greater ionization in the surrounding material.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  according to Δ\n  <em>\n   E\n  </em>\n  = Δ\n  <em>\n   mc\n  </em>\n  <sup>\n   2\n  </sup>\n  / identifies mass energy equivalence ✓\n </p>\n <p>\n </p>\n <p>\n  energy is released when nucleons come together / a nucleus is formed «so nucleus has less mass than individual nucleons»\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  energy is required to «completely» separate the nucleons / break apart a nucleus «so individual nucleons have more mass than nucleus» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept protons and neutrons.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  according to Δ\n  <em>\n   E\n  </em>\n  = Δ\n  <em>\n   mc\n  </em>\n  <sup>\n   2\n  </sup>\n  / identifies mass energy equivalence ✓\n </p>\n <p>\n </p>\n <p>\n  energy is released when nucleons come together / a nucleus is formed «so nucleus has less mass than individual nucleons»\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  energy is required to «completely» separate the nucleons / break apart a nucleus «so individual nucleons have more mass than nucleus» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept protons and neutrons.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.i)\n </div><div class=\"card-body\">\n <p>\n  (\n  <em>\n   m\n  </em>\n  <sub>\n   polonium\n  </sub>\n  −\n  <em>\n   m\n  </em>\n  <sub>\n   lead\n  </sub>\n  −\n  <em>\n   m\n   <sub>\n    α\n   </sub>\n  </em>\n  )\n  <em>\n   c\n  </em>\n  <sup>\n   2\n  </sup>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  (209.93676 − 205.92945 − 4.00151)\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  mass difference = 5.8 × 10\n  <sup>\n   −3\n  </sup>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  conversion to MeV using 931.5 to give 5.4 «MeV» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    MP1\n   </strong>\n   .\n  </em>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    [2]\n   </strong>\n   for a\n   <strong>\n    BCA\n   </strong>\n   .\n  </em>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    [1]\n   </strong>\n   for 8.6 x 10\n   <sup>\n    −13\n   </sup>\n   J.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.ii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n </p>\n <p>\n  energy ratio expressed in terms of momentum, e.g.\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <msub>\n     <mi>\n      E\n     </mi>\n     <mi>\n      α\n     </mi>\n    </msub>\n    <msub>\n     <mi>\n      E\n     </mi>\n     <mtext>\n      lead\n     </mtext>\n    </msub>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <msubsup>\n      <mi>\n       p\n      </mi>\n      <mi>\n       α\n      </mi>\n      <mn>\n       2\n      </mn>\n     </msubsup>\n     <mo>\n      /\n     </mo>\n     <mn>\n      2\n     </mn>\n     <msub>\n      <mi>\n       m\n      </mi>\n      <mi>\n       α\n      </mi>\n     </msub>\n    </mrow>\n    <mrow>\n     <msubsup>\n      <mi>\n       p\n      </mi>\n      <mtext>\n       lead\n      </mtext>\n      <mn>\n       2\n      </mn>\n     </msubsup>\n     <mo>\n      /\n     </mo>\n     <mn>\n      2\n     </mn>\n     <msub>\n      <mi>\n       m\n      </mi>\n      <mtext>\n       lead\n      </mtext>\n     </msub>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     p\n    </mi>\n    <mi>\n     α\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <msub>\n    <mi>\n     p\n    </mi>\n    <mtext>\n     lead\n    </mtext>\n   </msub>\n  </math>\n  hence\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <msub>\n     <mi>\n      E\n     </mi>\n     <mi>\n      α\n     </mi>\n    </msub>\n    <msub>\n     <mi>\n      E\n     </mi>\n     <mtext>\n      lead\n     </mtext>\n    </msub>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <msub>\n     <mi>\n      m\n     </mi>\n     <mtext>\n      lead\n     </mtext>\n    </msub>\n    <msub>\n     <mi>\n      m\n     </mi>\n     <mi>\n      α\n     </mi>\n    </msub>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <msub>\n     <mi>\n      m\n     </mi>\n     <mtext>\n      lead\n     </mtext>\n    </msub>\n    <msub>\n     <mi>\n      m\n     </mi>\n     <mi>\n      α\n     </mi>\n    </msub>\n   </mfrac>\n   <mo>\n    ≃\n   </mo>\n   <mfrac>\n    <mn>\n     206\n    </mn>\n    <mn>\n     4\n    </mn>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    51\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    5\n   </mn>\n   <mo>\n    ⇒\n   </mo>\n   <msub>\n    <mi>\n     E\n    </mi>\n    <mi>\n     α\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mn>\n    51\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    5\n   </mn>\n   <msub>\n    <mi>\n     E\n    </mi>\n    <mtext>\n     lead\n    </mtext>\n   </msub>\n  </math>\n  «so\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    α\n   </mtext>\n  </math>\n  has a much greater KE»\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mtext>\n     m\n    </mtext>\n    <mtext>\n     lead\n    </mtext>\n   </msub>\n  </math>\n  «much» greater than\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mtext>\n     m\n    </mtext>\n    <mtext>\n     alpha\n    </mtext>\n   </msub>\n  </math>\n  «so\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    α\n   </mtext>\n  </math>\n  has a much greater KE» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n </p>\n <p>\n  alpha particle and lead particle have equal and opposite momenta ✓\n </p>\n <p>\n  so their velocities are inversely proportional to mass ✓\n </p>\n <p>\n  but KE ∝\n  <em>\n   v\n  </em>\n  <sup>\n   2\n  </sup>\n  «so\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    α\n   </mtext>\n  </math>\n  has a much greater KE» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.iii)\n </div><div class=\"card-body\">\n <p>\n  alpha particle ✓\n </p>\n <p>\n  is electrically charged hence more likely to interact with electrons «in the surrounding material» ✓\n </p>\n</div>\n",
    "Examiners report": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Still several answers that thought that the nucleus needed to gain energy to bind it together. Most candidates scored at least one for recognising some form of mass/energy equivalence, although few candidates managed to consistently express their ideas here.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Still several answers that thought that the nucleus needed to gain energy to bind it together. Most candidates scored at least one for recognising some form of mass/energy equivalence, although few candidates managed to consistently express their ideas here.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.i)\n </div><div class=\"card-body\">\n <p>\n  Generally, well answered. There were quite a few who fell into the trap of multiplying by an unnecessary c\n  <sup>\n   2\n  </sup>\n  as they were not sure of the significance of the unit of u.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.ii)\n </div><div class=\"card-body\">\n <p>\n  Those who answered using the mass often did not get MP3 whereas those who converted to the number of particles or moles before the first calculation did, although that could be considered an unnecessary complication.\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b.iii)\n </div><div class=\"card-body\">\n <p>\n  Many did not interpret the stem correctly and failed to compare the ionisation of alpha particles versus gamma rays.\n </p>\n</div>\n",
    "topics": [
      "a--space-time-and-motion",
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "a-2-forces-and-momentum",
      "a-3-work-energy-and-power",
      "e-3-radioactive-decay"
    ]
  },
  {
    "question_id": "23M.2.HL.TZ1.3",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   A transverse water wave travels to the right. The diagram shows the shape of the surface of the water at time\n   <em>\n    t\n   </em>\n   = 0. P and Q show two corks floating on the surface.\n  </p>\n  <p style=\"text-align:center;\">\n   <img 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\"/>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State what is meant by a transverse wave.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The frequency of the wave is 0.50 Hz. Calculate the speed of the wave.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Sketch on the diagram the position of P at time\n   <em>\n    t\n   </em>\n   = 0.50 s.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iv)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the phase difference between the oscillations of the two corks is\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     π\n    </mi>\n   </math>\n   radians.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Monochromatic light is incident on two very narrow slits. The light that passes through the slits is observed on a screen. M is directly opposite the midpoint of the slits.\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     x\n    </mi>\n   </math>\n   represents the displacement from M in the direction shown.\n  </p>\n  <p style=\"text-align:center;\">\n   <img src=\"data:image/png;base64,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\"/>\n  </p>\n  <p style=\"text-align:left;\">\n   A student argues that what will be observed on the screen will be a total of two bright spots opposite the slits. Explain why the student’s argument is incorrect.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The graph shows the actual variation with displacement\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     x\n    </mi>\n   </math>\n   from M of the intensity of the light on the screen.\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <msub>\n     <mi>\n      I\n     </mi>\n     <mn>\n      0\n     </mn>\n    </msub>\n   </math>\n   is the intensity of light at the screen from one slit only.\n  </p>\n  <p style=\"text-align:center;\">\n   <img 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\"/>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Explain why the intensity of light at\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     x\n    </mi>\n   </math>\n   = 0 is 4\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <msub>\n     <mi>\n      I\n     </mi>\n     <mn>\n      0\n     </mn>\n    </msub>\n   </math>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The slits are separated by a distance of 0.18 mm and the distance to the screen is 2.2 m. Determine, in m, the wavelength of light.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The two slits are replaced by many slits of the same separation. State\n   <strong>\n    one\n   </strong>\n   feature of the intensity pattern that will remain the same and\n   <strong>\n    one\n   </strong>\n   that will change.\n  </p>\n  <p>\n   Stays the same:\n  </p>\n  <p>\n  </p>\n  <p>\n   Changes:\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  «A wave where the» displacement of particles/oscillations of particles/movement of particles/vibrations of particles is perpendicular/normal to the direction of energy transfer/wave travel/wave velocity/wave movement/wave propagation ✓\n </p>\n <p>\n  <em>\n   Allow medium, material, water, molecules, or atoms for particles.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  «A wave where the» displacement of particles/oscillations of particles/movement of particles/vibrations of particles is perpendicular/normal to the direction of energy transfer/wave travel/wave velocity/wave movement/wave propagation ✓\n </p>\n <p>\n  <em>\n   Allow medium, material, water, molecules, or atoms for particles.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   v\n  </em>\n  = «0.50 × 16 =» 8.0 «m s\n  <sup>\n   −1\n  </sup>\n  » ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  P at (8, 1.2) ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iv)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n  <br/>\n  Phase difference is\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mi>\n      π\n     </mi>\n    </mrow>\n    <mi>\n     λ\n    </mi>\n   </mfrac>\n  </math>\n  ×\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mi>\n     λ\n    </mi>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  ✓\n  <br/>\n  «=\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    π\n   </mi>\n  </math>\n  » ✓\n </p>\n <p>\n  <strong>\n   ALTERNATIVE 2\n  </strong>\n </p>\n <p>\n  One wavelength/period represents «phase difference» of 2\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    π\n   </mi>\n  </math>\n  and «corks» are ½ wavelength/period apart so phase difference is\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    π\n   </mi>\n  </math>\n  /\n  <em>\n   <strong>\n    OWTTE\n   </strong>\n  </em>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  light acts as a wave «and not a particle in this situation» ✓\n </p>\n <p>\n  light at slits will diffract / create a diffraction pattern ✓\n </p>\n <p>\n  light passing through slits will interfere / create an interference pattern «creating bright and dark spots» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  The amplitude «at\n  <em>\n   x\n  </em>\n  = 0» will be doubled ✓\n </p>\n <p>\n  intensity is proportional to amplitude squared /\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    I\n   </mi>\n  </math>\n  ∝\n  <em>\n   A\n  </em>\n  <sup>\n   2\n  </sup>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  The amplitude «at\n  <em>\n   x\n  </em>\n  = 0» will be doubled ✓\n </p>\n <p>\n  intensity is proportional to amplitude squared /\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    I\n   </mi>\n  </math>\n  ∝\n  <em>\n   A\n  </em>\n  <sup>\n   2\n  </sup>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  Use of\n  <em>\n   s\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      λ\n     </mi>\n     <mi>\n      D\n     </mi>\n    </mrow>\n    <mi>\n     d\n    </mi>\n   </mfrac>\n   <mo>\n    ⇒\n   </mo>\n   <mi>\n    λ\n   </mi>\n  </math>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      s\n     </mi>\n     <mi>\n      d\n     </mi>\n    </mrow>\n    <mi>\n     D\n    </mi>\n   </mfrac>\n  </math>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <em>\n   s\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      n\n     </mi>\n     <mi>\n      λ\n     </mi>\n     <mi>\n      D\n     </mi>\n    </mrow>\n    <mi>\n     d\n    </mi>\n   </mfrac>\n   <mo>\n    ⇒\n   </mo>\n   <mi>\n    λ\n   </mi>\n  </math>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      s\n     </mi>\n     <mi>\n      d\n     </mi>\n    </mrow>\n    <mrow>\n     <mi>\n      n\n     </mi>\n     <mi>\n      D\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    λ\n   </mi>\n  </math>\n  = «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      567\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        2\n       </mn>\n      </mrow>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      18\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        3\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      2\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  =» 4.6 × 10\n  <sup>\n   −7\n  </sup>\n  «m» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  Stays the same: Position/location of maxima/distance/separation between maxima «will be the same» /\n  <em>\n   <strong>\n    OWTTE\n   </strong>\n  </em>\n  ✓\n </p>\n <p>\n  Changes: Intensity/brightness/width/sharpness «of maxima will change»/\n  <em>\n   <strong>\n    OWTTE\n   </strong>\n  </em>\n  ✓\n </p>\n <p>\n  <em>\n   Allow other phrasing for maxima (fringes, spots, etc).\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-1-simple-harmonic-motion",
      "c-2-wave-model",
      "c-3-wave-phenomena"
    ]
  },
  {
    "question_id": "23M.2.HL.TZ1.5",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Identify with ticks [✓] in the table, the forces that can act on electrons and the forces that can act on quarks.\n  </p>\n  <p>\n   <img src=\"data:image/png;base64,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\"/>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the energy released is about 18 MeV.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <strong>\n    two\n   </strong>\n   difficulties of energy production by nuclear fusion.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <strong>\n    one\n   </strong>\n   advantage of energy production by nuclear fusion compared to nuclear fission.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the nucleon number of the He isotope that\n   <math class=\"wrs_chemistry\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mmultiscripts>\n     <mi mathvariant=\"normal\">\n      H\n     </mi>\n     <mprescripts>\n     </mprescripts>\n     <mn>\n      1\n     </mn>\n     <mn>\n      3\n     </mn>\n    </mmultiscripts>\n   </math>\n   decays into.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Estimate the fraction of tritium remaining after one year.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Weak nuclear: 2 ticks ✓\n  <br/>\n  Strong nuclear: quarks only ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  «𝜇» = 2.0141 + 3.0160 − (4.0026 + 1.008665) «= 0.0188 u»\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  <em>\n   In\n  </em>\n  MeV: 1876.13415 + 2809.404 − (3728.4219 + 939.5714475) ✓\n </p>\n <p>\n  = 0.0188 × 931.5\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  = 17.512 «MeV» ✓\n </p>\n <p>\n  <em>\n   Must see either clear substitutions or answer to at least 3 s.f. for\n   <strong>\n    MP2\n   </strong>\n   .\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  Requires high temp/pressure ✓\n  <br/>\n  Must overcome Coulomb/intermolecular repulsion ✓\n  <br/>\n  Difficult to contain / control «at high temp/pressure» ✓\n  <br/>\n  Difficult to produce excess energy/often energy input greater than output /\n  <em>\n   <strong>\n    OWTTE\n   </strong>\n  </em>\n  ✓\n  <br/>\n  Difficult to capture energy from fusion reactions ✓\n  <br/>\n  Difficult to maintain/sustain a constant reaction rate ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  Plentiful fuel supplies\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  larger specific energy\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  larger energy density\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  little or no «major radioactive» waste products ✓\n </p>\n <p>\n  <em>\n   Allow descriptions such as “more energy per unit mass” or “more energy per unit volume”\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  3 ✓\n </p>\n <p>\n  <em>\n   Do\n   <strong>\n    not\n   </strong>\n   accept\n   <math class=\"wrs_chemistry\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mmultiscripts>\n     <mi>\n      H\n     </mi>\n     <mprescripts>\n     </mprescripts>\n     <mn mathvariant=\"italic\">\n      2\n     </mn>\n     <mn mathvariant=\"italic\">\n      3\n     </mn>\n    </mmultiscripts>\n    <mi>\n     e\n    </mi>\n   </math>\n   by itself.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    λ\n   </mi>\n  </math>\n  = «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      ln\n     </mi>\n     <mo>\n     </mo>\n     <mn>\n      2\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      12\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      3\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  »0.056«y\n  <sup>\n   −1\n  </sup>\n  »\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <msup>\n    <mn>\n     5\n    </mn>\n    <mstyle displaystyle=\"false\">\n     <mfrac>\n      <mn>\n       1\n      </mn>\n      <mrow>\n       <mn>\n        12\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        3\n       </mn>\n      </mrow>\n     </mfrac>\n    </mstyle>\n   </msup>\n  </math>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msup>\n    <mi>\n     e\n    </mi>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      1\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mfrac>\n      <mrow>\n       <mi>\n        ln\n       </mi>\n       <mo>\n       </mo>\n       <mn>\n        2\n       </mn>\n      </mrow>\n      <mrow>\n       <mn>\n        12\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        3\n       </mn>\n      </mrow>\n     </mfrac>\n    </mrow>\n   </msup>\n  </math>\n </p>\n <p>\n  0.945\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  94.5% ✓\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    MP1\n   </strong>\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "e-3-radioactive-decay",
      "e-4-fission",
      "e-5-fusion-and-stars"
    ]
  },
  {
    "question_id": "23M.2.HL.TZ1.6",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The centres of two identical fixed conducting spheres each of charge +\n   <em>\n    Q\n   </em>\n   are separated by a distance\n   <em>\n    D\n   </em>\n   . C is the midpoint of the line joining the centres of the spheres.\n  </p>\n  <p style=\"text-align:center;\">\n   <img src=\"data:image/png;base64,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\"/>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Sketch, on the axes, how the electric potential V due to the two charges varies with the distance r from the centre of the left charge. No numbers are required. Your graph should extend from r = 0 to r = D.\n  </p>\n  <p style=\"text-align:center;\">\n   <img 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\"/>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the work done to bring a small charge\n   <em>\n    q\n   </em>\n   from infinity to point C.\n  </p>\n  <p>\n   Data given:\n  </p>\n  <p>\n   <em>\n    Q\n   </em>\n   = 2.0 × 10\n   <sup>\n    −3\n   </sup>\n   C,\n  </p>\n  <p>\n   <em>\n    q\n   </em>\n   = 4.0 × 10\n   <sup>\n    −9\n   </sup>\n   C\n  </p>\n  <p>\n   <em>\n    D\n   </em>\n   = 1.2 m\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The magnitude of the net force on\n   <em>\n    q\n   </em>\n   is given by\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mfrac>\n     <mrow>\n      <mn>\n       32\n      </mn>\n      <mi>\n       k\n      </mi>\n      <mi>\n       Q\n      </mi>\n      <mi>\n       q\n      </mi>\n     </mrow>\n     <msup>\n      <mi>\n       D\n      </mi>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mfrac>\n    <mi>\n     x\n    </mi>\n   </math>\n   . Explain why the charge\n   <em>\n    q\n   </em>\n   will execute simple harmonic oscillations about C.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The mass of the charge\n   <em>\n    q\n   </em>\n   is 0.025 kg.\n  </p>\n  <p>\n   Calculate the angular frequency of the oscillations using the data in (a)(ii) and the expression in (b)(i).\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The charges\n   <em>\n    Q\n   </em>\n   are replaced by neutral masses\n   <em>\n    M\n   </em>\n   and the charge\n   <em>\n    q\n   </em>\n   by a neutral mass\n   <em>\n    m\n   </em>\n   . The mass\n   <em>\n    m\n   </em>\n   is displaced away from C by a small distance\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     x\n    </mi>\n   </math>\n   and released. Discuss whether the motion of\n   <em>\n    m\n   </em>\n   will be the same as that of\n   <em>\n    q\n   </em>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Constant, non-zero within spheres ✓\n </p>\n <p>\n  A clear, non-zero positive minimum at C ✓\n </p>\n <p>\n  Symmetric bowl shaped up curved shape in between ✓\n </p>\n <p>\n </p>\n <p>\n  <img 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ty+qB1pBrKhuypy0WoOYE66VzPc6taqK+M/S8USqFTnwamLVIvwbdY7k2muvkYWLFkIS+5XTyVtBLN0UaT17ZfdAK4il6/HVG8QcepmEZCK219Fz6erenOt/w5Vfbr/9drhkfKUEP1PwaAVKB37lkWpHK1sS80qDUpUxf5zCOTYsB3/+I0kKjvIeDJhX6ZXB806FTzeVWs9uqR5Y3UCsQcse2vzgD+cHtaJ27dqqk7mVRFx1x2oHYmn162DXZUDMPF5BfTfJLTffIjNmTJefn3cecux3MKbBVR6KeGikGoUkkLDH5A8w96pyvrhRfYFA8dykxiW1J5fZPmiBYugJgYyf0RASnZiFyOOkZye1vfX7cA+sbiBGXpp1K5j2imBGUOPMZgJSFQxSZF9eEWO9VoMYK7LddNNNMmXyFPn1Rb/WND2tIOaU9IDk5xcNDSaWLJI+PWEAbgWxFbH8ct9zdQOxYCsJYHORcJRaUe/evZTqKVfXpVV3rPUgRnXyk08+kSsuv8KltG6VxDjdouokrWCsEMXPNckkC64EjlYQW3mLdHUEMUpjNTXL5IMPPoAw0E5GjhypkhkBbFVL4i0OYi091EmiarADvYqmn5HYxwZx5513yrvvvqtWSo37dOokf1WkyCcWfa/mDFzUtJzIiRVQJ9M+358f/E31kWrknDlz5Ouvv9LEkgMHDpRu3bqXVE+0peeAB93gfZPmxYpow8q6ZxbEmKmY7hVeetaeSN2MpL7iBkb6gM/1cZQ+5Xs5vAL4/NmzZ8sLL7wgGwzdQDbfYnPd5DJGNpYPW4VHiSAWDuosZmGl9RFJGgADLhfa4CQM/zd5+3uQg+zll16Wq6+5OiZdrGoQKzzuhTmxYvo6vOhBxoLXYDZbnbCYuMvczjpp4iT59re/LX0Rl9oWZK2vV7AK52Xs0YUkwdWpnS3VFtuHCVgetLzE0xwQi4JMNMwInFdtrTqQq18mUIt+mJ64nzWrSh5++GHZDtlgNh01Ss9bnY61GsRov7vv/vvkxRdflOuuvQ6VwcOD+b8EYnV19RD/MUnNPotkk7Xy5ptvymeffSr77ruf9O3TR9q0baPWJqb/Xt0maiuIlQJihTkrzo3OnTtpogUDz0bNlMx/z5w5Qx566GEZPXoL2f5b20sN5k1bzJPV6VirQawOVrYHH3xQxeAbbrghRlb/L4FYxnLrJul7770nr7z8ihx40IEydMhQ5wjMhVLYdWNVTd5WEGs+iEXHLKrdeDcJr1Zq6cP6BmSNmS8PPPCADB4yWHbddVd1rahAoZ7V7VirQQxu/nL//fdrUsXrr79eicjg8b8GYrQsVUKVfOHFFyCFvSVHHnmEDBkyJFNJxzsUcwKvaotTdKG0gtiKAzHybvPmzZU33nhDdt99d2nbpq1MmzZNnnv+ORk+fIRKYW3wmfLM+KFbxep0lAhiLf8qSRxYrsmdjxMjsf/vf/9bHoE+f/31N8R2kVL8xHK9ufpYOdcFtf6V0D3mzJqe//CPZDLJcgCWxpzitydsX3/9dRk3bhzSdY9VC9Py2uV6XvRZaTm3El4156VJz087T9K2rxTQzNX2NO31UrNvc1JfpH23+BoSGL/ekfPP/6X84Q9/UD/BV199VfbYfQ8ZNmxYYj2dNO9WaltzXb9WgxidXR9/7DF57PHH5cYbb4w5cLYkiJmTKAqpqGczMaH5AMSBKhXEkIVIXSbeAu+18y67INa0jXz2+Wdy2223aYm7bbceAwfGusyumuQXtiImX6F7Ji3cFb1w/pdAjBwoPfCvvvpqmTVrplogDzzoIEjpg3WIkgw9K3oskubeWg9iTz75pNx3330o8XaztG/fPtQfLQliilsEMfAJNTU1sWclDURsdyxREmNdqi+++AK76/ly+eWXa7QCHX93AaDtscce+NY89BUwc/BgSSCS9n3Snp/0/BW9cP6nQEwLhUClnDtPPv/icxkFC2S3rt0y4XlJDvkreiyS5s5aDWJNcMR79tlnVfq4+aabpVt3DEzgaFEQo/oIUFi2bBl2s1lq7YuCZtJgBL8vVRJjam6aya+88kr1/6qurkYiyRFyyCGHmFoNlYGTjwDGDCG+LoFvQxKIpHmX5pyb9PwVvXD+l0CM46M+lKwYpoWnQYSo15JpE0l9nfR9c8Y/zTWrNYglTaSMxc35iUXPJ4i98soryGRxrfzpT3/S3UVDatBDWqaKwayadNExQk4FzHrmFN+V3l+NKiWdAHnfNIGx8UWbzk8sOpGYhojWpClTp8gzzzwj66+/vuy4447qYkEQg5tr6OWSQKP4noif2dx7e+dLH9Ppx5uLLcnwEH1m1qFTZc9MZhTfWqMDTCJhH1kW4Ozh3KRzdoMf+zR9FBqvCPMQ5Hi1td4X0j0gti4S2NfoBlUq6GgGGd+WCG9r93ZGCG13LNlMrF9DvqMJPHCuudTiSRHTDGSucws5w+bibTIDnHEOzN6VIEZXgl/96ldy6623yoABA9QHSlP5AGQq3WCQjFc+y8xzzSLk3XC5iACPisX3RkuDGOsT6IF+UVKfmystS8xWgY/XBBDz7fedamovwLmIWL34BmhSBoeYXuiZznESh3rGZz9NZYFrDkgXmue2l2aRLbY5l8i3lgpiRV/vfNBbUh39nwMxEvtMw/OjH/1Iif2hQ4eahMRJrOKYhXSog5/LQWZitf2kmZyakBH3IRAWPcgBjGtpECOxT8AiQFvuNb4jpTtqknS1CANsmnctHpodVDRn0ekWbqoM2+bTG/tCr0lAFpPEaK7F/RguQ4NGZaQDzFPdJHSCXfT7lu6fKIgF7x8FsWh/pwW16HxszvwsNObxd3H5/3QA086W5Owv0Tuu1ZJYPYBl/PjxctKJJ8pVSFM9fOONZcqUqRpu06N7d2kPr2QGs5K74uSmlzIHhECnKXI0NXBxR2hiua0nzfi1NIg1wL/EJ49kZfRsLJypApURV5+WXqTBXmvOvdn3nqehBEZ+j+BL6y/HKklVjz6zAb5vk6dMUaMLAZD/tcV4d+zYQce9Q4eOGtFg7ijZeEX/Hs15h3QLP7/ktSaBGPtON52MMFDc+gmeVQhk1whJrNiB53kNDmQ8WERBBw4EmobnhBNOkJ1QdLeubrnWrrTo+3JpD4td+/bt1JGPC6Nr13V0Avfo0R1hGF3weTlCcdpKO6bwoVSDHZqSDfmlvn362s7OSd9QD9CjFGYbj0+86FNl19fXIcUNUmsrT2ZcmR/kbKLHyA7kidWMRGKSgh/ErHAT53dy92GG+XM5w2yy8QhmIrCwJDo0ZtPyKM9HKVNT9Fg7wiCV/asBfbFkyRLUZZgtS/Gb/BvflyDRpUtnPbFTp06ZMcg33hwH9vfX33wtU6dORfqXudK9ew99NrNsjBw5CvfpqNJlhWbcCBNL7F9zDWAc4HJ5/fU3NNC9H6pl8Xq+O0Ov+F6cDx07dsTnXaRXr94mTUc5schLs0/o6b54cbUsXLhAa6Hynow37Ny5M57TD6lqeuu8ii9Kizn2/Kmq9y79kdIjSo1Yn/vx4XvQf4ufeYnRpFEzzvhn8PvGslodP8/zsUZsAww97CeCeYVPeolzvR+h9hVuRy2F+5sBEd2F7N42/rbzNaCItiUPsAzKwQ0lF8isaElwtSP204CYBy2jELKL0t+joayNeh4fc+wxctSRR+niql5SLT179JSNIZX1XHddnYjjx3+DxIkzMNnrZdGiRVA3ajXsohzmy549e+ogLVi4EL5WFvjKASSQrTdokGyz9VbSRkEJX6iLhalxPHiP5ZAgqqsXq9WSXAzVFE4w2/0pATLRHCZOjhxeCih4L96DxU6qqwEKzjGVfl+Mb2SONC6UaOqcaD/yPn7isV1LYK1kUjuCjk48/E9fIU5aI9LL9d585/ZoJ5/LCe7DTqKTtRZOswTopUuXQdqdLDXLaqQjQIb34MLRugguYoLWUgIJv8t3MLqA4zBhwkQFmF691tXrudgIcIzfo2c51fhcwOrnhi5k3Kumtkb7qH37DhiXOjeOplPznnxv/qZkzvfIVRU72Faey1hDzhv64zFpIN/Jxxzyfuuu2wvA2y0jmQSvZ5s5T+rR/5QO58K9gWBoc8H5GmqfYQzw3nSR4Sag2SMckLFf6ajsNyG+p3K7bQ0ArV8MwHTeshg12j1n7nwFJra1EnORz+Qz7N6kH8w6SdDkwflqoGpzqAkgxkP3stiGFt5M9JTIBtDS6uwaDWK2a2V/oguiHoM2GxLBAQccIEcccYT0799f5iMejMDFQWPQq0/yRnWFE5hSAgeV4DVo0ADph2u4eOciLKMzvqM0RRV13LhH1XXhpJNOlMGD1pfamqWqjtg2agQ0QYKzgZPAW8QUbNlQNxOD3E5ssAMgxonewJTAkBwJtrzeS3bkvAg0hY4oiC3DAvQgpjwQ7s0FZWqcWf/YREoxnLjdunXTPmMfEYj9ruyf6XdrnfhcQEEpQa19ur/b6V7KLNhim/yeA/OkvqVJNknFP1PlkYjk5CUMzwOaVGHSnc/kYZKNibq2zmxFkh9NlsS4oJ2Ds7s3b2K2Idt8vJNorr6yTbJcsw7Tn4/zktdxgyVg8Ua8P0GXgM3POAbt2rXXZ3h6gEDKa5csWaqfUZps056/u0KDsLlCRpEAxvt/8MGHcuOtf4EUWqPj3AsbOQ1enO+UHumG1BbzlYBMibJLl3V0XrO9nIPs/8oyzBXMF7Ypt6RZeGBbQSzSP96yqOJv5DvkKFVJbOzYsTJ6iy1k3/320zAKDo4OAMBJVT0MEAeDOxCndHZXcjuOTkzuzuZbRTXkhRdfknGPPS477rCD7LffPgpwTeSe3CTmjTwXZdcC2BS4rJG+rDtXdDCHU+YVouok1QnnlOrF92xlJ5OeEqZOBkS8dGIhUn6nDBokTJWglObzTGWanoPo88Dn3yULgpYPy6y+wdb5P+K7dvAsShaU/HTSu/7woKMl+ZxzMW8eJfpNzeHiwyzA9T4elJ8p+KiV2jYT/qfqvREBGXAKtTiHOhnAZKUVvEoWvC7ID2U/z8ZB0sjA66iGeinMq4gZNd4GyW0wzj1Im26cL6VBvpcZI8qkU5f2KDLdT9Vv/t0AK49JUyIffvihPPrUM1ILybE9AHExtIRqqMTz5s2DtrFAuccecEUiiHGN+N/UJOYBLHm0KzNJ9uyzz5L11lsvLmkFBjvq3qFzP8pHJMzcpK/XKEks18uoJGYz3O2q2bNY4O1TpJo57bTT1HN9t912C0wUdKYTs/0Vsc4tyxL7XpJZDsmEIvhi7Hx33nW3TqLdd/sOovx3AdfAxdaoOxd3rcpAwHmpxHCp1ydNhNXhe5OwCCMGbqVM9lKuLaYv0o5HsD1J10a/Tzo/+q51jQbcVjeBaQ5MeqWqzySh/7z3AbVYDxg4QFVibsq1NbWauZXnd4CaSb6YUiudpLnZdYchrJPyhl2le+c2utEfe8wxsvHwjfWa4Lgl9V9Lj83aDWIQTiZNnAiV7wda7WiXXXZ2ZKSpHxUR42MiiGHgqXJR6qFH/LwFi+Svf/mzLAZfxowQm206SkGMcoZauXRB2pE0EZMGvtTrk+6/OnzfCmK550rS2MdADxmBTfq333XL62X69BnyxBNPIFPFmzIf0tfAAQNli9GjVVUlN6ZGDpxPLWUdGLXI1/Jz7if8rDP4OEpm5CepTlJzqUKyxIHrDWwFsVIXT0FJDIM5adIkOekHJ8lll14m22+/vSNxTX2oTCzZFpTE6GfkfZaQLG42rGU9e2nq69v//lcZhYwQ3x97vLQnGQ5JjJbToIqXNBGT+qHU65Puvzp83wpizQMxzxtmNIoKqs8sqdZBJsM6f9+994EzW6ab6g9+8AMYIhaqmq555FTuNV9C0hWq0qpEbBuv5w2zxgb62tmTCIy09nq+McN5JkymVkks0kGFQGw5rCjkxE6En9jZZ58te+65Z4awJSfSJsKixTs3rE56FYdcxYyqOdK73wBZDrXxkUcelk8/+Vh2haS3y3IBjDkAACAASURBVE472TMc8d4qiRUPj60g1jwQCwj8BkrOfWMZLMSXXHIpLNs1cvxxY8F7zZe9994bJyw3gCLHSiskfpMi8fwddmC1enpXDk9hkTNU1xKcT8tyVdUsWGDXxRPT5TpbZSAGehDiZp0zvzLeMIlILn7ylnJmIRBrQu8zKp8e+7/+9a81j3zwSAoAL8RjLF26BJabTur9PX3mTLntz3/B7tZGTgBg9oeoTncL+uNw0Nu2qQDnAI5M4zSN8+FEY/uKPf4XJLFi+6I55yX1X9qFlXS/aBsL3T/xXg5osueFa1tEn1UOTWARKI6PP/5EzkO9VUareGstM1RwbqY5MuDGmavGIJu3C/GMnj3ppmREf7FHGn4w1z2jfVk0J7Ymghi9k8Z/M15+9OMfyQUXXKDqZEuBGAeuTdtKBak6WDefePIpeREFSXbcaWfd7ehfReunuhyoaqnbowKYupO2glixc75FzksCijUZxKKSWD00EGoaZ511lrpN/OxnP1MLJl00evTokVr8yAVi5M9I+neBS0faoxXEIj1WSBJjeupvvvlGfvjDH8pFF10k3/rWt1oMxMrAt6lrhPOnmgtR/eGHH0HiwS/kwIMPlm9tu50qqyRO6+C0qV7gDsC8q0WrJJZ2+jf//LUZxKKcWB2MT48/8TgSgj6uBi06ZtOJuxP8Iulgm6KwvHZ4HMTgfgPOjZZ6cmVqAEhxtIJYChBjFoupiJX8vx/+n6qTW2+9dYuBmPqMQaM2L3iwAuAQJk6aLH/7+9+VezjxhBMRGrOJAl07iPfqQOlUSQvswdGqTqaY+qWdunaDWFg9/PTzz+Wqq65S/8hdv7Or+aHB8VXdfugPmbIrc4EY579GYkAMZJm/NMcqAzEE0UAdYowg9aA1gxNjjn3G3Y09/njlBnZHRtM06mTwXO8sYU6R5miIDoHLBR0yzZGQMPU5JLFrr7sOns/d5WRYgpg5Q0HLOcKaC4ZxGoVcPXMtOv9ZWtUnzQRbVecmgUy0XWn7IO39V3Q/FFrIsbaGOLE4H+adpQlQLHJ7yWWXyZgxY+Too482Cznm2qKFi9Q9QqWmCCeWj/PyfZBTnUSb6uEYy3sHC/Dk6ue0Y5W271d5Fos0qBztDFUlCzi7EsQmw8WCZPtvfvOb1MR+CMTUZZ3hG1lvc8aQqUWNjoX4XQ4LD10rXgI39ihy+w+CGE+3CwYqM75SgU/BLJ6uJzr4rSBWeCqnXRhrMoipJdElbMyGSGX7x/cFYziZgpzz8fQfna7OqeqxD0nso48+QuWi4Zq1I6pOJoFYdCR8XzJelM8OxsC2DIgFDV6FozrYtrUaxKhOzoTl8JSTT5Zzzj23RUCMg6YDpYHSmpJMgYx/MA6Tv/n3Cy+9JI+Me0R2QjbVPffYXcOSTAoz6yRl2VS7sUp/pXuyp93lVtb5aUGmFcSyI6PJHvEfC0U///zz8qsLL0A1936qOtJfjMcHH3wgm222mYY36aQNHKlBjOl28B/jMmmwaklJLGqkYDOTWJe1GsQoiTHf/SmnnCJn/PgM2e27u5WgTnLgbYcgv1VXV6tOrcxCUaeB3kqQaYwas07U4mfco+OQAuZ12XefvdWHjGFJBD7jxxAxEIh3bJXEknfc4OC1gli2Nzh3XnnlVbn99r/DiHWqbLnVGAdgDD+yjLZ0+ibBr/nYAumldT4H3CaC/863gWnOMPqLaTlAy+/mj1IlseZcv8pBrNSdPkmdpGmZnNj5v/ylVjG2gF87kvzEcu1W/nmLFi3ULBgEsczyc4HG3Jk40PMRlnTfffdq0O1hhx2KHPfftgmjSEa10vvcOIIssw0p6xbrmtVFEks70dJKWaXOiRVxfdI7pAXVaBsL3T9Dm7j5wbllPKxZyN955x3561//Jvvvv7/sgw1T/RAjUvsshAj16dMLmygzraTzE4u3VaFPg8V9br5CIFbqeCT17VoPYizFfuJJJ8kZZ5xhIOZ2Hv6OVgBPmkhqicTkIKdVvWSxxpL5XE4+fXJmMBuZHbZCpiJi4J5775XPv/xCvn/C92WrrbZWH7EyBpcjBk3LlLiYZ70HqTczHUQyP5Q6FVru+tz9FHbcDaoASQCQr2Vp+NLcCy37aZJKktQ7Se+QtNAK3T/p3t6rPnOehgiZZfyzTz+V36PgLX0gmfyT50Sz9voEk7Qi5s5WnH/scrXb77W0dtJQEM6gkk6iTup3fp/Ut2s1iDE8glH6J3z/+3LkUUfJYYceFgKGZoMYk9nB2ZUAxlgz5tzyCeX8oOAbcvgagjQBQeh/v+N2mQnV9tjjjpNtt90W85J8gp3dhGBycmWaCz+IXcU79BczF1rsnLjqG761ZY7JNj5xkeZpWSn3iPpOJeXkT+qcpHdIWmgtCWKkXkkUMdvtb+D/uPnmW2hMJJMTkGQvc0kLs9KRZZGlW0Su/F9RHiq5ryybLJOMMrW75ctruQ0j2ldJfbtWgxitNFVVVTrAxyK766GHHaYyjnYKftKCGNVAI1FFliyt1gSK+SQxWrEry5GJlIn3cP5HiK284x//wHVLZc+99pTdd99dOTVti3Jklt56zQSx8O6rbiirHMTCKlNyvrXCMLY6gRi3PEaJ0BJJEBl7/FhNlukTJUYlMX7O1NwEK2bIjUpj0XdL7isDMQoIlMSi9Q6SQCdpw2gFsUAPED7qYAY+HbGTW221lZwMKyUPjch3sY3Fdqi3SvqqRjNnzgDH0NuyYSAjgJUDC4hOmiHDbJEaEI7v3nv/fbhePKpZYvfZZ3/ZCSFKPMO7X5Aj08Bx36gSdKDoxMzlnhLePcNiX9KiDV6b61lJIJZ0/1IXQnShWhYGA1vnLVNw6JP6K9j+Ytqa1B85G8PpwCgPzANLoe02C9AU//7Pf+TFF1+UX8D/sQsSGPIc/84VER8KgszUqdN0w6XV0if3tL6I82f53j30DtBnl6k6ackcc80la27LqJd+Y/T39L/5+YDBm8S6rwwvln1yUz2kmRk4CY5tdCvQdq0Zzq4EMeZJYlLEHcgZwF9MOwOvQG4raqWJ90R2YfM6mqt9GbRJEye4XEq+cEbECVF70EDMhtLiJd8HyX/ffUyNUitHHH6UbLvNNgBBhnEgR71mcPZuGAZ8zT3SgliUgEsGmWzLks61M6PvUszkbv775zaMuJFQPinp3oXbG3/n4PnFvFt0ZANzzXWXAUwWaHgG/RBfg8X777ffIWedeaaM2AQL2IGdb1MUxHg7Orsyi2u/fv313T0gRUHMF4oJti5oJPDZbwmEzI5BEMvtYuGfkdwXWbCLO/L69OJW98Hcm3yf2BiXyXpDR67dIMYd7NxzzpUhQ4comGm6ZSaLw0AmWSeD3U8yn9YYWoW4401FMYwBAzkhGOTNPEzRGmgevNz6xfU1iKFkxsz//ve/cs89D0ldbSM4smNkzOgtwJ+RY7MoACe/5Vj4xUNaWhCL8iKFgCmJ8/ITzbfWsDgOGoUwOpe/UPFvH8d/z5H5VkRz6EfvHX1+tK2hfT7HOo0aNoL3i/df+On+Wr1GrekmLTHF9muvvip/u/12OfyIIzW1VKamaECisvLI2YOgxQ2YHFbnTp2zKb/19mFJrBgQ453pXsFMsFQngyBm3JvVHzC11HEkBQavIIipZhKo0aCA7X0m7T3XG4rMHJFjrZHESDLRIe+CC36lVWN+hd9afUf9W8CIRZz+4hM5MBm4CwTCNRYtXqRFGfRgR0d3dq+6uPXLO5U7tbMe95nwzVT521//hcDcBUjz+z351naM66RjogcxXpg2yi37BulBLDzxC4NYekfdXHO4kBpWnHSXf2VE7804P64nr5YkqYBp+i9XW5PUx6TvtbEOwHgu00c/+9xzKsUfc+yxssuu39GX95uyBzqbNVE+0GVTcYAS5CybA2J8FoGK1ai4nnKXbGsZScxG2O5l/WzSV/bfRYFYA9TJabjWFtiapE7S2ZWAxeBv1gCkJKY+XIx3ZNUcV5Iq71KI7LDacTa3dABZs5L/9lVvwpyY4188iFnfa+dbeusyhIJ8BgfF20GQLoEFdayM2XJ0RtSvYHYMtJ3Oiab+Whqf7JGkDuVf4Ia7hcX8pO9XJAAVbnnzvg0WxE0CsGKeUFL/eJ8a9yCjjsJjSwmf0pPnwx588CF5DHwqjVTkUqkVZEqsqd9h1v8xS2LYAzJcGayIVtQl/IZBdTHXu0e/9+qcWejN2TVXn2ZfyaQ9OycsmXn11INTLuk8qPpmuyrbX8mSGJIhVs2ahkaw7MaaB2Ic3MsQEMtO/MUvzldR2ndo1BSdNHkZVmQEMeoYYmekZcjzCwTGQipKdNI3kohFj06aOAkFR+7C78ly0EEH6wRlMYY6iOqo3Wvpgel+gZTD3ESyQBYmU5PanrTokq4Pfl+q5FEMiKZpj+4Tkdnfku9baGH779IAI+QY8KPZRZhVp+xuDfW+zJ9o5gnmxv8PiHz6gW0Fb3yWEEy3hbmEA3iQV/UK928yH8g2E2S5FljGz1s0LTFCFCRt0zQJMP7k5L7LXhSUwPyd1moQM+cGkT/AGZA70JkgQk38tnz5uQjQQoPrd3MvidE/hvnCyLGpoFVgZsVADOfXOXV2xoyZ8sD9D6D+4FcoxruNgll3VCOvAGlnNRCt/BtzmHkQo4NImqMlF3UriMUl2eSFmB0tM/IEQSwsFTNrMmmQOkg6d4DAf/u/b8tpp56G2MdN4UrRXuqRTTibiCB5FrBtLOrBcLgBA/onXlAsH0gthxs7Vcp8IOaUF6cEOnkrsk4KS/UxSIy1f60GMVoDac357WW/VT+aM38GEIMkZiI1p0qK8AtHKPoepIMrFzOLm3IwbRDzq2i5QIw5yOpZCBf76nhUuv7rX/6mFa+POPwI2WvPPWQdpL+mLw7V1kZV54Mglo4vawWxxLWb6oQkzqzQzZJATM3YOJhk8/7775djUBrtu9/9rlIh3IRVjUshi7GtTA7KKuN0tE5ye0h6N/891xFBLBh6FJXE7FzL/mLVv7LprX0flUpNrNUgxvKoLHhw5ZVXKodw3s/PM3XSgRjjF4s9dEfB3PLSGEVpWouYZodA5NXUfPeLg5gjKDmsiqXkyD6We1GZhp7YB+x/gOy8845aLstKyBN4gyCWTqFoBbFiR7q485IWemEQC8NI9F4sWkwV8pFx42S/ffeFT+G+agVUbovGCaNmiz44ZzmnPvjgfdntO7sVpD1406R3y4KYVUNi/HB+ScyBmFZLX1Ugthr7iUU7m3/rjznOwHTD8KB69WxmqfdfIgjcO7rmUyfzkZzRZ/G+DKplBWROujTqhE6UCEnfhN2Xg1xVNVv+ccc/5JNPP5Odd9kFQb37oaJMTwdkZmEjz5dODit6vuc9sSVBMNdDklTUmJCbsIq9tB2Nac3s/hEYMHXdbur5m0K9Zt6GdticY8RFfmkjeC/NP6c1IbOAoc/Gz3L4Nf4d2YHfe+89+d73vic7oMJ8puK7m9+eHs/3Lr5SfKh9uPa1117TFO3BrBPNnRm21oyzY44yq8ZuOfOSPf4LPzXetxF1O8LbJEtiazCIMXaSx/XXXy9zkPHyVygWkskHTiDIkWy8WBDj4M2ePUcGDhyokzGXf02hobJp7weHVyNgHJOAXMhilJW/H9aoZ559TkHykEMORqZOWC5B7nvrUkWCdbG5kzPfdasaxJKkg1ztprGF1t1ifJU86BULYiFQKkJlCp3vPQFJaWDMdRPEf4ytffDBBxFrOx7JNMfKiBEjAhKO26BJkLs3KnasqPIRCD///DPZcMMNWxTE6Eyu2gg2dQ9eaTf0guskxzyP3n+tBjGqk3zhW//0J5kyZYqcc8450rEDKhhDpWQcZC7rZLEgRvV08aLF0hN190zdi+v6hYEkaGmkDxp3ZSaYMz+22rpGefaFF+Vf//oXsmW0kx+jYtNmm2+qrh0Ezcr/QRALAlnSbm9cjUsKiL3CwCx75JLi00hicVAvzPsEn92AgP82sOgRAKxSfCPKq32s/Bfn1emnnyb9+/czdyBIOP5ZXtOIgljSBsOpQulrwYL5sHyv0yL7m5fErHRhF5NGHeVSCoglvQsb/78FYk5cv/POO+XLL7/Usm3eOZCLoJzpcCJHGhBbtmyZdO3aTSWq4E5e3CwJg5g6tqpgBmmLaQoq2qBIaZlO7kcffUSqZlfJ4chJNmarLVWarCwxJ1Rxbcy/6NNen3R+kjrpF7C/TxKILVu6TJYuWyrdu3VXXjRKZq9KEKtn1hIX6VFbW4PEmW/I/XBi3WL0aM0717NnD91oCWj+8M6eullGJLGkhW+qq7k3MEliErGfNFb83oPWggULsAbWUcDlxqFtSwzpyv+EpHdpFog1omDu7KrptuBBhCsTsIbETtLZlbvDP+74F6wz41G+6gJ0MHc2hg9hUBsLuykU6lBOMIZ8mKEgh8d+HnAMflzIa1vxzJeDmzMX3v1/R7jSu7LLLrvKgQceCOfdddX1wtg1T/qT+LW0PmWN6SrQJE3cYiZX0j3SfJ/0vOCuT1WMYTCUvKiOT0FI2ITxE6QzJITRAAYCQtIR5GF8rwavSWpP6FxdaeEn8npudFzsdXXk38o1dfp9992vG+yx8MLfBtW4KvEOynlGXDD4vtaGbJhQvnfKJSWG511Sb4S/LyRZsRQcN1Va6b1jbvj8/Bb7dK3If/agDTaNfRkKO1qTQQwlRFVFu/uue+Wzzz6XX190ofpeIbm05vIqbwrnQYr2RKGJa+qjBX9bSAv5jfxsczGSRngheOqfIRYC1bVaHnzoYXnyiacQ9DsCUtlhstFGGymQ2a7NdNlYrJj8GlYlhd8t7QRKs4jT3jvX+UnP8yBm16q1Q63EzBSyZEm15pNfd91e6o7AcUoO+C7c6qT2REHMeUnYx76x+E2wpQvF66+9ockyabQ56cSTZL1Bg/QdVMIkOR6YSgaAxQGYPS4MHAaApnU0py8KgRjjMel8y5hgtd5rsrPAodJfGltq+tmzVoMYJTFO8PvvexBSzDtyyaUXY8FTTqGYDrJT2hTssaSJm50rtjsWUnHSghjXJS1mleDI6rFz8z0orv/37Xc0fm769Jmak+yAA/eX7t27KZCpd7+6YkCuaGF1M6kv0k+90kHD+t+4GL77008/rS4p226zLTgnOCGTC1PTvhHbhY7o+5USARA02XhQ8amAKLk88sg4WApfx/h9V/aFCwVrQjKxgKVz4iuhvYH6C5rT3vGu/p3T+FaphMSNFgc1h7RHoWeR1+O8pIVS+zAqeLWCWHJ3q27uXCqiE1EDdtCpD9z/kLz88ivw3L8Kk5tm4Dru2wCxwipXoYXLhaGpebA4SJoGY/NytTotiKnJH9ZITj5GBtBFSAla/Ju5oR599AldtIMGrQdV5DjZBNIZ20EwU0BF6uuWPFZPEPMWO1SXQpWfSqhqrGNAvyWTfix2Nok/yyW9lAJiWgErok9yrpDfvOOOO0CEd5YjjzwCY7aJGZhUQjIXC/owVvqoEjeAPjOEVydNokoj9ZfJPPiJ8ejRs2fByJJcc6bQs/heLN3WAQYzbiS2WQTbthqokwz8XlPzidWDw6sAQf74Y08iePZx+ePVf4DKBdWigiIvJndTWBJLs1A5sSZMmACT9UZqIjc/mbAFLM1Ei6kAofg6knucGN5dQJDVoE4XxUNQMcejHZQ+jjjiCCS962s7bjnaxLAQlyaolEXZPDAMZBrgPC5Cowj5B7kNyC9c9i/BiX1tGUwZ7kJ+qU7efPNNqa6uRkWpXbFJIT0zwaCFJdFoH+SeK/ZcFuNQZhJAWgtrMovVjBv3qHwF7msb5I+j9Nyt2zr6Hj44Ozg+5sya7TBaL00ai8p4xY0ML/vm66+1UvfgwUMUbJKOQpZab2TQe+DeS2ChZJZjvwa8tOg99YsZ+6T2FPo+UZ1co0GMhWqhrz/99HPqCX/99ddhICs0bxfDeKLqZBoQ4yIaP368+okxENyrccHOLh3EPL/g7FEwqHg0MI6nDGmH58pzzz4vTz31FACsv+y99z6y6aabonBqpe6KXCgmMRZ2MShlEuW6Nqvq2U7cHF4kSGbzer4HSWRKVzz496effCofI/X3IYccqhKOFXT1iSpb+q2y98stWRv3VlsLugLzbkn1EvW8f+aZZ2TYsGEArwNk1MhRkL7IcZGr80CvHZS5eRTEPCfWfBBrQhHpyZqDf4MNNiiqU4oFMYLtYmwgVON1nPHjw4taQayorvbe0qaLx9VJEqSV4CAexWR6Uq6++o8AHKQNgSTWgCSElWVhdTINiLF5zFvOHahdO4KYJYJrORCDMpxxAfFGdZK+9ozGpuUK0I0w13OyTJo0VXd7cn+9e/eRIw47EAUkNrfCEWp0WHkgFgQwz2kngVh+ycZLH5aUkn5yXbqso9IEN5Hnn39BjjvuWAU3byXO56Vf5JQq6rRgeyklmU+aWUiXLK2Rr7+egI3zXjhEz0ZA/0HqKU8fLd1UGujrZ+kJHG0b5pIwxjGv9YB1sqgGBk4iqFdVzVLv+vXWMwNC0lE0iOHeCxcuUBDT1EDoi1YQS+rdyPeFODF67HMAn3zi3/LAAw/K9TdcB90dEfcAMbXmlbcL3S0NiFEaoDmfHJTPrhldqKVJYoVBTMpIqJqFlGomwbq2drl8inClu+++RyZP/Ea22GK0HHrooVAh1g9l3+RLp3nXlEOS8SHykoNl5iysTyaDmMiziGD45puv5dRTT5XJk6fIk08+IQcffIha+DwimHQTEmzSNr+o84PttQ3MArMnorLVE5hvn32OjCTbbK3ZV/v372/xGWplpJGBfzGNjXOQVlegLLCUKYhlNx2d4yWAGK+nPxe1B+2rIo6iQQwtnTtvnjq8akYX11Y/IJptowgqoYgm5T0lUZ1sgtg7Z/ZM7fTV3U/ML05P9DdgoVdWtpV/P/WM/Oufd8rNN98MdRKuB5BwyiHSlzU23w2Bg+Xr7nm1IEnaCI7CigARn1GAu/9Lr7+lqgwLpey0886yHbIXDB48WMlvbW/9sqxFVR0hs9labSLmNwxEF1l0dkUXXTEgljSJeY/nkNn0nnvvkd/97nfq3b7jjjuqm4nZdZKli/AzCvNCTRHQNcCxXHLaf42WQ8tyajXJFIDqyy+/JG+99ZYMWm8AwOu72ES2yFhIQ35oblF7YPJha759mY3ZfRDtT+9uoeoa8+VHUCITKB5QURnKxoMqd4wfpSUiY0XMqrgZKTHTDvuH2SCym8WsmbPUYEAQyzp9uzlF8M5sms56GQC1AHZnhidus/C59S3eNMQf4oO1HsQooTzzzPPyj3/8S2644QaIvbSi0NmVSbqav0VwYpF/aQsXCJdNLJXVp6VBTHd4jcODMQPS4XIU76W6+9JLL2lCPQbAMw0LVZsBAwZI20qTAnyNgODksEWUP02RgVhy3wV35TQAnwvQCBgTkUDymmuu1vcgQIwYsYmql220CntaECuchsncc7KHujg4p2Z9lybk9YJ6++VXXykf+TV+b7zxxur2MmzYUHCSzPqLXvSJNAPt8+q2B/csEW7Pi86N3JJYdmHHfOAcqGeeg/bWIQcZD7qeRKkFMy54j34DJ++64kHLf58F2mxbqxDzyczJvDffl2Nh4233LMSPai6+oBTKzTSX1J7ZqOye2aNM1h+W4Oy6Jkti9ULuoQLFFd6U6669Qa697lrp368POAkWu2X65+SFmGtB2USjk6ul4Mllmcx3XXYSpF10he/oJ4KXDsoq26slj8dM7JQvQUr497//jSwJywEAm6P607YyatQohIx0zRDlQRWC0mq+Y1WAmM9ddcMN16v0te+++2nRYvJj1ajikz4zQwKIRV7eWwjbuEIxkybNgJvLo5rehsVrWV2eAds82rfjYrb8bwZA4bhav2aDEk0hnioniGH65MvPlQUFP7+dBKSIZHn5g4fVUlURxyQd/Md7+7b77MVeWvdqsfkuNuhmSas4jUcW65mV1kyXzLrCRCWpJBDz7+J5TrXSBmpd0EVlyEabx6ZqyGN/jQYxJb8r5YP3P9bU1Ndcc60MH0GXCH7OWdB8EGOvWXYAb/2jalo8MLW0JEZezmpi2oKpxxplzCDdLDiRmCV0LiyZVHconc2ZU4VCqr1VJWPKY9YjDPMg+d/FmxnyA3yYw2kJdZLgTMmXrhSdO4N/YayeyxcfdFVI2jyK/b4houdwIZM+mDp1KoDrA9R8fBUS1wayxx57yjBY/LTijweARlIv3tBjokhcUsyvIkXbGFcn6XLhnJoDNIC/jlytxgbjh/OTvoZ+NDl2UYfXUBEVx18SLHzwOe/jjUOWboiGMUtdRGPGfHBifejaQ8lT55+hpYGebfg2333louy6S1In/btnAdTe3R/8fMhGWxQGsdXZxcIPjE83rQVGNZ2zcRfoauXEPvn4c6SmPlsuv/y3CLIlajOtLqyTUL+0u91ECHaOfhFdxyFd3jz0gylIgufnUm8KqWDR86Mgp20MqHDRnFHBHU85IgusDA22Bziqll/Bb+jp/zwtH6AOJnmSncGbUU0bvP5gy57APgqkV+H9dUGoemS0c3Zy5uBuI30VnWX6NnHyI3NalBdKAh8f2Kz9VoAjC/YjQZCHl6SN63ILhIVk3IZAL/uPP/5EXnjhefkKaiOljsMOO1wlMM2669QxnXP0F8S7p0kfnfRuURDjPPdt9pEAue7h3zVrLbR3jUqtWtsxcEQzfkTvHZybNCYxEQKjRijhEUCDooG2IaAe5tq8U1ENAQnUu3Csv+Fmay6I0audPBDhXicSJx06jAtNVxi+oiDy1VffIDX12ZrhddSoTdRHjE6v9RgAG2ADsii3EN0lgmuO51MysEovXNyRCuA5pbJCkl94IsUHO7zo486cWedSbXfkUaoiOIdc9R+raCvzAGYvQyp74skn1arWB7zG3nvvLVvDqjZo0EC9CZP0ketgTeQsuAAAIABJREFUeAn5M52UDItxebpspzXJKwya2b9yS53JIJZGsjXS3Xb7KMcUBXP2RTkiHyxHPDY6pnzW33ARwMV83zr8zbjASZMmqp/XO++8q+C+xx67azEX9g8lM37mqxJlVEc8cEWCWEY60Ykb59D8+wYBexkKzxCs6AqRewMMbniFYTU4nnR74dxgcRvOBVsH0Q208Fz4nwYxTlkvLbBjPZDwc8ae1YHALy9vI+++876cffbP5Zqrr5bNtyAJSPEane1WXpCjCA6fL7hqIBe2ivB5VG06duyoa43gWXghJ+239gx/5Fv4gTNCN/QLNyh+R0GF33HSsTpNzfIGcDftVB2YMXOGvPrKq1rUt6qqSnr06CGbjBwuW40ZA/V7hKpu9JanSmog5rOSGv/hzenZxRPvq9xvXzyoF9F7DsAMxPIJeX5h0z2FahUBiGQ0rbZ+E6PkNR6g/uyzz8onn3yipDUrtW+NLBO9+/RRnzTyqgRDuthkQcwAhW+1IkHM5qNtSsUANhs0ffoMlRp79KCLRXjHSQUivDpwOd1KOKcUHF2MZykxxInjvLZJYlTBqM9zAtJSxGouc0Eyzps/D24hc2TK9CngMGbIsqW1sCA9LXvActS9Rzfo7+vK0KGDZQDUgnWQC4kci485DINYWPeODvYkeEH36dM741AaVUeD5xfDgaU9P9hWLwX4SR1dRJROLUjcKj2VwUeuDguYM1IXMD5bsHChOme++MIL8tbbb8jCBQtl/cGDkVV2Sxm+8XDNtNAZzr1aE5P1CTJ8cXxRlPIuiRM5zwlZiTB/gkoPYk2IflApDJI0LZzz5y+QSZMnwc/uU1Sd+kIWwVgwePAQVbM33HAY1KUeTpL1rgUMts++d/Dfzi7X3NeIXRdVJ/UEpzIXC2ITUYCGIVmegA/PnfAjkzN+ZDcfSurc3BTEqAE5PizNhpYKRNc8EDP1wOtGtsOaukg1sh7xGRxgFkFgHCHF/o8++kglJE5O7jpd4CU9Y8Ys+fCDj2TkyJEabd+2baVQvK7FT69eveBNvR34oO00da+VnyI3wh3ViHIucM3RFZKURN559z1ZHwu7p+bAjxJoxUoj2QmUZuHnA0X/eVTGUb5HJ7/3qKZKGa4MTeMAr2d4ylLwHKy8ROsbHWjnzJktXQD2myEKYNSokXCaXBfJ+3qqJOrbnYmdY7iXkxb4SF/rMCjZkibxpnjfr0Gymmo+jfVZRjrLCPI9LGWNs3q5GeJnijmUMkNu1qHUc2bGf5arY/A8ENKfYN588MGHynVx7PujpBklrs2RRbd79+4WusV+cW4DPqCcIG4GBSPAswvfer40k1EYVKIglkad9P1PZ9d58+Za+iYagDKPsHz/ljgSa0tD9YyaoFFIk4i6/tbn4l2Z6MkOaj+owYq5wnWm2go+a6wHzULDCzdJxzcbXWOl6ArGGOdYR16ytlWYNRKY8UBk8IYJ1slVS+xTEuKPxQwq9wSzm6UtaZSFNUvkxZdeRKqd+1Xsp/8TY8MYCsTOp3sFXQgYnvLE40+Ay9gJ6uTm6l08C74tdDdg8Opbb76luwljDg8++GAN0uXibIJXfyMsTeRMKnXVWTZWTlByoe+8975a9ZhKWEEixwCEp2PxfyXdK/p9dDdLuj6pJfWw3Hqr1OLFi7ARzFTLJi1z06CaMDNpb0ihQ4cMgcQyWGsBDMRPR+SV6gi1BavBBRrDIIC+o9rqDyOOuSl4QHXqkdvJ2b9qHeSicGCVIYjd6uPfVON4cMPyZDff2/5mqm/juDjOBGZudkyOOXnyZJmFhIRUozmnNt98M/h4DVcrI4GLCxozrWAXldq/Sf0f/D4XiEW/D/4dnwuocQp3FNaEYNaTMtAsPssGS840aN1Ug12uLQIVPyGNUAvel/3MBI5M8T5j+nQZP2WGzg1f+ZtcIimIIUOHyLo9usrA/n10Q+D1Wqnc8YbmvW9yat7DqeP++2w/ew41Liys1iBmDpd+f7U89ExLw+rbb7zxhtz5wL0KXusjrGb99deXvn36qoQwbdo0JVyXL6/XzmSWz4cfeQS1+3ZTacynDyHYUZpgFW4O0NcIaeFEZ4UZVpoZNXwjJHtDXCR3JKw7634nHWLyfwSLFf2U1l9/UMBTOc30LDSW8cFKN3ELX5/UyiZsADy85EF1ncDFhINMBTRl2nStZTgV/bZw0UKkepknXbt1kyEAta223FJ6YRx6gUvqoMnywB1h3DqioIQe2jTs6C6bgklHNrF10nIi0wKKNug5+rcn7nO3nLv0clcLlJwWpfGJEycghvEbdQGogdpDyYtcKdtF9Xjj4RtrAD83NX7OZqm1GW2JxMvHHrqmgRgNQXw31nCoUB9A19+qb7iZrVYa8nnlUg2jxjfoO/KkH8KCPW36NFkAlZtgtXhZDSQvhhm1VeMGU4FzbPmb6coG9OsNt52tVBjYcKMNNV8auTM+Wy2hBanQcBIjLxdo0zIbWHg4VnMQ4ws7EIOXOK1js2ZWye3IyXTvPffJwA0GyXe+8x2X8tcIRmaUoOjMXaJtWzp8griG5PD444+pKjQGZDU7npYnnkPQ44TntSRs+ZsAydi8o486XE7+wQ+Qp70rRGRObluBKjKjWZOnTNUdiVIIA5JT6fYJKJK0SFa0JMaJ7dVP20ANRDLuBGg/x4PmdRb4nTVrpm4WH0E9mwKQq0YGB6op7ZD+hVk/aUToA1KcBzePfv36IR1NVwUQcjUEEaaKIU1ASagCz+uIsVTrH3OCOcmLY8fnUd1dgnEjhzcXatLsqjkaiMzx4znliE/kcwZB3aek2LdvHzzfNjmOu0mZ5usXBFAv8SWlDkwan6RNIs33pUpiPkzJV1ZSrYIzWSkGbiAsVkJutK1mRXnlldeRvupx5QbZhzRscHOiU+uW2KAmTZusGg7nwqKFi9RAMqD/AN3MJo7/Buplta4vljQcAx/EgxElsuWWY5xFGwaVSDKCUF9EJDH7LpDWiX8FeR38XQSINcBiNR1vbNlQLa07E7mt+MqHagpGh1fAYXU5wiYILHRYfRPq37e+tb1sNmYzBSlOZKqSlMA4QQlkmgMf1zEdCol+ZrHYdtttNBFdV5iDqyFRUHrg+V2xmLh7s+P5Pf9Nbu0dlI9nzOF5Pz8XUl5vtcpx/M2No0EHieA1YMBA5V+KSb6Xb/ImLYqk76MDW8jIkKsN0fs3Kvdo4KGqvMbo+eLB3Bb5l5KU/FbVD8+RLFy8BOlZlqhUSzcObhKTQZpzgfAg2HBHJnixnTXgJpdhd/d8nS5aPLsjsoN07NhJx9LzW1a02FLy0KyvhhksNBLL/IwgReDq26+ndAAlQPBk3xi9kHUwjfYB5xolEG/1q4gslCTQKUSw6zIM3C9pLHOdbwKq9bGBWjZcJzr28c2UxWewyToLeqU6aGNsyYNxc0LbGFv5MizUDz70kHzy0Req2RCY1oP6yapeg4cMls9g9Bg0aH1ZuGS+dgc3HEq/7FtuLDQazAPQVVcvkpGbjMQmP1kpCI7XpptuJocecohyje3ASVsbfdrtQP8UADG+s22oYVGuKBCbNWsaKT/3s/JAjIjBTDNcTIybu+p3v0dRha8gfe2GnWGoLG+q0Q5WXMULaqkzqA1cbaxyU714qYLURPj6MCniZpttKrugIC0PqjkEOCato1TAfEucyMw4QPWSBC+dQu+5527ZDmLxL8//hfTuta60UYe+5cq3cGfiM/v366+DuSpBLCqjR/3IkqTEGIgFqN/4Ag473nqN34MEpVSCoLWJwA9ve6p6zqlSkxqSIIYUxAB1fsf8+LSWUm3V3/h8CcBwGSoWkachGFF9oWRAwOK/O8BIQzVVJSsS0I541sleEQ5gL+RorPNH22mLg1IJWbE0RxBkoiBk9wkuvGJU/fD5URDz7gy8czHzzjhE0iIwRuBd1ScO19ZjDCZOmiL/REWwxx57Atb77jJ40DDdzGejwhYlLwoNHUCrkDqhJRd5RrX/aY0kp8yNSA1irpYBx6tzp84qpZN/pBT8HzhWL4OEfNwxRyJN1MGQwrurPx7H3ZP+biHn0DbDkliwL9lLg5PCjpi5YlWBWD0JRnT6IgAVw4a++Xq87Lbbd2UkYv4mjp8ole3t5ajOEe3Ja/FvqiCc2PUwAnDSk9h/+OGHNWiYlYIoJnPHpq5OQp9gZV7H3Y2/wbXkT9qhgstiuB08Aj7tlJNPkrHHH6uLrgMkPVpwFqn6Uq8ltmLe/mlWgAPhQpck7d5xm0J4oaQGsQKxk5TCGD+ZPUzl97xFNMjGdlAvrVkxCUtcaKEx2jaqqkqXOJnOuYJoXUbnRa+QqOdlQ3q8imtSFJth/BpTkIeOQjyMu28YxJIUyvDtC4FYfGwcv51nwHOdr0AbkMQKgVjQCmyPoFURPoJYI/QVK4OGQumWYPPCiy/LTbfcAj54gmwBumUw1MZKoBTV9W5QGbl+5oOeId/VDV757QBWc+fOVhzhOuP4MU8aBQIaSjbeaLim5vHcJiU0Chxz586RTz/7TD58713Za89dUVvzdDWIWYZeegS4TSNBnYz2Dce8iLCjVQdipB8XQsW76ndXAcmfkeOPH6uqJX126BPWVIbdGt+3w8Cwk9mZTAVMHZ4S0pQpIPjhpLkQQMQULiTsWQWHAEX1kx73nPys6UgdnwtG+RS1iGGc8DclgAnQ81988Xk5F8V3jzzicOPG0Jv0keH5DNspZjcsDaTSEf3RZ6UHsfzWOQ0AD4CYB9isuuZKx2UAxfrLh1YZqBF0HFC4mZlVydDBVH3wnw8NogQR5a7MtYESmKv0TQlQLW3x6u65wsCCfcRnrzgQi49dofHIvWEFIzJMDfPSdlLCSz6L1kUaxXr37qVEPvv/OSSUvOKK30l7qN0bIQPH0A2GqdFs/rw5almkOr548WKVfBWsIIlxLdWgVmYN1H/+pkZDECLhPx2Wy/btO0rPHuvqfSZMGK88KC2cHP9OuM+0KePl/Xfflk03GwWhYKyW1EsHYvG+HLrx6NjSCgWAUxKbORMENjJRlmF3Vp69hTgxz6NkLSW6n+sAqTUK/37xlVfkrLPPkh2/vaMCEDuNuwjBqx7xj57/4oTmd1TxaHGkmjgVxDtFYKqizCnG6jKjNt1Ed4mly5ZIt3W6KxnJQWJw9PARw7UGIO+p3AuqDFGdYXFQOoDSkZahSzuhGIVW4sZ0WKrg2cVxYn67d5JJATNMkmQVHRV/fhAwwoswPLj5zitWQCyUisc0zbho41gy3fmVuyCo8GTlcwJZI5zaplyaWQ8cQDk5TC8xvs0vUA0PcxKd01LNP4u8DgEysEXz3+rr5F42lxCWa0vwKqeCYESdLGa8siBcbC9nzyvEmXnOMVi2zVc/0pGIcETkq7W9mufafMA++eQzaB+9tYzdEtRnYG62a6+9FlLWIuQ+20NdighafAarenNOc4y54XP+0wCzAM7PFBSWYu3RGllVNVufQ2mNYEXAq61ZrhKfqatQy/FsuriY0Y2UQKUsBEf9MlyjhgwZLJdcfBHonL46XuQ9eV2s7Jsf8Iw0Gu63oiSxmTOnAMRIfNpEajkQwxT31kcPXlQxNBYR4i+kqbPPPRdZMj+DGniAdmzHTh2gXi5Uq9ec2fNVguKOwIEmsHGnoAPrIvg2LcNg9Os3UD768BOkoXlGUwRvjxQ0TDMzd24VAKpOdxCK2ho8zp3fxUBy8SwF2dkNFb69j9EL2LkGDlxPc/X37t0TQGfBr5TELFkex93I12ISB6aa6m5hFwtOGRUsRLwXemJ0qeeX/PJJCv7u/nvLeGD9UeqRS42IgnhUUgv2VXShx98hQd9M8Q7FAF68P8LPj9oVjPO1jcA2hOymEH1eOUoRNjKigpQAsrWQuP/kk8+RuLA3EjYOlgceeUwuu/RSBS2mY+oG1xhfdKUTDClVMJRRm6ETK3ksbupcb6RfZiEsjcJCD1AvS6AqEuQIYqRY6A5DEFwMwxiNNvyM87Ajvmc4G8GwU8fOsDxXyHi4M72NqJDdvrOz/OynZ2jhlHZIWNqghYXTqfKrFYjRqVVVDfxHEvI1VLE597xfwIN6DHI1DVekZpgPQYwkfG0t/F6gLhJwqJ/T65p6Oz8joM2bPxc6+gjsIItRQft2zfe0BzJuNiDHeVUVs9VWqhWGOwh3gNnwSue1nTp3UsmMfNjGw4cLk75xV/oGauWrr76G9Mg/lB+dfqrUATwXLV6o/JpNOrf7rYEglgQSUcAI/x1dkiaJtiyImUTnj2jiPM+72SJ3HJx7KXWbiKBCdOHn46Eyz0vCuEAXpAWxXH2fq72pQEyddQ3EODk//+IbrJO2mOtL5Ze/vkgNYN9BDjSqeqRVSK8Y0HRVR2ByYwvpqoR1xd90k6ETLM/lsQEKn/B8aifdIQjQIbwdQIuaEAUdLWVIr30XYE8Jjuomc/xXwU2KIXALFsyVZ1F28NBDD5CzzzoT4NjOZZZJ0dloy2oFYl4MtoQUTfKLX10gX0C9236H7RUkOnZsj86vUSLduCt0MACNoKfiMDqaHUtTOztx2rQpKolV4Lwbb7xFHV332HM3SGskHhswoMtUleTAEAT5w11l0qRJ2vnt1cTfUV0uODB0y/gK1lEaAn535eUyEsBKC84wxNZRWlMFZg2VxKILLw1nk08ya1kQCwNlLkmlFEksCXiSOMVCIJ8khebq+9JADCqZghiJPnpRVMr0GVVwd3gXhZcfko8//1St9My3T26LktY6AC+6KJGf4prgWiC/TCmNa41tJNHPfGoMMWLGE/LS3ieTQgM1IKqN1Ia4jtTHD3/z8zlwt9GkDIzcQLMaYFAjVfPhB++p5HbrLTfALQO1Ux09kNRnwe8TQYy51mfOME5M1UnusSR1Xfmw6GRK83CNjguok+p7hBsytGgCsggc//0TZAuYePfdZ2/o7vMUMOjaMGAgHOuwOyxHJgafKI88GMGGKiEd8OjFT/+jyagCRH+xxx97SsOKho+ABzHE1pqapbhXB1VdaSbmzqSOl9x5MAjckQhijLHk/QiM9HeiO8ATjz8pu+y0g1x2ycW682y40TBnQTNCu0XUSc8LRTo0qk7mW3xJamfSoi00jtlrvUUyt7qY9R9LMysKn1uIdwqCWPQuSSAUl8yyQeRBKS8rmcWlheZyYuFnW5+G2qssDq2yPmsFf+fPYAGvOKwCF+2ijo3046qT31z8WxTN+Y+M3ma0ptI2VyGzDNKKyFhHgg/5YKqABCjyX8zcQdqEgLQIWgu5aQoL7AGqnkMgtfF7ajRch/xN7YQaDKUzgiTXKYFOs8rS5aZ2GYwHcI3Byz6HmOcRiJ644oorYDzoCDcm08j4Y9ZpnzVF5eyYVJ0IYsxHPwvEPkl98mJhYt86vLlHDMQc0VsLy8ZNN98i/7rrLtl3v/0VtNZZB+Q7zLT0Du4EUpHiaN1yEutLdRD4wgQiSmP0TWEMZdXsWQCganR+o1bMpu/LdtttjWwN87DzwI9lKXLkY+chOPE6giDBymfFJHlJZ0sWHuWu0x/+ZCRJWWVnMQb4T7fcrGZiJoRj52oQcAuCWLD0VbSfPUA0F4zSXpdP2rLFFibWc8+H4jm3fPPJuH23SUTJ7AR1MX7Pwu1RXtzd00AsBouZD/Qr7uvaQNN6g+cnqapmubVr7JmRh+n33sGVD/Mgxs/Cz7KmWGwqBQSLLylHPrSP5Oxzzpce3daVTceMdLVSzR2Jz2Q+uaFDh+oGrk+AOsTQMbpX0Jmc0hQ/I4FPTYRrhkDlc6pRY6GQ0RUcMkGM9ySwkRfji5lmNE36Yy0T1GYDBDUjCj6fivX6DsKbfnHeeXLQ/vsC3Mzgo/UiFNDMchxcD77z2ecbDE+wTq5MEGOsHHV0Zhg47rixGm6yA4K2+SIErfbt21rCOgRmm7OdeZWzI6hvKxkJ0ZedSK/txeCrWAG8atZclGx7WAYPHqwgVldfo6BYW4v84AiK7Qcg4kBp0LfbAfi7I7gxdiAHjdOB4GqTs0yefupJ+SF8x773vaMBqhYeo5WVW0Eshhf5FnHaDbAlQawYDrCQNFvwnYwSzBw2pwpt9Vnk8/MrfHYAwBTQAiCGE2O5y9zznbMJaJAaOGtfBI/8t+AidIwsXFqFzbgc66mDSk5UEdXnCw+vhHREiz7BjLULGKrFtcGD9QVI2PMaCg8ESnr601OfgoP6lUEV5bUUCAh6NADQTYbrlUkX2sJCSX6NPpZ0SF8wb746vj70wEMQMobLDdf+Qfr27qFqaXA38CAW30wJYlvGOjfkYrEyQYwKPEXZaVOng+w7QkZuOlK2RCApU4isP3iQdlw7FGFg55oV0UKMaBXRop2agsXi+UgkzoYk1qtXXyUzx8Eiw47cYYftIOJWKom4ZAm8+3Fo6BFCWMbDr4Xe+wRB7UQMNAeHu49XNWfDrExp7IVnnpYhCMm46aYbNAYwk46lFcRygFgedTMlirUsiIXbFFU3qcJwjvGwSuph6Si4mDJgR+RSI0IEgtzGmA/GiruemOElMssyYZKfpUkPHqG2oU2vv/FfOeus87HJD8T830mmVn2j4MR1MhyGq3ffecdy5DsJLJjxlhpILQQDbvCs9E1rPqUoSmYEJzp/r4t/U4jgmhkIAwEJ/Rkzpms+OmY2Yfu4pghoS6FG0qrJdU66phHUUSN4MlZyp6R22cUXyF577Kpt8epk0EiUK6PxaiWJWZ4wFPZAupfDDz9Cdt9rbwDZpkrCMw8YJR0CFv1YrNpwmaI+O5iiLZPa0QzMkvEEnwkTvoH0tQE6t1EeevARvYbWSaam7gp1cvz4yarPU1fnbsLAb1or52N36Ay3iTo8i97968Gtoi3UTKqa8+HjQh7ttVdekhrsQnf843bkaNrQmb1bkNjHrdYWdTKf6prEU0UX/coEMS5knz6IWkC0QlAUxLz6aZbQ5oEYF2v+67OqtPcRS3J2dQw2qJnb5NY/3S6bb7Y15uoIWbisSrUWGrD8/Pe1Ihi1Ug3AocZD/y7lh7FJW7V5xl+WY11N0ESRS5Ys1c2bGz8BqDfAjC4Y5J4JYtOR6YTuTyytRw2JqmUNeLiFcH+i5Mcg/3Zt2kEqo3dABVJq3SfHHn24/Pi0U9RtiSFJpI80ssOpk3EQg6W0GEmMxD6cHvAi1K6N1M8XAJ5uYhr5qMk3lBCwwNQPkeLm5FNOAeDsoaZfSlucRCTR6f6gRkCc7/krhg7xM6I9CUTuEvRfWYpy8pSgeN0rcJoliDFfGDucwKShRc6Syc7m3wRDqo2MAqiuXqr3UydI/E8fGraDfADB7KUXX5QLLzwfUfr742tLGeP7RndKZwjJtQMb82Gz3Xy6vGSQncjBRRu9h9qenI6ifR7RV5Ii/xqQJ025P1xrz3E+SO5BSg4H7h8MqzJ5IHwExz3K6uQCMS0Jxj7Q59vd2LekEHi9JaLMooHnwvxTfTaN7KIPerSH+SxeSyAKHsxXpk8NSEk+BEqfBf43KIlF30H9SBV0eJNsSJX95XhCN0b2l42XttfNJ8+hOb1J51iusdTucV3B96aAqCFaer7xwV5SpARZUUZrItYosvcuql4mp5/xU4QVfSObjBoh/Qb0k07t1tFit1+D6+Vt6S/G59IqSYMZXSZI6tOvi4kX2Efe12sdrKcpUD/7QjuharkMUhWfz3XGdUEqiOooU6ATAGk0G4ZIAKqv6u2vwf5L4dXfQwWSeRAYaLVkG8aNG6cW/2v++HuorN0gfMD4hvqw1LJQt0mFB1XNIz5yw0ZsE1tiMXVyZYEYg1GJ9A8++LBciSrPBxx0oFpLOJmoHhJoKIJS36boOnjIYOwaVtnYZ3PlIBOYVP9GKh5ex12GNQJ57LfffhmzsHmMN2nOMHr390Ggqp+E7PSpUGu5sAhedKHgTGR7mBWDEfxvvP6abLP1aLnk0otQjNY8xw3EXNaxAIhFl70tAvvxNf702W4bDy7unCAQINNzkcG+fkBsdN0HlG71OrfCfPEIv8D4Hvk4IQ9AoXsHpA//bv77fO3372sTE13HycpsGWiX7rzOudPfJwiUYWdeL7V6ct1WuAGcNSymLnogdnyVZrFgaJMDHEZj+GeouhYVr3wCR/95YBPJ/DMDSrZJmLTGvdpCqLIg5t4wcH6wbw1U7RO2SbPJuo1cZQqCmCvOoe/RiIwgoFrKK9ojuHuafO+47wO0usswWNF79V4XwfUuAQI0EPK95JyHDt0ANM5UXS8cC6qHDP6m7yUdXTshoJvJMdkXNHZRpaTUxnXI9bDRRhtD8kKiCKyLdbp01TXH3HNsL8GOyTIpJOhmiTbzWnOJmqX9wjX7xuuvqzX0FlA0o0YNx7NYsNjyu5U5wSk3iG0dm+arDMToqbsMFsbHkYX1N5dcIsccc7SSgLQ6UqwkgJFUpCWFIMMkiOpch4PgQh2ffi0kIi1ZWy30dQwaOpRFH0ji7/DtHaCb99DBoPvEQKTRoVhNSyQ7SK0tcHhl2FL3bkZg+txjuqOD+KRvDVXYN157DaJ0b7nuuj9qxWedZ76zI5JYbCFj4Ly0FAUx29xNuvI7eHSUlBUJSEoxCThShisOZpZHSycFfjKpoTUZIUO/shJSEFD1FbV9+eDRTgh+nQvE/D38vSkls685sdkWmvO1klV2fYeASAHGAxUXt+sLA4Y4iEVbq15C+jLu/R0QZITaSAB8FMOYuVafn3nTrGxqTTHxSZ1ynaSbkcRcyh8d3cC5JqB5GM22OICP6mbBd1dpxL2/8rGugZoXTKVIcr0d5O13P5RTfngaXJVGyzrwimeNiQp49HONdIb0RJ6YEhKTQ3Jdadwx1guTSJLIJ1HPNcFzvMRlkh9ckwA4ugnj+czyS/WSamdbuG1Qoqb/FyUsTaWkhabJRbdHs5uULyNFQwsl3TRMXW+S1199VS6+6NfIVLMzxp/94zQcRetsRmDfO2zLsBGCth+oAAAgAElEQVSrEYhxsOqx+P76179p4sNDDztM9XGCGJGaIi6JRe4ets7LFGwIYCbaWwUYqoA6SJ0RygCxlmLrawAcqpG77rKr5qCiHxg7kqqovz8J/PFIX0yXDj6D/mV+kVugdxfdTbjrde7UBTvXFDjjfip33XmH9AFY6jwiiFGKYZ8HJTG3WDKL0u3KOt05KXWmmmTkVY4seZtdFP56DZIKgFgsAD0ixcQgh+4yrr90UeBeKgFRxWS6Fp07tjCDEg3/Nlo5uMiCf+H8YkFMBRwDS/MFAgkN6ZZ+eXvvtVe8yQFoNBCzRa/9npFssmqqgYez0TlJJTP5LUV/ZqPgAjJJLJsbLShkRYHYKj5lJb3g935D8XPHw1IWxAzic4F7bDOKnKeSmFbryhbPzeZ9MzCHh4JKYo2NFfLAQ4/J5UigsNMuAIU2FQCuTtK+bUejUgBgHsh9eJHFDdepoWs6nF0tpA6ggzHhdyaJIYsrk2ECxPi3gVMHXTO0ODLPHsn+rpDq+BkrZdEpnedQqlsKCU09+cGLkeumkEE+nPd99JFxcsoPTpITTzgObUNmZqdO6lg2GoiZB4AdBmJj4nMFX2TOonUyo07i4qC0EbvSZnzWp8MNdM7zrAmKyp4T40SuBZl3wQUXyqeffy6HI2OED3NQyyRzt6Nl/Mw3kR1gaXfYETQAdFRQ4vmU7HyU/fvvv49K4B8gRTXCjrBCPSjxt88Iy3MJlMwpplZIgBgnDQdPfV7Q4QQwxmV26tBJU//8979vyfWQxLbYfJQugApMHkrMutBdf+niUBXCxoCdSFJTe8ClmXH7ti0kt3vTkKEVlfVMu1gNGvyXCWr6qaVydplXndpSyQXmMz84gPQL2gSAbCZas6xm1Uf7dyCBoLveAMcVmXDFJLLChJN+dApQ/OeC0nwJDiDtcx4ayMx/uoIsHpAoed12222wpr0hN914IzK7ItSF/wWkSrunZZX13aI9E8ZR7Sv/WQbkFKytKy3BQHYj4LNNwnH5uSjNMJsvAd1ZvT0o8bkcP7/5WMGVbIZYG1jrjyBQ+SLPQZALgpaCnJsi9nLZPvMAqG2klOgWssb9+jTfbhO0GQKNAX6U5//y1/LqG2/Lt3faESBGj/nl0h2JD+j/RV9KzmG/iXP+0xJpFcItJZUPNaJFkZwZJSZyWNOgbvId6crE5JdM+U0KhwHmXDtUS5k1g4DIJAlMmKDGMRgMeH/2K6U7WvY1QSP+pgPtF599LvtgAzvrrJ+oJEYenrozOXgVDiIgxj4aNqIIF4uVCWKUxC6+5FJ5ExkhDzv8MPWQZwoQdhStIHxxghhByocMcew6duiYCY8gKHFAZs2areolwe3LL76Ujz/5WM9bCmKRA0TA84DoVUZf/ICgVYmKOTx4L4Yc8Tu1UJKMhP9ZDQwHNTXVsuXozaDjr6ODShCjv5tJv7aylK9wC9jzPeqTo4OMuoeYmFoyDudSldWJop7NfnWatEESl8/Xic+of05oB4IMBeE9qWbzvM54zyBRzetMfbHFTZrHiugaP2OpbrirIuYN7apAO7y4xcf5FNLaKDxbuQ7nKOkXMBcad1damijT8P5qhSJhT3VCVQZbmMx0UFZh4OuLgTD05Vbktvr8i88RDXGpqiUe0DMSmwNGf6+sSuaXvVv8zAjsnmeSilPetfl8eYV/2yBCG4KXRKHO4nr2sc9p5sGewdJNPhhbM64EuDfcLMMvOknXv3M0v7zNC0Ot4AZjXWzt4+E3DpVYWYBFVckMyqnV0M9bHQsIHlQn6xvK5fQf/0y+RtWqHXfeSaqXVmtu/Dps8iTg14MKuRAqH639zNhKWoX3IaitC9qGVA3pHA3Bw0ZOwxm1Ea4N8tIsb7cr4i9J9s9AvCWbzBx+TIjIHIAMD6SLhvFjSywtj6bxoUDSXi2YNMKxH7ieaTx48/U3ZXMEpV922cVYd+hncGKG1wQxk5LDGVFENtxkdQIx3SXL5O577pVrrr1O9tlnHw3opp7OwSFSe+sgFwdBiIDFjtUwCFzL89kpBDt2aB2sKx4QmI66L9J+sMMogVH05cFJRyKTYDkLRCM7lh0/f95Cdb3QtD8MxcDzKBZzMtU5R1lmw7jyikthbeluOzOyb6gUQ2EY+jx3c7+D8x189lJ+ziXEHYqJFclNsP2+ao/31eFzPSlsKZrNk7kBbea7K99AIFO1yYOeSC14O7NY2SphficvnbA9NbWQVJ2UZCo4Kjs50UXBEPGmZgmzKtl+IavFDrckZ6LAxN0a1/F9uCFo4K/Gv9ki80CqVl4H5BkrJCVIJy3yM44LVf4l2LlHuqK9Xk02ldOr3ZaQz/erl1KCMMbwtCCIaZEKpxlomp6IlGS+YAbo2k6sHN5DQYFyAL5T30Rcy2e3BciTM7J3AmA6NwxKdPy3ljbD+dw8OLYKZFS9tIaA+x2UfvGZV+V5TrD9Ks3pRuMqsOsGh3dQQwiTH2Qz27IOa2MdNtw29J+skD9ec71UYy6wZigdTSmNUcKdDMDipkFaxReBJjipGwXuTamJb8ZxZvsJQAQ5rjWuByYaJaixLif7gTVLzWt/Dlwtemv2CwoQpGyYfYZCiPmaLVarJ7kwtXJifWm2DPxQon3+medkfxjfzvv5Oej7WswltEIl8fyS2AbDE0q2rUx1ki4WtQCdT+D4Nvb735e9EDPJl/SVVZiKmpNiDsKPOLEINuxQn5CN6iYtiVQJuXPMm7dAU+lwcdA1gyZlDoj3OKaE5VPveELfdmXLkTQJaXs5aJQI+FyK7Uy+yF2o17p9tDDG119/IXff/U/pjoHh4jXjC35jETS4ArMmTWR5JNOk+Jk9K6he+IUYVF38wvKSgKkUWdVOr3cAZOoLBz7LmXiVJnhPn8rFE8Vsi0oQ7nJKoWYJy/JlCvhO5eIjvAuCltJTsKP6ZeoGF7Gqie7wIKSL2UmSen8HTmw///2vf/5Tx4khKJRKfZs9mOa6p24qdE4OHL6cm/8o+C78jJuA1Yxk+hjbEFSNJtTrZkPXGowTxtQoDUuFw0WuhhhKd8odokYApAttV0Ci4uap93RxgLyHt7YG+1lBx+X31z7Cv/Uz3o+SDTY4D54ZygBfaKoq3N94TbbNzuNPh3Yce+TtWrQMhVu+kGU4rxusgfWQamiJ74SfmVD9yEf5TZFzl+BM0OI9CYzksthuzn1KZ0wCavUpWQIOaiLWHp1Z+bnJH9iUa1lwB7wa2kNDHOMzeU9y03w2XSz4XE8BqRaCe3rqYyIyzG44bEPVbjp2ZFQODTwGYOSb2yAfGdvmD24+l1x5dWjsdY6VwonlIiaDTwhxAJEAcAUANJggdjTCefbedx/pDcmJQDJ/wXw4y1lCRIIWfxPVKQEQjAy05rnkbQAv7AIMeiXIEYQ44Uj2UyWlUyyLIMxdMEf1cU74Xsh4SUmNuwXBihOYVaHZyQRSdjpJSj6bEQPrInvlG6+9jklQL7f96SaoqYi5VDAxHzqDrPw5n2K9nvBBcPEWc22Qiynm/Og5ha7P9V103Lk47LwYWZV5VPQa/n0juLDx2ByuuOJy7XN/RJ8Zf17Y0BF9n6wV0b6JurzoZ24jSCLX7Q6RsaX0SkDRF9dlFGq7u3Xg3UOrwtpkneYuzV5v6GhttlMM5Lxa5TcTf8fKMljXmU0C7kcnn3Ka1ICX2mXX72rwdjtkXu0INY38FX29yI0ptUGpEmuEc5xkPn29uC4mwrGVHDEFB3JcBDO6R3wBlZ9APRwSMy3JtO5T2qeQwHMIqia9QyOhNkGwAkiyQhWB3W9QTINNWohriud/jhKMe+62CzK/bmZVkUg9sPYlVWYKCegAPs/nAGQ/XHn1jbEpvspATDkK7OrTp82Q7yODxZZbbSk9YPXzFkm1RELSUnEXnUVxlj4udKyjDwvBjJ0/CYVBlDdbUqcEI0HQm/AJdgQ2dlwVVEFLNQL+Cx1MrotSGg9W5CFv0ANqIkVdc+Kz+3A61WHHeR8VwAcO7If02b/VMCbuzq0g5kCimSD2OnyFuMDozxf0ki8VxIoB8hUFYjavw6AWBXdvFTXNkeprAMQcLvpNwTgy5xZDuAzcW+ETVrxyzNOFi6rl2ONPlLZIYTV4yDAFhP5wKZoyeYKqeAQlahVUKbkmLGd+mRLxVPkISlwbjLHkOqKQYPxtpdaj5HWDEeFCTUP5QwgE6jiLNvA3NSD9nNIrVWtnICOHxrqW1H604AvWLdfyAIDlX277i/z8rB/LkUceqVKfSZrZVOlq+VbV2jhcSq5DN95s9QMx+mHRQvk1khDuAKsKgYWFWj03xg43L37jJNgRpj406S5OnzCSlawCTSmKecQ2hjMerYrcASjWkgcoBz9AVCdpzcrG/VC1iPfWFCWumgv/7VUNOvxZ/Ca8kecvlLdgRTv44P3lzDN/AnEZYjZ191ZJzEkV6SQxqqHceMyz3lTl+MLPztW0klgSCK5oSSwkdzkeLfuZl1adu0hkSZoDcjYiwaQwp3LquUGpjaoUQAwAUAdO+IennS6zoGEMHz5KLdpdwQNXzZouQwYPRqzwBAUiSjpUN80Ag6w1cJGgtMW/uR54EGiMRwbPBeD7Gk6wJP1pnWTfWspqVKLCj2pIULO5Jjs5MGObyVdTPeba4r3443k3UkM8nnzsETn/3LNlv/33U7C0uqB8fVrMjZ/09RY8RTFsRBFZLNJYJ0tRJ5VbQcdzQj/11FNy5e+vkuPGHq+gwVhIdixfnMQpUZ9+YCTwKe5ShGUxhKeRKXLSxMny3d1300Ih7737PoJet5ctx2ypUtc0FHZl5Wf+LodDDXcdlpT6/PMvNMRJrSfYgcihaSVoZ0EkAJolzRwcG1Bd/InHH5f/+78fyLEoQ8WK0Sr+toJYs0DM7/A0cnAz8iS7X89JIBTlEKNbc9L1KxPEcrXNS2Ce/wwKV0HV3L+ngZhLERSRxASbt0oxcBH62VnnyKdILLr11t+SeaBkOsObvgyVoBgbybVEYYCqmSZNcMVy1PCFv0nmc95bjVBmeAV5D5DiWBGs1NUIGzvvY1lmrMYFvfPV+IN1xHhJ8xHrqNIf1ysNaOoMC+mLBUnUNQr3Y13LqpnT5LeX/FqL+hBE+b7ecKVo5rjHIM5sNHKrwpIYTZwsFMLYyeYUCikEauoMGkiKaLtxnZaM4m5wIlLdbLv9dup4x47zRUK81Ye5wvi5WYZQKBduEOPGPaod+t3v7q5VqJnAkBVedtxxR+W7yK1RsqN0NWfebAVIWq6Y8rpz5y4qTmuEgOrz5kbAe1Os5siocx++m4pCvhMgHd5++99k/UEDsMMAXAMgpupCxCmvGJUm36JN4rhK/T6pbUn3L3R9Mddynvhq3PZv41RMnbDCtsEjF6dVShuinFn0Xt5tIjs+4WpQYakxLh0l9W8ufjD0vjQmZIw3WT6M56gF1QEZz0HiKpVc2MKbbr5V7rjzblQV2krawNGUxrPevZBOGlIOtQ/GCqt7BM5lJgsCGO/HdUHpiMIDeTKWReQ5tK5Ti6F7Bvk0giDjLdU/ExIdwU2NAFhfrBRGYCSvxsSK1I74ChxXgiav8VZfOsF+8MGHMInVy03XX60AqmubBUeChCINYYGO4b+HbbIagRhBohFWFxKMJNzPQ8HaRRBNN0c9PJ+0kColrY9UPZjUkFwVQ4v4woznGjfuMY0T22P3PXRAHnzwQQWiAw5goRGT3GjFZJD3cuTaJ5jRmqIiMc7nOexQAiUHj857s2bN1F2G1Vp4PoH2OZiCt9t6G/n9H67AbkIVCMYA3TJ9cHwriOUD5JwLWq2jrkoS54GfrFicUUEjCRByfV8MkKYBQUpCwWN1ArEKEPtqLYQk9tTTz8gFF12MMJ7dpQt4rraY67OQ0GEIEiDS0ZVgRpWPLkoMPaKKufFGG6kRgNwVifdFWDOe+KfkRLAihUOgs+wXZQC7KaqiUsLiOuIPDQQ9evSUz1BvkrnG6I5DfovrjeuXRjlaNwlobMu7774rY7YYKeee/VOlgUwSizsRh/MqlMFPLCHsaGVKYqbbm/8Ld5KXXn1FrrjqStl///01LYhaEbE70OeEk7K6GqZdnEsXDEI8d5THoeKxw3gNxdy77rpbweeo7x0lC2BtpF5OVw3l0WBZ5E5gkle5Sm4k7ykFsB3kBzgINBoQCKnqWDhSuTz/7HNy0YW/loMO2g+DwTgzcytoBbE4FBQDILrrOh8q23gt6yg3M/KSvr6kv3sSbRFtRVIbkr6P3291BjGABWuDAgQmg1I57oSTkJ5qY+kGIxXVyeVw0FZHabp04Lf5W0IgwMZO8KEnP10w6KzKdeCLf1C6Iodm/mxlurFzTXqLJO9HLYfFQ5QPAyVDo9ykSZOVd2N1ca4h7yqkHBsoIkpzH374oaa9+uV5Z8luu35bJTreg5Jf0MDDdR5NDrPhJglZLFYmiBEDVF3DDkJJqBqevaeefpp2DHOE0XufHvdEbvVJWW6VkTgAA2B1Ifn/9NP/UZQ//PDDtdDB8y88r/c69NBD1U+HpuAZ02eoH9jSWsv5TSmPi4TPpqmXA+cdPDtjIKjmcNfh/TgwTMHTt3dfWFL+jGtZvp3mX4JvK4g1Vwpi33Ox0OpFPzH2PznK7bb7lkoINMAEKxy1gljWxSOqTpY1WR57phuqRR2KM352pkxGRha6LVSCOhFwYksRrM1DU+gwjz40HKZhXw+JPhmxwbxgtBbyO27w64DSmYkK37T+UxNS6ybWDL8n70XOrAoU0ACM1UysE1oitTAI3SHwHIIeJTAKDFrwGkIEjQm8F8fyq6++1DV4683XSq/uXcwvE3OAwBiqbJUTxFCGMXLkcLGYonxYPMd+esE+zeSDZin33H+/XHfDjZoGmqIqP6OZhSphOfg67hwEtz69+2D3mImSaq8C0b+UvffeS3eW559/ET5gPVFvcnvdFdiBlOroYsE4TbaHznjU39nhXlQmIC1BXUqWiKsGX8YdgG4UU6dMljffeFOuvPxSZKD8jkqMKje4VC5F90jEbO6dTAupYIV4m6gkEeVwktpl7+F4F+eTFORZ+GxfwNYcGwvfMYljYuymOQAzNpFV2OfKJZddJm+9/ZYMWn8gHDbbwwI2XivgnHfez1EibIhzfDVrVSUtKSGeKL8/WtK72/gVLgySJKkVsqTmen4SBxa8xktMwTboMnDOxHFLrUmJXPzs33GPPilXXXUtrPRbIrIEJQ+XAzic2weTf1JVpM8XQ+vIkS1dzPqtzCfWVaUsSmBcX199/ZVuJlbLgoV2GxAB008lOa5DcmOMoaSPGrWXnj3XVbcMEv0M9esFambxEgaOIzIA6ngXCBSkYmpqlsjzzz0rp592qow99nvgxbIAXczYJUpi5rG/akCsHoM0Fx1zwokngRjsi/xGY7QEO4lFVnDpDKc9ghKtjpSomGqHxP1jjz6OjoeKpyWjGmSvvfdUrotAoWKuS9tT6UqyMdTFMmGA2VK1BjsPBnAuwo6oWnZkCmwAJfOCv/zyK7LtNlvJ1X+8Cp7P7ZxHc1sFwJDYm9D7ZmXS5ZPTyTJp0URvHz0/7fVcCNE2BQHaVH3vdJkMYkmTj5sij/o65mOogIHkn3LNddcjc8lBcupp/4c+7yj/uOOfcsstt8nYsUfLj3/8I5UIfJHiSheAbl1YGoC1BIglvW/0+zSbOa/1kROZTS4AYvG5wNAht9NoCN4SOf1HZ8F4VQN+eYzMrWbOfAufYp8SbBhSxDQ5XAeLQLuQa2Z+PT6XmgszHlNIeOe/7xivRZ8vABfz4w8GF8bkCEw/XYb70SpJUOvJQiPINUbJjkIDQXUJAKwOa5KqahXu1x3pgd57579aGfxmlG3r3wexlAG/sGL6dbUGMbr01UGVu+vue+Ta669HnNaushFKTVUBrKiPl0ESoxRGL/yZM2aq4xvFYqbdYSyk17kphXHSkNT3WVvp5NcemSh6ovYeo+6pl3NQSWR6MbZjByaCQ6peWDu7orDIe++9K18iu8bVf/yjfBu5+qlCerUz6ryY1PlZU7lbhOoLE3WIzN4laZ3GQSvtwjaQCgJZUBLzz0+SwIrHFIKYhcdUV9fID089HcWJJ2Kcr5bRW26ulaCngc+5885/gaMZCnA7NARiFT6US6W5qKdUUu/Hvy9FEsvV0wmCanisi2huNl2TnRyUxGLP1yy9+NTFziItgfzxjzfIAw8+Kjvv9B2paUL4EDZqI9iZyooB20x4aE65dB/iuiK3TCGB3/Ec0jh0RqaaTzcl0jeTxsPXDDzzFqNHK4jVu8wr5Je1mA/+7te3H/jqGfrMnj17QYVcqGuK0vScOVXQbN6Qww49EP6WP5WOqKFRmdR5kf5arUGM8W3MFMnCmxddfAlqUU5CId0d1EO/HOjOXEMUgykkqPMqOsnHU7LjKTJTRKaDqzqoQi1kx2qQLh35sGNoILGaci1jAfV7qpQkJ+mHZrs8A5zr5AWIvDt++9ty8cW/gaTQFmK4SQb0WfPZIP6/vbOJtauq4viBFlosFVAwWMB+CP2utoEChUKcENBEwMREBRmpcdJYKiEqohMnKA5IDB9tE0EjAxNwzAAiDyryIVBaLTSAJJZSUwQakgI+aOv6rbX3ufvrnn1u+wrB3Nu8vL57zz1n77XX/u/1vXrwozGhGlWRbDSZRJmnG8S6QWlUyas0zi5JzCow2BhrQNZnLEj4JllNl+DId8VccJ1WZ7jzrjtEAjjN0lLEv7J/vzhhxFtM5QgDWVMnyQsuAW5f+ufSy+Grk6X51iStUdVPf+iVJLFcCjcamZ8MlXJas/W5Hc2G638kwanzm9mnnmwdv8V4jwSF1IS6iEdSs2AIaxHhAYeZk791n9FIh1I5S5ctlZ9lqlY+KHGZHORfkma8GqIk4ERmDRIc+4LCo9jTqNtPQdHjpaa+Bo3Lvpwmi/jSiztFO5rUQoirVn5RQ5WOEohZ89zDiRMblamixRUKYgcDaF586Z/N+g0bVAI7//wLBPEl4M7VDtsr/e7mzZ0nmfT79HEWeSxeDQErdHFfAgWDP0DHomnVCHEgsGjaGNelImE34zqkOOLT/iXVLvFuPvH4X5uzzpjT/PrWW0XyO11PEjaijdcvdSg51UEn2oTco3ACeZVzGB1rn7dMXxHlfM0uX9omMqYiM/nAysJcS4DA4yCN/51ec0ASe2meekAqyL4nFUGuvfY6dcFv3LxRNs8sTes6bjpOEyeh4pIiaRsrD++ptGFAxmsgNeq70YHQhwdHlcQsQbtm+et6cs4zEe/b5NqDg/9b/mwoMXvJOeE1/Z7a9rVQAGWj3n3vg+aee+5t7rn798080WYWnnOOmkCwZ70mJXEwyVA+B2lsUg53AsiJwsebqIeG7CnqvBFusXLlKu16j2azXbyKOLwuueRSrRCjrd4kHgzpCwDDdoaQwN5k75E2CLgRVP7vPbulRNYLzfXr1zXXXvNNPaBonEtFznA9Qiq2gO0PVPmwV2XXtnkuBjcI1NEopGvZ+pxY4UJCPJKxqW01KaD0jOQq/lTSkUDy1atXSwoFhH9bAUmD7oSAeFusNLUF07EZSXXA80VFV992HT39HdH7tVolIrQQGmkOl6+qmgJsRHzhkdnz2m7pynKc9O77sdjlVqlx0+WmDp1uzUbVR1rRcBMnCeYPShtjxFfkmNUNqioVBq/cWBx+Hl+bPmsALN5cVQIVC9iU1GORAN5pvvPd76skcNemOyV2aI5IA9MkenuvdOnZ1KxYvkyaKH/Faq45SUzLhQQvDqywXloKwlUgq4C8Ro3HuymSng9LeW8dE5YraXXVDIS95OUl9Eh9BNB0H5ZBzDAMddLADK2lkdixPXteb9avv6HZLeaYc8W+bBLu8aoysm+AZKSlN725Rr4LcLInCD7f8ugjUs5nptbeJ7YMSezvkrD9uny25qI1alvDCUCdOIQNSvS8IYZ9Ch8yH6rDEkuJtrNPQpW2PfesmIjWNj/csF7ql31Kx6xWAhf+UZL6lS4Oyj2PLlzWwzv5UYGY2UwsJZGFmBQw2i5Eu/32O7R7y1VXf03DI/B6vCG9KQEo3PGAEAvjq7wyWcusP9A6AjRMQ04oDPcAGgAGo5IbRrULIpT/I7XFnt/xvKQxvSLNC26Xllcr5GT6rxopKezWtVGONoiFTgH+n/ZFzEGpuo2jC9Lvp/MJVcqBRDm4BTRnTHaf0hZ3ByIFJAXIfnv375rfiBf6e5LGdfXVV2rpls0bNzd/uPePYtj/ljD6BsSvFsSsFUv8vHZTw+Q1nTchR+1QCavL8lVPb8Oc0fIHTOB2ZbAdECm9yFDQ2xlIeWnEOlLF9dRCm2r2dMVbqwBLVoy2W6Nf0LQZzZNPPt38/Be3qOeRVmrwP3uDH4AMDeY4uR6P/Wzhc+Ii4fdd0kjn2Wee1tzLcyWFj+cjudGzEg/n2rWXqMCB1kRmAEn8cyQX2dffI0yKpj5UopiU3Oi/Pf1Us2D+3OZnN9/UfH7BPFFXSV1yjVqCA0OdS6GG4g6bVgMR2ixZsSZj7uHNcz9kSSwEsQOyGVA3iNnaJXmPmzZvarY89ric0isk/mWFnhgAkXZF0h53khkvMV+IyQTHtieazB43MnlgkyLW0hCUU4UicKQW7REHASVKAMGnRIVEfL5+/Q+aq678qqo/GJRxDkwX13AX6x59EIuN8L54oF/NtHRPbVOnoJUCTw5isRMi/Ny0ILOdeWbLn089L4KKKaYsRfX2vd385Kab5JDaJpLYGVpccveu1zSn7mZh9EsvXeskFDvYrPJX/DoSG1m11FEJFFtJajTQ9LTyQOSzEzTNSqWxRBLT+myD2mexw2Xg3fbUoJ4dGSRai1+ADOlo1ixpvyaeYDqAPTjxRHPbbbdpRD7pQBjfKVdFYjZjOgHziuwLAlT5Gxs0Ti28/ytXrVS7MyC3U5xcOMWWy/7TNCEREs23VXkAAAyCSURBVE4mjEnTiww84SMKOuDN1LQj2b8vSIXluXM/19wghvwlixda4UMsoqSaMX8H5DrPRGUPJVTQjUsWLb+wDmKaAC42sTROrEXD7BaH90Zq3LZNANMayyIpYfB9X8AHoHp4y1+ajRs3qqp42WWXtRn1gJbGt8giYNjHa0Lmva+6CcAhleHlpAyvz79k1HtlUXA3kyqxaMHcZt26dc15551rpZ+dW1/zKonqH+G0DzdYRB20gqKk4kEgZ1JdZGHq9nuARli6xTHBKKsQ2cSGfNE2H+NK1cnSGAcgViIT98BYTPClVnqW2D9sm1uf2yrNV3aqXQazAZVDzxbvpNV9N1ppYr6b77DDoqQOh5ufe6V/96FXCtYe7NPn1Zw08X0Gjp3WxupMpF514reGWTgpReVbp1L6Te/n5Cs+6NiQxNRpJUKA9owQMDz2+OYpCSr+5S2/EiP8B828efOlZdvZWp0VwPqEdO4i5osDnm5gSGMTj0xoAxea6AA6+8X7iJeRFnAXrblIOZgMlxni8X+HQ17zXiXXEsebfIoK+apUcn1RCi2c+dlPNzfeeKOaZvBQWuViO9TQisKE79RM3NItsIn1UieHVbE4LBCL9ZCYb9zA/Js6gY7rJWBfCXPf/fc3Ew8/rNeulDzLOeJ50eqccgJRJ4wFoQY9LaRQMWEGGh9gxEcF5eQjtAKX8StSdpf4liukWcFVX5bmvaKeWvXP3K6TqlThZIaZWFIbl17n9fxIbLa7tUycqSyj2LB6bE8HpqGUEH6LzdWCmELJ8IKPJamtBCrhdZqKouqUJX/rSS5/Y1fhs1BS0iqgbhN3jTdej9j7aKpa/0BlP/9hz0sp3CX5ehU0pW90Dw5N+fG2L/UyOtAK1U0n6rq18cA8cBqYhB5DwUEtvT2jmZh4VFT4O+TweFNszBdqyBER+Qckoh8hgL3Fiz2zfft2jcpHJTwo3kScXbxPmSvUTQqIIjR8RlTIE06UTkm7X9UGufzGCUZnsJclWHbF0kXa4Zsu4SXHSMo7PTh3BEmMDuBJt6NRQaxkGckccgEypCCWXjvpmjTg7SAQ76EHH5KFmbB6+3JSz5+/QKWn08VT0pYVBvHl6H9dpDdiyuiC5HvqnSoxY5dffoW6i/HOSBsPZQ5f8C1iTO81c1QuSgThhG0yA0O9gob3rtmF4f0tuNGrZQMGbhc1IUa3Ib4HK2Qglp0vw0GscPtsXZNrVDIN3vONMcImEKHqEM5Py0gHKpcH+wgUSmMKQMtAzEYZ/n8YpTIQq5A0nH+qYQyTHkcBsXb+NoFOEEtNDVjPJ0UCmymewx07XhAgu7PZ8fxOjeFatHhJc4oY2dkTaD1GW8lTFvA6ReLBCGSdKeFFZMygJkJCTDN0FMfTj5Y0S21rtH2brXGVABmmGtrwXfONr4ut7DTVJAixQeryPTP9WvTg1uiS/urkVIBYQTzptNWoSD1gh/Tag2orsEqT6P0AFbo8yav/EAcAPy+//JKmGSnqyw/EpXY4GfTEr3zypNlyKnxBbGvLRaReoLq7r946DcAjDkxAz9c2ijZKwKk5Y5aX4uMiiaWnt/eY2YrEkphD4HgPBn+VTtf0QLOGvYNGIF4SY81Y1xBoSpJYptonvJaCFteHDWdroJuCWKcpoQefVyWOLkksAC4TzgZ0a9VRd0SUJDG2FPxM+MSxEsayT9TEiUe2NPfd9ydJGN8lIURnSUfvhbpfMPZzLfvqLfE0UnVin6QUYRdTuxlFRekChsdRtBrq3zO3t8TRtm3rswpsq8Uc821phH3hBRdoGzZtxSb3Jh6T74avKl0K26o/iE2BTaw0wJrBOfw8vfYDV6bD6g5ZATUTue30wO4FEXl5laRVS+QaksHRwRGNEdt9WzE/Tsnqc9JQTrlep2kmfcSSlwKFVyXdiee/4pmxnZN8EKqvNcN9jRmKwGJ6jsOkfFvbd8wIG7XNGvXoHHJ9STqK5+/GZMZSkxLc75okms63dn06xGH2tNJUanxeW5uQB9prA3XSz9s7Y3IQc3dwQBg+T6VCv8rQkUKf2Jzlh07cj0nfiAce+LN2A8cwj/RF9VbfX5J9NsOl7XHAY4hHasM0gydyl9iT94tDbVLiwBYvWigpeudLgPjFUn+MmnsWmoRGpw1IaNSr7yW14tJDIBxza3qBB2xP9AKxviEWfRdnFJ7vArHUIK79+PRkihncP682vozRA4Wnz3fr18QgNlDHh0XBD48Tqz+rpLwPKF8GseEAFkpmBmBT1wSl3ZSoeAFz1A64Lj6q0Sf9bi48JfQLT5DCgwvmzOiq6PNhBtOuCUU2MZO+vFcznWtb1cJt/hAUoalmO9hRpSWrATLShTDqc9833nxXtZjt27eJV3KrVkwmbhIPPofHiRKeQb4xUhpTIcmb10kSD3aW2KOXid3rUgl+PVOCw2eKbY28SJEi1Las50/RkWWjzIQDHaWZVfisbSsYxNQtnsoQi1EZpw+YdYHYMa45rb+P7/pip7dSJHqEJ8Cw5+andfemD+8TSgzD7//xBbGYlC43z010KtbdS8pIBWZD6sMdw68ZdUyZqSIJbu06Evwm86NRXgjB2G3C8PORZ5ca9gGFBPT9PclyGYxp0HTE2+asTbOzyTpQIV1I1Xl5/8ABifWiQbD8Tf/IXVK5hfaElHLHHPP++wc1XMI6GVn3sfnz5mvC+GniFKNwImli07XuWKMt3fAm47Eklowsgr570Ev/WpEDj7y2RLMKyzaNQ83HGsSIhcmAxKN5gNrtNZUTMGP8gNi1TfH/D2LhttQTIiBrt9TXZ8OGalN6+PT5fnpNbb3y67N3Mt4aNo6S4T5T4UbgpeJzEhBru78n0hbfHfQD9bmuBhotiCnIoouZVETlCfpEaviKAM306ScoQGlxUCQ3AQyKU3I19uSDAmLac9OlQXn11KQsqwmoZhLs1XSYJ9SWcWKyAYQ0fqz8yiQxdyCkntqRQOzQgUlJFCUDnZQmulYrOdwPqBirFaMyT41BI8N+EguVRm1HqRgezLoekIBa11bsmtcw9TUFWP4eqJDh/4erkx4sSovbPbVuYKkFd9Ykk/AwLQF4+P1htCupi3a4Okm6Q+2wy2r2uwGFTB2xv23so6nb+RwG0kQZxMJn+z3j34ufXdIAShqIqVNmp6WMu7dLpva6VnoJBJ5wjK5yXDtAAIwCBgCYr7oaai3cxpxdpOeJlCedxaGhNgMG5DTWy9ZNvY3cC3oryLm5IjWqDS6nfMQrZtBuX16qbYHSLeDgO4eaJcsvzrZCFLF/SEov75X8QaLlrbpmaISjpT1R1/FDuzbXkXxWNQD6DeAYHK9W16sGuKFSEIKP2wru1l0bbsBFo4JQKo2UbAWj0L0215ROo1yfgVhBnSp5D5OtnPBRCjSxCuJtJMbTuXriu237m6o6EoBeaorI6JvmSibPOCSJ6+ErBvV07Cl1tSTh4M1k+BpMXPhYQUw9uIYEBjT8+FpwHtTz52n3qBZSYsqn9EuDmeM9z9PodG8AZlsuzCtN5pYNhbl1HCAlbSknbntXxr50Bdkc8StOOwLEJAbLG8zjHL1UEsvMUEeCWdl3w3gSPvRR3P5CL/LapsqNhKNu1HAxh4FYy/xcEDCePT+Cmcrf2egiI2cNVGqfZ8SsqdY5sdp3dG5TrE6WxtclK2mgh9s8ltHRLd206og8SKWESvXQOj2DwzwBbZUkOzg/ldyyDVjY5P6g8LxtZZxsHTRhWsHEnpoe9uHzuCYHrRSQu0FOk764Dw9LwL02N2eJOyJcCNfGQKySAE6N/f0SplAedL5U3ct3RGOHYtENSuZBfb4DsBoj1j6PFqgkXSjjMKQesx6R0blnOL8udUZHUAGlmnqYb6SYujX1s+v7fdXJUDqxdRzwVwkUQsmqpJKFY7JUHC+pxF2lbS8ONzYbfeMqFsdo4vrgFZ9XFRBL9n5d+BhIXH6t20Na+cpkLK96xQELmKB8ypZclQSXGvfGr1QSS/cd+0Kb+fDPaiW1N1BDUwcpbQ2yJ8b7OrMfhtebShq+Tp8zN2U/7G8DsgJiuEfpnKKvjOKZLJzd8EN/wwHLEbu4+g7cPy/fyX3vML7uI6dAl+zE4LpBbmqHn4yFP6PHd6JEPpRUHUtRJt3T1amizroxVsC/SpcSqGX3rAwo6UmqqxWCWBgPlA3Igkyq4xxfMKbAmAJjChw1ChQgaAxiR43a4xuPKTCmwJRToA5iU/7I8Q3HFBhTYEyBo0qBRBI7qs8a33xMgTEFxhSYcgr8D4iUisfLu/OxAAAAAElFTkSuQmCC\"/>\n </p>\n <p>\n  <em>\n   Do\n   <strong>\n    not\n   </strong>\n   allow a bowl shaped down curve for\n   <strong>\n    MP3\n   </strong>\n   .