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<h2>SL Paper 1</h2><div class="specification">
<p>Sergei is training to be a weightlifter. Each day he trains at the local gym by lifting a metal bar that has heavy weights attached. He carries out successive lifts. After each lift, the same amount of weight is <strong>added</strong> to the bar to increase the weight to be lifted.</p>
<p>The weights of each of Sergei’s lifts form an arithmetic sequence.</p>
<p>Sergei’s friend, Yuri, records the weight of each lift. Unfortunately, last Monday, Yuri misplaced all but two of the recordings of Sergei’s lifts.</p>
<p>On that day, Sergei lifted 21 kg on the third lift and 46 kg on the eighth lift.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For that day find how much weight was added after each lift.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For that day find the weight of Sergei’s first lift.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On that day, Sergei made 12 successive lifts. Find the total combined weight of these lifts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>5<em>d</em> = 46 − 21 <strong>OR</strong> <em>u</em><sub>1</sub> + 2<em>d</em> = 21 and <em>u</em><sub>1</sub> + 7<em>d</em> = 46 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for a correct equation in <em>d</em> or for two correct equations in <em>u</em><sub>1</sub> and <em>d</em>.</p>
<p>(<em>d =</em>) 5 (kg) <em><strong>(A1) (C2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>u</em><sub>1</sub> + 2 × 5 = 21 <em><strong>(M1)</strong></em></p>
<p><em><strong>OR</strong></em></p>
<p><em>u</em><sub>1</sub> + 7 × 5 = 46 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution of their <em>d</em> into either of the two equations.</p>
<p>(<em>u</em><sub>1 </sub>=) 11 (kg) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a)(i).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{12}}{2}\left( {2 \times 11 + \left( {12 - 1} \right) \times 5} \right)">
<mfrac>
<mrow>
<mn>12</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>11</mn>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>12</mn>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mn>5</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into arithmetic series formula.</p>
<p>= 462 (kg) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from parts (a) and (b).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The Osaka Tigers basketball team play in a multilevel stadium.</p>
<p style="text-align: center;"><img 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"></p>
<p>The most expensive tickets are in the first row. The ticket price, in Yen (¥), for each row forms an arithmetic sequence. Prices for the first three rows are shown in the following table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOMAAACUCAYAAABhqZ41AAAgAElEQVR4Ae19DXBU15XmJ5khrAdkljIbXuOMGaSxkpSU9SCVnLWZccs4rTjYCQVryBLTMmIzUIUddigkRUzs9WLHGLdKFFmY+GdbEShmDXZr8XrigHALMaXEkbZFcERGSCNcsi26PbGDQepgMHTfrfv++vbr91pPajXdko6qcN9337nnnvude94793b7fjmMMQb6IwQIgYwjkJtxC8gAQoAQkBGgYKSJQAhkCQIzjHbk5OQYq+iaECAEJhgBs9VhQjDyPs0EJ9gWUkcITFsErF54lKZO2ylBA882BCgYs80jZM+0RYCCcdq6ngaebQhQMGabR8ieaYsABeO0dT0NPNsQoGDMNo+QPdMWAQrGaet6Gni2IUDBmG0eIXumLQIUjNPW9TTwbEOAgjHbPEL2TFsEJi4Yr3ejviAH/Kc+yf4V1HfjeqgFlbLcJrSErtsHf7ztTHsYRn/bIdRv2ofuMZhgqipp5XWEWjYpmFS2IJRU1nBzQsdr0E2XWYfAxAVj1g0tuUHXu1/Ct5Z9F9Vvf5ZckO4SAjcIAdMfio+r7xkl2DbAsE1tfL27Hl8urca5fA8CZ7ehJK6nEuxnDPvH1dFkazQD0soXwNgLYzdcWjmNcBo7PFOtRWbejBbpVzTUjZb6Sji0VNdRifrj/Qhbov45Qm3/A+Vc3rEBjWeHVUmegjaittyhpswVqG1sQ384CkBJG/+MPyi49LlqlP5ZDuT02awf3dYNaGz7J9RXFsd07u9CiKuU/z5ES2UBcnLK8VzL69gu9+1AReMZnLdIU0cdr963ls6LKe9BdHe3xOxxVGJ3Vwi6OdymcD+O63hWoHZ/Fz7sqkcBx6ug3jo91/sdbcxKH22NtYoPuN7yWjS2iT6L2Vzw3Os4tr1Cwa+iEf1xxqowIopw/7HYuMprsb+7H1315XK7OD/FjY8vj4pRWd+C7tDnijJ96VSO+rbueCxaziKMYfQf341KB2/rQHltc6ytrCHZPNLsncBPfuyG+Kf8H1RizfjK1wIelg8w5HtY4JpBR9DH3PweNjJfUL050sk8TokfAWL4V8SqfIMswlXEtfsTC/qfYk5ZfjnzBD5VO7nKhnybmZSgB0xyN7Hekass6Nto6AMs3xNgRjNlhXqfRrv4tcScnk42Igt+wHzufIPeElbjD8X6c/tYULWSjXm83LprMV0m4wMeZt6+z5QeIoPMV1VksKeIrXWvULAx84tmm90xm/bBcSlibm+Piou5zVKNn13S+hM+I0M+ViUZsJZWMPdaZSy6nyz7BpOqfGyIT5hrAebJN+jScXOxrTVrE+ZJzK7R5pE8IwXL7RetYiwzb8aEh8kV9B+uR3V7CHA+BX/wKhi7iqD/KThxBo2PvYj2YfExeg0Xz7yCHz7yFNrhQp3/RWwtmatoHe7ATx7bh5BUBW/vJfn/zWQjPfC6ixA68D/xs65hOW28FvAgn7fgafQ1hoFtJYjLpBNslOCsa0UwwsAiQXQ2uCEhhPaGI+iKsw2AswGBkQhY5J/xxNfnJWgCxjpeExVwocbXixHGEBnyoUriMqdw8szHsnB0wI8XG88AMj5DiHC5YANu/6BzDJtIycZ8HcPtL+KxxjOQ3E3o5eNlEYz0NsEtncGBHx1MxAXL4Ql8Csauof+Ju5GXMKwrGDj2Khr5Lpc4D35+Jz44yMcS+9PHp2HNrmLItxkchtDJ9/CROF2AmI0jnfA4uVQrGppn4Rl5jnyKgGe5rDzkO4V/5Rt6o86jCzFjJqpkjGerqDXKjXY9tjej9lbJZ27fB9aqTZ7Y+lNQbaX3qz8B45+M2pNPl0v2huA69T6Ftzivv+RnNfIT3Mk8Af5u1MYgMZe3V3mTyzYJbwb9zajJ2h2v1regy+VlffrD2ajvM9bnfVh5K8bJRdglf90Y3oxavyq4cWMOsYDHaXjziljzrODj+Ld5nC2qTvEj0su8Lp4dGTH8mPlrSuS+9Dej2i4SDLAjPh/zeWvULAkMUh3zX4oIb0bNFt5oRLdbmwu81jgf9OtR5pFovt2yVYxlx5vx+h/w3q/kFdyYnzGhxkb8799eVNtdx8fvDyhrQQtNoY8u4k8W95JW5xfg9vnCu/PmWzD/ZrMWDty56FYkBTaF8eo9LpiLOXon/x63F39Jv8XXxSMXlDekdOciLNDlcnHzLfNgarbQWi8mHfMFvN/zoS6aWLiIjy7G71TH25LYAtE/4cI5/lo0YjgLt8yfE98gfAaNlcW4yVGKFatWYdWG59GuSdw8D7fcrA8awBzMv2WWdlf/vHn+LRZYpHEe6b0nFkSLE+/eqJoZ/wGL7+FJ42V8dPFP8ZsQpjZIcHrewZC/DhJ+gertLepmQC7+fO48OVXR0k9+hEjcv/0rlfumepNUnuvCu+9diQlcvoSPL8cuYyVzx8fuAxjzeONa27iYgTnz5styodODQsoWxeVLF2BqtpnWpGP+d5i7QFka5HsCuGbEmQ1g/0rxAQFYT36189w/x7x8nkIGcXrwE2EeXMGlj0cEC3mavwMbDpwBnDXw+n6BQPAq9KWHIDm+YhrnURKDsiMYMR9F9y7h2T5amw+hXd4NiyJ8dr+607Uajf1CIODbePx7pVjo3Ii9VUVA627sOvI+oshFXun9WMf9eW4/fnLgjLwTGw0dV3c3S1Hb9kkSOJLd6kCz9y1lRzYaQpd3P5r5Q1z6T1jyV7bfNWoHYx1vMrvM7s1CwdJvwsVvtR5CU/t5eWJHQ34893TTGNaMycb8JZRWuOQH27mGf8QBeSdb3N3ejjbjWtrMVLEudxGWrllqmAdc5z48/Xy3IBnGUN978rW0+C5UrPgWSr74Mf7ZdzxpViQoGKWYznmUpGtjnmuVzxrlRrvWc26zNZnZOsxyd1FizrpWFuTro4R2ETYSaFDWCs4GFhjhQpdYr7cqYZeMj0vZTVUWWpE+L3MJ6wHjWkQfn96nuB7SysJOr75m1NaQmgZhnaevGfnSxWr3ONl4LXTp6yBhDWq62zgRu6nCmEd6mNdt3LHl2JjvplpirEHFGLO3m2qx03m3kzn5Oj5hzSj6JLZmFO1JnK/25pFguu2iVYxlyZsRwOwybD34Jnwevkup/klueHxv4uAz34BkamkuZpesRz3fCWv3YPvhfkSRhy9X7Ua734saedeM6yqC23MU7fvW4cuzFUW5BQ/gaXlHlN+X8CVEIL57NRNinxvxWqADTTXy+4Zvz8HT6sOelbcnXx/GFMSXxjXeeBVJr3Jvx8o9PrRqeKr27vvBPRbrJDNto4x5dhGq9vng99bAqTXX+qkqwmytbgyfuQtXYE/7UXjcRXIryd2A1va9+MFf3ypomYmFK/4BbzZp/Upw1hxA4PX/hce/kQ+EWnEskOpup715JBiVetEYzlZRa5SbNtf6m9Gws5jlAOhPeghvMvYpC3iWKzug4lvaOJaMjTn21oK0mfmGriqW6VmE8OY32jyJrq1iTNgeTD2wSUP2IDCj8G+xySmhuv0MGlctQmOcaUWo+k4JvhhXlw0XN6Ow/Ntwoh3toX1Yddu+eKOkzfjOXdlndbyR478yTf7Gr45aZg0CZmkwN47vPvpTSK/TOkC+7NiMgwGfnqYq3fE01At/+7NYuXBmWi3IpPIc/nYXDeD/+5OhSrxNZUKAEEgRAasYozdjisBSc0JgohCgYJwoJEkPIZAiAhSMKQJIzQmBiUKAgnGikCQ9hECKCFAwpgggNScEJgoBCsaJQpL0EAIpImD6pT/feqU/QoAQuLEImAYjfc94Y52QSm9W31mlopPaphcBq5cdpanpxZ20EwK2EaBgtA0VCRIC6UWAgjG9+JJ2QsA2AhSMtqEiQUIgvQhQMKYXX9JOCNhGgILRNlQkSAikFwEKxvTiS9oJAdsIUDDahooECYH0IkDBmF58STshYBsBCkbbUJEgIZBeBCgY04svaScEbCMwQcHIeezewOv1lSiobYPGkmjbChLMGAKcI/KN1+uVk9sd4ingInch57+04MqMhtC9X+VnNOOI5COzI6MjcBHd9Q8iJ+dB1HdrHCr6TaUw3IZaRw4cG1pw3sA2ZZCcXJfG4yatznQ0ysWuOeNRlc77JzL7xGRGKUU+YCdOvCcwN40iT7d1BMbuL63pVRbs3MvcUhFze15l/j6RLVE9sVuqYt5epT4SbGV1zrtVZilNBz+HdYV+4rsis0LgyuRydmQ0feqndk6qfkq8eF89+1U8V1W8PQnKVj7jJ8HF/VkJxgmZXah0XmMPRn5E/x5WFUejZtYB1ZkhMD5/qbQIkps1dAYTH4KmvlRo5kT/yhQJ2lH6snEq5ZxA/WZHJnFcGm2DSEbLpbR68WDmxNbZXmPlswlKU1PIBsIBvLDtJxhKquITtNWWyhTVL2u02HpKlYzq+Qr6G1cjR5flnUQx3LYdjhwDCY6c+hjqkto0iW/KmL+CxXt3YEuZlEhPkHsrFt3pQKjrXfyrTL3Ox8rJZi5jXcXXVJLTKxjoOIrW4gLcplImQCMe6jmKjgFOlmBHxgxHjbZhCdqrd+AFLV2V7d4HeLwxWgUxBTajMZf96kDFy8fRpaXTOTlwVO7G8f7sWlDdmGAMn0VLLedyVzjXu9p/g99yhqJwF+ofWoHq9nNo3fAV3GQMEKOf2t9Cx7xq9HNW4/aNKMsL42zj38P5yEks2NWtsvM+iQUnt6DwoT3oDs9U2JjiuBcuIHCsFaE42rEohgNvoxkuVJSaMQ0bDZnM1yprMpbhnuhrWC/z2XO/HFMYtuShzUPZ6u/B2b4VD21uxtnwFYTamnBsQR3+m1PlvIgOouNQB8w5FztwqGMQUTsyllDORcmmJ+FxnkL1tp+hO3wB3S/sQDU2o35TqcLjEX0fLd934aG2v8Aume06gpGffhUnH1mFLS2clUz7C6H17+rhm7Meb3LqusgQfr7wKFwbvejWHzaabAY/ja90q1eoUS7h2jS14VLKmrLKN6imQ1fZ0JFX2QnOLMv/5Hb5BrZf5VbsvypzbVxKpLEHm6QsMsOuyn5r1C9flyhrXD2dUvSLKVis7+wujdlfKh7OmgMsEORcFhE20tvE3JIxJdTWlJxVysgkrGE/Sr3oBxFGq3pRRi0rrFQSc7rXMieWC+tRjYX5Yebt+0xoqdZrc0VlW473rVVbQU0ai1Y+S/+bUX46vovr73XjtzLv4kws/M4aOPNS7Vp9m4W+gnuKvhifas12oLAY6OkLIixz/i1B66FfYyAKRAd+jUM9Ljy6+Vso7hnAEH8yDv8Ox5ohpGAZfDqmu+twEH09c1FW8QBKJH5Ufi5mf3kN/uGZpWivrsdhnQdzBubMvQ3FW3eixgm0btiCH7UpPI/pNlHUn7vwQezYuxJ9B04AniexqUQhaAXUDEcqwKIF4pH/uZh9WwGK47IhUSMvqzJ4D31DYePNjF2nGhGjG567GBUbv47j1atQWvJ91L/eLqRDoze3lvgcHw0OJCX+VFh7VeLQVr6OuYzw0ADOrbsfd5X+DdYUn5Spw6IfDeL0tEhRAXmsnOQ17k8jV9UmJyeqbcaWhgj+y9YfYpf//8FfB+xcthEN2vpNfODF6RIu7MgI4uZF/lDIk6nFy5YsTqSZC+3EsltuAj/KQvt3U+EGtJory+ra9AcjZmLhygZ0B96Ed91HqH64HIV3/AAt5z9PEZiZWLCoIMblaKJNW8/kFtyNNa7z6BsaRODYSeQXOjBb3qQATg9+iP6Oo+hZdz9KU35bmxiRZVW5CxbhTslI060ZuRiFt80Gov04vOVpDJV9VeHFzF2I+549hIAHMcp2nWVYa6t8KsG+FGuWLkKuHZn45mO/cnnRFzFQxcuU5gHsuk/kdBy76hvd4gYEIx/STEglD6Jq1zFEgh1o+MZJPPaTjhR/HKBRPffiV2f+TVis840/nooBxTzoePdy4F1Fs3cXvM0LlYmCeSituBc9zfXY2Xx+eqSoHIu8r6FinQM9v/oXhPQdjqicMfS4vomlBbNU/C4b5mIe/mrJ14SHn/I2LW5+GwGdLtygB3ZkDN3YvuT+c0HqOYUz8vJHaxhFuHs3ynOM1PPa/ez9vAHB+AnaW36jB17uF2/D7TO+EAsUGZvLyvou/C7eaPswPrCSYZdXivXPlOGXjz2JPV0hpV34DBof34LnC6vx7Oo71LWk4jgcPICD0NYY6rqh/SAO9N07DXZRNSBvhfMH2/HAL/87tjedAV8xRUPvwLv/fWx9diXu4DMibwlWb12C1h950HRW3f4P/wte3/8OHti4DAXqrMm9YyWe3dqLp5/zy4EdDfnx3NO9MT38OWhDRrNsbJ+5yHNuxN4HTuKx7S+jSw7IKML9R/D0Nv71xzasvmPW2FRmWtq4aWS102OUi11rO1Mazz3/FHe4/shO+X/BWn0vsRqnxAAXq2nqZEF1M5Wxqyzof4o5IXDZx5SrJYvdVPnuJdbn96q6ed8uVuP1s74RvQNFh9mumryzKDHou6oJHWd9xdj9xYcUYSN9R5nHXaSwGDtrWFPA8OV/JMgCTTXMCdWvkpt5WvvYiBGRSJB1NriZxOXM9Mjd2ZAx6tWvtflVYvj1jyow0sf8XoOdvkBsfpn5nSPQ52UuWOjU+05PwcpnxM+Y6adhiv3TuakpApiB5lY+uwFpagZGS10SApMQAQrGSeg0MnlqIkDBODX9SqOahAhQME5Cp5HJUxMBCsap6Vca1SREgIJxEjqNTJ6aCFAwTk2/0qgmIQIUjJPQaWTy1ESAgnFq+pVGNQkRMGUu5r8QoL/JgwD5a/L4KpmlpsFINOLJIMuue1Y/rcouK8kaEQGrhyelqSJKVCYEMogABWMGwaeuCQERAQpGEQ0qEwIZRICCMYPgU9eEgIgABaOIBpUJgQwiQMGYQfCpa0JARICCUUSDyoRABhGgYMwg+NQ1ISAiQMEookFlQiCDCGRxMH6OUPc/obH2QVQ0nrV/fGMGwaSuCYFUEJiAYDQw3JbXYn+3eoZpCpZF+3+OR0sfwobnT6WghZqOhoA1czFvqVLx6UfnO0wejBrFXux4/ZyKRvTrByQTc/FoPtDvG0+GtDrT0SinXHNGqb2sQTtPUz9DU2QLMm9pp1Y529KE6chO42kiMzZ/iaBoLFNmzMWKnMIAZXUerqorMsh8Ver5q/IZq0Z/EXOxiDovW/ksNebiyHvsxIkP4plv1YOB4ym4jObYu6ZgHB0nK8cmbzkKc7HcmAeR2/zgYF25osdV42ciCbl+WzssWKNnk2+ohxInPThaYyg20tRp9SY0gGKnWV628llqwWg66InjOhw9GLXTpl2s5qWdzC3xp7h2SnTyk8ZNT5Q2PX164sZjCleKlVaOTap2pJN5nCUsxplpIq1iwU8J9/pOJJ7QLjdRT3qXT3H3MX+fMSQV6vGEE9tl3eKp8yb9M/4wWM4gcjLKduczp6czdrK58eRzbq9fOPlc7ktirpdaWadwQrrkbmCtCfaa2THxdVY+S1MwugRH86B4lXncVczb92+sz1enHBkvVTFvr8F5IrBSFXvptZ3MZUbUqeOjBSOY5G5ivSMRFgkOsIGRC6zXW8UkgbM+EuxgDfw4e2cDC/Cj/xPe4DFdcZNHdqYW4HrHWVOwcqy1gWqA8En7mkd9gPFU9agQcKqMdrS/fHR/HfMZJq/yQBPTWBer8fUKgdLLvC6JJWRJWoB4e+OzKqPRcvBJqs/+qASn5j8uq6bIknsv64wjfhXenHJf3EbBtsgQ89e5YnPB2G+ar618NvHByAfvUic8EyY4nKzK84oKmvpEFVMVGaDlzFnXqvAkRIbYiYYqdretYDQEi+wAwSEauHGTwPjUVq6ltW62VtKe2qr9cWmWpiw7Pq0ca2mdbeZiruEqCwbeZN4al8rJofk1XnskGGBHdL4LYb8gDm+hjVW9IKIViblY394Za+Eiul/6v5j/7HqUzOYbtbnIu+8ZnPXXQcJ83PPtlSiT2XJn47bCxYDGHIwowr89jKebvoYnfrhM5wT82+X3JJJjjmqSTUZjla7MJZOoXgFkhuXzWPfoeiwr5lyOnJ9JYcfFVOJutM1czIHWqPzeRND/FJztr+Bw14UED+RKJfhO1S74g62oc55Cw+FTOutYgvAYK4i5eIyAKeKcF+9VHJ73XwWqZ7uKLqDr8CtoLy7AbXIQ221nJmeX0RhQSFRP4VDHIKJ8kp67FxV3lWHpmoVoPvY7DEc/weDpL0wp7kZ7zMVGXGdCum8znqiBgovxtnqdKy3DD594FNA4G4m52AIp8+oJ+J5RURw9fxQvn1mKJ6qKxvE2MzdufLX2GY0hM+suQU/fhzgfeBvN+fxhMEtmRMbpQQT7f41DPVOLu9EWc7Ep8DybKTTwahoFVc5L7aFKzMVGgJJeT0gwRkNt2HN4Fr67TgtEzgn/OhrbP0naeeymMW3ld1QW3JiQzdIYGI2hBC6a/xE/8raieM3dKMhV2/c0Y+fO5qlHL26HudgU6TCGBopR+581AlozIe6zP6Ck9tsK6SoxF5uBZFmXYjByptgW1K19BFu3LoPjJu1XGDdhzlcOAw6ZxNuy89iNWSio+C6qsBOPPP5ThYU2fBZvn7qAQoTQuuE+PDCWn8TZZjRWAw9HcOAgcOeiWxWmYzm96sOBAyNTKkVV8LbBXBwNofuNt9Ct0XNHQ+ja3YD2+9fBmadNGf5zxbfwhv5rq88R6noJP24vwePOW3XXEnOxDsXoBW3XSvscy+5c4i80hG1ueafUuEXOdz1/z/w1JcrunLx1Htu5FNl0+VcVvw+8xFx8C/6IwESrGSp/aru1ht1U+V7y7xljatSd3bgdU81uzbaYdLaVxuKvmO2jMBdrW/+yf6x+oaMxTis+l9we9pr4/V6sM8b0X2YlYTcW5ePKyXzMGCPm4tGDnCRuDAJ0VOONwXkie7HymZZzTGRfpIsQIATGgQAF4zhAoyaEQDoQoGBMB6qkkxAYBwIUjOMAjZoQAulAgIIxHaiSTkJgHAhQMI4DNGpCCKQDAQrGdKBKOgmBcSBAwTgO0KgJIZAOBCgY04Eq6SQExoEABeM4QKMmhEA6EDBlLrZiVk2HAaQzdQTIX6ljmA0aTIORaMSzwTX2bLD6naO91iSVCQSsHp6UpmbCG9QnIWCCAAWjCShURQhkAgEKxkygTn0SAiYIUDCagEJVhEAmEKBgzATq1CchYIIABaMJKFRFCGQCAQrGTKBOfRICJghQMJqAQlWEQCYQoGDMBOrUJyFggkCWBSNRh5v4iKqmCQITEozR0K+wu7IY/Gc+OeXb0dI/PC74iDp8XLCl1MiaRpwfSrwPlQ5+MLUD5bUt6A+L3OBqt/zA4/21KOe+d1Rid5cJhbwdGX0UF9Fd/yBych5EffdFvTauMNyGWkcOHBtacN7EpDjZyXQRd15sEopjo5x+PXKa+ZreUWncgqyzwc2kuAOBdUlbhdEJUm2pmTZC4zvEmMOTjEY8wkZOHWFNnUGZP1HjtkzgWZQJTVfoNH6RYCurc65gnsCnAv5EIy6AIRetfJYiP+NnbODEO2woInQnc++ZnfAtyCQpUjAmAcfklpVjTUSFqlFoxBPo4c15KmVfxT14VTmBd9OOjGCYWtTowqcXjXiKaeos5Du/joWCFplyrPB7WF02L00Jwidoqy1FTnktXq6vhENOj7ajbZjnK8Pob2tEbblDSZlzKlDb2KamV1fQ37gaOQ5NlpsXxXDbdjhySlHbJpD0yGmQoS5No8mI2nAAL2x7BYv37sCWMknhFxENyf1LOJ1fEuo5zd77KNy6AmU618YVDHQcRavGOCW310iDjqJj4AoAOzJix1o5F7NL1qPeswTt1TvwgpauynbvAzxe7Fl5u2KfmALLy6RaNLb1g7Nryn+yLx2oePk4urR0OicHjsrdOD7O5ZSmeqI/hTBKVbUSCHU/DqH24GaVLJXr5PWHUF9Zgdrj76JrdyUcjg1oPKuuK0UwHRvg/d0f7BnS/hY65lWjn11FsH0jyvLCONv493A+chILdnUjwhgiwSex4OQWFD60B93hmShY+k24Qq04FtAIPxUy1BCCOD34CZTlh0q2ChcqStP1QLE3xPRIXUH/4XpUYxnuib6G9fKasBiV9cfM14ThfrQ17sCPBx7Fwa1lMbo/mVy2A9Kdi7AgYRZ1KJyXdmQsBzkXJZuehMd5CtXbfobu8AV0v7AD1diM+k2lih3R99HyfRceavsL7ApeBWMRjPz0qzj5yCpsaXlf9SfvIITWv6uHb856vMkYWGQIP194FK6NXnSbrYMtbUrzDWOKMK60R05NNdIbgTs9jka8iLkbOljwUifzaOuKcVGHmxHVMMZkG0ahDlcptF0al7x8XcLWulcwSU+tFP2J6yMjUtlxPWZ/2aYR1whnVL8665iv71Js0FZU4GK9WI61VH0lMd0P4j1DmWjEx/oAyLsPu4L8TdSJphrg+VUPq08mkUb8C1jwHwsh5ZVh24n/g20leTeeOlwlR2099GsMRIHoACdDdeHRzd9CsUZpPvw7HGvGFKSCU51qm0ac++5ZBHnmETiAGjRhlXM7Ws5/PtbZkZI80YiPE75cqQyVO/fA6/ojftl5Lpa3m+rLBHX4LCVVbeVrmssIDw3g3Lr7cVfp32BN8Uk5fZXXvFM2RQXGTiM+E1LJOux88Rm4Qr9BZ5+6vLBDEW5HxnRuiJUzMGduHgAHypYsjqXJmkhoJ5bdcpO6R6Dwg95UuAGt2v1J9JmQ7adsuwV1dMp6kyqwTx2eW3A31rjOo29oEIFjJ5Ff6MDs3Fux6E7g9OCH6O84OvXYigXsxksjruD2hZgmCz8rwb4Ua5YuQq4dmZjG8ZVcXvRFGP9WwPAvgF33xUhbx6f8xraa+GBEGEN9l/DAXfmJT7G4sWWIOlwOvKto9u6Ct3mhMmkwD6UV96KnuR47m89P3RSV4z9eGnGe3sPDkVAAAAI7SURBVJ77a9xVyN9S/E/JMoqb30ZA3snmdSr1u+ubWFowy6aMom3s/+U+c0HqOYUzGsOyrCSKcPdulOesRmM/39GdRH+G9bLMKGyss7yODDJfVQlz1hxggeBV5Ytk/1PM5W5ivSPal4/aRkDid48a87Hk3ss6efuR3zOfZyNzyoy5Vgt8iw0cdon1equYJLlZg/plNRvpYV53EYOzgQUS7AGD8B2Z8v1mfJ3luLPoxpg3cBhjCu5FzO3tYSP8OtjBGtxr9S/rlfsuVtPUqf6YY4j56x7W5WPDt/OFvh2ZmMbEkvX8YfL8K2L6/GGckdnHapz5zOnplMembOyBGTfkFH8nzsnE/ie+xspnKX7prwaAHDx8IruZxydSfmt03HxHTmJ3O51subaTKY8xns7aHnW4VTByhTapw+VdPoOD5F1GiUHfVZ14J6RDo5Vjk/cVjzucNawpoPzaRm6nPcRUv3KKcJ94X1RuhyLcjoyoM66cJBi5HNGIT6JX/xQ3lY5qnHwOtvJZGtaMkw8cspgQyAYEKBizwQtkAyEACD8/JDgIAUIgowjQmzGj8FPnhEAMAQrGGBZUIgQyigAFY0bhp84JgRgCFIwxLKhECGQUAQrGjMJPnRMCMQQoGGNYUIkQyCgCFIwZhZ86JwRiCJgyF1sxq8aaUSmbECB/ZZM3xm9LQjAShfj4waSWhEAqCFCamgp61JYQmEAEKBgnEExSRQikggAFYyroUVtCYAIRoGCcQDBJFSGQCgL/H71LwRtAth3pAAAAAElFTkSuQmCC"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of the common difference, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
<mi>d</mi>
</math></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the price of a ticket in the 16th row.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total cost of buying 2 tickets in each of the first 16 rows.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
<mi>d</mi>
</math></span> =) − 250 <em><strong>A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {{u_{16}} = } \right)6800 + \left( {16 - 1} \right)\left( { - 250} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mn>16</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
</mrow>
<mo>)</mo>
</mrow>
<mn>6800</mn>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>16</mn>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>250</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span></span> <em><strong>M</strong><strong>1</strong></em></p>
<p>(¥)3050 <em><strong>A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {{S_{16}} = } \right)\left( {\frac{{16}}{2}} \right)\left( {2 \times 6800 + \left( {16 - 1} \right)\left( { - \,250} \right)} \right) \times 2">
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mn>16</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>16</mn>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>6800</mn>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>16</mn>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mspace width="thinmathspace"></mspace>
<mn>250</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mn>2</mn>
</math></span> <em><strong>M</strong><strong>1M1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong> </em>for correct substitution into arithmetic series formula.<br>Award <em><strong>M1</strong> </em>for multiplication by 2 seen.</p>
<p><em><strong>OR</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {{S_{16}} = } \right)\left( {\frac{{16}}{2}} \right)\left( {6800 + 3050} \right) \times 2">
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mn>16</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>16</mn>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>6800</mn>
<mo>+</mo>
<mn>3050</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mn>2</mn>
</math></span> <em><strong>M</strong><strong>1M1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong> </em>for correct substitution into arithmetic series formula.<br>Award <em><strong>M1</strong> </em>for multiplication by 2 seen.</p>
<p>(¥)158 000 (157 600) <em><strong>A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>For a study, a researcher collected 200 leaves from oak trees. After measuring the lengths of the leaves, in cm, she produced the following cumulative frequency graph.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_17.29.13.png" alt="M17/5/MATSD/SP1/ENG/TZ2/06"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the median length of these leaves.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of leaves with a length less than or equal to 8 cm.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>9 (cm) <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>40 (leaves) <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Mia baked a very large apple pie that she cuts into slices to share with her friends. The smallest slice is cut first. The volume of each successive slice of pie forms a geometric sequence.</p>
<p>The second smallest slice has a volume of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo> </mo><msup><mtext>cm</mtext><mn>3</mn></msup></math>. The fifth smallest slice has a volume of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>240</mn><mo> </mo><msup><mtext>cm</mtext><mn>3</mn></msup></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the common ratio of the sequence.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the volume of the smallest slice of pie.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The apple pie has a volume of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>61</mn><mo> </mo><mn>425</mn><mo> </mo><msup><mtext>cm</mtext><mn>3</mn></msup></math>.</p>