\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  Constant, non-zero within spheres ✓\n </p>\n <p>\n  A clear, non-zero positive minimum at C ✓\n </p>\n <p>\n  Symmetric bowl shaped up curved shape in between ✓\n </p>\n <p>\n </p>\n <p>\n  <img src=\"data:image/png;base64,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\"/>\n </p>\n <p>\n  <em>\n   Do\n   <strong>\n    not\n   </strong>\n   allow a bowl shaped down curve for\n   <strong>\n    MP3\n   </strong>\n   .\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   V\n  </em>\n  «= 2 ×\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      8\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      99\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       9\n      </mn>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        3\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      60\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  » = 6.0 × 10\n  <sup>\n   7\n  </sup>\n  «V» ✓\n </p>\n <p>\n  <em>\n   W\n  </em>\n  = «qV = 6.0 × 10\n  <sup>\n   7\n  </sup>\n  × 4.0 × 10\n  <sup>\n   −9\n  </sup>\n  =» 0.24 «J» ✓\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    MP1\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  The restoring force/acceleration is opposite to the displacement/towards equilibrium /\n  <em>\n   <strong>\n    OWTTE\n   </strong>\n  </em>\n  ✓\n </p>\n <p>\n  and proportional to displacement from equilibrium /\n  <em>\n   <strong>\n    OWTTE✓\n   </strong>\n  </em>\n </p>\n <p>\n  <em>\n   Allow discussions based on the diagram (such as towards C for towards equilibrium).\n  </em>\n </p>\n <p>\n  <em>\n   Accept F ∝ x\n   <strong>\n    OR\n   </strong>\n   a ∝ x for\n   <strong>\n    MP2\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   ω\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msqrt>\n    <mfrac>\n     <mrow>\n      <mn>\n       32\n      </mn>\n      <mi>\n       k\n      </mi>\n      <mi>\n       Q\n      </mi>\n      <mi>\n       q\n      </mi>\n     </mrow>\n     <mrow>\n      <mi>\n       m\n      </mi>\n      <msup>\n       <mi>\n        D\n       </mi>\n       <mn>\n        3\n       </mn>\n      </msup>\n     </mrow>\n    </mfrac>\n   </msqrt>\n  </math>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  use of\n  <em>\n   F\n  </em>\n  =\n  <em>\n   mω\n  </em>\n  <sup>\n   2\n  </sup>\n  <em>\n   r\n   <strong>\n    OR\n   </strong>\n   F\n  </em>\n  = 1.33\n  <em>\n   x\n  </em>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <em>\n   a\n  </em>\n  = 53.3\n  <em>\n   x\n  </em>\n  ✓\n </p>\n <p>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msqrt>\n    <mfrac>\n     <mrow>\n      <mn>\n       32\n      </mn>\n      <mo>\n       ×\n      </mo>\n      <mn>\n       8\n      </mn>\n      <mo>\n       .\n      </mo>\n      <mn>\n       99\n      </mn>\n      <mo>\n       ×\n      </mo>\n      <msup>\n       <mn>\n        10\n       </mn>\n       <mn>\n        9\n       </mn>\n      </msup>\n      <mo>\n       ×\n      </mo>\n      <mn>\n       2\n      </mn>\n      <mo>\n       .\n      </mo>\n      <mn>\n       0\n      </mn>\n      <mo>\n       ×\n      </mo>\n      <msup>\n       <mn>\n        10\n       </mn>\n       <mrow>\n        <mo>\n         -\n        </mo>\n        <mn>\n         3\n        </mn>\n       </mrow>\n      </msup>\n      <mo>\n       ×\n      </mo>\n      <mn>\n       4\n      </mn>\n      <mo>\n       .\n      </mo>\n      <mn>\n       0\n      </mn>\n      <mo>\n       ×\n      </mo>\n      <msup>\n       <mn>\n        10\n       </mn>\n       <mrow>\n        <mo>\n         -\n        </mo>\n        <mn>\n         9\n        </mn>\n       </mrow>\n      </msup>\n     </mrow>\n     <mrow>\n      <mn>\n       0\n      </mn>\n      <mo>\n       .\n      </mo>\n      <mn>\n       025\n      </mn>\n      <mo>\n       ×\n      </mo>\n      <mn>\n       1\n      </mn>\n      <mo>\n       .\n      </mo>\n      <msup>\n       <mn>\n        2\n       </mn>\n       <mn>\n        3\n       </mn>\n      </msup>\n     </mrow>\n    </mfrac>\n   </msqrt>\n  </math>\n  » = 7.299 «s\n  <sup>\n   −1\n  </sup>\n  »\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  the net force will no longer be a restoring force/directed towards equilibrium\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  the gravitational force is attractive/neutral mass would be pulled towards larger masses/\n  <em>\n   <strong>\n    OWTTE\n   </strong>\n  </em>\n  ✓\n </p>\n <p>\n  «and so» no, motion will not be the same/no longer be SHM /\n  <em>\n   <strong>\n    OWTTE\n   </strong>\n  </em>\n  ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion",
      "c-wave-behaviour",
      "d-fields"
    ],
    "subtopics": [
      "a-2-forces-and-momentum",
      "c-1-simple-harmonic-motion",
      "d-1-gravitational-fields",
      "d-2-electric-and-magnetic-fields"
    ]
  },
  {
    "question_id": "23M.2.HL.TZ1.7",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Explain, by reference to Faraday’s law of electromagnetic induction, why there is an electromotive force (emf) induced in the loop as it leaves the region of magnetic field.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Just before the loop is about to completely exit the region of magnetic field, the loop moves with constant terminal speed\n   <em>\n    v\n   </em>\n   .\n  </p>\n  <p>\n   The following data is available:\n  </p>\n  <table border=\"1\" cellpadding=\"4\" cellspacing=\"0\" style=\"height:114px;border-color:#000000;width:273px;\">\n   <tbody>\n    <tr>\n     <td style=\"width:153.533px;\">\n      Mass of loop\n     </td>\n     <td style=\"width:95.4667px;text-align:center;\">\n      <em>\n       m\n      </em>\n      = 4.0 g\n     </td>\n    </tr>\n    <tr>\n     <td style=\"width:153.533px;\">\n      Resistance of loop\n     </td>\n     <td style=\"width:95.4667px;text-align:center;\">\n      <em>\n       R\n      </em>\n      = 25 mΩ\n     </td>\n    </tr>\n    <tr>\n     <td style=\"width:153.533px;\">\n      Width of loop\n     </td>\n     <td style=\"width:95.4667px;text-align:center;\">\n      <em>\n       L\n      </em>\n      = 15 cm\n     </td>\n    </tr>\n    <tr>\n     <td style=\"width:153.533px;\">\n      Magnetic flux density\n     </td>\n     <td style=\"width:95.4667px;text-align:center;\">\n      <em>\n       B\n      </em>\n      = 0.80 T\n     </td>\n    </tr>\n   </tbody>\n  </table>\n  <p>\n   Determine, in m s\n   <sup>\n    −1\n   </sup>\n   the terminal speed\n   <em>\n    v\n   </em>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [4]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  The induced emf is equal/proportional/related to the «rate of» change of «magnetic» flux/flux linkage ✓\n </p>\n <p>\n  Flux is changing because the area pierced/enclosed by magnetic field lines changes «decreases»\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  Flux is changing because the loop is leaving/moving out of the «magnetic» field. ✓\n </p>\n <p>\n  <em>\n   Need to see a connection between the EMF and change in flux for\n   <strong>\n    MP1\n   </strong>\n   .\n  </em>\n </p>\n <p>\n  <em>\n   Need to see a connection between the area changing or leaving the field and the change in flux for\n   <strong>\n    MP2\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  The induced emf is equal/proportional/related to the «rate of» change of «magnetic» flux/flux linkage ✓\n </p>\n <p>\n  Flux is changing because the area pierced/enclosed by magnetic field lines changes «decreases»\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  Flux is changing because the loop is leaving/moving out of the «magnetic» field. ✓\n </p>\n <p>\n  <em>\n   Need to see a connection between the EMF and change in flux for\n   <strong>\n    MP1\n   </strong>\n   .\n  </em>\n </p>\n <p>\n  <em>\n   Need to see a connection between the area changing or leaving the field and the change in flux for\n   <strong>\n    MP2\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   mg\n  </em>\n  =\n  <em>\n   BIL\n  </em>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  I = 0.33 «A» ✓\n </p>\n <p>\n  <em>\n   BvL\n  </em>\n  =\n  <em>\n   IR\n   <strong>\n    OR\n   </strong>\n  </em>\n  ℰ = 8.25 × 10\n  <sup>\n   −3\n  </sup>\n  «V»\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  ℰ = 0.12\n  <em>\n   v\n  </em>\n  ✓\n </p>\n <p>\n  Combining results to get v =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      m\n     </mi>\n     <mi>\n      g\n     </mi>\n     <mi>\n      R\n     </mi>\n    </mrow>\n    <mrow>\n     <msup>\n      <mi>\n       B\n      </mi>\n      <mn>\n       2\n      </mn>\n     </msup>\n     <msup>\n      <mi>\n       L\n      </mi>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <em>\n   v\n  </em>\n  = «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      040\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      9\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      81\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      025\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <msup>\n      <mn>\n       80\n      </mn>\n      <mn>\n       2\n      </mn>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <msup>\n      <mn>\n       15\n      </mn>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </mrow>\n   </mfrac>\n  </math>\n  =» 0.068 «m s\n  <sup>\n   −1\n  </sup>\n  »\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   between steps if clear work is shown.\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter",
      "d-fields"
    ],
    "subtopics": [
      "b-5-current-and-circuits",
      "d-3-motion-in-electromagnetic-fields",
      "d-4-induction"
    ]
  },
  {
    "question_id": "23M.2.HL.TZ1.8",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Photons of wavelength 468 nm are incident on a metallic surface. The maximum kinetic energy of the emitted electrons is 1.8 eV.\n  </p>\n  <p>\n   Calculate\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   the work function of the surface, in eV.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   the longest wavelength of a photon that will eject an electron from this surface.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   In an experiment, alpha particles of initial kinetic energy 5.9 MeV are directed at stationary nuclei of lead (\n   <math class=\"wrs_chemistry\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mmultiscripts>\n     <mi>\n      Pb\n     </mi>\n     <mprescripts>\n     </mprescripts>\n     <mn>\n      82\n     </mn>\n     <mn>\n      207\n     </mn>\n    </mmultiscripts>\n   </math>\n   ). Show that the distance of closest approach is about 4 × 10\n   <sup>\n    −14\n   </sup>\n   m.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The radius of a nucleus of\n   <math class=\"wrs_chemistry\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mmultiscripts>\n     <mi>\n      Pb\n     </mi>\n     <mprescripts>\n     </mprescripts>\n     <mn>\n      82\n     </mn>\n     <mn>\n      207\n     </mn>\n    </mmultiscripts>\n   </math>\n   is 7.1 × 10\n   <sup>\n    −15\n   </sup>\n   m. Explain why there will be no deviations from Rutherford scattering in the experiment in (b)(i).\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Use of\n  <em>\n   E\n  </em>\n  <sub>\n   max\n  </sub>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      h\n     </mi>\n     <mi>\n      c\n     </mi>\n    </mrow>\n    <mi>\n     λ\n    </mi>\n   </mfrac>\n   <mo>\n    -\n   </mo>\n   <mi>\n    ϕ\n   </mi>\n   <mo>\n    ⇒\n   </mo>\n   <mi>\n    ϕ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi>\n      h\n     </mi>\n     <mi>\n      c\n     </mi>\n    </mrow>\n    <mi>\n     λ\n    </mi>\n   </mfrac>\n   <mo>\n    -\n   </mo>\n  </math>\n  <em>\n   E\n  </em>\n  <sub>\n   max\n  </sub>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    ϕ\n   </mi>\n   <mo>\n    =\n   </mo>\n  </math>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      h\n     </mi>\n     <mi>\n      c\n     </mi>\n    </mrow>\n    <mi>\n     λ\n    </mi>\n   </mfrac>\n  </math>\n  −\n  <em>\n   E\n  </em>\n  <sub>\n   max\n  </sub>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mfenced>\n      <mrow>\n       <mn>\n        6\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        63\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mrow>\n         <mo>\n          -\n         </mo>\n         <mn>\n          34\n         </mn>\n        </mrow>\n       </msup>\n      </mrow>\n     </mfenced>\n     <mfenced>\n      <mrow>\n       <mn>\n        3\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mn>\n         8\n        </mn>\n       </msup>\n      </mrow>\n     </mfenced>\n    </mrow>\n    <mrow>\n     <mfenced>\n      <mrow>\n       <mn>\n        468\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mrow>\n         <mo>\n          -\n         </mo>\n         <mn>\n          9\n         </mn>\n        </mrow>\n       </msup>\n      </mrow>\n     </mfenced>\n     <mfenced>\n      <mrow>\n       <mn>\n        1\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        6\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mrow>\n         <mo>\n          -\n         </mo>\n         <mn>\n          19\n         </mn>\n        </mrow>\n       </msup>\n      </mrow>\n     </mfenced>\n    </mrow>\n   </mfrac>\n  </math>\n  − 1.81» = 0.85625\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    ≈\n   </mo>\n  </math>\n  0.86 «eV» ✓\n </p>\n <p>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  Use of\n  <em>\n   E\n  </em>\n  <sub>\n   max\n  </sub>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      h\n     </mi>\n     <mi>\n      c\n     </mi>\n    </mrow>\n    <mi>\n     λ\n    </mi>\n   </mfrac>\n   <mo>\n    -\n   </mo>\n   <mi>\n    ϕ\n   </mi>\n   <mo>\n    ⇒\n   </mo>\n   <mi>\n    ϕ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi>\n      h\n     </mi>\n     <mi>\n      c\n     </mi>\n    </mrow>\n    <mi>\n     λ\n    </mi>\n   </mfrac>\n   <mo>\n    -\n   </mo>\n  </math>\n  <em>\n   E\n  </em>\n  <sub>\n   max\n  </sub>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    ϕ\n   </mi>\n   <mo>\n    =\n   </mo>\n  </math>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      h\n     </mi>\n     <mi>\n      c\n     </mi>\n    </mrow>\n    <mi>\n     λ\n    </mi>\n   </mfrac>\n  </math>\n  −\n  <em>\n   E\n  </em>\n  <sub>\n   max\n  </sub>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mfenced>\n      <mrow>\n       <mn>\n        6\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        63\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mrow>\n         <mo>\n          -\n         </mo>\n         <mn>\n          34\n         </mn>\n        </mrow>\n       </msup>\n      </mrow>\n     </mfenced>\n     <mfenced>\n      <mrow>\n       <mn>\n        3\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mn>\n         8\n        </mn>\n       </msup>\n      </mrow>\n     </mfenced>\n    </mrow>\n    <mrow>\n     <mfenced>\n      <mrow>\n       <mn>\n        468\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mrow>\n         <mo>\n          -\n         </mo>\n         <mn>\n          9\n         </mn>\n        </mrow>\n       </msup>\n      </mrow>\n     </mfenced>\n     <mfenced>\n      <mrow>\n       <mn>\n        1\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        6\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mrow>\n         <mo>\n          -\n         </mo>\n         <mn>\n          19\n         </mn>\n        </mrow>\n       </msup>\n      </mrow>\n     </mfenced>\n    </mrow>\n   </mfrac>\n  </math>\n  − 1.81» = 0.85625\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    ≈\n   </mo>\n  </math>\n  0.86 «eV» ✓\n </p>\n <p>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  Use of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      h\n     </mi>\n     <mi>\n      c\n     </mi>\n    </mrow>\n    <mi>\n     λ\n    </mi>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mi>\n    ϕ\n   </mi>\n   <mo>\n    ⇒\n   </mo>\n   <mi>\n    λ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi>\n      h\n     </mi>\n     <mi>\n      c\n     </mi>\n    </mrow>\n    <mi>\n     ϕ\n    </mi>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    λ\n   </mi>\n   <mo>\n    =\n   </mo>\n  </math>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mfenced>\n      <mrow>\n       <mn>\n        6\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        63\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mrow>\n         <mo>\n          -\n         </mo>\n         <mn>\n          34\n         </mn>\n        </mrow>\n       </msup>\n      </mrow>\n     </mfenced>\n     <mfenced>\n      <mrow>\n       <mn>\n        3\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mn>\n         8\n        </mn>\n       </msup>\n      </mrow>\n     </mfenced>\n    </mrow>\n    <mrow>\n     <mfenced>\n      <mrow>\n       <mn>\n        468\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mrow>\n         <mo>\n          -\n         </mo>\n         <mn>\n          9\n         </mn>\n        </mrow>\n       </msup>\n      </mrow>\n     </mfenced>\n     <mfenced>\n      <mrow>\n       <mn>\n        1\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        6\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mrow>\n         <mo>\n          -\n         </mo>\n         <mn>\n          19\n         </mn>\n        </mrow>\n       </msup>\n      </mrow>\n     </mfenced>\n    </mrow>\n   </mfrac>\n  </math>\n  =» 1.45 × 10\n  <sup>\n   −6\n  </sup>\n  «m»✓\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    a(i)\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  2e\n  <em>\n   <strong>\n    AND\n   </strong>\n  </em>\n  82e seen\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  3.2 × 10\n  <sup>\n   −19\n  </sup>\n  «C»\n  <em>\n   <strong>\n    AND\n   </strong>\n  </em>\n  1.312 × 10\n  <sup>\n   −17\n  </sup>\n  «C» seen ✓\n </p>\n <p>\n  <em>\n   d\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      8\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      99\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       9\n      </mn>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mo>\n      (\n     </mo>\n     <mn>\n      2\n     </mn>\n     <mi>\n      e\n     </mi>\n     <mo>\n      )\n     </mo>\n     <mo>\n      (\n     </mo>\n     <mn>\n      82\n     </mn>\n     <mi>\n      e\n     </mi>\n     <mo>\n      )\n     </mo>\n    </mrow>\n    <mrow>\n     <mn>\n      5\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      9\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       6\n      </mn>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mi>\n      e\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  = 3.998 × 10\n  <sup>\n   −14\n  </sup>\n  ≈ 4 × 10\n  <sup>\n   −14\n  </sup>\n  «m» ✓\n </p>\n <p>\n  <em>\n   Must see either clear substitutions or answer to at least 4 s.f. for\n   <strong>\n    MP2\n   </strong>\n   .\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  The closest approach is «significantly» larger than the radius of the nucleus / far away from the nucleus/\n  <em>\n   <strong>\n    OWTTE\n   </strong>\n  </em>\n  . ✓\n </p>\n <p>\n  «Therefore» the strong nuclear force will not act on the alpha particle.✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "e-1-structure-of-the-atom",
      "e-2-quantum-physics"
    ]
  },
  {
    "question_id": "23M.2.HL.TZ2.4",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the value of the maximum distance between the stars that can be measured in any reference frame.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the speed of shuttle S relative to observer P using Galilean relativity.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the distance between star A and star B relative to observer P.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (d)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the speed of shuttle S relative to observer P is approximately 0.6\n   <em>\n    c\n   </em>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (e)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the time, according to observer P, that the shuttle S takes to travel from star A to star B.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (f)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State and explain the reference frame in which the proper time for shuttle S to journey from star A to star B can be measured.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  4.8 «light years» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  «−» 0.48\n  <em>\n   c\n  </em>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Ignore sign\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    y\n   </mi>\n  </math>\n  = 1.6 ✓\n </p>\n <p>\n  <em>\n   D\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      4\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      8\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      6\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  = 3 «ly» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    MP1\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mo>\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      3\n     </mn>\n     <mi>\n      c\n     </mi>\n     <mo>\n      -\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      78\n     </mn>\n     <mi>\n      c\n     </mi>\n    </mrow>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mstyle displaystyle=\"true\">\n      <mfrac>\n       <mrow>\n        <mn>\n         0\n        </mn>\n        <mo>\n         .\n        </mo>\n        <mn>\n         78\n        </mn>\n        <mi>\n         c\n        </mi>\n        <mo>\n         ×\n        </mo>\n        <mn>\n         0\n        </mn>\n        <mo>\n         .\n        </mo>\n        <mn>\n         3\n        </mn>\n        <mi>\n         c\n        </mi>\n       </mrow>\n       <msup>\n        <mi>\n         c\n        </mi>\n        <mn>\n         2\n        </mn>\n       </msup>\n      </mfrac>\n     </mstyle>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  «−» 0.63\n  <em>\n   c\n  </em>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [2]\n   </strong>\n   if\n   <strong>\n    MP1\n   </strong>\n   correct and correct answer given to 1 significant figure.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (e)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi mathvariant=\"normal\">\n    Δ\n   </mi>\n   <msub>\n    <mi>\n     t\n    </mi>\n    <mi mathvariant=\"normal\">\n     p\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      3\n     </mn>\n     <mo>\n     </mo>\n     <mi>\n      ly\n     </mi>\n    </mrow>\n    <mrow>\n     <mo>\n      (\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      78\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      627\n     </mn>\n     <mo>\n      )\n     </mo>\n     <mi>\n      c\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi mathvariant=\"normal\">\n    Δ\n   </mi>\n   <msub>\n    <mi>\n     t\n    </mi>\n    <mi mathvariant=\"normal\">\n     p\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    6\n   </mn>\n   <mfenced>\n    <mrow>\n     <mfrac>\n      <mrow>\n       <mn>\n        4\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        8\n       </mn>\n       <mo>\n       </mo>\n       <mi>\n        ly\n       </mi>\n      </mrow>\n      <mrow>\n       <mn>\n        0\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        3\n       </mn>\n       <mi>\n        c\n       </mi>\n      </mrow>\n     </mfrac>\n     <mo>\n      -\n     </mo>\n     <mfrac>\n      <mrow>\n       <mn>\n        0\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        78\n       </mn>\n       <mi>\n        c\n       </mi>\n       <mo>\n        ×\n       </mo>\n       <mn>\n        4\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        8\n       </mn>\n       <mo>\n       </mo>\n       <mi>\n        ly\n       </mi>\n      </mrow>\n      <msup>\n       <mi>\n        c\n       </mi>\n       <mn>\n        2\n       </mn>\n      </msup>\n     </mfrac>\n    </mrow>\n   </mfenced>\n  </math>\n  ✓\n </p>\n <p>\n  = 19\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  20 «years» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    [2]\n   </strong>\n   for\n   <strong>\n    BCA\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (f)\n </div><div class=\"card-body\">\n <p>\n  shuttle measures proper time ✓\n </p>\n <p style=\"text-align:justify;\">\n  as the events occur at the same place for the shuttle / shuttle is at both events ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-5-galilean-and-special-relativity"
    ]
  },
  {
    "question_id": "23M.2.HL.TZ2.5",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline what is meant by an isotope.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the speed of the spaceship relative to Earth.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Estimate, using the spacetime diagram, the time in seconds when the flash of light reaches the spaceship according to the Earth observer.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the time coordinate\n   <em>\n    ct′\n   </em>\n   when the flash of light reaches the spaceship, according to an observer at rest in the spaceship.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  «An atom with» the same number of protons\n  <em>\n   <strong>\n    AND\n   </strong>\n  </em>\n  different numbers of neutrons\n  <br/>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <br/>\n  Same chemical properties\n  <em>\n   <strong>\n    AND\n   </strong>\n  </em>\n  different physical properties ✓\n </p>\n <p>\n  <em>\n   Do\n   <strong>\n    not\n   </strong>\n   allow just atomic number and mass number\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  0.6 c\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  = 1.8 × 10\n  <sup>\n   8\n  </sup>\n  «m s\n  <sup>\n   −1\n  </sup>\n  » ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  Line drawn at 45° from\n  <em>\n   ct\n  </em>\n  = 2 km to hit spaceship world line at\n  <em>\n   ct\n  </em>\n  = 5 km\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  <em>\n   ct\n  </em>\n  = 1.2/(\n  <em>\n   c\n  </em>\n  − 0.6\n  <em>\n   c\n  </em>\n  ) + 2 = 5 «km» ✓\n </p>\n <p>\n  <em>\n   t\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     5000\n    </mn>\n    <mi>\n     c\n    </mi>\n   </mfrac>\n  </math>\n  = 1.7 × 10\n  <sup>\n   −5\n  </sup>\n  «s» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    [2]\n   </strong>\n   for\n   <strong>\n    BCA\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  (\n  <em>\n   ct\n  </em>\n  ')\n  <sup>\n   2\n  </sup>\n  − 0 = 5\n  <sup>\n   2\n  </sup>\n  − 3\n  <sup>\n   2\n  </sup>\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    γ\n   </mi>\n  </math>\n  = 1.25 ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   ct\n  </em>\n  ' = 4 «km»\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  <em>\n   t\n  </em>\n  ' = 13 «\n  <em>\n   µ\n  </em>\n  s» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    (b)\n   </strong>\n  </em>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    MP1\n   </strong>\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion",
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "a-5-galilean-and-special-relativity",
      "e-3-radioactive-decay"
    ]
  },
  {
    "question_id": "23M.2.HL.TZ2.6",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mfrac>\n     <msub>\n      <mi>\n       g\n      </mi>\n      <mi mathvariant=\"normal\">\n       M\n      </mi>\n     </msub>\n     <msub>\n      <mi>\n       g\n      </mi>\n      <mi mathvariant=\"normal\">\n       P\n      </mi>\n     </msub>\n    </mfrac>\n   </math>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the net torque on the system about the central axis is approximately 30 N m.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The system rotates from rest and reaches a maximum angular speed of 20 rad s\n   <sup>\n    −1\n   </sup>\n   in a time of 5.0 s. Calculate the angular acceleration of the system.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State and explain the magnitude of the resultant gravitational field strength at O.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline why the graph between P and O is negative.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the gravitational potential\n   <em>\n    V\n   </em>\n   <sub>\n    P\n   </sub>\n   at the surface of P due to the mass of P is given by\n   <em>\n    V\n   </em>\n   <sub>\n    P\n   </sub>\n   = −\n   <em>\n    g\n   </em>\n   <sub>\n    P\n   </sub>\n   <em>\n    R\n   </em>\n   <sub>\n    P\n   </sub>\n   where\n   <em>\n    R\n   </em>\n   <sub>\n    P\n   </sub>\n   is the radius of the planet.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iv)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The gravitational potential due to the mass of M at the surface of P can be assumed to be negligible.\n  </p>\n  <p>\n   Estimate, using the graph, the gravitational potential at the surface of M due to the mass of M.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (v)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Draw on the axes the variation of gravitational potential between O and M.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the moment of inertia of the system about the central axis.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline why the angular speed\n   <em>\n    ω\n   </em>\n   decreases when the spheres move outward.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the rotational kinetic energy is\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mfrac>\n     <mn>\n      1\n     </mn>\n     <mn>\n      2\n     </mn>\n    </mfrac>\n   </math>\n   <em>\n    Lω\n   </em>\n   where\n   <em>\n    L\n   </em>\n   is the angular momentum of the system.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   When the spheres move outward, the angular speed decreases from 20 rad s\n   <sup>\n    −1\n   </sup>\n   to 12 rad s\n   <sup>\n    −1\n   </sup>\n   . Calculate the percentage change in rotational kinetic energy that occurs when the spheres move outward.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Work using\n  <em>\n   g\n  </em>\n  ∝\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mi>\n     m\n    </mi>\n    <msup>\n     <mi>\n      r\n     </mi>\n     <mn>\n      2\n     </mn>\n    </msup>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <msub>\n     <mi>\n      g\n     </mi>\n     <mi mathvariant=\"normal\">\n      M\n     </mi>\n    </msub>\n    <msub>\n     <mi>\n      g\n     </mi>\n     <mi mathvariant=\"normal\">\n      P\n     </mi>\n    </msub>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <msub>\n     <mi>\n      m\n     </mi>\n     <mi mathvariant=\"normal\">\n      M\n     </mi>\n    </msub>\n    <msub>\n     <mi>\n      m\n     </mi>\n     <mi mathvariant=\"normal\">\n      P\n     </mi>\n    </msub>\n   </mfrac>\n   <msup>\n    <mfenced>\n     <mfrac>\n      <msub>\n       <mi>\n        r\n       </mi>\n       <mi mathvariant=\"normal\">\n        P\n       </mi>\n      </msub>\n      <msub>\n       <mi>\n        r\n       </mi>\n       <mi mathvariant=\"normal\">\n        M\n       </mi>\n      </msub>\n     </mfrac>\n    </mfenced>\n    <mn>\n     2\n    </mn>\n   </msup>\n  </math>\n  = 0.75 ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    ΣΓ\n   </mtext>\n  </math>\n  = 50 × 0.5 + 40 × 0.2\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  33 «Nm» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept opposite rotational sign convention\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  «α =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     20\n    </mn>\n    <mn>\n     5\n    </mn>\n   </mfrac>\n  </math>\n  =» 4 «rad s\n  <sup>\n   −2\n  </sup>\n  » ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  g = 0 ✓\n </p>\n <p>\n  As g «=\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    -\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi mathvariant=\"normal\">\n      Δ\n     </mi>\n     <msub>\n      <mi>\n       V\n      </mi>\n      <mi>\n       g\n      </mi>\n     </msub>\n    </mrow>\n    <mrow>\n     <mi mathvariant=\"normal\">\n      Δ\n     </mi>\n     <mi>\n      r\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  which» is the gradient of the graph\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <br/>\n  As the force of attraction/field strength of P and M are equal ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  The gravitational field is attractive so that energy is required «to move away from P» ✓\n </p>\n <p>\n  the gravitational potential is defined as 0 at\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    ∞\n   </mo>\n  </math>\n  , (the potential must be negative) ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   V\n  </em>\n  <sub>\n   P\n  </sub>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    -\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi>\n      G\n     </mi>\n     <mi>\n      M\n     </mi>\n    </mrow>\n    <msub>\n     <mi>\n      R\n     </mi>\n     <mi mathvariant=\"normal\">\n      P\n     </mi>\n    </msub>\n   </mfrac>\n  </math>\n  <em>\n   <strong>\n    AND\n   </strong>\n   g\n  </em>\n  <sub>\n   P\n  </sub>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      G\n     </mi>\n     <mi>\n      M\n     </mi>\n    </mrow>\n    <msup>\n     <msub>\n      <mi>\n       R\n      </mi>\n      <mi mathvariant=\"normal\">\n       P\n      </mi>\n     </msub>\n     <mn>\n      2\n     </mn>\n    </msup>\n   </mfrac>\n  </math>\n  (at surface) ✓\n </p>\n <p>\n  Suitable working and cancellation of\n  <em>\n   G\n  </em>\n  and\n  <em>\n   M\n  </em>\n  seen ✓\n </p>\n <p>\n  <em>\n   V\n  </em>\n  <sub>\n   P\n  </sub>\n  = −\n  <em>\n   g\n  </em>\n  <sub>\n   P\n  </sub>\n  <em>\n   R\n  </em>\n  <sub>\n   P\n  </sub>\n </p>\n <p>\n  <em>\n   Must see negative sign\n  </em>\n </p>\n <p>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iv)\n </div><div class=\"card-body\">\n <p>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <msub>\n     <mi>\n      V\n     </mi>\n     <mi mathvariant=\"normal\">\n      M\n     </mi>\n    </msub>\n    <msub>\n     <mi>\n      V\n     </mi>\n     <mi mathvariant=\"normal\">\n      P\n     </mi>\n    </msub>\n   </mfrac>\n  </math>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <msub>\n      <mi>\n       g\n      </mi>\n      <mi mathvariant=\"normal\">\n       M\n      </mi>\n     </msub>\n     <msub>\n      <mi>\n       R\n      </mi>\n      <mi mathvariant=\"normal\">\n       M\n      </mi>\n     </msub>\n    </mrow>\n    <mrow>\n     <msub>\n      <mi>\n       g\n      </mi>\n      <mi mathvariant=\"normal\">\n       P\n      </mi>\n     </msub>\n     <msub>\n      <mi>\n       R\n      </mi>\n      <mtext>\n       P\n      </mtext>\n     </msub>\n    </mrow>\n   </mfrac>\n  </math>\n  = 0.75 × 0.27» = 0.20 ✓\n </p>\n <p>\n  <em>\n   V\n  </em>\n  <sub>\n   M\n  </sub>\n  = «−6.4 × 10\n  <sup>\n   7\n  </sup>\n  × 0.2 =» «−»1.3 × 10\n  <sup>\n   7\n  </sup>\n  «J kg\n  <sup>\n   −1\n  </sup>\n  »✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (v)\n </div><div class=\"card-body\">\n <p>\n  Line always negative, of suitable shape and end point below −8 and above −20 unless awarding\n  <em>\n   <strong>\n    ECF\n   </strong>\n  </em>\n  from\n  <em>\n   <strong>\n    b(iv)\n   </strong>\n  </em>\n  ✓\n </p>\n <p>\n  <img 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\"/>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    I\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mi>\n     Γ\n    </mi>\n    <mi>\n     α\n    </mi>\n   </mfrac>\n  </math>\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  33 =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    I\n   </mi>\n  </math>\n  × 4 ✓\n </p>\n <p>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    I\n   </mi>\n  </math>\n  = 8.25 «kg m\n  <sup>\n   2\n  </sup>\n  » ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    (a)\n   </strong>\n   and\n   <strong>\n    (b)\n   </strong>\n  </em>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    [2]\n   </strong>\n   for a\n   <strong>\n    BCA\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  moment of inertia increases ✓\n </p>\n <p>\n  Angular momentum is conserved ✓\n </p>\n <p>\n  <em>\n   <br/>\n   Allow algebraic expressions e.g. ω =\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mfrac>\n     <mi>\n      L\n     </mi>\n     <mi>\n      I\n     </mi>\n    </mfrac>\n   </math>\n   so ω decreases for\n   <strong>\n    MP2\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   E\n  </em>\n  <sub>\n   k\n  </sub>\n  «=\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <mi>\n    I\n   </mi>\n  </math>\n  <em>\n   ω\n  </em>\n  <sup>\n   2\n  </sup>\n  =»\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  (\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    I\n   </mi>\n  </math>\n  <em>\n   ω\n  </em>\n  )\n  <em>\n   ω\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  <em>\n   Lω\n  </em>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept equivalent methods\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   «E\n  </em>\n  <sub>\n   k\n  </sub>\n  =»\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  <em>\n   Lω\n  </em>\n  <sub>\n   1\n  </sub>\n  <em>\n   =\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mfrac>\n     <mn>\n      1\n     </mn>\n     <mn>\n      2\n     </mn>\n    </mfrac>\n   </math>\n   Lω\n   <sub>\n    2\n   </sub>\n  </em>\n  ✓\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <msub>\n     <mi mathvariant=\"bold-italic\">\n      E\n     </mi>\n     <mrow>\n      <mi>\n       k\n      </mi>\n      <mn>\n       1\n      </mn>\n     </mrow>\n    </msub>\n    <msub>\n     <mi mathvariant=\"bold-italic\">\n      E\n     </mi>\n     <mrow>\n      <mi>\n       k\n      </mi>\n      <mn>\n       2\n      </mn>\n     </mrow>\n    </msub>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <msub>\n     <mi>\n      ω\n     </mi>\n     <mn>\n      1\n     </mn>\n    </msub>\n    <msub>\n     <mi>\n      ω\n     </mi>\n     <mn>\n      2\n     </mn>\n    </msub>\n   </mfrac>\n  </math>\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  «\n  <em>\n   L\n  </em>\n  is constant so»\n  <em>\n   E\n  </em>\n  <sub>\n   k\n  </sub>\n  is proportional to\n  <em>\n   ω\n  </em>\n  ✓\n </p>\n <p>\n  40 % «energy loss» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    MP1\n   </strong>\n   is for understanding that angular momentum is constant so change in rotational kinetic energy is proportional to change in angular velocity\n  </em>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [0]\n   </strong>\n   if E = 0.5 I ω\n   <sup>\n    2\n   </sup>\n   is used with the same I value for both values of E\n  </em>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    [2]\n   </strong>\n   for\n   <strong>\n    BCA\n   </strong>\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion",
      "d-fields"
    ],
    "subtopics": [
      "a-4-rigid-body-mechanics",
      "d-1-gravitational-fields"
    ]
  },
  {
    "question_id": "23M.2.HL.TZ2.7",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the pressure of the gas at B.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Sketch, on the\n   <em>\n    pV\n   </em>\n   diagram, the remaining two processes BC and CA that the gas undergoes.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the temperature of the gas at C is approximately 350 °C.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (d)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Explain why the change of entropy for the gas during the process BC is equal to zero.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (e)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Explain why the work done by the gas during the isothermal expansion AB is less than the work done on the gas during the adiabatic compression BC.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (f)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The quantity of trapped gas is 53.2 mol. Calculate the thermal energy removed from the gas during process CA.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  use of\n  <em>\n   pV\n  </em>\n  = constant ✓\n </p>\n <p>\n  <em>\n   P\n  </em>\n  <sub>\n   B\n  </sub>\n  = 43 «Kpa» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [2]\n   </strong>\n   for\n   <strong>\n    BCA\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  concave curved line from B to locate C with a higher pressure than A ✓\n </p>\n <p>\n  vertical line joining C to A ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    MP1\n   </strong>\n   i.e.,\n   <strong>\n    award [1]\n   </strong>\n   for first process locating C at a lower pressure than A, then vertical line to A.\n  </em>\n </p>\n <p>\n  <em>\n   Arrows on the processes are not needed.\n  </em>\n </p>\n <p>\n  <em>\n   Point C need not be labelled.\n  </em>\n </p>\n <p>\n 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\"/>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n </p>\n <p>\n  use of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    T\n   </mi>\n   <msup>\n    <mi>\n     V\n    </mi>\n    <mfrac>\n     <mn>\n      2\n     </mn>\n     <mn>\n      3\n     </mn>\n    </mfrac>\n   </msup>\n  </math>\n  = constant «so\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    300\n   </mn>\n   <msup>\n    <mrow>\n     <mo>\n      (\n     </mo>\n     <mn>\n      3\n     </mn>\n     <msub>\n      <mi>\n       V\n      </mi>\n      <mi mathvariant=\"normal\">\n       A\n      </mi>\n     </msub>\n     <mo>\n      )\n     </mo>\n    </mrow>\n    <mfrac>\n     <mn>\n      2\n     </mn>\n     <mn>\n      3\n     </mn>\n    </mfrac>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <msub>\n    <mi>\n     T\n    </mi>\n    <mi mathvariant=\"normal\">\n     C\n    </mi>\n   </msub>\n   <msup>\n    <mrow>\n     <mo>\n      (\n     </mo>\n     <msub>\n      <mi>\n       V\n      </mi>\n      <mi mathvariant=\"normal\">\n       A\n      </mi>\n     </msub>\n     <mo>\n      )\n     </mo>\n    </mrow>\n    <mfrac>\n     <mn>\n      2\n     </mn>\n     <mn>\n      3\n     </mn>\n    </mfrac>\n   </msup>\n  </math>\n  » ✓\n </p>\n <p>\n  <em>\n   T\n  </em>\n  <sub>\n   C\n  </sub>\n  = 624 «K»\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <em>\n   T\n  </em>\n  <sub>\n   C\n  </sub>\n  = 351 «°C» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n </p>\n <p>\n  use of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    p\n   </mi>\n   <msup>\n    <mi>\n     V\n    </mi>\n    <mfrac>\n     <mn>\n      5\n     </mn>\n     <mn>\n      3\n     </mn>\n    </mfrac>\n   </msup>\n  </math>\n  to get either\n  <em>\n   p\n  </em>\n  <sub>\n   c\n  </sub>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    43\n   </mn>\n   <msup>\n    <mrow>\n     <mo>\n      (\n     </mo>\n     <mn>\n      3\n     </mn>\n     <mo>\n      )\n     </mo>\n    </mrow>\n    <mfrac>\n     <mn>\n      5\n     </mn>\n     <mn>\n      3\n     </mn>\n    </mfrac>\n   </msup>\n  </math>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <em>\n   p\n  </em>\n  <sub>\n   c\n  </sub>\n  = 268 «kPa» ✓\n </p>\n <p>\n  «\n  <em>\n   T\n  </em>\n  <sub>\n   C\n  </sub>\n  = 268 × 300/129 = so »\n </p>\n <p>\n  <em>\n   T\n  </em>\n  <sub>\n   C\n  </sub>\n  = 624 «K»\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <em>\n   T\n  </em>\n  <sub>\n   C\n  </sub>\n  = 351 «°C» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n </p>\n <p>\n  «the process is adiabatic so» ΔQ = 0 ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n </p>\n <p>\n  The compression is reversible «so ΔS = 0» ✓\n </p>\n <p>\n </p>\n <p>\n  <strong>\n   <em>\n    OWTTE\n   </em>\n  </strong>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (e)\n </div><div class=\"card-body\">\n <p>\n  area under curve AB is less than area under curve BC ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Do\n   <strong>\n    not\n   </strong>\n   allow\n   <strong>\n    ECF\n   </strong>\n   from part\n   <strong>\n    (b)\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (f)\n </div><div class=\"card-body\">\n <p>\n  «W = 0 so» Q = ΔU ✓\n </p>\n <p>\n  «ΔU =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     3\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  × 53.2 × R × (351 – 27) so » ΔU = 2.15 × 10\n  <sup>\n   5\n  </sup>\n  «J» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [2]\n   </strong>\n   for\n   <strong>\n    BCA\n   </strong>\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-4-thermodynamics"
    ]
  },
  {
    "question_id": "23M.2.HL.TZ2.8",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the net torque on the system about the central axis is approximately 30 N m.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The system rotates from rest and reaches a maximum angular speed of 20 rad s\n   <sup>\n    −1\n   </sup>\n   in a time of 5.0 s. Calculate the angular acceleration of the system.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the moment of inertia of the system about the central axis.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline why the angular speed\n   <em>\n    ω\n   </em>\n   decreases when the spheres move outward.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the rotational kinetic energy is\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mfrac>\n     <mn>\n      1\n     </mn>\n     <mn>\n      2\n     </mn>\n    </mfrac>\n   </math>\n   <em>\n    Lω\n   </em>\n   where\n   <em>\n    L\n   </em>\n   is the angular momentum of the system.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   When the spheres move outward, the angular speed decreases from 20 rad s\n   <sup>\n    −1\n   </sup>\n   to 12 rad s\n   <sup>\n    −1\n   </sup>\n   . Calculate the percentage change in rotational kinetic energy that occurs when the spheres move outward.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (e)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline one reason why this model of a dancer is unrealistic.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    ΣΓ\n   </mtext>\n  </math>\n  = 50 × 0.5 + 40 × 0.2\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  33 «Nm» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept opposite rotational sign convention\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  «α =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     20\n    </mn>\n    <mn>\n     5\n    </mn>\n   </mfrac>\n  </math>\n  =» 4 «rad s\n  <sup>\n   −2\n  </sup>\n  » ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    I\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mi>\n     Γ\n    </mi>\n    <mi>\n     α\n    </mi>\n   </mfrac>\n  </math>\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  33 =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    I\n   </mi>\n  </math>\n  × 4 ✓\n </p>\n <p>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    I\n   </mi>\n  </math>\n  = 8.25 «kg m\n  <sup>\n   2\n  </sup>\n  » ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    (a)\n   </strong>\n   and\n   <strong>\n    (b)\n   </strong>\n  </em>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    [2]\n   </strong>\n   for a\n   <strong>\n    BCA\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  moment of inertia increases ✓\n </p>\n <p>\n  Angular momentum is conserved ✓\n </p>\n <p>\n  <em>\n   <br/>\n   Allow algebraic expressions e.g. ω =\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mfrac>\n     <mi>\n      L\n     </mi>\n     <mi>\n      I\n     </mi>\n    </mfrac>\n   </math>\n   so ω decreases for\n   <strong>\n    MP2\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   E\n  </em>\n  <sub>\n   k\n  </sub>\n  «=\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <mi>\n    I\n   </mi>\n  </math>\n  <em>\n   ω\n  </em>\n  <sup>\n   2\n  </sup>\n  =»\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  (\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    I\n   </mi>\n  </math>\n  <em>\n   ω\n  </em>\n  )\n  <em>\n   ω\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  <em>\n   Lω\n  </em>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept equivalent methods\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   «E\n  </em>\n  <sub>\n   k\n  </sub>\n  =»\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  <em>\n   Lω\n  </em>\n  <sub>\n   1\n  </sub>\n  <em>\n   =\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mfrac>\n     <mn>\n      1\n     </mn>\n     <mn>\n      2\n     </mn>\n    </mfrac>\n   </math>\n   Lω\n   <sub>\n    2\n   </sub>\n  </em>\n  ✓\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <msub>\n     <mi mathvariant=\"bold-italic\">\n      E\n     </mi>\n     <mrow>\n      <mi>\n       k\n      </mi>\n      <mn>\n       1\n      </mn>\n     </mrow>\n    </msub>\n    <msub>\n     <mi mathvariant=\"bold-italic\">\n      E\n     </mi>\n     <mrow>\n      <mi>\n       k\n      </mi>\n      <mn>\n       2\n      </mn>\n     </mrow>\n    </msub>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <msub>\n     <mi>\n      ω\n     </mi>\n     <mn>\n      1\n     </mn>\n    </msub>\n    <msub>\n     <mi>\n      ω\n     </mi>\n     <mn>\n      2\n     </mn>\n    </msub>\n   </mfrac>\n  </math>\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  «\n  <em>\n   L\n  </em>\n  is constant so»\n  <em>\n   E\n  </em>\n  <sub>\n   k\n  </sub>\n  is proportional to\n  <em>\n   ω\n  </em>\n  ✓\n </p>\n <p>\n  40 % «energy loss» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    MP1\n   </strong>\n   is for understanding that angular momentum is constant so change in rotational kinetic energy is proportional to change in angular velocity\n  </em>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [0]\n   </strong>\n   if E = 0.5 I ω\n   <sup>\n    2\n   </sup>\n   is used with the same I value for both values of E\n  </em>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    [2]\n   </strong>\n   for\n   <strong>\n    BCA\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (e)\n </div><div class=\"card-body\">\n <p>\n  one example specified\n  <em>\n   eg\n  </em>\n  friction, air resistance, mass distribution not modelled ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [1]\n   </strong>\n   for any reasonable physical parameter that is not consistent with the model\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-4-rigid-body-mechanics"
    ]
  },
  {
    "question_id": "23M.2.HL.TZ2.9",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show, using the data, that the energy released in the decay of one magnesium-27 nucleus is about 2.62 MeV.\n  </p>\n  <p style=\"text-align:center;\">\n   Mass of aluminium-27 atom = 26.98153 u\n   <br/>\n   Mass of magnesium-27 atom = 26.98434 u\n   <br/>\n   The unified atomic mass unit is 931.5 MeV c\n   <sup>\n    −2\n   </sup>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the pressure of the gas at B.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Sketch, on the\n   <em>\n    pV\n   </em>\n   diagram, the remaining two processes BC and CA that the gas undergoes.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the conclusion that can be drawn from the existence of these two routes.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the difference between the magnitudes of the total energy transfers in parts (a) and (b).\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Explain how the difference in part (b)(ii) arises.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the temperature of the gas at C is approximately 350 °C.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The smallest mass of magnesium that can be detected with this technique is 1.1 × 10\n   <sup>\n    −8\n   </sup>\n   kg.\n  </p>\n  <p>\n   Show that the smallest number of magnesium atoms that can be detected with this technique is about 10\n   <sup>\n    17\n   </sup>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   A sample of glass is irradiated with neutrons so that all the magnesium atoms become magnesium-27. The sample contains 9.50 × 10\n   <sup>\n    15\n   </sup>\n   magnesium atoms.\n  </p>\n  <p>\n   The decay constant of magnesium-27 is 1.22 × 10\n   <sup>\n    −3\n   </sup>\n   s\n   <sup>\n    −1\n   </sup>\n   .\n  </p>\n  <p>\n   Determine the number of aluminium atoms that form in 10.0 minutes after the irradiation ends.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Estimate, in W, the average rate at which energy is transferred by the decay of magnesium-27 during the 10.0 minutes after the irradiation ends.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (d)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Explain why the change of entropy for the gas during the process BC is equal to zero.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (e)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Explain why the work done by the gas during the isothermal expansion AB is less than the work done on the gas during the adiabatic compression BC.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (f)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The quantity of trapped gas is 53.2 mol. Calculate the thermal energy removed from the gas during process CA.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  (26.98434 - 26.98153) × 931.5\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  2.6175 «MeV» seen ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  use of\n  <em>\n   pV\n  </em>\n  = constant ✓\n </p>\n <p>\n  <em>\n   P\n  </em>\n  <sub>\n   B\n  </sub>\n  = 43 «Kpa» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [2]\n   </strong>\n   for\n   <strong>\n    BCA\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  concave curved line from B to locate C with a higher pressure than A ✓\n </p>\n <p>\n  vertical line joining C to A ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    MP1\n   </strong>\n   i.e.,\n   <strong>\n    award [1]\n   </strong>\n   for first process locating C at a lower pressure than A, then vertical line to A.\n  </em>\n </p>\n <p>\n  <em>\n   Arrows on the processes are not needed.\n  </em>\n </p>\n <p>\n  <em>\n   Point C need not be labelled.\n  </em>\n </p>\n <p>\n  <img src=\"data:image/png;base64,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\"/>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  evidence for nuclear energy levels ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  Difference = 2.6175 – (1.76656 +0.84376) = 2.6175 – 2.61032 = 0.007195 «MeV»\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  Difference = 2.6175 – (1.59587 +1.01445) = 2.61032 = 0.007195 «MeV» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  Another particle/«anti» neutrino is emitted «that accounts for this mass / energy» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n </p>\n <p>\n  use of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    T\n   </mi>\n   <msup>\n    <mi>\n     V\n    </mi>\n    <mfrac>\n     <mn>\n      2\n     </mn>\n     <mn>\n      3\n     </mn>\n    </mfrac>\n   </msup>\n  </math>\n  = constant «so\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    300\n   </mn>\n   <msup>\n    <mrow>\n     <mo>\n      (\n     </mo>\n     <mn>\n      3\n     </mn>\n     <msub>\n      <mi>\n       V\n      </mi>\n      <mi mathvariant=\"normal\">\n       A\n      </mi>\n     </msub>\n     <mo>\n      )\n     </mo>\n    </mrow>\n    <mfrac>\n     <mn>\n      2\n     </mn>\n     <mn>\n      3\n     </mn>\n    </mfrac>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <msub>\n    <mi>\n     T\n    </mi>\n    <mi mathvariant=\"normal\">\n     C\n    </mi>\n   </msub>\n   <msup>\n    <mrow>\n     <mo>\n      (\n     </mo>\n     <msub>\n      <mi>\n       V\n      </mi>\n      <mi mathvariant=\"normal\">\n       A\n      </mi>\n     </msub>\n     <mo>\n      )\n     </mo>\n    </mrow>\n    <mfrac>\n     <mn>\n      2\n     </mn>\n     <mn>\n      3\n     </mn>\n    </mfrac>\n   </msup>\n  </math>\n  » ✓\n </p>\n <p>\n  <em>\n   T\n  </em>\n  <sub>\n   C\n  </sub>\n  = 624 «K»\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <em>\n   T\n  </em>\n  <sub>\n   C\n  </sub>\n  = 351 «°C» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n </p>\n <p>\n  use of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    p\n   </mi>\n   <msup>\n    <mi>\n     V\n    </mi>\n    <mfrac>\n     <mn>\n      5\n     </mn>\n     <mn>\n      3\n     </mn>\n    </mfrac>\n   </msup>\n  </math>\n  to get either\n  <em>\n   p\n  </em>\n  <sub>\n   c\n  </sub>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    43\n   </mn>\n   <msup>\n    <mrow>\n     <mo>\n      (\n     </mo>\n     <mn>\n      3\n     </mn>\n     <mo>\n      )\n     </mo>\n    </mrow>\n    <mfrac>\n     <mn>\n      5\n     </mn>\n     <mn>\n      3\n     </mn>\n    </mfrac>\n   </msup>\n  </math>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <em>\n   p\n  </em>\n  <sub>\n   c\n  </sub>\n  = 268 «kPa» ✓\n </p>\n <p>\n  «\n  <em>\n   T\n  </em>\n  <sub>\n   C\n  </sub>\n  = 268 × 300/129 = so »\n </p>\n <p>\n  <em>\n   T\n  </em>\n  <sub>\n   C\n  </sub>\n  = 624 «K»\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <em>\n   T\n  </em>\n  <sub>\n   C\n  </sub>\n  = 351 «°C» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  So 1.1 × 10\n  <sup>\n   −8\n  </sup>\n  kg ≡\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      1\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      027\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  × 10\n  <sup>\n   −8\n  </sup>\n  «mol»\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  Mass of atom = 27 × 1.66 × 10\n  <sup>\n   −27\n  </sup>\n  «kg» ✓\n </p>\n <p>\n  2.4 − 2.5 x 10\n  <sup>\n   17\n  </sup>\n  atoms ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   N\n  </em>\n  <sub>\n   10\n  </sub>\n  = 9.50 × 10\n  <sup>\n   15\n  </sup>\n  ×\n  <em>\n   e\n  </em>\n  <sup>\n   −0.00122×60\n  </sup>\n  seen ✓\n </p>\n <p>\n  <em>\n   N\n  </em>\n  <sub>\n   10\n  </sub>\n  = 4.57 × 10\n  <sup>\n   15\n  </sup>\n  ✓\n </p>\n <p>\n  So number of aluminium-27 nuclei = (9.50 – 4.57) × 10\n  <sup>\n   15\n  </sup>\n  = 4.9(3) × 10\n  <sup>\n   15\n  </sup>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  Total energy released = ans\n  <strong>\n   (c)(ii)\n  </strong>\n  × 2.62 × 10\n  <sup>\n   6\n  </sup>\n  × 1.6 × 10\n  <sup>\n   −19\n  </sup>\n  «= 2100 J» ✓\n </p>\n <p>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     2100\n    </mn>\n    <mn>\n     600\n    </mn>\n   </mfrac>\n  </math>\n  =» 3.4 −3.5 «W» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n </p>\n <p>\n  «the process is adiabatic so» ΔQ = 0 ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n </p>\n <p>\n  The compression is reversible «so ΔS = 0» ✓\n </p>\n <p>\n </p>\n <p>\n  <strong>\n   <em>\n    OWTTE\n   </em>\n  </strong>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (e)\n </div><div class=\"card-body\">\n <p>\n  area under curve AB is less than area under curve BC ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Do\n   <strong>\n    not\n   </strong>\n   allow\n   <strong>\n    ECF\n   </strong>\n   from part\n   <strong>\n    (b)\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (f)\n </div><div class=\"card-body\">\n <p>\n  «W = 0 so» Q = ΔU ✓\n </p>\n <p>\n  «ΔU =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     3\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  × 53.2 × R × (351 – 27) so » ΔU = 2.15 × 10\n  <sup>\n   5\n  </sup>\n  «J» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [2]\n   </strong>\n   for\n   <strong>\n    BCA\n   </strong>\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter",
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "b-1-thermal-energy-transfers",
      "b-4-thermodynamics",
      "e-3-radioactive-decay"
    ]
  },
  {
    "question_id": "23M.2.SL.TZ1.1",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Deduce the unit of μ in terms of fundamental SI units.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   draw a free-body diagram for the ball.\n  </p>\n  <p>\n   <img src=\"data:image/png;base64,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\"/>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   show that the speed of the ball is about 4.3 m s\n   <sup>\n    −1\n   </sup>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   determine the tension in the string.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the collision is elastic.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [4]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the maximum height risen by the centre of the ball.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Explain a possible reason for the systematic error.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iv)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the gradient of the graph.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The coefficient of dynamic friction between the block and the rough surface is 0.400.\n  </p>\n  <p>\n   Estimate the distance travelled by the block on the rough surface until it stops.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  [μ] = «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      kg\n     </mi>\n     <mo>\n      ×\n     </mo>\n     <mi mathvariant=\"normal\">\n      m\n     </mi>\n     <mo>\n     </mo>\n     <msup>\n      <mi mathvariant=\"normal\">\n       s\n      </mi>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        2\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mrow>\n     <msup>\n      <mi mathvariant=\"normal\">\n       s\n      </mi>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        2\n       </mn>\n      </mrow>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mi mathvariant=\"normal\">\n       m\n      </mi>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </mrow>\n   </mfrac>\n  </math>\n  » kg × m\n  <sup>\n   −1\n  </sup>\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept kg/m.\n  </em>\n </p>\n <p>\n  <em>\n   Do\n   <strong>\n    not\n   </strong>\n   accept g m\n   <sup>\n    −1\n   </sup>\n   .\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  Tension upwards, weight downwards ✓\n  <br/>\n  Tension is clearly longer than weight ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Look for:\n  </em>\n </p>\n <p>\n  <img src=\"data:image/png;base64,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\"/>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   v\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msqrt>\n    <mn>\n     2\n    </mn>\n    <mo>\n     ×\n    </mo>\n    <mn>\n     9\n    </mn>\n    <mo>\n     .\n    </mo>\n    <mn>\n     81\n    </mn>\n    <mo>\n     ×\n    </mo>\n    <mn>\n     0\n    </mn>\n    <mo>\n     .\n    </mo>\n    <mn>\n     95\n    </mn>\n   </msqrt>\n  </math>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  = 4.32 «m s\n  <sup>\n   −1\n  </sup>\n  » ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Must see either full substitution or answer to at least 3 s.f.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   T − mg = F\n   <sub>\n    net\n   </sub>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <em>\n   T − mg =\n  </em>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      m\n     </mi>\n     <msup>\n      <mi>\n       v\n      </mi>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </mrow>\n    <mi>\n     r\n    </mi>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <em>\n   T\n  </em>\n  «= 0.800 × 9.81 +\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      800\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      4\n     </mn>\n     <mo>\n      .\n     </mo>\n     <msup>\n      <mn>\n       317\n      </mn>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      95\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  » = 23.5 «N» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  Use of conservation of momentum. ✓\n  <br/>\n  Rebound speed = 2.16 «m s\n  <sup>\n   −1\n  </sup>\n  » ✓\n  <br/>\n  Calculation of initial KE = «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  × 0.800 × 4.317\n  <sup>\n   2\n  </sup>\n  » = 7.46 « J » ✓\n  <br/>\n  Calculation of final KE = «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  × 0.800  × 2.16\n  <sup>\n   2\n  </sup>\n  +\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  × 2.40 × 2.16\n  <sup>\n   2\n  </sup>\n  » = 7.46 «J» ✓\n  <br/>\n  «hence elastic»\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n  <br/>\n  Rebound speed is halved so energy less by a factor of 4 ✓\n  <br/>\n  Hence height is\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     95\n    </mn>\n    <mn>\n     4\n    </mn>\n   </mfrac>\n  </math>\n  =23.8 «cm» ✓\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n    <br/>\n   </strong>\n  </em>\n  Use of conservation of energy /\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  × 0.800 × 2.16\n  <sup>\n   2\n  </sup>\n  = 0.800 × 9.8 ×\n  <em>\n   h\n   <br/>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  Use of proper kinematics equation (e.g. 0 = 2.16\n  <sup>\n   2\n  </sup>\n  − 2 × 9.8 ×\n  <em>\n   h\n  </em>\n  ) ✓\n </p>\n <p>\n  <em>\n   h\n  </em>\n  = 23.8 «cm» ✓\n </p>\n <p>\n  <em>\n   <br/>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    b(i)\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  mass of tray of weights neglected/friction at pulley/friction at slider/thickness of slider/zero off-set error ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Do\n   <strong>\n    not\n   </strong>\n   allow vague answers like friction neglected / error in length measurement.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iv)\n </div><div class=\"card-body\">\n <p>\n  large enough triangle Δ\n  <em>\n   m\n  </em>\n  ≥ 50 g✓\n </p>\n <p>\n  answer in range 0.210 − 0.240 «kg m\n  <sup>\n   −1\n  </sup>\n  » ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept answers in g m\n   <sup>\n    −2\n   </sup>\n   .\n  </em>\n </p>\n <p>\n  <em>\n   Do\n   <strong>\n    not\n   </strong>\n   allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    MP1\n   </strong>\n   .\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n  <br/>\n  Frictional force is\n  <em>\n   f\n  </em>\n  «= 0.400 × 2.40 × 9.81» = 9.42 «N» ✓\n  <br/>\n  9.42 ×\n  <em>\n   d\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  × 2.40 × 2.16\n  <sup>\n   2\n  </sup>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <em>\n   d\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      5\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      5987\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      9\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      42\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n  <br/>\n  <em>\n   d\n  </em>\n  = 0.594 «m» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n  <br/>\n  <em>\n   a\n  </em>\n  = «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mi>\n     f\n    </mi>\n    <mi>\n     m\n    </mi>\n   </mfrac>\n  </math>\n  =\n  <em>\n   µg\n  </em>\n  = 0.4 × 9.81 =» 3.924 «m s\n  <sup>\n   −2\n  </sup>\n  » ✓\n </p>\n <p>\n  Proper use of kinematics equation(s) to determine ✓\n </p>\n <p>\n  <em>\n   d\n  </em>\n  = 0.594 «m» ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion",
      "inquiry",
      "tools"
    ],
    "subtopics": [
      "a-2-forces-and-momentum",
      "a-3-work-energy-and-power",
      "i-3-2-evaluating",
      "inquiry-3-concluding-and-evaluating",
      "tool-3-mathematics"
    ]
  },
  {
    "question_id": "23M.2.SL.TZ1.2",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the average rate at which thermal energy is transferred into the chocolate is about 15 W.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   one variable that must be controlled,\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   the main source of error in\n   <em>\n    T\n   </em>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   To determine\n   <em>\n    T\n   </em>\n   more precisely, the student measures the total time for 20 oscillations and divides by 20.\n  </p>\n  <p>\n   Explain why this is preferable to measuring the time for just one oscillation.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Compare the internal energy of the chocolate at\n   <em>\n    t\n   </em>\n   = 2 minutes with that at\n   <em>\n    t\n   </em>\n   = 6 minutes.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The student plots a graph with\n   <em>\n    L\n   </em>\n   on the horizontal axis. State the variable that must be plotted on the vertical axis in order to obtain a line of best fit that is straight.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculations using the data of the experiment show that\n   <em>\n    g\n   </em>\n   = 9.71622 m s\n   <sup>\n    −2\n   </sup>\n   with a percentage uncertainty of 8 %. Determine the value of\n   <em>\n    g\n   </em>\n   that can be obtained from this experiment. Include the absolute uncertainty in\n   <em>\n    g\n   </em>\n   to one significant figure.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Reads change in temperature to be 45 − 31\n  <strong>\n   <em>\n    OR\n   </em>\n  </strong>\n  14 °C ✓\n </p>\n <p>\n  <br/>\n  <em>\n   Q\n  </em>\n  = 0.082 × 1.6 × 10\n  <sup>\n   3\n  </sup>\n  × 14 = 1.84 × 10\n  <sup>\n   3\n  </sup>\n  «J» ✓\n </p>\n <p>\n  <em>\n   P\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      84\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      60\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  = 15.3\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    ≈\n   </mo>\n  </math>\n  15 «W»✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Must see either full substitution\n   <strong>\n    OR\n   </strong>\n   answer to at least 3 s.f. in\n   <strong>\n    MP3\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  mass\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  diameter\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  material of bob\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  « initial » amplitude/angle ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Do\n   <strong>\n    not\n   </strong>\n   allow statements about rulers, stopwatches, string, number of oscillations, constant gravity.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  student’s reaction time «in starting and stopping stopwatch» / starting/stopping stopwatch ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  it reduces «the random» error/uncertainty ✓\n </p>\n <p>\n  by a factor of 20 «compared to that in a single period measurement» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   For\n   <strong>\n    MP1\n   </strong>\n   , allow increasing accuracy/precision.\n  </em>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [0]\n   </strong>\n   for answers related to number of trials, 20 measurements of one period.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  Internal energy is greater at\n  <em>\n   t\n  </em>\n  = 6 min\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  internal energy is lower at\n  <em>\n   t\n  </em>\n  = 2 min\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  internal energy increases «as energy is added to the system» ✓\n </p>\n <p>\n  Because kinetic energy «of the molecules» is the same\n  <em>\n   <strong>\n    AND\n   </strong>\n  </em>\n  potential energy «of the molecules» has increased /\n  <em>\n   <strong>\n    OWTTE\n   </strong>\n  </em>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   T\n  </em>\n  <sup>\n   2\n  </sup>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   g\n  </em>\n  = 9.7 «m s\n  <sup>\n   −2\n  </sup>\n  » ✓\n </p>\n <p>\n  Δ\n  <em>\n   g\n  </em>\n  = 0.8 «m s\n  <sup>\n   −2\n  </sup>\n  » ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter",
      "inquiry",
      "tools"
    ],
    "subtopics": [
      "b-1-thermal-energy-transfers",
      "i-1-2-designing",
      "inquiry-1-exploring-and-designing",
      "tool-1-experimental-techniques",
      "tool-3-mathematics"
    ]
  },
  {
    "question_id": "23M.2.SL.TZ1.3",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   A transverse water wave travels to the right. The diagram shows the shape of the surface of the water at time\n   <em>\n    t\n   </em>\n   = 0. P and Q show two corks floating on the surface.\n  </p>\n  <p style=\"text-align:center;\">\n   <img 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\"/>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State what is meant by a transverse wave.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The frequency of the wave is 0.50 Hz. Calculate the speed of the wave.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Plot on the diagram the position of P at time\n   <em>\n    t\n   </em>\n   = 0.50 s.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Monochromatic light is incident on two very narrow slits. The light that passes through the slits is observed on a screen. M is directly opposite the midpoint of the slits.\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     x\n    </mi>\n   </math>\n   represents the displacement from M in the direction shown.\n  </p>\n  <p style=\"text-align:center;\">\n   <img src=\"data:image/png;base64,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\"/>\n  </p>\n  <p>\n   A student argues that what will be observed on the screen will be a total of two bright spots opposite the slits. Explain why the student’s argument is incorrect.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The graph shows the actual variation with displacement\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     x\n    </mi>\n   </math>\n   from M of the intensity of the light on the screen.\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <msub>\n     <mi>\n      I\n     </mi>\n     <mn>\n      0\n     </mn>\n    </msub>\n   </math>\n   is the intensity of light at the screen from one slit only.\n  </p>\n  <p style=\"text-align:center;\">\n   <img 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\"/>\n  </p>\n  <p style=\"text-align:left;\">\n   The slits are separated by a distance of 0.18 mm and the distance to the screen is 2.2 m. Determine, in m, the wavelength of light.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  «A wave where the» displacement of particles/oscillations of particles/movement of particles/vibrations of particles is perpendicular/normal to the direction of energy transfer/wave travel/wave velocity/wave movement/wave propagation ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow medium, material, water, molecules, or atoms for particles.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  «A wave where the» displacement of particles/oscillations of particles/movement of particles/vibrations of particles is perpendicular/normal to the direction of energy transfer/wave travel/wave velocity/wave movement/wave propagation ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow medium, material, water, molecules, or atoms for particles.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   v\n  </em>\n  = «0.50 × 16 =» 8.0 «m s\n  <sup>\n   −1\n  </sup>\n  » ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  P at (8, 1.2) ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  light acts as a wave «and not a particle in this situation» ✓\n </p>\n <p>\n  light at slits will diffract / create a diffraction pattern ✓\n </p>\n <p>\n  light passing through slits will interfere / create an interference pattern «creating bright and dark spots» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  Ue of\n  <em>\n   s\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      λ\n     </mi>\n     <mi>\n      D\n     </mi>\n    </mrow>\n    <mi>\n     d\n    </mi>\n   </mfrac>\n   <mo>\n    ⇒\n   </mo>\n   <mi>\n    λ\n   </mi>\n  </math>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      s\n     </mi>\n     <mi>\n      d\n     </mi>\n    </mrow>\n    <mi>\n     D\n    </mi>\n   </mfrac>\n  </math>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <em>\n   s\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      n\n     </mi>\n     <mi>\n      λ\n     </mi>\n     <mi>\n      D\n     </mi>\n    </mrow>\n    <mi>\n     d\n    </mi>\n   </mfrac>\n   <mo>\n    ⇒\n   </mo>\n   <mi>\n    λ\n   </mi>\n  </math>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      s\n     </mi>\n     <mi>\n      d\n     </mi>\n    </mrow>\n    <mrow>\n     <mi>\n      n\n     </mi>\n     <mi>\n      D\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    λ\n   </mi>\n  </math>\n  = «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      567\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        2\n       </mn>\n      </mrow>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      18\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        3\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      2\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  =» 4.6 × 10\n  <sup>\n   −7\n  </sup>\n  «m» ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-1-simple-harmonic-motion",
      "c-2-wave-model",
      "c-3-wave-phenomena"
    ]
  },
  {
    "question_id": "23M.2.SL.TZ1.4",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the speed of the spacecraft is 0.80\n   <em>\n    c\n   </em>\n   as measured in S.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the current in Q is 0.45 A.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the resistance of R.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the total power dissipated in the circuit.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Resistor P is removed. State and explain, without any calculations, the effect of this on the resistance of Q.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   An event has coordinates\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     x\n    </mi>\n   </math>\n   = 0 and\n   <em>\n    ct\n   </em>\n   = 0.60 ly in S. Show, using a Lorentz transformation, that the time coordinate of this event in S′ is\n   <em>\n    ct\n   </em>\n   ′ = 1.00 ly .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Label, on the diagram with the letter P, the point on the\n   <em>\n    ct\n   </em>\n   ′ axis whose\n   <em>\n    ct\n   </em>\n   ′ coordinate is 1.00 ly.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Draw lines to indicate R on the diagram.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine, using the diagram or otherwise, the space coordinate\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     x\n    </mi>\n   </math>\n   ′ of event R in S′.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  moves 4 ly in 5 years\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  slope of angle with time axis is 0.8 ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow evidence for mark on the graph.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  Voltage across P is 1.4 «V» ✓\n </p>\n <p>\n  Voltage across Q is 4.6 «V» ✓\n </p>\n <p>\n  And 6 – 1.4 = 4.6 «V» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Need to see a calculation involving the two voltages and the total voltage in the circuit for\n   <strong>\n    MP3\n   </strong>\n   (e.g. 1.4 + 4.6 = 6).\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  Current in R is «(0.45 − 0.4)=» 0.05 A ✓\n </p>\n <p>\n  So resistance is «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      4\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      05\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  » = 28 «Ω»\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    a(i)\n   </strong>\n  </em>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    MP1\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  «0.45 × 6.0» = 2.7 «W»✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  Q will have a smaller resistance ✓\n </p>\n <p>\n  «Because total resistance in the circuit is now larger so» the current «through the\n  <br/>\n  circuit/Q» is smaller /\n  <em>\n   <strong>\n    OWTTE\n   </strong>\n  </em>\n  ✓\n  <em>\n   <strong>\n    <br/>\n   </strong>\n  </em>\n </p>\n <p>\n  <em>\n   Allow similar argument for\n   <strong>\n    MP2\n   </strong>\n   based on voltage across\n  </em>\n  Q\n  <em>\n   becoming smaller.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   γ\n  </em>\n  = 1.67\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     5\n    </mn>\n    <mn>\n     3\n    </mn>\n   </mfrac>\n  </math>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <msqrt>\n     <mfenced>\n      <mrow>\n       <mn>\n        1\n       </mn>\n       <mo>\n        -\n       </mo>\n       <mn>\n        0\n       </mn>\n       <mo>\n        .\n       </mo>\n       <msup>\n        <mn>\n         8\n        </mn>\n        <mn>\n         2\n        </mn>\n       </msup>\n      </mrow>\n     </mfenced>\n    </msqrt>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <em>\n   ct\n  </em>\n  ' = «\n  <em>\n   γ\n  </em>\n  (\n  <em>\n   ct\n  </em>\n  −\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      v\n     </mi>\n     <mi>\n      x\n     </mi>\n    </mrow>\n    <mi>\n     c\n    </mi>\n   </mfrac>\n  </math>\n  )» =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     5\n    </mn>\n    <mn>\n     3\n    </mn>\n   </mfrac>\n  </math>\n  × (0.60 +0) ✓\n </p>\n <p>\n  «= 1.00 ly»\n </p>\n <p>\n </p>\n <p>\n  <em>\n   For\n   <strong>\n    MP2\n   </strong>\n   , working should be seen.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  identifies point with coordinates\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    x\n   </mi>\n  </math>\n  = 0,\n  <em>\n   ct\n  </em>\n  = 0.60 on vertical axis ✓\n </p>\n <p>\n  draws line parallel to the\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    x\n   </mi>\n  </math>\n  prime axis until it intersects the prime\n  <em>\n   ct\n  </em>\n  axis ✓\n </p>\n <p style=\"text-align:left;\">\n  <img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAGHCAYAAACebATvAAAgAElEQVR4XuydB1hUxxaAjw3sYu/GXmM3ltiiJmpMMRp7b6CiqIAooFgQBBTFhr0ndk3sLYm99967sYu9o/jOuQYfZXfv3LuzCyxnvi/fywtT7j33zPw7M6ck+YgFuLAEWAIsAZYAS0CjBJIwQDRKjKuzBFgCLAGWgCIBBggrAkuAJcASYAnokgADRJfYuBFLgCXAEmAJMEBYB1gCLAGWAEtAlwQYILrExo1YAiwBlgBLgAHCOsASYAmwBFgCuiRgAiAJx7r3Y8RHuHP3LmTKlBFSpkypSxDciCXAEmAJJG4JJNH8+oYB8jFCc0dx2eDdu3AIHhMMrVq2hIIFC8blo/DYLAGWAEsgYUogSVLNz20TAFm/YQM4dnOEBg0awPTp0yB58uSaBcENWAIsAZZAopZAYgTIvXv3oFmz5pAkaVLIkCEDdOvWFRr//HOi1gN+eZYAS4AloFkCiQ0gERER4OHhAQUKFISDhw4quxCPAR6wcuVKyJ4tm2b5cQOWAEuAJZBoJZDYALJt2zYIDZ0MCxYsAEcnRwgeHQwr/lgBV69eg6DAgESrB/ziLAGWAEtAswQSE0CePn0KvzRpokCjYsUK0LFTJ+Xf06VLC81btAR3dzf4pnZtzTLkBiwBlgBLIFFKIDEB5MCBA7B33z7o4+ICSZIk+QyQrFmzwMGDB2H9ho0wdIhPotQDfmmWAEuAJaBZAokJIDGFE7kDIYBwYQmwBFgC796+BTt7e0UQh/FH5ejgYPAcOBDKVajAwjEkAQZIMDBAeG6wBBK3BD58+ACbNm6EaVOmwKq1a4FSHrVs3hy2bNmiGNjUqFUrcQvI2NszQBggPDNYAoldAqdOnIA6detAczTvnzx1Krx69QpqVf8aUqdNC5s3/wUpU6VK7CIy/P4MEAYIzwyWQGKXwNIlS6BHj+4QGBAITj16wJMnT6BcmTIQGBgIrdq0SeziMf7+DBAGCM8OloAtSyDs4UM8hvoT1uBRFMW/K1myFHRAC8za33wDb/HOY3JoKO4yNimGNL/88guUL18BrTJbQJtWLWHLtu22LBrz340BwgAxX4u4B5ZA/JTA6VOnoH27dnDj5g1o1PB7yJkrFyxdugRe4hHVpImhUO3ratChXVs4f/EihIeHQ8H8+aFata+hn6srXL5yGep9+138fLH48lQMEAZIfNFFfg6WgEwJvH3zBr777lu4iHBYvGgJ1K7zjdL98aNHoeH3DaEQBlHdtWcvvH//Hgrjv+fNlw927tol8xFsvy8GCAPE9rWc3zAxSmDBb7+BSx8XGIChizy9B30WAVlY9erZAzJmzAT+AQFw/MgRqFOvrhKZe/LUaYlRVPrfmQHCANGvPdySJRB/JdAej6Y2bdoEu3GXUaRIEaMPSncggwcPgpCxIdCxc+f4+0Lx8ckYIAyQ+KiX/EwsAXMk8Pr1a6hVo7pySb5z9x4l6raxQpflmzZvhrNnz0K27DnMGTbxtbUlgDxEa4uHD8NifUQHhwyQI0dsxWBP9MSn7/zGiUMCz58/h4rly0PuPLlhy9ZtSuiiyHIUj6w+4IV5uYoVAT0GoVrVqsoF+mG8G0mWLFniEJCst7QlgAwYMBB+w3PPmKVd+/YwelRQrP/OAJGlRdwPSyB+SSByB0IX5Dt37Ya06dIpD/gMA6p+Xa0avHn7Bg4cOAgUYLVmzRpQr963MHfevGigiV9vFE+fxpYA8i2a3NljfvM+eHEWteTOnRu+LFWKARJPdZAfiyVgCQn069sXf1DOh3Hjxit+HffQB8TLywvvRTbCSP+R0L1nT4TIfmiIWUk7d+oMAUFBCkBSpEhhicexzT5tBSDPnj2DEiVKgqfnQHDBaLsihXcgIlLiOiyBhCmBuwiMpr80hgtoxks/Imn38RTXCdd+ruA1aJCSxvr4sWOKqS9BI1fOXLBg4UIoWqxYwnzhuHhqWwEIbUcbN26sJIoqWbIE3L5zB3Kh01CO7NmNipUBEhcax2OyBKwnAYLG6lWrlAtyBwcHaIjOhKXLlon2AFv+/hu2Y6K5dOnTQw/clUQed1nvKRPwSLYCkKlovz18+HCoU6cObN++XYmmSdvRzmiWN2iQN6QyEAyNAZKAFZcfnSXAEoh7CdgKQNzc3GHRokXQqnVr+LVpE9yepoC//voLJk+eDB06dICgoEC+A4l7deMnYAmwBGxJArYCkAsXLsCt27ehRvUaeJ6Z/PMn8vL2hmXLlsHOHTsgZ86cMGPmLDiBoZup0H+bGDoJHHDrau3yISJC2SUljyOzwXC0TqGxo5o3WksG9N5kNmlnZ2etIWONQ9Y59O5xYbZJuSc+4hPF1bd/h7JPgef/cfbtUfZ2cXBRTXNuGwZHrIH+IfZxoHv0zd+9excnYysTAPU9X968Jn1iNE9IWwGIsRffsGEDdOnSFVasWAFfY+A0+oARqEhUujk6QjBmHMuaxfoZCR8/fgwvXr6CvGinHhflwoWLkC9fXkiJVmvWLpT17SwCv2zp0tYe+vN4N27eBHvMPJc9WzarP8ODBw8QoO/xji6n1cemAc+dOw+FChWME2ujNxif6vLVq1CqRAmrv/vqNWvgjz/+gODRoyFLHMx5+uFw8vRpJUx8XBQKUU9BJAki0ootAIQ+zN69+/DYKhlURaegqGUjZhnr2s0R1qxeBRVipKWMyzsQAsjzFy/kfkwNWnH+/HkESD6Dd0MautFVlQBy+tw5KF+2rK72Mhpdv35dMfk2ZWQhYxxDfdwngLwLR8ugXJYawmS/Z86cxdAeheMMIJcuXzZoVm9JYRw+fBj80XTXG+9D83+RHwGS2ZLDGeyb1qnjJ09ChXLlrD42DWiRNccWAELHEc2btwD6dbNq1cpoRyPDfX2V3ccOvFgnK4yohQHCAGGAWHctozlqbYCEhYWBk1N3GBsyVjk6dcjgwACR9dltASAki2XLV6B9dz/o7dIb+vbpo5zvLlq0WLHMGuwzGLp17RpLZAwQBggDRNZKItaPtQHyGoFFToKOjt2gbt26mOPjCgOEj7BiKyvda8ycNQsmjJ+gBFAjJ6GkSZOCU3cn6N2rl8HLUgYIA4QBIrbwy6plbYAEBAZB5syZwQkBQoV2P7wD4TsQg/ocad1zDs/3IyI+QvHixRSLB2PWJgwQBggDRBYaxPqxFkBoLViK1pdbt2yFSZMmKj8oGSAWuHe1lSMsMfWNXosBwgBhgOiZOfrbWAsgp9Hayc/PH832Z0DaNGk+PzDvQCQb7jBA4iYfiEUsIjTMa7bCYiusuAgaaA2AkD9Yzx49YczYMVCkcOFos4IBwgDRsEyarso7EN6B8A5E2nQS6sjSACErK2fnXhh9oj2Gaa8Z65kYIAwQIUUVqcQAYYAwQERmirw6lgQI+VkMHToMcmDEiV7OPQ3efTJAGCDStJkBwgBhgEibTkIdWRIga9DTfMuWLRASEmL0WRggDBAhRRWpxABhgDBARGaKvDqWAAhZXB06dAhG4KU5JZDKYCK2HQOEASJNmxkgDBAGiLTpJNSRJQDy8OFD5d5jFKatzp8/v8nnYIAwQIQUVaQSA4QBwgARmSny6sgGyCsMDtgZg6U6OTlCPfQ0VysMEAaImo4I/50BwgBhgAhPFykVZQNk5MgAyI5ZR7t27SL0fAwQBoiQoohUYoAwQBggIjNFXh1ZAKF7jyVLl2JOn50wblyIcGRhBggDRJo2M0AYIAwQadNJqCNZADl16jT4YqTt+fPnacppwwBhgAgpqkglBggDhAEiMlPk1ZEBkDt37ig5fiZNnAAFCxbU9HAMEAaIJoUxVZkBwgBhgEibTkIdmQsQirTdp28/aN2qJXzzzTdCY0atxABhgGhWGmMNGCAMEAaItOkk1JE5AKGUDUOGDIWcuXKBc88eunK6M0AYIEKKKlKJAcIAYYCIzBR5dcwByArMZ06pq0cFBSq5fvQUBggDRI/eGGzDAGGAMECkTSehjvQC5MjRozB4sA8sWbwI0qVLJzSWoUoMEAaIbuWJ2ZABwgBhgEibTkId6QHIo0ePoBtemo8bNw7y5TMvmx4DhAEipKgilRggDBAGiMhMkVdHK0DI07wLepp3x9TUderUMftBGCAMELOVKLIDBggDhAEibToJdaQFIHRpHog5zXPkyAGdO3fSdWke86EYIAwQIUUVqcQAYYAwQERmirw6WgCyZMlS2LFjhyZPc7UnZYAwQNR0RPjvDBAGCANEeLpIqSgKELo0HzVqNMyZMxtSpUwpZWzqhAHCAJGmTAwQBggDRNp0EupIBCD37t2Djh07wZSpU6CASnh2oUGjVGKAMEC06ozR+gwQBggDRNp0EupIDSDkad7T2Rk6d+pkMKe50CAmKjFAGCDm6tDn9gwQBggDRNp0EurIFEAop7mv7wjIli0b9OrlLNSf1koMEAaIVp2JVv/Spcvw9NlT5b8NHzYcxoaMhcyZMpnVp57Gz58/h9ev3+Bkyaqnudltbt78Vxnb3t7e7L60dhAeHg7Xb9yAwoUKaW0qrT4dk6Sws4NMGTNK61O0oydPnsD79x8gS5bMok2k1iPZ58ZwIMmTJ5far0hn7969g1sYDLHAF1/Eqr5+wwbYv28/hivxgWTJkol0p7nOrdu3IW2atJAhQ3rNbc1tEIGAvHztGhSJI72nNQdN2SBfXvN8aaLJIYn2iABJMBb/x1jC/Bhhrnyt0n7lqtVw8eJFZaw/MTTCBIzomdHBwSpjRx2Efom9w4U0vRleteY8dNjjx5ABx46LRYR+aT5E57DsWeMGniS3p8+eKe+eJnVqc8Soq+3L16+BFpN0adPqam9uo4dhYZARwZlMZzgQc8Z/j+/9GAGaNXN0eB47dhxmz54NAYEBFv0mNDb9aEqdKpU5r6GrbQQumw8ePIDsuMOKi/IGjwfJi58BIkn6fITFR1h8hCVpMgl2Y+gIixZVR0cnCJ0cquyMLFn4CIuPsKTpFwOEAcIAkTadhDqKCZDXuBvr2KmzEl1XT3h2oUGjVGKAMEC06ozR+gwQBggDRNp0EuooKkDI09x/5EjIkzuP4mlujcIAYYBI0zMGCAOEASJtOgl1FAmQUiVLwpIlS2Dnrl0wHoMkWusujgHCABFSVJFKDBAGCANEZKbIqxMJkHd4oTs2ZBxMmzbVopfmMZ+cAcIAkabNDBAGCANE2nQS6ogAsmv3HggJCYEJ48dDoULacpoLDWKiEgOEAWKuDn1uzwBhgDBApE0noY5evXwJLVq1gsGDBkPVqlWE2sisxABhgEjTJwYIA4QBIm06qXZE/j/D0Hk3Lfq/DBjgISU8u+qgMSowQBggWnWGrbAMSOD8+fOY3Y0BwgCRNp1UO/oDHXe3Y3j2bo6OULpUKdX6lqjAAGGASNMr3oEwQBgg0qaTyY7279+vhGefMmUy3EfHwS8ZINYRfJRRHmP0iecvGCDSBM8AYYAwQKRNJ6Mdkad5j57OaK4bgvG/sig5ORgglpd7zBEYIJJlzgBhgDBAJE+qGN1RTvNO5GmOIdpr164FFK6dAVLOskI30jsDRLLYGSAMEAaI5EkVozs/Pz8oWLAgtGnTRvmLWj4Qyz4NZyTkIyyJGsYAYYAwQCROqChdUcDuhQsXwcGDB2HMmODP4dkZICehQjnegSTYcO5RpwsDhAHCALEMQE6cOKF4mk/FS/OUUXKaM0AYIAk6HwgD5JME2Iz3OtjjwsYAkQ+QmzdvQm8XFxiHMa5i5jRngDBAGCAS5pxFLrQ0PBcDhAGSIkUKDRojVpUuyfv06QvdunWDr76qFKsRA4QBwgARm0smazFAzkH5smUlSFJfF9evM0BkA4Q8zb28B0GxYsWgC4ZnT4LpU2MWBggDhAGib82K1ooBwgDJnduy2feMqemZM2ehSJHCIBsgK9DT/NjRozBixAijM4QBwgBhgDBAzJIAhfI+fY4BYisAIYur/QcOKJ7m8+fNVWJdGSsMEAYIA8Ss5fNTY96BMEBsBSDkaU73HmSum0slpzkDhAHCAGGAmCUB3oE8gPB34WALAHmBsZW6dO0GLr17Q82aNVT1ggGS8AAyZ+5cWLNmLcydMxvSp08f/RsnSar6zWNWYIBoFlnsBrwD4R1IQgcIHV1RePbixYtB69athWYFAyThAaRd+/Zw6eIl2Ldvb+xvzAAJhqxZswgpv8xKDBAGSEIGCMFj7tx5cPrMaQgMCBDOac4ASXgAqVKlKpSvUB6dQqckHoDcvXsXGjX6AX5t9isM8vY2uPazJzp7orMjob6fRYePHIHg4DHw2/x5wvCgkRggCQsg7969AwKIj89gaNq0aeIACNmjt2vXHrZt2wa98Wx20CAGSMwvz46E7Aei14z3xo0b0BPDs0+dOgXy5s2riUAMkIQFkNevX4Ofnz/07+8OGTNmtH2A0NZ6+oyZMHrUKHj//j04YvYzBkjs784AYYDoAQiFZ+/V2wW6OzliTvOqmuDBO5APcPxk/AAIRQw4ceIknD17FooWKwpVq1QBWjt3794Dp06dQkfQzmBnb6f+fW3tDuQc+hc0bvwLeGDO5dBJodCsWTMGiAE1YIAwQLQChHb2np5eULJUSejUsaOunOa8A4k/AKG8LCP9R8Lx48fRj2c/7N+3H4b7Dodb/97C05utkCdPnsQFkKdPn8LPPzeGShiDZ/CgQVC3bj0GiBEVYIAwQLQC5PffF8D5C+dh+LBhkDSpdvNN3oHEnx1I5LJwDOHRGNfMEMwW+e/Nf6FHj+5w//4DxcTcUCiaWMuJrexAIiIiYMiQobBt+3ZYu2a18p516tRlgDBADEqAY2FpC2Wyd+9eGDM2BObNnQNp0qRR/2VqpAbvQOLHDiTy87x8+RJq1aqtJP1avGghJEueXNu3tQWA0Nnd6jVrYIDHAFi6bCmULVMGnjx5YhAg02fMwHg9xxQh7d6zB0JDJ0GGDBm0CU1C7XC0bniPRwKpUqWS0Jv2LigzWWocO1myZNobm9mCYE/jZ4jplGRmv1qa01k+vbu9vb2WZlLq0vkz6WzUPBlSOhbs5Nnz55AWISC6i6CdvT8edbi7u0P27NkERzFc7QN+e1q00qdLZ1Y/ehvT2LTzsrMTON/XO4iRdvTNnz57Bg5xsN7QnNu5Yyd8//33UKhQwWhP6OjUHd6+eQ3z58/X/sa2AJDbt+/Ajz/+CB06doC+ffooWy9jALl37z6QZQGV/h79MfzCGMiSObN2wZnZ4hkq0ktcxHLmyGFmT/qaX716DcNO5IyTBTQ8PBwuXbkCJTBqa1yV27dv4yWhfZx8+0ePHkE4Gnhkz2beYqxXdpdR9l/kyydkfksLbjc0RPHo3x8qVKigd8jP7SgKwfV//4UihQqZ3ZeeDm5grhKCl4ODg57mZrWJwB+M5y5ehJLFi5vVj9bGtBYO9hkCeXLnhs5dOkPBAgU+d0F/c3Vzh4MYy+z48WPaf1DaAkDIHp1AUDTKgkQXfteuXoV0qCzZsmeHkJCxUKF8+WiyZz8Q9gNhPxDjyxHNId8RflCsaFHMaS7maa62uPERlnWPsC6iB7k7wt8JfwRUr/61svPPF8X0euGiRVD6yy+hQYOGsHLVSqhUsSI8fPgQson+uLEFgOzcuRN27doVTXffvHkLCxYswDALxRXBtWnTBr744gsGyH8S4Et0vkRXu0SfM2cunDl7BgJGjhTarajBg/7OALEeQNauWwezZ88GP/wRULJkic8BXGnX8fzZc3iOR5np0qXFxF+VoU7dungXUhPKYo6eatWqKTtUoWILADH0osaOsKLW5R0I70B4B2J4mdi7bx+GrpgK06ZNlXpXwwCxPEDojm3q1Gmf4Z8pUyblI0eGT1q+bDksX74c+rn2gxbNmyv3cWPRQILukYNHj0KgfCXEDqUSA4RjYYlri5yaHI03fkfjvXXrFnTFlLSzZs5Ec87ccj76f70wQCwLELpb9UYXhi/yfQH9+vWNljQsEiC5MeQ+OVmTIUGkqS4dV9I/mo0LbBUgr9+8gUV4vlcUz29rVK9ucBLwDoR3ILwDiT41aIF3dHQCFxcXqFxZwy9RQcwwQCwHkIuXLoEHWqJ27doFfmjUKJaVnUUCuNoqQET0mQHCAGGA/H+m0K9Sb8xpXgLPyzt36iQyhTTXYYDIBwgdQW3atAkm45FjUFAglDBi5cUA0ayuphswQBggDJBPc4QWod/R6ISsdoYNHSLsI6J1SjJA5AKETOInTpoEFy5cxLD6I02aJzNAtGqrSn0GCAOEAfJpkpBT7YTxE2DWrJkmc5qbOwUZIPIAQkAYNNhH8SLv3ctZ1diBAWKu9sZozwBhgDBAAG7fuQO9evWGKVMmg6XlwQCRA5DzFy6At5c3tMdsgb/80lhoZWSACIlJvBIDhAFi6QXTkDbefxB/rLBevnwFbdu1Bc+BA3WFZxefbZ9qMkDMB8hGvO8IDZ2MKSuCFD830cIAEZWUYD0GCAMkMQOEYoH5YIiLUuiJ3KZ1K8FZY141Boh+gFB2wE/3HRdgJDp3Zv7Pv0P0izBARCUlWI8BwgBJrAApXLgQLFi4EE6fOq1Y7lgrqCYDRB9AKH4aRRunaBpubq66vhcDRBAMotUYIAyQxAqQBw/uY/TV32DSpIlWjQjNANEOELKw8vb2hm7o3Fm//ne6LeQYIKJkEKzHAGGAJEaAbN26DUYHB2OoksmQTzTmkeCcUqvGANEGkPUbNsKMGdNhhK8vfIlHjeYUBog50jPQlgHCAElsAKE4Se3atQdPL0+oKCE8u9YpyQARAwj5d4yfMAHOnTuP8alGo3+H+TmLGCBatVWlPgOEAZKYAEKe5gM9PTGBmgNaXQ3QHvdIwvxjgKgDhO47vAcNhmLFikIvZ2dp34kBIkGBo3bBAGGAJCaAKJ7meJ7esmVLKFJEW0pbWVOPAWIaIGfPnYMhaBnXrn07zFX+syyxK/0wQKSKE4ABwgBJLADZgTlzJk2chPkhZsGNGzcZIFmsn4WUot0eP2kcIBs3boSp06YrVnFFixT5HClX1rLHAJElyf/6YYAwQBIDQG5h+t5+/Vxh4sQJiqf5mTNnGSDxCCB0tEj3HbQ79PMbAVmyZJG80n3qjgEiWawMEAaIrQOEUph27NgR+mNa02pVqyq/ahkgDrhIx48dCN13DBzoCYWLFoH+bm66/DtEl0UGiKikBOsxQBggtg4QL/QfqFC+AjRv3uzzrGCAxA+AnDp9GoYOHQZOTo5Q/7vvpB9ZxVwGGSCCYBCtxgBhgNgqQCg8+yzMh30ezUADAwOi/bJlgMQtQMqVKQObNm8Gyjk/xGew2f4dousdA0RUUoL1GCAMEFsFyIEDByF0cijMnDEjWlpTmhoMkLgDyJFjx2A7OnKev3AeggIDITJfueCSZVY1BohZ4ovdmAHCALFFgFy9eg369O0LoRh4L1++vLEUnwESNwB5+DAMeiupgiuDS+9escAueXmL1R0DRLKEGSAMEFsDyKtXr6BnT2e0uuoL5cuXNzhjGCDWBQgdJ54/fx6dOL3gO7zroORPcVEYIJKlzgBhgNgSQMjPwM29P1SsWBHaY44PsrgyVBgg1gMIwWP1mjUwf958NNH1g9dv30CFcuUkr2Ri3TFAxOQkXIsBwgCxJYD89tvvcPnKZcxpPtTkHGCAWAcglL9j0qRQuHz5MvhiMESKZ2XKkVB44dJZkQGiU3DGmjFAGCC2ApCdu3bBuHHjMUT7PEiTOjUDxIgELuFi7oCxwCztB/LkyRMYQP4dmHfFzdUVkidPDmqe6JKXN74DsbRAGSAMEFsACOU0d3HpA5NDJ0F29DRXK7wDsSxAyL+D8pU7YyDEhg0bfP4cDJBPokiC53ofYynpxwg1vY0Xfw8LC1PyMlPp5+oGY8eMsfivEUMv/vTpU6B81Lly5YwTuVy5cgXHzgUpU6a0+vi0tadfgiVLlLD62JED3rp1C+zs7SGrhcJGmHox0sFwDF8hA14v0NPcyak7AsQFqlWrKiTPi5cuQX7MbJciRQqh+jIrUTj56zduKLGe4qJcv34d0qdPDxkzZpQ+fAQui1u3bsX8HTPBd/gwKFq0aLQxCCDn8DK9VMmS0scW6ZDWnHcYJj5f3tiWeSLtDdZJklRz0wQNkOn4cY+jLTaV3bt3w0T81eaQwfxY+1qlSIvoe1So1KlSaW0qpT6FuKCxrZXKNOpDR0REwPPnzzGsuPXlHvkcZK2UFHOCp0SIWLvQIhoR8REzAZoHb1qQQkMnQ+nSX0KdOnWEX+MZyj5tmjS6M9sJD2SgIj3zS5R9+nTpzOlGd9uXL19CiuQp8MeDne4+DDWk/B2//74AHmNoEqfuTpA2bdpY1eh399Nnz+JkvaGHoTUna9asDBBZX56PsPgIS8YuQKs+3n/wAMLfhUPu3Lm0Nv1cnxYj+qV79do1zFY3XDljFy18hCX3COvR48eYX8UTSuCO2hlNdO3tDMOJj7A+aWiC3oFEnWQMEAZIQgXIvn37YPLkKTAHw7Mn0wAP0n8GiDyAnD17FrM7ekOPHt2hYYMGJuNZMUAYIKI/8lTrWcSkTnXU/1cgxybKh50qDo7Q3uERzmlMnFO+bFkNTyy3Kp2F2+P9T0IEyDXcdTj36gUzZ86EXDm136ExQMwHSKR/x1yMZzVqVBCGx1e/02GAMECkrWIMEAaIniOsF3iG7+zcC/q49IZKlSrp0kcGiHkAeYM/gCaMnwA3bt7E40NfvJB3EPoODBAGiJCiiFRigDBAtAKEEg8NGDAAyleoCO3attEd/psBoh8glL/DZ8gQKFCgILhiuBgtRigMEAaICBuE6jBAGCBaATJ7zhy4ib96fQYPNsuCigGiDyDnL1zAxFwe0BsDIX737beavwEDhAEiBAeRSgwQBogWgOzEnOaTp0zFe48Zqp7mavrHANEGELrvWIPxrObMnQeBAQFQrFh0/w41eUf+nQHCABHVFdV6DCB24cEAACAASURBVBAGiChAbt26rTgKTps2VbHjN7cwQMQBQj47EyZOhCtXrsJovCw35N8h+j0YIAwQUV1RrccAYYCIAIQcPrt07gJe3l6YmtZweHZVZYtRgQEiBpAwvO8g/44yZcuAk6Mj2JvpdMoAYYBonatG6zNAGCBqAKFL8yGYM7t8+XLQvNn/c5qbq4QMEHWAUDyr4cOGQ4eOHeGnH38wV+RKewYIA0SKIlEnDBAGiCmA0Lk7+XnQ8ZUP5s3WYu2jpqQMEOMAIbmvX78Bpk2fjnHygjGabmE1cQr/nQHCABFWFrWKDBAGiCmA7MBLc8rvMWniBLOPTmLqIgPEMEAoVtSYMWPh1u1bSv6OTJIDLjJAGCBqXBD+OwOEAWIMIOSgRs6Cs9DiSiQ8u7DS/VeRARIbIA8wPtlQPC4s9F/+DmPZHLXKOmp9BggDxBz9idaWAcIAMQSQ169fQ5eu3fDydgCUtVCoFwZIdICcw7A6FM+qTx8X+KZ2bc3+HaKLAgOEASKqK6r1GCAMkJgAUTzNBw6EKlWqQMsWLVR1SG8FBsj/AbJq1WoMw/47DB8+HEqWtGx+GgYIA0TvnI3VjgHCAIkKELq8JUe1O3dug5enp8V+BZMiMkAcIF26tDBu/Hi4fOky3nsE4/+3fH4SBggDhAEiQQIcjTd2PpAdO3bAjJmzYNrUKZBaJae5uZ8gsQPkw/sPEBQUBBUrVVT8O6yVmZEBwgAxd+5+bs87EN6BRO5AKCnUgAEDYcrkyVZJr5yYAfLX33/DxAkToUfPHtDo+++lzWeRjhggDBARPRGqwwBhgBBAKLVvq9ZtwG/ECMVh0BolMQKE8pWvX7cOJoWGKruPMqVL645mrPcbMUAYIHp1h+9AokiAj7A+HWHlzJlDie5as1ZNaPLLL9J0S62jxAYQMk4YHTwG7ty+De3at4OCGIo9S5bMamKS/ncGCANEmlLxDiRx70DevX0Hq1evhtu4qPliTvOkSZNK0y21jhITQB48fAgD8XiwVKlS4ObmCpevXAGHDOqhTNRkqOfvDBAGiB69MdiGAZK4AbJp02bYhd7mE9HT3M7OTppeiXSUWABy/PhxJZZYP0z8RP4d5Bx46fJlBkjevCJqIlYnifYfPknQ5PBjrN4/RogNGI9qdezUCYJHB2OI7CxWfyoGSOIFyPETJ8DDwwPmzZ2Lx1jac5qbq6y2DpCIiAhYs3YtLF68BIZiHLHiJf7v38EAeQH5GCDmTqFP7Rkg+SBVqlRyhKmhl8R8B/ISc5q3a98BBiBAqlWrqkFq8qraMkAonlXIuHGYv+MKjMLL8gwZMkQTHAOEAWJ0Jr0LD4cNGEnzyJEjkDx5cqhRozrUqVPHaH0GCAMkR/bs8lZmlZ7oMrdv335QslRJaNy4MeTJndtqY0cdyFYBEhYWphglVKxYEbp3dzLo38EAYYAYnHSvXr2CPjg5t23dCl9V/gqS4tnc7j17oPHPPyuepgSUmIUBwgCxJkCmY4jwsLBH0LVbV8UKSy0fiKXoYmsAoRP105i/w2fIUOjZozvUr1/fqOgYIAwQg8oREjIOLyQnwqJFi6AyAoSU6q+//oLOmM1txowZ8MMPjRggUSRw/vx5yJePAWItgPzzzxaYNWsW/jMTKMsgA6SUFD7SfcfKVatgwe8LYPToUVCwYEGT/TJAGCCxFISUaNTo0fDwwUN0EgqMlnynbNly8H2jRhAYMJIBwgD5LIHr16+DfcqUYA2AXLl6VUmNOnlyKPofZIH7GDqcAWI+QJT8HWPHwr1792HoEB/IKJC/gwHCABH+5XLp0iWoXfsbCAgIgA4d2jNAGCBWB8jTp08VYw1vb2+o/NVXyvgMkMvwJfplmFPovmOglxeURAurvn36CGdsZIAwQFT17tDhw7B1y1blOKtosWIwG48NDAWo4zsQPsKy9A7EBRe3Bngm/+OPP37WWwaIeQA5cfKk4hzY36M/1KtbV3U9iFqBAcIAMakwdJzl0qcvXEaHofOYKKZp06YYqM7jc2a3jRs3KSZ+VBYtXgQTJkwQ2vpq0lKBypQ46C16Izs4RDczFGgqpQp56DqgiaO1IpFGfegPaI10H8fPmSOHlHfR08mTJ08Uw4q0adPqaa7eBu/gli1fDlevXgN3d7dov5DJlJe8ktOnT6/ejwVqEMAyZ8ok/Ktd5iO8R0vJsMePIXu2bJq7pXvNPbv3KD8MXdGrvFChQpr7oJ0Lma5bOuKxoQejtenuvXuQKw58f+h5aM1JkyYN+4GY0hpSMpqc6HYK169dh/bt2yu24CtX/qnklj6Hl8fkxEfF398fQsaGQKZMGTUrorkNXuBF6uvXb+LEiZGe/d9btyBb1qxW94Kmscmc9TqmbS1UoIC5YtTdnhZRgmdGBwfdfZhquHPXLliFl7ujR42KFbSPjrXeY0jxzJkzWWRstU4pZW6uXLkgebJkalWl/z0cAXLrzh3IjwYcWsrbt28hdPIUePQoDAYPGgQp8f5KT7mNY6dNkxbhbfn8HzGfjwBCkZcLqVz063kvkTa05iTBkDnsSCgirf/qLFq8GJ22BsA6jMRZpkzpaC35CIuPsCxxhHXx4kVwc+8P06dNNehpzkdY2o6wHj16hPJ0xzukytANTaDNCf3CR1h8hBULH/SLdtnyFej7AdCyZctof9+8+S/ohJeYf/zxB1StWoUB8p8E2IzXMlZYFJ7dyak7DB48GAP4lTT4U4cBIg6QEydOwpAhQ6BXr17w7bf1zA7BzgBhgMSalLQ1bNeuPVzAX35//7UZ7xU+HUvQcdYwzHW8GHchOzFwHR3ZRC28A+EdiMwdSKSnee3ataB58+ZGFzsGiDpAaO7++edKmP/bbzAWHYHV/DtEDyUYIAwQg7qyZ89ehEg7qFWrFjg6OSrnnGvWrIaZmCZ0oOdA9FDtEasdA4QBIhMgU6ZOhadPnoIn6pupwgAxDZA3b95AcHCw4rU/bNjQWPGsRGFhqB4DhAFiVH/2YOgSX98RcOPGDaBwwVnRaatnz554rNXCYL4FBggDRBZA/v77H5gzZ47iaa52wcsAMQ6Q+/fRKXDYcChevDi49O4lPU8KA4QBYvIHCHmnkokmFbK+IssrY4UBwgCRARAyiXZydFLgkQnNY9UKA8QwQM6h2T0ZHwxA/w46SbBEki0GCANEbX4K/50BwgAxFyB0Vu+L+cx/QkfBChUqCOkeAyQ6QEiGK9DIhfJ3BGDIoSKFCwvJUU8lBggDRI/eGGzDAGGAmAuQU6dOwbr169EzeoCwXjJA/g8Qcm4bP2Gicuw8Jni0xfPTMEAYIMITVa0iA4QBYg5A7qBTWtdujnj3MVuTZzUD5BNAHqJXuDv6d1T/+mvF1N4c/w61uR75dwZIAgII/aqgC8WsaD5L+YjjW2GAMED0AoQshXr3dsGFryMmLquhSbUZIJeBQpr4jwyArl27QMMGDTTJz5zKDJAEBJDJGHogJCQEaqFdfIvmLZQMgRSDJr7AhAHCANEDEPI7GoLJi/LkzQPdnZw063NiBggdWU1Gc+cd23fAuJCxUMDK4WwYIAkIIBRO/XdM9LJhwwbljDM7pg+tXbs2NGzYAOrVq2eVLaupXysMEAaIHoAsXbYcDh44oOSe0WMplFgBQhaSIzG1wq1/bynJnyIdfs3ZUWhtywBJQACJ/LgU3HD7jh0YTuRP2Iu+Grdv31bMHX9t9iv8gMmeypYtq2o7r1VRROozQBggWgFyGFMF+PmPhPnz5kK6dPoC8iVGgNy9exeGDh0GRYoUgYbfNzQ7H4jI/DZUhwGSAAES9UM+wUikR48cVY62Dh48qISULlCwAHTs0BE6duxg1fDiDBAGiBaAUCjwzl26wqSJE5R0wHpLYgIImeieOXMGvLy8lbQKFdHU+TJmaDQ3oZRe2TNAEihAKJTwnr17Ye2atbAD41I9QI/T8uXLQx1MCHMKE8Rs274datasATOmTzfp/KdXcQy1Y4AwQEQBQmf33dDiygnD5NAxrDklMQGEgpz+sWIFxqQbBsWKFgUyPqBFnAFijgbpa0tpLJ7jOpxgwrmTshw/fgKdhFbA6lWrgRLp5MRkKt9//z10wN1Ggfz5lTNk+pWyYMFC8PDwgH+2/KOkqbRGYYAwQEQAQpfmAYGBGIwzmxJO3FwjkMQAEJr7ISHj4Nr1azAW85anQeMZKgyQk1ChXDlrLG+xxkhwAJk7d56SCzo9hhRphWHWG+DleTm876CMYDHLyZOnoAGa821BgFAcHGsUBggDRAQgCxcuxOPWQzBqVJCUI1ZbBwiFdnHt5wq1v6kNndG/gzI/RhYGCAMkCe4YKFZh9PIxItZ/2rV7N0bUDFNyQqsFmKOtFaU6taZlBgOEAaIGkCN4X0eRYWfMmK6kA5VRbBkgx44fx0yfIzE2mCN89923scTFAGGACANExmSzZB8MEAaIKYDcvXtP8ZCehpkFv/jiC2mqaIsAoWO+9WiuT6cOFJKEjAwMHfUxQBggJgHi4tIHyGRPtNSpWwecMeR6XBQGCAPEGEAoB7dT9x7KnUdNjZ7marpsawAhM/2goFEQhqlnBw/yhowZMxoVAQOEAWISIF26dEE/jztqc+jz3+s3qA9urq7C9WVWZIAwQAwBJNLTPG/evNC9u5NMlVP6siWAPHjwALy8B0HZMqWVtLNqjpUMEAYIH2FJWFIsYhGh4bk4J7rhnOh0vbdkyRI4dozO8v0UPyXZxRYAQnKiSMSDfYag9WR/JSCiiHUaA4QBwgCRsKIwQM5BebTIi6ty/bphgBw6dAgCg4Jg9qxZkD59eos8XkIHCO3QVq1ejZEl/oAhPj6Kd7loYYAwQBggorPFRD0GSPwDCKVTpXuPSRMnQp48uSV8ZcNdJGSA0N0Q5e+4it7kZNacLm1aTXJigDBAjAKEHAWvXbsOpUqV1KRUcVWZ70D4DiTyDoQWtg4dO2IebhclIoIlS0IFCF2Su7u5w9d4XNWlS+do/h2i8mKAMECMAuQRKliDBg2hYqVK0LuXM4KklNC5qKjyya7HAGGAEEDoSGbECD/Imy8vdOncWbaaxeovIQLkxIkTMNx3BF6UO0PdOnV0y4gBwgAxChC6WLt16zbmNQ6AzZs3ww8//IAZx9zwOCBPvAQJA4QBkj1bNli0eDHsxThtIRhyI6rXtO5VUqVhQgIIwXXlypWwGA0LRo8ajf4w+oNIklgYIAwQoTsQ8kidggmltm7bCq1atYZezj2VfCDxqTBAGCB0mR4aGoq6Olmap7majicUgNB9x1iMZ0X3dYO8vSADhiQytzBAGCBCAIlUtP3798Oo0aPh0sVL4IjhDdq2aQMZMxl3NDJXQbW0Z4AkboA8fvwEvAcNgkmTJkJBK2bGSwgAefjgIXgPHgxlSpeGHj17QHJJ5swMEAaIJoDQgh6O+Y8pLtZIjJFDgdZ69+6F+T+sm/sjEizkNRsZyotyOwRj2IWsWbJo4Y6Uuo+fPAEKcZ8Xj/fioly4cEEJN6EWo8wSz0aZ6c6eO4fOZ2Us0b1Qn2RF5ObeHzw9B0KVypWF2siqRHMg/F045MqVU1aXmvo5e/YcFC5cyGhgSPLvIOdAj/79oVatmpr6Vqv8lsK5X7kCpUrGjaHNZRzbIYMDZM6cSe1Rpf89AteeEyhbCigbF+UJrTlo6JRgwrnHFBJticl+PHRSqLKI93ZxgV8a/2zV1LYzZs6CE3i8RmUn5iWZGDoJFcr8rblWhaBF9MP7D5AqdezIxFr70lOfglemxqjIlnCUU3semkg0vowjEbWxDP2dzvVDQydDjhzZoVmzZla/n6NFlEKPpkqZUs/jm93m2fPnkBYDQ8b0Gie5bNmyBXbv2g1dunYB8sSXXegHHFlrWsrHRu156UebXQo7sLO3U6sq/e8fUb5PUfZxsd7Qy9CakzVr1oQLkMgvQjuSORh0bTomj6JfIuS0lSy5fI9fNQ3gI6zEeYS1ZOlS2LRpE4wcORLUovGq6ZCev8fHIyw6Wpo4aRJcRzN8ylduKOWCnneN2YaPsPgIS/MRljHFo8u5vXv3KeHeGSAypqd4H4k1lMlB8jQPDML83EMgG1pgMUAA6GijT9++UKtmLYunlWaAMECkAUR8ubNMTd6BJK4dyJ07d4CiRY8bFwJ0lGKPR0iJHSDHyb9juC/KpTd8g6l6ReJZmTMbGSAMEAaIOTPov7YcysS6oUwop3nXrt2U6Lq1atWCGzduJGqAFCpUENav3wDz58+H8ePHKQYV1igMEAaIMECOHj0Kr1+/gapVq6iGebaG8sYcg3cgiWcH4oNRYylVctu2bRQ1MBZM0Rp6GNd3IMePn4Dly5fD23dvwQdNddOlS2eN11bGYIAwQEwC5OzZs0BB6QoWLITROlfAhg0bYc2a1VJyScvWcgaI7QOErP0WLlwEhw4fhmC8HI60OkusALl37x54enlD5a++UnZjavk7ZM85BggDxCRA6GimTt168BLN5WjypkqdGvriBV3dOt9A7tx5ECTJPyvt4sVL0C/kAcbN6mXxs1dDE4EBYvsAOXz4CIzDI5oZaPEX1eclsQGE5uIZ/HHn5ekFv/76K7Ru3cqq5vOR848BwgAxCRBSVNqFkHXVatx5HD50WLmwpJIbneaKFC4MFSpWgOLFisPGTRvh8qXLuENZo4DF2oUBYtsAuXXrFjg791LO+PPnzx9NvRIbQJYuXQZ/Ykwrf78ReIz0FnN4FI6TUwEGCANE+A5k4cKFCIe1MHHiBDhw4CDs2rULTp8+rVxgPgwLg/foD9IGQ5uMGRNsbXYo4zFAbBcgr9GvoWePntCnjwtUqFAhln4lFoC8evUK/TtC4ebNmzAW55mdnR2cOXOWAZIls9XXHPohffwkA0QYICQwcp1Pj5d0keaBtEN5+uwZ0Fls2MMwKF36S6te4kXVGgaIbQKEPKoH4eVw0SJFoVOnjgaPRxMDQMLCHinHx99++61iPJAiRQpF/RkgDpCFASIHoEmSau5HGCDU85EjR2Dq1GlQtVrVz7kWKA4UufNb2uZc7c0YILYJkMUYnv3kyVNKTnNjxdYBchiNBgKDRoGTkyN8hwCJWhggDBC1tVH475YEyLVr15QEUxQWwQWPErp26aI814ABAxUzSgqZYC37c0MCYYDYHkDoqDQ4OBjmzJltMjy7rQKEdv3r1q2HmRgeaDw6TBYwEGWYAcIAEQaEWkVLAsTPzx82btwIf/75hxLEK7JQsinKbkaWWmvXrYU8uS2Xf9rU+zNAbAsgd+/eA2fMmEc5zXPlymVS9W0RIBQsb4SfH7zAgH3Dhg0zGqySAcIAUeOC8N8tCZD+/T2UUO5kBROzkK9IkyZNofY3tTHMu7/w88qsyACxHYBQlNXueGnes0d3qFFDPae5rQHk9u3b+KPMF+8USytm8aYKA4QBIm0dtSRAxo+fAGvXrsV/1oC9vX2sZ6ajhi1bt8HqVSutkko05gMwQGwDIHRpTp7mJUqWgHZt2wrNDVsBiOLfgVZVXl5e4OHRH6pXr67qHMgAYYAITRKRSpYECO0y6tSpq+RG98KUmBkdHD4/Eil+fw8PuHL5CoZVWBYneSkYIAkfIKRHs+fMhYsXL4LfCF/hHyK2AhAKTb/yjz9hOL570SJFRKY8W2FhQim2whJSFfVKlgQIjU4Xem5ubgogfvjxB6hYoaKSROnQwUMwb948GIJhtbt17ar+oBaowQBJ+AA5hOHZx44Ngbl4aW5nYJdrTG0SOkAoOOS4ceOBDFXGhoyFNBjxQbTwDoQBIqorqvUsDRB6gCuYRnLO3LmwYvkKoFAnVFKjwvfr1w/PrbtjhrBP9unWLgyQhA0Qco6je48Z06dhmBxthhgJGSAP0X+qd+/ein8H+bkkT64tigMDhAEiba21BkAiHzY8/D3QZd/79+8hZ84cCkTisjBAEi5AKC1qTwxT0hutrirryGmeUAFyCEMDBQQGgnPPnlCvXl1d04cBwgDRpTiGGlkTINIeWlJHDJCECRDydfDEoIBffvkldOjQXpdDakIDCL3zGjRImT//NwjBI6t8mK9cryMuA4QBImkJBWCABKOPShZp8hTtiBNK6U8oNQ+TINGlue/w4aoWR7ZwB/IBd+wj0NT9Ofp3UP4OhyjGKKL6FrUeA4QBokdvDLZhgDBApCmTYEfv3r6F0+f0AWT3rt0wKTQUZs6cYdLTXO1REsoO5O7duzAQd1uVKlWEXs7OuoHJAPkkgUuXL2MYJQaI2vwQ/jsDhAEirCySKuoFyG3Mad6zpzNMnTIZ79BymvU08R0gZJ58/PhxDArpA95oAv91tWq6j6xiCop3IAwQsyZP1MYMEAaINGUS7EgPQMjTvEuXruDu7gZVqlQRHMl4tfgMEHKMXI4Wi6tWr4bhw4ZCYcyhI7MwQBgg0vTJlgCyZ88emDxlKuzbuxcoLtDX6JVL1io1ahj2zuVL9IRxiU5We74jRmAOiyLQvl07KbofXwFC/h0hIeOU/B3BwaPNOqYzJigGCANEyiSiTmwFIBswaCMlEKpfvz60wnSdyZMlh99++w0ocOOECROgceOfY8mMAZIwADILI8tewsyVIzCbXnJ0SJVR4iNAHj58iP4dLvDdd99Bx44dNPt3iMqFAcIAEdUV1Xq2ABD6hdqiZSugo5HlK5ZDyv88ksn0sXXrNkryqi1b/okVLoUBEv8Bsnv3Hpg+YwZMmzolWk5zVcVWqRDfAEJ5c3xH+EFfFxeoU7eOua9nsj0DhAEiTcFsASC07Xd374/B9EqCS+/okUj9R46E39B2/sCBA5A+fbpocmOAxG+A/Pvvv9CtmyPMnj0bw7Obd2kec8LEF4DQj5w//vgDFi5chKlnJ1oltQEDhAHCABGQANnP12/YED5GfIS///4rlgkkAyT+AuTVq9fQFWOk0aV5pUqVBL62tirxASAU0C8gIBDeYP52Ly9Po/k7tL2Zem0GCANEXUsEa9jCDsTQq9KxVmBgEEyZMgX/mQw//8x3IFHldP78eSUbJGWLtHZRs8KK9DQvXZo8zTtY5PHiGiC0uwqdFArly5dD0+SeVo1GzQBhgEibVLYIkPfvP8AEzEo3BvONtG7TBoICAz5P0NNnzsCjR48U+QXir7+QkBDIlCmjNHmKdkRmqa/fvIWs+Cs0Lsq/t25BNswSaWdnZ/XhCe43cAEtmD+/wbFXYHjy8+hoSL/K9YbrUHup+w8eYBBPO/TqzqBWVfrfjx47jhkDh0J/PHatWVM9+ZXsB7iJss+FfjQUIdvahRLM3UbnyC8wFEtclDs4dto0aSBduujH2dZ4FjLPvoqpvAsZSDNsjfFpzUmK35zC4EgrtgYQUtBBgwYrFliOjo5KHpJUKVN+ltc//2xR8rFTmY8hMcZPGA8ZM1ofIK9evVJMjc0NS6FXEShXC713ijiIhExHi/dwfENpZ/ft24c+EMvBD1Ozpozy3fS+p7F2FEqGothacyGhBWTFihVo0LEVXF1doWhRsfwdst+djEqyZMkSJwB5j/PzYVgY5MiRQ/ZrCfVHlm60606DELF2oe9/B51htUaOlvWctOZQAFsGiBGJknJ0794DDh8+rEzQ3nihbupXFt+BxK8jrBs3bkDfvv2UY8ccObLLmjcG+7H2ERZNXsrfcQujUQ8cOACSJU2GC4npvO2WEgAfYfERljTdspUdCE3QZs2aY7a1M+hMOAW+b9hA9fiDAWJ9gFCIDro03oM7jYoVKkB6PEqg/0+lXbv2yrHVV199JU2/jXVkTYDQkakzhp6v36C+4gj5+MkTCH8XzgCx+FeOPQDHwnrBO5CYakGL0iCMUrpk8RIIGRei5IWOWpJAErRwSc9+IFGEEheX6AT5SZMmwfETJ5UzeMrp8fTp0895YerWrYt+O62ssqxYCyDk3zHCzx/69nGB2rVrKz9q6P6FAVLKKt855iAMEAZILMULwzPV6tVrKItR0qRJY/2dzju3bdsa68yddyDW24HQxbnHgIFK3m5Hx27K/QOB/wn+Gndzc1e+WUM0uW7ZsoVVFhZLA4TOu/9AYwDKxEnBH/NGubhkgFyGL0sxQKyi6FEGsUgKCVs4wqK7j5WrVhn9HimSp4CmTZvihWnaaHUYINYDyJ8rV8LBAwfxcnxELMg/R+sQKl06d4Ep6HGeJbPlLdMsCRA6kvP1HaFk3vTx8YmldwwQBoi14UHjMUAkS50BYj2AkEf5oEHeUMCECWMo5vnIgMmS2rVtK/lLx+7OUgChlM3Dhg2HChUrgBNaARraETNAGCAWV3ADAzBAJEudAWI9gPz440+wevUqkwmRNv/1N5w6eRKPtFwlf2nLA4SO406ePAWeXl6KlVWtmjWNGnEwQBggFldwBojlRcwAsR5AKBEUgYFCshsr5NSZM1cuaNWypcU/vuwdyIIFC2EVHqMGjQqCAkYcJCNfigHCALG4gjNALC9iBoj1ALJp0yaMR/YPhpf5f1SAyC9Mxg9U2rfvAPPmzbWKY6csgNDOY+GiRbB/334YPXoU2P8XCdqU9jJAGCCWX91ij8BHWJKlzgCxDkBokV2OHtge/T2gp3NPNGnt83mhvYte0a79Ph1ZtWnbBn7+6SfJX9lwdzIAQpZWBI8LFy7AELwsJ8sykcIAYYCI6InsOgwQyRJlgFgeIBRahjzL/8HwHU+fPoFffvkFc32fgA/vwzGMih18xG/aoUN75ct+g34S1irmAoRSCFCwTvrf4cOHaQpKyQBhgFhLz6OOwwCRLHUGiGUBQosrmbPS/1IAP3c3N6hWraqS+Os0BkssX7as8kUtFTDRlLqYAxCKJTVgoCdUxdzs3bs7mTQMMPQMDBAGiOSlTKg7BoiQmMQrMUAsBxBy7uyBKYZ/wjD6R9Ebu1q1atCiRXPl46iFcxf/gvpr6gXIoUOHwWeID3h7e0PNGvoi6TJAGCD6NVd/SwaIftkZ+AOqzAAAIABJREFUbMkAsQxATp8+DUPRF6JXL2e4euWqckfg7+/3OZRMQgQI5ShZunQZrEJT5FGjRpkVT4gBwgCRvJQJdccAERKTeCUGiFyA0GX5PrRGCgwKguDg0XAfj3qmTpsOs2bOiJZ3JKEBhI7ggoPHKGFXyJPe3CRcDBAGiPgqJa8mA0SeLJWeGCByATJv3nzMdbEF07SOBLo8d+nTF0JDJ0HePHmifbmEBBDKm+Lm7g51vvkGOnTsCCkELa1MqSoDhAEieSkT6o4BIiQm8UoMEDkAeYuX4mNDxgFdLgf+B4/uPXrAAA8PKFeuXKwPklAAcvDQIcUIwKN/f6hVq6a4YqnUZIAwQKQpk4aOGCAahCVSlQFiPkCePXsO7v3doUzpMpjbu4diUTUAo+6Ww1zfFNPKkIVVfAcI+XcsWboUli9bDuPHj4M8MXZQIrrFOxDDEqBAkxRSnaPxmqtF2tszQLTLzGQLBoh5AKHAgQSLX39tCr80bgxJMJT+rFmzgTILkm+EsRKfAUI5S/z9Px3BDRk6RMmfLbvwDoQBIlunRPpjgIhISUMdBoh+gJAz4EBPTxiKi2y1qlUVqe/cuQsm4Z3HPMyBYSqfeXwFCKWbHeIzBCpXqQzdnZw0aJK2qgwQBog2jZFTmwEiR46fe2GA6APIuvXrYcaMmTB+3Dj44ot8ijz/RUfBXr16w/Tp0yB7dtP5zOMjQI4fP47h5gejf4eX4rNiSedGBggDRPJSJtQdA0RITOKVGCDaAEIJkuiI6sDBAxAydiykT59eEfaz58/Byak79OvXV/HOVivxCSDZs2UDiqS7es0aGIXmx/nzf6H2+Gb/nQHCADFbiXR0wADRITRTTRgg4gAhSyvK7Z0EBerjM/izXwc52HkPGgTly5cXDsMeXwDy4UMEzJ03D14gAMn0WCSSrgwVZIAwQGTokdY+GCBaJaZSnwEiBpBHjx5BH/TpqFu3LnTs2OGzRzmJdxo6CtLdwVAM75EsWTKhLxQfAHL06DHw8/eHH3/8Adq3ayccSVfoBVUqMUAYIDL0SGsfDBCtEmOAGJXA+fPnIV8+dYBcvHQJPD298IjKERrUrx+tvz179mCk3akwEz3Ntfx6j2uAHMDc7MOHDwdnZ2f44YdGkrVKvTsGCANEXUvk12CASJYp70CMA4TCkuw/cAACRgZAEN4NFC9eLJr0r12/rlyaU5iSHDlyaPoycQUQ8u9YSv4dmJvE1dUVChUqBDlULvw1vZhgZQYIA0RQVaRWY4BIFSeHMjG1A1m8ZAmsX7cej3n8YgUOfP7iBZq5dgd3dzeoWLGi5q8SFwCheFZ+eIej+HfgcRtFC7ZPmZIBovnrmdeAHQlPQgUD0RnMk6pYawaImJyEa/EOJPYO5N27dxi/KhTOnD2neGGnTpUqmjzJEoucBwkcbTGDoJ5ibYDcunULvLy8oUbNGuDk6Kg8st5w7nreN2Yb3oHwDkSGHmntgwGiVWIq9Rkg0QHyCn+l9+vXD4oWKQp9+/bBjIEpYklwxsyZQAsypXBNip7neoo1AXLw4EHcRY0Eby8vqFz5q8/+HQyQwga/r57vqaUN70B4B5IEz8cpE2n08jFCix7Fi7oMkP8DhBwBfYYMgYYNG0LLFi0Mfp/t27crfiBTp06B1KlT6/6G1gAI3XfQMdy6teuUEOwFChSI9rwMEAaIbgXW2ZBM3o+fZIAkaICEjBsP9KuUyrFjxyB0cihk+M8hTqde6GoWjkdBpFAp7e11tTe3Ee02aGzaRVy9eg2mYt7yVq1bYfTc8vgrPXbv9zCs+QSUnceAAeDgkMGs4SMiPsKr168sEmeKHuzNm7ew4Pff4Tn6d/TAAI+GwqpQHXp3O7vYuyyzXk6gMR0T0k8we3s7gdryq7zEeF+pUqbC9zfwoeUPF61HAvtrDKiYxowfIOY8It2FJU+eAndfyc3pRldb+t398iXqfVr58dVEHojWnJxo8JIvb16R6mJ1kmg/hUjQACEFonN8Kt0x5eqYMcGQNUsWMWFJrPUYkxO9fPESI73mltireFcXL16EvKhI27fvgJmzZqEXdmCsX+mRvdFC3KVrN/T1GAJffllKfBAjNWkHcg6zFJYpXdrsvmJ2QMdrHnhH80OjRtCmdWsM8Gh4kbxx86Ziekye6NYuDx4+VC7zc+XMae2hlfHOoQl3oYIF4+wI6wr+YClZonicvPuVq1fxB2MGyJw5k9XHpx+MpzBbZ9kyZaw+Ng1ICdHohyMDRJL4E8IRFoXZmISX2jFLGowSW7xYMcWxr1KlSppjN505cwb+/ucfOIYOdZQ9MFMmwxOKfrX4DPaBSl9Vgma//ipF8pY4wqJfd4cwf8fIgEBwc+0HNWuazt/BR1h8hCVFmTV0wkdYn4SVoHcgUb93QgDItGnTFPPT9u3bR1vknzx9CqtXrQIKP75y5Z+4M/hSWJUpLMnQYcPA3s4enQQHmkzRSuPfuXsPL80H6740j/lgsgFCxyILFy2GNatXw9ixYyB3bvVdHQOEASI8YSRVZIAwQCSpEoCoSR0t4IGBQbD5r81QpHDhaOPTIli/fgM0T62pOPSJlMePn8CAgQMgW7bsaJnkCbSTMVa2bt0GCxYuhMkYot3OTt55vUyA0JGk/8iReCz5AQZhJN106dKJiIHNeIswQIQURWIlBggDRJo6yQAIPUyzZs3hMmZ4O3r0iOqzXbt2HbMH9ofOnTpCkSJFTIYyITiRp/nsObMhW9asqn1rqSALILfv3AE3N3eoV7cOdOvWTdMxHu9AGCBadFZGXQYIA0SGHil9yAJI3br1ICU6+61ft9bks+3ZuxcjzgbgcZifcolnKhYWWel07NARk0UNhdKlxY/GRIUjAyB79uzFzIH+yjOSf4fWwgBhgGjVGXPrM0AYIObq0Of2WgASgBfDy1csh4JoORNZHqIlz7y582D27NkwEo9wOnfuZPTZVuJdyTLM7x0w0l/ZdVAxBhBS8v4eHvB1ta+hefNm0t43akfmAIQs6JYuXQYbNm5QYPjFf++j9UEZIAwQrTpjbn0GCAPEXB3SBZBhw4Yr4cajZsmji2O6l2jStAkEBQYaDEdOi21o6GQ4fuIETMCwJGnTpv08viGAkCUTeZo/uP9Aycxnqax8egFC9x0E02fPnin5O1LFCLOi5eMwQBggWvRFRl0GCANEhh4pfWjZgZAVlscADwz89/+otwSDokWLKL4bhvJwkHXWgIED0eY7nxKWJGa4dUMA2blzJ+5o5sDkKZPR0SyltHeN2ZEegNzB+44+ffvBT5i/o23btsK5R4y9BAOEAWIxBTfSMQOEASJN57QAxJgVlrGHuY0Jnnx8hkCt2rXxLqO9wWoxAXIBHQu9MO/HtGlTIYuFHSu1AuQAhpWneFZeaHJM+cplFAYIA0SGHmnpgwHCANGiLybrWgogl9Aiy9XVDQbijqV69epGj6GiAoQ8zTt07AjD8aisTBn53uF6dyA04ciRcu3atRgZeDzkzKkt74ipD8AAYYBIm8yCHTFAGCCCqqJezRIAIb+NSZMmoV+Ev+KlbqpEAoTuVtzc+0PdOt9AkyZN1B9cQg2RHQgdwfmO8IPkmCaXnB2j3t9IeAT2A2E/EBlqpKkPBggDRJPCmKosEyCkmIsXL4ZVq9coTn8iR1CRAJk/bz7cvnNbSfFqraIGEIpn5e09SAlH0qVLZ2ke8FHfj3cgvAOxlr5HjsMAYYBI0zlRgFB8p127dkN7vMvIbCBeFSml74gR8O7tOyXTnqhl0rlz5+HsubOwDrMOyvY0VxOSMYCQFRhFSh6M9zcjfH2hSpXKal3p/jsDhAGiW3l0NmSAMEB0qk7sZqIAMTXg8+cvMDvgACiOkU2de/bUFF2VjrvGjB2rhEDJbuW84DEBQhOLyu+/L4DNmzdD0KggyCMQz8qcj8EAYYCYoz962jJAGCB69MZgG3MBQsc8vXq7QJfOneGnn37U5LPxFAMxtkdPc390xLOEp7makKIC5OXLlxgNeIzS5Ble5gfi/U0KiXG3jD0LA4QBoqansv/OAGGASNMpcwByEI+1yGJq6LCh8BWGctdSSIn7uboq/iM9e/QQPvLSMoZa3UiA5MLkNn369IUff/xRadIaE1rRpb41CgOEAWINPYs6BgOEASJN5/QAhO4INmzYCPPnz4fRo0cpCaG0FGpPnunkyf3rr01NBlPU0q/WugSQBRh+feXKlXgEh+bGX3+ttQuz6zNAGCBmK5HGDhggDBCNKmO8ulaAkPJNxdDuhw4dhnEhYyFDBu1pZbdu3Qpz5syFmTNmwNVrV+MEIPQelLtj6dKlMB2dFnPGUVY+BggDRNpkFuyIAcIAEVQV9WpaAPIGc0gPwaizadOmgwEe/Q3m+FYb8cKFi+hP4QnTp09TzHxNReNV60vv38m3Y+jQYYpZblPMblhFRxRdvWPHbMcAYYDI0iXRfhggDBBRXVGtJwqQe/fuKT4RVapWBSfHbqr9GqpAl+aOTk7gibGxKlSooFSxNkBowR423Ffx7WjXpjWcPncOypctq+t9ZDRigDBAZOiRlj4YIAwQLfpisq4aQOi+4houuv36uUJ/dzclLAn9ctdaSGld8KK6QYP60Pjnnz83txZA6D2OHDmCPipDYRhe+lP+9vB37xgg78Ix9W4urZ9TSv0zZ85iQjEGiBRhauiEAcIA0aAupquqAWTnzl0wDuM/kXMgJYDSW0JDQyHs0WMYPMg7GoCsBRCK7vv3339jWt5AvHP5dOmv5omu9121tOMdCANEi77IqMsAYYDI0COlD2MAoTwfK/74Q3GqmzljOmQ1I53sli1bFYutmegsGNM81tIAef7iBQRi7o63aHEVGBgQbXwGyAPchfEORNpk0tARBRt1yOCA94CZNbSSU5UBkoAAcvPmTeXopHHjxka/fsdOnSB4dDAu0lnkaIiGXgwBJDw8XPml/vTZc/TzGApp0qTR0GP0qpcuXVbyn8/AS/Ns2bLF6seSAKFw8q5uborsW7ZoESt3BwOEAfJlqVK6dduchgyQF5gjSJv5v0l5J9F+rJ4Ez7U/xur0Y4Q531Vq2xf467dNm7ZgZ28Py5ctTRAAefr0mRLQME+e3ODi4qIpLEnMF3zy5Ak4OXVHy60hYGyiWgogu3fvgbEYIsUVnRVr1KhuUPYMEAYIA0TqkifUmdqxuVAnMSvZGkDu3r2reDdTdr3qNWokCIDcuXNXWXApPW3zZs10XZZHftdwTGPrhvlAamMyKXIWNJaWVjZAaHu+CP07Vq9ejbk7xpn072CAMEAYILqWa7MaMUBUxLdw0SLl3D1d+vRgj/GUMmXOHO8B8ijsEQzHyLMe6N/xtYRsexMxHwjtwLzQ58NUkQkQylVOVla04/P28lQ9emOAMEAYIGaxQFdjBoiK2Lp07QY5c2RXItT26OkMdKcQX4+wHj16BGvWrIU1mG0vGMOS5M+fX5dSRG20+a+/MIPfArz3mA52KgEJZQHk+o0bip/Kd99+C506dRR6BwYIA4QBIjRVpFZigKiIk1KzUuY6OrZpjXcg8RUgZGk1DRf5gwcOwqhRo6RYhFy5ckVJZTtnzmzIZCBvSEzRmQsQugbbv38/jBwZgN7lQ9FBsbxwRGAGCAOEASKVDUKdMUCExPSpkjGAXLx0CeiSmYqv7wgIwQvfTJkzaejZvKof8I5i/ISJcE+5q+kDufHS3NzyAvOC9O3bF/rgP2XLivmMkJVa9mzZ8djJTvPwHyM+wuo1azAZ1Tr0LxkE+b7Ip6mP97gzpJ1LoUKFNLWTWZk8/GmXljFjRpndCvVF+vf+/QcpPxyEBoxRiXxgcmO+FWtFPo46PDmR3kIrPRk7bj3vThaCadOkhfQZ0utpblabiA8RcOXqVShcOG70ntYJSAJshSXyFY0BZMHChXDq5Cmli7//+QdC8c7AwUF7YEKRZ4hZJwyPrchMtyZe7tdv0AB3SO8hXVr9prrUP+2yAgKD4JtvakMtDBMiWh7jIpYuXTol57iW8hLjWdE9Syr7lODcyxlS6Ai/Thfuj3D8rHhHFVeFco/QApo6VSqrP8IrvDOiXWhaM8y0zXnoR48fK8E4k+mIbGDOuNT2PX77pxgNOnMcgJvGf4Jj0/1oqpQpzX0Vze0jcNceFhYGWTEWXVyUN+iT5eDgwAAREX58O8K6evUa+mW4Q69evaBunTrKLoic7cy1ySZv9devXsPAgQM0WW/pOcK6+e+/GFqlHzRDSzHy79ATWoW+HR9h8REWH2GJrGJy6/ARlgZ5xieA7Nm7F8aOGQueaKFUqWJF5S1kfEzaQS1Cy7NpU6dqPo7QAhC679iL7xCM70DWYtUwsKM5hQHCAGGAmDOD9LWVsebEGtnW/EAiXzA+AIQW3lWrVmE4kd8wkdOkaL4R5n7MixcvKpfm8+bNg8w67nBEAUJn9QsWLoD16zfABPTvkJE/nQHCAGGA6IOAOa3MXXMMjs0AsUwok/d4WT5mzBigy2qyVEqfPl00+ZvzMZ88eQrdHB2VcCeldIaEEAEI+XcMw9S59nhePBB3HmnQwk1GYYAwQBggMmaStj7MWXOMjmSrAOnm6ARk7TN37hyj726pWFh0tzFihB8Gbcug3E0kM3BRrfdjEpgoxHvdunWhKXqu6y1qAKH7jv79PaBhwwbQqWNHYRNdkedhgDBAGCAiM0VuHb1rjsmnsFWAUN5vKunRK91YsQRAyMqiJzoxNmnSBFq0aG4QHnrvQOhIjCygXr18hdkFB5qlXcYAQmPs2rUbAgICwM/PT/HvkF0YIAwQBojsWaXeHwNEXUaaasgGyJmzZ8HLyxvcMRJtrVqmTWr1fEzyNF+2dBlMnDhBV1rbqMIxBBDa3fz2+++wY/sO3EH5YmDHPJrkKVqZAcIAYYCIzhZ59fSsOaqj2+oORPXFsYIsgNCv9h07duJdx0iYNm0aOkl9oTq81o95GfMYfLo0nyvF+S0mQF6+fAkjMY7Y69evIADfwx7jWlmqMEAYIAwQS80u4/1qXXOEnpABYv4l+sxZs5SwHv545GMo94ahD6HlYz7H47h27TsoiZlKlCgh9F3VKkUFCHkG93LuBa1atYLmzZsZPXZT61P07wwQBggDRHS2yKunZc0RHpUBoh8g7zAsQ1BQEDzHEAFDKQFU6tTCchf9mDQGXWbXq1fXZHIs4YH/qxgJkMOYdGs0JtUa5O0FlStX1tqNrvoMEAYIA0TX1DGrkeiao2kQBog+gNAlPR0pUewp8i43ZGll6kOIfswJEycCxbDxQidEY7k9NH3w/yqfOXMWtu/YDlu3bsNwLhPNSp2rdXwGCAOEAaJ11phfX3TN0TQSA0Q7QK5duwYeAwYq4ct/aNRIk7wjK4t8zHXr16Mj4moIxUvzFCrh2bU8xEu04nJ1c4VcuXKBB6a9NSd1rpZxI+syQBggDBA9M8e8NiJrjuYRGCDaAHLw4CElBDuF9DDnyEftY17CqMHu7v1h1uxZkEVi0MEbGAV30GAfKF68GLhiXKvUGo7dNCuXkQYMEAYIA0TWbBLvR23NEe8pSk0GiBhAyNKKwnnMnjMHxoWMhbxmJqY39THJ05wsxMgaqmRJOZfm9Pz79u1TPMv9/f2USLz58uWDVHEQjZYBwgBhgOhars1qxAAxS3yxG4ua8VL48QmYw+PsubPKpXlGDIlsbjH2MWksyuneoEF9+Pnnn80dRmlPfc6ePRt27NwFo4IClZhcap7oUgbmHYhBCdx/wABhgFhyhhnumwEiWeYiAKH84oFBoyBFihQwGC2VkunIf2HosQ19TMoRQZfmb968Ac+B5nmaR45Jl/2jg4OBrLlG+vt/vuxngFxXYnzlyJ5dslapd8cAuQwMEHU9kV2DASJZomoAoQRQLr1d4IcffoCWLVtoDplu6nENfcx/MDz74sVLYBJaRclw5Ltz565iIUb+HU1/bRoteRQDhAFCP4qsXejH0SV0imWAWFvyclJIxHpqvgMxfAdCqW89B3qCs7MzBi6sI9WElj5CTICcOXMGfHyGwPTp0zA8u/mZ+sgzPmRcCMbM8oQqBvw7GCAMEAaIdRdxOko+fvIkVChXzroD/zca70Aki93QDuRTWJIdeNcxCsZivnSyVrJEifox6ZipU+fOMMLXV3d49shnpHhWlLZ39eo1MGVyqFHPeAYIA4QBYomZbbxPBsgn2STBRfZjLDF9jLDu1zBjNMojfvDQYRg0aBB069oVGv3QSLkYpzsIWny3bduGYUn8IUcOy52PRwKEzuBdXPrAjz/9BD/9+IMZbwVA8awomCMlmBowYIBJCysGCAOEAWLWdNPcmAFiAwA5cvSo4sdRqFAhKIz/kMks7TjI4unBwwdKAqhADCqYJo14WBLNmhTlCGs1Ogo+e/YUvL299XTzuQ0FW/QdMQK+++47aNe2rWpfDBAGCANEdZpIrcAASeAAuXr1KrigiSyF7iAfiMjQIJR5z2fIEHgU9gij6U5VLK4sXR7hBf2y5Svg8KFDSrpbvWPSZvDw4SMwHI+/KENh+fLlhe5rGCAMEL06Z87c4Et0vgNJsEdYw4f7QsPvGxq8VKbjH0en7sq9QQbMJGjpcvLUKTxu8oK5s+dAlqxZdA83a9ZsJaYVhZLPkzu3cD8MEAYIA0R4ukipyDuQBL4DoZDo03GHYSx8B/lL1McjoLJly0pRGGOd0O6jY8dOyrFVtWpVdY31/PlzCAgMUu5t/PDoKnnyZJr6YYAwQBggmqaM2ZUZIAkcIM1btIQFv/8GdkYCE06bPgPKlikDVatWMVtZjHVAStQbfUu+rv411K5dG/JpDIlCR1Z37t5VvNVbt24FvzRurDkSMD0bA4QBwgCx2DQ32DEDJIEDpHuPnso9QY4cOQx+4D59+0J/d3flfsQS5SPuFsaOG6+EFnHs1hWeo5e7VoDs2rVLCavi5u4GVavoBx0DhAHCALHELDfeJwMkgQNk/YYNcGD/ARg8eFA0r/JI34+5c+fBzJkzdP2iF1HFv/76Gy/Ol8Hk0FBMQvVcE0BI+RYtWgxr165FgIwXznxo7LkYIAwQBojIrJVXhwGSwAFC/h90b/Dg/n3lF3yB/PmVbIJLly2FTRs3KZ7buTFHhiXK2bNnYcjQYTBt6lTIlCljLE90U2OSldhgHx9Iny69EkZeRgh2BggDhAFiiZnOOxA1qSZYKyx6MdptbNiwEf78808lJk92dOSrWqUydOnSBdKnT6/27rr+/vjxE+iJIVF8cOdTqlQppQ/RsALXrl3H/B2DoRFaj7UV8O8QfUAGCAOEASI6W+TU4x1IAt+BRFUDAkkHtIQKDh4N2bNlk6MhBnqhXY9Lnz7Q5JcmSoj2yKIGkMj8HUGjRsPw4cOgTOnSQv4doi/CAGGAMEBEZ4ucegwQGwAI3XOcwIBmVChkCUW+zZDB/PwexlRsxYrl8BRjXXXu1DkaAN69ewsUtyp16jSxmn7EsDAUmXfbtu24c+mJx2ri/h2iqv7s+TNIg2NrzeUu2r+pehERHxSZZHTIKKM7XX28fPlCefeUKVPpam9Oozdv3wAZVKRKZdloB8ae8enTp0pCsaRJk5rzGrra0iJKKRKs4Wtl6AGfv3gOdinspES71ioAmtePnzyBTBkzaW0qpT6ldKAwR1oNd0wOntii8ZIPxpu3bxWZ9OvnCmPHjIEsWcyPfmtIyJs2b4b169ZjUMYxsRZqmsSUmzxXrpzRmpJDo7//SOWS3wePrlLYWcYr/vLlK5A7dy5cQFNKUU4tnZAiU7TjUiVLamkmte6/t26BvZ09ZDXDiVPvA4WFhUF4+HuLxloz9WwXL17C+78vILkVIi7EfI63OPeuXb8OxYoW1Ss+s9rR2BnwqDpjRuv/eIlAeJ45dx5D2ceN3tOa8xbnHgPELBX6f2O1fCDmDHPhwgXwxMCGs9Cqy5CyGjrC+vfff5XAiu3atYOmTX6BJBb8hchHWHyExUdY5sxw7W35COuTzBL0JXrUz24pgNAupwf6nPj5jYCiRn5pRQUI3Xfs3r0bxo0fr2QirFSpknbt1NiCAcIAYYBonDRmVmeAMEBUVYguzfu5ukHDhg3hRwwTHxmwMWbDSIDkwvzkCxcugvXr18MkDKqYRUIyKdWHxAoMEAYIA0RkpsirwwBhgKhq0xhMQpU8WXLo27ePyboEEEqZO2XyFMiYKRO4ufaT4t+h+oD/VWCAMEAYIKKzRU49BggDxKQmrV27DtatXwfjx40zGm8rsoNz585h0qeBmGu9JbRp01qqia6IujNAGCAMEJGZIq8OA4QBYlSbCAgDMf/4/HnzTJoofrrv2APD0LeDvMu/qVVLnoZq6IkBwgBhgGiYMBKqMkAYIAbViC7Nuzk6YRpcPyhRorhRVSMFmjNnLuzbvx/c3VwhTdq0ck3qNCg5A4QBwgDRMGEkVGWAMEBiqRHZtVMU36ZNmkbzNI9ZkZynAgIDFQeyYcOGKfnL9UTjlaDHShcMEAYIA0TWbBLrhwHCAImmKXQcRUmoyLO1Tx8Xo569t2/fBmfnXtCufTto0qQJJEP/DrVQJmIqqb8WA4QBwgDRP3/0tGSAMECi6c3qNWswiu9GGI/+G+Q5bqjs3LkLQkJClBDyFSpU+FyFAXIOyls486OpSX4dPZLt0Qs/BwbTtHa5/+ABhL8LVyIBxEU5c+YsFClSGBgg1pU+A4QB8lnjKDw7eZrPmzsXHBxi51CnOFcLFixUrLIohHtMb3QGCAOEAWLdBZxGowjcDhj7zlLhi0y9EQOEAaJIgPw3unTuokTyLVKkSCydeYX5OzwHekIOdBJ07dcXg+bFDtjHAGGAMEAYINaUgEXWnMQWTDHqB9MTyoQ8zXtjvKrGP/8MjRp9H+v7X712Tbkkb9igIbRq2cJoPCuLfEwN2sh3IHyExUdYGiaMhKq8A0nkO5AItKAaNToQaoGmAAASnklEQVQYI9jaQz+0vIpaPuXv2I+5O4bDiBG+8NVXX5lUOQYI70B4ByJhVdbYBR9hvZDrOsA7kGDhkN5r8NL8b8zTMSooKFo+AfplMWPGTNizdy8EBQZATjy6UisMEAYIA0Rtlsj/OwOEASJNq7QcYZ0+fQYtqQajI+BsvDT/fwIqirFPuxLMlQtDhw5RDWES+fAMEAYIA0TaVBbuiAHCABFWFrWKogB5glnEOmJGQUo+VahQQaVbOrK6c/cu9O7tAi1btIBmzX7VlN2PAcIAYYCozVD5f2eAMECkaZUIQN68eaMkefoVAdGwQYPPY2/fsQODJmL+Di9P+ArzdxgL227sYRkgDBAGiLSpLNwRA4QBIqwsahVFABKMnubJ7eygX59P4dnJv4Pyd6xctQqmTp4M2bJnUxvG4N8ZIAwQBoiuqWNWIwYIA8QsBYraWA0gK1b8AVu2bIFx40IUr91Xr16Bh8cAyJYtG4Zi9zDo3yH6cAwQBggDRHS2yKvHAGGASNMmUwA5e/YcDEV/junTpiqX5pcuXQZfX1/4vlEjvPNobjTulejDMUAYIAwQ0dkirx4DhAEiTZuMAeTBw4eKp/mYsWOgSOHCsH//ARgZEABDfAZDxYoVNd93GHpgBggDhAEibSoLd8QAYYAIK4taRUMAIZ+OHj17ohd5K6hXry5MnToN9qJ/x8iR/hj8Lrdal8J/Z4AwQBggwtNFWkUGCANEmjLFBAjBI2jUaEiNsau6dOkMfn7+il/HkCE+wv4dog/HAGGAMEBEZ4u8egwQBog0bYoJkLXr1sHmzZsxAGI/6N/fA1q3bo35O37R5N8h+nAMEAYIA0R0tsirxwBhgEjTpqgAOXbsOPj5+0ObNq1hIYZhJyurypUrSxsrZkcMEAYIA8Ri08toxwwQBog0rYsESLJkyaBT585QFhMcXbx4ESaMH6eY6lqyMEAYIAwQS84ww30zQLQDpD+6LtSuVRMaNmwYOwlZYg+mONJ/JPT38IBjx45BGzyycnd3g9SpU1tcsxkgDBAGiMWnWawBGCDaAXL16lUYNtwX3r59q+RAyhPVmCixAyRr1mywGr3Khw4bCm3btLGaRjNAGCAMEKtNt88DMUC0A4SER6ksli1bBlOnTVeO+Tu0b/8pInliA8gjzCZI8a2o9HN1gxMnTiie5qW//FKKf4folHjy5Cl6tr+EXLniJi/25ctXlJzcKTEvuLXLu3fv4OKlS1CqZElrD/15vH9v3QJ7O3vhUP4yHzQsLAzCw99DjhzWz8dO70HHtPnz54+TnOj0K/Ya5qMvVrSoTJEK90Vjp0+XHjJlyijcRlZFsvI8e+4cfFmqlKwuNfVDkcNfvtS/5lAAWcrG6us7QulnXMhYKFa8hKZnoMpJsKOPsVp9jNDcUVw0WLRoMZw6dRKuXbuuhCkhS6tUqay/iNK7//nnSsXKKy7KnTt34Nmz51CsWNxM5O3bd0DVqlWi5VWxphzu3LkLN2/eREMJ04m/LPFM9OOBFpJq+P5xUfbs2QvlypXDo9rYqZYt/TwvX76Cw4cPQy08U4+LsmvXbiiFC3jGjP9PyWCt53j79h0mndsHtWvXstaQ0cY5f+ECpEubDn+0qucrMvWAZHB0/Phx8EHH6u49emp+lwQNEHpb2oWs+ONP+Pvvv2HSxIlx8iuUnqNu3XoIsX80fwAZDXbt3o0QvQbt2raV0Z3mPlz69MVfMsMhY5TcKpo7MaPB7j174J+//1F8fKxdaPc1d+488PcbYe2hlfEGDvQENzdXyJ7d+jsgSoEQgFEdJowfHyfv7t6/Pzh2c4TixYtZfXxKC+HjMwQmTpxg9bFpwAUYBDZf3jxQs6Y+eNOxe2joZKBI5IMGecM3tWsnviMsEuSzZ88gbdq00LlLFwjGZFBZs2aJkw/KAGGAxIXiMUAYIFr0ju4/6LTGf2QA/PTTj+Dk6Kisn0pJbHcgUQW3dNlyaPR9w/8LQ4tUJdSdNXs2dEWIxUWhI7xHjx9BhfLl42J4WLl6NdT/9lurWLwZesGruPu6cuUK1Ktb1+rvT7HWjhw5Cg3qf2f1sWnAjZs2QY3q1eNE7+nH2zY8vvwZF6K4KOvWr4dKmL8nu4XN9A2926vXr9FR+S/4pfHPcfHqcBQtTR0yZIACBQpoGt/TywuuX78Bnp4DoWyZMtHb2iJAwsPD4dbt2/AKL3pom54pUyarXpBr+jpcmSXAEmAJxGMJkOVaQTS6SIr+crGKrQHk3v374OTkBCdPnITXSPwsWbJAWzznJ8/ypEmTxuPPxI/GEmAJsAQSmARsCSCU8OmXJk0pYTkEBAYo0XP//F97VwIU1ZVFr6i4oKasjGNpVERlJpHEBTUiURYVWdxAGowLGMcdEA0qyoyKLCoQFUeBViIgLigY1wRRGMUtpaLBZOJC1DFqFMaYKq0CjFUhydz7Mlh2C6j8bn73//dVWSXK/++98173ee8u5+7fD6vRdrcSZUoCAiab2erwcBkBRoARMGEElEQgxwsLIWByAOTkZMMHaOOlRhHHCxYshIsYOnii8DjfQv6/FykmfOxYb5g/fx54e8sTStzQHwuKwy8oKIAtaenwDdqDW6DigJubG4TODYEuXboo2sxJZt3du7MhPSMD7qD/5z20ZZMz1MPD3ShioQ29tq/THzmEZ86cBZmZW599T7zO8+b2uykpWlGSQr/5ajTS/TFKIpC4uDjYjJmSJSXXdPIL/nXsOBLLZDh16iTY2tqa2/obfLzl5RUQOm8eHMnLg6SkJPD1xVubCtpGnGvc6jhh0nTGEMSKigpIxrr2FeXlcODAfkEiSm0xsbGQtiUNgoKCoFfvXnDx4kXYgj+HffwxhIbOVeq0X5jXw4cPwctrJNy7d08cNOsb0mpOgA0f7gb/xfBp/e++iZMmgh+SiKSmJAKZNm06lGKCXN7hXB1MbmLc/ZAhTpD6aSqMHiVP9IekRTLQw3Qbu3TpEuY+RMKVq1fhKfqI1EIgFIPv4uIqiCMRM2ir/WGUE0T/TjeRtWvXGAhp03rNTxj11dfeHoLmBEFExJJnN/Pw8MVwHG/lhXgib9OmjWkN2gijIQWE6ZgDUlRUBHQDVwOB/ISqB0743TcRZZqWLv2H4VFVEoGMG+crwkJ37NiuAxSdOnr16g1RUSuEg12tjciDMKJM3NlzZouEKrUQyB2UsJiNWbOUQEdkUd2IVH19NdC4SWPYk5OjyK1B+78Ak2aHDRumE766YcNG0Gq1cOJEoSxJhQ0N9o4dOyEmJgYi/h4BEUsiVEEg/8ZgIq+RIyFx3Trw85N426hpwZhAGnoby9cfZZ6TBAHJMt+69T1mwg9VDYHUhjrpUjmiv8zTw1Nooqml/fjjQwgMDEQ/UAvIRt+IpWVTRU+d1Lb9/MdDfHwc/OnNN2E8lqxWww1k/4EDEBIcgrWOYuH69RtwG5V1//r22/DRlEChhya5KYlAAgICgZJ19n62RweXu3fvwsCBDkJCQCPV5icZcdN4wbVrJaonEArznoGO5LNnz0HekTz4iwr8Y9dRSDEhPgGT+U7gbaQ9ZO3KAmsF+37o00bRmfS572LdFZKTNsKXKOOjFgJZuWoVyjUlCRMlWR4wUgSuofn6l6oqPDjsgn79+kn7QlISgSxduhQOHjyECrvf6ETUnDt/Hny8fSAXfSNyZV5LWyXDP612AiFVWIrO27dvH0o0rMQT2RRFR2FV7yBSny4qugB0qNqLcycxSdKDs7KyMvwmM4E3kolyMZqrzmEUUm7uF9C6dWsMpjmlGgJZ/88NgjBX4g2k+oD0H0wMpNtYhw4d4IvPD0nb90oikOrrGoXpPa8yG5+QABnpGWi++Vo29VcT+CzpDEHNBEKO8zlBweJLZXlkJEz9aIoqw7vPojLsOMybiomJRufydFPbogYZD4Vtz5o1G7KysoT6MzU1EUhtIKZhKDsduCmgoDMKLNa7KYlASGPIDUPWHBwcICEhXmj9kM3fH+2dpDobGbm83jgp7UG1Egg50wMCp0AZSt2sWr0KNL6+0k5gZrIxyIzTokULnbnS6XzU6DHCJ0A5EUpsGo0ffFX8FXTr1v3Z9CoxfJv2gbW1NVijLtSW1M3iZqLERkKI9KdJkyY60yssPCEis0iR3M5OQl0eJREIIXQ0Px/mz5svruSkgUWCeb379IZPU1PFz9z+QECNBHIfi0j5YBTa7/iBSklJhgEDGr4WiBz77zDm+8TGroT0tLQXZMyHODmLwl6bNmnlGJrR+8zYuhUdx7d1+rl//x6asw7DSIxO6tnzHZiD4c1y1QQyNgBkqurfvx8sDg/X6SodLTLLli9Hf8gVaSHcSiMQQomKBeXnHwUq3NMTPxwuLs6yVF8z9uaQ8n61EQjlAEyYMBGovnMGZmPrR6BYWDRS7Cn0wYMH4Oj4gQjjTU5OEp8Fun3k5uaKjOxUPIGPUlF+lJpMWGFhC+AwKhAfwSCR6j1fWlqG4fzjhAOd9oOkpkQCkQSISh5WG4FcwMzrsWPGiqs8mXL0W+fOnfE6X6DY1SebdzTmQPTHL42BA9+HW3gqL8DbugeWM1iHOQLNLC0VO3f9iamJQOjA5O/vT/KAopbHb7/9DnQjtcRDxB6MVu2IjnRJjQlEEnxm+zAll2Vu246yDp7Q853Xr2tsbhP/9tvLwrxZW3vjjTaYWKlMRzLNmezg59FhSuKiZXgCbdeuHbhhPRL3ESNUF0BA/o89n+1FGQ9f4QdReiOF8uzsbPgaE4ktLBoLkxaRikFM+kwgSt8+PD9GgBFgBIyEABOIkYDl1zICjAAjoHQEmECUvsI8P0aAEWAEjIQAE4iRgOXXMgKMACOgdASYQJS+wjw/U0XgKcqpkKSIGjS4THUNeFwSEWACkQggP84I1BOBNEzm+rXqF50SA1S749Chz1FyfjhKTHSu55v5MUaggRBgAmkgoLkbRuA5BCorK2EGJvFt35apU1L28uUrol4JaTe5urowZoyAaSPABGLa68OjUyYC69Ylgk03G1SJ1q1HzwSizPVW7KyYQBS7tDwxE0aACcSEF4eH9uoIMIG8Olb8m4yAIRAoKyuD0NB5sH37NmjevLnOK5+/gTg7OwH5RFqiMGgrvXodjx49gl8xu5yUdLkxArIhwAQiG/TcsZkiQLIgVM2wpOQ7sLXtIdRMqUDV6TNfwvsD+r9U3TQeKwIOGuQATk5OLyDwPIGQCOho1O8ivaLNmzc9k2InYUhPr5Fg26OHYlV0zXRrqG/YTCDqW3OesTQESFsoDwXp1ieuBydnZ/gEC5bNnDUT8o/mQ0xsDEyfNq3WDu5g2G50VLT44idVXP2m7wPRajdBdHQ0XLhQBJ06/VH4pxg1jUgYMg7re0/Cmg7cGAHZEGACkQ167tjMEcjK2gWLFi2CtWvXojS2PVQ++Rm6YHW32kTq6OaycOEilNL2gcGDB9c4e30C+e76dfBw94CIiAgM950hnklI+AS0Wq0oVdqxo0Q1VTNfAx6+zAgwgci8ANy92SJw48YNGOHuDsuWLYO/TZ360nncvHkTklNSIBHl02tr+gRSVVUFY/C2QWaynTt3iJDfgQ6DoEf37uJnboyArAgwgcgKP3duxgiQ38N16DBYsmQxjBk9us6Z0O0jGOuwB4eEwLvv2r0ygdAvkhlrzZo1cObMaayw+T1oNBpIS08DL09PM0aPh64IBJhAFLGMPAkZEKAIKbodaLCuRFhYWJ0jOHv2HOzevRvWr0+sswZ7TXkgjx8/hr729rAAq8vduXsH8g7nwenTp6Bt27YyzJq7ZASeQ4AJhLcDI1A/BHaiD+TnJ0+guLhY1FinyKyaqh3S20PmhoqbSqe33qqzs9oSCaehY/4+FoKqrKgAOzs70Z+FhUX9Bs5PMQKGQoAJxFBI8nvUgMC9H34Aq1atRCRU0yZNRRivn/94yMbbBZVKnTDhwxdgOHbsOJw8eRKiolbUefugB2sjkL379kFIcIh4t1abAt56GexqwJ7naIIIMIGY4KLwkEwWgQkTJ8FtrDMdHh4OPj7eolSsq+tQcHR0hBUrIqFZs2Y6Y3/69CkEBE6BpI0boH379i+d15UrV7HMsBeWG84EFwwRrm6UONi3r71IKryIIb0tW7Z86bv4FxgBoyPABGJ0iLkDBSFAteQrUAjRpmvXZ7O6X1oKf8Ya4zXldZCjvRT/38bG5pVQoKir8vJysEKisLS01CEQB4y+8h/vDzGYF8KNETAJBJhATGIZeBCMQI0IEKE0atQItmZuwwTEKDh48AD06dOH0WIETAMBJhDTWAceBSNQEwLZOTmQkpwiCk+NcB+Bf0/WkX9n1BgBWRFgApEVfu6cEWAEGAHzRaAeBPI/po5lSN//458AAAAASUVORK5CYII=\"/>\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [2]\n   </strong>\n   for correct position of P without working shown.