<p>Find the total number of slices Mia can cut from this pie.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub><mi>r</mi><mo>=</mo><mn>30</mn></math> <strong>and </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub><msup><mi>r</mi><mn>4</mn></msup><mo>=</mo><mn>240</mn><mo>,</mo></math> <em><strong>(M1)</strong></em><em><strong><br></strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for both the given terms expressed in the formula for <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math>.</p>
<p><strong>OR</strong><br><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><msup><mi>r</mi><mn>3</mn></msup><mo>=</mo><mn>240</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><msup><mi>r</mi><mn>3</mn></msup><mo>=</mo><mn>8</mn></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for a correct equation seen.<br><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>r</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>2</mn></math> <em><strong>(A1)</strong></em><em><strong> (C2)</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub><mo>×</mo><mn>2</mn><mo>=</mo><mn>30</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub><mo>×</mo><msup><mn>2</mn><mn>4</mn></msup><mo>=</mo><mn>240</mn></math> <em><strong>(M1)</strong></em><em><strong><br></strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution in geometric sequence formula.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo></mrow></mfenced><mo> </mo><mn>15</mn></math> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)<br></strong></em></p>
<p><em><strong><br></strong></em><strong>Note:</strong> Follow through from part (a).</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>15</mn><mfenced><mrow><msup><mn>2</mn><mi>n</mi></msup><mo>-</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mn>2</mn><mo>-</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mn>61425</mn></math> <em><strong>(M1)</strong></em><em><strong><br></strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted geometric series formula equated to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>61425</mn></math>.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>n</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>12</mn></math> (slices) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)<br></strong></em></p>
<p><em><strong><br></strong></em><strong>Note:</strong> Follow through from parts (a) and (b).</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>H</mi></math></em> of a solution is given by the formula <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>H</mi><mo>=</mo><mo>−</mo><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mi>C</mi></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> is the hydrogen ion concentration in a solution, measured in moles per litre (<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>Ml</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>H</mi></math> value for a solution in which the hydrogen ion concentration is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>8</mn></mrow></msup></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>H</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the hydrogen ion concentration in a solution with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>H</mi><mo> </mo><mn>4</mn><mo>.</mo><mn>2</mn></math>. Give your answer in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>×</mo><mn>10</mn><mi>k</mi></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>≤</mo><mi>a</mi><mo><</mo><mn>10</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> is an integer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#999;font-size:90%;font-style:italic;">* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>H</mi><mo>=</mo><mo>-</mo><msub><mi>log</mi><mn>10</mn></msub><mfenced><mrow><mn>5</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>8</mn></mrow></msup></mrow></mfenced><mo>=</mo><mn>7</mn><mo>.</mo><mn>29</mn><mo> </mo><mfenced><mrow><mn>7</mn><mo>.</mo><mn>28399</mn><mo>…</mo></mrow></mfenced></math> <strong>(M1)A1</strong></p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><msup><mn>10</mn><mrow><mo>−</mo><mi>p</mi><mi>H</mi></mrow></msup></math> <strong>(M1)A1</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong>M1</strong> for an exponential equation with <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> as the base.</p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn><mo>.</mo><mn>2</mn></mrow></msup><mo>=</mo><mn>6</mn><mo>.</mo><mn>30957</mn><mo>…</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>31</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>5</mn></mrow></msup></math> <strong>A1</strong></p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A ball is dropped from a height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>8</mn></math> metres and bounces on the ground. The maximum height reached by the ball, after each bounce, is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>85</mn><mo>%</mo></math> of the previous maximum height.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the maximum height reached by the ball after it has bounced for the sixth time is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>68</mn><mo> </mo><mtext>cm</mtext></math>, to the nearest <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>cm</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of times, after the first bounce, that the maximum height reached is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mtext>cm</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total <strong>vertical</strong> distance travelled by the ball from the point at which it is dropped until the fourth bounce.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>use of geometric sequence with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>85</mn></math> <em><strong>M1</strong></em></p>
<p><br><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mn>6</mn></msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>8</mn></mrow></mfenced></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>678869</mn><mo>…</mo></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mn>5</mn></msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>53</mn></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>68</mn><mo> </mo><mtext>m</mtext></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>68</mn><mo> </mo><mtext>cm</mtext></math> <em><strong>AG</strong></em></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mn>6</mn></msup><mfenced><mn>180</mn></mfenced></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mn>5</mn></msup><mfenced><mn>153</mn></mfenced></math> <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>68</mn><mo> </mo><mtext>cm</mtext></math> <em><strong>AG</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mi>n</mi></msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>8</mn></mrow></mfenced><mo>></mo><mn>0</mn><mo>.</mo><mn>1</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>53</mn></mrow></mfenced><mo>></mo><mn>0</mn><mo>.</mo><mn>1</mn></math> <em><strong>(M1)</strong></em></p>
<p><strong><br>Note:</strong> If <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>8</mn><mo> </mo><mtext>m</mtext></math> (or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>180</mn><mo> </mo><mtext>cm</mtext></math>) is used then <em><strong>(M1)</strong></em> only awarded for use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mi>n</mi></msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>8</mn></mrow></mfenced><mo>></mo><mn>0</mn><mo>.</mo><mn>1</mn></math>. <br>If <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>53</mn><mo> </mo><mtext>m</mtext></math> (or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>153</mn><mo> </mo><mtext>cm</mtext></math>) is used then <em><strong>(M1)</strong></em> only awarded for use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>-</mo><mn>1</mn></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>53</mn></mrow></mfenced><mo>></mo><mn>0</mn><mo>.</mo><mn>1</mn></math>.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mn>17</mn></msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>8</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>114</mn><mo> </mo><mtext>m</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mn>18</mn></msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>8</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>0966</mn><mo> </mo><mtext>m</mtext></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>OR</strong></p>
<p>solving <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mi>n</mi></msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>8</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn></math> to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>17</mn><mo>.</mo><mn>8</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn></math> <em><strong>A1</strong></em></p>
<p><strong><br>Note:</strong> Evidence of solving may be a graph <strong>OR</strong> the “solver” function <strong>OR</strong> use of logs to solve the equation. Working may use <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>cm</mtext></math>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>distance (in one direction) travelled between first and fourth bounce</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mfenced><mrow><mn>1</mn><mo>.</mo><mn>8</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mfenced><mrow><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><msup><mn>85</mn><mn>3</mn></msup></mrow></mfenced></mrow><mrow><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfrac><mo> </mo><mfenced><mrow><mo>=</mo><mn>3</mn><mo>.</mo><mn>935925</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p>recognizing distances are travelled twice except first distance <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>+</mo><mn>2</mn><mfenced><mrow><mn>3</mn><mo>.</mo><mn>935925</mn></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>9</mn><mo>.</mo><mn>67</mn><mo> </mo><mtext>m</mtext><mo> </mo><mo> </mo><mfenced><mrow><mn>9</mn><mo>.</mo><mn>67185</mn><mo>…</mo><mo> </mo><mtext>m</mtext></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>OR</strong></p>
<p>distance (in one direction) travelled between drop and fourth bounce</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mfenced><mrow><mn>1</mn><mo>.</mo><mn>8</mn></mrow></mfenced><mfenced><mrow><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><msup><mn>85</mn><mn>4</mn></msup></mrow></mfenced></mrow><mrow><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfrac><mo> </mo><mfenced><mrow><mo>=</mo><mn>5</mn><mo>.</mo><mn>735925</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p>recognizing distances are travelled twice except first distance <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mfenced><mrow><mn>5</mn><mo>.</mo><mn>735925</mn></mrow></mfenced><mo>-</mo><mn>1</mn><mo>.</mo><mn>8</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>9</mn><mo>.</mo><mn>67</mn><mo> </mo><mtext>m</mtext><mo> </mo><mo> </mo><mfenced><mrow><mn>9</mn><mo>.</mo><mn>67185</mn><mo>…</mo><mo> </mo><mtext>m</mtext></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>OR</strong></p>
<p>distance (in one direction) travelled between first and fourth bounce</p>
<p><em><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mfenced><mrow><mn>1</mn><mo>.</mo><mn>8</mn></mrow></mfenced><mo>+</mo><msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mn>2</mn></msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>8</mn></mrow></mfenced><mo>+</mo><msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mn>3</mn></msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>8</mn></mrow></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>3</mn><mo>.</mo><mn>935925</mn><mo>…</mo></mrow></mfenced></math> <strong>(A1)</strong></em></p>
<p>recognizing distances are travelled twice except first distance <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>8</mn><mo>+</mo><mn>2</mn><mfenced><mrow><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mfenced><mrow><mn>1</mn><mo>.</mo><mn>8</mn></mrow></mfenced><mo>+</mo><mn>2</mn><msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mn>2</mn></msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>8</mn></mrow></mfenced><mo>+</mo><mn>2</mn><msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mn>3</mn></msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>8</mn></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>9</mn><mo>.</mo><mn>67</mn><mo> </mo><mtext>m</mtext><mo> </mo><mo> </mo><mfenced><mrow><mn>9</mn><mo>.</mo><mn>67185</mn><mo>…</mo><mo> </mo><mtext>m</mtext></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><strong><br>Note:</strong> Answers may be given in <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>cm</mtext></math>.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Most of the candidates who tackled this question effectively realized that they were dealing with a geometric sequence and were able to correctly identify the common ratio and identify the sixth term.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates misunderstood the instruction: ‘<em>Find the number of times, after the first bounce…</em>’ So, the incorrect answers of 16 or 18 were seen frequently.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Few candidates saw that they needed to calculate the distances identified by the seven dotted lines on the given diagram. Those that attempted the question often scored just one mark for using a correctly substituted formula determining the distance travelled in one direction.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Juliana plans to invest money for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> years in an account paying <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>5</mn><mo>%</mo></math> interest, compounded annually. She expects the annual inflation rate to be <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>%</mo></math> per year throughout the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math>-year period.</p>
<p>Juliana would like her investment to be worth a real value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>4000</mn></math>, compared to current values, at the end of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math>-year period. She is considering two options.</p>
<p><strong>Option 1:</strong> Make a one-time investment at the start of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math>-year period.</p>
<p><strong>Option 2:</strong> Invest <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>1000</mn></math> at the start of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math>-year period and then invest <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mi>x</mi></math> into the account <br> at the end of each year (including the first and last years).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For option 1, determine the minimum amount Juliana would need to invest. Give your answer to the nearest dollar.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For option 2, find the minimum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> that Juliana would need to invest each year. Give your answer to the nearest dollar.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1 </strong>– <em>(with</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>V</mi><mo>=</mo><mn mathvariant="italic">4000</mn></math><em>)</em></p>
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>N</mtext><mo>=</mo><mn>10</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>I</mtext><mo>=</mo><mn>1</mn><mo>.</mo><mn>5</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>FV</mtext><mo>=</mo><mn>4000</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P/Y</mtext><mo>=</mo><mn>1</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C/Y</mtext><mo>=</mo><mn>1</mn></math> <em><strong>(A1)(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong> </em>for <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>3</mn><mo>.</mo><mn>5</mn><mo>-</mo><mn>2</mn><mo>=</mo></mrow></mfenced><mo> </mo><mn>1</mn><mo>.</mo><mn>5</mn></math> seen and <em><strong>M1</strong> </em>for all other entries correct.</p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4000</mn><mo>=</mo><mi>A</mi><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>015</mn></mrow></mfenced><mn>10</mn></msup></math> <em><strong>(A1)(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong> </em>for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>015</mn></math> seen, <em><strong>M1</strong> </em>for attempt to substitute into compound interest formula <strong>and</strong> equating to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4000</mn></math>.</p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mtext>PV</mtext><mo>=</mo></mrow></mfenced><mo> </mo><mo>$</mo><mn>3447</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A0</strong> </em>if not rounded to a whole number or a negative sign given.</p>
<p> </p>
<p><strong>METHOD 2</strong> – <em>(With</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>V</mi></math> <em>including inflation)</em></p>
<p>calculate <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>FV</mtext></math> with inflation</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4000</mn><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>02</mn><mn>10</mn></msup></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>=</mo><mn>4875</mn><mo>.</mo><mn>977</mn><mo>…</mo></mrow></mfenced></math></p>
<p><br><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4000</mn><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>02</mn><mn>10</mn></msup><mo>=</mo><mtext>PV</mtext><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>035</mn><mn>10</mn></msup></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>N</mtext><mo>=</mo><mn>10</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>I</mtext><mo>=</mo><mn>3</mn><mo>.</mo><mn>5</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>FV</mtext><mo>=</mo><mn>4875</mn><mo>.</mo><mn>977</mn><mo>…</mo></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P/Y</mtext><mo>=</mo><mn>1</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C/Y</mtext><mo>=</mo><mn>1</mn></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong></em> for <em>their</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>FV</mtext></math> and all other entries correct.</p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mtext>PV</mtext><mo>=</mo></mrow></mfenced><mo> </mo><mo>$</mo><mn>3457</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A0</strong> </em>if not rounded to a whole number or a negative sign given.</p>
<p> </p>
<p><strong>METHOD 3</strong> <em>– (Using formula to calculate real rate of return)</em></p>
<p>(real rate of return =) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>47058</mn><mo>…</mo><mfenced><mo>%</mo></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4000</mn><mo>=</mo><mtext>PV</mtext><mo>×</mo><mn>1</mn><mo>.</mo><mn>0147058</mn><msup><mo>…</mo><mn>10</mn></msup></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>N</mtext><mo>=</mo><mn>10</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>I</mtext><mo>=</mo><mn>1</mn><mo>.</mo><mn>47058</mn><mo>…</mo></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>FV</mtext><mo>=</mo><mn>4000</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P/Y</mtext><mo>=</mo><mn>1</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C/Y</mtext><mo>=</mo><mn>1</mn></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong></em> for all entries correct.</p>
<p><strong><br>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mtext>PV</mtext><mo>=</mo></mrow></mfenced><mo> </mo><mo>$</mo><mn>3457</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1 </strong>– <em>(Finding the future value of the investment using <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>V</mi></math> from part (a))</em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>N</mtext><mo>=</mo><mn>10</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>I</mtext><mo>=</mo><mn>3</mn><mo>.</mo><mn>5</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>PV</mtext><mo>=</mo><mn>3446</mn><mo>.</mo><mn>66</mn><mo>…</mo></math> (from Method 1) OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3456</mn><mo>.</mo><mn>67</mn><mo>…</mo></math> (from Methods 2, 3)<br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P/Y</mtext><mo>=</mo><mn>1</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C/Y</mtext><mo>=</mo><mn>1</mn></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong> </em>for interest rate <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>5</mn><mo> </mo></math><strong>and</strong> answer to part (a) as <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>PV</mtext></math>.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mtext>FV</mtext><mo>=</mo></mrow></mfenced><mo> </mo><mo>$</mo><mn>4861</mn><mo>.</mo><mn>87</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>4875</mn><mo>.</mo><mn>97</mn></math> <em><strong>(A1)</strong></em></p>
<p>so payment required (from TVM) will be <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>294</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>295</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A0</strong> </em>if a negative sign given, unless already penalized in part (a).</p>
<p> </p>
<p><strong>METHOD 2</strong> – <em>(Using</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>V</mi></math><em>)</em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>N</mtext><mo>=</mo><mn>10</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>I</mtext><mo>=</mo><mn>3</mn><mo>.</mo><mn>5</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>PV</mtext><mo>=</mo><mo>-</mo><mn>1000</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>FV</mtext><mo>=</mo><mn>4875</mn><mo>.</mo><mn>977</mn><mo>…</mo></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P/Y</mtext><mo>=</mo><mn>1</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C/Y</mtext><mo>=</mo><mn>1</mn></math> <em><strong>(A1)(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong> </em>for <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>I</mtext><mo>=</mo><mn>3</mn><mo>.</mo><mn>5</mn></math> <strong>and</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>FV</mtext><mo>=</mo><mo>±</mo><mn>4875</mn><mo>.</mo><mn>977</mn><mo>…</mo></math>, <em><strong>M1</strong></em> for all other entries correct and opposite <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>PV</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>FV</mtext></math> signs.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mtext>PMT</mtext><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mo>$</mo><mn>295</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>295</mn><mo>.</mo><mn>393</mn></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Correct 3sf answer is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>295</mn></math>, however accept an answer of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>296</mn></math> given that the context supports rounding up. Award <em><strong>A0</strong></em> if a negative sign given, unless already penalized in part (a).</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Very few candidates appeared to be familiar with real rate of return on an investment and attempted the question by ignoring the inflation rate. There was a mix of candidates who attempted to use the financial app on their graphic display calculator and those who attempted to use the compound interest formula, both of which are accepted methods. The preferred method of the IB for calculating the real rate of return is by simply subtracting the inflation rate from the nominal interest rate, however the exact formula is of course accepted too.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Was very poorly done, both in recognition of an appropriate future value with inflation and realizing that PV and FV must have opposite signs when using the financial app on their graphic display calculator. In both parts of the question, there seemed to be little consideration as to the appropriateness of the answers, and often unreasonable answers were presented.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The ticket prices for a concert are shown in the following table.</p>
<p style="text-align: center;"><img 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"></p>
<ul>
<li>A total of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>600</mn></math> tickets were sold.</li>
<li>The total amount of money from ticket sales was <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>7816</mn></math>.</li>
<li>There were twice as many adult tickets sold as child tickets.</li>
</ul>
<p>Let the number of adult tickets sold be <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>, the number of child tickets sold be <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>, and the number of student tickets sold be <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down three equations that express the information given above.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of each type of ticket sold.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>600</mn></math> <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mi>x</mi><mo>+</mo><mn>10</mn><mi>y</mi><mo>+</mo><mn>12</mn><mi>z</mi><mo>=</mo><mn>7816</mn></math> <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>2</mn><mi>y</mi></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Condone other labelling if clear, e.g. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> (adult), <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> (child) and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math> (student). Accept equivalent, distinct equations e.g. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>y</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>600</mn></math>.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>308</mn><mo>,</mo><mo> </mo><mi>y</mi><mo>=</mo><mn>154</mn><mo>,</mo><mo> </mo><mi>z</mi><mo>=</mo><mn>138</mn></math> <em><strong>A1A1</strong></em></p>
<p> <br><strong>Note:</strong> Award <em><strong>A1</strong></em> for all three correct values seen, <em><strong>A1</strong></em> for correctly labelled as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>,</mo><mo> </mo><mi>y</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math>. <br>Accept answers written in words: e.g. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>308</mn></math> adult tickets.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Many candidates had at least two of the three equations written down correctly. The interpretation of the phrase “twice as many adult tickets sold as child tickets” was enigmatic. Consequently, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo>=</mo><mi>y</mi></math> was a popular but erroneous answer.</p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Too many candidates spent considerable time attempting to solve three equations with three unknowns by hand with pages of working rather than using their GDC.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The strength of earthquakes is measured on the Richter magnitude scale, with values typically between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> is the most severe.</p>
<p>The Gutenberg–Richter equation gives the average number of earthquakes per year, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math>, which have a magnitude of at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math>. For a particular region the equation is</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mi>N</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>M</mi></math>, for some <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>.</p>
<p>This region has an average of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math> earthquakes per year with a magnitude of at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math>.</p>
</div>
<div class="specification">
<p>The equation for this region can also be written as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mfrac><mi>b</mi><msup><mn>10</mn><mi>M</mi></msup></mfrac></math>.</p>
</div>
<div class="specification">
<p>The expected length of time, in years, between earthquakes with a magnitude of at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mi>N</mi></mfrac></math>.</p>
<p>Within this region the most severe earthquake recorded had a magnitude of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>2</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo><</mo><mi>M</mi><mo><</mo><mn>8</mn></math>, find the range for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the expected length of time between this earthquake and the next earthquake of at least this magnitude. Give your answer to the nearest year.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mn>100</mn><mo>=</mo><mi>a</mi><mo>-</mo><mn>3</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>5</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><msup><mn>10</mn><mrow><mn>5</mn><mo>-</mo><mi>M</mi></mrow></msup></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><msup><mn>10</mn><mn>5</mn></msup><msup><mn>10</mn><mi>M</mi></msup></mfrac><mfenced><mrow><mo>=</mo><mfrac><mn>100000</mn><msup><mn>10</mn><mi>M</mi></msup></mfrac></mrow></mfenced></math></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>=</mo><mfrac><mi>b</mi><msup><mn>10</mn><mn>3</mn></msup></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>100000</mn><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><msup><mn>10</mn><mn>5</mn></msup></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>001</mn><mo><</mo><mi>N</mi><mo><</mo><mn>100000</mn><mo> </mo><mo> </mo><mfenced><mrow><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo><</mo><mi>N</mi><mo><</mo><msup><mn>10</mn><mn>5</mn></msup></mrow></mfenced></math> <em><strong>A1A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong></em> for correct endpoints and <em><strong>A1 </strong></em>for correct inequalities/interval notation.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mfrac><msup><mn>10</mn><mn>5</mn></msup><msup><mn>10</mn><mrow><mn>7</mn><mo>.</mo><mn>2</mn></mrow></msup></mfrac><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>0</mn><mo>.</mo><mn>0063095</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p>length of time <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mrow><mn>0</mn><mo>.</mo><mn>0063095</mn><mo>…</mo></mrow></mfrac><mo>=</mo><msup><mn>10</mn><mrow><mn>2</mn><mo>.</mo><mn>2</mn></mrow></msup></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>158</mn></math> years <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Many candidates did not attempt this question. Of those who did attempt the question, most of these candidates arrived at the correct answer to this part with the most common incorrect answer being 103.</p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Those that were successful in part (a) answered this well.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was only answered correctly by the strongest candidates.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This part of the question was a discriminator as correct responses were few and far between.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>In an arithmetic sequence, the first term is 8 and the second term is 5.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the common difference.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the tenth term.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the sum of the first ten terms.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>subtracting terms <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="5 - 8,{\text{ }}{u_2} - {u_1}">
<mn>5</mn>
<mo>−</mo>
<mn>8</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msub>
<mi>u</mi>
<mn>2</mn>
</msub>
</mrow>
<mo>−</mo>
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d = - 3">
<mi>d</mi>
<mo>=</mo>
<mo>−</mo>
<mn>3</mn>
</math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into formula <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_{10}} = 8 + (10 - 1)( - 3),{\text{ }}8 - 27,{\text{ }} - 3(10) + 11">
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mn>10</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mn>8</mn>
<mo>+</mo>
<mo stretchy="false">(</mo>
<mn>10</mn>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>3</mn>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>8</mn>
<mo>−</mo>
<mn>27</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<mn>3</mn>
<mo stretchy="false">(</mo>
<mn>10</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>11</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_{10}} = - 19">
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mn>10</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mo>−</mo>
<mn>19</mn>
</math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into formula for sum <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_{10}} = \frac{{10}}{2}(8 - 19),{\text{ 5}}\left( {2(8) + (10 - 1)( - 3)} \right)">
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mn>10</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>10</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mo stretchy="false">(</mo>
<mn>8</mn>
<mo>−</mo>
<mn>19</mn>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> 5</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mo stretchy="false">(</mo>
<mn>8</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mo stretchy="false">(</mo>
<mn>10</mn>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>3</mn>
<mo stretchy="false">)</mo>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_{10}} = - 55">
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mn>10</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mo>−</mo>
<mn>55</mn>
</math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The pH of a solution measures its acidity and can be determined using the formula pH <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>−</mo><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mi>C</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> is the concentration of hydronium ions in the solution, measured in moles per litre. A lower pH indicates a more acidic solution.</p>
<p>The concentration of hydronium ions in a particular type of coffee is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>3</mn><mo>×</mo><mn>10</mn><msup><mrow></mrow><mrow><mo>-</mo><mn>5</mn></mrow></msup></math> moles per litre.</p>
</div>
<div class="specification">
<p>A different, unknown, liquid has <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> times the concentration of hydronium ions of the coffee in part (a).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the pH of the coffee.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine whether the unknown liquid is more or less acidic than the coffee. Justify your answer mathematically.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(pH =)<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mo>-</mo><msub><mi>log</mi><mn>10</mn></msub><mfenced><mrow><mn>1</mn><mo>.</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>5</mn></mrow></msup></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>89</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>4</mn><mo>.</mo><mn>88605</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>calculating pH</p>
<p>(pH =)<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mo>-</mo><msub><mi>log</mi><mn>10</mn></msub><mfenced><mrow><mn>10</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>5</mn></mrow></msup></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>89</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>3</mn><mo>.</mo><mn>88605</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p>(<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>89</mn><mo><</mo><mn>4</mn><mo>.</mo><mn>89</mn></math>, therefore) the unknown liquid is more acidic (than coffee). <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Follow through within the part for the final <em><strong>A1</strong></em>. A correct conclusion must be supported by a mathematical justification linking the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math>-value to the pH level to earn the final <em><strong>A1</strong></em>; a comparison of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math>-values only earns <em><strong>M0A0A0</strong></em>.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>referencing the graph</p>