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  <img src=\"data:image/png;base64,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\"/>\n </p>\n <p>\n  R located at (4,4) ✓\n </p>\n <p>\n  «as intersection of» vertical line through 4 ly and photon worldline at 45 degrees✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    MP2\n   </strong>\n   even if one of the lines is not drawn.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  <strong>\n   <em>\n    ALTERNATIVE 1\n   </em>\n  </strong>\n </p>\n <p>\n  <em>\n   Using diagram:\n  </em>\n </p>\n <p>\n  line from R parallel to prime ct axis until it intersects space axis ✓\n </p>\n <p>\n  use of scale from (b) to estimate coordinate to\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    x\n   </mi>\n  </math>\n  ' = (1.3 ± 0.2) ly ✓\n </p>\n <p style=\"text-align:center;\">\n  <img src=\"data:image/png;base64,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\"/>\n </p>\n <p>\n </p>\n <p>\n  <strong>\n   <em>\n    ALTERNATIVE 2\n   </em>\n  </strong>\n </p>\n <p>\n  <em>\n   Using Lorentz transformation:\n  </em>\n </p>\n <p>\n  event R has coordinates\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    x\n   </mi>\n  </math>\n  =\n  <em>\n   ct\n  </em>\n  = 4.00 ly in S ✓\n </p>\n <p>\n  so\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    x\n   </mi>\n  </math>\n  ' = «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    y\n   </mi>\n  </math>\n  (\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    x\n   </mi>\n  </math>\n  −\n  <em>\n   vt\n  </em>\n  ) =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     5\n    </mn>\n    <mn>\n     3\n    </mn>\n   </mfrac>\n  </math>\n  × (4.00 − 0.80 × 4.00)» = 1.33 ly ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion",
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "a-5-galilean-and-special-relativity",
      "b-5-current-and-circuits"
    ]
  },
  {
    "question_id": "23M.2.SL.TZ1.5",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   According to laboratory observers\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mfrac>\n     <mrow>\n      <mi>\n       number\n      </mi>\n      <mo>\n      </mo>\n      <mi>\n       of\n      </mi>\n      <mo>\n      </mo>\n      <mi>\n       muons\n      </mi>\n      <mo>\n      </mo>\n      <mi>\n       detected\n      </mi>\n     </mrow>\n     <mrow>\n      <mi>\n       number\n      </mi>\n      <mo>\n      </mo>\n      <mi>\n       of\n      </mi>\n      <mo>\n      </mo>\n      <mi>\n       muons\n      </mi>\n      <mo>\n      </mo>\n      <mi>\n       produced\n      </mi>\n     </mrow>\n    </mfrac>\n    <mo>\n     =\n    </mo>\n    <mfrac>\n     <mn>\n      1\n     </mn>\n     <mn>\n      2\n     </mn>\n    </mfrac>\n   </math>\n   .\n  </p>\n  <p>\n   Calculate\n   <em>\n    D\n   </em>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the energy released is about 18 MeV.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   determine the time taken for the detector to reach the muon source.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate, using the answers to (b)(i) and (b)(ii) the ratio\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mfrac>\n     <mrow>\n      <mi>\n       number\n      </mi>\n      <mo>\n      </mo>\n      <mi>\n       of\n      </mi>\n      <mo>\n      </mo>\n      <mi>\n       muons\n      </mi>\n      <mo>\n      </mo>\n      <mi>\n       detected\n      </mi>\n     </mrow>\n     <mrow>\n      <mi>\n       number\n      </mi>\n      <mo>\n      </mo>\n      <mi>\n       of\n      </mi>\n      <mo>\n      </mo>\n      <mi>\n       muons\n      </mi>\n      <mo>\n      </mo>\n      <mi>\n       produced\n      </mi>\n     </mrow>\n    </mfrac>\n   </math>\n   in S.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <strong>\n    two\n   </strong>\n   difficulties of energy production by nuclear fusion.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <strong>\n    one\n   </strong>\n   advantage of energy production by nuclear fusion compared to nuclear fission.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (d)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Discuss the ratios in (a) and (c).\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the nucleon number of the He isotope that\n   <math class=\"wrs_chemistry\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mmultiscripts>\n     <mi mathvariant=\"normal\">\n      H\n     </mi>\n     <mprescripts>\n     </mprescripts>\n     <mn>\n      1\n     </mn>\n     <mn>\n      3\n     </mn>\n    </mmultiscripts>\n   </math>\n   decays into.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     T\n    </mi>\n    <mfrac>\n     <mn>\n      1\n     </mn>\n     <mn>\n      2\n     </mn>\n    </mfrac>\n   </msub>\n  </math>\n  = 2.00 × 1.56 × 10\n  <sup>\n   −6\n  </sup>\n  or  3.12 × 10\n  <sup>\n   −6\n  </sup>\n  s ✓\n </p>\n <p>\n  <em>\n   D\n  </em>\n  = «3.12 × 10\n  <sup>\n   −6\n  </sup>\n  × 0.866 × 3 × 10\n  <sup>\n   8\n  </sup>\n  =» 811 m\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [2]\n   </strong>\n   for\n   <strong>\n    BCA\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  «𝜇» = 2.0141 + 3.0160 − (4.0026 + 1.008665) «= 0.0188 u»\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  <em>\n   In\n  </em>\n  MeV: 1876.13415 + 2809.404 − (3728.4219 + 939.5714475) ✓\n </p>\n <p>\n </p>\n <p>\n  = 0.0188 × 931.5\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  = 17.512 «MeV» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Must see either clear substitutions or answer to at least 3 s.f. for\n   <strong>\n    MP2\n   </strong>\n   .\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  transit time =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     405\n    </mn>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      866\n     </mn>\n     <mi>\n      c\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  = 1.56\n  <em>\n   µs\n  </em>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [1]\n   </strong>\n   for\n   <strong>\n    BCA\n   </strong>\n   .\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  transit time is one half life ✓\n </p>\n <p>\n  so ratio has to be\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [2]\n   </strong>\n   for\n   <strong>\n    BCA\n   </strong>\n   .\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  Requires high temp/pressure ✓\n  <br/>\n  Must overcome Coulomb/intermolecular repulsion ✓\n  <br/>\n  Difficult to contain / control «at high temp/pressure» ✓\n  <br/>\n  Difficult to produce excess energy/often energy input greater than output /\n  <em>\n   <strong>\n    OWTTE\n   </strong>\n  </em>\n  ✓\n  <br/>\n  Difficult to capture energy from fusion reactions ✓\n  <br/>\n  Difficult to maintain/sustain a constant reaction rate ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  Plentiful fuel supplies\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  larger specific energy\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  larger energy density\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  little or no «major radioactive» waste products ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow descriptions such as “more energy per unit mass” or “more energy per unit volume”\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  the answers are the same ✓\n </p>\n <p>\n  count rates cannot vary from frame to frame /\n  <em>\n   <strong>\n    OWTTE\n   </strong>\n  </em>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Do\n   <strong>\n    not\n   </strong>\n   allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    (c)\n   </strong>\n   .\n  </em>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [2]\n   </strong>\n   for “count rates cannot vary” if student made a mistake\n   <strong>\n    OR\n   </strong>\n   no answer in\n   <strong>\n    (c)\n   </strong>\n   and well discussed here.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  3 ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Do\n   <strong>\n    not\n   </strong>\n   accept\n   <math class=\"wrs_chemistry\" xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mmultiscripts>\n     <mi>\n      H\n     </mi>\n     <mprescripts>\n     </mprescripts>\n     <mn mathvariant=\"italic\">\n      2\n     </mn>\n     <mn mathvariant=\"italic\">\n      3\n     </mn>\n    </mmultiscripts>\n    <mi>\n     e\n    </mi>\n   </math>\n   by itself.\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion",
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "a-5-galilean-and-special-relativity",
      "e-3-radioactive-decay",
      "e-4-fission",
      "e-5-fusion-and-stars"
    ]
  },
  {
    "question_id": "23M.2.SL.TZ1.6",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The moment of inertia of the rod about the axis is 0.180 kg m\n   <sup>\n    2\n   </sup>\n   . Show that the moment of inertia of the rod–particle system is about 0.25 kg m\n   <sup>\n    2\n   </sup>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the angular speed of the system immediately after the collision is about 5.7 rad s\n   <sup>\n    −1\n   </sup>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the energy lost during the collision.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   the angular deceleration of the rod.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   the number of revolutions made by the rod until it stops rotating.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (e)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   In another situation the rod rests on a horizontal frictionless surface with no pivot. Predict, without calculation, the motion of the rod–particle system after the collision.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  0.180 + 0.200 × 0.60\n  <sup>\n   2\n  </sup>\n  «= 0.252 kg m\n  <sup>\n   2\n  </sup>\n  » ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  angular speed of particle = «12/0.6 = » 20 «rad s\n  <sup>\n   −1\n  </sup>\n  »\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  angular momentum of particle «0.200 × 12.0 × 0.60» = 1.44 «Js» ✓\n </p>\n <p>\n  <br/>\n  «angular momentum of rod-particle system 0.252\n  <em>\n   ω\n  </em>\n  »\n </p>\n <p>\n  equating\n  <em>\n   ω\n  </em>\n  = «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      44\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      252\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  » = 5.71 rad s\n  <sup>\n   −1\n  </sup>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   For\n   <strong>\n    MP2\n   </strong>\n   , working or answer to at least 3 SF should be seen.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  × 0.200 × 12.0\n  <sup>\n   2\n  </sup>\n  −\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  (0.252) × 5.71\n  <sup>\n   2\n  </sup>\n  ✓\n </p>\n <p>\n  10.3 J ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [1]\n   </strong>\n   for answer 11.5\n  </em>\n  J\n  <em>\n   that neglects moment of inertia of particle but do not penalize this omission in\n   <strong>\n    (d)(i)\n   </strong>\n   .\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    α\n   </mi>\n  </math>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      152\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      252\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  = 0.603 rads\n  <sup>\n   −2\n  </sup>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept negative values.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   θ\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      5\n     </mn>\n     <mo>\n      .\n     </mo>\n     <msup>\n      <mn>\n       71\n      </mn>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      603\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  = 27.0 rad ✓\n </p>\n <p>\n  <em>\n   N\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      27\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      0\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mi>\n      π\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  = 4.3 ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (e)\n </div><div class=\"card-body\">\n <p>\n  the rod will rotate «about centre of mass» ✓\n </p>\n <p>\n  «centre of mass» will move along straight line\n  <br/>\n  «parallel to the particle’s initial velocity» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   For\n   <strong>\n    MP2\n   </strong>\n   , mention of translational motion is not enough.\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-3-work-energy-and-power",
      "a-4-rigid-body-mechanics"
    ]
  },
  {
    "question_id": "23M.2.SL.TZ1.7",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Suggest why AC is the adiabatic part of the cycle.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the volume at C is 3.33 × 10\n   <sup>\n    −2\n   </sup>\n   m\n   <sup>\n    3\n   </sup>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Suggest, for the change A ⇒ B, whether the entropy of the gas is increasing, decreasing or constant.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (d)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the thermal energy (heat) taken out of the gas from B to C.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (e)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The highest and lowest temperatures of the gas during the cycle are 602 K and 92 K.\n  </p>\n  <p>\n   The efficiency of this engine is about 0.6. Outline how these data are consistent with the second law of thermodynamics.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n </p>\n <p>\n  «considering expansions from A» an adiabatic process will reduce/change temperature ✓\n </p>\n <p>\n  and so curve AC must be the steeper ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n </p>\n <p>\n  temperature drop occurs for BC ✓\n </p>\n <p>\n  therefore CA must increase temperature «via adiabatic process». ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n </p>\n <p>\n  Use of adiabatic formula «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     p\n    </mi>\n    <mi mathvariant=\"normal\">\n     A\n    </mi>\n   </msub>\n   <msup>\n    <msub>\n     <mi>\n      V\n     </mi>\n     <mi mathvariant=\"normal\">\n      A\n     </mi>\n    </msub>\n    <mfrac>\n     <mn>\n      5\n     </mn>\n     <mn>\n      3\n     </mn>\n    </mfrac>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <msub>\n    <mi>\n     p\n    </mi>\n    <mi mathvariant=\"normal\">\n     C\n    </mi>\n   </msub>\n   <msup>\n    <msub>\n     <mi>\n      V\n     </mi>\n     <mi mathvariant=\"normal\">\n      C\n     </mi>\n    </msub>\n    <mfrac>\n     <mn>\n      5\n     </mn>\n     <mn>\n      3\n     </mn>\n    </mfrac>\n   </msup>\n   <mo>\n   </mo>\n   <mo>\n    ⇒\n   </mo>\n  </math>\n  »\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     V\n    </mi>\n    <mi mathvariant=\"normal\">\n     C\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <msup>\n    <mfenced>\n     <mfrac>\n      <msub>\n       <mi>\n        p\n       </mi>\n       <mi mathvariant=\"normal\">\n        A\n       </mi>\n      </msub>\n      <msub>\n       <mi>\n        p\n       </mi>\n       <mi mathvariant=\"normal\">\n        C\n       </mi>\n      </msub>\n     </mfrac>\n    </mfenced>\n    <mfrac>\n     <mn>\n      3\n     </mn>\n     <mn>\n      5\n     </mn>\n    </mfrac>\n   </msup>\n   <msub>\n    <mi>\n     V\n    </mi>\n    <mi mathvariant=\"normal\">\n     A\n    </mi>\n   </msub>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     V\n    </mi>\n    <mi mathvariant=\"normal\">\n     C\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <msup>\n    <mfenced>\n     <mfrac>\n      <mrow>\n       <mn>\n        5\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        00\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mn>\n         5\n        </mn>\n       </msup>\n      </mrow>\n      <mrow>\n       <mn>\n        4\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        60\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mn>\n         3\n        </mn>\n       </msup>\n      </mrow>\n     </mfrac>\n    </mfenced>\n    <mfrac>\n     <mn>\n      3\n     </mn>\n     <mn>\n      5\n     </mn>\n    </mfrac>\n   </msup>\n  </math>\n  × 2.00 × 10\n  <sup>\n   −3\n  </sup>\n  «= 3.333 × 10\n  <sup>\n   −2\n  </sup>\n  m\n  <sup>\n   3\n  </sup>\n  » ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   For\n   <strong>\n    MP2\n   </strong>\n   , working or answer to at least 4 SF must be seen.\n  </em>\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n </p>\n <p>\n  <em>\n   V\n  </em>\n  <sub>\n   C\n  </sub>\n  =\n  <em>\n   V\n  </em>\n  <sub>\n   B\n  </sub>\n  <em>\n   <strong>\n    AND\n   </strong>\n  </em>\n  <em>\n   p\n  </em>\n  <sub>\n   A\n  </sub>\n  <em>\n   V\n  </em>\n  <sub>\n   A\n  </sub>\n  =\n  <em>\n   p\n  </em>\n  <sub>\n   B\n  </sub>\n  <em>\n   V\n  </em>\n  <sub>\n   B\n  </sub>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     V\n    </mi>\n    <mi mathvariant=\"normal\">\n     C\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      5\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       5\n      </mn>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      2\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        3\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      3\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       4\n      </mn>\n     </msup>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 3\n   </strong>\n  </em>\n </p>\n <p>\n  <em>\n   V\n  </em>\n  <sub>\n   C\n  </sub>\n  =\n  <em>\n   V\n  </em>\n  <sub>\n   B\n  </sub>\n  <em>\n   <strong>\n    AND\n   </strong>\n  </em>\n  <em>\n   n\n  </em>\n  = 0.2 mol ✓\n </p>\n <p>\n  <em>\n   V\n  </em>\n  <sub>\n   C\n  </sub>\n  = (0.2 × 8.31 × 602) / 4 × 10\n  <sup>\n   4\n  </sup>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  Increasing ✓\n </p>\n <p>\n  because thermal energy/heat is being provided to the gas « and temperature is constant,\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi mathvariant=\"normal\">\n    Δ\n   </mi>\n   <mi>\n    S\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi mathvariant=\"normal\">\n      Δ\n     </mi>\n     <mi>\n      Q\n     </mi>\n    </mrow>\n    <mi>\n     T\n    </mi>\n   </mfrac>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    Q\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mi mathvariant=\"normal\">\n    Δ\n   </mi>\n   <mi>\n    U\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     3\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <msub>\n    <mi>\n     V\n    </mi>\n    <mtext>\n     C\n    </mtext>\n   </msub>\n   <mi mathvariant=\"normal\">\n    Δ\n   </mi>\n   <mi>\n    P\n   </mi>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    Q\n   </mi>\n   <mo>\n    =\n   </mo>\n  </math>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     3\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  × 3.33 × 10\n  <sup>\n   −2\n  </sup>\n  × (3.00 × 10\n  <sup>\n   4\n  </sup>\n  − 4.60 × 10\n  <sup>\n   3\n  </sup>\n  )» = 1268.7 ≈ 1270 «J» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [2]\n   </strong>\n   for\n   <strong>\n    BCA\n   </strong>\n   .\n  </em>\n </p>\n <p>\n  <em>\n   Accept negative values.\n  </em>\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    R\n   </mi>\n   <mi>\n    n\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      5\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       5\n      </mn>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      2\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        3\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mn>\n     602\n    </mn>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    66\n   </mn>\n  </math>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <em>\n   T\n   <sub>\n    c\n   </sub>\n  </em>\n  = 4.6 × 10\n  <sup>\n   3\n  </sup>\n  × 3.33 × 10\n  <sup>\n   −2\n  </sup>\n  × 1.66 = 92.2  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi mathvariant=\"normal\">\n    Δ\n   </mi>\n   <mi>\n    U\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     3\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    661\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mo>\n    (\n   </mo>\n   <mn>\n    602\n   </mn>\n   <mo>\n    -\n   </mo>\n   <mn>\n    92\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    21\n   </mn>\n   <mo>\n    )\n   </mo>\n   <mo>\n    =\n   </mo>\n   <mn>\n    1270\n   </mn>\n  </math>\n  «J» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    MP1\n   </strong>\n   if T\n   <sub>\n    c\n   </sub>\n   = 92 taken from\n   <strong>\n    (e)\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (e)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   e\n  </em>\n  <sub>\n   c\n  </sub>\n  = 1 −\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     92\n    </mn>\n    <mn>\n     602\n    </mn>\n   </mfrac>\n  </math>\n  = 0.847 ✓\n </p>\n <p>\n  this engine has\n  <em>\n   e\n  </em>\n  &lt;\n  <em>\n   e\n  </em>\n  <sub>\n   c\n  </sub>\n  as it should ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [0]\n   </strong>\n   if no calculation shown.\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-4-thermodynamics"
    ]
  },
  {
    "question_id": "23M.2.SL.TZ1.8",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The moment of inertia of the rod about the axis is 0.180 kg m\n   <sup>\n    2\n   </sup>\n   . Show that the moment of inertia of the rod–particle system is about 0.25 kg m\n   <sup>\n    2\n   </sup>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the angular speed of the system immediately after the collision is about 5.7 rad s\n   <sup>\n    −1\n   </sup>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the energy lost during the collision.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   the angular deceleration of the rod.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   the number of revolutions made by the rod until it stops rotating.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (e)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   In another situation the rod rests on a horizontal frictionless surface with no pivot. Predict, without calculation, the motion of the rod–particle system after the collision.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  0.180 + 0.200 × 0.60\n  <sup>\n   2\n  </sup>\n  «= 0.252 kg m\n  <sup>\n   2\n  </sup>\n  » ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  angular speed of particle = «12/0.6 = » 20 «rad s\n  <sup>\n   −1\n  </sup>\n  »\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  angular momentum of particle «0.200 × 12.0 × 0.60» = 1.44 «Js» ✓\n </p>\n <p>\n  <br/>\n  «angular momentum of rod-particle system 0.252\n  <em>\n   ω\n  </em>\n  »\n </p>\n <p>\n  equating\n  <em>\n   ω\n  </em>\n  = «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      44\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      252\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  » = 5.71 rad s\n  <sup>\n   −1\n  </sup>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   For\n   <strong>\n    MP2\n   </strong>\n   , working or answer to at least 3 SF should be seen.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  × 0.200 × 12.0\n  <sup>\n   2\n  </sup>\n  −\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  (0.252) × 5.71\n  <sup>\n   2\n  </sup>\n  ✓\n </p>\n <p>\n  10.3 J ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [1]\n   </strong>\n   for answer 11.5\n  </em>\n  J\n  <em>\n   that neglects moment of inertia of particle but do not penalize this omission in\n   <strong>\n    (d)(i)\n   </strong>\n   .\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    α\n   </mi>\n  </math>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      152\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      252\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  = 0.603 rads\n  <sup>\n   −2\n  </sup>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept negative values.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   θ\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      5\n     </mn>\n     <mo>\n      .\n     </mo>\n     <msup>\n      <mn>\n       71\n      </mn>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      603\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  = 27.0 rad ✓\n </p>\n <p>\n  <em>\n   N\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      27\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      0\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mi>\n      π\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  = 4.3 ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (e)\n </div><div class=\"card-body\">\n <p>\n  the rod will rotate «about centre of mass» ✓\n </p>\n <p>\n  «centre of mass» will move along straight line\n  <br/>\n  «parallel to the particle’s initial velocity» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   For\n   <strong>\n    MP2\n   </strong>\n   , mention of translational motion is not enough.\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-3-work-energy-and-power",
      "a-4-rigid-body-mechanics"
    ]
  },
  {
    "question_id": "23M.2.SL.TZ1.9",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Suggest why AC is the adiabatic part of the cycle.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the volume at C is 3.33 × 10\n   <sup>\n    −2\n   </sup>\n   m\n   <sup>\n    3\n   </sup>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Suggest, for the change A ⇒ B, whether the entropy of the gas is increasing, decreasing or constant.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (d)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the thermal energy (heat) taken out of the gas from B to C.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (e)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The highest and lowest temperatures of the gas during the cycle are 602 K and 92 K.\n  </p>\n  <p>\n   The efficiency of this engine is about 0.6. Outline how these data are consistent with the second law of thermodynamics.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n </p>\n <p>\n  «considering expansions from A» an adiabatic process will reduce/change temperature ✓\n </p>\n <p>\n  and so curve AC must be the steeper ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n </p>\n <p>\n  temperature drop occurs for BC ✓\n </p>\n <p>\n  therefore CA must increase temperature «via adiabatic process». ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n </p>\n <p>\n  Use of adiabatic formula «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     p\n    </mi>\n    <mi mathvariant=\"normal\">\n     A\n    </mi>\n   </msub>\n   <msup>\n    <msub>\n     <mi>\n      V\n     </mi>\n     <mi mathvariant=\"normal\">\n      A\n     </mi>\n    </msub>\n    <mfrac>\n     <mn>\n      5\n     </mn>\n     <mn>\n      3\n     </mn>\n    </mfrac>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <msub>\n    <mi>\n     p\n    </mi>\n    <mi mathvariant=\"normal\">\n     C\n    </mi>\n   </msub>\n   <msup>\n    <msub>\n     <mi>\n      V\n     </mi>\n     <mi mathvariant=\"normal\">\n      C\n     </mi>\n    </msub>\n    <mfrac>\n     <mn>\n      5\n     </mn>\n     <mn>\n      3\n     </mn>\n    </mfrac>\n   </msup>\n   <mo>\n   </mo>\n   <mo>\n    ⇒\n   </mo>\n  </math>\n  »\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     V\n    </mi>\n    <mi mathvariant=\"normal\">\n     C\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <msup>\n    <mfenced>\n     <mfrac>\n      <msub>\n       <mi>\n        p\n       </mi>\n       <mi mathvariant=\"normal\">\n        A\n       </mi>\n      </msub>\n      <msub>\n       <mi>\n        p\n       </mi>\n       <mi mathvariant=\"normal\">\n        C\n       </mi>\n      </msub>\n     </mfrac>\n    </mfenced>\n    <mfrac>\n     <mn>\n      3\n     </mn>\n     <mn>\n      5\n     </mn>\n    </mfrac>\n   </msup>\n   <msub>\n    <mi>\n     V\n    </mi>\n    <mi mathvariant=\"normal\">\n     A\n    </mi>\n   </msub>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     V\n    </mi>\n    <mi mathvariant=\"normal\">\n     C\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <msup>\n    <mfenced>\n     <mfrac>\n      <mrow>\n       <mn>\n        5\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        00\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mn>\n         5\n        </mn>\n       </msup>\n      </mrow>\n      <mrow>\n       <mn>\n        4\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        60\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mn>\n         3\n        </mn>\n       </msup>\n      </mrow>\n     </mfrac>\n    </mfenced>\n    <mfrac>\n     <mn>\n      3\n     </mn>\n     <mn>\n      5\n     </mn>\n    </mfrac>\n   </msup>\n  </math>\n  × 2.00 × 10\n  <sup>\n   −3\n  </sup>\n  «= 3.333 × 10\n  <sup>\n   −2\n  </sup>\n  m\n  <sup>\n   3\n  </sup>\n  » ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   For\n   <strong>\n    MP2\n   </strong>\n   , working or answer to at least 4 SF must be seen.\n  </em>\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n </p>\n <p>\n  <em>\n   V\n  </em>\n  <sub>\n   C\n  </sub>\n  =\n  <em>\n   V\n  </em>\n  <sub>\n   B\n  </sub>\n  <em>\n   <strong>\n    AND\n   </strong>\n  </em>\n  <em>\n   p\n  </em>\n  <sub>\n   A\n  </sub>\n  <em>\n   V\n  </em>\n  <sub>\n   A\n  </sub>\n  =\n  <em>\n   p\n  </em>\n  <sub>\n   B\n  </sub>\n  <em>\n   V\n  </em>\n  <sub>\n   B\n  </sub>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     V\n    </mi>\n    <mi mathvariant=\"normal\">\n     C\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      5\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       5\n      </mn>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      2\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        3\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      3\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       4\n      </mn>\n     </msup>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 3\n   </strong>\n  </em>\n </p>\n <p>\n  <em>\n   V\n  </em>\n  <sub>\n   C\n  </sub>\n  =\n  <em>\n   V\n  </em>\n  <sub>\n   B\n  </sub>\n  <em>\n   <strong>\n    AND\n   </strong>\n  </em>\n  <em>\n   n\n  </em>\n  = 0.2 mol ✓\n </p>\n <p>\n  <em>\n   V\n  </em>\n  <sub>\n   C\n  </sub>\n  = (0.2 × 8.31 × 602) / 4 × 10\n  <sup>\n   4\n  </sup>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  Increasing ✓\n </p>\n <p>\n  because thermal energy/heat is being provided to the gas « and temperature is constant,\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi mathvariant=\"normal\">\n    Δ\n   </mi>\n   <mi>\n    S\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi mathvariant=\"normal\">\n      Δ\n     </mi>\n     <mi>\n      Q\n     </mi>\n    </mrow>\n    <mi>\n     T\n    </mi>\n   </mfrac>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    Q\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mi mathvariant=\"normal\">\n    Δ\n   </mi>\n   <mi>\n    U\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     3\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <msub>\n    <mi>\n     V\n    </mi>\n    <mtext>\n     C\n    </mtext>\n   </msub>\n   <mi mathvariant=\"normal\">\n    Δ\n   </mi>\n   <mi>\n    P\n   </mi>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    Q\n   </mi>\n   <mo>\n    =\n   </mo>\n  </math>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     3\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n  </math>\n  × 3.33 × 10\n  <sup>\n   −2\n  </sup>\n  × (3.00 × 10\n  <sup>\n   4\n  </sup>\n  − 4.60 × 10\n  <sup>\n   3\n  </sup>\n  )» = 1268.7 ≈ 1270 «J» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [2]\n   </strong>\n   for\n   <strong>\n    BCA\n   </strong>\n   .\n  </em>\n </p>\n <p>\n  <em>\n   Accept negative values.\n  </em>\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    R\n   </mi>\n   <mi>\n    n\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      5\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       5\n      </mn>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      2\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        3\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mn>\n     602\n    </mn>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    66\n   </mn>\n  </math>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <em>\n   T\n   <sub>\n    c\n   </sub>\n  </em>\n  = 4.6 × 10\n  <sup>\n   3\n  </sup>\n  × 3.33 × 10\n  <sup>\n   −2\n  </sup>\n  × 1.66 = 92.2  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi mathvariant=\"normal\">\n    Δ\n   </mi>\n   <mi>\n    U\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     3\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    661\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mo>\n    (\n   </mo>\n   <mn>\n    602\n   </mn>\n   <mo>\n    -\n   </mo>\n   <mn>\n    92\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    21\n   </mn>\n   <mo>\n    )\n   </mo>\n   <mo>\n    =\n   </mo>\n   <mn>\n    1270\n   </mn>\n  </math>\n  «J» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    MP1\n   </strong>\n   if T\n   <sub>\n    c\n   </sub>\n   = 92 taken from\n   <strong>\n    (e)\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (e)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   e\n  </em>\n  <sub>\n   c\n  </sub>\n  = 1 −\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     92\n    </mn>\n    <mn>\n     602\n    </mn>\n   </mfrac>\n  </math>\n  = 0.847 ✓\n </p>\n <p>\n  this engine has\n  <em>\n   e\n  </em>\n  &lt;\n  <em>\n   e\n  </em>\n  <sub>\n   c\n  </sub>\n  as it should ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [0]\n   </strong>\n   if no calculation shown.\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-4-thermodynamics"
    ]
  },
  {
    "question_id": "23M.2.SL.TZ2.1",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Estimate, using the graph, the maximum height of the bottle.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Estimate the acceleration of the bottle when it is at its maximum height.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the fraction of the kinetic energy of the bottle that remains after the bounce.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The mass of the bottle is 27 g and it is in contact with the ground for 85 ms.\n  </p>\n  <p>\n   Determine the average force exerted by the ground on the bottle. Give your answer to an appropriate number of significant figures.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (d)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The maximum height reached by the bottle is greater with an air–water mixture than with only high-pressure air in the bottle.\n  </p>\n  <p>\n   Assume that the speed at which the propellant leaves the bottle is the same in both cases.\n  </p>\n  <p>\n   Explain why the bottle reaches a greater maximum height with an air–water mixture.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the absolute uncertainty in\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <msubsup>\n     <mi>\n      F\n     </mi>\n     <mi>\n      max\n     </mi>\n     <mn>\n      3\n     </mn>\n    </msubsup>\n   </math>\n   for Δ\n   <em>\n    p\n   </em>\n   = 30 kPa. State an appropriate number of significant figures for your answer.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Draw the absolute uncertainty determined in part (d)(i) as an error bar on the graph.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Explain why the new hypothesis is supported.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (e)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The maximum height reached by the bottle is greater with an air–water mixture than with only high-pressure air in the bottle.\n  </p>\n  <p>\n   Assume that the speed at which the propellant leaves the bottle is the same in both cases.\n  </p>\n  <p>\n   Explain why the bottle reaches a greater maximum height with an air–water mixture.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n </p>\n <p>\n  Attempt to count squares ✓\n </p>\n <p>\n  Area of one square found ✓\n </p>\n <p>\n  7.2 «m» (accept 6.4 – 7.4 m) ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n </p>\n <p>\n  Uses area equation for either triangle ✓\n </p>\n <p>\n  Correct read offs for estimate of area of triangle ✓\n </p>\n <p>\n  7.2 «m» (accept 6.4 – 7.4) ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  Attempt to calculate gradient of line at\n  <em>\n   t\n  </em>\n  = 1.2 s ✓\n </p>\n <p>\n  «−» 9.8 «m s\n  <sup>\n   −2\n  </sup>\n  » (accept 9.6 − 10.0) ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  Attempt to evaluate KE ratio as\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msup>\n    <mfenced>\n     <mfrac>\n      <msub>\n       <mi>\n        V\n       </mi>\n       <mi>\n        final\n       </mi>\n      </msub>\n      <msub>\n       <mi>\n        V\n       </mi>\n       <mi>\n        initial\n       </mi>\n      </msub>\n     </mfrac>\n    </mfenced>\n    <mn>\n     2\n    </mn>\n   </msup>\n  </math>\n  ✓\n </p>\n <p>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msup>\n    <mfenced>\n     <mfrac>\n      <mrow>\n       <mn>\n        4\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        5\n       </mn>\n      </mrow>\n      <mn>\n       10\n      </mn>\n     </mfrac>\n    </mfenced>\n    <mn>\n     2\n    </mn>\n   </msup>\n  </math>\n  =» 0.20\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  20 %\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     5\n    </mn>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept ± 0.5 velocity values from graph\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  Attempt to use force = momentum change ÷ time ✓\n </p>\n <p>\n  «=\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mo>\n      (\n     </mo>\n     <mn>\n      4\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      5\n     </mn>\n     <mo>\n      +\n     </mo>\n     <mn>\n      10\n     </mn>\n     <mo>\n      )\n     </mo>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      027\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      85\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        3\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n   </mfrac>\n  </math>\n  = 4.6»\n </p>\n <p>\n  Force = «4.6 + 0.3» 4.9 «N» ✓\n </p>\n <p>\n  Any answer to 2sf ✓\n </p>\n <p>\n  <em>\n   Accept ± 0.5 velocity values from graph\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  Mass «leaving the bottle per second» will be larger for air–water ✓\n </p>\n <p>\n  the momentum change/force is greater ✓\n </p>\n <p>\n  <em>\n   Allow opposite argument for air only\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  15 % seen anywhere ✓\n </p>\n <p>\n  «Δ(\n  <em>\n   F\n  </em>\n  <sup>\n   3\n  </sup>\n  ) =» 39.4 × 10\n  <sup>\n   5\n  </sup>\n  × 0.15 = 5.9 × 10\n  <sup>\n   5\n  </sup>\n  ✓\n </p>\n <p>\n  ±6 × 10\n  <sup>\n   5\n  </sup>\n  ✓\n </p>\n <p>\n  <em>\n   <strong>\n    <br/>\n    MP1\n   </strong>\n   is for the propagation of 5 %. It can be shown differently, e.g. 3 × 5% Allow students to use 40 × 10\n   <sup>\n    5\n   </sup>\n   (from the graph).\n  </em>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    MP3\n   </strong>\n   for\n   <strong>\n    any\n   </strong>\n   uncertainty rounded to 1 significant digit\n  </em>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [3]\n   </strong>\n   for a\n   <strong>\n    BCA\n   </strong>\n   .\n  </em>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    MP1\n   </strong>\n   and\n   <strong>\n    MP2\n   </strong>\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  error bar drawn at 30 kPa from 34 × 10\n  <sup>\n   5\n  </sup>\n  to 46 × 10\n  <sup>\n   5\n  </sup>\n  N\n  <sup>\n   3\n  </sup>\n  ✓\n </p>\n <p>\n  <em>\n   <br/>\n   Allow ± half square on each side of the bar or one square overall (± 2 × 10\n   <sup>\n    5\n   </sup>\n   )\n  </em>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   from\n   <strong>\n    d(i)\n   </strong>\n   .\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  a «straight» line can be drawn that passes through origin ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (e)\n </div><div class=\"card-body\">\n <p>\n  Mass «leaving the bottle per second» will be larger for air–water ✓\n </p>\n <p>\n  the momentum change/force is greater ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow opposite argument for air only\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion",
      "inquiry",
      "tools"
    ],
    "subtopics": [
      "a-1-kinematics",
      "a-2-forces-and-momentum",
      "a-3-work-energy-and-power",
      "i-2-3-interpreting-results",
      "inquiry-2-collecting-and-processing-data",
      "tool-3-mathematics"
    ]
  },
  {
    "question_id": "23M.2.SL.TZ2.11",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine which star will appear to move more.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate, in m, the distance to star X.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the ratio\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mfrac>\n     <mrow>\n      <mi>\n       luminosity\n      </mi>\n      <mo>\n      </mo>\n      <mi>\n       of\n      </mi>\n      <mo>\n      </mo>\n      <mi>\n       star\n      </mi>\n      <mo>\n      </mo>\n      <mi mathvariant=\"normal\">\n       X\n      </mi>\n     </mrow>\n     <mrow>\n      <mi>\n       luminosity\n      </mi>\n      <mo>\n      </mo>\n      <mi>\n       of\n      </mi>\n      <mo>\n      </mo>\n      <mi>\n       star\n      </mi>\n      <mo>\n      </mo>\n      <mi mathvariant=\"normal\">\n       Y\n      </mi>\n     </mrow>\n    </mfrac>\n   </math>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  Star Y ✓\n </p>\n <p>\n  because parallax angle is greater\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  star Y is closer «and that means movement relative to distant stars is greater» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow reverse argument for star X\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  «distance =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfenced>\n    <mfrac>\n     <mn>\n      1\n     </mn>\n     <mrow>\n      <mn>\n       0\n      </mn>\n      <mo>\n       .\n      </mo>\n      <mn>\n       019\n      </mn>\n     </mrow>\n    </mfrac>\n   </mfenced>\n  </math>\n  × 3.26 × 9.46 × 10\n  <sup>\n   15\n  </sup>\n  »\n </p>\n <p>\n  1.6 × 10\n  <sup>\n   18\n  </sup>\n  «m» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      Luminosity\n     </mi>\n     <mo>\n     </mo>\n     <mi>\n      of\n     </mi>\n     <mo>\n     </mo>\n     <mi>\n      Star\n     </mi>\n     <mo>\n     </mo>\n     <mi mathvariant=\"normal\">\n      X\n     </mi>\n    </mrow>\n    <mrow>\n     <mi>\n      Luminosity\n     </mi>\n     <mo>\n     </mo>\n     <mi>\n      of\n     </mi>\n     <mo>\n     </mo>\n     <mi>\n      Star\n     </mi>\n     <mo>\n     </mo>\n     <mi mathvariant=\"normal\">\n      Y\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <msub>\n      <mi>\n       b\n      </mi>\n      <mi>\n       x\n      </mi>\n     </msub>\n     <msubsup>\n      <mi>\n       d\n      </mi>\n      <mi>\n       x\n      </mi>\n      <mn>\n       2\n      </mn>\n     </msubsup>\n    </mrow>\n    <mrow>\n     <msub>\n      <mi>\n       b\n      </mi>\n      <mi>\n       y\n      </mi>\n     </msub>\n     <msubsup>\n      <mi>\n       d\n      </mi>\n      <mi>\n       y\n      </mi>\n      <mn>\n       2\n      </mn>\n     </msubsup>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  = 10.8 ≈ 11 ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    MP1\n   </strong>\n   if ratio shown with distance or parallax angle.\n  </em>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    MP1\n   </strong>\n   for any correct substitution into ratio expression\n  </em>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [2]\n   </strong>\n   for\n   <strong>\n    BCA\n   </strong>\n  </em>\n </p>\n <p>\n  <em>\n   Allow\n   <strong>\n    ECF\n   </strong>\n   for incorrect distances from\n   <strong>\n    b(i)\n   </strong>\n   or\n   <strong>\n    b(ii)\n   </strong>\n   .\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter",
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "b-1-thermal-energy-transfers",
      "e-5-fusion-and-stars"
    ]
  },
  {
    "question_id": "23M.2.SL.TZ2.12",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the main element that is undergoing nuclear fusion in star C.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Explain why star B has a greater surface area than star A.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   White dwarfs with similar volumes to each other are shown on the HR diagram.\n  </p>\n  <p>\n   Sketch, on the HR diagram, to show the possible positions of other white dwarf stars with similar volumes to those marked on the HR diagram.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Hydrogen ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  stars have same/similar\n  <em>\n   L\n  </em>\n  <em>\n   <strong>\n    AND\n   </strong>\n  </em>\n  star B has lower\n  <em>\n   T\n  </em>\n  ✓\n </p>\n <p>\n  correct reference to luminosity formula (\n  <em>\n   L\n  </em>\n  α\n  <em>\n   AT\n  </em>\n  <sup>\n   4\n  </sup>\n  ) ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    MP1\n   </strong>\n   Allow reverse argument i.e., star A has higher T\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  Any evidence of correct identification that three dots bottom left represent white dwarfs ✓\n </p>\n <p>\n  line passing through all 3 white dwarfs\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  line continuing from 3 white dwarfs with approximately same gradient, in either direction ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    MP2\n   </strong>\n   if no line drawn through the three dots but just beyond them in either direction\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter",
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "b-1-thermal-energy-transfers",
      "e-5-fusion-and-stars"
    ]
  },
  {
    "question_id": "23M.2.SL.TZ2.17",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the main element that is undergoing nuclear fusion in star C.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Explain why star B has a greater surface area than star A.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   White dwarfs with similar volumes to each other are shown on the HR diagram.\n  </p>\n  <p>\n   Sketch, on the HR diagram, to show the possible positions of other white dwarf stars with similar volumes to those marked on the HR diagram.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Hydrogen ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  stars have same/similar\n  <em>\n   L\n  </em>\n  <em>\n   <strong>\n    AND\n   </strong>\n  </em>\n  star B has lower\n  <em>\n   T\n  </em>\n  ✓\n </p>\n <p>\n  correct reference to luminosity formula (\n  <em>\n   L\n  </em>\n  α\n  <em>\n   AT\n  </em>\n  <sup>\n   4\n  </sup>\n  ) ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    MP1\n   </strong>\n   Allow reverse argument i.e., star A has higher T\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  Any evidence of correct identification that three dots bottom left represent white dwarfs ✓\n </p>\n <p>\n  line passing through all 3 white dwarfs\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  line continuing from 3 white dwarfs with approximately same gradient, in either direction ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Award\n   <strong>\n    MP2\n   </strong>\n   if no line drawn through the three dots but just beyond them in either direction\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter",
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "b-1-thermal-energy-transfers",
      "e-5-fusion-and-stars"
    ]
  },
  {
    "question_id": "23M.2.SL.TZ2.2",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the unit for\n   <em>\n    pV\n   </em>\n   in fundamental SI units.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine, using the graph, whether the gas acts as an ideal gas.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate, in g, the mass of the gas.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  kg m\n  <sup>\n   2\n  </sup>\n  s\n  <sup>\n   −2\n  </sup>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n </p>\n <p>\n  Graph shown is a straight line/linear\n  <br/>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <br/>\n  expected graph should be a straight line/linear ✓\n </p>\n <p>\n  If ideal then\n  <em>\n   T\n  </em>\n  intercept must be at\n  <em>\n   T\n  </em>\n  = −273 °C ✓\n </p>\n <p>\n  Use of\n  <em>\n   y\n  </em>\n  =\n  <em>\n   mx\n  </em>\n  +\n  <em>\n   c\n  </em>\n  to show that\n  <em>\n   x\n  </em>\n  = −273 °C when\n  <em>\n   y\n  </em>\n  = 0 ✓\n  <br/>\n  (hence ideal)\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n </p>\n <p>\n  Calculates\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      p\n     </mi>\n     <mi>\n      V\n     </mi>\n    </mrow>\n    <mi>\n     T\n    </mi>\n   </mfrac>\n  </math>\n  for two different points ✓\n  <br/>\n  Obtains 1.50 «J K\n  <sup>\n   −1\n  </sup>\n  » for both ✓\n </p>\n <p>\n  States that for ideal gas\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      p\n     </mi>\n     <mi>\n      V\n     </mi>\n    </mrow>\n    <mi>\n     T\n    </mi>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mi>\n    n\n   </mi>\n   <mi>\n    R\n   </mi>\n  </math>\n  which is constant and concludes that gas is ideal ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  Use of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    n\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi>\n      p\n     </mi>\n     <mi>\n      V\n     </mi>\n    </mrow>\n    <mrow>\n     <mi>\n      R\n     </mi>\n     <mi>\n      T\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    N\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi>\n      p\n     </mi>\n     <mi>\n      V\n     </mi>\n    </mrow>\n    <mrow>\n     <mi>\n      k\n     </mi>\n     <mi>\n      T\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  Mass of gas =\n  <em>\n   n\n  </em>\n  ×\n  <em>\n   N\n  </em>\n  <sub>\n   A\n  </sub>\n  × mass of molecule\n  <br/>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <br/>\n  Mass of gas = N\n  <em>\n  </em>\n  × mass of molecule ✓\n </p>\n <p>\n  5.1 «g» ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter",
      "tools"
    ],
    "subtopics": [
      "b-3-gas-laws",
      "tool-3-mathematics"
    ]
  },
  {