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mfenced><mi>x</mi></mfenced></math> shows that as the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> increases, the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> decreases. <em><strong>M1</strong></em></p>
<p>Since the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math>-value (<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-value) of the unknown liquid is larger than that of the coffee, the pH level (<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-value) is lower. <em><strong>R1</strong></em></p>
<p>The unknown liquid is more acidic (than coffee). <em><strong>A1</strong></em></p>
<p><strong><br>Note:</strong> Follow through within the part for the final <em><strong>A1</strong></em>. A correct conclusion must be supported by a mathematical justification linking the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math>-value to the pH level to earn the final <em><strong>A1</strong></em>; a comparison of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math>-values only earns <em><strong>M0R0A0</strong></em>.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Evaluation of logarithms was well done, although the notation when substituting into the logarithmic formula was not always correct, with several candidates including a multiplication sign between the base and the argument. Even when the substitution was done correctly, some candidates still used multiplication, so not fully understanding logarithmic notation.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Several candidates multiplied their answer to part (a) by 10 rather than multiplying the C-value by 10, and several attempted to compare the C-values rather than calculating the pH of the unknown liquid. Most were able to make a correct contextual interpretation of their result.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>In this question, give all answers correct to 2 decimal places.</strong></p>
<p>Raul and Rosy want to buy a new house and they need a loan of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>170</mn><mo> </mo><mn>000</mn></math> Australian dollars (<math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>AUD</mi></math>) from a bank. The loan is for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> years and the annual interest rate for the loan is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>8</mn><mo>%</mo></math>, compounded monthly. They will pay the loan in fixed monthly instalments at the end of each month.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the amount they will pay the bank each month.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the amount Raul and Rosy will still owe the bank at the end of the first <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> years.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your answers to parts (a) and (b)(i), calculate how much interest they will have paid in total during the first <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> years.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>360</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>%</mo><mo>=</mo><mn>3</mn><mo>.</mo><mn>8</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>V</mi><mo>=</mo><mfenced><mo>±</mo></mfenced><mn>170</mn><mo> </mo><mn>000</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>V</mi><mo>=</mo><mn>0</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>12</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>12</mn></math> <em><strong>(M1)(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for an attempt to use a financial app in their technology with at least two entries seen, award <em><strong>A1</strong></em> for all entries correct. Accept a positive or negative value for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>V</mi></math>.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>P</mi><mi>M</mi><mi>T</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>792</mn><mo>.</mo><mn>13</mn><mo> </mo><mtext>AUD</mtext></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Accept an answer of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>792</mn><mo>.</mo><mn>13</mn></math>. Do not award final <em><strong>A1</strong></em> if answer is not given correct to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> dp.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>120</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>%</mo><mo>=</mo><mn>3</mn><mo>.</mo><mn>8</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>V</mi><mo>=</mo><mfenced><mo>±</mo></mfenced><mn>170</mn><mo> </mo><mn>000</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>M</mi><mi>T</mi><mo>=</mo><mfenced><mo>∓</mo></mfenced><mn>792</mn><mo>.</mo><mn>13</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>12</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>12</mn></math> <em><strong>(M1)(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for an attempt to use a financial app in their technology with at least two entries seen, award <em><strong>A1</strong></em> for all entries correct. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>V</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>M</mi><mi>T</mi></math> must have opposite signs.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>F</mi><mi>V</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>133019</mn><mo>.</mo><mn>94</mn><mo> </mo><mtext>AUD</mtext></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Do not award final <em><strong>A1</strong></em> if answer is not given correct to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> dp, unless already penalized in part (a). Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>133020</mn><mo>.</mo><mn>30</mn></math> from use of exact value for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>PMT</mi></math>.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>amount of money paid: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>120</mn><mo>×</mo><mn>792</mn><mo>.</mo><mn>13</mn><mo> </mo><mo>(</mo><mo>=</mo><mn>95055</mn><mo>.</mo><mn>60</mn><mo>)</mo></math> <em><strong>(M1)</strong></em></p>
<p>loan paid off: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>170</mn><mo> </mo><mn>000</mn><mo>-</mo><mn>133019</mn><mo>.</mo><mn>94</mn><mo> </mo><mfenced><mrow><mo>=</mo><mn>36980</mn><mo>.</mo><mn>06</mn></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p>interest paid: <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>95055</mn><mo>.</mo><mn>60</mn><mo>-</mo><mn>36980</mn><mo>.</mo><mn>06</mn><mo>=</mo><mo>)</mo><mo> </mo><mn>58075</mn><mo>.</mo><mn>54</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AUD</mtext></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Allow <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>58075</mn><mo>.</mo><mn>60</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>58075</mn><mo>.</mo><mn>90</mn></math> from use of some exact values from parts (a) and (b)(i). If their answer to part (b)(i) is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>170</mn><mo> </mo><mn>000</mn></math> then award at most <em><strong>(M1)(M1)(A0)</strong></em> for follow through in part (b)(ii).</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This question was quite challenging for many candidates. In part (a), it was commendable that a significant minority of candidates arrived at the required answer, but others simply used <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>30</mn></math> or attempted to use the compound interest formula. Candidates were not using their GDC efficiently. Those candidates who showed their calculator entries could score at least one mark out of three for communicating their method. For those candidates who were comfortable with the financial application in their GDC in parts (a) and (b)(i), five out of six marks was a popular score. Some neglected to round their answers to two decimal places as required. Part (c) proved to be particularly difficult for candidates to decipher which values were necessary to find the amount of interest paid. Most candidates scored only one mark for the amount of money paid over the ten years. Many incorrect or unnecessary calculations were shown. Some candidates attempted to find an interest rate.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was quite challenging for many candidates. In part (a), it was commendable that a significant minority of candidates arrived at the required answer, but others simply used <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>30</mn></math> or attempted to use the compound interest formula. Candidates were not using their GDC efficiently. Those candidates who showed their calculator entries could score at least one mark out of three for communicating their method. For those candidates who were comfortable with the financial application in their GDC in parts (a) and (b)(i), five out of six marks was a popular score. Some neglected to round their answers to two decimal places as required. Part (c) proved to be particularly difficult for candidates to decipher which values were necessary to find the amount of interest paid. Most candidates scored only one mark for the amount of money paid over the ten years. Many incorrect or unnecessary calculations were shown. Some candidates attempted to find an interest rate.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was quite challenging for many candidates. In part (a), it was commendable that a significant minority of candidates arrived at the required answer, but others simply used <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>30</mn></math> or attempted to use the compound interest formula. Candidates were not using their GDC efficiently. Those candidates who showed their calculator entries could score at least one mark out of three for communicating their method. For those candidates who were comfortable with the financial application in their GDC in parts (a) and (b)(i), five out of six marks was a popular score. Some neglected to round their answers to two decimal places as required. Part (c) proved to be particularly difficult for candidates to decipher which values were necessary to find the amount of interest paid. Most candidates scored only one mark for the amount of money paid over the ten years. Many incorrect or unnecessary calculations were shown. Some candidates attempted to find an interest rate.</p>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Tomás is playing with sticks and he forms the first three diagrams of a pattern. These diagrams are shown below.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_17.25.44.png" alt="M17/5/MATSD/SP1/ENG/TZ2/05"></p>
<p>Tomás continues forming diagrams following this pattern.</p>
</div>
<div class="specification">
<p>Tomás forms a total of 24 diagrams.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Diagram <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n">
<mi>n</mi>
</math></span> is formed with 52 sticks. Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n">
<mi>n</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total number of sticks used by Tomás for all 24 diagrams.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4 + 3(n - 1) = 52">
<mn>4</mn>
<mo>+</mo>
<mn>3</mn>
<mo stretchy="false">(</mo>
<mi>n</mi>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>52</mn>
</math></span> <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substitution into the formula of the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n">
<mi>n</mi>
</math></span>th term of an arithmetic sequence, <strong><em>(A1) </em></strong>for correct substitution.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = 17">
<mi>n</mi>
<mo>=</mo>
<mn>17</mn>
</math></span> <strong><em>(A1)</em></strong> <strong><em>(C3)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{24}}{2}(2 \times 4 + 23 \times 3)">
<mfrac>
<mrow>
<mn>24</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo>×</mo>
<mn>4</mn>
<mo>+</mo>
<mn>23</mn>
<mo>×</mo>
<mn>3</mn>
<mo stretchy="false">)</mo>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><strong>OR</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{24}}{2}(4 + 73)">
<mfrac>
<mrow>
<mn>24</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mo stretchy="false">(</mo>
<mn>4</mn>
<mo>+</mo>
<mn>73</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(M1)(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(M1) </em></strong>for substitution into the sum of the first <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n">
<mi>n</mi>
</math></span> terms of an arithmetic sequence formula, <strong><em>(A1)</em>(ft) </strong>for their correct substitution, consistent with part (a).</p>
<p> </p>
<p>924 <strong><em>(A1)</em>(ft)</strong> <strong><em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (a).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the geometric sequence <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_1} = 18,{\text{ }}{u_2} = 9,{\text{ }}{u_3} = 4.5,{\text{ }} \ldots ">
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>=</mo>
<mn>18</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msub>
<mi>u</mi>
<mn>2</mn>
</msub>
</mrow>
<mo>=</mo>
<mn>9</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msub>
<mi>u</mi>
<mn>3</mn>
</msub>
</mrow>
<mo>=</mo>
<mn>4.5</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>…<!-- … --></mo>
</math></span>.</p>
</div>
<div class="question">
<p>Write down the common ratio of the sequence.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}{\text{ }}(0.5)">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>0.5</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>The following table shows four different sets of numbers: <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathbb{N}">
<mrow>
<mi mathvariant="double-struck">N</mi>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathbb{Z}">
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathbb{Q}">
<mrow>
<mi mathvariant="double-struck">Q</mi>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathbb{R}">
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the second column of the table by giving <strong>one</strong> example of a number from each set.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Josh states: “Every integer is a natural number”.</p>
<p>Write down whether Josh’s statement is correct. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><img 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"><em><strong>(A1)(A1)(A1)(A1)(C4)</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Incorrect <em><strong>(A1)</strong></em></p>
<p>Natural numbers are positive integers. Integers can also be negative. (or equivalent) <em><strong>(R1) (C2)</strong></em></p>
<p><strong>Note:</strong> Accept a correct justification. Do not award <em><strong>(R0)(A1)</strong></em>.<br>Accept: a statement with an example of an integer which is not natural.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The first three terms of a geometric sequence are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\ln {x^{16}}">
<mi>ln</mi>
<mo><!-- --></mo>
<mrow>
<msup>
<mi>x</mi>
<mrow>
<mn>16</mn>
</mrow>
</msup>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\ln {x^8}">
<mi>ln</mi>
<mo><!-- --></mo>
<mrow>
<msup>
<mi>x</mi>
<mn>8</mn>
</msup>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\ln {x^4}">
<mi>ln</mi>
<mo><!-- --></mo>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x > 0">
<mi>x</mi>
<mo>></mo>
<mn>0</mn>
</math></span>.</p>
</div>
<div class="question">
<p>Find the common ratio.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>correct use <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\log {x^n} = n\log x"> <mi>log</mi> <mo></mo> <mrow> <msup> <mi>x</mi> <mi>n</mi> </msup> </mrow> <mo>=</mo> <mi>n</mi> <mi>log</mi> <mo></mo> <mi>x</mi> </math></span> <strong><em>A1</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="16\ln x"> <mn>16</mn> <mi>ln</mi> <mo></mo> <mi>x</mi> </math></span></p>
<p>valid approach to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{u_{n + 1}}}}{{{u_n}}},{\text{ }}\frac{{\ln {x^8}}}{{\ln {x^{16}}}},{\text{ }}\frac{{4\ln x}}{{8\ln x}},{\text{ }}\ln {x^4} = \ln {x^{16}} \times {r^2}"> <mfrac> <mrow> <mrow> <msub> <mi>u</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mi>u</mi> <mi>n</mi> </msub> </mrow> </mrow> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mrow> <mi>ln</mi> <mo></mo> <mrow> <msup> <mi>x</mi> <mn>8</mn> </msup> </mrow> </mrow> <mrow> <mi>ln</mi> <mo></mo> <mrow> <msup> <mi>x</mi> <mrow> <mn>16</mn> </mrow> </msup> </mrow> </mrow> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mrow> <mn>4</mn> <mi>ln</mi> <mo></mo> <mi>x</mi> </mrow> <mrow> <mn>8</mn> <mi>ln</mi> <mo></mo> <mi>x</mi> </mrow> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>ln</mi> <mo></mo> <mrow> <msup> <mi>x</mi> <mn>4</mn> </msup> </mrow> <mo>=</mo> <mi>ln</mi> <mo></mo> <mrow> <msup> <mi>x</mi> <mrow> <mn>16</mn> </mrow> </msup> </mrow> <mo>×</mo> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \frac{1}{2}"> <mi>r</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>Siân invests <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="50\,000">
<mn>50</mn>
<mspace width="thinmathspace"></mspace>
<mn>000</mn>
</math></span> Australian dollars (AUD) into a savings account which pays a nominal annual interest rate of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="5.6">
<mn>5.6</mn>
</math></span> % <strong>compounded monthly</strong>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of Siân’s investment after four years. Give your answer correct to two decimal places.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>After the four-year period, Siân withdraws <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="40\,000"> <mn>40</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </math></span> AUD from her savings account and uses this money to buy a car. It is known that the car will depreciate at a rate of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="18"> <mn>18</mn> </math></span> % per year.</p>
<p>The value of the car will be <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2500"> <mn>2500</mn> </math></span> AUD after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> years.</p>
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="FV = 50\,000{\left( {1 + \frac{{5.6}}{{100 \times 12}}} \right)^{12 \times 4}}"> <mi>F</mi> <mi>V</mi> <mo>=</mo> <mn>50</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <mn>5.6</mn> </mrow> <mrow> <mn>100</mn> <mo>×</mo> <mn>12</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mn>12</mn> <mo>×</mo> <mn>4</mn> </mrow> </msup> </mrow> </math></span> <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into compound interest formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p> </p>
<p><em><strong>OR</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N = 4"> <mi>N</mi> <mo>=</mo> <mn>4</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="I\,\% = 5.6"> <mi>I</mi> <mspace width="thinmathspace"></mspace> <mi mathvariant="normal">%</mi> <mo>=</mo> <mn>5.6</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="PV = \left( \mp \right)50\,000"> <mi>P</mi> <mi>V</mi> <mo>=</mo> <mrow> <mo>(</mo> <mo>∓</mo> <mo>)</mo> </mrow> <mn>50</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P{\text{/}}Y = 1"> <mi>P</mi> <mrow> <mtext>/</mtext> </mrow> <mi>Y</mi> <mo>=</mo> <mn>1</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C{\text{/}}Y = 12"> <mi>C</mi> <mrow> <mtext>/</mtext> </mrow> <mi>Y</mi> <mo>=</mo> <mn>12</mn> </math></span> <em><strong>(A1)</strong><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C{\text{/}}Y = 12"> <mi>C</mi> <mrow> <mtext>/</mtext> </mrow> <mi>Y</mi> <mo>=</mo> <mn>12</mn> </math></span> seen, <em><strong>(M1)</strong></em> for all other correct entries.</p>
<p> </p>
<p><em><strong>OR</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N = 48"> <mi>N</mi> <mo>=</mo> <mn>48</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="I\,\% = 5.6"> <mi>I</mi> <mspace width="thinmathspace"></mspace> <mi mathvariant="normal">%</mi> <mo>=</mo> <mn>5.6</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="PV = \left( \mp \right)50\,000"> <mi>P</mi> <mi>V</mi> <mo>=</mo> <mrow> <mo>(</mo> <mo>∓</mo> <mo>)</mo> </mrow> <mn>50</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P{\text{/}}Y = 12"> <mi>P</mi> <mrow> <mtext>/</mtext> </mrow> <mi>Y</mi> <mo>=</mo> <mn>12</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C{\text{/}}Y = 12"> <mi>C</mi> <mrow> <mtext>/</mtext> </mrow> <mi>Y</mi> <mo>=</mo> <mn>12</mn> </math></span> <em><strong>(A1)</strong><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C{\text{/}}Y = 12"> <mi>C</mi> <mrow> <mtext>/</mtext> </mrow> <mi>Y</mi> <mo>=</mo> <mn>12</mn> </math></span> seen, <em><strong>(M1)</strong></em> for all other correct entries.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {FV = } \right)\,62\,520.97"> <mrow> <mo>(</mo> <mrow> <mi>F</mi> <mi>V</mi> <mo>=</mo> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace"></mspace> <mn>62</mn> <mspace width="thinmathspace"></mspace> <mn>520.97</mn> </math></span> (AUD) <strong><em>(A1)</em> <em>(C3)</em></strong></p>
<p><strong>Note:</strong> The final <em><strong>(A1)</strong></em> is not awarded if the answer is not correct to 2 decimal places.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2500 = 40\,000{\left( {1 - \frac{{18}}{{100}}} \right)^t}"> <mn>2500</mn> <mo>=</mo> <mn>40</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mfrac> <mrow> <mn>18</mn> </mrow> <mrow> <mn>100</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mi>t</mi> </msup> </mrow> </math></span> <strong>OR </strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2500 = 40\,000{\left( {0.82} \right)^{t - 1}}"> <mn>2500</mn> <mo>=</mo> <mn>40</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mn>0.82</mn> </mrow> <mo>)</mo> </mrow> <mrow> <mi>t</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></span> <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into compound interest formula or term of a geometric sequence formula and equating to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2500"> <mn>2500</mn> </math></span>, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p> </p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="I\,\% = - 18"> <mi>I</mi> <mspace width="thinmathspace"></mspace> <mi mathvariant="normal">%</mi> <mo>=</mo> <mo>−</mo> <mn>18</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="PV = \left( \pm \right)40\,000"> <mi>P</mi> <mi>V</mi> <mo>=</mo> <mrow> <mo>(</mo> <mo>±</mo> <mo>)</mo> </mrow> <mn>40</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="FV = \left( \mp \right)2500"> <mi>F</mi> <mi>V</mi> <mo>=</mo> <mrow> <mo>(</mo> <mo>∓</mo> <mo>)</mo> </mrow> <mn>2500</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P{\text{/}}Y = 1"> <mi>P</mi> <mrow> <mtext>/</mtext> </mrow> <mi>Y</mi> <mo>=</mo> <mn>1</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C{\text{/}}Y = 1"> <mi>C</mi> <mrow> <mtext>/</mtext> </mrow> <mi>Y</mi> <mo>=</mo> <mn>1</mn> </math></span> <em><strong>(A1)</strong><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="FV = \left( \mp \right)2500"> <mi>F</mi> <mi>V</mi> <mo>=</mo> <mrow> <mo>(</mo> <mo>∓</mo> <mo>)</mo> </mrow> <mn>2500</mn> </math></span> seen, <em><strong>(M1)</strong></em> for all other correct entries. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="PV"> <mi>P</mi> <mi>V</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="FV"> <mi>F</mi> <mi>V</mi> </math></span> must have opposite signs.</p>
<p> </p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="32800{\text{, }}26896{\text{, }}22054.72{\text{, }}18084.87{\text{, }}14829.59{\text{, }} \ldots "> <mn>32800</mn> <mrow> <mtext>, </mtext> </mrow> <mn>26896</mn> <mrow> <mtext>, </mtext> </mrow> <mn>22054.72</mn> <mrow> <mtext>, </mtext> </mrow> <mn>18084.87</mn> <mrow> <mtext>, </mtext> </mrow> <mn>14829.59</mn> <mrow> <mtext>, </mtext> </mrow> <mo>…</mo> </math></span> <em><strong>(M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{t_{13}} = 3031.38"> <mrow> <msub> <mi>t</mi> <mrow> <mn>13</mn> </mrow> </msub> </mrow> <mo>=</mo> <mn>3031.38</mn> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{t_{14}} = 2485.73"> <mrow> <msub> <mi>t</mi> <mrow> <mn>14</mn> </mrow> </msub> </mrow> <mo>=</mo> <mn>2485.73</mn> </math></span> <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for a list of at least <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="5"> <mn>5</mn> </math></span> correct terms beginning with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="32800"> <mn>32800</mn> </math></span>, <em><strong>(A1)</strong></em> for identifying <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{t_{13}}"> <mrow> <msub> <mi>t</mi> <mrow> <mn>13</mn> </mrow> </msub> </mrow> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{t_{14}}"> <mrow> <msub> <mi>t</mi> <mrow> <mn>14</mn> </mrow> </msub> </mrow> </math></span>.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {t = } \right)\,14.0\,\,\,\left( {13.9711 \ldots } \right)"><mrow><mo>(</mo><mi>t</mi><mo>=</mo><mo>)</mo></mrow><mo> </mo><mspace width="thinmathspace"></mspace><mn>14.0</mn><mspace width="thinmathspace"></mspace><mspace width="thinmathspace"></mspace><mspace width="thinmathspace"></mspace><mrow><mo> </mo><mo>(</mo><mn>13.9711</mn><mo>…</mo><mo>)</mo></mrow></math></span> <strong><em>(A1)</em> <em>(C3)</em></strong></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The first two terms of an infinite geometric sequence, in order, are</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2{\log _2}x,{\text{ }}{\log _2}x">
<mn>2</mn>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x > 0">
<mi>x</mi>
<mo>></mo>
<mn>0</mn>
</math></span>.</p>
</div>
<div class="specification">
<p>The first three terms of an arithmetic sequence, in order, are</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\log _2}x,{\text{ }}{\log _2}\left( {\frac{x}{2}} \right),{\text{ }}{\log _2}\left( {\frac{x}{4}} \right)">
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>x</mi>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>x</mi>
<mn>4</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x > 0">
<mi>x</mi>
<mo>></mo>
<mn>0</mn>
</math></span>.</p>
</div>
<div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_{12}}">
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mn>12</mn>
</mrow>
</msub>
</mrow>
</math></span> be the sum of the first 12 terms of the arithmetic sequence.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the sum of the infinite sequence is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4{\log _2}x">
<mn>4</mn>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
<mi>d</mi>
</math></span>, giving your answer as an integer.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_{12}} = 12{\log _2}x - 66">
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mn>12</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mn>12</mn>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
<mo>−</mo>
<mn>66</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_{12}}">
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mn>12</mn>
</mrow>
</msub>
</mrow>
</math></span> is equal to half the sum of the infinite geometric sequence, find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>, giving your answer in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{2^p}">
<mrow>
<msup>
<mn>2</mn>
<mi>p</mi>
</msup>
</mrow>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p \in \mathbb{Q}">
<mi>p</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">Q</mi>
</mrow>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>evidence of dividing terms (in any order) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\mu _2}}}{{{\mu _1}}},{\text{ }}\frac{{2{{\log }_2}x}}{{{{\log }_2}x}}">
<mfrac>
<mrow>
<mrow>
<msub>
<mi>μ</mi>
<mn>2</mn>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>μ</mi>
<mn>1</mn>
</msub>
</mrow>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<mn>2</mn>
<mrow>
<msub>
<mrow>
<mi>log</mi>
</mrow>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
</mrow>
<mrow>
<mrow>
<msub>
<mrow>
<mi>log</mi>
</mrow>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
</mrow>
</mfrac>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \frac{1}{2}">
<mi>r</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2{{\log }_2}x}}{{1 - \frac{1}{2}}}">
<mfrac>
<mrow>
<mn>2</mn>
<mrow>
<msub>
<mrow>
<mi>log</mi>
</mrow>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
</mfrac>
</math></span></p>
<p>correct working <strong><em>A1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2{{\log }_2}x}}{{\frac{1}{2}}}">
<mfrac>
<mrow>
<mn>2</mn>
<mrow>
<msub>
<mrow>
<mi>log</mi>
</mrow>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
</mrow>
<mrow>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
</mfrac>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_\infty } = 4{\log _2}x">
<mrow>
<msub>
<mi>S</mi>
<mi mathvariant="normal">∞</mi>
</msub>
</mrow>
<mo>=</mo>
<mn>4</mn>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
</math></span> <strong><em>AG N0</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of subtracting two terms (in any order) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_3} - {u_2},{\text{ }}{\log _2}x - {\log _2}\frac{x}{2}">
<mrow>
<msub>
<mi>u</mi>
<mn>3</mn>
</msub>
</mrow>
<mo>−</mo>
<mrow>
<msub>
<mi>u</mi>
<mn>2</mn>
</msub>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
<mo>−</mo>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mfrac>
<mi>x</mi>
<mn>2</mn>
</mfrac>
</math></span></p>
<p>correct application of the properties of logs <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\log _2}\left( {\frac{{\frac{x}{2}}}{x}} \right),{\text{ }}{\log _2}\left( {\frac{x}{2} \times \frac{1}{x}} \right),{\text{ }}({\log _2}x - {\log _2}2) - {\log _2}x">
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mfrac>
<mi>x</mi>
<mn>2</mn>
</mfrac>
</mrow>
<mi>x</mi>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>x</mi>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>1</mn>
<mi>x</mi>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
<mo>−</mo>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo>−</mo>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
</math></span></p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\log _2}\frac{1}{2},{\text{ }} - {\log _2}2">
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mn>2</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d = - 1">
<mi>d</mi>
<mo>=</mo>
<mo>−</mo>
<mn>1</mn>
</math></span> <strong><em>A1 N3</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into the formula for the sum of an arithmetic sequence <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{12}}{2}\left( {2{{\log }_2}x + (12 - 1)( - 1)} \right)">
<mfrac>
<mrow>
<mn>12</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mrow>
<msub>
<mrow>
<mi>log</mi>
</mrow>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
<mo>+</mo>
<mo stretchy="false">(</mo>
<mn>12</mn>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>correct working <strong><em>A1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6(2{\log _2}x - 11),{\text{ }}\frac{{12}}{2}(2{\log _2}x - 11)">
<mn>6</mn>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
<mo>−</mo>
<mn>11</mn>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<mn>12</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
<mo>−</mo>
<mn>11</mn>
<mo stretchy="false">)</mo>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="12{\log _2}x - 66">
<mn>12</mn>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
<mo>−</mo>
<mn>66</mn>
</math></span> <strong><em>AG N0</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct equation <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="12{\log _2}x - 66 = 2{\log _2}x">
<mn>12</mn>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
<mo>−</mo>
<mn>66</mn>
<mo>=</mo>
<mn>2</mn>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
</math></span></p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10{\log _2}x = 66,{\text{ }}{\log _2}x = 6.6,{\text{ }}{2^{66}} = {x^{10}},{\text{ }}{\log _2}\left( {\frac{{{x^{12}}}}{{{x^2}}}} \right) = 66">
<mn>10</mn>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
<mo>=</mo>
<mn>66</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mi>x</mi>
<mo>=</mo>
<mn>6.6</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mn>2</mn>
<mrow>
<mn>66</mn>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mrow>
<mn>10</mn>
</mrow>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msub>
<mi>log</mi>
<mn>2</mn>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mrow>
<mn>12</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>66</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = {2^{6.6}}">
<mi>x</mi>
<mo>=</mo>
<mrow>
<msup>
<mn>2</mn>
<mrow>
<mn>6.6</mn>
</mrow>
</msup>
</mrow>
</math></span> (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = \frac{{66}}{{10}}">
<mi>p</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>66</mn>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</mfrac>
</math></span>) <strong><em>A1 N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>Give your answers in this question correct to the nearest whole number.</strong></p>
<p>Imon invested <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo> </mo><mn>000</mn></math> Singapore dollars (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>SGD</mtext></math>) in a fixed deposit account with a nominal annual interest rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>6</mn><mo>%</mo></math>, compounded <strong>monthly</strong>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of Imon’s investment after <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> years.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>At the end of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> years, Imon withdrew <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mtext>SGD</mtext></math> from the fixed deposit account and reinvested this into a super-savings account with a nominal annual interest rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>7</mn><mo>%</mo></math>, compounded <strong>half-yearly</strong>.</p>
<p>The value of the super-savings account increased to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mn>000</mn><mo> </mo><mtext>SGD</mtext></math> after <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math> months.</p>
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>F</mi><mi>V</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>25</mn><mo> </mo><mn>000</mn><mo>×</mo><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mrow><mn>3</mn><mo>.</mo><mn>6</mn></mrow><mrow><mn>100</mn><mo>×</mo><mn>12</mn></mrow></mfrac></mrow></mfenced><mrow><mn>12</mn><mo>×</mo><mn>5</mn></mrow></msup></math> <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for substituted compound interest formula, <em><strong>(A1)</strong></em> for correct substitutions.<br><br><strong>OR</strong><br><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>5</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>%</mo><mo>=</mo><mn>3</mn><mo>.</mo><mn>6</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>V</mi><mo>=</mo><mo>∓</mo><mn>25</mn><mo> </mo><mn>000</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>1</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>12</mn></math> <em><strong>(A1)(M1)</strong></em><br><br><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>12</mn></math> seen, <em><strong>(M1)</strong></em> for <strong>all</strong> other correct entries.<br><br><strong>OR</strong><br><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>60</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>%</mo><mo>=</mo><mn>3</mn><mo>.</mo><mn>6</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>V</mi><mo>=</mo><mo>∓</mo><mn>25</mn><mo> </mo><mn>000</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>12</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>12</mn></math> <em><strong>(A1)(M1)<br><br></strong></em><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>12</mn></math> seen, <em><strong>(M1)</strong></em> for <strong>all</strong> other correct entries.<br><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>F</mi><mi>V</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>29</mn><mo> </mo><mn>922</mn><mo> </mo><mfenced><mtext>SGD</mtext></mfenced></math> <em><strong>(A1) (C3)</strong></em><br><br><strong>Note:</strong> Do not award the final <em><strong>(A1)</strong></em> if answer is not given correct to the nearest integer.<br><br><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mn>000</mn><mo>=</mo><mi>P</mi><mi>V</mi><mo>×</mo><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mrow><mn>5</mn><mo>.</mo><mn>7</mn></mrow><mrow><mn>100</mn><mo>×</mo><mn>2</mn></mrow></mfrac></mrow></mfenced><mrow><mn>2</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>5</mn></mrow></msup></math> <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for substituted compound interest equated to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mn>000</mn></math>. Award <em><strong>(A1)</strong></em> for correct substitutions.<br><br><strong>OR</strong><br><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>5</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>%</mo><mo>=</mo><mn>5</mn><mo>.</mo><mn>7</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>V</mi><mo>=</mo><mo>±</mo><mn>20</mn><mo> </mo><mn>000</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>1</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>2</mn></math> <em><strong>(A1)(M1)</strong></em><br><br><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>2</mn></math> seen, <em><strong>(M1)</strong></em> for <strong>all</strong> other correct entries.<br><br><strong>OR</strong><br><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>3</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>%</mo><mo>=</mo><mn>5</mn><mo>.</mo><mn>7</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>V</mi><mo>=</mo><mo>±</mo><mn>20</mn><mo> </mo><mn>000</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>2</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>2</mn></math> <em><strong>(A1)(M1)<br><br></strong></em><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>2</mn></math> seen, <em><strong>(M1)</strong></em> for <strong>all</strong> other correct entries.<br><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>18</mn><mo> </mo><mn>383</mn><mo> </mo><mfenced><mtext>SGD</mtext></mfenced></math> <em><strong>(A1) (C3)</strong></em><br><br><strong>Note:</strong> Do not award the final <em><strong>(A1)</strong></em> if answer is not given correct to the nearest integer (unless already penalized in part(a)).<br><br><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The company Snakezen’s Ladders makes ladders of different lengths. All the ladders that the company makes have the same design such that:</p>