    "question_id": "23M.2.SL.TZ2.3",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Explain the pattern seen on the screen.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate, in nm,\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     λ\n    </mi>\n   </math>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate, in nm,\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     λ\n    </mi>\n   </math>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The student moves the screen closer to the double slit and repeats the measurements. The instruments used to make the measurements are unchanged.\n  </p>\n  <p>\n   Discuss the effect this movement has on the fractional uncertainty in the value of\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     λ\n    </mi>\n   </math>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The student changes the light source to one that emits two colours:\n   <br/>\n   • blue light of wavelength\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     λ\n    </mi>\n   </math>\n   , and\n   <br/>\n   • red light of wavelength 1.5\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     λ\n    </mi>\n   </math>\n   .\n  </p>\n  <p>\n   Predict the pattern that the student will see on the screen.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Mention of interference / superposition ✓\n </p>\n <p>\n  Bright fringe occurs when light from the slits arrives in phase ✓\n </p>\n <p>\n  Dark fringe occurs when light from the slits arrives 180°/\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    π\n   </mi>\n  </math>\n  out of phase ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   s\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      15\n     </mn>\n    </mrow>\n    <mn>\n     8\n    </mn>\n   </mfrac>\n  </math>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  = 0.0188 «m» ✓\n </p>\n <p>\n  use of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    λ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi>\n      d\n     </mi>\n     <mi>\n      s\n     </mi>\n    </mrow>\n    <mi>\n     D\n    </mi>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  450 «nm» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   s\n  </em>\n  =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      15\n     </mn>\n    </mrow>\n    <mn>\n     8\n    </mn>\n   </mfrac>\n  </math>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  = 0.0188 «m» ✓\n </p>\n <p>\n  use of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    λ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi>\n      d\n     </mi>\n     <mi>\n      s\n     </mi>\n    </mrow>\n    <mi>\n     D\n    </mi>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  450 «nm» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  «As the measurements decrease» the fractional uncertainty in D/s increases. ✓\n </p>\n <p>\n  «Fractional uncertainties are additive here» so fractional uncertainty in\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    λ\n   </mi>\n  </math>\n  increases ✓\n </p>\n <p>\n  <em>\n   Answers can be described in symbols e.g. Δs/s\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  Blue fringe is unchanged ✓\n </p>\n <p>\n  Red fringes are farther apart than blue ✓\n </p>\n <p>\n  By a factor of 1.5 ✓\n </p>\n <p>\n  At some point/s the fringes coincide/are purple ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "c-wave-behaviour",
      "tools"
    ],
    "subtopics": [
      "c-3-wave-phenomena",
      "tool-3-mathematics"
    ]
  },
  {
    "question_id": "23M.2.SL.TZ2.4",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The designers state that the energy transferred by the resistor every second is 15 J.\n  </p>\n  <p>\n   Calculate the current in the resistor.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The resistor has a cross-sectional area of 9.6 × 10\n   <sup>\n    −6\n   </sup>\n   m\n   <sup>\n    2\n   </sup>\n   .\n  </p>\n  <p>\n   Show that a resistor made from carbon fibre will be suitable for the pad.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The power supply to the pad has a negligible internal resistance.\n  </p>\n  <p>\n   State and explain the variation in current in the resistor as the temperature of the pad increases.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   outline the magnetic force acting on it due to the current in PQ.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   state and explain the net magnetic force acting on it due to the currents in PQ and TU.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (d)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The design of the pad encloses the resistor in a material that traps air. The design also places the resistor close to the top surface of the pad.\n  </p>\n  <p style=\"text-align:center;\">\n   <img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAe0AAADVCAYAAAB66qiPAAAgAElEQVR4Xu2dBZhVVffGl2BhAKIgXdId0iUNgmAQdoGB4F/Ajs8uDNDPACUFsRADxVaQBhWku0NUUFGxwf/6rXHPd7nOwMwwce/M2s/DM3HP2Wef95zh3e/KQ/7WIT4cAUfAEXAEHAFHIOYROMRJO+afkS/QEXAEHAFHwBEwBJy0/UVwBBwBR8ARcATiBAEn7Th5UL5MR8ARcAQcAUfASdvfAUfAEXAEHAFHIE4QcNKOkwfly3QEHAFHwBFwBJy0/R1wBBwBR8ARcATiBAEn7Th5UL5MR8ARcAQcAUfASdvfAUcgExGY9OabsnHTRjku/3FStGhROblePTn22GPlkEMOycRV+KUcAUcgXhFw0o7XJ+frjjsEfvvtN2nevKn8+utvcthhh0mxYsXkjz/+kC5dushlvS+Tww4/3Mk77p6qL9gRyFwEnLQzF2+/Wg5GYOHChXLppZcIRQj37PnLkDj00MPsa7ezuslNN99s37vqzsEvid+6I3AABJy0/RVxBDIJgWFDh8rQYU/LkUfmkWOOOUZ27txhV4bEa9aoJQMGDpRatWplOmlz/bBRiPw+k2DxyzgCjkAqEHDSTgVYfqgjcDAI9OjeXdauWyuPPPyIfP311zJq9Cj9ut0I85hjjpWePXtKv35XZzpph42Dq/yDebp+riOQOQg4aWcOzn6VHI7At99+K23btpamTZrJE08+KcuWLZMF8+fLmOfGyI4d35raPq1zF+ncubM0bNQo09DCpz558tsy7dNp0r1HD2ncuHGmXdsv5Ag4AqlHwEk79Zj5GY5AqhF479135brrr5N77r5HmjZrJl999ZX8+eefQjT5a6+/JrlyHSLly1WQM886U9q1ay/HH398uiruaLP3d999J7NmzpQFCxbIqlWrZN36tbqG3PLGG2/atX04Ao5AbCLgpB2bz8VXlc0QGDJksLz44gty5hlnSdWqVaVS5cry0UcfSs2ateSyy3pZNPmePXvljNPPkPr160vn005LdwQCcU+fPl3WrFkt06dNl6XLlsovv/xi1+LzMWOek5NPPjndr+0TOgKOQPog4KSdPjj6LI5AsghAhl27dpGNGzfIVVf1lYYNG8m333wj8+bNM7L+66+/ZNJbk5Q8d5vavf7666VJk6ZSsmTJdFPbP//8syxatEh269cdGgD37jvv2lcU/6GH5rbUs717/5annx4qzdQS4MMRcARiEwEn7dh8Lr6qbIQAhHnqqR3tjh5+6GFZrSq3fPkKSpJ7ZcWK5dKqVWt5ftw4mfjaRCPpypUqS+06teWaa/oroR5qCjglaWDRx/EzY+qUKbJBNwyLFy0W1kIwHH505mzcqIkRN+r/rbcnyWOP/VdatmyZjdD3W3EEshcCTtrZ63n63cQgAijpQNoPKWkfffTRsnLlCjkqz1FSpmxZ+UYjyX/VwisDBw4wf/L27dulQf0GUqNGDVm/fr0q9I2SP39+KVWqlJxQ8ATJlzefFCxYUMqedJIVaDnqqKOM2BmR5L5hwwZZumSJFnP5VZ4d/qxtEr799hszw5915lm6cSivm4M6pvYHPfigLFq8UB58YJC0btMmBlH0JTkCjoD9jesfe8Jfuw9HwBHIEAT27NkjHTq0lyOOOEKGDx9h6V6UMF345ZdKlIvMDI7yHjd2rCxeslh27dplJuu8Ss4cS8Bam9ZtNEjtLClQoICR8ObNm/T8hTJ/wXw5S3/fo0dPyZMnT+L6v9S5ly9fJsWLl5D+/a9RE/yf9lnRosXk7LPPlrJlysLwkufII015P6ikzYbh5ptudtLOkLfAJ3UE0gcBJ+30wdFncQSSRQDSbteurRQvVlxOUnV8yaWXGmmjoLdu3WqpX9WrVzdyflejzOd9NtcIGwWMOZvxyisT5IQTTtjnGuy3+fzll1+SLxd8KVdceaVUq1ZNqLy2atVKyXtsXnn4kYflG/WfN27UWBo3aazXqWHqfMeOHfLjjz+aykfF/+f2/9j1Bz04SJq3aOFP0xFwBGIUASftGH0wvqzsgwDm8csvu0zJsLkFfFWpXMVM2xA3qnnnzp1qst6jxLtA6mrk9pjRozUw7U05/PAEZf7uu+9I+/YdpEqVKnYcfu7Igdl79qxZsmTpEiP6bVu3yU8//SSfTvtUdu/eLRdffLFUrFDRzOgFVE3v0JxxzOLjn39efy4ghU8sLP0H9JfcuXPJqFFjpG7dutkHfL8TRyCbIeCknc0eqN9O7CHw+++/S9+rrpJzzjnHOnyVLlXa1CwEjkkbtYzKpaHI1KlTpE6dumY6v+vuO+WOO+7USmlnW4Q5/4gAJyWMERl4xmeva7739q+2y9taLIVKa3/9tUfOP/98qVO7jqxbt04uUvI203yRIvL555/bXBRUueSSiy2ynTkmTnxdKlWqFHsg+oocAUfAEHDS9hfBEchgBFDTKO3vf/heqlWtpv7ozXLhhRdK+w4d7MqYqVHBfCVnunjx4kagY8aMFvK7H37oESN5VPObb74hnTp1toCzIkq+fEVpP/XUkzJ+/HhV54frPLvkuOOO003CuVJBFfZ2jQ7vpiVUUeisZYbmaf+8+2dN7Woui9SU/uGHH9rGYdbsWTr/JLu+D0fAEYhNBJy0Y/O5+KqyEQKrV6+WNfpv+PDhclqX02Tw4MFy4403GqnmypXrX+lcQUFD4kP02FcnvipPPPGk9d3++KOPpFfv3pbG1fHUU02pf6SkO0Ajz0uUKGER6evWr7Po8Fq1a2mQWympVLGi5MqdW7Zt22bmdQLdMKOzQUDdL9MCK29qZTbM9B9++JH60/NmI/T9VhyB7IWAk3b2ep5+NzGIAKT92WfzNOBsgZQuU1p+3PWjKeHGTZpYABpqOTrHGsKG0AlWG6FkTxDZcccVUOLdqr7tqpY2hkmdbmHXXXutXP1//6e9upvLDz/8IKu1LGmNmjVNdedWsoaYORYy5itqm98dqZHjBKR17nyqzVOwYCF566237bo+HAFHIDYRcNKOzefiq8pGCGDqpnToo48+Il26dNEyofWMpCloAnEmVRQFRUx98FGjRlq616ZNm+TwIw6XwoWLSG4l1a1K3h07nip33Xmnmb7J6Q4DX3kIVsOkjrI+8cQTTWWjpolYh/Qxr48f/7yMGDHcTu3c6TS59777UlTIJRs9Hr8VRyCuEHDSjqvH5YuNRwQg7d69elkOdj0l7GHPPGP+aRQ2ShhTdSiKEr4u0aIoFSpUML82fvCP1CwO0Xbo2FHKlCkjW7ZsMfVeskRJadK0qfnD8UsHfzTXZG6UN1HpfN353U6rvsYmARU+d84c84Ov37DOyqfef9/9Nr8PR8ARiF0EnLRj99n4yrIRAjdoPfHvv/9eemtAGpXNCDybM3u2FFa1S7etY/MeK6XU/9ygYUMjVdQvivybb762iO9TT+0kn06daqRMlzBys1HaqGeOx9yeVKlTCzDT+fFzQ/ClSpe2fG9agy7RTcSECRMscO1YzemePPkd92dno3fObyV7IuCknT2fq99VjCFwmQaP9dRKZG20RCjkPWnSm1YQBR8zyhnzN+q5du3aUrBQQVmxfIW0bt3aFHm+fPmMzD/TBiMVNKgs+KapGY55vXDhwvY71DnpWqhqypyGgQrn88WLF8vaNWssR/zFF16Qjz/5SAPZjrKc7iFDHpNTTjklxlDz5TgCjkA0Ak7a/k44AhmMAHnarVqdIiNHjjZSRRlDxpAoJUxJ2YJ4qWS2VYl7qirq5dpIZED/ARZx3qlzJ6lVq7YFiL3x+utG/kSKX3/ddVaS9OR69eSdyZOlhZIufnCixFtoilikyZ1rQt78e/ihh7Tq2jwpVKiQ1iL/Vk7rfJrccuutGYyCT+8IOALpgYCTdnqg6HM4AvtBYJZWK3vl5ZdlyGOPmbJGCUOo+JUhWSspqsFiKODSar4mj/p5rVZWo2YNefXVCXJc/gJajvQRi/AmkIwa4ZO1gMprr70m1w681q5MJTUImaCz+V98YcFmtNisrgFqqGx83GwGXnrxRTtu85bNZqLH9D5u3POm8H04Ao5A7CPgpB37z8hXGOcI3HnHHRbdTcOP1yZOtGpkc+fNNfLupL5qSHj8C88LirzXpb2thjjKGZP52HFjNaq7s9yged0Q7BYtzPLjTz/KbbfdqpXVysg9995rkeFsBghow+z+6dRPLSiNwLX+AwZYlDoq/dqBA61FJ9fBV87GoXq1GtoBbPg+zUbiHG5fviOQrRFw0s7Wj9dvLqsRCG05UbMo22eGDZPnxj5ndb6POeZYef/9D0z5tm3bRupq+VK6dl1yySVy2WWXm8p+9NFHLcise7fu1gzkW+2D/ZCatzGpP/PMs1rytI6RP6RNG89NmtdNgxAUOcFmFGS5Q9PCCH57+aWXtNTp67JLA884B2K/7bbbrEyqD0fAEYgPBJy04+M5+SrjFAF8xuecc7ZFZq9YsULmqcImjSt07xr69DCLIL/88svMP/3kk08YmU+ZMlVJeZjmaY+yfGqixGnsQdoY/umWp7SUQUrekDNdumj7SX42QWXTPv1UKOjC9TCxX3DBhXbMHbffLrPnzDYkMcsfdtihamJ/w8uWxum75cvOmQg4aefM5+53nUkI4Fu+6KILZdCgh4x4p0+bJi+9/KJ+v1dqaJtMTNR33nWXEnZP63l91lndZMP6DUbIl6ri3rR5o7bVbCLTpk8zkj1Ty5O++OILcuWVfexY5pym3bxQ18W0V3abtm1NXWNaf27MGJk5a6ZU1QpqlD6drbXF2RRgNi9U8ERT4DW1clpSqWKZBI9fxhFwBFKJgJN2KgHzwx2B1CCAKr7yiivk/665xnzJBJmNGj1SataoJdffcIOMGjlS07gqyM4dCQFml2oRlgu0MxftNK+/4XpTyCfXPVnJd4a0a9tem3rM1MC1nRoB/rBs105eNAo5tWMnmfjaRLlOo8knacOPehpNTj44JnBywWfrvyv79DEz+1VX9dGKarnNR964cePU3Iof6wg4AjGAgJN2DDwEX0L2RADChjiHP/usFC9R3NK2HtUocCK3aZ3ZqGFj6/b1zjvvyMJFC6W5dt0i7WvxkkUW7U0p0nz58psSRj03bNBQVfpL9v09d9+j9cb7WYAZJvZevS+VsWOfl3LlyplqL6R1xO+6+26rqsZmgahycrev0RrlbBL69bs6e4Lud+UIZHMEnLSz+QP228taBCikQkOPbt26GVkvW7pMpkz9RIui5DE/dKuWraxb1+rVqzQyfIt13ip7UlmZPWu2zJk7WwPWDjUfNscSyLZz5w6NOO9sJEwK2OR3JkvbNm3lgw/f12Yfk6Vs2bJy7z33yHvvv2ebgKv69jXyJ72M/O1rrx0oDeo3kGtVlVO0xYcj4AjEFwJO2vH1vHy1cYRAaASybt06eeThh+UiNXm/qmVD8XMTUJYr1yFW8xu1DJE+OGiQ+ZvxU9N/m05c5FgTYLZs+VJV33v0s7/kscf+K+M1j/u+++/XSPOLrfNXy1NayeAhQ2TGjBly9dV9bV5M6x07dLRCLKSbsY4+fa6QU1q0lAIFClhnMB+OgCMQXwg4acfX8/LVxikCjz02RE44/gTr9lWzVk0rYUokN6lfkDuKuq+qYtK/6tSuIwNVEdNDGwJfMH++1K9f31K9UMcEri388kvNyZ5kTUGWaj9scrm3b9+upUk/ts0A5Un37t0jTRo31RrlHaVtu3aydu1a6d69m1SsUNH8282aN7Oe3h6IFqcvlS87RyLgpJ0jH7vfdHoiENlak+8ZkURITjV1we9Wsm3dprWMHj1KFfCpaiafYs06GJx36KGHqXl8twWcfTH/CzN7M0jbOlRJfezYseaz7tChg/rIS5hv+/PPPrO58x+X38qSosoXL1psBN6ocSNT8du/2m5FVogo79mzhyrtU5S8u2sk+ZNyq+ZpU3zFhyPgCMQHAk7a8fGcfJUxjAA51xu1qMnGDRvk119/tZXig6a++G4l4d0/77Z86kWLFsl5550nJbXQyZjRoy0inEFeNor6119/SSRv0r8Ye/f+rV25jldT+e/qB8cH3tp81IWLFDaC/ls///W3X+13s2bOkh92/aBlT4+zRiKNmzSWY3Vu/NmdTztNy5WOlWHDhipZPy0/qK+9kUaPP/jAA5YOhi/chyPgCMQ+Ak7asf+MfIUxiADqOVQgg5zLKOlBfHny5DHijTY58zsiwyk/SvcucrHXrltrlcw4n6AyvifQLG/efKbAg2rn9pmPn884/UxZtWqVrFy10sgYZR4+4zh+R153pcqVtPZ4cwtwW7tmrRVzQXVXr1Fd13mSLNdqaTQeIaDtAfWNX65paSdp7XMfjoAjENsIOGnH9vPx1cUJAhAqqVX4pIkYR8lClJA7ZLnzu50WCLZxw0YjbTp8US2NeuLkZ0Om9Lu+7/575dJLe8kfv/8h454fa2o6bAAoyNK7V29ZsGCBLPhyviETCDshLSyvkT0qnypoRYsUNT/2u++9Y4odH3n58uWtOEu5k8qpT7u5zUFUeX/NI6egiyvuOHnhfJk5FgEn7Rz76P3GDwaBoILJw162dKmsUkULWdeqWcv8zZQeRT0Hwg3q+/b//MfKi1ILnFKjBJYRSV60aFENCjvHTNz4qh948EF5ftw4LX862eYpVqyYBZn1VlP2/C/ma4W0T/dZflgPxM6x1CUnL7tHj+7WRewkVddjnnvOzOinn95VI9AfTyRozqUu+WZtRkLBFx+OgCMQuwg4acfus/GVxTACqGjIl85aKGU6bfF95IAMUdOUGF2nihdzOvnT+Jl/Uf815UXxha9dt8YUdeHCRaTeyfUs9/r0rqfLbUrw1AjnOss0QvyFF16Q+++7X45WEh+tNckXLV6oyvonK3/KIGL8hBNOkIInFJRzz9WocFX433//nTynZE0Z1SpVqpj6f1xbhHbv0UMqVqxo57FOemzPmTNHntFCMJC9D0fAEYhNBJy0Y/O5+KriFAH80itXrpQNG9ZLPvVNlyhZ0oiU/GtU9/PPj7PCKVQ8m6W1wEn5wqzNZ7s0iIxBFDlETO718hXLZYsWZSFY7dJLL9V2nKWtfOnMGTNtzipVq1h0OOljmOFJ5yK3GzM9EeRr1q6RK9RfTScvirNgLidIDTUe6Qun1/Z9991r6WaXXX65Ral7KlicvoS+7GyNgJN2tn68fnMZhUBkalcwfeMbJsCrYqVKiaQYrs8xy5cvt7Qv8qppFoI6R0lDwgSgUbJ0h7beZGDmhpQJUuvapau15VyqZvgvF36pPbCrmzrGbJ770NyyauUqOwdfNhXVlq9YZhXXOAYip3Y5ip+e3g0aNLB/h+uxkQMFfustt5iJHFM/5/S56ipr/RltQcgoTH1eR8ARODACTtoHxsiPcAT2iwDtMCFsyC0ykAvShAwh613/9LxGvV53/bVaAa2h+ZdDq0zOpRhKgQLHS9kyZdVUXtjO/fCjDzQi/AirYPbTTz9asBuFWBj4vsuULmOfYXpnDuYkrezFF19U8l0pzZo2NxN89erVZfqM6Ubs5Gj36NHTlDcjbDruu/de+/n0M85QU/lsKwDDxmHAwIGWA85w9e1/DI5A1iLgpJ21+PvVswECfyiRolwjU70gXHzEx6oaRnlTUpTfUViFXGnSrui21fuy3kaOE159xZDAr125UmVtu3mW+a7f1WYiFE+hRecRRxwpJxY60XzRzEW6Fir9O41MxycOmWOKR23zGVXSSpYqqdXUGkjp0qXl888/125iO+TVV1+Vn3f/rN3ELpBTO3VKDJgjGI10MnzpkDP3NWXKFPOJUz3toosuTiT6bPDY/BYcgbhEwEk7Lh+bLzqWEIg0lUOY8+bNs+Vhhg552xAvpEjbzKFK2hDzosWLzAyNCbqs5kgTLf7JlE+sDCkpWgnlTXPZXKFxCGq8ZMlSdh7FWlDL5GajiLds2WJR6Zi4y5QpY+lkxYsXtxrlfI9K53PI+IMPPjA1vktTxG679TZp0LChpaE9pPXPnx0+3OYNmxCu8+QTT9hm4B5V42wAXHHH0hvoa8lJCDhp56Sn7feaoQhgJh8+/Fltt3mRRZQHYqOHNoFelBKFXE87rbNVQCNdjBQucrfLlS+n0d1V5Qbtoc3vaQwSGSiGj/vvv/ea+bto0WJysapezOKQL5XP7r//Po0YP8/85KR3keZVTnOyiTKnWQhEfbJuGDCPR847YcIrGlk+SFt19lOz+vnWn7uFljllIxEGZM+a7tFWn+SHP64NS5grjKSKyWQo0D65I5CDEXDSzsEP3289/RAgLWupqunTtFzoYap8GZisX3hhvBQvVlxatmplhAsBtmp1ikWM83sULdHeBIrho27btq2MHz/eypGipgudWMiUNGZxNgW///G7XqOLETaDKmtj1Xx9cr2TtUzpOOlzZR+rzoaiJlCNTmGDNOe7YKGC2pCk379uGMLFH/7Ef/9rG4rzzj9fo9G/svUy2Fw8/vhjthHYq5uGJYuXqDXgY117CTlDfd8UaPEUsfR7j3wmR+BACDhpHwgh/9wR2A8CKNC56rsmtYs86KA6IVjaZ5IPjeoOA190c/UPo3bP1Q5bBKl16dJFPvzwQyP1evXrGdFWKF9BjlUyp60m/ukvtQrab79rq04lewiVqHLIkutN+/RTU9w9evbUnO7laoKvbwFxfEaAHAVc2FSsXbNGup5+uqV8JTU+0+Yjr7/2mnTt2lVrmxcx4mdwrWeffcb6fTdq1MgC2+hWxobjq+3btLpaeWnarKk0bdrMzPJErPtwBByBjEHASTtjcPVZcwAC+JDxH+O7hoSD2RnT9CuvvGzlSPFpRw4airRq1dLKiJILfeFFF1l7zU6dTpUzzzjTCrFAmhA0Sr2U+q/53adKzJAtgWPbtB933ZNPNjLmWgS5sQ7M8DT/YCNARTZysRnBTM+1v9SWnrVq1frXusIaOQZ1TXpZhQoVbO5wX6j6qdqZ7Juvv5GT9frbvtpmrT1ZAwFwH3/8ka5hhir9MtK4cROpXbu2RbS7/zsH/DH4LWYaAk7amQa1Xyg7IUDJUsixsXbKio4av/OOO+Qu9f9ibo729/Jz165d5EiNBMcs/vTQofLxRx+Z0obAL774Qunff4D5uYsWK2rETC73tE+nmZn8P7ffbu04u2na1h4t0BLyrZkXhf7aaxPNN01QGUqZa0QOjqP4CxHoyZEpx1AnHf84JnZGuA+IG7/4Ft0kVKpc2Uq3kk4WgvH4Sm30YXpf1F0n15tGJNyHK/Ds9Bfg95JVCDhpZxXyft24RuAr9fuSSx1JfFQ5Gzv2Oas+BmEnNx588AFLpSqmAWXX9O+vfukvZfOmzdJG/dm0ysQEjfqGDFevWa053rssXaunmr9ra4BYdF3zyOugevGPV9I0M9T3cccdZ77yyM0DVdv4bH/NQVDcEye+Ki1btkpU7FwH9f/Jxx/bnFW0DzcV1lDk/ByJBb779997TzcRr5kfn0YldBIjmt2HI+AIpB0BJ+20Y+dnOgKJCECK+LApTBLUaXLwoJxR2xRRgZjxGYd86rffestIcsvWLdK582lmjoYQKVWKuRkCrK6VzUi7Sm5AyvjHIVF86NHrYa0cA8GzAUhKcXMMKV74ubEmBDM3v4e433jjdSuVetlll5vPHUWf1Dyof/zqGzTY7ZVXXrF2oC1btkyyfam/To6AI3BgBJy0D4yRH+EIHBAByLZO3brJkmD0BE8++YS1yKQyGr2vi2hRlRo1a5pf+DCtPQ6x8/MPP3xvXb3wZ+M7JzJ8f32vg5kavzSEiU8d1R49OA7zNZuAUBktHBNUOV9nz54tefTaKHxG+IzAtimaU3755VfY/ClJ+9q5c6dFqSdUhbt+v9aIAwLuBzgCORQBJ+0c+uD9ttMPAXzERGYTJJYS8uLK+Ib79r1KSfM3ad6sharqzlJK1fOHH36girqOKtx5Fo2NiXnu3LkaGd7DSJiqZPsbmOghfIgYokdxH+ygyQmqn6C0MFDq06dNk1NUNafUV01qGRYCItRnzZolD2p+eHqs72Dvz893BOIJASfteHpavtaYQ4BALMgLwk4NAWFabtasiQV14f++4467zCz+xuuvS/sOHbSq2lyL4l4wf4EpWVK/OmsOeFX1I0eboYO6xsw+R5Xx8RrJjU87OnI9reBhYsdMjnk+EDfXZEPRuEmTfwW7JXcdgtswubO2NbrJmT//C+nWrbsF2PlwBByBlCHgpJ0ynPwoR+BfCEBcEOWBfNhJQQchn6c9rxcvWaSkl0/atmmryrppQs1v9RnTaWvTxk2WSkWwV526dSyNKrJSWZg3rOPll18ydV5Sc8bTi7D399gxrdP+M+RzH+gVYZ3z1GpQUJuPEAQHiY8ZPdpM5dFR7geayz93BHIqAk7aOfXJ+31nKQIQ2MMPPSRvvf2WFDyhoBVK6aAKm6Im5GGjPmfOnGn9sokeb6gR5aRNEakdSdZBdQcfdVL+6yy90aiLk3POpiT088avv27tOrn1tttiaZm+FkcgZhFw0o7ZR+MLy+4IkMs86a1JUrdOXStIQsWx8hXKy5rVa+SYY4+xIiYtWrSQndrF6wwtvEKaFvnV0YOAspT6lbMaUzYXVIsjGh1rAGu/Q3PPqRxHv++UxgRk9X349R2BrELASTurkPfr5ngEHnn4YXn5FTVpN2mmQWilrFUnfuMRI0aYmZzAM5qM/KVBX/ipqcDWpk0bwy2QW6hZHhqBxAuoIRWN+6AULPXR6SAWUtXi5T58nY5AZiPgpJ3ZiPv1HIF/ELjrzjuNtFu3amNK+/TTz5DHhgyxYK3KWm1swqsT5Jabb7GOWlRNQ52eeeaZ1pAklBb9QouuRHbcSi9wM0LxRs6JTx/rQLgPUst+101KaFSSXvfh8zgC2Q0BJ+3s9kT9fuIGAVpdvvb6a+bf7dyps9Ui37ptqyxauMhSoxGH/30AACAASURBVJ4f/7w008Cy+7Uf9uAhg6VG9RpSpGjRxMhwiqNs2LDB6oBnxAhR6elVO5xI+8ha5hA3Pnjmp0AL1eT69bvaa5VnxMP0ObMNAk7a2eZR+o3EGwKYhCe99aYWVikqLU5pYZ29Cmlk9VNPPWVFTyDzKVoR7ZFHHrX0r51K0lWrVbNOWgSqQXI0HmmiUefpPSBsTO+UQU0vkzXFVULHM+anVCpqm3xyfibdjUYoRL/7cAQcgaQRcNL2N8MRyCIEiB4fO26s9c3u27evreItraxWT83hL730kpytJT+naQ44hI2vG3JrroFpFE6B7O6/7z7LD6fMaOSAAPEZU/70YAZBYhSOYSMR2V40rXOitNkEhPGHbkz26DVCehr13KkIR8OT9FL3aV2rn+cIxCoCTtqx+mR8XdkegWeeGSZPPvmk9OrVS6pXqy7NmjcXgtMoPEIRFYi3SFFSwLaZn5u63USPB1/wyJEjlNjPsVzuMEJtcMzNmJ4LFChwUAS4adMm2yxA3Ac7KChDTntyke6s/bWJE+UkdRPQPtSHI+AI/BsBJ21/KxyBLEJg0ptvyi233iI9e/SUm2+5xczQlAe9qk8fq5S2ctVK6dC+g+Q+NLf8/NPP0rdfPwtGQ3mT6zxz5gxp2LCRdRuLHKSGYYpOD+KDaKM7eKUVLjYS3GNyHdBQ9mxORowYLtdc0/+gNhtpXaOf5wjEOgJO2rH+hHx92RYBKoJddNGFFpz13HNjTRUz+P3Lah6nVedDWp+bBiEEm3FcBVXafKUS2VZNAaOpSLTp+ssvvzRyR60f7GBzgGJPj6ItzIWvHrWdlPkbywIqnFrn3bv32MeUfrD34ec7AtkFASft7PIk/T7iDgGUJaVMN2/ZbGq76+mnW41xCG358uXWMQzVfMstN1uZ03z580k1NaNTPQ3yI1CMCmmQfTA5k9uN7xilHjYBBwtMekWRh8Iq+LDZVEQPfNqsn3v7Ti0F1DX34Qg4Avsi4KTtb4QjkIUITJkyRW688Xol2SOlX99+0q17d1O1EBhmbwj83nvuMbMxUdVElFNohdrdEPXXX39tSjy014T0SAOjKUd6jPQi7Mi1JJcDzmZjyiefSJeuXbX39sty7rnnpcct+ByOQLZCwEk7Wz1Ov5l4QwACwwT+wovjrcgK+dlX/9//md8aAsaUTCU0WnXOmT1HTj31VNn+9XY54fgTrBDJqFEjrV1npHKF8FHp6TFQveSDs1lIrxGC5bAGRJP55Mlva9W3tmYi79Wrt/u10wt0nyfbIOCknW0epd9IvCKAf7pLl84a8JVXSpcqrSlP50n9Bg2MsAjaCsp02LChZvLeqg1Fli1dZiVNlyxZInerEg+VxQgcg7STU9qprVNO9DikTcpZeqZhUX88qZQ0/Pn8fvmyZVJa89E9Zzte32pfd0Yh4KSdUcj6vI5AChGAlCdMeEUmvjrRgq8whffo2UOqVKlqQWZEgqO4Ub0XXni+dO16ukyaNElaNG9hivzGm25KjMjeuHGj5T3n145gh0cpWZaT2vKktAVF8adHUFtKTOTc+4oVK6yM64zp06Vtu3YpRNEPcwRyBgJO2jnjOftdxjgCKOCLLrzQVkkUNeboy6+4Qn7UNKkdO3fI3j17LXJ83ry5smrlKvNnz5k7J6Ewi6aCoUjxbxOchsqG4PFzM28oFUrvbwidc5Mib35HMZVIlU4rzeRytKP93Sj8E0880RT5gVQ5GwHWlVRA2udaT71KlSpWb/20Ll1i/Mn58hyBzEXASTtz8farOQLJIrB48WLp0+dKKV6suOTNm1cqVqoo1apWkxM0WnyHkjEkfKIGpz2gtciLag3yNye9aWR93733Se06dWTB/PmyV4m3bt26ptYpdUred6g4Rp40Pbkh9Gh/cljUokWLrEVmGKE+ePSiA+kH4iadCzM662KEzUJSNxt6f3NOWBu/Y824Az6dOtUix9984w3p0LGjWRl8OAKOQAICTtr+JjgCMYQAAViYyVHDRI9XrVZVSpYoKTW1QthS9V9Daq9rjW5813NVdTNuu+026aEpY0Reo8r5HmKGBCFDSO+vv/4yVRvINKjvyFvnWKqxlS9fPkWI0FKTeebNnWubCUzoKGyuSxEVNg37G9FqPxRyCf5u/OlLdCPTqXPnFK3HD3IEcgICTto54Sn7PcYNAhDZrJkzZcDA/kayv/zyq/bbbqrKs7F89913VraU7mCo2o2bNip577J+3D169JA3VJlC9DfceKPdL+THP9QvzTlQ6swfzOT8LlLFYpYnLxx/ckoGqnzBgvlSsUJFadCwYeIpq1atsk1D9erVE5SBEnlKRjSJ8zPpbrf95z8pniMl1/FjHIF4RsBJO56fnq892yJARbRhzwxVct4pdevUVbXZSQoVLCQrVq4wtQxBt2zZUsaPH2/pXS1PaWkBXBRegbT5imkbHzefBzO2dQvTwDY2BJjIQ0lRTOd8tnTpUmnWrFmKcP3wgw+sTjhdxwI5R5rLUdopJezkLkg63JVa1hV3gQ9HwBFw87i/A45AzCAQqTQhUFp3vvX2W9KubTspe1JZKV+uvLbjHCuXXHqpPKWNRho1biSjR49S0/ceadigoZmqaR6Cmbqj5nNDmEbaqr5DJDnkTHAZpVAhbr4yIHLGtGmfyhlnnJkiTJZpWhaqPBBzZGAaUexsLgKhp2jCJA6aN2+e/KBFV9q1b5/WKfw8RyBbIeBKO1s9Tr+Z7IQAPt7zzz9PypYpK4WLFJYWLU6x9KtcSsaTJ0+2GuU/706o143pnBxvmoQQfNZEA7n4Ss5zcS2NihmcdDJIEBVO5y5IOyjybdu2Gflu1Gpq++vPnZoKaVx/f724U5Izzv0+NmSI3HTzzdnp0fq9OAJpRsBJO83Q+YmOQMYjgLn6xhtvMOKuWaum+aXzahEW8qfHPT9WSfEwKVa0mGzZukVq1qgppUqV0mjzEywtrJyaro/Mk0DOBKJdcMGFMmbMaKs4BmGSVgap4uMmyC2Pzo1Jm/afkDPnRAaThdrhmNRT0kAkMsI8JWZyjp+qkeOnnHLKPur97rvukmuvu86jyDP+dfMrxAECTtpx8JB8iTkbAczklDLFtA3ZVqtWTeuPHy/Tp02Xrdu2mtKGmNu3a2/NQo7Ne6wSX0uNQn/VAtP2/r1X1q9bL/fce6+89dYkNZcXMfKvqPnczEdQG4S5ViPHmQdTNOby116bKJde2ssIms9R4+t0s9BUfd7RJJzaoi1JPVHmePeddyxSPqSOcR38+1gKPIo8Z/8d+N0nIOCk7W+CIxDjCFC29NJLLzElPWv2LFO/FcpXMOJdsnSJESy/w59NJDcke8WVV6pqnWJ9uA8/4nDZ/tV284XTg3vB/AVaca2nfKPFWMjb/kv95/ieP/10qgWnkTJ2s1ZZY57rb7jB0suoCb5m9Rp5QDcQSaVypQdp48cfN26stNce4pG10ykaQxT5f5944qAD22L8UfvyHIEDIuCkfUCI/ABHIOsRmK+FU/7zn9sslQp1jOn6BiXUoUOHGmmjSCFxcqQpb4oqXb16lR23Yf0G83nXb1BfDj/scPlAo77r1a+nRVhONgW7TE3wVD177rnntPnIRVJXe3c3btxQhj87QvIqqc/WjcKsmbPkkUcf3ad3N/5mCJ1UMRqa/PnHn+p7L2LqHtM7PvTUDOYZMWK4tG7dxqwJQc1zv9dde630ueqqFOeQp+a6fqwjEE8IOGnH09PyteZoBB5+6CF5fvw4wyBv3nxSv159I+P5C76QqlWqyeIli02hEpCGSibYrHyF8rJp4yYhmvunn3+S6tqPG7KFWE8/4wwjRkzq5FsT3Hb77XcYgbdu3VI++WSqTJnyiV2je/ceRsSh1/c2Vf9r1q6x/O+2Gt1OH3ACz7AKENyG3zs0BAnNTJKKMo98oKSssW7+0Xo0crw2caJ8u+NbufzyK1xt5+i/Ar95J21/BxyBOEHg/ffe04Csa5XUcikh5zFTOA1FZs6aoQTeQBYtXpRYU5zANT5DaZsJXL9OUn82qWGQOQFoXbVvdREtvDL82We1jvlsPf4EefTRwUa8ffv2kaefGmopY2W1X3fo8vXB+++boj9C51i0aKGZ31trt7HixYtb+hgkTkEXzqPPN+b2QNrAnFxAGusjhQxV/Z1aDqiwRv3xcDxFX0aNHCm3avU31u7DEcipCDhp59Qn7/cddwjQwrNTp1ON2FDDlBFtUL+BrFu/znzcy5YvM8LNoxHjuXMfaoobMsTfvH7Dev3+T1XBhaxIC6ZrlDCtPt+c9IZFkBcvXkKeeOJJefyxx2TpsqXWjOTsc86xWuSQJ+br27U6WSjWcla3bkbKKOvkapmzZtZJVDume/zTHM98bCoCKVNFbdHChVJSjyMvu03bthZgxwhpZk899aQUPKGg+eNTEo0edw/YF+wIpAABJ+0UgOSHOAKxggDNQl5+5SULBqt3cn1Zu26tnFjoRFm+YpkpZaLMq1SuItu/3q6q9xdtOFJdzeaLzHQdgsVKlixlaWOrVq9UYi+j5y6X2rVqW1GWOtp45Iknn7ByprfccouceeZZield48c/ryr4O4seJx98f8o5kC3kStT7nNmzZZeWXF23dp1Uq15NjsqT4H8PVdmIgmfD0ahhI6lRs2ZiI5GAO2v/8ssv5cEHHpAx6nsPjUZi5bn4OhyBzELASTuzkPbrOALpgMD0adOk39V9NVK8oJQpXUa+2v6Vqc9NmzcZEUNm+K6/+eZrM6Fjst6uxyR01IIod//TOjOXKvY9ajrPb4obsiT1CwX+2eefaeOQ1fLOO+9ZVHlQtXfdeaf85/bb91HAKVG8Ieeb1C384rOVwCmVSmcyAuswqaOq+b506dLJppNhdif97Zxzz033/t7p8Gh8CkcgUxBw0s4UmP0ijkDKEYDkCP6CyCDdSGKkC9cZZ5ye+PvffvtVy5tWUHP2EjV1H6/qu54FpO3QoK0//0wojkKEOD8X05afdM469NDciYupUL6i1KtXz8zjKN1VFnH+p55zrLw16a3E8qeYtd9//z0r0BIZWBad6oVCZ81sEuivjVkcHzoWAL5iAj9OTfJsBjCTp2SwNvzoXPeTjz+2U1q1bp2SU/0YRyDbIeCkne0eqd9QvCMwTNO4nnn2GS10cqhWOyuuFdFulIaNGtltQYQdOrQzXzRR35DyyXXraSDZHPu8Y4eO1rKTNDAiuH9W1c0xqFhIL1eu3KawIVu+hzjxXeOvxo8NuTMeG/K4tGzVKhFK/NKYuNt36JD4u8gAMzYDHEMUOWukqhqDc+rX11Qz9X2zXgbKnmCylOZ2szY2MBD3QiX9z9US0KtX73h/zL5+RyBNCDhppwk2P8kRyDgErrj8covmPlbN3fiDIdYXXnjR0rSIym7TppUFmqFmq1apqp2/lhsBE3TWuVNnef+D942YDzkkl/2uRvUasnoNCnqPdvL6y8gbIidtDDI85uhjtAzqZiN25oHEnx0+fB+FT7tQotN7977sXyVMZ8+aJd99/52VR8XEDoHTlhOFz/pRylQ4S4kpPSlUIXvuAxzICx8yeLDcoaZ6H45ATkTASTsnPnW/55hG4NFHH7HKYChRaovjpy6hkd1DNKobkm3Xro2RLoFnEO3OnTsS76d9uw5K2u8ZQRJwtkl7blevVsOix3/66Uebj+hz1C6kj4rFj01f7kCqjz32X6v/HQapZg89/JAWd7ldamqQWCiawvrYRKxaudJKj4a8bCqbJaz94FOzWCsR6JjWsS5A3uSr36xBcj4cgZyIgJN2Tnzqfs8xjcDq1au1lGh3Jb69Rn4QNCq5aZOmWsikrarMO0xJM4466mgLLgujSeOmlre9d+/fFly2ctVKy5sOCjscV1SbjGDG5hoMrsMm4Omnh1rONZ9t0oIsn332mXzw4QdWyKVb9+5aRa2uHQ/BE0BGpzEUMCloGTFQ7pjFuRYpYoynn37KFH9S5VQzYg0+pyMQSwg4acfS0/C1OAL/IHC9drX68KMP9vH70swDUiZgjK5eqGQKrQRFjuquW6eufLlwgc2Cqj7yyCO0AtrvFlwWOVCtO3bsVOV+iJnaIfWuXU63UqH4oUmvmjlrpv3+xEKF5YorrpBTWrZMJGyuSV9u1kKaWEr902l5wJjEUe2QN+NZ9fefe+553vUrLWD6OXGPgJN23D9Cv4HshgAEOGHCK3LfffcmkmS4xz179iZUH9NUrWXLl+5DonxWrWo1y9kOA781ZvEQeIZ5ORA9ahzSxnf+xx+/q5JvJg9qStVmjfSmQUfevHnNlH6Z+tjxUUf6pPEzYxavrFXLOC4jB2tH0VNhLZA2Ueyeq52RqPvcsYqAk3asPhlfV45GgACus8/uqWbqbYkVwQAkECembEzWkCcV0TAjU0CF0qYEnYXIboiZAfFhCic4jYImBIZxLkFiVFODnFu3aS21ataSsWPHag51bSl3Ujkrc1pJW3hGjlCmlHMjG3tk1ANj7Uu03zcbB8aA/v2teUlKenpn1Jp8XkcgqxBw0s4q5P26jsABEMCvfIcWM5k9Z7ap40C+qGdIuXy58pba9ZeasIupj5oAMIqs8JVR4LgC1q6Tn8mdDj5gTM0lS5W0qmR8TwDZho0bNE2rknytQV/0365du46RdSghGjYBEDWNPQhioypaMFln5MNk/cuXL08sqNJXTfhPa1qcD0cgJyLgpJ0Tn7rfc9wgAGmepxXAgimchR9xxJFGmihnIrlRzNQNh7ipZkaqFSSNSZljOB4VDvEX0pKn+MZp0YlfG9InwKt9h/ZyxOFHGIk3b9Ei0V8cnabFPJyfWYP7h7S5x1CMpY/2Ch86bFhmLcGv4wjEFAJO2jH1OHwxjsC/Efj888/l2msHWuBZCCiL7pxFMFlQ4uFriDAPM2IWx+/NHIGMqaKWT5V7iNDGX968eXOpoMVRIP/IMqZZ9Wy4bzAIaWj9r7lGHnv88axajl/XEchSBJy0sxR+v7gjsH8Egnl6zpw5ctddd1qXrJAKFk3c0absUAGNKxAFzkiqtzV+b9RzOIaoc/zZKPF69etp2dQz/1VONTOf29KlS20DQUlUBkFyt2m3MR+OQE5EwEk7Jz51v+e4RACT+MABA+TzLz63Dl6BhPlKyVJyualFHknm4Uaj64WHc0NZUwLUIjcDKPcQnU0/7po1akrPs89ObNO5PwDTM/2LuahbzgaCe+RnWnT263d1XD5DX3TaERg69Gl54IH7ZfLkdzQosUaKJrrpphtts9enz1UpOj4eDnLSjoen5Gt0BBQB/MmdO3eyrl2hfzVEHWqJR5J4Uqp7f78jSC2074SwOZZ5TzyxsKnwrZoXDrGPGDHS8rIjNwORDyepa4TP00rm69evT+z+xRzPPDNMrryyj78TjsB+EVisZXfpP3/zzbc4afu74gg4ApmPAOU822haFl26ihQpauVLUd+MQIi03wwqPBAon2PyJjiNPO1du35IPD6cF0moqG8G5nLaezZu1Fjrm6+w6/HZoAcHSQstc5oUCYdrYsanKAoFX2jHScBcWmqPM9+CBQssRxvFzxgzZrRcfPElmf8A/IpxhYCTdlw9Ll+sI5D9EFi2bJl063amKV/IFLVNVDUFUiBEgspq16otUz+dasfQphPTMmlgEB7HBhM4ed5ff73d1DNR5YFQOQ/FHTYCfIWoTzzxRDlW23X+qIVa+PyUFqdIfzXVky4WzoVg2RTwOWul49dvv/1mx1A9DfLG5J6amuREjkP+/CtZsqRdi77cmOp9xBYC1BaoXr2qVaubMWP6P41japg5m4FpGxN3GNEKePLkt2X8+PF2LoN39qqr+iaq5GjzOI1pEszlbyfOybUf1E0lv+vT58rE3zPX4sUJxYheeGG8XQdSZzRt2kzOO+88VeWdE9fJMfzMV8bQocMSP89q1N08ntVPwK/vCKQQARTnueeebfXG+U8IgqTRRyDYwoWLSIvmLeTlV14yZY0Kp4gK5BxKlQYlzOf9+vWToqrYh2n61KrVK43oIfHoqHNImw0C9cW7dOmi/5G9YKq7SuWq2kL02X0qorExGD/+ea2R3s5StCjEwhrI737ttYnWCQzyTc1YvHixVK5cObGd51uTJkmXrl1TM4UfmwkIBNKOJDnIE/I799xzjCQhVH7m9/ib+Z7fcW7Tpo0Tf06YI8GHzeeQcTRpY/pmhE0B83OdMGdSShsS5rqB3Dmfc9go0EkPAg+bC77nd+EeMgHCFF3CSTtFMPlBjkDWI/DFF1/IBRecZ0VSjlHVS3lSRggyowkI/bRHq/mYrliYySHrkOIV6W+GoJ97bpyRIcp4wfz58pIq2I8+/siUe+RgfpQ5XymfinImGA6TN6bziy6+eJ+qaRs2bLASp+R7o6ohbgLJMJmjjggMgtBTai6nyAznUhGNxiEzZ8zYp6931j8ZXwEIBNJmUzZjxqxEUAJRRivrSBLmvUAZB4JOCtHI4+lgF1Q95yQ1kiJtNgb59B0ORB/Oi/x9IO39rSUrn7iTdlai79d2BFKBwLx589SXe6GRdlL+ZAqstFUlO2r0SCNEcrLz5DnS/MqRBMm5+fMfJ4888qgpaAi0SJEiptxffvkleVRLhEZ2BYv0jbNc0q/qnVxfC7nM0/mPsiYldACrV69eYgU1irZQjS16oJq5DtXWuDatRg8UoEaRmM36n/pe60R2vPysm4DGTZqkAjk/NDMQCKSN0sWcHAbKFuKGyCOtLJGkivLt1KmjtZNt1qyZHRfM1WGeaKUdqd4TSH/fCPFo0t6fjztyjViKuFZqotQzA99wDSftzETbr+UIHAQCs2bO1OYdvf/lEw5Km//wWrVqJaNGjUose8rlokmX48udVN6qoP32629WHrRJ06bC/Mrucpiq4wcHaeMQ9YUzogkf8zy1ypup+XDBlwvMX125UmWN0r1Za5YnRJYnF6SGmXzNmjWyUgPbWrZsZcFxCWb5fdU9c1BUBZcAfvCvtm0zon733XekceMmUrZs2YNA0k/NCASSI20UdKTfOfrakC0qHOKFMCF45mJA3HwGiSeV8oUqnqGWl6T809EkHfzcSUWTB3UNUb/99ttO2hnxgvicjkBOQ+DTqVOlb7++Fj0eTcRgAWnj037jzTeU8H6yvGaIL6kiLKj1Tqd2loULF8rv2uHroosuMr8z+a81atQwdX67FjCZNn1aYtGVQOCQbNUq1WTxksXW4/vTaVNN/bMReHTwYClcuPB+Td/85/zO5MlGwgSqodCjSZv7I1oeZT192jQ7rlPnzvJ/V18t9z/wgLfljMGX/0BKm0CwkAFwoOUzF33TIWreScj0QHnafA7pcy6qftOmjfukfKVEabPGcF1X2gd6Sv65I+AIJIsAJEbU9AMP3m+50z/88P0/9cf/Tgwyg7Tp0gVRT5n6ifmhd+z4dp8qaMyDn7tD+w4y6a1JFm2OuRrf9tq1a6Vjx47Stl07I8vvvvtO07selHdU3YaGJUFFYyInQI0NRNkyJ5lfHOJt1LiR9t6+8oD+avzSmzdvlpradAS1HYgeszrBbKyJNSzXKPRCGrm+VtV5B13b+RrlO14D4TCr+8haBO688w7p3r1HYiOX5Eg7+LSjI7CD8t1fZDYqnSAxyPRApA0akcckKPV987T359PmeMg+UnWntIhLZj4JN49nJtp+LUcglQgEMzOkeFnv3vLF/C8sipvKZz/++FNib2ymLV+ugileTNcrVi7fJxc7XBZiPbvnOTJg4EB5/LHH5NWJE8w/vWTpEjO7869smbJyVd++1naTVCuU7h36HzR+7kizd1D7mMu7ajT3zz/9LHPnzZVrtDY4Zs3kAs3Cecx7tJI/AW1bNTUt+KkhZAh9gxZV4XcEonH/kPhVffoYafvIWgQGDhxgCxg8eEjiQpIj7UCe1AfANM27geqFkNlohghtfo40XUdHmEcHokHAkCrnM0IwG9+jkvmZYzC/n3fe+WZiT030uCvtrH3H/OqOQNwh8O2335q/9yj16b777rtab/s2i+xGKWP6Jt0rMke6QvmKsvO7nRZVHoquRN40x0J+RI3XrVvXzqXN5UY1I27dujUx1atihUpSp24dufDCi+z6P/zwg/27/PLLEo+hXnnIDw+BbTQdKV2qtKxctVKuv+566XhqQkpOcoMNAXnkkDRR4Tv0flu3aWM/s06+kqeN2R7zOOMW9ZuPHjMm7p5ldlvwyJEjpFev3vvc1v5ImwOj87Qj0674PDp/mt9Fkni00ob4H1BXScjrTtgcJKSQBTN8CDDjs2CeT0metgeiZbc31u/HEchgBFCaN1x/vWz7apupW9KmKIzCCAVQov3aNWvUkqXLllqKF6brcHxYKsc3a9pc/vvEE4nm5W0a4NW9+1lmUmewIaDTVw1VMO07dDB1Armiuj94/33dONxqG4LIWuZsIH7VgDYi0CHtGTOna0R6IRk37nn73f4GQWy//PKLXWfHjh3WbQzTO6RN6hgBZ1yPFDbWik/7pZdfztT2oBn8qH16RyBVCMSEeZxdzcaNG22HdLAj0geS0rlS6iuJXGNKzknp9THjsCMk+jYWfSgpvQ8/Ln0QwLyNKXzN2jVKaLuNtDBB8z0jMi+bIicEjVHWNI9WSVu3fq0FhKF2IyudQdgQ+Zgxz0nNmjVtnkD6X2jby8e11SXXQ6Hkzp3b/rVv315aaOUzNgm/qNotV768zJ07V1PCHlEC3WrriCzawhqYk+OJPC+lBD5y5KjEPthJoRMdZc7fGOldudVMT4Aa68AKQAQ5yrufmu0HPfSQbSx8ZC4CdFsj08BH1iIQE6RNkjzVZyJz+zITlpQQcPQaU3JOSu8hPedK6TX9uNhFgEInl/a61IK8GjZoZKZjlObsObNNRQcCJ8855GDXrXOyLFq80AieSmVr162xz8LAnH3jDTfKeeef/68ULsiXdt9tTwAAIABJREFUSO0XX3zB0sWoYIaqLV+uvCnf2nVqy4+7fpRTWra0xh1TpnxiZSBRyfjAKXH6lVoE2BQcdVQeC4Djs5IlSsovWuDlvvvut4h0ItUJeAvNTsLaQtlUTOHcZyBygtFIQyuhKpzgNM4dMXy4VKhQwYurZPLriw87b968cuedd2Xylf1y0Qg4aSsiKSFNJ23/48ksBC6/7DLzWVOdrIdG5y5atEh+0CCeb7752oiRMqMQLSVHITbqgEOyf/z5h3UAYxxxxJHm2w6qHNP5iJEjLVAtcnA+xPuHEvwuNYNfcsnFdh0UNMqe4ynSUr1adalSpYrky69tOjVC/dUJE7S4ymf/+NUT2noG9U6JVEbzZs3NFz1n7hxpUL+BXH/DDRZgdqiq51q1a//jl//RiBrCZh1B5XM+xM8gEI3NAqRBRPvw4c+qZermzHocOf46SQWd5XhQshCAFJF2IDWCAsiDw5zL4OemWpQhMhggJMqHe4ouAs/vQwBCZK3a/x2f0Cs1uhg8Pi+Kx3MuI6QLcL1QhJ7vOS+kCIQ5owMgmP8qDcAJFXf2R9rJrZGEfublmqwlYBIdXJFUUXusCrgCuKfotUVXE8rCd8MvnQUIQFDt2rWVLqd1kXffe1fq16svy5YvM6WJok1Ih0pIr8IMjUkaP/LyFcvN743ShtRpHgLxQ+YEjI0bN14qVqz4r/Qv5sGfvfDLL2XixInyyZSPE+865HkHRX/Wmd2MQDHfo3Yxl34x//PE4yPzwY89Nq8RPrXN+f13338nBY4rYE1GKJSyectmI+ESWsWNILfKuiEgKp4SqSEAjeu8+cYbluoFobMBwOowbuxYuaZ//38p9ix4XNn+kk7YsfeIU0XakB0mbMgmROXhAwtF4KMLvIdk9kgiD2H8kBukz4hWsRAlJe2oERuuFz13IO2EMP6XEpFNqJCTkNfHwMfNOjgmlNAL5e/IyWP9B6O0Eyr1DPunAEBCZ5nI+yXlIKQ1sJ7otAR+l5Lrx96r4ys6WAQwF0cPSPfGG28wxYnSRbWGut2QJyT3tSrhYlpnHIWKaXmRvt8QdbFixbWa2WFGZstXLDNVzqhZo6YFtEHOGzast99BpHVq15Xt2kyE62ByL6INR+ji9e23CQo3jEgyDn23IXSiukuoCRx1Hx2tjlKnjCnHH6clUzFtE2hGcBmR66tXrzYrAffQsFFDu9+ECPIddr9HavlVUsiWLFli3cEg8/zH5Zf169ZbUZdGDRtZCtjuf/z8rJVNQJUqyftcGzVqdLCPLMedn1SUeI4DIcZuOFWkHVlAHWKE/KJLwkHAIeweYue4yOLx3H90d5Zo0g4bgug8uUDAzBdIO1rZRgaihTy9pFrAcVxI6k8JaSZnHo8uKh+ZvB9yAqPvI6jrkIKQkuvH2HuTI5ezRdXh5s1b7N7x9VIDe95n8+znv9VnzICIv1HSi8xRpmwnedXRI2/efEY8YQRfLiRH6hZK+n/9svcqMf8tJxY6Uc3YP5j5mpQvzuEYKpShVDEfr1dihqAhRAiQtoN7/tqTeB2CuAjsuuvuuyygjEHdcjYEmLxR8skN7ovNADnbDGqYF9ZiL+SFRw5ah6KYy5Quo+vdZaScT+8XM/9RWq+czS7rpqgKipqGIPjgK1SsILt/3i1FihaRjz78SE4++WQtrpJwX9xDwUIF1WowzhqX1NLCLJF+ewg+cuTSlqNhrPjHEpHUfdVX0709Q32EuXMnlFMtWrS4bkgSgt1CIRfcAzyzMNgkeGBWsq+Kf5BBCKSKtCPJJ7mScEkFlUFeRIUyQp3YUJqO30WfA/ElHPu/TjH8HMiNZHrUeHQyPsckFT0eSuLxOd9H90hNCWmm1KcdvSHhmmBFPduE7xcn5hU6aWfQW32AaUlhwrTLgPjo/Qz58W/p0mVKeD8aQe7S4KuVUWRUT83V9h+5+pMZmJwhxzD4j5xArsjB58cn0TwjuWVCGyholOe69euMvDFdV6pYyUzJmKRbnpJQt5tiJvh++R5VSwU0yDBUK+tyWldtk9lWErYU/xvfKEneetutiRHmqHSULwRK32wC2SAo8KEpCB3DGJAxqh58GBRGqVhB88O1khnpZtEdwjiG7mP4rGkRatj9k46G3511/6FlVAsVPNEIECVOFDvKuk7tOlK6TGlT3Ecfc7S5AcBirJrHQ0OSXhplfzDje90MMFf0WLVq1T6/SrBSbLDfHfJP//LojQBrrly5CuXbbdMWiD8h/uAQaajWgTC4V96VWBweJR6LT+V/a8pQ0kbp0v83QfE2s9Z6tOUj8pQR2qNFEyI/h4LxScEXosxTQtpB1WIGD/5w1oCaTw+lHa2io0k79Gplk4L/n/+k+I+XjYKTdvr9cUQS8TIlD94fSHiuBkHx9Ycf9iXgStrgAhMvbEaQE7nBjONPOF6OV39wGKjSI1WVZuWAxN966y1bIwVXCObq3qO79cGGqDFPQ6Z06yI9KqhgiPWRhx+RvPruR4/PP/tMXnt9opJjXt1QJ5ARpnhUdiicEnkOxM28J5xQ0PzsbBaILsfkHYqhYFonijypgfkd4udZkMON/52NCRuAYGHAegApn1T2JFPiJUqWMHXNsyxcpLD5xNkksJl5+JGH1OxewILbYmVQ1Y21hRFJ/Gys+AfhswGA8MOoWLGyETgqH9Ln/6pIks9MRe9R4rHyNiW/jgwl7WjfcVhGdP3XpJR2Uj1PI28juY4tkUo7mPCjg+Oia+FmlNIO80bX1g3mfyftlP2BBLN0UMWoQch4z56/9T+/ZUYADCNiJQfIuEyZMv8i4Vgg4JTd8b+PWq7BaEOGDLFNHz5r2mGiXjEvj3t+rH4tYkoWEg8m4+bNWsj5muJFS8vosXDhl/L8888n9uTmc+b988+/bHMA1tEDMj9BNzUFTyhkGPMc8JWDP8SC2fsnbVSC2t/fQGnzLCB8rAIJbUBzGYGf1rmLzUvAHXXMFy9abAFo3Cs+6UMPO9Q2VYMeGmS+8muvuy6tkMbMeWvUv88gPW7LP+6XoOwx8Ucqegg+f/68utnKp5aJKrZhCgr+YNW7B53FzCux34VkKGlDxgRhRTYcZ9ccgrOSU9qQGqQcAsXCHaCaQ19WCPlASjs50gzqO6OVdmhJF93dBjWOydxJO+HJBpWcQM6b1TKzWRUj329Vn2uCDxmz9F5NPaIyF6O4+hshCXyzxXJAoQ1M17epORsl/MsvvxrBEUiGn/XVia9aENnadWtNqWKeJ8r74Yceljzqe09q7NH5ID46IUUOFF6IGg+/J+WrRIkS0lm7bNGCkznNz6ubAaqZ7VGSxWc/aJASqSphniHrS6iD/vc+PnJ87BA0RWHCCAFzXJt2n1gT8PVTXhUrArXRcTGAwalaGpX13XnXnebf76cV0nLK+E1VPGVfGXwF+6DgCcgL6j2B2PMlpOipak8g8/A1aZO8E3b8vEUZStqBtAI5hspfEC7mr+CzjlTekHqIHsekHFKjgjoOQWUpUdrB745pPhSVD0TOIwpBZClR2tFrZD2Q//7M42HeSKUf2Vs2NIWPVP7cc2Sj+Ph5lfa/0khi5j3Ad4yam6dm1mhSJsgrBEvlBEJOyTPGRI7aBMd58+bJhFcnGEFCln+pCZk8aciVUe6kcnL2OWdLKd0w/1tj/+9q1Poe9swwixaHSBMqr+UxszXNR3AbWD3xMqW1nOhJwhqSm4/PUNyzZs2yftn02aYiG8QdHVkOgUA4jFByFYsBQXGY0Tud2skC07jX8lqFjfagRMCjwLt0USWum4UbbrhOzjzjLCv44mNfBIJyD+Z5AvR+3v2z9TBP+FtrYGRerVpVI3SCEOdo4Z7oWuKOa2wikKGkHYLFQkH34Ffm95FKOpAWEEUSfAIpJgRwcS552hAgIyWkzXGBXIOPHAJv1qxZYo41m4CUkHb0Gv+Xf52QVx5GtE87qSL5+NQTfj/MIu0jcYoM0IvNV+bAq5o9e7YGdy21WAa+EujFf+gVNZAKdYTpOviO49lkfWAkMuaIXOQ9awDVYUqIlAslDYqBwkYRF1CVuj+CDavimEP+acrxlxI1fnNM0bVq15JqVaslaVY/0B2FOb/WCmvPPPuMKsLN/zolKHA+CE1HgkkfJb5jx04z0QdCx/Term07CxijtCkKfOaMmWYaT66T2IHWmVM/D4F3QalD6F+pNYMNEwqd9wcyb9QoIRiYCHpI3UfsIJAi0o6d5fpKYg0BCHr27FmaT5tAzpizI8kZMzY+SFfMGffkEpKUklfBKb1yes0Troc5m8ppUz+dkuwSIHD6cUPEBKoRaU7+N1YYCsQQtEnU+AYNlsMCQIEZXAD9+vaT48zUHlad0rv04wICEDgYhoFCh8wxuRMpT9Dc55oCSFQ8+e/EFLTXPuye5pa175CTdtbiHzdXJw0EE9rixUvMZ/nZZwlmbQia/suYUlHNNJXw4QgEBPB9L1gwX15++SVT0NEpYfi8Ca5jYIUhxxxzet68x5q5P6SahfkgadLYOnXqZL50J+20vWtjRo+2v9mUuBcg91WrV8nyZcutgxsk3qNHT+nd+7KYTVtLGyrxcZaTdnw8pyxZJabNESNGyHtaThPzdu1adf7xgWEyy/pUqCwBxS+aagTQwvijv5j/hbq1Jpuaw98dOTCL//ZbQoMT1DfvW0hdIxWMwTmdO50mLdWPjWsgukNYqheWQ0+AsBkXX3JJmhBYtGihTJ82XWMNPpVu3brLwIED3YSeJiTTdpKTdtpwy9ZnYfIePPgRM3c3bdJM6tSto12aEto5+nAE0opAIO+1a9fK8uXLha9b1Zf6s6aJJZDyoYnpavThxs8d+oi3btVGWrdubVHlIYXNSTv1T+JgCTvyiijwN998U6bPmGaqe+DAa1O/ID8j1Qg4aacasux7Asqa1A9M4UTmtmrVKssLi2RftHP2nYWAtb9VgWMOh6ApTPK7VkcLP+PbJne8uFZrQ4nvLxI+Z6OZ8rufOmVKikziKZ9RhKIyBB3iqhgy5DH3eacGvDQc66SdBtAy6xRIFAIl+COjx+DBj8pjjw2Riy682Mk6o8H2+R2BbIjAO+r6eG7sGHnkkcHq8+6RDe8wNm7JSTs2nkOSqyBPtUePbpY/2V37KmfE4Bq9el1qUbpXXH6FR3lnBMg+pyOQhQhER4ln5FJQ3Xfcebu2l21vqttH+iPgpJ3+mKbrjJAqJusRI0am67xMhopnU4Df+uyzz3ZTeLoj7BM6AlmLQGqixNNrpWwShqjVjuqFTtzpher/5okL0g6V1G6++eZ9CpmkPxwZP2NKCrlk/CoSCLt797PkgvMvTHcfV2as36/hCDgC+0cgPYPOUos1JVfv1wJSTtypRe7Ax8cFaccK0R0Yzvg4IhD25WoOb9CgYXws2lfpCDgCKUYgKwk7LBLi7nd1XxkwYKBFl/tIHwSctNMHx0ybZcKEV+xaafVxY25v1KiBnH/eBa6wM+2p+YUcgcxFICOixNNyB8HHPWLEKKuo5uPgEYh50o6u3U2tbroN0XiDOuSocEZoykFNcvp1h3rnfEYfbZqDMEITEWqOT58+PfE45g19ujkuep7o2ufJQc96xo9/3upuM6LPi7YaUKucYxisme+ju5tFXutgg9Pat29nZSHTWljh4F85n8ERcARyEgK00R0+/FktdzzXK6ilw4OPedLmHqOJLjQLoRvWCy+8lAjDrl0/aHnDUxMJPJAvrT4hbog6kDafhY5h/I5NAG1E6QYW2odC5IHswxpCZ7CksE+qFWj075Ii7YTrX2Xr4d647v5GWombtK53331X7r77nlS/OtQlDl2DUn2yn+AIOAIZjgB57bQtzahBx7eGDRumKWD1qSeflIKFCnpgWjo8nLgm7UgFDRaQM2o1tPwM+ER23gqkHa2sA5kG0obE90fQSWFP+066dEUqdjYA9BUPpJwcaYc2nSl9pqmNKseP3bFjexn86JBUp3VRtvC+++5N6dL8OEfAEcimCNBr4BYVF0dqH/vUjODfdjN5alBL+ti4Ju2glKNvjTaaGzdutF/PmDHD1HVoeRlIO5qQI83mbAY6depoyps2nij6A6nfyDVAzOQ9M1hLQuvNBCWdFGlv0g5HixcvPfinuZ8ZunfvJpX0D+5UbbSQ2vHQoEFaN/rz1J7mxzsCjkA2ROC+e+9PU2Mgiq+sWLlcJkyYmA1RybxbylakjR/53HPPNn8yfbOrV68u9K7Gx82YPPmdRPN46GUdoI5WxMyBbzqQLsdB3BAvJJ7UCGZ7PoP48U9D+ueee06Wkvb7778nd9xxuzxw/4Op3iFzL0SivvveO5n3VvqVHAFHIGYRSIu1jptxtZ0+jzRbkTbkiGKODuTCbJ0vX/79knak0kYVRw4I/emnnzKVHBR7UvBjBkedszkII2ED0TjDSXt/UeXkYzdp0jTN6V2hWMLKlSvS563zWRwBRyAuETjrzG7So2fPNK8dtb112zYZNWpUmufI6SdmK9JOijRDUFkg00DOwVwdXoBInzYqPamBnxufeVKm7OTmDeo7o83jyQWn0bGrd+9LtaKa/5Hk9D92v39HIKsRQG1fdPGFMmvWbG/nmcaHERekjYmaIDNM2ijdEO0d7dOGVCHJYPoOldQgWkzaKPDI6PHg1+Yc5mduAtEC0UbOH46JjCiPxhxFzSCinetxDilrCWb7hLSzjPRpJ0XcAwb0F9ojHczuOI3vlp/mCDgCjsC/ECCS/JSWp3jBlTS+G3FB2gmBXAkqF2K96qqr7Odo0o48DjzwKUOW/B4ChbQJ+iKaHPKFTCFxRvRcbBTwhYfPkzomGnOOvemmmxLPYa3klOMbD+b5jCRt1hMdVV61amW56867Ux0xnsb3yU9zBBwBR2C/CJC3PXPmDA9IS+N7EhekncZ7S/K0/fmu0/M6sTAXpvEBA67R3MjHY2E5vgZHwBFwBCwgDRP5pk1bHI00IOCknQbQ4uUUiqls3rTZTePx8sB8nY5ADkEAtx0dwLy0aeofuJN26jGLmzPIzS5erLiUKl0qzZHjcXOzvlBHwBGIGwTwa7ds1VJ69eodN2uOlYXmONKOFeAzYx34s/HVP/fcc+rD7+TEnRmg+zUcAUfggAiQ+pX/uPxy7bXXHfBYP2BfBJy0s/EbUbJkcXn55QnmQ6K3rRN3Nn7YfmuOQBwhQDDarFkz5ZVXXo2jVcfGUp20Y+M5pPsqqDXeo0e3xPxsiHvkyJHSt1+/dL+WT+gIOAKOQGoQoAHRpLcmaQS5k3ZqcONYJ+3UIhYnxxM5/sgjD8t1110fJyv2ZToCjkBOQQDSfnPSm/Lqq16HPLXP3Ek7tYjFyfFO2nHyoHyZjkAORADSHvbMMM3XnpUD7/7gbtlJ++Dwi9mzD0Ta+JQYDRo0jNl78IU5Ao5A9kQA0h48ZLC0bNlSBg8ekj1vMoPuykk7g4DN6mkhbTp73XXX3UkuxYPTsvoJ+fUdgZyLAKT91tuTpEqVqtK9ew+pWrVqzgUjlXfupJ1KwOLlcMqZVqtWxaLHkxtO3PHyNH2djkD2QoCUr1y5cyUrKrLX3abv3Thppy+eMTVbSPna36I8qjymHpkvxhHIEQi88vLLUqJkCRk48Noccb/peZNO2umJZozN1bZtW7nwggukXPnyMbYyX44j4AjkZAQeemiQ3HDDjfuUMR05coSQquo+7v2/GU7a2fgvp3///nJioULaBq9lNr5LvzVHwBGINwR69uwuS5Ysk7x58+6z9IEDB9jPTtzJP1En7Xh721OxXnauUz6ZkqqCKh5VngqA/VBHwBFINQKLFi2UiRMnygcffJjkuU7crrRT/VJllxO2bNksjRs32m8wWvS9enBadnn6fh+OQGwiMGb0aClStIjceeddyS7wzjvv8KjyZNBxpR2b73W6rap9+7bSseOpqcrHhrgX6m7Yc7jT7TH4RI6AI/APAr17X2o1xz3NK22vhJN22nCLm7NGjBguU6dMTZWJPG5uzhfqCDgCcYUA7rd3331H3n8/adN4XN1MFi3WSTuLgM+sy4Z87WFDn5HjChTIrMv6dRwBR8AR+BcCt9/+H7nsssu1mVGPFKNDRPmECa/s15ye4smywYFO2tngIR7oFgjs2P3zbrn4kksOdKh/7gg4Ao5AhiBAANro0WNkzpyEEsqpGR6c9j+0nLRT8+bE6bEhIG3wo0OkWPHicXoXvmxHwBGIZwQGDLhGi6lclyqVHXm/TtwJaDhpx/NfQSrWPnjwozJ9+nQraODDEXAEHIHMRICypfM+m3vQvmyPKnfSzsz3NkuvhW+7Xbs20rXL6V5sJUufhF/cEchZCGzdskUGXjtAA9De94jxdHj0rrTTAcR4mYLOX1QicjN5vDwxX6cjEN8IkD568y03qUm8p9cZT6dH6aSdTkDGyzSkgPHvgfsflCPz5ImXZfs6HQFHIA4ReGjQIClwfAEZOXJUuq8+p0aVO2mn+6sU+xMOGNBf6/4ukVtuvsWJO/Yfl6/QEYhLBKh8tmHjek3XmvivGuPpdUM5MTjNSTu93p44m8eJO84emC/XEYgjBDKDsAMcOY24nbTj6A8hvZcaiPuKy6/wVLD0BtfncwRyIAL4sP/73//KL7/uzlCFHQ1tTooqd9LOgX9YkbfMy061of/7v2ukRo2aORwNv31HwBFIKwJEiT/y6MMaIV5Nhgx5LMNM4mldX3Y5z0k7uzzJg7iP999/TyM7B0i7tu2lS5cu7uc+CCz9VEcgJyJAHvZzY8fI7bffIb17X5YTIci0e3bSzjSoY/tCVE3jD27u3Nly/nkXeC53bD8uX50jEBMI0ADkpZdelBIlSlpt8Fjo3JXdo8qdtGPi1Y+dRZDLPXBgf/n777+tEEvDhg1decfO4/GVOAJZjkBo3QtZi+TS/y8Gprk0aUbdTCwFp02e/Lb06XOlDB06TDp16nzQt+ykfdAQZs8JIO/hw4fLRx99IM2btZCT650sFcpX8E5h2fNx+105AvtFAKJetXqVzP9ivsyYOV2qVKliBVO6d095t67MhjhWiNtJO7OffA6/Hmbz9957T2sGv6+m8zlStGgxKVK4iFSrVs2QqVChghTXJiReqCWHvyh++9kGgTWrV8sWDSr75ZdfZP369fL1N1/LypUrpEGDBtK+fQfp0KGD/s2XiIv7jYWociftuHhVsu8i8RctW7ZUNm/eLLt27RIU+YoVy43My51UTsqUKWNEfvzxx7sqz76vgd9ZNkAA9Qw582/Dhg2ybv06I+dKlSqrkq6qfurikj9/fvu+UaNG2eCOk74FTNebNm2Szp07ywMP3G8HlSxZUm7W4lOR5mzId/z48TJjxvTEic499zx58MFB+0zMHEOHPm2/q169hv6rLi+8MN7N49n2DYrTG4O8IXNefr7OnTtXjj32WCXwilK6VGk55phjnMzj9Nn6suMbgUDOO7/bKTt37LRqiF9t/0q2bduaSNAlS5ZQYm5sgWR58+aN7xtO5eohbQgZgsXvDGHfdNONRrQvvPCiNG3aTBYvXqQEfqr6pq8yMmdwDsdB3OF3zAWpQ+QQfjgGgeM+7VQ+GD888xHAtL558xZV47OUzDfL1q2bjcwZFStWkmOOPsbM7EcddZSZ2F2dZ/4z8itmDwQCMf/y6y+yRf/mvvnmG/nm229k1aqV8tNPP+nfW2VVziX0762qETPm7ViI9M5M9JOLKg+kPXnyO0bcYTRt2lgJvJQRN+QMGc+YMWufJUPkCQT+TiKxQ+CQexhBeTtpZ+bT9mulKwK0CeUPKIHUN+vOf6mZ2j/TfruM4DcvVKiQ8O/4E46X4wvoPze5p+tz8MniB4FAyqx41apVtnAUc67cufTvZt4/G+HKctxx+dT33DDRrI2JO178z5nxNJIKToO0UdLRhBxU8+LFSxOXhvreuHGj/Txjxgw7D6KHtDGJQ9BBnYeTIPtzzz3HlXZmPGC/RtYggKmdMWfObNm7d68FwO3Z87f6zpeZasDsjt9t7569Urp0guk9EDvnlStfPmsW7ld1BNKAwPfffSc7d+60MwMhEwC2+5fd8tVXCWZsBmo5f/58FrmdL18+U84QshNz6kAfOXKE9OrVO/Gk4NOGeCNHUMiQNqLi3HPPNvcf5nL81KVKlTIfNyOStKMVezCtu9JO3XPyo7MRAsHs/uOPu9R/vsyIfelSCH2X/PDDjxpMs9zuNpLcg2rn95EE7+o9G70YMXQrRGCHEYiYn1HHcojI7t27LYAzvKeVK1eRXLkOEb5CyPwjAIyRnYPAYuGRJUfakUobpRzUOM8mDEzo+fLld6UdCw/S1xD/CGCCxxTPQLVTMIZ/KHf9Yt/Pm5dgkt+H5HUTIPp5UPHhc6LiI4enusX/O7K/O4hUwBwXArnCOaaGlXwxUWMBCiTM50WLYpYuZkTM96jhXLlyWexGMFfnxKCvWHxjAjljHo8m5ODTrl69qvm3I9U46jv4vfl9ggpvvE+wGvcbzOautGPx6fua4hqBSJIPKj4QPQF127ZtSST7Xbv+p+ijSd/O2ausr+Poo4+2NLjoUVz/Ez8qz1H/+n2ePHm841oa3qJIZRt5ejTRhs9M8f4zIF1G8A1Hnl+/fgN75rlzqzzWgb+YAQETZR3UML9zEk7Dg4uBU0IgGmZviBXiRlnjiw7+6XBMIF4IOgSnEW0e/OH8johxjx6PgQfrS3AEDoRA8MVHHofCZwTy5/uwAUj4fcJnYUQq/+SuV69e/X0+itwkRJ+T3KbhQPeSkZ///PPPlhec3AgkGj6PVrFJnReUbcA0kCw/B6Lle8iWEal4w3zuG87Ipx67cwelTYoWgWYMCPzmm29OjCZHVYfj+DyB2M8zXzckHanSg7LmOAj9vPPOtwA1V9qx+w74yhyBDEMgqY1BchcL1oKULiZyY5HScyKPO+SQQ4R/KR0NG6a8YIcTakpR9eNSi0BSUeIysb9VAAABTklEQVSpnSMzj/fa45mJtl/LEXAEHAFHIKYQcNKOqcfhi3EEHAFHwBFwBJJHwEnb3w5HwBFwBBwBR8ARyBAE3DyeIbD6pI6AI+AIOAKOQPoj4KSd/pj6jI6AI+AIOAKOQIYg4KSdIbD6pI6AI+AIOAKOQPoj4KSd/pj6jI6AI+AIOAKOQIYg4KSdIbD6pI6AI+AIOAKOQPoj4KSd/pj6jI6AI+AIOAKOQIYg4KSdIbD6pI6AI+AIOAKOQPoj4KSd/pj6jI6AI+AIOAKOQIYg4KSdIbD6pI6AI+AIOAKOQPoj4KSd/pj6jI6AI+AIOAKOQIYg4KSdIbD6pI6AI+AIOAKOQPoj4KSd/pj6jI6AI+AIOAKOQIYg4KSdIbD6pI6AI+AIOAKOQPoj4KSd/pj6jI6AI+AIOAKOQIYg4KSdIbD6pI6AI+AIOAKOQPoj8P+gp7p/EfwH5QAAAABJRU5ErkJggg==\"/>\n  </p>\n  <p>\n   Explain, with reference to thermal energy transfer, why the pad is designed in this way.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   I\n  </em>\n  = «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msqrt>\n    <mfrac>\n     <mi>\n      P\n     </mi>\n     <mi>\n      R\n     </mi>\n    </mfrac>\n   </msqrt>\n  </math>\n  =» 1.9 «A» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 1\n   </strong>\n  </em>\n  (Calculation of length)\n  <br/>\n  Read off from graph [2.8 − 3.2 × 10\n  <sup>\n   −5\n  </sup>\n  Ω m]✓\n  <br/>\n  Use of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    I\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi>\n      R\n     </mi>\n     <mi>\n      A\n     </mi>\n    </mrow>\n    <mi>\n     ρ\n    </mi>\n   </mfrac>\n  </math>\n  ✓\n  <br/>\n  <em>\n   l\n  </em>\n  = 1.3 − 1.4 «m» ✓\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 2\n   </strong>\n  </em>\n  (Calculation of area)\n  <br/>\n  Read off from graph [2.8 − 3.2 × 10\n  <sup>\n   −5\n  </sup>\n  Ω m]✓\n  <br/>\n  Use of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    A\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mi>\n    ρ\n   </mi>\n   <mfrac>\n    <mi>\n     I\n    </mi>\n    <mi>\n     R\n    </mi>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <em>\n   A\n  </em>\n  = 8.3 − 9.5 × 10\n  <sup>\n   −6\n  </sup>\n  «m\n  <sup>\n   2\n  </sup>\n  » ✓\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 3\n   </strong>\n  </em>\n  (Calculation of resistance)\n  <br/>\n  Read off from graph [2.8 − 3.2 × 10\n  <sup>\n   −5\n  </sup>\n  Ω m]✓\n  <br/>\n  Use of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    R\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mi>\n    ρ\n   </mi>\n   <mfrac>\n    <mi>\n     I\n    </mi>\n    <mi>\n     A\n    </mi>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <em>\n   R\n  </em>\n  = 3.6 − 4.2 «Ω» ✓\n </p>\n <p>\n  <em>\n   <strong>\n    ALTERNATIVE 4\n   </strong>\n  </em>\n  (Calculation of resistivity)\n  <br/>\n  Use of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    ρ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi>\n      R\n     </mi>\n     <mi>\n      A\n     </mi>\n    </mrow>\n    <mi>\n     I\n    </mi>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <em>\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     ρ\n    </mi>\n   </math>\n  </em>\n  = 3.2 × 10\n  <sup>\n   −5\n  </sup>\n  «Ω m» ✓\n </p>\n <p>\n  Read off from graph 260 – 280 K ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  «Resistivity and hence» resistance will decrease ✓\n </p>\n <p>\n  «Pd across pad will not change because internal resistance is negligible»\n  <br/>\n  Current will increase ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  «The force is» away from PQ/repulsive/to the right ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  The magnetic fields «due to currents in PQ and TU» are in opposite directions\n  <br/>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <br/>\n  There are two «repulsive» forces in opposite directions ✓\n </p>\n <p>\n  Net force is zero ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  Air is a poor «thermal» conductor ✓\n </p>\n <p>\n  Lack of convection due to air not being able to move in material ✓\n </p>\n <p>\n  Appropriate statement about energy transfer between the pet, the resistor and surroundings ✓\n </p>\n <p>\n  The rate of thermal energy transfer to the top surface is greater than the bottom «due to thinner material» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Accept air is a good insulator\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter",
      "d-fields"
    ],
    "subtopics": [
      "b-1-thermal-energy-transfers",
      "b-5-current-and-circuits",
      "d-3-motion-in-electromagnetic-fields"
    ]
  },
  {
    "question_id": "23M.2.SL.TZ2.5",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline what is meant by an isotope.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   mass number.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   proton number.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (e)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   A beta-minus particle and an alpha particle have the same initial kinetic energy.\n  </p>\n  <p>\n   Outline why the beta-minus particle can travel further in air than the alpha particle.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  «An atom with» the same number of protons\n  <em>\n   <strong>\n    AND\n   </strong>\n  </em>\n  different numbers of neutrons\n  <br/>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <br/>\n  Same chemical properties\n  <em>\n   <strong>\n    AND\n   </strong>\n  </em>\n  different physical properties ✓\n </p>\n <p>\n  <em>\n   Do\n   <strong>\n    not\n   </strong>\n   allow just atomic number and mass number\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  3 ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  2 ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (e)\n </div><div class=\"card-body\">\n <p>\n  Alphas have double charge «and so are better ionisers »✓\n </p>\n <p>\n  alphas have more mass and therefore slower «for same energy» ✓\n </p>\n <p>\n  so longer time/more likely to interact with the «atomic» electrons/atoms «and therefore better ionisers» ✓\n </p>\n <p>\n  <em>\n   Accept reverse argument in terms of betas travelling faster.\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "e-3-radioactive-decay"
    ]
  },
  {
    "question_id": "23M.2.SL.TZ2.6",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mfrac>\n     <msub>\n      <mi>\n       g\n      </mi>\n      <mi mathvariant=\"normal\">\n       M\n      </mi>\n     </msub>\n     <msub>\n      <mi>\n       g\n      </mi>\n      <mi mathvariant=\"normal\">\n       P\n      </mi>\n     </msub>\n    </mfrac>\n   </math>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (e)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline one reason why this model of a dancer is unrealistic.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Work using\n  <em>\n   g\n  </em>\n  ∝\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mi>\n     m\n    </mi>\n    <msup>\n     <mi>\n      r\n     </mi>\n     <mn>\n      2\n     </mn>\n    </msup>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <msub>\n     <mi>\n      g\n     </mi>\n     <mi mathvariant=\"normal\">\n      M\n     </mi>\n    </msub>\n    <msub>\n     <mi>\n      g\n     </mi>\n     <mi mathvariant=\"normal\">\n      P\n     </mi>\n    </msub>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <msub>\n     <mi>\n      m\n     </mi>\n     <mi mathvariant=\"normal\">\n      M\n     </mi>\n    </msub>\n    <msub>\n     <mi>\n      m\n     </mi>\n     <mi mathvariant=\"normal\">\n      P\n     </mi>\n    </msub>\n   </mfrac>\n   <msup>\n    <mfenced>\n     <mfrac>\n      <msub>\n       <mi>\n        r\n       </mi>\n       <mi mathvariant=\"normal\">\n        P\n       </mi>\n      </msub>\n      <msub>\n       <mi>\n        r\n       </mi>\n       <mi mathvariant=\"normal\">\n        M\n       </mi>\n      </msub>\n     </mfrac>\n    </mfenced>\n    <mn>\n     2\n    </mn>\n   </msup>\n  </math>\n  = 0.75 ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (e)\n </div><div class=\"card-body\">\n <p>\n  one example specified\n  <em>\n   eg\n  </em>\n  friction, air resistance, mass distribution not modelled ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   <strong>\n    Award [1]\n   </strong>\n   for any reasonable physical parameter that is not consistent with the model\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion",
      "d-fields"
    ],
    "subtopics": [
      "a-4-rigid-body-mechanics",
      "d-1-gravitational-fields"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.1",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the principal energy change in nuclear fission.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the principal energy change in nuclear fission.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The energy released in the reaction is about 180 MeV. Estimate, in J, the energy released when 1 kg of\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mmultiscripts>\n     <mtext>\n      U\n     </mtext>\n     <mprescripts>\n     </mprescripts>\n     <mn>\n      92\n     </mn>\n     <mn>\n      235\n     </mn>\n    </mmultiscripts>\n   </math>\n   undergoes fission.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State and explain the decay mode of\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mmultiscripts>\n     <mtext>\n      Te\n     </mtext>\n     <mprescripts>\n     </mprescripts>\n     <mn>\n      52\n     </mn>\n     <mn>\n      132\n     </mn>\n    </mmultiscripts>\n   </math>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate, in s\n   <sup>\n    −1\n   </sup>\n   , the initial activity of the sample.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the decay constant of a nuclide is given by −\n   <em>\n    m\n   </em>\n   , where\n   <em>\n    m\n   </em>\n   is the slope of the graph of ln\n   <em>\n    A\n   </em>\n   against\n   <em>\n    t\n   </em>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iv)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine, in days, the half-life of\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mmultiscripts>\n     <mtext>\n      Te\n     </mtext>\n     <mprescripts>\n     </mprescripts>\n     <mn>\n      52\n     </mn>\n     <mn>\n      132\n     </mn>\n    </mmultiscripts>\n   </math>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline the role of the heat exchanger in a nuclear power station.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the maximum temperature of the gas during the cycle.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline why the entropy of the gas remains constant during changes BC and DA.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iv)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the efficiency of the cycle.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (d)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the rotational kinetic energy of the turbine decreases at a constant rate.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a.i)\n </div><div class=\"card-body\">\n <p>\n  Mass-energy «of uranium» into kinetic energy of fission products ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  Mass-energy «of uranium» into kinetic energy of fission products ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  Mass of uranium nucleus\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    ≈\n   </mo>\n   <mn>\n    235\n   </mn>\n   <mtext>\n    u\n   </mtext>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mtext>\n     energy\n    </mtext>\n    <mtext>\n     mass\n    </mtext>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      180\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       6\n      </mn>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      60\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        19\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      235\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      661\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        27\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    7\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    4\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     13\n    </mn>\n   </msup>\n  </math>\n  «J» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  beta minus decay ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mmultiscripts>\n    <mtext>\n     Te\n    </mtext>\n    <mprescripts>\n    </mprescripts>\n    <mn>\n     52\n    </mn>\n    <mn>\n     132\n    </mn>\n   </mmultiscripts>\n  </math>\n  has more neutrons / higher\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mi>\n     N\n    </mi>\n    <mi>\n     Z\n    </mi>\n   </mfrac>\n  </math>\n  ratio than stable nuclides of similar\n  <em>\n   A\n  </em>\n  «and beta minus reduces\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mi>\n     N\n    </mi>\n    <mi>\n     Z\n    </mi>\n   </mfrac>\n  </math>\n  » ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msup>\n    <mi>\n     e\n    </mi>\n    <mn>\n     25\n    </mn>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <mn>\n    7\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    2\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     10\n    </mn>\n   </msup>\n  </math>\n  «s\n  <sup>\n   −1\n  </sup>\n  » ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  Takes ln of both sides of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    A\n   </mi>\n   <mo>\n    =\n   </mo>\n   <msub>\n    <mi>\n     A\n    </mi>\n    <mn>\n     0\n    </mn>\n   </msub>\n   <msup>\n    <mi>\n     e\n    </mi>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mi>\n      λ\n     </mi>\n     <mi>\n      t\n     </mi>\n    </mrow>\n   </msup>\n  </math>\n  , leading to\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    ln\n   </mi>\n   <mo>\n   </mo>\n   <mi>\n    A\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mi>\n    ln\n   </mi>\n   <mo>\n   </mo>\n   <msub>\n    <mi>\n     A\n    </mi>\n    <mn>\n     0\n    </mn>\n   </msub>\n   <mo>\n    -\n   </mo>\n   <mi>\n    λ\n   </mi>\n   <mi>\n    t\n   </mi>\n  </math>\n  ✓\n </p>\n <p>\n  «hence slope\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mo>\n    -\n   </mo>\n   <mi>\n    λ\n   </mi>\n  </math>\n  » ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iv)\n </div><div class=\"card-body\">\n <p>\n  Slope =«−»\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    2\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    5\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      6\n     </mn>\n    </mrow>\n   </msup>\n  </math>\n  «s\n  <sup>\n   −1\n  </sup>\n  » ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     T\n    </mi>\n    <mfrac>\n     <mn>\n      1\n     </mn>\n     <mn>\n      2\n     </mn>\n    </mfrac>\n   </msub>\n   <mo>\n    =\n   </mo>\n  </math>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      ln\n     </mi>\n     <mo>\n     </mo>\n     <mn>\n      2\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      5\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        6\n       </mn>\n      </mrow>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      60\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      60\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      24\n     </mn>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n  </math>\n  » 3.2 «days» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  Collects thermal energy from the coolant and delivers it to the gas ✓\n </p>\n <p>\n  Prevents the «irradiated» coolant from leaving the reactor vessel ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  Correct read offs of pressure and volume at B ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    8\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     6\n    </mn>\n   </msup>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    6\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      3\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    8\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    31\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mi>\n    T\n   </mi>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    T\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    1500\n   </mn>\n  </math>\n  «K»  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  From\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    Δ\n   </mtext>\n   <mi>\n    S\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mi>\n      Q\n     </mi>\n    </mrow>\n    <mi>\n     T\n    </mi>\n   </mfrac>\n  </math>\n  , the change in entropy is zero when\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    Δ\n   </mtext>\n   <mi>\n    Q\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    0\n   </mn>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iv)\n </div><div class=\"card-body\">\n <p>\n  Net work done  = «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    8\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    23\n   </mn>\n   <mo>\n    +\n   </mo>\n   <mn>\n    9\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    11\n   </mn>\n   <mo>\n    -\n   </mo>\n   <mn>\n    4\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    32\n   </mn>\n   <mo>\n    -\n   </mo>\n   <mn>\n    3\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    25\n   </mn>\n  </math>\n  » 9.77 «kJ» ✓\n </p>\n <p>\n  Efficiency =«\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      9\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      77\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      20\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      58\n     </mn>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n  </math>\n  » 0.47 ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  Rotational KE is proportional to\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msup>\n    <mi>\n     ω\n    </mi>\n    <mn>\n     2\n    </mn>\n   </msup>\n  </math>\n  ✓\n </p>\n <p>\n  Calculation of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msup>\n    <mi>\n     ω\n    </mi>\n    <mn>\n     2\n    </mn>\n   </msup>\n  </math>\n  for at least four points, e.g. {96.1, 76.7, 57.6, 38.4, 19.3}×10\n  <sup>\n   3\n  </sup>\n </p>\n <p>\n  Shows that the differences in equal time intervals are approximately the same, e.g. {19.4, 19.1, 19.2, 19.1, 19.3}×10\n  <sup>\n   3\n  </sup>\n  ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow a tolerance of ±1×10\n   <sup>\n    3\n   </sup>\n   s\n   <sup>\n    −2\n   </sup>\n   from the values stated in MP2.\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion",
      "b-the-particulate-nature-of-matter",
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "a-4-rigid-body-mechanics",
      "b-3-gas-laws",
      "b-4-thermodynamics",
      "e-3-radioactive-decay",