<p style="padding-left: 90px;">the first rung is 30 cm from the base of the ladder,</p>
<p style="padding-left: 90px;">the second rung is 57 cm from the base of the ladder,</p>
<p style="padding-left: 90px;">the distance between the first and second rung is equal to the distance between all adjacent rungs on the ladder.</p>
<p>The ladder in the diagram was made by this company and has eleven equally spaced rungs.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_10.59.54.png" alt="M17/5/MATSD/SP1/ENG/TZ1/05"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the distance from the base of this ladder to the top rung.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The company also makes a ladder that is 1050 cm long.</p>
<p>Find the maximum number of rungs in this 1050 cm long ladder.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="30 + (11 - 1) \times 27">
<mn>30</mn>
<mo>+</mo>
<mo stretchy="false">(</mo>
<mn>11</mn>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo>×</mo>
<mn>27</mn>
</math></span> <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substituted arithmetic sequence formula, <strong><em>(A1) </em></strong>for correct substitutions.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 300{\text{ (cm)}}">
<mo>=</mo>
<mn>300</mn>
<mrow>
<mtext> (cm)</mtext>
</mrow>
</math></span> <strong><em>(A1)</em></strong> <strong><em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Units are not required.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1050 \geqslant 30 + (n - 1) \times 27">
<mn>1050</mn>
<mo>⩾</mo>
<mn>30</mn>
<mo>+</mo>
<mo stretchy="false">(</mo>
<mi>n</mi>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo>×</mo>
<mn>27</mn>
</math></span> <strong><em>(M1)(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substituted arithmetic sequence formula <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \leqslant 1050">
<mo>⩽</mo>
<mn>1050</mn>
</math></span>, accept an equation, <strong><em>(A1) </em></strong>for correct substitutions.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = 38">
<mi>n</mi>
<mo>=</mo>
<mn>38</mn>
</math></span> <strong><em>(A1)</em>(ft)</strong><em> </em><strong><em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from their 27 in part (a). The answer must be an integer and rounded down.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>In an arithmetic sequence, <em>u</em><sub>1</sub> = −5 and <em>d</em> = 3.</p>
</div>
<div class="question">
<p>Find <em>u</em><sub>8</sub>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg </em>−5 + (8 − 1)(3)</p>
<p><em>u</em><sub>8</sub> = 16 <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>Yejin plans to retire at age 60. She wants to create an annuity fund, which will pay her a monthly allowance of $4000 during her retirement. She wants to save enough money so that the payments last for 30 years. A financial advisor has told her that she can expect to earn 5% interest on her funds, compounded annually.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the amount Yejin needs to have saved into her annuity fund, in order to meet her retirement goal.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Yejin has just turned 28 years old. She currently has no retirement savings. She wants to save part of her salary each month into her annuity fund.</p>
<p>Calculate the amount Yejin needs to save each month, to meet her retirement goal.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>Use of finance solver <em><strong>M1 </strong></em></p>
<p><em>N</em> = 360, <em>I</em> = 5%, Pmt = 4000, FV = 0, PpY = 12, CpY = 1 <em><strong>A1 </strong></em></p>
<p>$755000 (correct to 3 s.f.) <em><strong>A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>N</em> = 384, <em>I</em> = 5%, PV = 0, FV = 754638, PpY = 12, CpY = 1 <em><strong>M1</strong></em><em><strong>A1 </strong></em></p>
<p>$817 per month (correct to 3 s.f.) <em><strong>A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A geometric sequence has a first term of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{8}{3}">
<mfrac>
<mn>8</mn>
<mn>3</mn>
</mfrac>
</math></span> and a fourth term of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="9">
<mn>9</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the common ratio.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the second term of this sequence.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The sum of the first <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span> terms is greater than <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2500"> <mn>2500</mn> </math></span>.</p>
<p>Find the smallest possible value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="9 = \left( {\frac{8}{3}} \right){r^3}"> <mn>9</mn> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>8</mn> <mn>3</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <msup> <mi>r</mi> <mn>3</mn> </msup> </mrow> </math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted geometric sequence formula equated to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="9"> <mn>9</mn> </math></span>.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {r = } \right)\,1.5\,\,\,\,\left( {\frac{3}{2}} \right)"> <mrow> <mo>(</mo> <mrow> <mi>r</mi> <mo>=</mo> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace"></mspace> <mn>1.5</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(A1) (C2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4"> <mn>4</mn> </math></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C1)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a).</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2500 < \frac{{\left( {\frac{8}{3}} \right)\left( {{{\left( {1.5} \right)}^k} - 1} \right)}}{{1.5 - 1}}"> <mn>2500</mn> <mo><</mo> <mfrac> <mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>8</mn> <mn>3</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mn>1.5</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mi>k</mi> </msup> </mrow> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>1.5</mn> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for <em>their</em> correctly substituted geometric series formula compared to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2500"> <mn>2500</mn> </math></span>.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 15.2\,\,\left( {15.17319 \ldots } \right)"> <mi>k</mi> <mo>=</mo> <mn>15.2</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mn>15.17319</mn> <mo>…</mo> </mrow> <mo>)</mo> </mrow> </math></span> <strong><em>(A1)</em>(ft)</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {k = } \right)\,16"> <mrow> <mo>(</mo> <mrow> <mi>k</mi> <mo>=</mo> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace"></mspace> <mn>16</mn> </math></span> <strong><em>(A1)</em>(ft) <em>(C3)</em></strong></p>
<p><strong>Note: </strong>Answer must be an integer for the final <strong><em>(A1)</em>(ft)</strong> to be awarded.<br>Follow through from part (a).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A disc is divided into <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math> sectors, number <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math>. The angles at the centre of each of the sectors <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> form an arithmetic sequence, with <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub></math> being the largest angle.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAYAAAADwCAYAAAAJkrPKAAAgAElEQVR4Aex9d3hVVfru/efen9KbithFQdGx/NQZZ9QZHZVUCL33Kki1oFjp6b0DIQkQehICCS30QCCUAKEkISG993rKLue9z7f2OSFISK9k7efZnMM+u6z1rp3vXeur/wd84whwBDgCHIFOicD/6ZS95p3mCHAEOAIcAXAC4C8BR4AjwBHopAhwAuikA8+7zRHgCHAEOAHwd4AjwBHgCHRSBDgBdNKB593mCHAEOAKcADrYOyDrdNDpZOh0EmSdzHZJJ0GSJdAn/Q5ZB9An3zgCHAGOQC0IcAKoBZz2+JNOFvSCXwedJCu7LEEnS5BlGaKeHAC5PTaft4kjwBFoRwhwAmjBwWCzcZqIP7DT7FyZoNMkXafTQdaJ0LFd+YGO55eqkJBVgrj0YsSlFyIuLR+3k3Nw4U4a9p2+Aae9Z7Bmywn8tPEY/txyGn/6nYZPWDSOXoxDdEIu7qTmIT69QNkzCpCaUwytILHnKSsIWkXIkKj/OjoOiNQW6MD+ZSsNKKuJFsSI35ojwBFoOwQ4AbQg9rJM6hpSy5CKRoYkidDJMmRZgihrkVVcinO303D+Vhq8QqIx8c9AjPtzHyx+D8KbU1zQy3gtehhZoquRDboZ26PLUFt0NdmALsY2+B9je/QwssETX2/Ak0Mt0cXEEl2HrkcXIxt0Nabdln3vYmSLrl9boc9wW/xnuT/G0DNWBWKuTTDCLibg8q0kXLmbgQqtFrJM7VNWFqIsgnZSK/GNI8AReDwR4ATQguNKwl7QydDKIrKKKhF8Khb+h29gxAoffLLYF69McEV3Ixv0HLoBTxrZ4J1pbhi/NhgT1+3H1A0h+H3zGRy+kIgr8em4rN+vxGbgalwmrsRl4VJsCl4a44SfPI8hKj4Dl+OycCVW2S/HZbBrLt5Jhe/ha1joEIppa4IwcV0IzH8LRG9zK3Q3Xo8nTWzRzXg9/neeFz791gtL3cIQeOYmjl9OgCCJEDkBtOAbwm/NEWhbBDgBNAF/NluWSYWjzPRptk+7WtShTCVi14lrsNt5AR/P9sDA8W7oZWyNvhYOGDLdC9+7H8NPXkcQHBGLxKxiJGSVobBcrVe/SABTCSlqGlITMR0NPUevoiEDsFrSYOB4Jzjui2I2AHo2ICp79Wtkg11YZveRZB1Sc8twL7MEt5PzYbvrAlZ4nMA0yzA8Z2GHvsOc0MPEAX+bsRGjVu6CZ9AFXEvMQKVaWc3oaKXADNA6RW2k77+i62oCoPxSjgBHoFUR4ATQBLhFEtKyAEkno6C8AtdSirDe9wSMftiO58c5oYepAwaOd8CwX3bCcttZnLiehMLSCpRUCtBJAkiQSnph2uBm6ACNqMXACS5wDIyEjmQ7MzbU705EKlW7rGWqHq0oI7+0Eun5FfA9EAXLbSfw/iwvPD3GBX2GO+PV8U5Y6HYEHsFRyCyohFYQoRMFgIzRMpEV9zyqH/r8LI5A+0CAE0ATxiG3iHT4qVjqchxvT3JCLzNbPDfOFR/N84ZzYBQORtxGmUZiqhTy2FFcNUnwkszUgWwEdKxRgrM5CYAJcMWNlMiMVhfULlEnMCGfkFUM39BLmGsXhHdnb0FPM2v0NbPC8JW74LjnAmJTc6EVBDAWagKe/FKOAEegdRHgBFAL3jpJgpYZbRXjKAnGCkHEmZhkLHYIxaDJznhyqBXemOqO8av2IPhCHNJzC5g7ZqOEei1teeinJhLAQ/erzwEZUEtanL+ZDMd95/D5Mj/0NLVEV2NLfP3dTmzcfxnxaXkQZFrdCIzkyJBM7qmKlxN3Ta0PzPwcjkBrIcAJoBakyStG1mkhSjrE3MvA7/5n8Pc5G9HtazsMGOOI2dZhOHEjGdmF5Yr3DJvNK6oQEnoturUBAZDNg1xGQTEHkgRJkHA7KRcbg6Ng9tMePGlshX6jXGDy/TYEnb6F0koVdCLZC2jVw1VELfo+8JtzBBqBACcAAo356SuG1uqRtmTIDTobi2Erd6L/CDv0MbZCLzM77DgVg6yCUsVFUiKVicEQrKh1lBlvC+vD24AASMVDJEA8QOQosH6TCkuEWhCRmFHAbB0fz/dC92FWeG2SC1Z4H0NcRgkEUYlcJv0XEQLRIzMZcLtBI/5s+SUcgeZBgBOAPtaJdN+k95YlNXKKVXDbexFvTXNBLzMbfDDXB3Y7z2HL4VvobWaLA5F3mAG3eYagkXdpCwKoo6ks8E0WUaSWcPxKIhY4hGDAOBf0HW6L8X/swNFLCShXayBJFGugxES0uKqsjjbznzkCnRkBTgA0+jSrlSTczS7Car9TeHGsI/oOt4fJigCEnI6BRitClkSoBBHvznDF2FWB7Pw2fXHaIQEwVQ/p+6tSU0hIySnDOv/TeHOGF7oPtcFXy/1wIPI2CpgnFKnYWnil1KaDxB/OEWjfCHQ6AmCJDpgqw+C6KCIluwhLXA6jv4Uz+g9zxjeOh3A5IVuvGZKZmyepLChNwh+bTuClCS7IKCjX67bbSIC1QwIgFRFThzH1jqRX8yixEWVqAUERt/DJtz540sgO/5jrhYAjN1CuVrPIaCIPiXYWPd3C9pP2/TfJW8cRaDUEOh0BkP5aZEnUBJSpVdh06BpeG++MvsNsscQ5DHHp+ZBlDfNiqWkU7qQWoPcwFxYcxWa8ep12Tee26LH2SACP6LABJ0GWUKZSI+z8HfxnmT+eHGoL4x93Ijo+C7KsBSTCXSGRR9yKH+YIcASaEYFOSAA6aDRaBEXE4eMFm1iw1qTVO3E3vRiyRK6LFNykgyjXnANHrRHw5fdb8e/FvpAkxYefBFyrbx2QAMhYLOhzIlVUVCDsXCw+XOCNp0baY5ZlCOLT8yHIIk9A1+ovE39gZ0XgsSYAli+f6aTJwKthnijHLsfj6+/90XuYPf67PACHI+OgoWjWem40Q90cdhXdTK0ReTOFJUyjY62+dSACqAkbw6qgpFKDddtO46XR9ug33BorvI4ip7CM2VwoDoPcR/nGEeAItAwCjzUBkOwgnTIlZEvNLsG3TiHobWqHIVM9sS38BlQiZcDUsEyd9YVXpxOQlleGFyzssNwtXNF5S20gpB4TAmApJAQNUnJLscjuIHoMd8Q7M73gd+waytUq5nZa37Hh53EEOAINQ+DxIwB93jTS9UMnQCVI2Hr4KgZM9MTzoxyx3u80MorKWYpmVlClgUZHluJZ0mGeXSgGT3ZHdkEZi3RtGOzNcPZjQgC0ShNZXIHEbDNX7qTD4qet6DqUUk3sRExKQVWeIZbviGnb2kDl1gxDxm/BEWhvCDx2BEDqeJqlk775xt0cDP9lN7qaWGPMbwG4nlLEPE2aMgjMy0UWcDImCd2MrBB4NpY9qyn3bNS1HZwAauozqYWIYNVaCb5hURgy3QNPWdhiXUAESlQa6HT6mgVtYXOpqcH8GEeggyPwGBKAkq/Hencknh1lj1cmOGH3iZsg460sadnMvyljpiRKE5n74kcLfDB2bTCbuTblno269rEkAEoXoUQMS5KA1NxyLLQ5hJ4mtvhy8VacvJmuGN7bQOPWqDHiF3EE2jkCHZoAmCFRH3hEM0eNICPkQhw+XeiD1ya6YZX/WeQVV1T5mbOgoybOHg3GS/r0CIpEd3Mb3EzIZhk0WQBUaxktH0sCMKSoVuoWUK4IQdLiYmwGRvy2D/1HOGC+fQiz57CqajoeSNbO5QtvXjtHoGMTgD6lsigDOcXlsPh1G3qbOmH8mv1Izi1j6Rp0LNd9y0wZswvL8Mokd3zvfQISFWun/P6tNeCPIQHUBJ2SNluCVhIRfO4O3p62GU+PcIL3wWuQBDX3EqoJNH6MI1BPBDoeATAdvz6hmEgzQBFhF2Lx7iwfPD/aBc6BZyGIMlj+fX10KZ3TEhvlDlpgG4JXxtuhqJKeSW6LLfGkGu7ZSQjAoBJirrayjKyicgz/2Q89TK0x2yYUeSWV+mpoCvCGFVoNiPFDHAGOwF8Q6HAEwEoRskheERUaDdyCotHfwhHvztqIm8l5TBj8pY8t9l8igEMX49B3mAN2h8eAVhskgFpl6yQEUB1LyrJKqj6tIMNl3yX0MrXGpwu342pyrpJcjhmRedrp6pjx7xyB2hDogASgY0K+sELE1DV70P1rWyx3D0MeuXZKGlajtrYON+dvlEBOLUl4Z4Y7hq3cDioRydxPm/Mhj7pXJyQA8uwi3T8RAUVqn76RgY/muuDZEa7YfuImMxC3SiruR40JP84R6GAIdBgCoIk1JWOTJRm3UvJg9tM2PDXCDmu3nWO+/mTgpXOUwuitMwpk9BV1MtZuO4mnxzkjIS239bJbdkoCUGb3ippHMRTfyy7F0OVb0NvCAc67IlGpMeQTat13oXXeOP4UjkDzItBxCICW/5IWZ66l4oVxznhtvBMu3E5n+Xsot3xbbKSOogyWiVnl6DPMHvZ7zgGtZQbuhARQ0xjTiqBcXYnfN59Bj2F2sPh1O0orNNCRy+8j8jnVdB9+jCPQGRHoMARA6pZjV5MwYIwrhkx1xvXEHKYKIgFMqpe22Aypi7UaDcb8uQcfzvFGpaaV/IA4AbAhl1ncgARR1sJ66wl0M7XH8F+2I6+M0ky3zXvRFu8ifyZHoDEItGsCoKU+0/lKEnYdv8mKtExcvRfJuSWQye2ytQyudSBLK4GAEzF40mgDImIy2KpE29KzT04AD42KLOmw72QMXp7ggk8W+CAlpxA6qj6mk3hOoYfQ4gc4AkC7JwDyrw+MiEdfC2vMczgClYYShJHPPemD28kQ6iTkFpVj8BQ3zLQ8wGae5K3SohsngIfgpXTetMfcy8eQqe7450JfZBRSIKCq9byzHmoVP8ARaL8ItEsCYK6eoJmbFvvOJKCfuSVG/7oH5VoVcwMUyeBLAraFZWx9h43UUBQDsNghFC+PdUZ6fgGkls4QygngoeEhJwGq7QydiNspeRg4wRGffeuHtIIygGJDmJMAJQl86FJ+gCPQKRFolwRAs35J0mL3mbvoO2wdPpy1GakFpZB0GnIFaocblTKUcTEuB92NreB3LJoZrFu0oZwAHgkvyXdKCHjwYiJ6m27Av77dgnQq4SkLyt5ulo6P7AL/gSPQKgi0SwKg0oG7T8eit4U1Pp63Bal5pPMXWdh/qwVaNQB+HRRvIJVWxL8WbcGoP/ZDLWgbcIdGnMoJ4JGgKTN9JTWH79Hr6G1mic8WbkZSfoWeAB55Kf+BI9CpEGg3BMDUPlRUXJYQePImeg6zxr/meyElr5T5/rPCIfo0EO1vhHTMIE198Nh/GT1NrRGXUVRVNL5FSKsRBMCM6qxwu8xy7FMRd9qZkZSpsdrl8uqh4WZ46osDkCqQ/v8Axvr3hIiAorX9jtxEH1M7fLZgMzLZSkCExA3DD+HKD3Q+BNoNAZDRVJYrsOdUHHoPt8MH32xBSk4JBHZcCQDqCMNzNy0PT49xhtXW41WC6QHh1FydaAQBkBKcciRRAXbFfVLRmbMgOrKptLThupn6TkTLhD4J/5oIoNpzKHpY1AnwPRKDnmbr8c8FZBguZd5BRAJ84wh0ZgTaDQHoZBFhUffwlLktPpztjeTM4iq1D5FDiwjRFhh5EqwWv+7EW9PcoNUquYFapO2NIAAS9Ml5JbAJiIBlwEVYBUTCdtdF5BWW6lcwHUMgUj/I8F5aXomysnK9R1jNll1yA6VkgPQO+R6NQS+T9TD7fjsKK4gEeZxAC/wJ8Ft2IATalABoiS5SCmVRRGJGLgZNcsHrk92QlJOvL/zRMVQS1cebZqT+4TfQd5gdTlxJ0OcHaoF+NIAAmLpD0OFodCKeH+2AF8e5YfSvO/HlUj9WdWvrkWtKJlOZspnqyZY+9TPs6v0zfDf8Zjjf8FlaocKekzFQC0pepAfIT39Pg/+u4RrDPQ2fhuOGT8NxUZYhyRrkFFXAalcEXhjrjP+dvwWyqPf+MZxYwye9ayTwtxy+gT7DbLHCIxwiuY3qVWKQW2CMamgHP8QRaE8ItDEBkJDRIrukEp8v9sMTQ23w/AhHnI5OhCxqIdU8qWtP+D3UFlJPVGhFvDTBFbOtg1hyugeE4ENXNPJAAwiAhJwgivh86RZ8MMcdibklkIh4KbOmBIiiCLDYivv6dEX4kjdNze2j48p+/xqamfscvIIBY71RoaYZ9oMXs/NBgvj+NTXd3SD4DZ+Gc2gWn5ZfgsGzNuG9Gc7oM9web8/0BsXcUU6m2ja6lyxr2IRjU9g19LSwheOeSEi0CiC1WB3X13Zv/htHoKMi0CYEQLNH+oOjz7xSFT5fsoXNTPecvo13Z7nj6dFOCI9O0edzqea/3QFQJiM2uYQucT2KVye5KkbHlhAuDSQAtSjglcmesN99DjpJA4qaJUEs65SIavKfp3aTCkullXH00l0cuZiAwlIVSMKyWAcmuCVKyYf8YhXCLiTgyIU4xKbkMeN9XkkZnPZdxLNjHJGck4+0ggpo2UqAiF6ESiPixJV77LpbybnMEKu0AaysZoVGZvETmQUVOBmdqBT0qUYizE4kCThy8S5KytV4Y4oz3prtAVLlM///2t4Ptvog0lJiNlZ4HEJXY2vY7Tyn2ESq2RLoHL5xBDoDAm1DACT8JRkarRYTV+9CNyMb+B+NZoIpPb8ME1btRX8LB2wKvQq1SEngqCB4x/ijpAyh5LJ69W4eepo5wv/QzZbJUNoAAqDAOVGU8MZUF7wzxQsJWYVVeZSEarNx8pO/lpCHv8/fjH4WtnjGgozxfkjKJnuMEmVbVKHGL5tO4tVJ7ugzzIYlwXt+ggtORCdi8u978PwIZ3Qbuh6DJ7jhzQkuOE8J+2QJJ6+n4O1ZG9Hb3Aa9zGml54BFDsdQXqECuf3eTs7GW9M9EHLpDt6d7I2/zfCGQPEgf/krVGbyMjSSgDcmu+GtWZ71I4Bq96FXqbRcA/OfAtDb3A4nrtFkg9yMaZXQcRwOqnWJf+UINAqBNiEAmmVS1S63kKvoZ2YDt4NXIMgySBiJsg6VKi2+cTyC7saWWOJ8COVageKCG9XB1r6IVjWUnE6l0uCr5VvxxRJ/iC2hy2oAATCPH1nGgcg4DBjmiCFTHeARdB4ZReoqwUfC725GMQZPdMX4NfuQnleB3IIKzNoQjM+XbEa5SmA680VOh9HNyAobfMORVViMnPwy3E4pgFatQWFZOZyCItF/jBPu5RUiq1AFrVaNqDsZeGWcE+ZaBiMtvxI5RWU4EBWL/qPsYLXrHHPVvJaQwXIpvTzGAT9vDkdceiF04sMV1thEgPreBAJgQl7SIr9cA9OftuOt6V64k1ZYJfzZM1r7xeHP4wi0AQKtRgBKIJfeyCgL2BYeg54m1vjW8QhESantqrj3kWpIQoWoxRKHI+j6tS2+sQmBhlQJTEXRBig14JFsFslUK4Br4Dl0M7fB3fR8ReUl/XU+24Ab//XUBhCAwW2S1G4nrqfjq+93oK+ZPZ4dYQ/3/ZegEQRWYGXN1vN4bbQdskoM+ZYEVnuhq4ktYpJyEZ9ahD4j7PGj1zHFPRcSUyOJzB6gqJB8QqPx3DhXVKgEppah+A0ilIHj3VCi1qudQKs6GSu8jmHIjM2o1Iq4npCBJ4Y6YKZlMLNPMBxroP3mIAAyXjCLgU5CUkYRBox2xgezXVhdaSXepGNMNv76SvD/cwQaikCrEYAh2Ij0uMlZRXhtigc+X+SNbIOwqdZymkVT2ocKUcDPHkfQy9QGv28/B51YyfTU1U5t11/TcovwzEg7eO2/yPIaaZvT06QBBGAAiXAl1ZtW1uLUzXv4atk2dDGxhf3eC6yo/effbcOgqW6YtDYIE9YEYcLaYAz/ZRe6GNvjxr0sOOyKwBPGGxB2PtZwywc+iWi2hF7Dc+NcFCMwIwjgb3M9scgpjKmCqi7QaREadRdPj7RDaaUG1xOy0dVoA4LO3mW6/6rzavrSxBVA9VsSER08fxd9LBzxo8cJaEWBF5qvDhD//lgj0IoEQPpVHcpKy/GP+V54eZwn0gqKmUBXiqnfnx0bDMR0XBAEbD9+B8+NcsAqvwio1JoOMyCkCpqyZj8mrgmB4sLYjH7njSEApmJT6uqSzptUNn+ftxFDprkz75gvl2/Hm1NcMW7VATZrn7A6GJNWBWLcuv1ITS+GZcAFdDNaj5PRaTWOwaMI4L05W7Da//gDgWa0motPzcOAMY6MAK4RAZhY40Jc+kPeQw89rBkJgNyQZUmE465IPGliC7fAc3U//6EG8QMcgY6JQKsRAPlgC1oRv3odZ37YO0/FKukIasGNlvuGfcuRaHQ13YDJq/agsJyqPZGfee2uf7XculV+IlfLk1eTmEtobnFZnf1tUKMaQAC0+mLqM0mJiqV2CRKp1ET84nMKQ2Z5su///W4rvljuy2wwzCOIFWFX0nPQOHjtj8KTxjbYFX6DCU3mSqpT0ioQuZMRmVwsnx/rinK1lhVpIZvOu3M346ulm1n9ZJEVcFFUQM57zuPpEfYoUalx7W46uhlb42JcJjmK1g5FMxKA4UGVGgGTV+/HK+NtcPluBkRm9L4/KTGcxz85Ao8TAq1GAKRbDT5/l1Vs+sMvAjqhok7XPYPwp08KFtuwLQJPmtpgxK9EAmQ3aN+6WiKoojIVXpviitDz8XX2t0EvVoMIQHGvTMgshkarCH4ScFmFlXhjkiv+9Y0v84ffcfI2epnYYO/ZO8rKjAVeiajQkKuoCnmlGgwYTb73XriXWcDcdHWyBoJIhExEIcDnwEX0MrPF2atJkHQCMzL/5nMSTw23xbEryaDKbrRTwNhnS7dj0vqDjHzICNyWBEB2geyyCgyZ5IkP521CiVrN2tmgMeEncwQ6GAItSgAkn5mMprq56QUYNMUNZiu2sZqtzO+8HjN4AwlQNKsoaeGwOxI9zayZbpqEq05viDSc157wpz7SrHi6TShG/ryb+dw3W/saQgCyhJS8Erw+xhEjfgvCYrcjWOh2AgMnuWPgRGdcScgC5cwRBAkzrEPw9HAbzHE4hqXux7DI/Ri+tT6gRDRLEg5FpeBZc1sMmeKMpa7hWOx2HFM3hOBSYh6z21yKz8FTwx3wxVJfLHU/joT0XJSUqTHs5914YaQVFrkdw0KPY/ji+wC8PMEJt5LzmPtvNFsB2OF8XGbdOnidDipJgzcmeWDIrI3MtkBBbU3ZWHCaKOLUjRT0HeaIxQ4HIVK8BIsgphe5jlVJUx7Or+UItBECLU4AFH1ZKYiYsS4E/S1sQLrepmykzjhwPhavTHDCv5dsRUxKPnSishpobyRgaI/v4St4dqQ97mXlN6XrD17bAAIgN1CaxQdfuIcxf+zA58sC8PmybfjdPwJxqffbRGSlFUXsPH0HJj/44z9Lt8J85S6cuJbKZvgkZGn2fjEhA/Mcw/AfcnNd7oefN55Ack4JS7UgSjL8j8bg6+Xb8Ml3AbiRlAVaJZRotHA/cB1fLvPF58v8sdL7KGJTFe8o6ASk5hbjR9cjSM4j9886hLkMaGUNrPzPwnLHWUayZGNpykbKHlJTUv+pbX2H2yH8yj0lGE2firwp9+fXcgTaIwItTAAUVKOBV2g0ulKw1+EYyKLQJBwoIpWyWcYk5ePtKc54ZYwDwq+mVNkKSOi2l81AACk5RehtZgO7HRHN17QGEIAhwpcEsZINlIK6tNDJ6gdSKNAsmILGlAysyqSXVDs6ypnD1EGku2cJnFjBFdLvs5rNpOqRtcq9mW2BVEKKy69E/6e6vBJlm9AyAiF1ID1DlKmYuxJ4xZ5DgpbttY8hTcaJrAyZPslZgK5vykbVxGRQWySUqzX49FsfDJrogqySCiVNRlNuzq/lCLRTBFqEANhynAy4soj45Dy8PM4Zk9YGo0KlARkBm7Sx1bhiHL6TkofB07zx9HBbHL10T586gn5TioCT22Nbb0QCNCse+gPNurejolKjF5pNbFsDCICC6KgdJOApkQPJcIKGBOkDhnSDzk7/yQhMb5JVUjaw0jdMRcNUJtQF/X3p/8p3/b0VKc3EKl3F2gAiGKrISP9I7Ch90nPoWvY8/Wdt46Y81tAnep5yfW3X1Plb1fMJFwlX43LQf5QzFjmSKojiHeq8Az+BI9DhEGgRAqA/ZJp1aiUdJqzeh5cnuOBGUjZbDdSZs6UBENKSPT4tHx/O9MIzFvbYH5nA/NkVj5RmEAoNaEutp+ok7D4Th27Gloi8k8U8aB4QvLVe/IgfG0AAj7gDP/wIBMidVdKp8IfPSfQwt8eBqESWMO4Rp/PDHIEOi0DLEIAsQasDAk9fR6/h9vAMimLphplgbkZjGi39iWgyi8owfX0g+o10gnfIBZZ0TJlNNk0t0FyjSmqrzNwCvD7JGYvdDjOPJk4AzYVu89+HGX4lgdUb+OdCH3yyeDsKyyqa/0H8jhyBNkaghQhARlGpCm/P3IhPF22GSqtknGzJvqoELb5zO4oextb4xuYASlUalmOG2QyakXQa0wd6PKUdXugYhgGjHVBUTqqwJpITXwE0ZigafM2Ry3fR09gea/xOQSKbCUtH0sSxa3Ar+AUcgZZBoEUIgDxF1vmfRXejtbgQnwOZFd5omQ4Y7kpGRyKBHzxP4P8ZbcC0dftYOgLIGpbK2HBeW3wqKjEJp6LvoZ+FPbaEXmGGxSa1hRNAk+Cr78WiJOIb+xC8ONIFsVnFSuGcptqx6vtwfh5HoIURaDYCYEKOFXXX4cyNFPQwtcEav9PMgEa/tbQfNUt4RgVORAE+oVfw+iQ3fPnjNsRTIjZK0aw3VrZFUlHmX8KeL+OrZf74YvFWaA2uhY01YHICaN4/DTYOUpVRm+VN0slIyyvGz94n0dXUCv/9zhdl5ZUspUnzPpzfjSPQNgg0LwHIAioq1PhsoT8+W7QNKg256rWu+wQ9j7w47uWUwvT7ADw71hV+R69BENV6ImjGfDyNGLNdZBcxdcKRyDv6ojjk09gIjDgBNAL9Wi5hheaVPEkUwbZm3t4AACAASURBVJxVWIqVG8Px7BhnDBjjjPm2B/GEqRW8Qi61+jtdS6v5TxyBJiHQjASgpAP2PXId3c2tcPRyEgvxp9YxodwYIdeIrtGz2GxfFlFSVoFhvwagm/EG5oOvuPO1rf62qFyLF8a64Bvb/RCZ7Cc3yEa4xnICaMTbUfsl9O5UqjUIPHkb78zwRE9zO3zndBApuUXQSiLGr96Lt2e4I7eksvYb8V85Ah0EgWYjAPJqyS0uZpkljZdvhZZV/WrEzLYZgaN4hMIKDUauDGCBaJY7TkMQySCtqIToD761N/Jc+snrCAZO9kJuQQm0zCe+EasSTgDNMnSSLLHKYxRIduxSPL5Y6o8+pnb46vsARMQkVz2DSDr6bjb6mVviT//TYAFuTQw+q7o5/8IRaCMEmo0ASJiu8T+DHpQI7FaaUu9VboRga0YgSI8rS2qUlqswY90edDe1xVr/86ikCmNUCLwNonsIpwu3M9DDeD12n9QnXWtMnzkBNAa1h66RRDUoSd4C+0PobmaLt2d4IPhMLMs7RcntDBuNG2VPnWMZiP6jHZCYVca8zAy/80+OQEdEoMkEwIyvOiC/tAIDx7lgzK872QybZt9tMcOuPggsfQEFpelkqLVaeIRcRh9zS0xZG4LcUpUSMcxsBq23EqCkdhUqLT5fugPmP+9g6RC4DaD6qLXUd7INsdBnJdk02as0WqzadhoDRrvg5XGOsNx2Gvkl5fpi9TJ7jw2tIbWiKGtx9W4unrawxXK3cE4ABnD4Z4dFoMkEQH72OlGE3+HLrAh61O2MdgkGkQHV5g04eRtPmVviH994Iim3hOUVIqNxa21KDn0t7HZfQV9za5YQrVEeUnwF0KAho8UevatsMiBI2HHiNv422wc9zewwfd0e3MkoZsGLNGmhSc1fNzrCMqbKMubYBeGFUc7IKebBYX/Fif+/YyHQDARAuea1MPtpN8av2gNBaFu1z6PgZysVSkomCwg4cQd9h9ng7/O9EZ9d0jgj7KMeVMdxpkrQiYhNy0Wf4fZY63u2cS6ynADqQPovP1N6B1GDq4m5GLlyB3NTtlixDaeiU1lNZFqZkR1LIYC/XKt3ZKDfaSJx/V4mnrZwwsaDlx4+kR/hCHQgBJpMAIIsIyGrCM8Ms8f5mBRW0Ltd9t/gHcT+iEUcjEzES2Od8MHcjUjPL72f4KyFAwUMAoZSWIz8fQ/+d7YPiktVzEW1QXmSOAE88jUjsicsSW3DVqiygNS8UiywP4A+JrZ4c/ImeBy4hjKyBdFsX7/Td7qmJoUgm0BQGjt9FtMZa4Nh8dtuSJIMyoraqFXcI3vAf+AItA4CTSYA8ob42TscnyzyBZXVa5AQa50+PvAU5W+VqlKJuJ2ai38u2ISPF2zB3exCVvWq1ezCOgkh5+LRw9gK4dcp374KLIvqA62t5T+cAB4JDss9SllGqe5xeSlc90dj0BR39LNwxOpt55FTXA6dRHEhD6t6HnnTaj8QCVyOz8Izw6wQn16kTw9R7QT+lSPQQRBoMgFk5Jcyl0b7vRcByv3eGJ/21gSLGX2VNMiUnye7oBLvzd2Iv011xrXEnBr1vy3RPFoJlJSpmL/5TKtQiIKSN7/ez+IE8Eio2CxeFnH2Zhrem+2BHl9bY+LaPbiVnM9UgAKrY0xxK/e9fB55sxp+oHxAWq2Ar3/cjR8c94NWwY2K5ajh3vwQR6A1EWgwASgqDEr3rETcegadQ3djWyRlFbVmu5vlWfRHS/24GpeBF8Y44Y0pLoi+l8dyF4kt7cKqA7Q6ESvcD6PvGEfkFasalrOIEwB7B1gBGX1NAZrRk6E2v6QSf24+gf4jnfDRgo04fDEeWqFxwr6mF41qWpDjgNO+83h5vAdyaUXRakvHmlrEj3EEGodAgwlA8aSgCk8CKgQJ/14UgK9/2gmNoG1cC9rwKvqjJddAUltR7MJb0z3x6kQvXLiVBUlqPoFRUxdJp0zVty7HZ+CZEfZwC7zwYHGWmi6qfowTAEOD6e3Jw0vWobJShb1n7+KtmRvRy9wWa7eeRKmaqp+JzMZSHb6mfGeBhJKMG0l56GVuCf8jN1jxo6bck1/LEWgLBJpAAGqcupGMLkYbsPf0rQ45A1IIQO/2xwyFZRj1y048O9oR/mE3FJ28Polbcw8OraQkSYIgqfGv+T74YqlfwwzonZkAqnnrMEOvKOLk1QR8sXQLupnYwnjZZkTEpLFaEQZ1EH0218YMwjoZgiDA5KcA/HP+JmhEWhUolc+a6zn8PhyBlkag4QSgrw1LCbNmWYXgrekbkVtcyrwnWrqxrXH/4koNxv6+Ez1NLLHK7xRTHbREnIBBlUZqC6+gi+hn4YArcen172InJgCGHQlbWYuEjAIsdQlHz2EUxeuJfecTWWF3RR3UfEK/xoHRydh44Cq6m1ojKjaTrQJohcw3jkBHQaDBBGCY/aQWlGHACBv86H6YFQhnUZYdpde1tJPUBRWVKoxftQtdjS3x25aTEFogTsxAAPSZXaTCUyPs8fuWM7W07C8/dXICKKjU4s8tp/DiWHs8N9oZG7aeQXZRKSt0z1w/WUBXCwtjnQ45ReV4ZZwj5tiGMQIQ2rsTxF9eI/7fzo1AwwmAgqkkHTaFXkYPEytExaZAljSPzQqACqaTT3eFWsQ3jgfQw9QOKz0PMxdXWgkYBHdjXQirv26Ge5EXyVy7MLwz25MVsaEcRVTvuNatkxAA5d9hen59umaNIGPPqVv4aI4nupvbYcKafbibWcryOlHdB2UCrqQhIXxbcqP7i7KEedZBeH2qF3IKSyC0tPNAS3aI37vTIdBgAlBptaDdfMVW/HuBHypFkXlEPI5OEFpBi80HrqDvcAeMWRWElPxi1lf6w28OAqh622QR+yMS0N3YGkev3GP3rtOdtpMQgEApHKigjyTh8t1MmK3wR3dTOwz9fhvOXI1nBYBIFdScOv6qcanjC/ELkc75O5nobrQeO0/eRPUEcnVczn/mCLQ5Ag0mgISMQtDee7grXPZFshJ5SuK3xgXVtDkCtTRAFkWQy9/+s3fwtLkNPpzjjcRMqjCmpAyo5dIG/UTG6IJyNd6Z5oYJa4KYUKlz9tpJCIBWAJl5xVjgeBR9TK3w8mR3eO+PRIVG8eyhVZlAq4NGBnU1aKD+ejKLONahrEKLf87zwWSrEAgd0Bvur93i/+88CNSPAGRAQ39kkswKq9jtiMCzo71wL7OgUyBFwiUwIg59Lezw9kwvxBMJiIKy8mFFwpuoamCZU7X42fsMnhvjgKTMwrojqh9DAqA8TUSubBcFFFWqsenAFbw8yR3PWNjiT/8zyCtU0na0hxePSNqw/+F9GH0tbJFZxIvFtIex4W2oHwL1IwByWaR6u5KIf3+7ke2fL9jM3Ozq95iOfRZT+YgahF5IxMAJbnhvpjtiUnJA6gnmZthEXTO7v05AdGIquprYwHl/NCOXWlF7DAlASbamYV48IZFxeH+mN7oZr8eENXtx7V42c5OVRAFSO1lsGoQ/fZ69noTepuvhE3a51mHjP3IE2hMC9SQAZVYWm56Dp0c7sN1+x8VOo+80GCHJOJuQmo9/LwnAqxNcsP/cbWYEJDUEyzHEkoo1fDVABl8iEkGQYLR8Oz7/zg/llZWsVjATMjWlJ6uDAJT0xUp5TMMLx1pGCc/Izl3TPQ0ntsJndeGpfAcEUcSlhGxM+DMYvYbZ4eP57jganaJ3xSU1D/WnfaVdMPRDJUp4f+5mzLY9yAzShj61ApT8ERyBRiNQTwJQjF0+h6+izwgntt9NKwXl0ulsG6mDMktUMPrOF31MbeEaHMUyQlZPSdAUTLYcvY5uJtaIScpj6gWZvK5qyE9P8lsjajFwggscAyOVhJbVhDpdU1CqQmZBSVVzSCiJghZJOaXQaDVVx9vii0FwshWULCCnpBJ/bDyOPsPtMGiSM5yDLqNc27y2lpbsp04n4EePk3h+vAtKVSJbHRNh8Y0j0J4RqBcB0GtMs1TTH/zx/ixPtqvU6k6jAqo+gJT+VyerkFumhsn325jnjnPgRWgliZUMbKp2IrOgEAMneeJHj6PQMPuCMvOt3gb2vQ4CID36TLsD+GhRQNWllPvo6NUU9DCzZonS6AcSxG2x0XOpjSqNFu77ozBomgueGuGIBfahSMslf35KjqetmfzaosF1PJOwDTlzi61c9p6+rdgxaiLuOu7Df+YItCYC9SMAHZBbWoLB07zwm08422VyvWvFSlqtCUqtz6rS+8soqtRi0qpd6G5qCasd56AVNZCp1jBTUzROsJKhfeqGfXh9ohOKVOTpQmUMa6CVOgiguFKLl0c7YOaGwKru6CDjp43hGDzBCTmF5ex4axKADkSSShJBcu0kj6qpawPxhPF6jPx1D24m57AYDFpl0eRZiaptHI5VnW6lLzTm5RqB2YhWbjnNUlHTMb5xBNozAvUiAIquOXolAT2MrHH8RjLbSfi399z/LQ086f5VggSHvZfQZ5gt5tqGIa9YzaJRG5seWCdJOHQpkZWL3HrkKnQS+bjX0JM6CKCoXIunLJyx+3hM1cXUpoVOx/DPBVvQsqnuqh75wBfy5aeSmKXlAtb4nsZzYzzw9uyNCAiPgbqNVVIPNLQR/yGiFiUJY/8IxPszXaryEDXiVvwSjkCrIVBPAgBW+RxHbzM7ZBaWsp10t519hkM+6lTZS5YE+B25jt4mVvj3Ih+k5ZdT9FKjBpFmyGpRxJBpnhi1ai8knVYpYv7Xu9VBALtO3kY3U2scjIirurKkUmSz/1G/7gStBlp7U6u12HPqDj76ZhP6mtlj+vo9yC4ohSxqlfTienVUa65KmgsDCtwjArAJOIMBo1xYrExn//toLmz5fVoOgXoRAP1BfrlyG6asC2FRmbR859t9BJg+Wydiy+EY9DW1wb++3Yy0vCJWHIcIokYj7v3LH/hGQoMKlazffgIvjHFDUnYe8wZ64CT6T00EwFQOSllD64DzGDjRGUUVKuapRKqpjJIKPDPcETtO3UJ5ZQW2H7uGRS7HcepKHERWDrH5jPo026fXRIni1eJGQi7MVmxHN1Mr/HeZHw5fvQdy6XxcDKXMC0wSEJOUjd7mjth79lannyA99M7yA+0OgXoRQEpOGZ4b5YKfXSnxmxL80u560oYNYikBJAGirMX+s7F4fowj/rnAD0k5+tQRNepwam4wczmVZdxMLUGf4ZZwD4qqud7sowiApScAVnoeZzYbEsAsOZqshmvQBXQ3dkDgmRhEXE/DDOtDGDDGAQ57L7PaBHWmn6i5yTUepSLrkqxBWkEZvnM5xoqwD57oysozqjRUA1mrd+usSb9V4y3b9UF6B8h2UVSuwvOjnTDP+sBjQ27tGnjeuCYhUDsB6NU8VxJz0N1oAy7GpymZP3UCuQWxWWiTnv64XMxIUXFZJF3wjcRM/GP+Jgya5IHDF++ycoFMu6FXcdTWbWU1oYOoFWHx+y78Y74PE87k50lqt6qtRgJQipbTecudQjFouhcEUQtZ0CAxuxBvTnPFK2PdkFNcylYFlLbglYnucN1HMR1EFFV3b8AXJdZAeR30LqvMIKqB94EbeH2sC/qa22KN32nkFBSDakjTuWyl0wRjeQMa2CqnsnGjOAVJxnz7UHy6aAtbVbXKw/lDOAKNRKBWAtDptCwXzlr/s+hhYom7KblMV0tRwbQL1fzOG/n8x+4yEmw0E0zOr8CnCzejt4U9jkQlKLr8BqQKJgOz7+EY5lZ44Y4+13x1b6CaCIDCu/QrNIedZ/CkmR2mrA7Ezz7n8PGCTRi9KhBvTveBQCkXdDIrYjJwojvIjVUim0AjCEB5HvWZ0jiI0AoiDkcl4t05m9DNZAPG/7kLV5LyWcwIPbMzbL9uPMZWASnZnSNVSmcY08e1j7USAPn+k6fPLNuj+HDWZiRklSKnRMV2tahutKHzcQWT+kWqD4UEBKTnl+PTb33w6nhXxKTmN0gnTII1Pb8Ez460wTcORwBJZLP2KuzqIID8Mg3WbD2NsX/swopNx3EvPQ/nbiTDOTASkqhj40pVrJpKAGzmL4sQRAnRiTmYuX4fepjZ4ZP57jgVnQSNVtHzyyKtGBvBMFUd7jhfou/loOtQG0TezOg4jeYt7ZQI1EoApDsuLlfjvXle6DJ0A3qY22GAuS3bR/2xDys8jmPrkeu4l1GMgtJKNgMkox7NXulaxVNICTYiF0Tm300S4zHeSMZRsgX2KYvIKijFp4u24a0prohOzGB+/YQDC92tBQeyBVCu+QV2+zF4xkZk5ZXggUL1dRAAWKF0qjssgb4zOwBTuVD6buW4VpDx+kRnuARF4ZERx49oI0vLQCkwoENucRl+2XgSvYfb4MUJTnDeE4VyQSmPSP8q38hxoHOsAO5l5aOHkQ3cgy8w3GmsOwn3PeJt4YfbKwK1EgDNZJOyi9HTaD3WbjmJ4LM38bvPObb/e4kP3p27EU8YW+FJI3sMmuqJCWsOYKXXYUTeScX1e1lKrnamuybhT2oHEZ2pYhKtnnSSBun5pfhiuS9enuCKHadvQBYrFb1+LW8FCQwizbMxqehmtA57zsQxj5qqSx5BAFW/1/GFSJrcTV+c6A7HfZeYDYAFndVxneFnWumUqVTwPnAJb8zYiL7DbLHY7iDS8sohy22bZsLQxrb6pIpynyzZitF/7NYTL60KH++JT1thzZ/bNARqJwBZxOkbqehibIcT1+6xIB4lcZlSpUmlFRCfkovriRmw3xmBFd6n8PE8b/xtpheesbDGO7M24sN5m7HULRzrd5zD/og7SEgvRGZhhV5XrSQlM+it2Yqhmh5bOU4zWMXtsWldbf2rSYATiZInTmmFGt+7HkJvU1sWjFVaqWKzQsVFtAbhQCsAMqaqNfhqmS+++H4byivVVTp+wqYqF1DQBTarp3spxMFcUpRVxiNWXNQuKn8Zl56P/JIKfeqCh917KWkcRfAqY0GkJCO3pBJeB67gvflb8NJoO/zoEY7EzCK28qNVC+2deaP+T19zEP/9zg8qgVRgioNAZ8aE9719IlArAVClpV82H8drE92QVVjOZvCKgHm4MyQYyOedinOQO+TNpFycvJ4Gm+0RGPnLbvxrWQC6GK9HFxNLPGdhhaHfBWDsLzuw71QcTlyKR0F5BQRSH0kkbMhTRGZ6alJdkCAkAdRRN2o7za4lSYLjnkj0MrbE19/5IrdUBZ1AKTUe7pkicJXrdobfQDdTG5y/mV4jASxxDMOp6GRWqY353bPnkZ5fB00TSxQS7NRuSlGhUQvw2n8Rr45zQv+Rdvh14wkkZ5Nq6r7x+eGedL4j5E7ruPsS85y7m57FsKthiDsfMLzH7Q6BWgmAytv9vPkkPp7vw1I/CxAV988aZpWKkKNcL4Lep5xSSCuzH4oI0qhVuJOcjYuxGfjZ+yTmOYbj9cnu6GFqja5mNnh1sjc+mr8Fc21D4HvoMg5fTkalIEAt0T3EDm1ANAhz+pQkLXaevI0XR7ngqyVbkZhTVqN6oPo1xRUaDJnhjYUOYYoNgXn6KNlAXx7riP9rZIUnjNbjrRke+HieK2wCInDpThqr30CE2pSNVEUaWcC+87H4ZPEWdDGxw/CfA3AjMZsFcon62a0yRlzMEdY0478Sn4Fuxja4k5KrkH9jXKyaMnD8Wo5APRColQDUgoAvvtsGKv6iZYE9giKIa5iNk6KAVDjsJ6a/VmaFdIDN4lnmSWUmT6oR6EQUlVcio7Ach6ISscb3CGbahuLlMU54ZqwLy7I5aII73p3hgp83nYRL4AXkFVUgv1xgKwXFyEmrBVpx0LOVpiltoOcoaqp6YNDip1QX5ob2XUvKx7uzvTBkijvCryRB1glspli9MYbryLd8sUMInh/nipJKyg2krJBofCjh2zPf78Dzq4/imZVh6DF7K7qa2uFpc2t8uWwrDkbGQSsoOXgUjGqZretdSA2rL1oBpuaVYfrqfehtYo9PvvVB2IVEVGo0DHfDmDMdHbl41vBeVO9PZ/lOK+Ho+Cx0Md6APWfjmfGesOIbR6C9IVArAZRUaPDsKAes9DquGLNkqXnV8SQwmPCmnDqUXlpEuVpEXokKfocuw27fZZj8sANvzNiMZ0Y4oJ+FEwaMcsCkDUH42fsoAs/HIj6rCLkllD5YUFRGeh93UkWR90l73Yi4EjKL8P5MD/Qb4YSgiLhHGk9pFn7qejKeMnfAltDLegLQQS2IeHm0I55ddwRvHsrF62GZGHwgC4P3JeGFDeHoOtoT3YZuwPg/diI+tYgF8ZEqykAsf8WGkRPlNxIFaNQiAo7fwmtTPBgp2+2ORKGafP21EOW2SCX319a23/9TjExGfileGueE5S6hzDWYk2P7Ha/O3LJaCaC4XIunR7hi54nriiGLhLXera85QGPmRTbr1NeBZWSgF1ASuSuSsFEKs0fHZ2D3yVtY6hyKzxZuwZvTvfGkkQ26G1nh9YnuLE/Rt46HcS4mGdF301Ghad+55EnYSpIGCZnF+HCWO/oNs0dgxJ0aYaUEcVRv4O9zPWDy43ZGdDThNhDAgLXhGHIgF4MOZuCNgxmMBAaFZeO1A8l4wfIkupg64Y0pzgg6dVvR5z9ipk6HSdcfFZuF4b8G4H9MrDDxz11Iyy9jBKuTBCXddRPtCjV28jE6SN5fZDf5YtkOLHI+qqRNr8nQ8xj1mXelYyJQKwGk5Jah33Bb7Ay/n1K4rbtJM2eaxRZWaHDxZjIORcVj6vogDP9tD54fbYeuRtYsCOf9+T748nt/rPYJR+jFBETFZkBgHioiy9ooSiIElnee7BZ0T4pfUMintfuYmVeG0b/txlPD7bE5LBqCqKlqC2sbCwLTwnZHBAaMsMede3nMv99AAM+uOYYhB4kAMjH4YNZD+8CABPSc7sPcSe13n2P91olKoRmK3iWvFZ2kQ1ZhKZY4haGnqS0+mL0JvkeuQaVRtzYcHf55FPRG9rLPl+3GXLuDShBfO16NdnjAeQcajUCtBOB/+DqeMLZG8JkbjX5Ac19IM2eRrRqUuALys2cRy7KA1Lxi3E4rgG/YZSxxPophvwTiKXNb9DB1RC8zG3wwZzP+s8gXdnsuwjf0EjLyS1AhUB538sQhm4Hi7tjcba7rfuSOqdZoscL7OHqZ2WKR82GUVKqrDL4skEiScS+3FL2H22PD9ouMIOpLAINDMjE4OAW9pm9Gj6HOcA86V0UwlLW6uFwF2x1n8MokR/QcZovffU4hv7QCoqxhbair/fz3BxGg8pC0CjBathUfzN2IMpWGi/8HIeL/aycI1EoADjsi8Pw4F2QVKdWj2kWb9YZKxXxA1bIMxmeavSs+9yLF4uokULKzrKJKJGUVwnHXeazyO4WP5rji1bH26D3MDv1HueOlid6YviEElttP4UJMKvKKNSjTCPeNyHoXVDJkkwXEYMQlIzPpdcnK0FRLAxEPkZogiPhzy3F0MbbFhD93oYQEB6XjoLrAEiBIGoxfvRcfz9sCtSBBIwh4abQD6loBsFUB2QaCk9Fn+iYMGG2HGyl5oDgOytvz8dzN6GVmj5nrg3ErpRBKKmdaESlRw+1i3DtQI2g1SZOS1VtPoY+ZLTKLKO6lA3WAN7XTIFArAdjtjMCgKR7QNrK4SXtCUUl/oEO5IKFcpei5vYIvYoXnMbw70w0vj3dHLzM7PD3MFh/M98b3HsewevspxKTkIykjlwlbHWXWZGojRWXEPJFIfdKMgU8aQWLVsnqY2mDs73tQUkkrHMMKRYf9Z++g61BbnLxBeXY0eGG0ff0I4GAW3jiYhdeCk9F1jAven+YGi5/2oreJHT5d4IOwy6mdPoCrud5XVgNClhB09g76mNsip6CyyZOE5mobvw9HoDoCdRLA4Kmej0X6BqbjZ66stD6gACvFhZT+WMnQnJpXhKDIO9h0KBpDl/nhH9/64SlTW3QxtkdPI0sY/bwbE9cGwzv0Ki7cSUZCVgG0ehfX5iQACuQSRQGeB6/huZG2GP7TdqQVqCASCUgScgtK8OoEF8yxCWHlKCkSt14rgINZGHIgC4P2JKLftM140mg9Bo63gUfIJagEKsCuAeVr41vTEaBVIr1fBy8moM8wO04ATYeU36GFEHgkAZCr4G8+xzFoqhdzAW2h57fabUm2sWV4VdSqcoB5vuhjCJRgAiVfPamTbqXkIiI2G+u2Hse4NXvwyWI/dB1qzSI8+490wn+Wb8HE33di1/GbCLsQj8JyKnRCKwIKn1VWCeQSSH71pOYhtRT9xATEI1IjUygVc9OURZy9nYnXJjjj/RneuHgng0VJU+DVco+j6D/aFkmZxXhpTM0E8HqoYhAedCAbg9j3DDy/7hT+7whH9De3wg/ux5GcV6pEqerjNrieonleRxo/GvODF++ij5kNK4pDx/jGEWhvCNRKAKN/C8CQqR4sxUN7a3hrtIfZFMjorE9RUV6pRUJaPiLjMvHLxqNY6nYMr0x0Q59h9uhmbIuBU73xzpyNWOx0AJ4hUTgSFY9KtYbNsJmBWVK8eygIDqg9Qpd+peCw60l5eH2yC/qPdMWxa0msfu6F2Az0NLNhdYgpErimFcCQkCzmFjo4NAPPu0Sh1/iN6GpsCaMftuJyXBrzIhJ1VMCeC6bmfpcYAQAIuxiHHsY2iLiZzIPkmhtkfr9mQaBWAvjH/M34aO5GJZClWR7XsW5S3eBLQWqSjgKhyG1UMY5SMfi8sgpkFVbiwIWbWO9/GrM3hODFsW54Yawbepna4aVxrvhssS9WbzsHj/1XkJ1fjIKS8jrtKizdMsukKuNmYg4GT3XHs6McEX41AVqtFp8tDoDR99vw/MiabQCvh+bg9T330HveVjz55Vr8Y6EPjkTGQ6XRMB91KmBOdpH2HCzXsd6W+601EMDxqwno8rUt/A5f4our+/Dwb+0IgYcIgF5e2imQZcgUV3y51Je5tLWjNrfrgMSr6AAAIABJREFUptBqoVIjIr+oDNuO3oDz/ij8d/EmvDfDEz1M7NBruD2eGeGMaRsOYpnLYYRGxeNOej7yWJlGSoBHldQpMlrxaFJiFETcS8/H50u2oP8oRxyIiIXrgSh0MyJ11Ho8t/o43gjNxZsH01kMwBuBKej3UyCeMLbBi+McYLXtPKvrQEn1+NbyCCjuxMDFm6noarQBLrvPdZJKCC2PLX9C8yJQKwG8PtkDc6m4NQklvtULASVPD+XeoVoAlMhOywKvNKKIiBsJCIq8hW8dDuKL5f4YPN0bXYxs0O1rOwya6Ilxf+7FEvujOBOTgqtxqajQalhhdVIFUWK9kopKzLffz+IaFroexksjndDl67V4du0xDDpEkb8peM42El1GOjM7xVzLYCTlFLFrKdagcTV/69VtflI1BBQC0OF2Yjb6DLNlK0OuaKsGEP/abhColQBem+qNX73DOQE0YLiUFZQhFb/iD86MwEx1pNQLJvUOzfQLyypwJS4ToRcSMcc6CGNX7cUzFvZMb9zV1Ap/m+uDTxf7Yv3209h9Ng7X4jOh0ohY5h6Obl+txRNfWzICeGbtCbyy+Tr6TPJGl/+uwogf/XD+ViZbuVEiObI/KoZosj3wraURINsRvQfp2UUYMNYFq/3Psv+39HP5/TkCDUWgVgJ4fbInVvseZ9l/Gnpjfn79ESBbAwWakZBOyStEbFYRNoZewAqPcIz8KRjPmrmgn7kzMza/M90L/17qi1fGO6HL0HVs7z7CEj2+tsbAyc7wOx6DSm37yYRafxQenzNJ+NOWV1iGlya4Ys3WM80QLvj44MN70n4QqJUABk3xgs2u85wAWni8lFUDrQ6UwitshUDRv7IGKlGF7LJyJGQWwH73eazeegYfz9uE7maWVQTw5FfrMGrVPmTlV7AqX1SSkUiFb22DACeAtsGdP7XhCNRKAK9P9cC6bbR85TaAhkNb/ytIVLNdH49ABEBChFYEZASm1QFl6aT8MrFpOfhj82k8N9oBT361Bl2/XotuX65BT2MrfLHUF9vCY5BfXMbOJ1XE/bgD5lda/0bxMxuNgELoOuQWlePl8S5Y58dXAI0Gk1/YogjUSgCUC/7PLadZjp0WbQW/+UMIMAKgIDJZZNlBI29nY9Kavcy1tO8IW3zrEoY3p7vg+TEueHLoBvyP0VrmcdJtqBXemOKBNf5nEZddUM1tVWQZTx96ED/Q7AgYCCArvxQvjHPBev8IbgNodpT5DZsDgToIwAvLHUP5y9scSDfwHrTqKlNpsetELIZ+54/eZnZ4a5o7fvUNR1JmPs5fT2UJ7awDzqCPmRXem+OJHkYbMMf2CGZsCEaf4dZ4YaQzZlkFIeJmGvNI4mqhBg5CI083EEBCajaeHuGAtf7neC6gRmLJL2tZBB4iAMPjSPUwcKonRv2ygxVlNxznn82PAKl6WBERfa6ionIN3IIu4O3pLuhhbIuP5m2Cz7FoFJSWs/MEQcKIX3fi/Vk+KFGpQLaaOTb7sXbrGfQaaQ/vg1G4m1GA77yO46XRTugzzBkmP21D8NlbKKWqXpSuWCJXVYEngGv+4VSyxOqAq3Hp6GFqBZvtEU1PGdsS7eT37PQI1EoA78z0wGffbn4scgG155GmcpaiJOP2vRwsdzuCV8e7MKE9/s8ghJ6LQ7laYOUyyZefyjGev5mBHqZ28DxwhamIft14Aq9O8URphQpr/CLQ29we3sFXIUoq5JVUwCXkIv4xzwc9Te3w/uyNcAmMRE5xBUtZTIVh+NbMCLBgSuDsjWR0MdoAr6AoTgDNDDG/XfMgUCsBkOrh7eluoARkfGs8AgaVgPIpsyxAzElHJ7OMnpfv5mK61X50N7PBc2PcMN1yL67czQBlBiUbAFsdyJSxUwdBK2HkH3swZJob8mlFIMs4GZ2E3qYO2HvmFkRBxQz33Yfbw2nfJWhFkSWRqxBF7D1zByY/+KPPcEeWomK513HcTMpXolSZ0FJqKuiz5jW+w538SjbO0OHwxbvoYmyJsHOxPBVEJ38n2mv3H0kA1OCFDqF4Y4orTxPcxNGrTgCiTql1XFKhwvbwa/hyiQ+6m9jgzRkesAqIQGJ2AUSdBjrhvhtn9eujbqfiSRNL2O84pxSnkWWUq7QYNMkD437fAQ0VwtFK2BAQgV5m1rDZGQlJoNTXWuZmSqUwL8XnYJ5dCPqPtEYvU1tMXb0HETfTodaSSkhRR/EccY0fdBovyrJ06EIiI/WEjEKeCqLxcPIrWxCBWgnAesc5vDnZEwI3YTVpCAwCnPTumYUVcAm+gndnb0R3I1t8ssQf3qGXkVtEqZmpBCPYjJ8EiGFjAoXqFogixq/Zi4ET3JBTUAqqR8YqhskarPA4hdcmuSG7qIQJcapxYL0rCj1NN8Ay4DzUWqWYDQs4YymrRSRlFWDD1jN4e8YmdDe1xKffuGNLWLRSEY2v+gzwN/jzPgFQPQAbZBVWsLFq8I34BRyBFkagVgJwCDiHN6Z4ssInLdyOx+b2SqEZHagOgFJkXinpGJuahx+dD+KlcVR31w6jf9+BI5cTUVFBQl9fnIapYSQldXD1QC4WDyDi6p1M9DK1xnrfM/rSlLRKkCHqBETdzEAXEzscvZzA6g5IrJSkiA07I9gs9E/f49AKSqlLSg9B7YP+uYXFFdgSfgNfLNnG7ARvTXWB1Y4IJOeUQZa0SkwCC0wzxCfwuJDaXlhS2ZHqLjQyAb3NbJFTSBXB7hN6bdfy3zgCrYlArQRgs+scBk5xRqVWaM02dehnKbNyyuipJHC7nVGMJS4H8cxwRwwY64wFdvtxNTYLWqrCRXp9ShpXXdjX0HtK4kYG4BnrA/HyeFdk5JNgvi+Eyb2zsFSNwdO9MHn1LmYwJvsBKBGdJMImIBI9zG3xs8cxVGi0SonJas+UiBAkNVQaAUevxmPsmr3oN8IJT42wZwXi0wpKWUI5SVKKnfOkojUMUrVDLHBPp4Zv+A30MaeKYHwFUA0e/rUdIVArATjtiUCPYfaIuJ7SjprcvptC/vtqUcK1xAxMtgxFP1MbvDjBBRu2n0EKy8ypFFu/r2tXZtW19YoqiUXH5qKvhR1+9TrOZvzkOmrYyDhMq43FzkfwygRHpBeUQycRuVAFMhlaWYDtjnPoYeKAJY5hTNdfnXRIXVRV54CEvCjiVlIuVrqHYcBoZzw30gEL7A7gSkIWtDIluuMTAgP2NX1SJDcR+7jfduPpkQ4sIrga39Z0CT/GEWgTBGolgMuxqehh7oDdR2+0SePa+0NJp0+1hlmxGFlguvMD52JhsmInM+ySAf0nz6NIzSlms/zqQreuvjE9MhVs0e8zrEPw9ChrpOYWKG651QiAzqU96k4mnjCxwfGohAdWFUQgZPy13HGR2QQWOR1ChVoR+iSsatooLxHNZOMz87HIIQwvjnJGTzNrTPgjEKeu3YNGEKETqbiMDFHSQdS3oaZ7dbZjtDqjbK+fL9+JCav2QqDiOzydSmd7DTpEf2slgPwyFZ4a7YDd4ZwAahpNHc28JS3yKzRwC76E92a7o6uJJd6b5wvfA1eQVVQOWdY2qqKaQajTZ1xaPp6y8MDP7kdZeUoSunTcsBnOLS5T4Z3ZmzDPfj8UZ1PlDFabQCQyEWC75xK6GlthzoZgFGlUzNXUcJ/qn4Z70kqFjNOpeaVwCryEd+d4o6uJI96ftQkeIdEoriQbAQWXqXnKED2ARNqMAJYFYKHTEaWkajXCro4z/84RaEsEaiWA4nItnh7pAo/gaPbHzYQOCZ5qwqctG99qz6Y/XprhMn09CV+aUcu4lZaPX7yP4bXJXqzwx+jfdiHozG2UUnF4qvtLs3eDYbeBjSWs6VpaXSy1P4h+I2xwL5tWEjSbVH4z3JKNC8v1JmGJUxgGDLdHdrGKnUe/EVHRbJ52UdLCYe8FdDGxx9Q1e1CmUuoUs2Ix1cZVaTetLBSDMf2fKsoUV1Ri14kYmKwIQF9zWwye4oU/fE8hLrWYrQagP5+9I3rcDO3sLJ9EAKVqNf537mYscT6qZHnlK4DOMvwdqp+1EkBppQavj3PEiJX+LAKV6Z3JPbCTuQgqOl0SxjLUGgFXE7Ix3yoY/YY74oXRLpi6ZifO38rQe9ncN8425U0geUszdkoD/cJYJ/zodZwZjWu9p6xDeHQSuprYI/jcHVZAnmaiho3q/5JqRyPqYLMrAt2NbTHu910s0lina1gKaY1Wg7Mx6Zi2ei8GjHJEPwtLzLIORnRCHjQaFQRZYvsjNEyGJj2Wn6QWjEnKRk/j9bDaepaNG/cCeiyHusN3qlYCoFwxy5zD8fECL1AAE+l5lZndffVDh0egHh0QRBG3U3Kxyvc0Pv3WB09ZOMJ0ZQC2H7uB9JwyKEZUJWLXMBuvx21rPYUEpyBoMM/hCAZP8UB6TvEj1TWGG9EsvVxTiQ/m+mHcml3QapXawobf2WqAGSglSJKIHcdv4NlRTvjvEj8kZOQxg7Hh3Lo+DbYJUScxu4T/kRsYtnIX+o9wxD8W+TLvoWv3siAIna8KGZHspfgMdDWywY172Syug3uB1vVG8d/bAoFaCUCUtVi5+STemuaNwrIypkKgmczjNpshwUiGUnLLpD9eUVRcOAtKKhB45i5G/bEHPUyt8eYMT/zhcxbXkzNBvvQtsTEhzdRNEiJvZaCH0Xq4h1xmbSOjc20bjQytUlz3RKLvKDdkFpY/UqgzV0VZQGRsKl4a58IqjF27m8WuZyu9auqg2p5Z/TdyE43NKMSfvqcweKoHq1Fg/usubD9+A4XFJYoqRNZBoGhophqr2wOq+v07yney+2wKi2Z1mW9nFIDVd2AJQDpKD3g7OwsCtRIArQACz8aj61ArHL92T3mRmQ66dkHU0cAzzIzpU5Qk5BSXwfPAJbw3ywtdhlrhw/mb4B16FUXllHuHZtVapldviX4aBKMoShi7Jhhvz/RCflklS+WgrUso620DV+Oz8dQwa7juv/hIomI6fZmK1ouIikvDS2McmQvp+buZzM2zrkfV1HeyIzCjsSyiqKwYfodv4Z/fbEZXY2u8NdMTdrsjkZJXBFmsZp9ozINqeng7OkYEN3XtQXywcBNKKikCW7HbtKMm8qZwBBgCtRIAzQSTs0tZkfKjV4gAlNl/h14B6LVYLBCWIKhmVL2dnIsf3EPx2jQP9BhqjXG/78axqHsoUZGHi94gyqpsKcbZlniHaAVC6R0u3ExnEbweQVGKTz8L+q1D9UYEIOugFSX8e6E3Pl28WTHM1tRQfb/ZSkCUEBWfjlfGu+OVcU64EJ+pN/pTEss6nlnt3vS+MCM1raLou6xDmUaDk9cSMXVdEHqaWOLVCe6Ybb0fl26n6WMPyKakFK1nbaEh6eAeM2RoH/1nIMb8uZcl8KPVZQNgrIYo/8oRaFkEaicAWYfMvGL0G2aNxU4hTLjoIJGioWVb1YJ3r5rt00xekpiP9pWEbMzeEIj+I+zRf4QD5todxOX4DFSKpNdXBH8LNumBW5OLpyCpMGH1fgyZ7oGiCm2DvK4MunnL7adZ5HFqVsED96/pPyS4Sf11LjYTr453wCvj7XEuLoMZoZsqjElRRgKQIp9vpuRimWsoBox0QD8LB4xbRUnoUqAWtMyrigLMmCqug68KMvKL8NwIR3xrG8j8JZgKqDNaw2t62fixdoVArQSgqEREjFkbgpG/7NUH+zRIHrWrzlJj2MxfEqEWJFxOyME82xBGcK9PdsU6/9