      "e-4-fission"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.10",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the angular impulse applied to the flywheel.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The angular speed of the flywheel increased by 280 rad s\n   <sup>\n    −1\n   </sup>\n   during the application of the angular impulse.\n  </p>\n  <p>\n   Determine the moment of inertia of the flywheel.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The flywheel was rotating at 150 rev per minute before the application of the angular impulse. Determine the change in angular rotational energy of the flywheel during the application of the flywheel.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Attempt to find area of triangle ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    8\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    180\n   </mn>\n   <mo>\n    =\n   </mo>\n   <mn>\n    720\n   </mn>\n  </math>\n  «kg m\n  <sup>\n   2\n  </sup>\n  s\n  <sup>\n   −1\n  </sup>\n  » ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Attempt to find area of triangle ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    8\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    180\n   </mn>\n   <mo>\n    =\n   </mo>\n   <mn>\n    720\n   </mn>\n  </math>\n  «kg m\n  <sup>\n   2\n  </sup>\n  s\n  <sup>\n   −1\n  </sup>\n  » ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  Use of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    Δ\n   </mtext>\n   <mi>\n    L\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mtext>\n    Δ\n   </mtext>\n   <mfenced>\n    <mrow>\n     <mi>\n      I\n     </mi>\n     <mi>\n      ω\n     </mi>\n    </mrow>\n   </mfenced>\n  </math>\n  ✓\n </p>\n <p>\n  2.6 kg m\n  <sup>\n   2\n  </sup>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  Correct conversions to a consistent set of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    ω\n   </mi>\n  </math>\n  units ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <mo>\n    ×\n   </mo>\n   <mi>\n    L\n   </mi>\n   <mo>\n    ×\n   </mo>\n   <mfenced>\n    <mrow>\n     <msubsup>\n      <mi>\n       ω\n      </mi>\n      <mtext>\n       f\n      </mtext>\n      <mn>\n       2\n      </mn>\n     </msubsup>\n     <mo>\n      -\n     </mo>\n     <msubsup>\n      <mi>\n       ω\n      </mi>\n      <mtext>\n       i\n      </mtext>\n      <mn>\n       2\n      </mn>\n     </msubsup>\n    </mrow>\n   </mfenced>\n  </math>\n  or correct substitution seen ✓\n </p>\n <p>\n  113 kJ ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-4-rigid-body-mechanics"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.11",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Explain why the gas in configuration B has a greater number of microstates than in A.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Deduce, with reference to entropy, that the expansion of the gas from the initial configuration A is irreversible.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Configuration A has only one microstate ✓\n </p>\n <p>\n  In configuration B, pairs of particles can be swapped between the halves ✓\n </p>\n <p>\n  Every such change gives rise to a new microstate «so there is a large number of microstates in B» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Configuration A has only one microstate ✓\n </p>\n <p>\n  In configuration B, pairs of particles can be swapped between the halves ✓\n </p>\n <p>\n  Every such change gives rise to a new microstate «so there is a large number of microstates in B» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  The entropy of the gas is related to the number of microstates\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     S\n    </mi>\n    <mtext>\n     A\n    </mtext>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <msub>\n    <mi>\n     k\n    </mi>\n    <mtext>\n     B\n    </mtext>\n   </msub>\n   <mo>\n   </mo>\n   <mi>\n    ln\n   </mi>\n   <mo>\n   </mo>\n   <msub>\n    <mtext>\n     Ω\n    </mtext>\n    <mtext>\n     A\n    </mtext>\n   </msub>\n  </math>\n  and\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     S\n    </mi>\n    <mtext>\n     A\n    </mtext>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <msub>\n    <mi>\n     k\n    </mi>\n    <mtext>\n     B\n    </mtext>\n   </msub>\n   <mo>\n   </mo>\n   <mi>\n    ln\n   </mi>\n   <mo>\n   </mo>\n   <msub>\n    <mtext>\n     Ω\n    </mtext>\n    <mtext>\n     B\n    </mtext>\n   </msub>\n  </math>\n  ✓\n </p>\n <p>\n  <br/>\n  Since\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n   </mo>\n   <msub>\n    <mtext>\n     Ω\n    </mtext>\n    <mtext>\n     B\n    </mtext>\n   </msub>\n   <mo>\n    &gt;\n   </mo>\n   <msub>\n    <mtext>\n     Ω\n    </mtext>\n    <mtext>\n     A\n    </mtext>\n   </msub>\n  </math>\n  , the entropy in configuration B is greater ✓\n </p>\n <p>\n  A process that results in an increase of entropy in an isolated system is irreversible ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-4-thermodynamics"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.12",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State what is meant by an isolated system.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State and explain the number of microstates of the system in configuration A.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Configuration B has 120 microstates. Calculate the entropy difference between configurations B and A. State the answer in terms of\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <msub>\n     <mi>\n      k\n     </mi>\n     <mtext>\n      B\n     </mtext>\n    </msub>\n   </math>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (d)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The system is initially in configuration A. Comment, with reference to the second law of thermodynamics and your answer in (c), on the likely evolution of the system.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Neither mass nor energy is exchanged with the surroundings ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Neither mass nor energy is exchanged with the surroundings ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  6 microstates ✓\n </p>\n <p>\n  Any of the six particles can be the one of the highest energy ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     k\n    </mi>\n    <mtext>\n     B\n    </mtext>\n   </msub>\n   <mo>\n   </mo>\n   <mi>\n    ln\n   </mi>\n   <mo>\n   </mo>\n   <mn>\n    120\n   </mn>\n   <mo>\n    -\n   </mo>\n   <msub>\n    <mi>\n     k\n    </mi>\n    <mtext>\n     B\n    </mtext>\n   </msub>\n   <mo>\n   </mo>\n   <mi>\n    ln\n   </mi>\n   <mo>\n   </mo>\n   <mn>\n    6\n   </mn>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    3\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <msub>\n    <mi>\n     k\n    </mi>\n    <mtext>\n     B\n    </mtext>\n   </msub>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  The second law predicts that isolated systems spontaneously evolve towards high-entropy states ✓\n </p>\n <p>\n  From (c), the entropy of B is greater than that of A ✓\n </p>\n <p>\n  The final state will likely be similar to B / contain relatively many low-energy particles «of different energies» ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-4-thermodynamics"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.14",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the fractional number of throws for which the three most likely macrostates occur.\n  </p>\n  <p>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   A throw is made once every minute. Estimate the average time required before a throw occurs where all coins are heads or all coins are tails.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   In one throw the coins all land heads upwards. The following throw results in 7 heads and 3 tails. Calculate, in terms of\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <msub>\n     <mi>\n      k\n     </mi>\n     <mtext>\n      B\n     </mtext>\n    </msub>\n   </math>\n   , the change in entropy between the two throws.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Recognises that 4 heads and 6 tails also required ✓\n </p>\n <p>\n  Total number of microstates = 672 ✓\n </p>\n <p>\n  Fractional number = 672/1024 = 0.66 ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow ecf for MP3\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Recognises that 4 heads and 6 tails also required ✓\n </p>\n <p>\n  Total number of microstates = 672 ✓\n </p>\n <p>\n  Fractional number = 672/1024 = 0.66 ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow ecf for MP3\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  Two chances in 1024 so once every 512 throws ✓\n </p>\n <p>\n  512 throws take 8.5 h so (a reasonable estimate is half way through) on average 4.3 h ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    Δ\n   </mtext>\n   <mi>\n    S\n   </mi>\n   <mo>\n    =\n   </mo>\n   <msub>\n    <mi>\n     k\n    </mi>\n    <mtext>\n     B\n    </mtext>\n   </msub>\n   <mo>\n   </mo>\n   <mfenced>\n    <mrow>\n     <mi>\n      ln\n     </mi>\n     <mo>\n     </mo>\n     <mn>\n      120\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mi>\n      ln\n     </mi>\n     <mo>\n     </mo>\n     <mn>\n      1\n     </mn>\n    </mrow>\n   </mfenced>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    4\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    8\n   </mn>\n   <msub>\n    <mi>\n     k\n    </mi>\n    <mtext>\n     B\n    </mtext>\n   </msub>\n  </math>\n  ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-4-thermodynamics"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.15",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   orbital speed;\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   escape speed from its orbit.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   in its initial circular orbit;\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   in its final orbit.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msqrt>\n    <mfrac>\n     <mrow>\n      <mn>\n       6\n      </mn>\n      <mo>\n       .\n      </mo>\n      <mn>\n       67\n      </mn>\n      <mo>\n       ×\n      </mo>\n      <msup>\n       <mn>\n        10\n       </mn>\n       <mrow>\n        <mo>\n         -\n        </mo>\n        <mn>\n         11\n        </mn>\n       </mrow>\n      </msup>\n      <mo>\n       ×\n      </mo>\n      <mn>\n       5\n      </mn>\n      <mo>\n       .\n      </mo>\n      <mn>\n       97\n      </mn>\n      <mo>\n       ×\n      </mo>\n      <msup>\n       <mn>\n        10\n       </mn>\n       <mn>\n        24\n       </mn>\n      </msup>\n     </mrow>\n     <mrow>\n      <mn>\n       6\n      </mn>\n      <mo>\n       .\n      </mo>\n      <mn>\n       70\n      </mn>\n      <mo>\n       ×\n      </mo>\n      <msup>\n       <mn>\n        10\n       </mn>\n       <mn>\n        6\n       </mn>\n      </msup>\n     </mrow>\n    </mfrac>\n   </msqrt>\n   <mo>\n    =\n   </mo>\n  </math>\n  »\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    7\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    71\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     3\n    </mn>\n   </msup>\n  </math>\n  «m s\n  <sup>\n   −1\n  </sup>\n  » ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msqrt>\n    <mfrac>\n     <mrow>\n      <mn>\n       2\n      </mn>\n      <mo>\n       ×\n      </mo>\n      <mn>\n       6\n      </mn>\n      <mo>\n       .\n      </mo>\n      <mn>\n       67\n      </mn>\n      <mo>\n       ×\n      </mo>\n      <msup>\n       <mn>\n        10\n       </mn>\n       <mrow>\n        <mo>\n         -\n        </mo>\n        <mn>\n         11\n        </mn>\n       </mrow>\n      </msup>\n      <mo>\n       ×\n      </mo>\n      <mn>\n       5\n      </mn>\n      <mo>\n       .\n      </mo>\n      <mn>\n       97\n      </mn>\n      <mo>\n       ×\n      </mo>\n      <msup>\n       <mn>\n        10\n       </mn>\n       <mn>\n        24\n       </mn>\n      </msup>\n     </mrow>\n     <mrow>\n      <mn>\n       6\n      </mn>\n      <mo>\n       .\n      </mo>\n      <mn>\n       70\n      </mn>\n      <mo>\n       ×\n      </mo>\n      <msup>\n       <mn>\n        10\n       </mn>\n       <mn>\n        6\n       </mn>\n      </msup>\n     </mrow>\n    </mfrac>\n   </msqrt>\n  </math>\n  = »\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    09\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     4\n    </mn>\n   </msup>\n   <mo>\n   </mo>\n   <mo>\n    «\n   </mo>\n   <mi mathvariant=\"normal\">\n    m\n   </mi>\n   <mo>\n   </mo>\n   <msup>\n    <mi mathvariant=\"normal\">\n     s\n    </mi>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      1\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n    »\n   </mo>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  Negative ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  Positive ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "d-fields"
    ],
    "subtopics": [
      "d-1-gravitational-fields"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.16",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The radius of the dwarf planet Pluto is 1.19 x 10\n   <sup>\n    6\n   </sup>\n   m. The acceleration due to gravity at its surface is 0.617 m s\n   <sup>\n    −2\n   </sup>\n   .\n  </p>\n  <p>\n   Determine the escape speed for an object at the surface of Pluto.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [4]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Pluto rotates about an axis through its centre. Its rotation is in the opposite sense to that of the Earth, i.e. from east to west.\n  </p>\n  <p>\n   Explain the advantage of an object launching from the equator of Pluto and travelling to the west.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     v\n    </mi>\n    <mtext>\n     esc\n    </mtext>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <msqrt>\n    <mfrac>\n     <mrow>\n      <mn>\n       2\n      </mn>\n      <mi>\n       G\n      </mi>\n      <mi>\n       M\n      </mi>\n     </mrow>\n     <mi>\n      r\n     </mi>\n    </mfrac>\n   </msqrt>\n  </math>\n  AND\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    g\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi>\n      G\n     </mi>\n     <mi>\n      M\n     </mi>\n    </mrow>\n    <msup>\n     <mi>\n      r\n     </mi>\n     <mn>\n      2\n     </mn>\n    </msup>\n   </mfrac>\n  </math>\n  seen ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     v\n    </mi>\n    <mtext>\n     esc\n    </mtext>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <msqrt>\n    <mfrac>\n     <mrow>\n      <mn>\n       2\n      </mn>\n      <mi>\n       g\n      </mi>\n      <msup>\n       <mi>\n        r\n       </mi>\n       <mn>\n        2\n       </mn>\n      </msup>\n     </mrow>\n     <mi>\n      r\n     </mi>\n    </mfrac>\n   </msqrt>\n  </math>\n  ✓\n </p>\n <p>\n  Leading to\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     v\n    </mi>\n    <mtext>\n     esc\n    </mtext>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <msqrt>\n    <mn>\n     2\n    </mn>\n    <mi>\n     g\n    </mi>\n    <mi>\n     r\n    </mi>\n   </msqrt>\n  </math>\n  ✓\n </p>\n <p>\n  1.2 km s\n  <sup>\n   −1\n  </sup>\n  ✓\n  <sup>\n  </sup>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     v\n    </mi>\n    <mtext>\n     esc\n    </mtext>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <msqrt>\n    <mfrac>\n     <mrow>\n      <mn>\n       2\n      </mn>\n      <mi>\n       G\n      </mi>\n      <mi>\n       M\n      </mi>\n     </mrow>\n     <mi>\n      r\n     </mi>\n    </mfrac>\n   </msqrt>\n  </math>\n  AND\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    g\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi>\n      G\n     </mi>\n     <mi>\n      M\n     </mi>\n    </mrow>\n    <msup>\n     <mi>\n      r\n     </mi>\n     <mn>\n      2\n     </mn>\n    </msup>\n   </mfrac>\n  </math>\n  seen ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     v\n    </mi>\n    <mtext>\n     esc\n    </mtext>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <msqrt>\n    <mfrac>\n     <mrow>\n      <mn>\n       2\n      </mn>\n      <mi>\n       g\n      </mi>\n      <msup>\n       <mi>\n        r\n       </mi>\n       <mn>\n        2\n       </mn>\n      </msup>\n     </mrow>\n     <mi>\n      r\n     </mi>\n    </mfrac>\n   </msqrt>\n  </math>\n  ✓\n </p>\n <p>\n  Leading to\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     v\n    </mi>\n    <mtext>\n     esc\n    </mtext>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <msqrt>\n    <mn>\n     2\n    </mn>\n    <mi>\n     g\n    </mi>\n    <mi>\n     r\n    </mi>\n   </msqrt>\n  </math>\n  ✓\n </p>\n <p>\n  1.2 km s\n  <sup>\n   −1\n  </sup>\n  ✓\n  <sup>\n  </sup>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  Object at equator has the maximum linear/tangential speed possible ✓\n </p>\n <p>\n  It therefore has maximum kinetic energy before takeoff (and this is not required from the fuel) ✓\n </p>\n <p>\n  Idea that the object is already moving in direction of planet before takeoff ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "d-fields"
    ],
    "subtopics": [
      "d-1-gravitational-fields"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.17",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the energy of the scattered photon is about 16 keV.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the wavelength of the incident photon.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline why the results of the experiment are inconsistent with the wave model of electromagnetic radiation.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (d)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the scattering angle of the photon.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      24\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        6\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      7\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      80\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        11\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n   </mfrac>\n  </math>\n  «= 15.9 keV» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      24\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        6\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      7\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      80\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        11\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n   </mfrac>\n  </math>\n  «= 15.9 keV» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  Energy of incident photon =«\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    15\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    9\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     3\n    </mn>\n   </msup>\n   <mo>\n    +\n   </mo>\n   <mn>\n    500\n   </mn>\n   <mo>\n    =\n   </mo>\n  </math>\n  »\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    16\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    4\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     3\n    </mn>\n   </msup>\n  </math>\n  «eV» ✓\n </p>\n <p>\n  Wavelength of incident photon =«\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      24\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        6\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      16\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      4\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n  </math>\n  »\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    7\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    56\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      11\n     </mn>\n    </mrow>\n   </msup>\n  </math>\n  «m» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  The wavelength of the X-rays changes ✓\n </p>\n <p>\n  According to the wave model, the wavelength of the incident and scattered X-rays should be the same ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfenced>\n    <mrow>\n     <mn>\n      7\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      80\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mn>\n      7\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      56\n     </mn>\n    </mrow>\n   </mfenced>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      11\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      24\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        6\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      511\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       6\n      </mn>\n     </msup>\n    </mrow>\n   </mfrac>\n   <mfenced>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mi>\n      cos\n     </mi>\n     <mo>\n     </mo>\n     <mi>\n      θ\n     </mi>\n    </mrow>\n   </mfenced>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    θ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    89\n   </mn>\n   <mo>\n    °\n   </mo>\n  </math>\n  ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "e-2-quantum-physics"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.18",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline why the pattern observed on the screen is an evidence for matter waves.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   A typical interatomic distance in the graphite crystal is of the order of\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mn>\n     2\n    </mn>\n    <mo>\n     ×\n    </mo>\n    <msup>\n     <mn>\n      10\n     </mn>\n     <mrow>\n      <mo>\n       -\n      </mo>\n      <mn>\n       10\n      </mn>\n     </mrow>\n    </msup>\n   </math>\n   m. Estimate the minimum value of\n   <em>\n    U\n   </em>\n   for the pattern in (a) to be formed on the screen.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [4]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Protons can also be accelerated by the same potential difference\n   <em>\n    U\n   </em>\n   . Compare, without calculation, the de Broglie wavelength of the protons to that of the electrons.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  The pattern is formed when the electrons scattered from adjacent planes in the graphite crystal undergo interference / diffract ✓\n </p>\n <p>\n  Interference / diffraction is a property of waves only ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  The pattern is formed when the electrons scattered from adjacent planes in the graphite crystal undergo interference / diffract ✓\n </p>\n <p>\n  Interference / diffraction is a property of waves only ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  The de Broglie wavelength of the electrons should be comparable to or shorter than the interatomic distance /\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    2\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      10\n     </mn>\n    </mrow>\n   </msup>\n  </math>\n  m ✓\n </p>\n <p>\n  Momentum of electrons\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    ≈\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      6\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      63\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        34\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        10\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n   </mfrac>\n  </math>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    3\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    32\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      2\n     </mn>\n    </mrow>\n   </msup>\n  </math>\n  N s» ✓\n </p>\n <p>\n  Kinetic energy of electrons = «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <msup>\n     <mi>\n      p\n     </mi>\n     <mn>\n      2\n     </mn>\n    </msup>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mi>\n      m\n     </mi>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <msup>\n     <mfenced>\n      <mrow>\n       <mn>\n        3\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        32\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mrow>\n         <mo>\n          -\n         </mo>\n         <mn>\n          24\n         </mn>\n        </mrow>\n       </msup>\n      </mrow>\n     </mfenced>\n     <mn>\n      2\n     </mn>\n    </msup>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      9\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      11\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        31\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n  </math>\n  »\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    6\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      18\n     </mn>\n    </mrow>\n   </msup>\n  </math>\n  «J»  ✓\n </p>\n <p>\n  <em>\n   U\n  </em>\n  = «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mi>\n     E\n    </mi>\n    <mi>\n     e\n    </mi>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      6\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      10\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        18\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      6\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        19\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n  </math>\n  »40 «V» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  The protons have the same energy but greater mass hence a greater momentum than the electrons ✓\n </p>\n <p>\n  From\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    λ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mi>\n     h\n    </mi>\n    <mi>\n     p\n    </mi>\n   </mfrac>\n  </math>\n  , the protons will have a shorter wavelength ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "e-2-quantum-physics"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.19",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the de Broglie hypothesis.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the maximum speed of the electrons in the beam.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   After passing through the circular hole the electrons strike a fluorescent screen.\n  </p>\n  <p>\n   Predict whether an apparatus such as this can demonstrate that moving electrons have wave properties.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [4]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  a moving particle has wave properties ✓\n </p>\n <p>\n  de Broglie wavelength = Planck constant÷momentum (must define p if quoted as equation) ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  a moving particle has wave properties ✓\n </p>\n <p>\n  de Broglie wavelength = Planck constant÷momentum (must define p if quoted as equation) ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  use of ½\n  <em>\n   mv\n  </em>\n  <sup>\n   2\n  </sup>\n  =\n  <em>\n   eV ✓\n  </em>\n </p>\n <p>\n  1.33 × 10\n  <sup>\n   7\n  </sup>\n  m s\n  <sup>\n   −1\n  </sup>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  idea that de Broglie wavelength and hole size must be similar ✓\n </p>\n <p>\n  Use of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    λ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mi>\n     h\n    </mi>\n    <msqrt>\n     <mn>\n      2\n     </mn>\n     <mi>\n      m\n     </mi>\n     <mi>\n      e\n     </mi>\n     <mi>\n      V\n     </mi>\n    </msqrt>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  Leading to\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    λ\n   </mi>\n  </math>\n  around 5 x 10\n  <sup>\n   −11\n  </sup>\n  m (which is unrealistic for a practical situation) ✓\n </p>\n <p>\n  It would not be possible to construct this hole\n  <br/>\n  <strong>\n   OR\n  </strong>\n  <br/>\n  hole must be smaller than an atom so impossible ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "e-2-quantum-physics"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.2",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the movement direction for which the geophone has its greatest sensitivity.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the movement direction for which the geophone has its greatest sensitivity.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline how an emf is generated in the coil.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Explain why the magnitude of the emf is related to the amplitude of the ground movement.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iv)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   In one particular event, a maximum emf of 65 mV is generated in the geophone. The geophone coil has 150 turns.\n  </p>\n  <p>\n   Calculate the rate of flux change that leads to this emf.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Suggest\n   <strong>\n    two\n   </strong>\n   changes to the system that will make the geophone more sensitive.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [4]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that, when sound travels from clay to sandstone, the critical angle is approximately 40°.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The angle between the clay–air surface and\n   <strong>\n    path 1\n   </strong>\n   is 80°.\n  </p>\n  <p>\n   Draw, on the diagram, the subsequent path of a sound wave that travels initially in the clay along\n   <strong>\n    path 1\n   </strong>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (d)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate\n   <em>\n    d\n   </em>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [4]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a.i)\n </div><div class=\"card-body\">\n <p>\n  Vertical direction / parallel to springs ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  Vertical direction / parallel to springs ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  The magnetic field moves relative to the coil ✓\n </p>\n <p>\n  As field lines cut the coil, forces act on (initially stationary) electrons in the wire (and these move producing an emf) ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  The springs have a natural time period for the oscillation ✓\n </p>\n <p>\n  A greater amplitude of movement leads to higher magnet speed (with constant time period) ✓\n </p>\n <p>\n  So field lines cut coil more quickly leading to greater emf ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iv)\n </div><div class=\"card-body\">\n <p>\n  Use of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    ε\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mo>\n    -\n   </mo>\n   <mfrac>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mfenced>\n      <mrow>\n       <mi>\n        N\n       </mi>\n       <mtext>\n        Φ\n       </mtext>\n      </mrow>\n     </mfenced>\n    </mrow>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mi>\n      t\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mtext>\n     ΔΦ\n    </mtext>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mi>\n      t\n     </mi>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfenced>\n    <mo>\n     -\n    </mo>\n   </mfenced>\n   <mfrac>\n    <mrow>\n     <mn>\n      65\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        3\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mn>\n     150\n    </mn>\n   </mfrac>\n  </math>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    43\n   </mn>\n  </math>\n  mWb s\n  <sup>\n   −1\n  </sup>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  Any two suggestions from:\n </p>\n <p>\n  Increase number of turns in coil ✓\n  <br/>\n  Because more flux cutting per cycle ✓\n </p>\n <p>\n  Increase field strength of magnet  ✓\n  <br/>\n  So that there are more field lines ✓\n </p>\n <p>\n  Change mass-spring system so that time period decreases ✓\n  <br/>\n  So magnet will be moving faster for given amplitude of movement ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   <sub>\n    c\n   </sub>\n   n\n   <sub>\n    s\n   </sub>\n  </em>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      3\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      0\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      4\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      7\n     </mn>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    57\n   </mn>\n  </math>\n  ✓\n </p>\n <p>\n  Critical angle\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <msup>\n    <mi>\n     sin\n    </mi>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      1\n     </mn>\n    </mrow>\n   </msup>\n   <mfenced>\n    <mfrac>\n     <mn>\n      1\n     </mn>\n     <mrow>\n      <mn>\n       1\n      </mn>\n      <mo>\n       .\n      </mo>\n      <mn>\n       57\n      </mn>\n     </mrow>\n    </mfrac>\n   </mfenced>\n   <mo>\n    =\n   </mo>\n   <mn>\n    39\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    6\n   </mn>\n   <mo>\n    °\n   </mo>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  ray shown reflected back into the clay (and then to Z) at (by eye) the incidence angle ✓\n </p>\n <p>\n  ray shown refracted into the sandstone with angle of refraction greater than angle of incidence (by eye) ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  distance difference\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mfenced>\n    <mrow>\n     <mn>\n      3000\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      00667\n     </mn>\n     <mo>\n      =\n     </mo>\n    </mrow>\n   </mfenced>\n   <mn>\n    19\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    8\n   </mn>\n  </math>\n  m ✓\n </p>\n <p>\n  ½ distance difference\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    9\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    9\n   </mn>\n  </math>\n  m so YZ\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    49\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    9\n   </mn>\n  </math>\n  m ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    d\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfenced>\n    <msqrt>\n     <msup>\n      <mtext>\n       YZ\n      </mtext>\n      <mn>\n       2\n      </mn>\n     </msup>\n     <mo>\n      -\n     </mo>\n     <msup>\n      <mfenced>\n       <mfrac>\n        <mtext>\n         XZ\n        </mtext>\n        <mn>\n         2\n        </mn>\n       </mfrac>\n      </mfenced>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </msqrt>\n   </mfenced>\n   <mo>\n    =\n   </mo>\n   <msqrt>\n    <mn>\n     49\n    </mn>\n    <mo>\n     .\n    </mo>\n    <msup>\n     <mn>\n      9\n     </mn>\n     <mn>\n      2\n     </mn>\n    </msup>\n    <mo>\n     -\n    </mo>\n    <msup>\n     <mn>\n      40\n     </mn>\n     <mn>\n      2\n     </mn>\n    </msup>\n   </msqrt>\n  </math>\n  ✓\n </p>\n <p>\n  <br/>\n  29.8 m ✓\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n </p>\n <p>\n  Recognises situation as (almost) 3:4:5 triangle ✓\n </p>\n <p>\n  <br/>\n  30 m (\n  <em>\n   1 sf answer only accepted in this route\n  </em>\n  ) ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion",
      "c-wave-behaviour",
      "d-fields"
    ],
    "subtopics": [
      "a-1-kinematics",
      "c-1-simple-harmonic-motion",
      "c-3-wave-phenomena",
      "d-4-induction"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.20",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The quantity\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mfrac>\n     <mi>\n      h\n     </mi>\n     <mrow>\n      <msub>\n       <mi>\n        m\n       </mi>\n       <mtext>\n        e\n       </mtext>\n      </msub>\n      <mi>\n       c\n      </mi>\n     </mrow>\n    </mfrac>\n   </math>\n   is known as the Compton wavelength.\n  </p>\n  <p>\n   Show that the Compton wavelength is about 2.4 pm.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the wavelength of the photon after the interaction.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline why the wavelength of the photon has changed.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Deduce the scattering angle for the photon.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iv)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine, in J, the kinetic energy of the electron after the interaction.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  2.43 pm ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  2.43 pm ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  8.43 pm ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  (Energy of photon inversely prop to wavelength)\n </p>\n <p>\n </p>\n <p>\n  photon transfers some of its energy to the electron. ✓\n </p>\n <p>\n  If its energy decreases so its wavelength increases. ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  (for this interaction)\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    Δ\n   </mtext>\n   <mi>\n    λ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mi>\n     h\n    </mi>\n    <mrow>\n     <msub>\n      <mi>\n       m\n      </mi>\n      <mtext>\n       e\n      </mtext>\n     </msub>\n     <mi>\n      c\n     </mi>\n    </mrow>\n   </mfrac>\n   <mfenced>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mi>\n      cos\n     </mi>\n     <mo>\n     </mo>\n     <mi>\n      θ\n     </mi>\n    </mrow>\n   </mfenced>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mi>\n     h\n    </mi>\n    <mrow>\n     <msub>\n      <mi>\n       m\n      </mi>\n      <mtext>\n       e\n      </mtext>\n     </msub>\n     <mi>\n      c\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  and therefore\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfenced>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mi>\n      cos\n     </mi>\n     <mo>\n     </mo>\n     <mi>\n      θ\n     </mi>\n    </mrow>\n   </mfenced>\n  </math>\n  must equal 1 ✓\n </p>\n <p>\n  so cos theta = 0 and theta = 90 deg ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iv)\n </div><div class=\"card-body\">\n <p>\n  (Because energy is conserved)\n </p>\n <p>\n  <br/>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     E\n    </mi>\n    <mtext>\n     k\n    </mtext>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mi>\n    h\n   </mi>\n   <mi>\n    c\n   </mi>\n   <mfenced>\n    <mrow>\n     <mfrac>\n      <mn>\n       1\n      </mn>\n      <msub>\n       <mi>\n        λ\n       </mi>\n       <mtext>\n        i\n       </mtext>\n      </msub>\n     </mfrac>\n     <mo>\n      -\n     </mo>\n     <mfrac>\n      <mn>\n       1\n      </mn>\n      <msub>\n       <mi>\n        λ\n       </mi>\n       <mtext>\n        f\n       </mtext>\n      </msub>\n     </mfrac>\n    </mrow>\n   </mfenced>\n  </math>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    6\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    63\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      34\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    3\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    00\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     8\n    </mn>\n   </msup>\n   <mfenced>\n    <mrow>\n     <mfrac>\n      <mn>\n       1\n      </mn>\n      <mrow>\n       <mn>\n        6\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        00\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mrow>\n         <mo>\n          -\n         </mo>\n         <mn>\n          12\n         </mn>\n        </mrow>\n       </msup>\n      </mrow>\n     </mfrac>\n     <mo>\n      -\n     </mo>\n     <mfrac>\n      <mn>\n       1\n      </mn>\n      <mrow>\n       <mn>\n        8\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        43\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mrow>\n         <mo>\n          -\n         </mo>\n         <mn>\n          12\n         </mn>\n        </mrow>\n       </msup>\n      </mrow>\n     </mfrac>\n    </mrow>\n   </mfenced>\n  </math>\n  ✓\n </p>\n <p>\n  9.6 fJ ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "e-2-quantum-physics"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.21",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Suggest one problem that is faced in dealing with the waste from nuclear fission reactors. Go on to outline how this problem is overcome.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Strontium-90 is a waste product from nuclear reactors that has a decay constant of 7.63 x 10\n   <sup>\n    −10\n   </sup>\n   s\n   <sup>\n    −1\n   </sup>\n   . Determine, in s, the time that it takes for the activity of strontium-90 to decay to 2% of its original activity.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the energy released when one mole of strontium-90 decays to 2% of its original activity forming the stable daughter product.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Strontium-90 decays to Zirconium-90 via two successive beta emissions. Discuss whether all the energy released when strontium-90 decays to Zirconium-90 can be transferred to a thermal form.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Waste is very hot …\n </p>\n <p>\n  … So has to be placed in cooling ponds to transfer the (thermal) energy away ✓\n </p>\n <p>\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n </p>\n <p>\n  Waste is very radioactive … ✓\n </p>\n <p>\n  … So has to be placed in cooling ponds to absorb this radiation\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n </p>\n <p>\n  … So has to be handled remotely\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n </p>\n <p>\n  … So has to be transported in crash resistant casings / stored on site ✓\n </p>\n <p>\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n </p>\n <p>\n  Waste will be radioactive for thousands of years … ✓\n </p>\n <p>\n  … So storage needs to be (eventually) in geologically stable areas ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Waste is very hot …\n </p>\n <p>\n  … So has to be placed in cooling ponds to transfer the (thermal) energy away ✓\n </p>\n <p>\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n </p>\n <p>\n  Waste is very radioactive … ✓\n </p>\n <p>\n  … So has to be placed in cooling ponds to absorb this radiation\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n </p>\n <p>\n  … So has to be handled remotely\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n </p>\n <p>\n  … So has to be transported in crash resistant casings / stored on site ✓\n </p>\n <p>\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n </p>\n <p>\n  Waste will be radioactive for thousands of years … ✓\n </p>\n <p>\n  … So storage needs to be (eventually) in geologically stable areas ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    ln\n   </mi>\n   <mo>\n   </mo>\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      02\n     </mn>\n    </mrow>\n   </mfenced>\n   <mo>\n    =\n   </mo>\n   <mo>\n    -\n   </mo>\n   <mfenced>\n    <mrow>\n     <mn>\n      7\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      63\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        10\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n   </mfenced>\n   <mi>\n    t\n   </mi>\n  </math>\n  or equivalent seen ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    t\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    5\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    1\n   </mn>\n  </math>\n  Gs ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  Idea that the Yttrium half life is much less than Strontium so can assume all Yttrium energy is included. ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    98\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    6\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    02\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     23\n    </mn>\n   </msup>\n   <mo>\n    ×\n   </mo>\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      52\n     </mn>\n     <mo>\n      +\n     </mo>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      3\n     </mn>\n    </mrow>\n   </mfenced>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     6\n    </mn>\n   </msup>\n  </math>\n  seen ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfenced>\n    <mrow>\n     <mo>\n      =\n     </mo>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      67\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      1030\n     </mn>\n     <mo>\n     </mo>\n     <mtext>\n      eV\n     </mtext>\n    </mrow>\n   </mfenced>\n  </math>\n </p>\n <p>\n  Answer\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    ×\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    6\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      19\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <mn>\n    270\n   </mn>\n  </math>\n  GJ ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  (No)\n  <br/>\n  (anti-)neutrinos are released in (both) decays ✓\n </p>\n <p>\n  Carrying away energy because they interact poorly with matter ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Ignore arguments relating to energy transferred to nucleus as this appears eventually as thermal energy.\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "e-4-fission"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.3",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the vertical component of the total momentum of the balls after the collision.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the vertical component of the total momentum of the balls after the collision.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Hence, calculate the vertical component of the velocity of ball B after the collision.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the angle\n   <em>\n    θ\n   </em>\n   that the velocity of ball B makes with the initial direction of motion of ball A.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Predict whether the collision is elastic.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [4]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a.i)\n </div><div class=\"card-body\">\n <p>\n  Zero ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  Zero ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    m\n   </mi>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mi>\n    sin\n   </mi>\n   <mo>\n   </mo>\n   <mn>\n    45\n   </mn>\n   <mo>\n    °\n   </mo>\n   <mo>\n    +\n   </mo>\n   <mi>\n    m\n   </mi>\n   <mo>\n    ×\n   </mo>\n   <msub>\n    <mi>\n     v\n    </mi>\n    <mi>\n     y\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mn>\n    0\n   </mn>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     v\n    </mi>\n    <mi>\n     y\n    </mi>\n   </msub>\n  </math>\n  = «−»0.71 «m s\n  <sup>\n   −1\n  </sup>\n  » ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  The use of conservation of momentum in the horizontal direction, e.g.\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    m\n   </mi>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mi>\n    cos\n   </mi>\n   <mo>\n   </mo>\n   <mn>\n    45\n   </mn>\n   <mo>\n    °\n   </mo>\n   <mo>\n    +\n   </mo>\n   <mi>\n    m\n   </mi>\n   <mo>\n    ×\n   </mo>\n   <msub>\n    <mi>\n     v\n    </mi>\n    <mi>\n     x\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mi>\n    m\n   </mi>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    2\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     v\n    </mi>\n    <mi>\n     x\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n  </math>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    2\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    -\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mi>\n    cos\n   </mi>\n   <mo>\n   </mo>\n   <mn>\n    45\n   </mn>\n   <mo>\n    °\n   </mo>\n   <mo>\n    =\n   </mo>\n  </math>\n  »\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    3\n   </mn>\n  </math>\n  «m s\n  <sup>\n   −1\n  </sup>\n  » ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    θ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <msup>\n    <mi>\n     tan\n    </mi>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      1\n     </mn>\n    </mrow>\n   </msup>\n   <mfenced>\n    <mfrac>\n     <msub>\n      <mi>\n       v\n      </mi>\n      <mi>\n       y\n      </mi>\n     </msub>\n     <msub>\n      <mi>\n       v\n      </mi>\n      <mi>\n       x\n      </mi>\n     </msub>\n    </mfrac>\n   </mfenced>\n   <mo>\n    =\n   </mo>\n   <mn>\n    29\n   </mn>\n   <mo>\n    °\n   </mo>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  Initial kinetic energy\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <mi>\n    m\n   </mi>\n   <msup>\n    <mfenced>\n     <mrow>\n      <mn>\n       2\n      </mn>\n      <mo>\n       .\n      </mo>\n      <mn>\n       0\n      </mn>\n     </mrow>\n    </mfenced>\n    <mn>\n     2\n    </mn>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <mn>\n    2\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n   </mo>\n   <mfenced>\n    <mi>\n     m\n    </mi>\n   </mfenced>\n  </math>\n </p>\n <p>\n  Final kinetic energy\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <mi>\n    m\n   </mi>\n   <mfenced>\n    <mrow>\n     <msup>\n      <mfenced>\n       <mrow>\n        <mn>\n         1\n        </mn>\n        <mo>\n         .\n        </mo>\n        <mn>\n         0\n        </mn>\n       </mrow>\n      </mfenced>\n      <mn>\n       2\n      </mn>\n     </msup>\n     <mo>\n      +\n     </mo>\n     <msup>\n      <mfenced>\n       <mrow>\n        <mn>\n         0\n        </mn>\n        <mo>\n         .\n        </mo>\n        <mn>\n         71\n        </mn>\n       </mrow>\n      </mfenced>\n      <mn>\n       2\n      </mn>\n     </msup>\n     <mo>\n      +\n     </mo>\n     <msup>\n      <mfenced>\n       <mrow>\n        <mn>\n         1\n        </mn>\n        <mo>\n         .\n        </mo>\n        <mn>\n         3\n        </mn>\n       </mrow>\n      </mfenced>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </mrow>\n   </mfenced>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    6\n   </mn>\n   <mo>\n   </mo>\n   <mo>\n    (\n   </mo>\n   <mi>\n    m\n   </mi>\n   <mo>\n    )\n   </mo>\n  </math>\n  ✓\n </p>\n <p>\n  Final energy is less than the initial energy hence inelastic  ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-2-forces-and-momentum"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.4",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State what is meant by an elastic collision.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State what is meant by an elastic collision.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   No unbalanced external forces act on the system of the curling stones. Outline why the momentum of the system does not change during the collision.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <msub>\n     <mi>\n      v\n     </mi>\n     <mtext>\n      B\n     </mtext>\n    </msub>\n    <mo>\n     =\n    </mo>\n    <mfrac>\n     <mrow>\n      <mi>\n       sin\n      </mi>\n      <mo>\n      </mo>\n      <mn>\n       70\n      </mn>\n      <mo>\n       °\n      </mo>\n     </mrow>\n     <mrow>\n      <mi>\n       sin\n      </mi>\n      <mo>\n      </mo>\n      <mn>\n       20\n      </mn>\n      <mo>\n       °\n      </mo>\n     </mrow>\n    </mfrac>\n    <msub>\n     <mi>\n      v\n     </mi>\n     <mi>\n      A\n     </mi>\n    </msub>\n   </math>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine\n   <em>\n    v\n   </em>\n   <sub>\n    A\n   </sub>\n   . State the answer in terms of\n   <em>\n    v\n   </em>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a.i)\n </div><div class=\"card-body\">\n <p>\n  No change in the kinetic energy of the system  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  No change in the kinetic energy of the system  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  From\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    F\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mi>\n      p\n     </mi>\n    </mrow>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mi>\n      t\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  , zero net force on the system implies that\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    Δ\n   </mtext>\n   <mi>\n    p\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    0\n   </mn>\n  </math>\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n </p>\n <p>\n  From Newton’s third law, the impulse delivered to A is equal but opposite to the impulse delivered to B, hence\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    Δ\n   </mtext>\n   <mi>\n    p\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    0\n   </mn>\n  </math>\n  for the system  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  The vertical momentum is zero hence\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    m\n   </mi>\n   <msub>\n    <mi>\n     v\n    </mi>\n    <mtext>\n     A\n    </mtext>\n   </msub>\n   <mi>\n    sin\n   </mi>\n   <mo>\n   </mo>\n   <mn>\n    70\n   </mn>\n   <mo>\n    °\n   </mo>\n   <mo>\n    -\n   </mo>\n   <mi>\n    m\n   </mi>\n   <msub>\n    <mi>\n     v\n    </mi>\n    <mtext>\n     B\n    </mtext>\n   </msub>\n   <mi>\n    sin\n   </mi>\n   <mo>\n   </mo>\n   <mn>\n    20\n   </mn>\n   <mo>\n    °\n   </mo>\n   <mo>\n    =\n   </mo>\n   <mn>\n    0\n   </mn>\n  </math>\n  ✓\n </p>\n <p>\n  «leading to the expected result»  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  Energy is conserved hence\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <mi>\n    m\n   </mi>\n   <msup>\n    <msub>\n     <mi>\n      v\n     </mi>\n     <mtext>\n      A\n     </mtext>\n    </msub>\n    <mn>\n     2\n    </mn>\n   </msup>\n   <mo>\n    +\n   </mo>\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <mi>\n    m\n   </mi>\n   <msup>\n    <msub>\n     <mi>\n      v\n     </mi>\n     <mtext>\n      B\n     </mtext>\n    </msub>\n    <mn>\n     2\n    </mn>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <mi>\n    m\n   </mi>\n   <msup>\n    <mi>\n     v\n    </mi>\n    <mn>\n     2\n    </mn>\n   </msup>\n  </math>\n  ✓\n </p>\n <p>\n  Eliminate\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     v\n    </mi>\n    <mtext>\n     B\n    </mtext>\n   </msub>\n  </math>\n  using the result of part (a), e.g.,\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msup>\n    <msub>\n     <mi>\n      v\n     </mi>\n     <mtext>\n      A\n     </mtext>\n    </msub>\n    <mn>\n     2\n    </mn>\n   </msup>\n   <mo>\n    +\n   </mo>\n   <msup>\n    <mfenced>\n     <mfrac>\n      <mrow>\n       <mi>\n        sin\n       </mi>\n       <mo>\n       </mo>\n       <mn>\n        70\n       </mn>\n       <mo>\n        °\n       </mo>\n      </mrow>\n      <mrow>\n       <mi>\n        sin\n       </mi>\n       <mo>\n       </mo>\n       <mn>\n        20\n       </mn>\n       <mo>\n        °\n       </mo>\n      </mrow>\n     </mfrac>\n    </mfenced>\n    <mn>\n     2\n    </mn>\n   </msup>\n   <msup>\n    <msub>\n     <mi>\n      v\n     </mi>\n     <mtext>\n      A\n     </mtext>\n    </msub>\n    <mn>\n     2\n    </mn>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <msup>\n    <mi>\n     v\n    </mi>\n    <mn>\n     2\n    </mn>\n   </msup>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     v\n    </mi>\n    <mtext>\n     A\n    </mtext>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    342\n   </mn>\n   <mi>\n    v\n   </mi>\n  </math>\n  ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-2-forces-and-momentum"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.5",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the component of momentum of the first curling stone perpendicular to the initial direction.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the component of momentum of the first curling stone perpendicular to the initial direction.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the velocity component of the first curling stone in the initial direction.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the velocity of the first curling stone.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Deduce whether this collision is elastic.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a.i)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     v\n    </mi>\n    <mn>\n     17\n    </mn>\n   </msub>\n   <mo>\n   </mo>\n   <mi>\n    sin\n   </mi>\n   <mo>\n   </mo>\n   <mi>\n    θ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      19\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      5\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mi>\n      sin\n     </mi>\n     <mfenced>\n      <mn>\n       30\n      </mn>\n     </mfenced>\n    </mrow>\n    <mn>\n     17\n    </mn>\n   </mfrac>\n   <mfenced>\n    <mrow>\n     <mo>\n      =\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      279\n     </mn>\n     <mo>\n     </mo>\n     <mtext>\n      m\n     </mtext>\n     <mo>\n     </mo>\n     <msup>\n      <mtext>\n       s\n      </mtext>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        1\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n   </mfenced>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     v\n    </mi>\n    <mn>\n     17\n    </mn>\n   </msub>\n   <mo>\n   </mo>\n   <mi>\n    sin\n   </mi>\n   <mo>\n   </mo>\n   <mi>\n    θ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      19\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      5\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mi>\n      sin\n     </mi>\n     <mfenced>\n      <mn>\n       30\n      </mn>\n     </mfenced>\n    </mrow>\n    <mn>\n     17\n    </mn>\n   </mfrac>\n   <mfenced>\n    <mrow>\n     <mo>\n      =\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      279\n     </mn>\n     <mo>\n     </mo>\n     <mtext>\n      m\n     </mtext>\n     <mo>\n     </mo>\n     <msup>\n      <mtext>\n       s\n      </mtext>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        1\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n   </mfenced>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     v\n    </mi>\n    <mn>\n     17\n    </mn>\n   </msub>\n   <mo>\n   </mo>\n   <mi>\n    cos\n   </mi>\n   <mo>\n   </mo>\n   <mi>\n    θ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      17\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      5\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mn>\n      19\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      50\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mi>\n      cos\n     </mi>\n     <mfenced>\n      <mn>\n       30\n      </mn>\n     </mfenced>\n    </mrow>\n    <mn>\n     17\n    </mn>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    2\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    02\n   </mn>\n   <mo>\n   </mo>\n   <msup>\n    <mtext>\n     m s\n    </mtext>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      1\n     </mn>\n    </mrow>\n   </msup>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  2.04 m s\n  <sup>\n   −1\n  </sup>\n  ✓\n </p>\n <p>\n  At 7.9° to initial direction  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  Total angle between stones is 38°, angle will be 90° when elastic\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n </p>\n <p>\n  Compares kinetic energies in a correct calculation (initial ke = 53 J, final ke = 34 J +2.4 J) ✓\n </p>\n <p>\n  <br/>\n  Collision is not elastic ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-2-forces-and-momentum"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.6",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the recoil velocity of the cannon.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the initial kinetic energy of the cannon.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Suggest what happens to the vertical component of momentum of the cannon when the shell is fired.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Momentum must be conserved in initial direction of shell (20° above horizontal)  ✓\n </p>\n <p>\n  Recoil velocity is 4.2 m s\n  <sup>\n   −1\n  </sup>\n  at 20° below horizontal  ✓\n </p>\n <p>\n  3.95 m s\n  <sup>\n   −1\n  </sup>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Momentum must be conserved in initial direction of shell (20° above horizontal)  ✓\n </p>\n <p>\n  Recoil velocity is 4.2 m s\n  <sup>\n   −1\n  </sup>\n  at 20° below horizontal  ✓\n </p>\n <p>\n  3.95 m s\n  <sup>\n   −1\n  </sup>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     E\n    </mi>\n    <mi>\n     k\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mfenced>\n    <mrow>\n     <mfrac>\n      <mn>\n       1\n      </mn>\n      <mn>\n       2\n      </mn>\n     </mfrac>\n     <mi>\n      m\n     </mi>\n     <msup>\n      <mi>\n       v\n      </mi>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </mrow>\n   </mfenced>\n   <mo>\n    =\n   </mo>\n   <mn>\n    11\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    7\n   </mn>\n   <mo>\n   </mo>\n   <mtext>\n    kJ\n   </mtext>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  Must be transferred into the ground beneath the cannon\n  <strong>\n   OR\n  </strong>\n  into the suspension system  ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-2-forces-and-momentum"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.7",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the angular impulse delivered to the flywheel during the acceleration.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the average magnitude of\n   <em>\n    <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mi>\n      F\n     </mi>\n    </math>\n   </em>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State\n   <strong>\n    two\n   </strong>\n   assumptions of your calculation in part (b).\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    Δ\n   </mtext>\n   <mi>\n    L\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mtext>\n    l\n   </mtext>\n   <mi>\n    Δ\n   </mi>\n   <mi>\n    ω\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    8\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <msup>\n    <mn>\n     15\n    </mn>\n    <mn>\n     2\n    </mn>\n   </msup>\n   <mo>\n   </mo>\n   <mfenced>\n    <mrow>\n     <mn>\n      9\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mn>\n      4\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      0\n     </mn>\n    </mrow>\n   </mfenced>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    10\n   </mn>\n  </math>\n  «N m s»  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    Δ\n   </mtext>\n   <mi>\n    L\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mtext>\n    l\n   </mtext>\n   <mi>\n    Δ\n   </mi>\n   <mi>\n    ω\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    8\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <msup>\n    <mn>\n     15\n    </mn>\n    <mn>\n     2\n    </mn>\n   </msup>\n   <mo>\n   </mo>\n   <mfenced>\n    <mrow>\n     <mn>\n      9\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mn>\n      4\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      0\n     </mn>\n    </mrow>\n   </mfenced>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    10\n   </mn>\n  </math>\n  «N m s»  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  Average torque\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mi>\n      L\n     </mi>\n    </mrow>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mi>\n      t\n     </mi>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      10\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      24\n     </mn>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    42\n   </mn>\n  </math>\n  «N m» ✓\n </p>\n <p>\n  Average force\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mi>\n     τ\n    </mi>\n    <mi>\n     R\n    </mi>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      42\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      15\n     </mn>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    2\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    8\n   </mn>\n  </math>\n  «N» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  No other forces than\n  <em>\n   F\n  </em>\n  provide the torque ✓\n </p>\n <p>\n  The thread unwinds without slipping ✓\n </p>\n <p>\n  The thread is weightless ✓\n </p>\n <p>\n  <em>\n   F\n  </em>\n  is always tangent to the flywheel ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-4-rigid-body-mechanics"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.8",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate:\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   the angular acceleration of the ring;\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   the angular velocity of the ring after a time of 5.0 s.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   the angular impulse delivered to the disc and to the ring during the first 5.0 s.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   the final kinetic energy of the disc and the ring.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    α\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mi>\n     τ\n    </mi>\n    <mi>\n     l\n    </mi>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      20\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      32\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <msup>\n      <mn>\n       25\n      </mn>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    10\n   </mn>\n  </math>\n  «rad s\n  <sup>\n   −2\n  </sup>\n  »  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    α\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mi>\n     τ\n    </mi>\n    <mi>\n     l\n    </mi>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      20\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      32\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <msup>\n      <mn>\n       25\n      </mn>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    10\n   </mn>\n  </math>\n  «rad s\n  <sup>\n   −2\n  </sup>\n  »  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    10\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    5\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    =\n   </mo>\n   <mn>\n    50\n   </mn>\n  </math>\n  «rad s\n  <sup>\n   −1\n  </sup>\n  »  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  The angular impulse is the product of torque and time ✓\n </p>\n <p>\n  Both factors are the same so the angular impulse is the same ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  The disc has a smaller moment of inertia «because its mass is distributed closer to the axis of rotation» ✓\n </p>\n <p>\n  From\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     E\n    </mi>\n    <mi>\n     k\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <msup>\n     <mi>\n      L\n     </mi>\n     <mn>\n      2\n     </mn>\n    </msup>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mi>\n      l\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  , the disc will achieve a greater kinetic energy «because\n  <em>\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     L\n    </mi>\n   </math>\n  </em>\n  is the same for both» ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-4-rigid-body-mechanics"
    ]
  },
  {
    "question_id": "EXE.2.HL.TZ0.9",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   For the propellor,\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     L\n    </mi>\n    <mo>\n     =\n    </mo>\n    <mn>\n     5\n    </mn>\n    <mo>\n     .\n    </mo>\n    <mn>\n     0\n    </mn>\n    <mtext>\n     cm\n    </mtext>\n   </math>\n   and\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     M\n    </mi>\n    <mo>\n     =\n    </mo>\n    <mn>\n     0\n    </mn>\n    <mo>\n     .\n    </mo>\n    <mn>\n     035\n    </mn>\n    <mo>\n    </mo>\n    <mtext>\n     kg\n    </mtext>\n   </math>\n   .\n  </p>\n  <p>\n   Calculate the moment of inertia of the propellor.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the angular impulse that acts on the propellor.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate, using your answer to (b)(i), the time taken by the propellor to attain this rotational speed.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State and explain the effect of the angular impulse on the body of the aeroplane.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    7\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    3\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      6\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n   </mo>\n   <msup>\n    <mtext>\n     kg m\n    </mtext>\n    <mn>\n     2\n    </mn>\n   </msup>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    7\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    3\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      6\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n   </mo>\n   <msup>\n    <mtext>\n     kg m\n    </mtext>\n    <mn>\n     2\n    </mn>\n   </msup>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  190 rev s\n  <sup>\n   −1\n  </sup>\n  = 1190 rad s\n  <sup>\n   −1\n  </sup>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    Δ\n   </mtext>\n   <mi>\n    L\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mtext>\n    Δ\n   </mtext>\n   <mfenced>\n    <mrow>\n     <mi>\n      I\n     </mi>\n     <mi>\n      ω\n     </mi>\n    </mrow>\n   </mfenced>\n   <mo>\n    =\n   </mo>\n   <mn>\n    7\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    3\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      6\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    1190\n   </mn>\n   <mo>\n    =\n   </mo>\n   <mn>\n    8\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    7\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      3\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n   </mo>\n   <msup>\n    <mtext>\n     kg m\n    </mtext>\n    <mn>\n     2\n    </mn>\n   </msup>\n   <mo>\n   </mo>\n   <msup>\n    <mi>\n     s\n    </mi>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      1\n     </mn>\n    </mrow>\n   </msup>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    Δ\n   </mtext>\n   <mi>\n    t\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mi>\n      L\n     </mi>\n    </mrow>\n    <mi>\n     τ\n    </mi>\n   </mfrac>\n  </math>\n  used ✓\n </p>\n <p>\n  0.25 s ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  As the motor is internal, angular momentum is conserved (ignoring the torques due to resistive forces) ✓\n </p>\n <p>\n  The body of the plane will (try to) rotate in the opposite direction to the propellor ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-4-rigid-body-mechanics"
    ]
  },
  {
    "question_id": "EXE.2.SL.TZ0.10",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the pressure of the gas in the container.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the mass of the gas in the container.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the average translational speed of the gas particles.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (d)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The temperature of the gas in the container is increased.\n  </p>\n  <p>\n   Explain, using the kinetic theory, how this change leads to a change in pressure in the container.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [4]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    p\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi>\n      n\n     </mi>\n     <mi>\n      R\n     </mi>\n     <mi>\n      T\n     </mi>\n    </mrow>\n    <mi>\n     V\n    </mi>\n   </mfrac>\n  </math>\n  seen\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    12\n   </mn>\n   <mo>\n   </mo>\n   <mtext>\n    kPa\n   </mtext>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    p\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi>\n      n\n     </mi>\n     <mi>\n      R\n     </mi>\n     <mi>\n      T\n     </mi>\n    </mrow>\n    <mi>\n     V\n    </mi>\n   </mfrac>\n  </math>\n  seen\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    12\n   </mn>\n   <mo>\n   </mo>\n   <mtext>\n    kPa\n   </mtext>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    6\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    4\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      2\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n   </mo>\n   <mtext>\n    kg\n   </mtext>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    v\n   </mi>\n   <mo>\n    =\n   </mo>\n   <msqrt>\n    <mfrac>\n     <mrow>\n      <mn>\n       3\n      </mn>\n      <mi>\n       P\n      </mi>\n      <mi>\n       V\n      </mi>\n     </mrow>\n     <mi>\n      M\n     </mi>\n    </mfrac>\n   </msqrt>\n   <mo>\n    =\n   </mo>\n   <mn>\n    450\n   </mn>\n   <mo>\n   </mo>\n   <msup>\n    <mtext>\n     m s\n    </mtext>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      1\n     </mn>\n    </mrow>\n   </msup>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  increased temperature means increased average KE and hence increased average translational speed ✓\n </p>\n <p>\n  This increases the momentum transfer at the walls for each collision /\n  <em>\n   mv\n  </em>\n  is greater per collision ✓\n </p>\n <p>\n  This increases the frequency of collisions at the walls / particles cover the distance between walls more quickly ✓\n </p>\n <p>\n  Ideas that\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     F\n    </mi>\n    <mtext>\n     wall\n    </mtext>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mi>\n      p\n     </mi>\n    </mrow>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mi>\n      t\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  AND\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    P\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mi>\n     F\n    </mi>\n    <mi>\n     A\n    </mi>\n   </mfrac>\n  </math>\n  (can be in words) so that force increases and pressure\n  <span style=\"text-decoration:underline;\">\n   increases\n  </span>\n  ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-3-gas-laws"
    ]
  },
  {
    "question_id": "EXE.2.SL.TZ0.11",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   A comet orbits the Sun in an elliptical orbit. A and B are two positions of the comet.\n  </p>\n  <p style=\"text-align:center;\">\n   <img src=\"data:image/png;base64,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\"/>\n  </p>\n  <p style=\"text-align:left;\">\n   Explain, with reference to Kepler’s second law of planetary motion, the change in the kinetic energy of the comet as it moves from A to B.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   An asteroid (minor planet) orbits the Sun in a circular orbit of radius 4.5 × 10\n   <sup>\n    8\n   </sup>\n   km. The radius of Earth’s orbit is 1.5 × 10\n   <sup>\n    8\n   </sup>\n   km. Calculate, in years, the orbital period of the asteroid.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  The areas swept out in unit time by the Sun-comet line are the same at A and B ✓\n </p>\n <p>\n  At B, the distance is greater hence the orbital speed/distance moved in unit time is lower «so that the area remains the same» ✓\n </p>\n <p>\n  A decrease in speed means that the kinetic energy also decreases ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  The areas swept out in unit time by the Sun-comet line are the same at A and B ✓\n </p>\n <p>\n  At B, the distance is greater hence the orbital speed/distance moved in unit time is lower «so that the area remains the same» ✓\n </p>\n <p>\n  A decrease in speed means that the kinetic energy also decreases ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  An attempt to use Kepler’s 3\n  <sup>\n   rd\n  </sup>\n  law, e.g.,\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msup>\n    <mfenced>\n     <mfrac>\n      <mi>\n       T\n      </mi>\n      <mn>\n       1\n      </mn>\n     </mfrac>\n    </mfenced>\n    <mn>\n     2\n    </mn>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <msup>\n    <mfenced>\n     <mfrac>\n      <mrow>\n       <mn>\n        4\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        5\n       </mn>\n      </mrow>\n      <mrow>\n       <mn>\n        1\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        5\n       </mn>\n      </mrow>\n     </mfrac>\n    </mfenced>\n    <mn>\n     3\n    </mn>\n   </msup>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    T\n   </mi>\n   <mo>\n    =\n   </mo>\n  </math>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msup>\n    <mfenced>\n     <mfrac>\n      <mrow>\n       <mn>\n        4\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        5\n       </mn>\n      </mrow>\n      <mrow>\n       <mn>\n        1\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        5\n       </mn>\n      </mrow>\n     </mfrac>\n    </mfenced>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      5\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n    =\n   </mo>\n  </math>\n  » 5.2 «years» ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "d-fields"
    ],
    "subtopics": [
      "d-1-gravitational-fields"
    ]
  },
  {
    "question_id": "EXE.2.SL.TZ0.12",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     k\n    </mi>\n    <mo>\n     =\n    </mo>\n    <mfrac>\n     <mn>\n      1\n     </mn>\n     <mrow>\n      <mi>\n       G\n      </mi>\n      <mi>\n       M\n      </mi>\n     </mrow>\n    </mfrac>\n   </math>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p style=\"text-align:left;\">\n   The table gives data relating to the two moons of Mars.\n  </p>\n  <p style=\"text-align:left;\">\n  </p>\n  <table border=\"1\" style=\"height:68px;margin-left:auto;margin-right:auto;\" width=\"245\">\n   <tbody>\n    <tr>\n     <td style=\"width:74.8295px;text-align:center;\">\n      Moon\n     </td>\n     <td style=\"width:74.8295px;text-align:center;\">\n      <em>\n       T\n      </em>\n      / hour\n     </td>\n     <td style=\"width:74.8295px;text-align:center;\">\n      <em>\n       r\n      </em>\n      / Mm\n     </td>\n    </tr>\n    <tr>\n     <td style=\"width:74.8295px;\">\n      Phobos\n     </td>\n     <td style=\"width:74.8295px;text-align:center;\">\n      7.66\n     </td>\n     <td style=\"width:74.8295px;text-align:center;\">\n      9.38\n     </td>\n    </tr>\n    <tr>\n     <td style=\"width:74.8295px;\">\n      Deimos\n     </td>\n     <td style=\"width:74.8295px;text-align:center;\">\n      30.4\n     </td>\n     <td style=\"width:74.8295px;text-align:center;\">\n      -\n     </td>\n    </tr>\n   </tbody>\n  </table>\n  <p>\n  </p>\n  <p>\n   Determine\n   <em>\n    r\n   </em>\n   for Deimos.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the mass of Mars.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Equates centripetal force (with Newton’s law of gravitation\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    m\n   </mi>\n   <mi>\n    r\n   </mi>\n   <mo>\n   </mo>\n   <msup>\n    <mi>\n     ω\n    </mi>\n    <mn>\n     2\n    </mn>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi>\n      G\n     </mi>\n     <mi>\n      M\n     </mi>\n     <mi>\n      m\n     </mi>\n    </mrow>\n    <msup>\n     <mi>\n      r\n     </mi>\n     <mn>\n      2\n     </mn>\n    </msup>\n   </mfrac>\n  </math>\n  )\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    T\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mi mathvariant=\"normal\">\n      π\n     </mi>\n    </mrow>\n    <mi>\n     ω\n    </mi>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <br/>\n  Uses both equation correctly with clear re-arrangement ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Equates centripetal force (with Newton’s law of gravitation\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    m\n   </mi>\n   <mi>\n    r\n   </mi>\n   <mo>\n   </mo>\n   <msup>\n    <mi>\n     ω\n    </mi>\n    <mn>\n     2\n    </mn>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi>\n      G\n     </mi>\n     <mi>\n      M\n     </mi>\n     <mi>\n      m\n     </mi>\n    </mrow>\n    <msup>\n     <mi>\n      r\n     </mi>\n     <mn>\n      2\n     </mn>\n    </msup>\n   </mfrac>\n  </math>\n  )\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    T\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mi mathvariant=\"normal\">\n      π\n     </mi>\n    </mrow>\n    <mi>\n     ω\n    </mi>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <br/>\n  Uses both equation correctly with clear re-arrangement ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msubsup>\n    <mi>\n     r\n    </mi>\n    <mtext>\n     De\n    </mtext>\n    <mn>\n     3\n    </mn>\n   </msubsup>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <msubsup>\n      <mi>\n       T\n      </mi>\n      <mtext>\n       De\n      </mtext>\n      <mn>\n       2\n      </mn>\n     </msubsup>\n     <msubsup>\n      <mi>\n       r\n      </mi>\n      <mtext>\n       Ph\n      </mtext>\n      <mn>\n       3\n      </mn>\n     </msubsup>\n    </mrow>\n    <msubsup>\n     <mi>\n      T\n     </mi>\n     <mtext>\n      Ph\n     </mtext>\n     <mn>\n      2\n     </mn>\n    </msubsup>\n   </mfrac>\n  </math>\n  seen or correct substitution ✓\n </p>\n <p>\n  23.5 Mm ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  Converts\n  <em>\n   T\n  </em>\n  to 27.6 ks\n  <strong>\n   and\n  </strong>\n  converts to m from Mm ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    k\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    7\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    33\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      14\n     </mn>\n    </mrow>\n   </msup>\n  </math>\n  «s\n  <sup>\n   2\n  </sup>\n  m\n  <sup>\n   −3\n  </sup>\n  » ✓\n </p>\n <p>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    M\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mrow>\n     <mi>\n      k\n     </mi>\n     <mi>\n      G\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  »\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    2\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    04\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     23\n    </mn>\n   </msup>\n  </math>\n  «kg» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   MP1 can be implicit\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "d-fields"
    ],
    "subtopics": [
      "d-1-gravitational-fields"
    ]
  },
  {
    "question_id": "EXE.2.SL.TZ0.13",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     T\n    </mi>\n    <mo>\n     ∝\n    </mo>\n    <msup>\n     <mi>\n      r\n     </mi>\n     <mfrac>\n      <mn>\n       3\n      </mn>\n      <mn>\n       2\n      </mn>\n     </mfrac>\n    </msup>\n   </math>\n   for the planets in a solar system where\n   <em>\n    <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mi>\n      T\n     </mi>\n    </math>\n   </em>\n   is the orbital period of a planet and\n   <em>\n    <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mi>\n      r\n     </mi>\n    </math>\n   </em>\n   is the radius of circular orbit of planet about its sun.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline what is meant by one astronomical unit (1 AU)\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Pluto is a dwarf planet of the Sun that orbits at a distance of 5.9 × 10\n   <sup>\n    9\n   </sup>\n   km from the Sun. Determine, in years, the orbital period of Pluto.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Equates centripetal force (with Newton’s law gravitation\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    m\n   </mi>\n   <mi>\n    r\n   </mi>\n   <mo>\n   </mo>\n   <msup>\n    <mi>\n     ω\n    </mi>\n    <mn>\n     2\n    </mn>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi>\n      G\n     </mi>\n     <mi>\n      M\n     </mi>\n     <mi>\n      m\n     </mi>\n    </mrow>\n    <msup>\n     <mi>\n      r\n     </mi>\n     <mn>\n      2\n     </mn>\n    </msup>\n   </mfrac>\n  </math>\n  )\n </p>\n <p>\n  AND\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    T\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mi mathvariant=\"normal\">\n      π\n     </mi>\n    </mrow>\n    <mi>\n     ω\n    </mi>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  leads to\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msup>\n    <mi>\n     T\n    </mi>\n    <mn>\n     2\n    </mn>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <msup>\n    <mi>\n     r\n    </mi>\n    <mn>\n     3\n    </mn>\n   </msup>\n   <mo>\n    ×\n   </mo>\n   <mfenced>\n    <mfrac>\n     <mrow>\n      <mn>\n       4\n      </mn>\n      <msup>\n       <mi mathvariant=\"normal\">\n        π\n       </mi>\n       <mn>\n        2\n       </mn>\n      </msup>\n     </mrow>\n     <mrow>\n      <mi>\n       G\n      </mi>\n      <mi>\n       M\n      </mi>\n     </mrow>\n    </mfrac>\n   </mfenced>\n  </math>\n  hence result ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Equates centripetal force (with Newton’s law gravitation\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    m\n   </mi>\n   <mi>\n    r\n   </mi>\n   <mo>\n   </mo>\n   <msup>\n    <mi>\n     ω\n    </mi>\n    <mn>\n     2\n    </mn>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mi>\n      G\n     </mi>\n     <mi>\n      M\n     </mi>\n     <mi>\n      m\n     </mi>\n    </mrow>\n    <msup>\n     <mi>\n      r\n     </mi>\n     <mn>\n      2\n     </mn>\n    </msup>\n   </mfrac>\n  </math>\n  )\n </p>\n <p>\n  AND\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    T\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mi mathvariant=\"normal\">\n      π\n     </mi>\n    </mrow>\n    <mi>\n     ω\n    </mi>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  leads to\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msup>\n    <mi>\n     T\n    </mi>\n    <mn>\n     2\n    </mn>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <msup>\n    <mi>\n     r\n    </mi>\n    <mn>\n     3\n    </mn>\n   </msup>\n   <mo>\n    ×\n   </mo>\n   <mfenced>\n    <mfrac>\n     <mrow>\n      <mn>\n       4\n      </mn>\n      <msup>\n       <mi mathvariant=\"normal\">\n        π\n       </mi>\n       <mn>\n        2\n       </mn>\n      </msup>\n     </mrow>\n     <mrow>\n      <mi>\n       G\n      </mi>\n      <mi>\n       M\n      </mi>\n     </mrow>\n    </mfrac>\n   </mfenced>\n  </math>\n  hence result ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  «mean» Distance from centre of Sun to centre of Earth ✓\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  Suitable ratio in terms of parsec and arcsecond ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msubsup>\n    <mi>\n     T\n    </mi>\n    <mtext>\n     Pluto\n    </mtext>\n    <mn>\n     2\n    </mn>\n   </msubsup>\n   <mo>\n    =\n   </mo>\n   <msubsup>\n    <mi>\n     T\n    </mi>\n    <mtext>\n     Earth\n    </mtext>\n    <mn>\n     2\n    </mn>\n   </msubsup>\n   <mfrac>\n    <msubsup>\n     <mi>\n      r\n     </mi>\n     <mtext>\n      Pluto\n     </mtext>\n     <mn>\n      3\n     </mn>\n    </msubsup>\n    <msubsup>\n     <mi>\n      r\n     </mi>\n     <mtext>\n      Earth\n     </mtext>\n     <mn>\n      3\n     </mn>\n    </msubsup>\n   </mfrac>\n  </math>\n  used ✓\n </p>\n <p>\n  Earth orbital radius = 1.5 × 10\n  <sup>\n   11\n  </sup>\n  m (from AU)\n  <strong>\n   AND\n  </strong>\n  uses 1 earth year (in any units) ✓\n </p>\n <p>\n  247 years ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "d-fields"
    ],
    "subtopics": [
      "d-1-gravitational-fields"
    ]
  },
  {
    "question_id": "EXE.2.SL.TZ0.14",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State and explain the magnitude of the force on a length of 0.50 m of wire Q due to the current in P.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the current in wire Q.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the direction of the current in R, relative to the current in P.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Deduce the current in R.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  From Newton’s third law, the force on a length of Q is equal but opposite to the force on the same length of P ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    2\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      5\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n   </mo>\n   <mtext>\n    N\n   </mtext>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  From Newton’s third law, the force on a length of Q is equal but opposite to the force on the same length of P ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    2\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      5\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n   </mo>\n   <mtext>\n    N\n   </mtext>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        5\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      50\n     </mn>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      4\n     </mn>\n     <mi mathvariant=\"normal\">\n      π\n     </mi>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        7\n       </mn>\n      </mrow>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      5\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msub>\n      <mi>\n       I\n      </mi>\n      <mi>\n       Q\n      </mi>\n     </msub>\n    </mrow>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mi mathvariant=\"normal\">\n      π\n     </mi>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      10\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     I\n    </mi>\n    <mi>\n     Q\n    </mi>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mn>\n    4\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n  </math>\n  «A» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  Opposite ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  The force on Q due to R must have the same magnitude «but opposite direction» as the force on Q due to P ✓\n </p>\n <p>\n  The distance is halved therefore one half of the current is needed to produce the same force, so 2.5 A ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "d-fields"
    ],
    "subtopics": [
      "d-3-motion-in-electromagnetic-fields"
    ]
  },
  {
    "question_id": "EXE.2.SL.TZ0.15",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the fundamental SI units for permeability of free space,\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <msub>\n     <mi>\n      μ\n     </mi>\n     <mn>\n      0\n     </mn>\n    </msub>\n   </math>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   magnetic field at A;\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   magnetic force on section AB of the loop.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   magnitude of the net force acting on the loop;\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   direction of the net force acting on the loop.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  kg m s\n  <sup>\n   −2\n  </sup>\n  A\n  <sup>\n   −2\n  </sup>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  kg m s\n  <sup>\n   −2\n  </sup>\n  A\n  <sup>\n   −2\n  </sup>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  Into the page ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  Repulsive / to the right ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfenced>\n    <mrow>\n     <mfrac>\n      <mrow>\n       <mn>\n        4\n       </mn>\n       <mi mathvariant=\"normal\">\n        π\n       </mi>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mrow>\n         <mo>\n          -\n         </mo>\n         <mn>\n          7\n         </mn>\n        </mrow>\n       </msup>\n       <mo>\n        ×\n       </mo>\n       <mn>\n        2\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        0\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <mn>\n        1\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        0\n       </mn>\n      </mrow>\n      <mrow>\n       <mn>\n        2\n       </mn>\n       <mi mathvariant=\"normal\">\n        π\n       </mi>\n       <mo>\n        ×\n       </mo>\n       <mn>\n        0\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        30\n       </mn>\n      </mrow>\n     </mfrac>\n     <mo>\n      -\n     </mo>\n     <mfrac>\n      <mrow>\n       <mn>\n        4\n       </mn>\n       <mi mathvariant=\"normal\">\n        π\n       </mi>\n       <mo>\n        ×\n       </mo>\n       <msup>\n        <mn>\n         10\n        </mn>\n        <mrow>\n         <mo>\n          -\n         </mo>\n         <mn>\n          7\n         </mn>\n        </mrow>\n       </msup>\n       <mo>\n        ×\n       </mo>\n       <mn>\n        2\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        0\n       </mn>\n       <mo>\n        ×\n       </mo>\n       <mn>\n        1\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        0\n       </mn>\n      </mrow>\n      <mrow>\n       <mn>\n        2\n       </mn>\n       <mi mathvariant=\"normal\">\n        π\n       </mi>\n       <mo>\n        ×\n       </mo>\n       <mn>\n        0\n       </mn>\n       <mo>\n        .\n       </mo>\n       <mn>\n        50\n       </mn>\n      </mrow>\n     </mfrac>\n    </mrow>\n   </mfenced>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    20\n   </mn>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      7\n     </mn>\n    </mrow>\n   </msup>\n  </math>\n  «N»  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  Repulsive / to the right ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "d-fields"
    ],
    "subtopics": [
      "d-3-motion-in-electromagnetic-fields"
    ]
  },
  {
    "question_id": "EXE.2.SL.TZ0.16",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the magnetic force acting on the 15 Ω wire due to the current in the 30 Ω wire.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [4]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The magnetic field strength of Earth’s field at the location of the wires is 45 μT.\n  </p>\n  <p>\n   Discuss the assumption made in this question.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Use of combination of resistors OR\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    V\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mi>\n    I\n   </mi>\n   <mi>\n    R\n   </mi>\n  </math>\n  ✓\n </p>\n <p>\n  To show that current in 30 Ω wire is 5.0 A ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mi>\n     F\n    </mi>\n    <mi>\n     I\n    </mi>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        7\n       </mn>\n      </mrow>\n     </msup>\n     <msub>\n      <mi>\n       I\n      </mi>\n      <mn>\n       15\n      </mn>\n     </msub>\n     <msub>\n      <mi>\n       I\n      </mi>\n      <mn>\n       30\n      </mn>\n     </msub>\n    </mrow>\n    <mi>\n     r\n    </mi>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        7\n       </mn>\n      </mrow>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      10\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      5\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      20\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfenced>\n    <mrow>\n     <mi>\n      F\n     </mi>\n     <mo>\n      =\n     </mo>\n     <mn>\n      5\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        5\n       </mn>\n      </mrow>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      25\n     </mn>\n     <mo>\n      =\n     </mo>\n    </mrow>\n   </mfenced>\n   <mo>\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    3\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      5\n     </mn>\n    </mrow>\n   </msup>\n  </math>\n  N ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Use of combination of resistors OR\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    V\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mi>\n    I\n   </mi>\n   <mi>\n    R\n   </mi>\n  </math>\n  ✓\n </p>\n <p>\n  To show that current in 30 Ω wire is 5.0 A ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mi>\n     F\n    </mi>\n    <mi>\n     I\n    </mi>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        7\n       </mn>\n      </mrow>\n     </msup>\n     <msub>\n      <mi>\n       I\n      </mi>\n      <mn>\n       15\n      </mn>\n     </msub>\n     <msub>\n      <mi>\n       I\n      </mi>\n      <mn>\n       30\n      </mn>\n     </msub>\n    </mrow>\n    <mi>\n     r\n    </mi>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        7\n       </mn>\n      </mrow>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      10\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      5\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      20\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfenced>\n    <mrow>\n     <mi>\n      F\n     </mi>\n     <mo>\n      =\n     </mo>\n     <mn>\n      5\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        5\n       </mn>\n      </mrow>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      25\n     </mn>\n     <mo>\n      =\n     </mo>\n    </mrow>\n   </mfenced>\n   <mo>\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    3\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      5\n     </mn>\n    </mrow>\n   </msup>\n  </math>\n  N ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  Use of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    F\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mi>\n    B\n   </mi>\n   <mi>\n    I\n   </mi>\n   <mi>\n    l\n   </mi>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    45\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      6\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    10\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    25\n   </mn>\n   <mo>\n    =\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    15\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      4\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n   </mo>\n   <mtext>\n    N\n   </mtext>\n  </math>\n  ✓\n </p>\n <p>\n  Concludes that the assumption is not valid ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "d-fields"
    ],
    "subtopics": [
      "d-3-motion-in-electromagnetic-fields"
    ]
  },
  {
    "question_id": "EXE.2.SL.TZ0.17",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Draw the magnetic field lines due to A.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Draw the magnetic field lines due to A.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State and explain, using your diagram, why a force acts on B due to A in the plane of the paper.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Both wires are 7.5 m long and are 0.25 m apart. The current in both wires is 12 A. Determine the force that acts on one wire due to the other.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a.i)\n </div><div class=\"card-body\">\n <p>\n  At least one circle centred on centre of wire A\n  <br/>\n  <strong>\n   <em>\n    AND\n    <br/>\n   </em>\n  </strong>\n  indication of clockwise direction ✓\n </p>\n <p>\n  More than 2 circles with increasing separation between circles from centre outwards (by eye) ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  At least one circle centred on centre of wire A\n  <br/>\n  <strong>\n   <em>\n    AND\n    <br/>\n   </em>\n  </strong>\n  indication of clockwise direction ✓\n </p>\n <p>\n  More than 2 circles with increasing separation between circles from centre outwards (by eye) ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  B lies in magnetic field of A OWTTE ✓\n </p>\n <p>\n  Explained use of appropriate rule together with drawn indication of rule operating in this case ✓\n </p>\n <p>\n  To show that force on B is to left and in plane of paper ✓\n  <br/>\n  <em>\n   <strong>\n    OR\n    <br/>\n   </strong>\n  </em>\n  Magnetic field lines of B merge with those of A to give combined field line pattern ✓\n </p>\n <p>\n  Sketch of combined pattern to show null point somewhere on line between wires. ✓\n </p>\n <p>\n  Wires will move to reduce stored energy and this is achieved by moving together so force on B is to left ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mi>\n     F\n    </mi>\n    <mi>\n     l\n    </mi>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        7\n       </mn>\n      </mrow>\n     </msup>\n     <msub>\n      <mi>\n       I\n      </mi>\n      <mtext>\n       A\n      </mtext>\n     </msub>\n     <msub>\n      <mi>\n       I\n      </mi>\n      <mtext>\n       B\n      </mtext>\n     </msub>\n    </mrow>\n    <mi>\n     r\n    </mi>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        7\n       </mn>\n      </mrow>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       12\n      </mn>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      25\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    8\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    6\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      4\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n   </mo>\n   <mtext>\n    N\n   </mtext>\n  </math>\n  ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "d-fields"
    ],
    "subtopics": [
      "d-3-motion-in-electromagnetic-fields"
    ]
  },
  {
    "question_id": "EXE.2.SL.TZ0.18",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline, with reference to the decay equation above, the role of chain reactions in the operation of a nuclear power station.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate, in MeV, the energy released in the reaction.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Two nuclides present in spent nuclear fuel\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mmultiscripts>\n     <mtext>\n      Cs\n     </mtext>\n     <mprescripts>\n     </mprescripts>\n     <mn>\n      55\n     </mn>\n     <mn>\n      137\n     </mn>\n    </mmultiscripts>\n   </math>\n   are  and cerium-144 (\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mmultiscripts>\n     <mtext>\n      Ce\n     </mtext>\n     <mprescripts>\n     </mprescripts>\n     <mn>\n      58\n     </mn>\n     <mn>\n      144\n     </mn>\n    </mmultiscripts>\n   </math>\n   ). The initial activity of a sample of pure\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mmultiscripts>\n     <mtext>\n      Ce\n     </mtext>\n     <mprescripts>\n     </mprescripts>\n     <mn>\n      58\n     </mn>\n     <mn>\n      144\n     </mn>\n    </mmultiscripts>\n   </math>\n   is about 40 times greater than the activity of the same amount of pure\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mmultiscripts>\n     <mtext>\n      Cs\n     </mtext>\n     <mprescripts>\n     </mprescripts>\n     <mn>\n      55\n     </mn>\n     <mn>\n      137\n     </mn>\n    </mmultiscripts>\n   </math>\n   .\n  </p>\n  <p>\n   Discuss which of the two nuclides is more likely to require long-term storage once removed from the reactor.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  The four neutrons released in the reaction may initiate further fissions ✓\n </p>\n <p>\n  «If sufficient U-235 is available,» the reaction is self-sustained ✓\n </p>\n <p>\n  Allowing for the continuous production of energy ✓\n </p>\n <p>\n  The number of neutrons available is controlled with control rods «to maintain the desired reaction rate» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  The four neutrons released in the reaction may initiate further fissions ✓\n </p>\n <p>\n  «If sufficient U-235 is available,» the reaction is self-sustained ✓\n </p>\n <p>\n  Allowing for the continuous production of energy ✓\n </p>\n <p>\n  The number of neutrons available is controlled with control rods «to maintain the desired reaction rate» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    137\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    8\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    389\n   </mn>\n   <mo>\n    +\n   </mo>\n   <mn>\n    95\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    8\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    460\n   </mn>\n   <mo>\n    -\n   </mo>\n   <mn>\n    235\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    7\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    591\n   </mn>\n  </math>\n  ✓\n </p>\n <p>\n  169 «MeV» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  «For the same number of nuclei,» the activity is inversely related to half-life ✓\n </p>\n <p>\n  Thus\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mmultiscripts>\n    <mtext>\n     Cs\n    </mtext>\n    <mprescripts>\n    </mprescripts>\n    <mn>\n     55\n    </mn>\n    <mn>\n     137\n    </mn>\n   </mmultiscripts>\n  </math>\n  has a longer half-life and will likely require longer storage ✓\n </p>\n <p>\n  Half-lives of their decay products need also be considered when planning storage ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "e-3-radioactive-decay",
      "e-4-fission"
    ]
  },
  {
    "question_id": "EXE.2.SL.TZ0.19",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Compare and contrast spontaneous and neutron-induced nuclear fission.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Every neutron-induced fission reaction of uranium-235 releases an energy of about 200 MeV. A nuclear power station transfers an energy of about 2.4 GJ per second.\n  </p>\n  <p>\n   Determine the mass of uranium-235 that undergoes fission in one day in this power station.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State\n   <strong>\n    two\n   </strong>\n   properties of the products of nuclear fission due to which the spent nuclear fuel needs to be kept safe.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Spontaneous fission occurs with no external influence, neutron-induced fission requires an interaction with a neutron «of appropriate energy» ✓\n </p>\n <p>\n  Both result in the release of energy\n  <br/>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <br/>\n  both have a large number of possible pairs of products ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Spontaneous fission occurs with no external influence, neutron-induced fission requires an interaction with a neutron «of appropriate energy» ✓\n </p>\n <p>\n  Both result in the release of energy\n  <br/>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <br/>\n  both have a large number of possible pairs of products ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  Fissions per day\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      4\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       9\n      </mn>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      60\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      60\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      24\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      200\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       6\n      </mn>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      6\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        19\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n   </mfrac>\n  </math>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    6\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    5\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     24\n    </mn>\n   </msup>\n  </math>\n  » ✓\n </p>\n <p>\n  Mass of uranium\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      6\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      5\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       24\n      </mn>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      6\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      05\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       23\n      </mn>\n     </msup>\n    </mrow>\n   </mfrac>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    235\n   </mn>\n  </math>\n  ✓\n </p>\n <p>\n  2.5 «kg» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  Have relatively short half-lives / high activity ✓\n </p>\n <p>\n  Their decay products are «usually» also radioactive ✓\n </p>\n <p>\n  Volatile / chemically active ✓\n </p>\n <p>\n  Biologically active / easily absorbed by living matter ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "e-3-radioactive-decay",
      "e-4-fission"
    ]
  },
  {
    "question_id": "EXE.2.SL.TZ0.2",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   A tram is just leaving the lower railway station.\n  </p>\n  <p>\n   Determine, as the train leaves the lower station,\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   the pd across the motor of the tram,\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   the mechanical power output of the motor.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Discuss the variation in the power output of the motor with distance from the lower station.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The total friction in the system acting on the tram is equivalent to an opposing force of 750 N.\n  </p>\n  <p>\n   For one particular journey, the tram is full of passengers.\n  </p>\n  <p>\n   Estimate the maximum speed\n   <em>\n    v\n   </em>\n   of the tram as it leaves the lower station.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [4]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (d)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The tram travels at\n   <em>\n    v\n   </em>\n   throughout the journey. Two trams are available so that one is returning to the lower station on another line while the other is travelling to the village. The journeys take the same time.\n  </p>\n  <p>\n   It takes 1.5 minutes to unload and 1.5 minutes to load each tram. Ignore the time taken to accelerate the tram at the beginning and end of the journey.\n  </p>\n  <p>\n   Estimate the maximum number of passengers that can be carried up to the village in one hour.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [4]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (e)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   There are eight wheels on each tram with a brake system for each wheel. A pair of brake pads clamp firmly onto an annulus made of steel.\n  </p>\n  <p>\n   The train comes to rest from speed\n   <em>\n    v\n   </em>\n   . Ignore the energy transferred to the brake pads and the change in the gravitational potential energy of the tram during the braking.\n  </p>\n  <p>\n   Calculate the temperature change in each steel annulus as the tram comes to rest.\n  </p>\n  <p>\n   Data for this question\n  </p>\n  <p style=\"padding-left:60px;\">\n   The inner radius of the annulus is 0.40 m and the outer radius is 0.50 m.\n  </p>\n  <p style=\"padding-left:60px;\">\n   The thickness of the annulus is 25 mm.\n  </p>\n  <p style=\"padding-left:60px;\">\n   The density of the steel is 7860 kg m\n   <sup>\n    −3\n   </sup>\n  </p>\n  <p style=\"padding-left:60px;\">\n   The specific heat capacity of the steel is 420 J kg\n   <sup>\n    −1\n   </sup>\n   K\n   <sup>\n    −1\n   </sup>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [4]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (f)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The speed of the tram is measured by detecting a beam of microwaves of wavelength 2.8 cm reflected from the rear of the tram as it moves away from the station. Predict the change in wavelength of the microwaves at the stationary microwave detector in the station.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Resistance of cable = 0.072 Ω ✓\n </p>\n <p>\n  Pd is (500 − 0.072 × 600) = 457 V ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  Resistance of cable = 0.072 Ω ✓\n </p>\n <p>\n  Pd is (500 − 0.072 × 600) = 457 V ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  Power input = 457 × 600 = 274 kW ✓\n </p>\n <p>\n  Power output = 0.9 × 274 = 247 kW ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  The pd across the motor increases as the tram travels up the track ✓\n </p>\n <p>\n  (As the current is constant), the power output also rises ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  Total weight of tram = 75 × 710 + 5 × 10\n  <sup>\n   4\n  </sup>\n  = 1.03 × 10\n  <sup>\n   5\n  </sup>\n  N ✓\n </p>\n <p>\n  Total force down track = 750 + 1.03 × 10\n  <sup>\n   5\n  </sup>\n  sin (10) = 1.87 × 10\n  <sup>\n   4\n  </sup>\n  N ✓\n </p>\n <p>\n  Use of\n  <em>\n   P\n  </em>\n  =\n  <em>\n   F ×\n  </em>\n  <em>\n   v ✓\n  </em>\n </p>\n <p>\n  (\n  <em>\n   v\n  </em>\n  = 247 000 ÷ 1.87 × 10\n  <sup>\n   4\n  </sup>\n  )= 13 m s\n  <sup>\n   −1\n  </sup>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  Time for run =\n  <em>\n   s/v\n  </em>\n  = 3000 ÷ 13.2 = 227 s ✓\n </p>\n <p>\n  3 minutes loading = 180 s\n </p>\n <p>\n  So one trip = 407 s ✓\n </p>\n <p>\n  And there are 3600/407 trips per hour = 8.84 ✓\n </p>\n <p>\n  So 8\n  <em>\n   complete\n  </em>\n  trips with 75 = 600 passengers ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (e)\n </div><div class=\"card-body\">\n <p>\n  Work leading to volume = 7.1 x 10\n  <sup>\n   −3\n  </sup>\n  m\n  <sup>\n   3\n  </sup>\n  ✓\n </p>\n <p>\n  Work leading to mass of steel = 55 .8 kg ✓\n </p>\n <p>\n  Kinetic Energy transferred per annulus =\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mstyle displaystyle=\"true\">\n      <mfrac>\n       <mn>\n        1\n       </mn>\n       <mn>\n        2\n       </mn>\n      </mfrac>\n     </mstyle>\n     <mi>\n      m\n     </mi>\n     <msup>\n      <mi>\n       v\n      </mi>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </mrow>\n    <mn>\n     8\n    </mn>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     16\n    </mn>\n   </mfrac>\n   <mo>\n    ×\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      03\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       5\n      </mn>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      9\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      81\n     </mn>\n    </mrow>\n   </mfrac>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     13\n    </mn>\n    <mn>\n     2\n    </mn>\n   </msup>\n  </math>\n </p>\n <p>\n  = 110 kJ ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mtext>\n    Δ\n   </mtext>\n   <mi>\n    T\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <msub>\n     <mi>\n      E\n     </mi>\n     <mtext>\n      k\n     </mtext>\n    </msub>\n    <mrow>\n     <mi>\n      m\n     </mi>\n     <mi>\n      c\n     </mi>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      1\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       5\n      </mn>\n     </msup>\n    </mrow>\n    <mrow>\n     <mn>\n      55\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      8\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      420\n     </mn>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    4\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    7\n   </mn>\n  </math>\n  K ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (f)\n </div><div class=\"card-body\">\n <p>\n  Use of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mi>\n      λ\n     </mi>\n    </mrow>\n    <mi>\n     λ\n    </mi>\n   </mfrac>\n   <mo>\n    ≈\n   </mo>\n   <mfrac>\n    <mi>\n     v\n    </mi>\n    <mi>\n     c\n    </mi>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  1.2 nm ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion",
      "b-the-particulate-nature-of-matter",
      "c-wave-behaviour"
    ],
    "subtopics": [
      "a-1-kinematics",
      "a-2-forces-and-momentum",
      "a-3-work-energy-and-power",
      "b-1-thermal-energy-transfers",
      "b-5-current-and-circuits",
      "c-5-doppler-effect"
    ]
  },
  {
    "question_id": "EXE.2.SL.TZ0.20",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State\n   <strong>\n    one\n   </strong>\n   source of the radioactive waste products from nuclear fission reactions.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline how this waste is treated after it has been removed from the fission reactor.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [4]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Fission fragments from the fuel rods\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n  activated materials in (e.g.) fuel rod casings\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n  nuclei formed by neutron activation from U-235\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n  stated products, e.g. Pu, U-236 etc. ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Fission fragments from the fuel rods\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n  activated materials in (e.g.) fuel rod casings\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n  nuclei formed by neutron activation from U-235\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n  stated products, e.g. Pu, U-236 etc. ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  Waste (fuel rod) is placed in cooling ponds for a number of years ✓\n </p>\n <p>\n  After most active products have decayed the uranium is separated to be recycled/reprocessed ✓\n </p>\n <p>\n  The remaining highly active waste is vitrified / made into a solid form ✓\n </p>\n <p>\n  And stored (deep) underground ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "e-4-fission"
    ]
  },
  {
    "question_id": "EXE.2.SL.TZ0.3",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate:\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   the initial temperature gradient through the base of the pot. State an appropriate unit for your answer.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   the initial rate, in kW, of thermal energy transfer by conduction through the base of the pot.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The electrical power rating of the hot plate is 1 kW. Comment, with reference to this value, on your answer in (a)(ii).\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Describe how thermal energy is distributed throughout the volume of the water in the pot.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      180\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mn>\n      10\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      005\n     </mn>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    3\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    4\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     4\n    </mn>\n   </msup>\n  </math>\n  ✓\n </p>\n <p>\n  K m\n  <sup>\n   −1\n  </sup>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      180\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mn>\n      10\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      005\n     </mn>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    3\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    4\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     4\n    </mn>\n   </msup>\n  </math>\n  ✓\n </p>\n <p>\n  K m\n  <sup>\n   −1\n  </sup>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  45 × 0.15 × 3.4 × 10\n  <sup>\n   4\n  </sup>\n  = 230 «kW» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  The answer is unrealistically large / impossible to sustain ✓\n </p>\n <p>\n  Due to much lower actual power, a lower temperature gradient through the base of the pot is quickly established ✓\n </p>\n <p>\n  The surface of the hot plate becomes colder from contact with pot\n  <br/>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <br/>\n  there is a temperature gradient also through the hot plate ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  By means of convection currents ✓\n </p>\n <p>\n  That arise due to density difference between hot and cold water ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-1-thermal-energy-transfers"
    ]
  },
  {
    "question_id": "EXE.2.SL.TZ0.4",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The temperature of the air outside of the bottle is 20 °C. The surface area of the bottle is 4.0 × 10\n   <sup>\n    −2\n   </sup>\n   m\n   <sup>\n    2\n   </sup>\n   . Calculate the initial rate of thermal energy transfer by conduction through the bottle.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Explain why the rate calculated in part (a) is decreasing.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Estimate the initial rate of the change of the temperature of the water in the bottle. State your answer in K s\n   <sup>\n    −1\n   </sup>\n   . The specific heat capacity of water is 4200 J kg\n   <sup>\n    −1\n   </sup>\n   K\n   <sup>\n    −1\n   </sup>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    90\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    4\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      2\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n    ×\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      60\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mn>\n      20\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      003\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  480 «W» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    90\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    4\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      2\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n    ×\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      60\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mn>\n      20\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      003\n     </mn>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  480 «W» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  The temperature gradient decreases as the water cools down ✓\n </p>\n <p>\n  The rate of energy transfer is proportional to the temperature gradient ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    480\n   </mn>\n   <mo>\n    =\n   </mo>\n   <mn>\n    4200\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    50\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mfrac>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mi>\n      T\n     </mi>\n    </mrow>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mi>\n      t\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mi>\n      T\n     </mi>\n    </mrow>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mi>\n      t\n     </mi>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    23\n   </mn>\n  </math>\n  «K s\n  <sup>\n   −1\n  </sup>\n  » ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-1-thermal-energy-transfers"
    ]
  },
  {
    "question_id": "EXE.2.SL.TZ0.5",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Discuss the mechanism that accounts for the greatest rate of energy transfer when:\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <em>\n    T\n   </em>\n   <sub>\n    t\n   </sub>\n   &gt;\n   <em>\n    T\n   </em>\n   <sub>\n    b\n   </sub>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <em>\n    T\n   </em>\n   <sub>\n    b\n   </sub>\n   &gt;\n   <em>\n    T\n   </em>\n   <sub>\n    t\n   </sub>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The liquid now freezes so that the vertical column is entirely of ice. Suggest how your answer to (a)(ii) will change.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  Conduction identified ✓\n </p>\n <p>\n  energy transfer through interaction of particles in liquid at atomic scale ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  Conduction identified ✓\n </p>\n <p>\n  energy transfer through interaction of particles in liquid at atomic scale ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  Convection identified ✓\n </p>\n <p>\n  energy transfer through movement of bodies of liquid at different densities ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  the solid cannot now move relative to material above it ✓\n </p>\n <p>\n  so conduction only ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-1-thermal-energy-transfers"
    ]
  },
  {
    "question_id": "EXE.2.SL.TZ0.6",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The side of the rod can be unlagged or ideally lagged. Explain the difference in energy transfer for these two cases.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the temperature at Y.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The temperatures are now reversed so that X is at 45 °C and Z is at 90 °C. Show that the rate of energy transfer is unchanged.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  When ideally lagged, no energy transfer can occur through the sides of the bar. ✓\n </p>\n <p>\n  All the power input/ energy input per second at one end will emerge at the other end. ✓\n </p>\n <p>\n  When unlagged, energy transfer occurs from the sides of the bar and the power /energy input per second at input &gt; the energy output per second at the other end. ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Max 1 if answer does not refer to rate of energy transfer in MP2 and MP3.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  When ideally lagged, no energy transfer can occur through the sides of the bar. ✓\n </p>\n <p>\n  All the power input/ energy input per second at one end will emerge at the other end. ✓\n </p>\n <p>\n  When unlagged, energy transfer occurs from the sides of the bar and the power /energy input per second at input &gt; the energy output per second at the other end. ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Max 1 if answer does not refer to rate of energy transfer in MP2 and MP3.\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  idea that\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mi>\n      d\n     </mi>\n     <mi>\n      Q\n     </mi>\n    </mrow>\n    <mrow>\n     <mi>\n      d\n     </mi>\n     <mi>\n      t\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  is same in both bars because lagged ✓\n </p>\n <p>\n  work to show that\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    90\n   </mn>\n   <mo>\n    -\n   </mo>\n   <mi>\n    θ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    2\n   </mn>\n   <mfenced>\n    <mrow>\n     <mi>\n      θ\n     </mi>\n     <mo>\n      -\n     </mo>\n     <mn>\n      45\n     </mn>\n    </mrow>\n   </mfenced>\n  </math>\n  <br/>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n  <br/>\n  Temperature difference across XY is twice temperature difference across YZ ✓\n </p>\n <p>\n  solves to show that\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    θ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    60\n   </mn>\n   <mo>\n   </mo>\n   <mo>\n    °\n   </mo>\n   <mtext>\n    C\n   </mtext>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  repeats calculation to show that\n  <em>\n   θ\n  </em>\n  = 75 °C ✓\n </p>\n <p>\n  temperature difference across YZ is still 15 K which gives the same rate of energy transfer (but in opposite direction) ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-1-thermal-energy-transfers"
    ]
  },
  {
    "question_id": "EXE.2.SL.TZ0.7",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State\n   <strong>\n    two\n   </strong>\n   assumptions of the kinetic model of an ideal gas that refer to intermolecular collisions.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Discuss how the motion of the molecules of a gas gives rise to pressure in the gas.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The average speed of the molecules of a gas is 500 m s\n   <sup>\n    −1\n   </sup>\n   . The density of the gas is 1.2 kg m\n   <sup>\n    −3\n   </sup>\n   . Calculate, in kPa, the pressure of the gas.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  The collisions are elastic ✓\n </p>\n <p>\n  The time for a collision is much shorter than the time between collisions ✓\n </p>\n <p>\n  The intermolecular forces are only present during collisions ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  The collisions are elastic ✓\n </p>\n <p>\n  The time for a collision is much shorter than the time between collisions ✓\n </p>\n <p>\n  The intermolecular forces are only present during collisions ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  The momentum of a molecule changes when it collides with a container wall ✓\n </p>\n <p>\n  From\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    F\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mi>\n      p\n     </mi>\n    </mrow>\n    <mrow>\n     <mtext>\n      Δ\n     </mtext>\n     <mi>\n      t\n     </mi>\n    </mrow>\n   </mfrac>\n  </math>\n  and Newton’s third law, this leads to a force exerted on the wall by the molecule ✓\n </p>\n <p>\n  The average force exerted by all the molecules on a unit area of the wall is equivalent to pressure ✓\n </p>\n <p>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     3\n    </mn>\n   </mfrac>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    2\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     500\n    </mn>\n    <mn>\n     2\n    </mn>\n   </msup>\n  </math>\n  ✓\n </p>\n <p>\n  100 «kPa» ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-3-gas-laws"
    ]
  },
  {
    "question_id": "EXE.2.SL.TZ0.8",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the average translational speed of air molecules.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The air is a mixture of nitrogen, oxygen and other gases. Explain why the component gases of air in the container have different average translational speeds.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The temperature of the sample is increased without a change in pressure. Outline the effect it has on the density of the gas.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    8\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     5\n    </mn>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     3\n    </mn>\n   </mfrac>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    2\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mi>\n     v\n    </mi>\n    <mn>\n     2\n    </mn>\n   </msup>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    v\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    520\n   </mn>\n  </math>\n  «m s\n  <sup>\n   −1\n  </sup>\n  »  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    8\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     5\n    </mn>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     3\n    </mn>\n   </mfrac>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    2\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mi>\n     v\n    </mi>\n    <mn>\n     2\n    </mn>\n   </msup>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    v\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    520\n   </mn>\n  </math>\n  «m s\n  <sup>\n   −1\n  </sup>\n  »  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  Average kinetic energy of the molecules is determined by the temperature only ✓\n </p>\n <p>\n  The mass of a molecule is different for each component gas ✓\n </p>\n <p>\n  From\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     E\n    </mi>\n    <mtext>\n     k\n    </mtext>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     2\n    </mn>\n   </mfrac>\n   <mi>\n    m\n   </mi>\n   <msup>\n    <mi>\n     v\n    </mi>\n    <mn>\n     2\n    </mn>\n   </msup>\n  </math>\n  , the same\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     E\n    </mi>\n    <mtext>\n     k\n    </mtext>\n   </msub>\n  </math>\n  and different mass implies a different average velocity  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  <strong>\n   <em>\n    ALTERNATIVE 1\n   </em>\n  </strong>\n </p>\n <p>\n  The average translational speed increases «because\n  <em>\n   T\n  </em>\n  increases» ✓\n </p>\n <p>\n  From\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    P\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mn>\n     3\n    </mn>\n   </mfrac>\n   <mi>\n    ρ\n   </mi>\n   <msup>\n    <mi>\n     v\n    </mi>\n    <mn>\n     2\n    </mn>\n   </msup>\n  </math>\n  , the density decreases «to keep\n  <em>\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     P\n    </mi>\n   </math>\n  </em>\n  constant»  ✓\n </p>\n <p>\n  <br/>\n  <strong>\n   <em>\n    ALTERNATIVE 2\n   </em>\n  </strong>\n </p>\n <p>\n  From the ideal gas law, the volume of the gas increases ✓\n </p>\n <p>\n  Since\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    ρ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mi>\n     m\n    </mi>\n    <mi>\n     v\n    </mi>\n   </mfrac>\n  </math>\n  and\n  <em>\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     m\n    </mi>\n   </math>\n  </em>\n  is constant, the density decreases  ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-3-gas-laws"
    ]
  },
  {
    "question_id": "EXE.2.SL.TZ0.9",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline how the concept of absolute zero of temperature is interpreted in terms of:\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   the ideal gas law,\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   the kinetic energy of particles in an ideal gas.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   A container holds a mixture of argon and helium atoms at a temperature of 37 °C.\n  </p>\n  <p>\n   Calculate the average translational speed of the argon atoms.\n  </p>\n  <p>\n   The molar mass of argon is 4.0 × 10\n   <sup>\n    −2\n   </sup>\n   kg mol\n   <sup>\n    −1\n   </sup>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [4]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Discuss how the mean kinetic energy of the argon atoms in the mixture compares with that of the helium atoms.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  it is the temperature at which the volume\n </p>\n <p>\n  <strong>\n   <em>\n    OR\n   </em>\n  </strong>\n </p>\n <p>\n  the pressure extrapolates to zero (can be shown by sketch)  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  it is the temperature at which the volume\n </p>\n <p>\n  <strong>\n   <em>\n    OR\n   </em>\n  </strong>\n </p>\n <p>\n  the pressure extrapolates to zero (can be shown by sketch)  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  it is the temperature at which all the (random) motion stops\n </p>\n <p>\n  <strong>\n   <em>\n    OR\n   </em>\n  </strong>\n </p>\n <p>\n  at which all the motion can be extrapolated to stop\n </p>\n <p>\n  <strong>\n   <em>\n    OR\n   </em>\n  </strong>\n </p>\n <p>\n  at which the kinetic energy of all particles is zero ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  Use of\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      4\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        2\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <msub>\n     <mi>\n      N\n     </mi>\n     <mtext>\n      A\n     </mtext>\n    </msub>\n   </mfrac>\n   <mfenced>\n    <mrow>\n     <mo>\n      =\n     </mo>\n     <mn>\n      6\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      6\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        26\n       </mn>\n      </mrow>\n     </msup>\n     <mo>\n     </mo>\n     <mtext>\n      kg\n     </mtext>\n    </mrow>\n   </mfenced>\n  </math>\n  ✓\n </p>\n <p>\n  Work showing that\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    v\n   </mi>\n   <mfenced>\n    <mrow>\n     <mo>\n      =\n     </mo>\n     <msqrt>\n      <mfrac>\n       <mrow>\n        <mn>\n         3\n        </mn>\n        <mi>\n         p\n        </mi>\n       </mrow>\n       <mi>\n        ρ\n       </mi>\n      </mfrac>\n      <mo>\n       =\n      </mo>\n      <msqrt>\n       <mfrac>\n        <mrow>\n         <mn>\n          3\n         </mn>\n         <mi>\n          p\n         </mi>\n         <mi>\n          V\n         </mi>\n        </mrow>\n        <mi>\n         m\n        </mi>\n       </mfrac>\n      </msqrt>\n     </msqrt>\n    </mrow>\n   </mfenced>\n   <mo>\n    =\n   </mo>\n   <msqrt>\n    <mfrac>\n     <mrow>\n      <mn>\n       3\n      </mn>\n      <mi>\n       k\n      </mi>\n      <mi>\n       T\n      </mi>\n     </mrow>\n     <mi>\n      m\n     </mi>\n    </mfrac>\n   </msqrt>\n  </math>\n  ✓\n </p>\n <p>\n  Correct substitution AND conversion to K (310 K)  ✓\n </p>\n <p>\n  430/440 «m s\n  <sup>\n   −1\n  </sup>\n  » ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  the gases are in the same container at the same temperature so are\n  <span style=\"text-decoration:underline;\">\n   in equilibrium\n  </span>\n  ✓\n </p>\n <p>\n  they must have the same mean/average kinetic energy ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-3-gas-laws"
    ]
  },
  {
    "question_id": "SPM.1B.HL.TZ0.1",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The students vary\n   <em>\n    V\n   </em>\n   and measure the time\n   <em>\n    T\n   </em>\n   for the ball to move\n   <strong>\n    once\n   </strong>\n   from one plate to the other. The table shows some of the data.\n  </p>\n  <p style=\"text-align:center;\">\n   <img src=\"data:image/png;base64,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\"/>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <em>\n    V\n   </em>\n   is provided by two identical power supplies connected in series. The potential difference of each of the power supplies is known with an uncertainty of 0.01 kV.\n  </p>\n  <p>\n   State the uncertainty in the potential difference\n   <em>\n    V\n   </em>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <em>\n    T\n   </em>\n   is measured with an electronic stopwatch that measures to the nearest 0.1 s.\n  </p>\n  <p>\n   Describe how an uncertainty in\n   <em>\n    T\n   </em>\n   of less than 0.1 s can be achieved using this stopwatch.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline why it is unlikely that the relationship between\n   <em>\n    T\n   </em>\n   and\n   <em>\n    V\n   </em>\n   is linear.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iv)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the largest fractional uncertainty in\n   <em>\n    T\n   </em>\n   for these data.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine\n   <em>\n    A\n   </em>\n   by drawing the line of best fit.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the units of\n   <em>\n    A\n   </em>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The theoretical relationship assumes that the ball is only affected by the electric force.\n  </p>\n  <p>\n   Suggest why, in order to test the relationship, the length of the string should be much greater than the distance between the plates.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  0.02 «kV» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  0.02 «kV» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  by measuring the time for many bounces ✓\n </p>\n <p>\n  and dividing the result by the number of bounces ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  it is not possible to draw a straight line through all the error bars ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iv)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   T\n  </em>\n  = 0.5 s ✓\n </p>\n <p>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      1\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      5\n     </mn>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n  </math>\n  » 0.2 ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  a best-fit line drawn through the entire range of the data ✓\n </p>\n <p>\n  large triangle greater than half a line or two data points on the line greater than half a line apart ✓\n </p>\n <p>\n  correct read offs consistent with the line,\n  <em>\n   eg\n  </em>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      6\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mn>\n      0\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      40\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mn>\n      0\n     </mn>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    4\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n  </math>\n  ✓\n </p>\n <p>\n  <em>\n   Accept answer in the range 3.8–4.2\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  kV s ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  the angle between the string and the vertical should be very small «for any position of the ball» ✓\n </p>\n <p>\n </p>\n <p>\n  so that the tension in the string is «almost» balanced by the ball’s weight\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  restoring force from the string / horizontal component of tension negligibly small «compared with electric force» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   OWTTE\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "inquiry",
      "tools"
    ],
    "subtopics": [
      "i-1-2-designing",
      "inquiry-1-exploring-and-designing",
      "tool-1-experimental-techniques",
      "tool-3-mathematics"
    ]
  },
  {
    "question_id": "SPM.1B.HL.TZ0.2",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The group obtains the following repeated readings for\n   <em>\n    d\n   </em>\n   for\n   <strong>\n    one\n   </strong>\n   value of\n   <em>\n    W\n   </em>\n   .\n  </p>\n  <p>\n   <img src=\"data:image/png;base64,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\" style=\"display:block;margin-left:auto;margin-right:auto;\"/>\n  </p>\n  <p>\n   The group divides into two subgroups, A and B, to analyse the data.\n  </p>\n  <p>\n   Group A quotes the mean value of\n   <em>\n    d\n   </em>\n   as 2.93 cm.\n  </p>\n  <p>\n   Group B quotes the mean value of\n   <em>\n    d\n   </em>\n   as 2.8 cm.\n  </p>\n  <p>\n   Discuss the values that the groups have quoted.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The variation of\n   <em>\n    d\n   </em>\n   with\n   <em>\n    W\n   </em>\n   is shown.\n  </p>\n  <p>\n   <img src=\"data:image/png;base64,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\" style=\"display:block;margin-left:auto;margin-right:auto;\"/>\n  </p>\n  <p>\n   Outline\n   <strong>\n    one\n   </strong>\n   experimental reason why the graph does not go through the origin.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Theory predicts that\n  </p>\n  <p style=\"text-align:center;\">\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     d\n    </mi>\n    <mo>\n     ∝\n    </mo>\n    <mfrac>\n     <mrow>\n      <msup>\n       <mi>\n        W\n       </mi>\n       <mi>\n        x\n       </mi>\n      </msup>\n      <msup>\n       <mi>\n        L\n       </mi>\n       <mi>\n        y\n       </mi>\n      </msup>\n     </mrow>\n     <mrow>\n      <mi>\n       E\n      </mi>\n      <mi>\n       I\n      </mi>\n     </mrow>\n    </mfrac>\n   </math>\n  </p>\n  <p>\n   where\n   <em>\n    <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n     <mi>\n      E\n     </mi>\n    </math>\n   </em>\n   and\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     I\n    </mi>\n   </math>\n   are constants. The fundamental units of\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     I\n    </mi>\n   </math>\n   are m\n   <sup>\n    4\n   </sup>\n   and those of\n   <em>\n    E\n   </em>\n   are kg m\n   <sup>\n    −1\n   </sup>\n   s\n   <sup>\n    −2\n   </sup>\n   .\n  </p>\n  <p>\n   Calculate\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     x\n    </mi>\n   </math>\n   and\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     y\n    </mi>\n   </math>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Suggest an appropriate measuring instrument for determining\n   <em>\n    b\n   </em>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the percentage uncertainty in the value of\n   <em>\n    A\n   </em>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  3 sf is inappropriate for\n  <em>\n   A\n  </em>\n  ✓\n </p>\n <p>\n  rejects trial 3 as outlier for\n  <em>\n   B\n  </em>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  3 sf is inappropriate for\n  <em>\n   A\n  </em>\n  ✓\n </p>\n <p>\n  rejects trial 3 as outlier for\n  <em>\n   B\n  </em>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  beam bends under its own weight / weight of pan\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  specified systematic error in\n  <em>\n   d\n  </em>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  units of\n  <em>\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     W\n    </mi>\n   </math>\n  </em>\n  : kg m s\n  <sup>\n   −2\n  </sup>\n  ✓\n </p>\n <p>\n  work leading to\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    x\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    1\n   </mn>\n  </math>\n  and\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    y\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    3\n   </mn>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  instrument (capable of reading to 0.05 mm) with reason related to resolution of instrument ✓\n </p>\n <p>\n  <em>\n   eg micrometer screw gauge, Vernier caliper, travelling microscope\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  attempt to calculate fractional uncertainty in either\n  <em>\n   a\n  </em>\n  or\n  <em>\n   b\n  </em>\n  [0.0357, 0.0167] ✓\n </p>\n <p>\n  0.0357 + 0.0167 = 0.05 = 5% ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "inquiry",
      "tools"
    ],
    "subtopics": [
      "i-2-3-interpreting-results",
      "inquiry-2-collecting-and-processing-data",
      "tool-1-experimental-techniques",
      "tool-3-mathematics"
    ]
  },
  {
    "question_id": "SPM.1B.SL.TZ0.1",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The students vary\n   <em>\n    V\n   </em>\n   and measure the time\n   <em>\n    T\n   </em>\n   for the ball to move\n   <strong>\n    once\n   </strong>\n   from one plate to the other. The table shows some of the data.\n  </p>\n  <p style=\"text-align:center;\">\n   <img src=\"data:image/png;base64,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\"/>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <em>\n    V\n   </em>\n   is provided by two identical power supplies connected in series. The potential difference of each of the power supplies is known with an uncertainty of 0.01 kV.\n  </p>\n  <p>\n   State the uncertainty in the potential difference\n   <em>\n    V\n   </em>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   <em>\n    T\n   </em>\n   is measured with an electronic stopwatch that measures to the nearest 0.1 s.\n  </p>\n  <p>\n   Describe how an uncertainty in\n   <em>\n    T\n   </em>\n   of less than 0.1 s can be achieved using this stopwatch.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline why it is unlikely that the relationship between\n   <em>\n    T\n   </em>\n   and\n   <em>\n    V\n   </em>\n   is linear.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iv)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the largest fractional uncertainty in\n   <em>\n    T\n   </em>\n   for these data.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine\n   <em>\n    A\n   </em>\n   by drawing the line of best fit.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the units of\n   <em>\n    A\n   </em>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The theoretical relationship assumes that the ball is only affected by the electric force.\n  </p>\n  <p>\n   Suggest why, in order to test the relationship, the length of the string should be much greater than the distance between the plates.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  0.02 «kV» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  0.02 «kV» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  by measuring the time for many bounces ✓\n </p>\n <p>\n  and dividing the result by the number of bounces ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  it is not possible to draw a straight line through all the error bars ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iv)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   T\n  </em>\n  = 0.5 s ✓\n </p>\n <p>\n  «\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      1\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      5\n     </mn>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n  </math>\n  » 0.2 ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  a best-fit line drawn through the entire range of the data ✓\n </p>\n <p>\n  large triangle greater than half a line or two data points on the line greater than half a line apart ✓\n </p>\n <p>\n  correct read offs consistent with the line,\n  <em>\n   eg\n  </em>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      6\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mn>\n      0\n     </mn>\n    </mrow>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      40\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mn>\n      0\n     </mn>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    4\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    0\n   </mn>\n  </math>\n  ✓\n </p>\n <p>\n  <em>\n   Accept answer in the range 3.8–4.2\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  kV s ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  the angle between the string and the vertical should be very small «for any position of the ball» ✓\n </p>\n <p>\n  so that the tension in the string is «almost» balanced by the ball’s weight\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  restoring force from the string / horizontal component of tension negligibly small «compared with electric force» ✓\n </p>\n <p>\n  <em>\n   OWTTE\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "inquiry",
      "tools"
    ],
    "subtopics": [
      "i-1-1-exploring",
      "i-1-2-designing",
      "i-1-3-controlling-variables",
      "inquiry-1-exploring-and-designing",
      "tool-1-experimental-techniques",
      "tool-3-mathematics"
    ]
  },
  {
    "question_id": "SPM.1B.SL.TZ0.2",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The group obtains the following repeated readings for\n   <em>\n    d\n   </em>\n   for\n   <strong>\n    one\n   </strong>\n   value of\n   <em>\n    W\n   </em>\n   .\n  </p>\n  <p>\n   <img src=\"data:image/png;base64,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\" style=\"display:block;margin-left:auto;margin-right:auto;\"/>\n  </p>\n  <p>\n   The group divides into two subgroups, A and B, to analyse the data.\n  </p>\n  <p>\n   Group A quotes the mean value of\n   <em>\n    d\n   </em>\n   as 2.93 cm.\n  </p>\n  <p>\n   Group B quotes the mean value of\n   <em>\n    d\n   </em>\n   as 2.8 cm.\n  </p>\n  <p>\n   Discuss the values that the groups have quoted.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The variation of\n   <em>\n    d\n   </em>\n   with\n   <em>\n    W\n   </em>\n   is shown.\n  </p>\n  <p>\n   <img src=\"data:image/png;base64,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\" style=\"display:block;margin-left:auto;margin-right:auto;\"/>\n  </p>\n  <p>\n   Outline\n   <strong>\n    one\n   </strong>\n   experimental reason why the graph does not go through the origin.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Theory predicts that\n  </p>\n  <p style=\"text-align:center;\">\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     d\n    </mi>\n    <mo>\n     ∝\n    </mo>\n    <mfrac>\n     <mrow>\n      <msup>\n       <mi>\n        W\n       </mi>\n       <mi>\n        x\n       </mi>\n      </msup>\n      <msup>\n       <mi>\n        L\n       </mi>\n       <mi>\n        y\n       </mi>\n      </msup>\n     </mrow>\n     <mrow>\n      <mi>\n       E\n      </mi>\n      <mi>\n       I\n      </mi>\n     </mrow>\n    </mfrac>\n   </math>\n  </p>\n  <p style=\"text-align:left;\">\n   where\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     E\n    </mi>\n   </math>\n   and\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     I\n    </mi>\n   </math>\n   are constants. The fundamental units of\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     I\n    </mi>\n   </math>\n   are m\n   <sup>\n    4\n   </sup>\n   and those of\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     E\n    </mi>\n   </math>\n   are kg m\n   <sup>\n    −1\n   </sup>\n   s\n   <sup>\n    −2\n   </sup>\n   .\n  </p>\n  <p style=\"text-align:left;\">\n   Calculate\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     x\n    </mi>\n   </math>\n   and\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     y\n    </mi>\n   </math>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Suggest an appropriate measuring instrument for determining\n   <em>\n    b\n   </em>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the percentage uncertainty in the value of\n   <em>\n    A\n   </em>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  3 sf is inappropriate for\n  <em>\n   A\n  </em>\n  ✓\n </p>\n <p>\n  rejects trial 3 as outlier for\n  <em>\n   B\n  </em>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  3 sf is inappropriate for\n  <em>\n   A\n  </em>\n  ✓\n </p>\n <p>\n  rejects trial 3 as outlier for\n  <em>\n   B\n  </em>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  beam bends under its own weight / weight of pan\n </p>\n <p>\n  <em>\n   <strong>\n    OR\n   </strong>\n  </em>\n </p>\n <p>\n  specified systematic error in\n  <em>\n   d\n  </em>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  units of\n  <em>\n   W\n  </em>\n  : kg m s\n  <sup>\n   −2\n  </sup>\n  ✓\n </p>\n <p>\n  work leading to\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    x\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    1\n   </mn>\n  </math>\n  and\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    y\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    3\n   </mn>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  instrument (capable of reading to 0.05 mm) with reason related to resolution of instrument ✓\n </p>\n <p>\n  <em>\n   eg micrometer screw gauge, Vernier caliper, travelling microscope\n  </em>\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  attempt to calculate fractional uncertainty in either\n  <em>\n   a\n  </em>\n  or\n  <em>\n   b\n  </em>\n  [0.0357, 0.0167] ✓\n </p>\n <p>\n  0.0357 + 0.0167 = 0.05 = 5 % ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "inquiry",
      "tools"
    ],
    "subtopics": [
      "i-2-3-interpreting-results",
      "inquiry-2-collecting-and-processing-data",
      "tool-1-experimental-techniques",
      "tool-3-mathematics"
    ]
  },
  {
    "question_id": "SPM.2.HL.TZ0.1",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the nature and direction of the force that accelerates the 15 kg object.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (b)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Determine the largest magnitude of\n   <em>\n    F\n   </em>\n   for which the block and the object do not move relative to each other.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  static friction force «between blocks»\n </p>\n <p>\n  <em>\n   <strong>\n    AND\n   </strong>\n  </em>\n </p>\n <p>\n  directed to the right ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  static friction force «between blocks»\n </p>\n <p>\n  <em>\n   <strong>\n    AND\n   </strong>\n  </em>\n </p>\n <p>\n  directed to the right ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (b)\n </div><div class=\"card-body\">\n <p>\n  <em>\n   F\n  </em>\n  = 60\n  <em>\n   a ✓\n  </em>\n </p>\n <p>\n  <em>\n   F\n  </em>\n  <sub>\n   f\n  </sub>\n  = 0.6 × 15 × 9.8 «= 88.2 N» ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mn>\n    88\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    2\n   </mn>\n   <mo>\n    =\n   </mo>\n   <mn>\n    15\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <mfrac>\n    <mi>\n     F\n    </mi>\n    <mn>\n     60\n    </mn>\n   </mfrac>\n   <mo>\n    ⇒\n   </mo>\n   <mi>\n    F\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    350\n   </mn>\n  </math>\n  «N» ✓\n </p>\n <p>\n </p>\n <p>\n  <em>\n   Allow use of a =\n  </em>\n  0.6\n  <em>\n   g leading to 353 N.\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-2-forces-and-momentum"
    ]
  },
  {
    "question_id": "SPM.2.HL.TZ0.2",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     γ\n    </mi>\n   </math>\n   for a speed of 0.80\n   <em>\n    c\n   </em>\n   .\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    γ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <msup>\n      <mn>\n       80\n      </mn>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     5\n    </mn>\n    <mn>\n     3\n    </mn>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    67\n   </mn>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    γ\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     1\n    </mn>\n    <mrow>\n     <mn>\n      1\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <msup>\n      <mn>\n       80\n      </mn>\n      <mn>\n       2\n      </mn>\n     </msup>\n    </mrow>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mn>\n     5\n    </mn>\n    <mn>\n     3\n    </mn>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    67\n   </mn>\n  </math>\n  ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-5-galilean-and-special-relativity"
    ]
  },
  {
    "question_id": "SPM.2.HL.TZ0.3",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline how this standing wave pattern of melted spots is formed.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  standing waves form «in the oven» by superposition / constructive interference ✓\n </p>\n <p>\n  energy transfer is greatest at the antinodes «of the standing wave pattern» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  standing waves form «in the oven» by superposition / constructive interference ✓\n </p>\n <p>\n  energy transfer is greatest at the antinodes «of the standing wave pattern» ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-4-standing-waves-and-resonance"
    ]
  },
  {
    "question_id": "SPM.2.HL.TZ0.4",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Draw an arrow on the diagram to represent the direction of the acceleration of the satellite.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  arrow normal to the orbit towards the Earth ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  arrow normal to the orbit towards the Earth ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion",
      "d-fields"
    ],
    "subtopics": [
      "a-2-forces-and-momentum",
      "d-1-gravitational-fields"
    ]
  },
  {
    "question_id": "SPM.2.HL.TZ0.5",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline why the magnetic flux in ring B increases.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (d)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline why work must be done on ring B as it moves towards ring A at a constant speed.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  ring B cuts an increasing number of magnetic field lines ✓\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n </p>\n <p>\n  magnetic field from current in A increases at the position of B ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  ring B cuts an increasing number of magnetic field lines ✓\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n </p>\n <p>\n  magnetic field from current in A increases at the position of B ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  the current induced in B gives rise to a magnetic field opposing that of A\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n </p>\n <p>\n  there will be a magnetic force opposing the motion ✓\n </p>\n <p>\n  work must be done to move B in the opposite direction to this force ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion",
      "d-fields"
    ],
    "subtopics": [
      "a-3-work-energy-and-power",
      "d-4-induction"
    ]
  },
  {
    "question_id": "SPM.2.HL.TZ0.6",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   A nucleus of americium-241 has 146 neutrons. This nuclide decays to neptunium through alpha emission.\n  </p>\n  <p>\n   Complete the nuclear equation for this decay.\n  </p>\n  <p>\n   <img src=\"data:image/png;base64,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\"/>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (d)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the maximum current in the chamber due to the electrons when there is no smoke in the chamber.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mmultiscripts>\n    <mtext>\n     Am\n    </mtext>\n    <mprescripts>\n    </mprescripts>\n    <mn>\n     95\n    </mn>\n    <mn>\n     241\n    </mn>\n   </mmultiscripts>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mmultiscripts>\n    <mtext>\n     Np\n    </mtext>\n    <mprescripts>\n    </mprescripts>\n    <mn>\n     93\n    </mn>\n    <mn>\n     237\n    </mn>\n   </mmultiscripts>\n   <mo>\n    +\n   </mo>\n   <mmultiscripts>\n    <mi>\n     α\n    </mi>\n    <mprescripts>\n    </mprescripts>\n    <mn>\n     2\n    </mn>\n    <mn>\n     4\n    </mn>\n   </mmultiscripts>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (d)\n </div><div class=\"card-body\">\n <p>\n  Each alpha gives rise to\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      5\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      5\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       6\n      </mn>\n     </msup>\n    </mrow>\n    <mn>\n     15\n    </mn>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    3\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    67\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     5\n    </mn>\n   </msup>\n  </math>\n  ion pairs ✓\n </p>\n <p>\n  So\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      3\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      67\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       5\n      </mn>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      42000\n     </mn>\n    </mrow>\n    <mn>\n     3\n    </mn>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    5\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    13\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     9\n    </mn>\n   </msup>\n  </math>\n  ion pairs per second ✓\n </p>\n <p>\n  current\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    6\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      19\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    5\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    13\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     9\n    </mn>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    82\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      9\n     </mn>\n    </mrow>\n   </msup>\n  </math>\n  «A» ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter",
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "b-5-current-and-circuits",
      "e-3-radioactive-decay"
    ]
  },
  {
    "question_id": "SPM.2.HL.TZ0.7",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the surface temperature of\n   <em>\n    δ\n   </em>\n   Vel A is about 9000 K.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  correct substitution into\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     λ\n    </mi>\n    <mtext>\n     max\n    </mtext>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      9\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        3\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mi>\n     T\n    </mi>\n   </mfrac>\n  </math>\n  OR 9350 K ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  correct substitution into\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     λ\n    </mi>\n    <mtext>\n     max\n    </mtext>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      9\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        3\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mi>\n     T\n    </mi>\n   </mfrac>\n  </math>\n  OR 9350 K ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-1-thermal-energy-transfers"
    ]
  },
  {
    "question_id": "SPM.2.HL.TZ0.8",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the theoretical equilibrium temperature of the mixture.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   The mixture was held in a large metal container during the mixing.\n  </p>\n  <p>\n   Explain\n   <strong>\n    one\n   </strong>\n   change to the procedure that will reduce the difference in (b)(i).\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      030\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      7\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      5\n     </mn>\n    </mrow>\n   </mfenced>\n   <mo>\n    +\n   </mo>\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      030\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      220\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mrow>\n   </mfenced>\n   <mo>\n    +\n   </mo>\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      030\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      13\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mrow>\n   </mfenced>\n   <mfenced>\n    <mrow>\n     <mi>\n      T\n     </mi>\n     <mo>\n      -\n     </mo>\n     <mn>\n      47\n     </mn>\n    </mrow>\n   </mfenced>\n  </math>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      150\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      13\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mrow>\n   </mfenced>\n   <mfenced>\n    <mrow>\n     <mn>\n      240\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mi>\n      T\n     </mi>\n    </mrow>\n   </mfenced>\n  </math>\n </p>\n <p>\n  One heat capacity term correctly substituted ✓\n </p>\n <p>\n  latent heat correctly substituted\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      030\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      220\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mrow>\n   </mfenced>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    T\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    190\n   </mn>\n  </math>\n  «°C» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      030\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      7\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      5\n     </mn>\n    </mrow>\n   </mfenced>\n   <mo>\n    +\n   </mo>\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      030\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      220\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mrow>\n   </mfenced>\n   <mo>\n    +\n   </mo>\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      030\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      13\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mrow>\n   </mfenced>\n   <mfenced>\n    <mrow>\n     <mi>\n      T\n     </mi>\n     <mo>\n      -\n     </mo>\n     <mn>\n      47\n     </mn>\n    </mrow>\n   </mfenced>\n  </math>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      150\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      13\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mrow>\n   </mfenced>\n   <mfenced>\n    <mrow>\n     <mn>\n      240\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mi>\n      T\n     </mi>\n    </mrow>\n   </mfenced>\n  </math>\n </p>\n <p>\n  One heat capacity term correctly substituted ✓\n </p>\n <p>\n  latent heat correctly substituted\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      030\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      220\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mrow>\n   </mfenced>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    T\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    190\n   </mn>\n  </math>\n  «°C» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  Insulate the container\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n </p>\n <p>\n  Carry out experiment quicker\n </p>\n <p>\n  <strong>\n   OR\n  </strong>\n </p>\n <p>\n  Use larger volumes of substances ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter",
      "inquiry"
    ],
    "subtopics": [
      "b-1-thermal-energy-transfers",
      "i-1-3-controlling-variables",
      "inquiry-1-exploring-and-designing"
    ]
  },
  {
    "question_id": "SPM.2.HL.TZ0.9",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Draw the electric field lines due to the charged plates.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Draw the electric field lines due to the charged plates.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (ii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Draw the forces acting on the oil drop, ignoring the buoyancy force.\n  </p>\n  <p>\n   <img src=\"data:image/png;base64,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\"/>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (iii)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the electric charge on the oil drop is given by\n  </p>\n  <p style=\"text-align:center;\">\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     q\n    </mi>\n    <mo>\n     =\n    </mo>\n    <mfrac>\n     <mrow>\n      <msub>\n       <mi>\n        ρ\n       </mi>\n       <mi>\n        o\n       </mi>\n      </msub>\n      <mi>\n       g\n      </mi>\n      <mi>\n       V\n      </mi>\n     </mrow>\n     <mi>\n      E\n     </mi>\n    </mfrac>\n   </math>\n  </p>\n  <p>\n   where\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <msub>\n     <mi>\n      ρ\n     </mi>\n     <mi>\n      o\n     </mi>\n    </msub>\n   </math>\n   is the density of oil and\n   <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n    <mi>\n     V\n    </mi>\n   </math>\n   is the volume of the oil drop.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a.i)\n </div><div class=\"card-body\">\n <p>\n  equally spaced arrows «by eye» all pointing down ✓\n </p>\n <p>\n  edge effects also shown with arrows ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  equally spaced arrows «by eye» all pointing down ✓\n </p>\n <p>\n  edge effects also shown with arrows ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (ii)\n </div><div class=\"card-body\">\n <p>\n  Weight vertically down\n  <em>\n   <strong>\n    AND\n   </strong>\n  </em>\n  electric force vertically up ✓\n </p>\n <p>\n  Of equal length «by eye» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (iii)\n </div><div class=\"card-body\">\n <p>\n  Mass of drop is\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     ρ\n    </mi>\n    <mi>\n     o\n    </mi>\n   </msub>\n   <mi>\n    V\n   </mi>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    q\n   </mi>\n   <mi>\n    E\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mfenced>\n    <mrow>\n     <msub>\n      <mi>\n       ρ\n      </mi>\n      <mi>\n       o\n      </mi>\n     </msub>\n     <mi>\n      V\n     </mi>\n    </mrow>\n   </mfenced>\n   <mi>\n    g\n   </mi>\n  </math>\n  ✓\n </p>\n <p>\n  «hence answer»\n </p>\n <p>\n  <br/>\n  <em>\n   MP1 must be shown implicitly for credit.\n  </em>\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion",
      "d-fields",
      "tools"
    ],
    "subtopics": [
      "a-2-forces-and-momentum",
      "d-2-electric-and-magnetic-fields",
      "tool-3-mathematics"
    ]
  },
  {
    "question_id": "SPM.2.SL.TZ0.1",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   State the nature and direction of the force that accelerates the 15 kg object.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  static friction force «between blocks»\n </p>\n <p>\n  <strong>\n   AND\n  </strong>\n </p>\n <p>\n  directed to the right ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  static friction force «between blocks»\n </p>\n <p>\n  <strong>\n   AND\n  </strong>\n </p>\n <p>\n  directed to the right ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion"
    ],
    "subtopics": [
      "a-2-forces-and-momentum"
    ]
  },
  {
    "question_id": "SPM.2.SL.TZ0.2",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Outline how this standing wave pattern of melted spots is formed.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  standing waves form «in the oven» by superposition / constructive interference ✓\n </p>\n <p>\n  energy transfer is greatest at the antinodes «of the standing wave pattern» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  standing waves form «in the oven» by superposition / constructive interference ✓\n </p>\n <p>\n  energy transfer is greatest at the antinodes «of the standing wave pattern» ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "c-wave-behaviour"
    ],
    "subtopics": [
      "c-4-standing-waves-and-resonance"
    ]
  },
  {
    "question_id": "SPM.2.SL.TZ0.3",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Draw an arrow on the diagram to represent the direction of the acceleration of the satellite.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  arrow normal to the orbit towards the Earth ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  arrow normal to the orbit towards the Earth ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "a--space-time-and-motion",
      "d-fields"
    ],
    "subtopics": [
      "a-2-forces-and-momentum",
      "d-1-gravitational-fields"
    ]
  },
  {
    "question_id": "SPM.2.SL.TZ0.4",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   A nucleus of americium-241 has 146 neutrons. This nuclide decays to neptunium through alpha emission.\n  </p>\n  <p>\n   Complete the nuclear equation for this decay.\n  </p>\n  <p>\n   <img src=\"data:image/png;base64,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\"/>\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (c)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the maximum current in the chamber due to the electrons when there is no smoke in the chamber.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mmultiscripts>\n    <mi>\n     Am\n    </mi>\n    <mprescripts>\n    </mprescripts>\n    <mn>\n     95\n    </mn>\n    <mn>\n     241\n    </mn>\n   </mmultiscripts>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mmultiscripts>\n    <mi>\n     Np\n    </mi>\n    <mprescripts>\n    </mprescripts>\n    <mn>\n     93\n    </mn>\n    <mn>\n     237\n    </mn>\n   </mmultiscripts>\n   <mo>\n    +\n   </mo>\n   <mmultiscripts>\n    <mi>\n     α\n    </mi>\n    <mprescripts>\n    </mprescripts>\n    <mn>\n     2\n    </mn>\n    <mn>\n     4\n    </mn>\n   </mmultiscripts>\n  </math>\n  ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (c)\n </div><div class=\"card-body\">\n <p>\n  Each alpha gives rise to\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      5\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      5\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       6\n      </mn>\n     </msup>\n    </mrow>\n    <mn>\n     15\n    </mn>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    3\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    67\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     5\n    </mn>\n   </msup>\n  </math>\n  ion pairs ✓\n </p>\n <p>\n  So\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfrac>\n    <mrow>\n     <mn>\n      3\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      67\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       5\n      </mn>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      42000\n     </mn>\n    </mrow>\n    <mn>\n     3\n    </mn>\n   </mfrac>\n   <mo>\n    =\n   </mo>\n   <mn>\n    5\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    13\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     9\n    </mn>\n   </msup>\n  </math>\n  ion pairs per second ✓\n </p>\n <p>\n  current\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mn>\n    1\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    6\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      19\n     </mn>\n    </mrow>\n   </msup>\n   <mo>\n    ×\n   </mo>\n   <mn>\n    5\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    13\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mn>\n     9\n    </mn>\n   </msup>\n   <mo>\n    =\n   </mo>\n   <mn>\n    0\n   </mn>\n   <mo>\n    .\n   </mo>\n   <mn>\n    82\n   </mn>\n   <mo>\n    ×\n   </mo>\n   <msup>\n    <mn>\n     10\n    </mn>\n    <mrow>\n     <mo>\n      -\n     </mo>\n     <mn>\n      9\n     </mn>\n    </mrow>\n   </msup>\n  </math>\n  «A» ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter",
      "e-nuclear-and-quantum-physics"
    ],
    "subtopics": [
      "b-5-current-and-circuits",
      "e-3-radioactive-decay"
    ]
  },
  {
    "question_id": "SPM.2.SL.TZ0.5",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Show that the surface temperature of\n   <em>\n    δ\n   </em>\n   Vel A is about 9000 K.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [1]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  correct substitution into\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     λ\n    </mi>\n    <mtext>\n     max\n    </mtext>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      9\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        3\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mi>\n     T\n    </mi>\n   </mfrac>\n  </math>\n  OR 9350 K ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  correct substitution into\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <msub>\n    <mi>\n     λ\n    </mi>\n    <mtext>\n     max\n    </mtext>\n   </msub>\n   <mo>\n    =\n   </mo>\n   <mfrac>\n    <mrow>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      9\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mrow>\n       <mo>\n        -\n       </mo>\n       <mn>\n        3\n       </mn>\n      </mrow>\n     </msup>\n    </mrow>\n    <mi>\n     T\n    </mi>\n   </mfrac>\n  </math>\n  OR 9350 K ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-1-thermal-energy-transfers"
    ]
  },
  {
    "question_id": "SPM.2.SL.TZ0.6",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Calculate the theoretical equilibrium temperature of the mixture.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [3]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      030\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      7\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      5\n     </mn>\n    </mrow>\n   </mfenced>\n   <mo>\n    +\n   </mo>\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      030\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      220\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mrow>\n   </mfenced>\n   <mo>\n    +\n   </mo>\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      030\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      13\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mrow>\n   </mfenced>\n   <mfenced>\n    <mrow>\n     <mi>\n      T\n     </mi>\n     <mo>\n      -\n     </mo>\n     <mn>\n      47\n     </mn>\n    </mrow>\n   </mfenced>\n  </math>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      150\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      13\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mrow>\n   </mfenced>\n   <mfenced>\n    <mrow>\n     <mn>\n      240\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mi>\n      T\n     </mi>\n    </mrow>\n   </mfenced>\n  </math>\n </p>\n <p>\n  One heat capacity term correctly substituted ✓\n </p>\n <p>\n  latent heat correctly substituted\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      030\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      220\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mrow>\n   </mfenced>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    T\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    190\n   </mn>\n  </math>\n  «°C» ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (a)\n </div><div class=\"card-body\">\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      030\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      7\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      5\n     </mn>\n    </mrow>\n   </mfenced>\n   <mo>\n    +\n   </mo>\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      030\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      220\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mrow>\n   </mfenced>\n   <mo>\n    +\n   </mo>\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      030\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      13\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mrow>\n   </mfenced>\n   <mfenced>\n    <mrow>\n     <mi>\n      T\n     </mi>\n     <mo>\n      -\n     </mo>\n     <mn>\n      47\n     </mn>\n    </mrow>\n   </mfenced>\n  </math>\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mo>\n    =\n   </mo>\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      150\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      2\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      13\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mrow>\n   </mfenced>\n   <mfenced>\n    <mrow>\n     <mn>\n      240\n     </mn>\n     <mo>\n      -\n     </mo>\n     <mi>\n      T\n     </mi>\n    </mrow>\n   </mfenced>\n  </math>\n </p>\n <p>\n  One heat capacity term correctly substituted ✓\n </p>\n <p>\n  latent heat correctly substituted\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mfenced>\n    <mrow>\n     <mn>\n      0\n     </mn>\n     <mo>\n      .\n     </mo>\n     <mn>\n      030\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <mn>\n      220\n     </mn>\n     <mo>\n      ×\n     </mo>\n     <msup>\n      <mn>\n       10\n      </mn>\n      <mn>\n       3\n      </mn>\n     </msup>\n    </mrow>\n   </mfenced>\n  </math>\n  ✓\n </p>\n <p>\n  <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n   <mi>\n    T\n   </mi>\n   <mo>\n    =\n   </mo>\n   <mn>\n    190\n   </mn>\n  </math>\n  «°C» ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "b-the-particulate-nature-of-matter"
    ],
    "subtopics": [
      "b-1-thermal-energy-transfers"
    ]
  },
  {
    "question_id": "SPM.2.SL.TZ0.7",
    "Question": "<div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (a.i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Draw the electric field lines due to the charged plates.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n <div class=\"t_qn_question_content\">\n <div class=\"qn_code_number\">\n  (i)\n </div>\n <div class=\"qc_body js-toggle-question\">\n  <p>\n   Draw the electric field lines due to the charged plates.\n  </p>\n </div>\n <div class=\"qc_marks_available\">\n  <p>\n   [2]\n  </p>\n </div>\n</div>\n",
    "Markscheme": "<br><div class=\"qn_code_number\">\n  (a.i)\n </div><div class=\"card-body\">\n <p>\n  equally spaced arrows «by eye» all pointing down ✓\n </p>\n <p>\n  edge effects also shown with arrows ✓\n </p>\n</div>\n<br><div class=\"qn_code_number\">\n  (i)\n </div><div class=\"card-body\">\n <p>\n  equally spaced arrows «by eye» all pointing down ✓\n </p>\n <p>\n  edge effects also shown with arrows ✓\n </p>\n</div>\n",
    "Examiners report": "None",
    "topics": [
      "d-fields"
    ],
    "subtopics": [
      "d-2-electric-and-magnetic-fields"
    ]
  }
]