NIyikF6bJJlUGFU5RZbf1nwU3tMOnwI++kod8IZ7jujWQpH+o7Czeoj+gzJjkPfcwdsOlQdJ1NYqsOZv8QcD42A6+Od8RLYx0REU8k0LS+K22SmKqJ+kbG55zSSlaTgFJa9zK3x4jfdiL8yl1UaijVBKml6mxyuz4hMbMQXY1scep6irJyJK+5Dk5q7Rpw3rhGI1ArAZALIUU1LrQLw5DJm5BdVKYsZZsmExrd2IZeWN1nnoQPJT+rUKtwLCoeY3/fg67GlnhpgjvW+52s0tUy/3em+CAVhvJ3S0KstTZRljB5TRAGT3VBbhkZo0Vmdq/P86sTgEqtxaeLt+KzxRsZibFZ/iMkq6F4POnwaRYeGZ+N/9/elcdFWe19/nvfFDOoNG/ZvTevb97uUub1Vtbt5r0pICruphapWe6pmWamZaUiDLsCioKJqLjgAi5o4oILLqgogiKLgjpssg7M9izf9/M7zwwhYbLMwADn4TOfeZh5nrN8zzPne85vfWl0EF4c5Y20nEKmR2CxhRoDg0nZy4iXcKQ2kCWSLKHKICEo+hxe/SScmaQ6zY/AhkMXkUehLNiuRPGopWU0Bbez9cOM/4aYK7AftBwXb9ytFh1yGZCtj177bN9vEgCzf5cFxF7MQKcBK5CcrTbPiK0CLTLUUZS2AvJKShESew19Z/yEDk6r8M/PNiJ4zwWoC0uV8MumoGzNOdnXBWJS2n08O8QfvjsvMC9jcihrzIKYlLsrI46jy8gAlh7SHHG0rjrNn1E9dB/5H1wgncCY1XhreigKqqogiaQHMV/Z9HfzZEkEp6mqwrZj1/Am5UYY6IVe7qH4cfNZZKuL2fhRRFJjE3ciTW/xb5dg7g+9L1x7GH2mbIRO4DGTfhs1/m1LI/B4AhAlJGfdRycnb4THXKw232vphtenfgrLm1FQiB83nsSfPgxGRydPDPgyAlHx16Gp0jFrHpLxk9y85g+4PmVb65qPVuxGj3GBKChVsn0pIqiGUwDZ56fdeYCOTquw4cBFtoqnPv7mwRS3SgA5UvhfuHUPLwwPhPP8n1BQoVNW779ZQP2/NGNOu0wj4S+J0GqNOJuSg0+89sPR1QPPj1mNCStikZBym11T/9Kb/0rz86PVavHPWevx71kRzJO7+VvCa+QI1B+B3yQAczGCUUS/OZH4zCemeqI0f2cr72y3IirKTKNBwOnr9zBpxS50HRmAZ9y88JkqFhdv3YdOZ7CVJle3gyZr2Sgi6ZYanQersHLzaSb6qb6gESdUprbKgP/O24LBX+9gTmSPJYAa9TDlt2jEjpOp6OTiCZcvN6OwXKfENrKSD4S5eiLuG7kP8EXQEbw02g+Ow/ww5Ost2H0yxUTcZClFY00KevNdLftO2NJOpaC0Co7DfLA57lqjYkC1bC947e0NgXoRAD3cY5dswd8/DkKpxshetgaUJGpRqtHhwOk0jPl2FxwGe+PlCcGYH3wYqXfyYGSx7EnJaCMzRg0ASbpNzmcTPWLQfVQAsgpKIDdxkqVukijn+/BjeGaIBzLulTRoRcoIQDIyhXjA7jPoPMgTzgs2I19TyUigRvMtfmqW/5OzXUmFDmtjLuMfk0PRwdUfvSetRvCeROSXVLIgdKTnsYWD2ky7mJ8OXoTjIC/EX8hs9cpsW8CVt8G6CNSTAETsPHMLTw3yQHa+hr3YiqcZJ1OqT3mRiELxRGDVSxJKynVYv/8SXp+8HvbOnvj7pBCE7L3IFLvKD1OxSVeUwg0Xp1h3CEiyIjP9ytPOq/B16AlTHP+mEZXi1SwjOfMuOg7ywtrdSY/0Cq6rf2Tqy8RjFEROFBG05zw6DVwJl4WRKKrQs0TzDP+mNbOuqpXxZf4WpP+g1b4InVFA1PFkuFIQuiH++OO4NZgfFIeU2yZPW/Z8ULw683OijHmdFVjhQ2oj6VkWbTiBv3wchCoKAU1JefjBEbBhBOpJADIupeegi5svfKNOsJckUSrDZpxM2XafIlpSdEolVMP17DwsDTuCXpOC0cnZF4MXb8POUzdQWlXJnKdoYm0NhyjKmO63H91Hr0amupgpYkku3pTDLCLR6gW8MysCH3y/mzmINbRMgpAUw0ZBRODuc7B39oDTFxEorNBCEmk30HwY045AEvW4dLsQE1fuxrPD/NDZzRtjvo/C8eRsGMhvQ1JCXDPiZyFOG9rjxl1PvwWDKOJvHwVg2JIohTybEZvGtZrf1d4RqCcBkDWNFm9OC8cHK/awl5HFy2k++OgHTYlH9KKMCzfuY4rXXjw/wp9ttz9eHoOktHswGg1stUpB64y0gmwl7pfp98vw7FB/zF19UAnDwJLANHFiNREmKZG9Np+sTk7e0BFTdnpKnCRa4a7Zew5PuXjBaX448irIOqj5zDONtB9gsnYyTxaQde8BfLaext8/XofOLj54c+Z6bDp0DeU6I3tW6JlproNwTrtdgi7DfbB6DxlLNCy6anO1k9fDEaiJQD0JgCxlDFgWdgLdRgayV0mVQUl0UbM0S52ziJXKap/CItAPWas3YHt8CgZ8vgHPDPHBS+MC8ONPx5CeVwGByfdJ6E1WqvSjN23/m1FE1eCuk8iAyeklzAmIwXPD/ZCWW/hLsNWmrh6JP5g4RELi9bvoONgboXvOslDepCCuNzeaRCqsrcxiyoh1+5OYTsBlwWYUlVUxUQd5MNe7zAaDZbqBGmHqEw0tEwXKBjyoNCD8wAX0mxkOh8F++Kt7MFZEnEBesYaFLwEzDqD2KY5o7EFpbBsecR8lBgradwHPDgtAtrqEETmRAj84AraMQD0JgCwuRBw4cwNPDvJgrx1HrzCZvDU6R2IFsqiQRREVVTocuXwHzl9uxlOu3nh1UhACdp1nSdAFUlKSBU1TJ0trdOJxZbIELRIy88rwwghvfOodwyaNx93WmO+JIN+YvgFDF0exVI60im6M+YziKEbELyD0wEU8OdgTRAL5FVrIEgWsa0zrmnYPs/6i3SEE6Ax6nEjOxpjvd+IZNxV6jguE945E3HlQojjUsRSetKBoWp113U2iyf/O3oy3p4dBbzRW66vqupZ/xhGwFQTqRQD0i6FJQ2MU0eOjQPaa5rW/QVYlDekwTfwF5eUIP3gZ78zciI4DPfD2zA2IOXULOkFg2baU8AXKSp9FtmxIBTZwLSlZKdzE4qAD6DzMnyVhp/Db1jhE2QCvrWfxwnBf3C/VsABlFASvoQfJuek5YHoYQUR43GU85aqIgwrKWyYlJPPcpl2BSKt7sTpa65X0e5iqOoCnh/nhhRH+mOlzAJey1CCMSaxl6SNLXYLnR6/B8k3H2M6ObYf4DsDSMPPyLIxAvQjAbIFDP7Cvg/az15/c10IrNG2LK0ICs4GXJCXjmCQgU10Cj4gEvDwxFJ1cPPCfeZuxLT4NVbq25VVJE5e6sAQvjgvCNO9Y6ARFzm7h8WXF0cR9+momOrv5I3RPEpNPN3VuIvEGxUyKOJKMZ928MWB+BIpMfgJSMypfH4fX9dtqTPc7hOeHe6MzxR1avBVxFzKgNRqYHoF2m0TENTOnPa7M6u/JiY24RBKwLf4a7F28kHqnsPprfsIRsHUEGkQARASUapBeDq7eiDmV0qT+0SREK3mjaMD5m3ksMNvvRvvDwWUl3D1icS71LioNAktKbo1VW5Ma38SbSUH9fVgCOg9ahZTbhYCsZxNRE4ut83ZSipO4rM+nQXD6PJydN3URTDsBmeVFMGJHwk08PcwLA+ZvQl55VZOd2OrsRCM/pNhKFN/oTmEZ/HedxWtTwlg+5D6frkNI7GWUU05kMtl8TLKdOqs37YwNkh4ui7fgjWmbUF5ZVeel/EOOgC0iUG8CoFUkTcKllVr2ojgx43/YxUxBFY/Mx2yrmfJOUdKadxQVWiMOnr+Jkd/uYordP471xfzVh1nYYNpt0LaeZLyk2G1Oiw5rDhRNvGQznldciR7j12CWXyyL2U9iFdKzWOOg1a1BkvHDT0fw+zEhuFtU2qA4/3W1icaQWktEQO3eeyoNvx/hi4ELt6KgVGtS1ra8py49PyJTHtMOy4jiSh2ijl7FwC/C4TjEDz3Hr8HisHhk3C9RjBroORcVXwI8JnOZ8lzKuHW3GM+5eeKH9fGQZOuI8eoaA/4ZR6CpCNSLAGpWIou0IhewaH08XhwdiDsFD0xhBn5bHESrUHPcl6KycoQfuoJ+U0NZqsW/uAcicNc55FXoIQnNZ1ZYs1/Nda6snI3w3Hoaz47wQ0pWvlWUkjX7Q7ssQQbOZeTD0UWFiMPJjVIC1yyz+txklWOQgbiLGXhhVCCcv4xEfhll/dI2r69IdaMecyLKMBgNSEi5C/eVu9FlhB+eHeyFqaoYXLxxD5UkHqIgfCYiMC9YflUqs+IS4b/jDJ5yVeH6nQdMx/Cr6/gHHAEbRaDBBKAk7BBBaQc7Oq1A5NE0SLL+sYo1uu9GbiF+DI/HXyeGMOXh+3N/QmR8Kiq0ijyW9AFMpmqjYFmiWbTSzy+pQo/xqzHFi5LsKBYjlij7UWWYFaUagwHvTgvD+/PCLGayaZ4c2btkxJGkbPxxzBoMnBeBvAqdTXrD0mKEdq3KrkuP67ml+GbDcfzfR2vwpLMnBs6NwM7jqSit1DwUKLA2voRrpd6I/8yLxICvtrFwHszEtvaF/H+OgI0i0AgCUJKqaA0GvP/lFrjMj4SRWeYodtZKrHdltU9iI1pJXbtVgKneMeg21BudXbwxZukeJKYqCciVbbRpQcqUAtYRg9gK/jTh++w8i67DvHHpTiFkwfoZ1kg4p0zUEr5ZfxSkZ7mjLmWiKCLmphxMB6rItZgoiPqXeC0XfxobiPfnbUVRmWKLr9TflJosdy+J4Ni2S3EdYf4B9KwWlWiwNiYJb82mkOHe6DN5PQJ3nsKdgiK2yyXFt/Iy+XDIAs7dyEMnp1XYejyNKYOJVPjBEWgtCDSYAMwrPvrBBEafh6OrCtfu5Jtiw5jCKktGaI0CdhxPw+AFkXh6+Bq8OCYQ32xMwPUcJTCbLOqsZkZqy+AXluvxp/EBmOSxD4KkY9aYzZZjWRKRnF2ITi4rEBZ3jRFAo6xfHgEwkTnz4ZCB02l30fODQPSftwX3yVlMJD+Bx+iJHlFuc3xM0zaJykifoaky4PClTIz6djvsB/ug+6ggzA04gBt3iiEIJAI1QKZQKLKAL4IP409jg3D/AQWnM+kOmqPBvA5xGsOXAAAgAElEQVSOgAUQaDABKGkSKUqkhHsFJSyR+JzVB9n/tCUuK9dg0+HLeHN6ODoP8WQROX2iTpo8Rindn+LGLzDlXPtbLamiTqDL8CBcunEXZKFCK8bmUnCT/qGisgrvfR6OYUt2MF2OIFlO58KUp8yLm2LyiEi6mY+Xx63BgLmboC4lZzEbHm8yNjBlKqPscbQz0xmMuJKhxpzV+9Ft9Bo8M8wHo5ZsR+zpW9AYdCgtN+CF4X74YvVBtjOwZYKzwFzBi2iDCDSYAGpj8IlXDJ4f6Y0bOSX4fsNh/OGDNXjK1QcDv9iKXSdTmIy0OSe52u2zif9pZSxKeKCpxEvj1+KD77e3zO6H2btL+HrtQTwzfA1y8ijwnHUmZZoMaZd4OT0XvT5ci/6MBEgcpKyybWJc6tEIcz8KijXwjDyNP7sHM3v/d+duwjz/WHR2C0Di1dvMGqoexfFLOAI2hUCTCeBc2l2WwvDFsb7oOnw1Pli2A8cuZzMnG+aZadoWt+fVEfWdsPDcdgpPD/ZEYpqaiV+a+0kg3wMK43A5Q42Ozsux8eAVq9nsM/0PMx0WkHK7CK98GIR3Z4fj7gNSrOqbu+uNro/Gjo0fC9AnoFwrIDohDf+dG4EOzivx78/DWCwqa8QXanSj+Y0cgXoi0GQCIG/QIYsi0W/6RqTfU5RlJNIg2TJb7dE7UxLWs0Vt8DLqf2FpBV6ZEIQxy3bBYDRCaAFlISk/SbxRpRfRb/YGfPhjDAQrRfOkPjMSYO9GJGfn49WJa/DuzE3IL6tkilf2XNj4eFMblRf5rSuhMMgMOq9Mi66DPbHr9A0mSuOB32x8IHnz6kSgyQRAiUf2nbmJ54f74F5RBYsdX2dN7fhDmhwCdp5FRycVTqXkKvkMWoQATKtZGfhuw8/oMtQX94sqrDoy5gmUyCDtbgn+/tFa/GtmKO6S0lSkuE62qxh+FDCk6PbbmYDXJoeiXK+DLMi0t3rU5fxzjoDNItBkAiC7Z70g4C8fBcFj6ynbdPxpYfjJe/pl91C4Ld4GvZ5W/0LLRDCl1Sx5V8sSEq9moJOLN8JjzlsVHTMBsHfJiBu5xfjbxBC8PT0UWQWaBmUps2pDG1B4qVbAnz8OxpdBB5RwGGyXYB1dSgOaxS/lCDQYgSYTAFl70Cru67Vx6DnBjyUOJ1EDC+FgQ0HBGoyMBW6glT+tcg8k3kQHZx8cvpDOzM+ZN3BLrHwVo30m0jDIMnp/th7jl+2CIJhEG1ZoE038dNA7PScUlyfjfhFenRyCfjM3Iq+EYufTzsTGV9CkxyGdhmRA8O5EdB7sjQtpOZSCwrSLaX07GQs84ryIVo5AkwmA7Kbpx33tVj7sXQPgv/U05d9QdgJWmFBaE95k+UNxaD5YthP/mbcJVVqdzTSf0jwu23QS3Ub6Q11RATLvNU/W1moklW9+pd97gNcnrsPIpbtQZSB/CMuZo1qj/bRroqihD8q1+NukYPzr800w0oPOD45AK0agyQSgZOxSTPvcvtmOHhPW4EEJTSitYFVn5YEjAsgtKMYLw/yx72w6C59s5SrrXTzJ5M8k34bjEG+sj71ocuSz7ircPPnTu1Ey4Nb9Yrz84WrM8I5Fpc62LYPIWY8IYB3lRXbyRGziLatZUNV7EPmFHIEmItBkAqiuX5Zw/Gounhnkg8WhRyFRco52vgMgK6glYcfRe/IGaPXk+Ww7K0Za0eolGa9NDILbNzuYB2xzimGIBIiEjl/KwtNDfDFxZTSLCSXLRtvUI8ky8ovK8eePA/H+F5uh1fOcv9W/fX7SahGwGAHQD1oUDVi4Nh7PjfDFlawiZgbaapGxQMPT7hSi24jVCN5LK2zBpgiRuFkWjVgZmYDnR/rh5t2SZvNIJmjNuwGKHXTsShZ6fRiMQV9G4MadIpsiSvNjQM6MS8Lj8cKYNbicmcdCQZBOgB8cgdaMgEUJgPQBpRVVeG3SOjgtiITBSGZ+Jp+AdqIjo1U0ib9EQcR0VQx6fhCEgrIKJfaYDe2IaAdAJrzqB5VwHOYHv21nGpcVq5FPv5kAzIpVSqT+6pT1+L8P1uBCajYoSJ2iLG9kBRa6jUSc5LNBYaIdh/pgVVSCkpKUW/5YCGFeTEsiYDECoE6Yf9Rbj15HRxdPbPk5mVl9sBgrsG0ln8UGgeLISwYkZxfAYfAqfBdOE4btrRQVApBgMBgx6tud6DczDMYWWNGanxkSB2Xml6D35BD0mBCC+Cs5LOga5XJpyYMIqkKvw4B5kfj7hyHIK67gTr8tOSC8bosiYDECMP+Q6V1TqcHAL7bglXGrca+8khIrtR9HGVGGIBow2/8Q/vhBAO4VNq9opb5PBxGAMmaAb1QCOg9R4WqWur63W+w6agNN/vROXuVEAq99uh4vjPLFUSKBFiZPUdBj86FreHKIFyIOJkOUjRbLpWAxEHlBHIFGImAxAqhZP/2gT6XmostIXyzbeAqiSJEga17Rds9JDJZyOx9dR3hj6YZ4FhPJ1jufnV+Mzi4qeG49zmIWGc3hO5p5mBRCknFbXYzXP1mH54b74ND5DCaqEmkVUcfBdjIsfagFtwosMiiRkoDcomL8xT0IQ77aCp1AYjMDKKYSPzgCbQEBqxAAhdIVZB2mecWi6xA/nEm/TxrHtoDXY/sgyEbM8j+E50cGoqC4nBEABQqw5UMQDBi+ZAcGLNgKg1Fnkr03P2ObCYB8FDLVpXh9Sgi6DPfB4fO3WBC7ujAkPwuWk9qC4ivmyCjLoJDlcwIOwHGYP85czWJEpDit1dUS/hlHoPUhYBUCIHtp+hGpS3V45aNgjPwuClU6gaUSsyE9qAVHS/GkJU1vWk4Ruo8IwI8b45nnKE1QLS3GeFxHKUJo6J5kdBq0AldzH4By05MJa3MfZgJQPIb1yFSX4Z9T1qLrCB/sP5NuitdPjxFl5iIzJgppkQWjqGSgs1R7SQEtiCLOXb+Lrm4+WLz+qMlPQqnb1sfTUjjwcto+AlYhgGrYZBEbj6TCfsAKrNt7GaJsYPbm1d+3lRPyEiVZtmjA3NVH0G2EP+6VVLWa3pHI7ubtAjgO8YFXxDElIXoLMnU1EUgSstTleP3Tteg6zAt7WeRNPYulRHjrDQJGLd6KM6l3LOqURRN8hc6Itz4LQe/JwSjSUG5j297FtZqHjTfUphCwKgHQD8kgipi0ci+ec/NhljEtsbK0NuLMykkScet+CX43wg/fbDzByMDa9VqqfGa2Khnxny+2wHXhTpYJi0Ift9RBBGBWDFPsnay8MvSZshbPunlid0KaaWcl4eqdYji6eGG8x26LhpKgVI8LQ46gs+sqHLt8B7KotykfjpYaF15v20PAqgRAseDoB5ymLsHLHwXDdcF2lGsqQWnQ2YKqjayqaLEsSnrMD/oZL45cjaz8MiZCaC2PCxO5yAJCD1yCg4sn0u8+UJKmt1AHzDsARgRkby8akZNfhj6froXDEE/EnEhjBLF43UH8r5Mni2eUqX5gsmpSxI8NbTqROAtsKMk4cTkTTw/3xtzVhyEYKdYVldlyhNjQvvDrOQL1RcCqBEDzOzkbSaIeEYcuwt7VB4G7zirbdRZFtL7NtO3raKLKUJei6zAV5gUfZjkRKD9uaznME+6t3EL8buRqeG89ZbVUkQ3FxNw2es/KK0Wfz9bhKTc/7DiWhj9/tAb/+/736DhwBQJ2JSoJ6U36p4bWI1E8f0FCYYUWr00JxauTQlBYrm1oMfx6jkCrQsCqBEA/WkW8oIiCFqw+BAdXFeIuZrBJknYCbeEgZ6Fv1h1iysobTIkqwUj24q3oYGMlyXhr9jq4zNsMvY0QWE0CID8BIoE3ZoTCcdAqdBywCk8MXIaOAz3wj0/Xo6K8slp01FDoqR6jJODjH/fi2RH+uHjzHsvj3NBy+PUcgdaEgFUJoCYQFORLXViOvp+F4a0ZG5BbXFa9rTb/yGte3xrOWdpLQUZWQTkch6owxy+mVduIk5gjeN9ZdHHzR0pOEShOT0ukrqw59kSukqgksnlQpsGBc5kYsmgrnhjwIzoMWI4OA395nUjOhiAZGmTBRDF+mAhMkhB97Doch3riu/BjENgOlYt9ao4FP297CDQbATB7bVGPc9dy4OjqB7dFW2AQSLbaencBZO4qCgYsDIlDFzdvXM1+AFu3+f/NR1gGcgpIkb0GPjvOQhYVn4DfvMfKX5KN//WcAqzadhr/mBzCZP7/M2CFQgADl1e/ExFMWL4HRsHYoDEgAqAkNedv5MHRTYURS7fBKIgAiS5b8bNp5WHhxbcRBJqNAJgijTntSAjdfwGOg/3gv/OsEiyulYJJ3qnZReXoPjoYn3nsZSvm1qzXpglPZ9Th/dmb8Mbs9Sz+fUsTNHneHjqXidHfRqOT00p0GPgDnhhIq//v8cT736OD00o8YdoFOLp64FZBBVCP5DLmXSfZ/OeV6fDenE14bXIQKCgdE1vS5M83AK30l8mbXV8Emo0AajbIIAqYtHI3Og1SYd/pmxBFfavcCVAWrSXr4+HoqsLZ1LtKNM1WvGokkhYkAX5bzqDLCB9cuXWvxe3fyWyYVulVgsh2WIvWxuFP4/3R0ckDHQaswv+8vxz/O4B2AiQKWonlm0881iS0evKXJGi1Ogz7OhJPDvLEsZRcyLQrbSO6qZq/OX7OEagLgRYhAIqXU1hegYHzI/CKezAy7pW2SgKgyJAvfRCMD1fsYKIHck5qzeaCxF1kDpn7oALPDPZDcMylFheD0GSteP5SHB6RTe6lGgMiDlyA2+It6Oa2Ah0H/ID/GUi7gxXoOS4QpVpDXc969WdmAhBFESF7L+OpwasQtOssG0PSN5AfAD84Au0BgZYhAJpoZBE5hRr8aWwAXp8UhNsF5coP3YIxXawygJTfQJKZcnTlpuPo7KTCmet3WFgCJv5pvSoNFuWSCICylw1ZFIV/zw5lTldWwbGehTIFLXtelHzChDGbwKGE37iSWYQfN5/Bn92D0dFpOf7XaQW2xF0yZTirW4bDypRkhO8/jyedV+GrkCPV1kPsOy77qefo8MtaOwItQgBm0IgE9iVm4NnBnhi2OAoaXRVzxjF/b4vvNEFIooCi0gq8/FEIPvh+D/TGtrNiZCtuSULgjnN4ZpA/stVFtjgM1W2SyUpIElGsqUBsYjqGLo7GoLmboWPK3brHRRIExCVn4mlXf7w7ayOKK6taXNRV3SF+whFoRgRamACU+Dm7Tt2Ao5snvl4XD0Gybft5EvGQc5vvjkvo7OSBM9dz2W6mGcfMalWZRSP0nq0uRQfXldhz4obV6rNEwWSKS5nDyFrIIJIOw4DM+/nME5vIoa4jp6AYr04Kw79nhyGvpAIGbvJZF0z8s3aAQIsTgHnFGbrvHJ4c5Itv1sdBZ6CsWkZm/21rY0CrzQcVZfjrxGCMWBwFnaBvkw5DZAo5ePEWLAimSJh6GBQFga0NR73bw3Zukh63Cyvw5pR1+NvkUOQUVdT7fn4hR6AtImATBEAkYBAMmOIdiyecvbB0w1HojOTQY4MCdUlEyL4reNpVhVMpuRaPRW8rDxlZ36zefZ5NlIJplc0SG9tKAxvaDlnC7cJKvPFZCByG+eBUcjYL8dzQYvj1HIG2hIDNEABt4SurdBj/4w50HLgKP24+CUGQlBwCLY04s+4hJSRQodWj92fhGLpoM5M9WzoZSUt31Vw/WcLcyM7DC8O9cDVDrcQGskVCNjf4Ee+08qeByyksx5tT1+EZN19sP36dWWuRMp8fHIH2jECLEkBN4FnkUNGAMq0RY5Ztg72TF3y3J8JgNCrB1Vrwt8pk4xRkTDLip/2XWIaoE8m5NZvf5s5JQU9mra9/EowNBy4p5q0tOAaNBZiyi917oMXbM0LxzBBPRB5NbdXhOhqLA7+PI1AXAjZDAMzWWxLYZF+m1WPMsig85eIBnx3nYBCUkLx1daA5PiNvUYruWW7Q441PNmLIosgWN4+0dr8Z6YkiFqw7BqcvNsEgCK3SPepuUSXenh4KR1cvRManQpLI6bBu5bC1MeXlcwRsDQGbIQBmXUN5AkAhpCkjkwFjl+3Gky5eWL7pBATByPwEaGJq7oNaRXkNwuIu45khgTh2KQNiPcINNHc7LVmfedezLyENTw3yxI3b+a1m5azoqwXkl2rwxmdr4DDEB1HH0phHMT1nLfAIWXJoeFkcAYshYDMEULNHFIkRogEanQETvt+JDoNUCI5JgiQYWmT1RpOhpsqIf0wJheuibdAZydywba8ilYlSxm11OZ5y9ULonnMNirJZczyb+5zEVzqDHqO+3QmHwd7Yduw6C3HR3O3g9XEEbB0BmyQAUkCyML2ShHKtDuO/347nhvrgcFI2i77Z3KCSnXnUz1fwhIsK8VcyAcFg8w5rTcWIYu/TREpK7vfnRWDQ19thMDZ/ovjG9ENnFPB54EE4DlYh6lgqy9ZGu0p+cAQ4Ag8jYJMEYG4i/WRJiVeuM2DY4kg8O1yFg+cymPxdiQ9jXXEQTRq00i/TVKLP1AgMnh8Bmlza1SHLWH8gCU86q3CnsErJEWBDk2l17mBZBkVnLanSYYbvIXRyWYWQPefb1VDxznIEGoqAzROAEgDMgMLySny4Yg+eGuqLHyNPsng11lbm0eQiCXpEHbuBDk4eiLuQ3SqD1jX0oah5PYm/kjNy8LxbILyjTjMvaErSYisH01UwT2AJaXeL8M6sjXh+hB+2HUtleiNbaSdvB0fAFhGwaQKgHzfZcZPggVb8Wr0R8wMPoIOzJyZ77YfOQMpZyuikJJah6y15UMyfkkot/vlZGP77+QZUaHXtkAAo6Y2Ad6dtwH8XRkJnMEAWW5oAmFqePRts7CUB1zLz0HPCGjw/MgA/X8xghgT0HT84AhyBRyNg0wRQs9nmlZ5elLA49Gc4uq7EqGVbcPNeiRLD3eSsZUlZryQasf1ECuwHeWF3wk1mF9/esoQQ7qSPCd2XhK4jAlgE10fF2Kk5XtY8p3j95olfbzRgS/w19BgfgD4fh+DYtbuQ5d8OB23NtvGyOQKtCYFWRwC0KhclAw5czEH3Eb744xhvnL15vzqcryV3AVq9Hm/MjEC/6SGo1BtZ0DG0s1WlQrwirt/Ox3PD/eAdlQC5hePls5DQkgCNQcTSjfGwH+iB4Uu3oaCconoabDKGVGuaFHhb2w8CrYoAaFjMOwGyULl4S41XPl2H7sO8odqSAL2RJmmhxjUNFwmRcIGsfqiemNOpeMLVB5viLjOLGEYuFhYz2fyjRjsAUYRWlNF/zga8MzOsxSygFHEfWSYZkXW/BEMWRKLzYB987heHsiolqxwL+ia3Dmslmx973sA2j0CrIYC6RoIUxGWaCvzwUwKeG+EP16934PjlOywUsCiRvL7hMmAlSbiIiiotek8KxYB5P0Grb78TiplwKSzE+r1J6DrMF5cz7tU1HFb/jPxDKqr0UG1LwEvjAvHW9A04npwNQVR0QVZvAK+AI9DGEGjVBEARK0kWTHL/jPvF+PesDXAc7IN5aw7jQYWOWawQBZiJgK3gHzOAFPZBEkSs2n4aDoNUOHjxVpuJ9/+Yrtf5tZkACMOisip0Ge7N8jbQ/2QN1AiOrbOehz/8JfsXEQ+oHlnEqevZ6Dd7IzoP8oRHxCnoDYp3OMvi28JiqYfbz//jCLQOBFo1AdSEWBYNKKnQ4oefTuNpV1/0mxGOwxcymPcw2fKbJ3/ze817a55TCOrSSi3+MikEboujoGchKBouSqpZZls5p4Txn/geQp+pG6ETKFicaBUCILSZKIc5o+lRrjXgh4iT6OLmgb9PDMXxlFwYRKpb4Mkb28rDxfvRIgi0GQIwSIrs3iAZEX8tA69/FgzHod5YtC4exZW0G6ifqSjtKoL3J6GTsxeOXMyERErF9ib3f8SjSB7aO+NT0NF5Fc5ez4Ek0wrc8uIxgpsUzQZJwKlrd/H+vE1wHOyBGb6Hcb+skoWkoO9prB5H6I/oCv+YI8ARANBmCIBEBNXiClFCXkkVFoQcwpNDVXj90/U4cDYNRiYyIrERXSuyRO7sKWB+BAqBlOuq8ObUMAz5aotJxECzUcN1CW3x6aJJN6dQg+fcPPFFECVSV8JFWKqvpORlOhhRRkFJOZaEH8MzQ7zxF/f1LN8vc0CjFBHMDFQxCOCR3SyFPi+nPSLQZgjAPHjVJMCsVwScuZaLf80Mw5ODVuFjr324ebcQLI8sKQ5NK3uyKydxApkQhscl4QknTxxJyjIXyd9NCIg08UpGTFixD29O34hyrWVDK4uSEUbJgD2n0vHKR6vh4OaPL9f8jPzycpZ8hw8ER4AjYFkE2jYBSDLzWq3UGaCKOo0XR6/B70b5YtWWBGh0umrRDsmciQBKtEb8a1Y43p8fiSqD3rJIt4HSSAREBLAjIRWdnDxwNTtfyRRmob5dyyrA4K+2o8MgD/xn3iYlbaNEfh+Uj4HvwiwEMy+GI1CNQJsjgOqe1ToxyiIy7pVhzHc74DDUF30mhyLiSDJL8UgrTxI/bDl2DZ1dfHAkMQ2i1M6CvtXCq65/SUEuQo87eSV4YWwwvlxzpNEWUuRbQJI18tu4nV+Ouf578KybP34/yhvrYi6yAIBM98LFb3UNBf+MI2ARBNoNAVD+VwrtYBCMOJmcjUGLt8FhiC/enhGBQxcyUKUz4N3PN+E/cyNgZOGeueVP7SeMRGZkdkuOcqO+iUTfz9ajvLJxYRdkUUB5lQ6B28/imeHe6DrGH4vXH4G6uJxZF9F4MXFeq8xDVhs5/j9HwDYRaDcEoCgslUmFVvcGUcKO4yl4Y8p6ph9wXRyJp90Csf98NrNuEUSRhf15SFlsm2PYbK1iBMDiMIiITriBDoO8kJxRyJTkRAp1z9WkayHNrRLYj/Akkdzmo1fx1vSNeNp1FaZ77UXG3QcMd5l2BixBtNlqq9m6xyviCLQ7BNoNAdQ1spTkvbxKD6+tp/G74V5wGOSBD5dH49wNNUSRzD8VqxSaj/jxMAJ3i0rRfUIQloadhCwalUB5RA61DoocTTiSBValVouNh5LR+5MgPDHAC2/NWI/YpGwIsgEiD+BWCzn+L0fA+gi0awJQFpoi82jNzivFV2En8eJYfzw92A9Dl2zBoQtZqDQKoFUpPx5GgJTmo5ZswSsfrUGFQc8wrMtclkxu7xVr4Ls9EX9zD0EHVx8M+HIzdpy8Ag1ZEQnKip/7WjyML/+PI9AcCLRrAmAiC7ODGFmXyyLUJZVYsyMRr36yAZ1dvdD3s7VYty8JBWVVzHyUlMVMNm3KVaCctz8LFUkSsDEuGY5DfXA2jeLvk4moKRCfJEGr1eNqdgFmBxxG9xH+eHqYH8Z+H4W4pCxodUrgNsKbpf4kPwyW9aE5HnleB0eAI2BGoH0TgBmFGu8krpYFHTRGHTYfucbMEZ8a4o0X3AIwy/sgzqXfRyl5Fot6lrieJrH2uHolmX9hmQ7dxgThh/DjzGNalPTIzi/DT3HJeH/+ZnQeHICXJgRiht8BXLqphlEQIYkUQ+jXoqIaQ8BPOQIcgWZCgBNALaBpRUqiIVrRCqKerWrP3byHmT4x6Dl+LTo6rcSb08KwaG08LqXnQGskr+L2ZzJKZrWSYMQ4j93o9cFqxJy7idE/7MHzwzzQ0dkL734egfDY88gvrgTzH5ANIDNSwtUcnK8W9PxfjgBHoJkR4ARQD8BpwqJYQnmlGuw9nYYPlu1C1yE+6OjigX/OCMOKzSdw4tIdGElxzJyWjCaRCOUnIIJofSIi2tUwqx+R4u/TxC0pyl7JCEGQUFCqwZ4T1/DvWeFMofuk8yr0nrIeX4X8jMs377IcAgQtlcEPjgBHwDYR4ARQj3GhOYxNgJIyoZNJ6Z2CMmyIvYjxy/egy3BfPDXID3/7JBCzVx9BeGwiHmj00BskQDC0SgJgq3VZgiAbmVOcRi/iQkYeVkcn4j/zf8IfJ6xFp8FeePmjNZgfFIeElHsoqdAxr11yrOMHR4AjYPsIcAKoxxixlTDLjUsxgygJPZk2kgJTZMln8ku1CI+9gFmrD+PlsYFwcFGh6+hAvDFzI5ZtPImD5zNxv0QPvVEAaEdgXhmTvoGZz7NoRIBspGg79K1J0UxxkdnF7DNmaM9uMH3PFNdUiOllulcxyGe1KPcplbDrFJ0FtcH0x/qihF9mq3WTcrtYU4ncEi1CdidiZuAhvPRBAFP4/m7EGrzxaQhWRSbgXMptlGmNpnJNynGTiIev/OvxYPFLOAItjAAnAAsMgLJDMIJCUZPZ6IlLuQjddw5vz1yHVz4OQmeXVeg81BsuX0ViRkAcVkefR9qdAqTfLYRWbwDlMqCsVmQvz6yMaBKViGDIvt5kKcOogWxllBcT0ZB1Km0yZHrJ7MUiZZquNZ8LpminVDYpOBRZPIW/UKJ55j8oxY3sIlxIv4+Faw5iml8cXh6/Bs+6qvDMUD+89ul6fOq5B+GxScgp0kAr8BW+BR4bXgRHoMUR4ARggSFgBMBk5gJESmJCegBJgiAZUKEXcPxiBnM2Gzg/Am9OXw/7QSvRwXklnnJahXdmRGD4kp0YvXQ7QvddwsmU2zh5/Q4Sb9xFTkEFjCIRgPCIFyVlUYKlke6BgqbVdW2FzoDrdwqRcO0OTqbcwdErtzFnzSG4Ld2JYUt344XxgbB39kJHl+V4bpQv+s/fjlGLt2BXQhqS0nOYCIj6xMw8JSNLxmIB2HgRHAGOQAsjwAnAAgNA4g6FBMwx6kkcokhvFHERiX4U0ZHOKOFqZj6SMvOwastJuHscxLjle/H3yWvRwWklOjp5wt55FToN9MSLo/3wxrQN6DdzA96aGYY3Z2zAWzM2oN/09fjP7DCMWLQZE1fsw4ivt7D8Be/OWI93ZoTh7Zlh6EcvunZGGHpPCoGjqwc6OK+CvbMHOjp54OlBnnBasBkTVu7DJ6v2ITYxE5dv5SMnr8wk5lJ2CtaUwqgAAAwQSURBVEoAOBbJQVHoUsfoxQ+OAEeg1SPACaCFhtCc0YqZRYqU3F6LrPxiZKkf4MrtIgTsOI+vQo9h4bqjWLg2HvOD4jHD+wDGfLsTfT4Jwe9H+aPLEBW6DvWG43A/dBnuhf+bEIh/zdqISatiMDvwML4MPYYFocexYN0RfB92BLFnbyFLXYpMdQly8itgNNJuhUJekGMWWS5xj+cWehx4tRyBFkGAE0CLwG5S/pLcn8wqTRE2mWyeZPSmVItsZ0Fye/IzkEnZSnoGCqZmRGmVHg8qtChmr0o8qKhCWZUBOoPimEYB70TJALLIIQsmcyx/yaQDINER1cfyJbNrlWBtLQQHr5YjwBFoAQQ4AbQA6LxKjgBHgCNgCwhwArCFUeBt4AhwBDgC1QjIEIpuIelqLjRWVrdxAqgGnZ9wBGwPAUGdiMgAFVQqeoUgYtdexCWmo0hX07u8ClnR32HitFAkaWp+bnv94S2qDwIaJKneg10PFZKsHGWGE0B9xoNfwxFoIQTU0VNhZ9cNfVzHw919JN7rYQ87O3v0GLoMe9LLTDl4ypEcMAz2PRcjvoQr8iHdRuzX0/F17G3mGln30OmRE/sDJn0dixyb40xOAHWPGf+UI9DOEFAI4D2okjRKz+UqqJO24av+3WHX90ck8An/10+EkARVDzv0UCXh0Qvo5ptkf93Ax33SfG3jO4DHjQX/niPQggj8igBYW2RUJXnjLbs/YFjELUhQVrMTZ0UhnW0A9FAnbsHy2cPQx94O9n2GYU7AYWRpzLsDGYL6LMKWjEMfe/Puwh3u7nMRklQCKScWX09ahl1nD0A1ti8c+s5HTI4eEO4jMWIlZg/tA3valQydi4C4DJOc2ryi3o6zpzdhyei+sO/hjDlrT0NdlYekyG8xuk939Og/E4En7z1iYjaXsQMXzm/BUlbGQExT7Ud6ddsBCAVIjvbFHHM7Rn+FkMOmdpQkQOXuauq3Kz50n4hpIRdhok/TSBYiQTUFrn26wc6+D1w/dId7tfhMj8LkPVDNMWM3FgtDjtTArvbDoEdhkqmtdj3xnvuPiE4310bjsAlL3fujh30fDJ3jh1i2ayP8ExGxfBaGmtowdE4g4rLKTTu6OghAyEdS5DK4v9eTtXnonGCcVOtrN6bB/3MCaDBk/AaOQPMhUDcBANAnYvkf7GA/NRaFqDVh0Aq4Zz9M9PoJu6KjsWvDQvS3746BIVdhoKZXXULAgD+gp7s3Yk4eR4xqInra9cTo5buQpNZDSFKhh50d7Ox6wXXOD/D61g/7c5TPe/adDK9NOxEdvQMbFjrD3n4kQq5XAuY20H09x2P5pihsWj4ePe3+ChfXd9DTdSFCtoVh+dhXYecwHdH36wonYuoHldHDDQtDtiAqeC7es++OAQGXUEVtl4txUeUGe/sBmBO8FdHRWxGy0A097N7CvLj7kHXpiPWfC1cHOzi4zoGnSoXA2HToHhoyDdJjAzDHtQfsHFwxx1MFVeABpOsElF/0wwD77nhvTiCionchKmQhXHs4oNe8QyioQyErq2MwvWcvjF6xCwlnjyI65Dssj1MDEFFy1gv97XvBdWEQosztdI+GmmE1EH0nemDTrmhE71qHhf27w37gWlw3UCW1xtPcZ8J12xEkxO+Ayr037Pt74WwTd4CcAB56MPg/HAHbQuCRBCDfRtTYP8CuekKpqTQUUKnRm1aTNGnWvBYQkwPQ2+4dLE8sUzrLRCb26B2QzPKyKQTggL6LfkZhzUlPqIKmhvJZzo3CWLsecI/O/WXScvgQa1NMugn9RahetYddfz8ksRW8DENyIPrZvYo5cfl1AG2a+GqWId9D7LS/wm5gGNLJJeZ+NCY5dMOAkBRUU4iQjoixPaqvQWNFQHIOoif1gt2AtUg1mjuuQ1bERNjbjUZY+sM0Qh1QsKqBpblXcjaixvWAvVsY0s1lyVXIu1sMATKEykrozFXAiNyoSbCzm4poNQmtHiYAuSAW0xx6YFxUdvWYytkRcHskjuZGPP6dE8DjMeJXcARaDIFHEoCYgpB3HFA3AdDMVIKsxDhsDwuESrUY7n3M1wJSehgG2vXG3Lg8NqHIxXGY260bBobdYEpTZVKroXeo7r0MoTQTiXE7EEaWSUvd0ac2ATxkuZKLaPcepjaaClFHw736nuqCTScPT3zKhzU/k1GZ8B2629Vum+ka+9mILRRpVm6cDqAyAUu7/1p3oODRC1Nj79dusGk31R12PYZibuAeJKmrlEn6EWX9UoARpVnnELc9DAEqTyx1f+uRBKDU3wOuc5abrMHM2P8yZr+U27AzTgANw4tfzRFoVgQeRQDKqtAef11+FlW1VozQpSJiYm/Y9RiIqUs9fkUAMKYgZIBZ/j2eycLt+6/AyUJFZVo3AcjQpUdiYk8H9Oj/KZZ6mSehWjsAqxKAiMLY2bB/FAGYV9CNJYDCWEy1fxQBmPtZe/iJFNMRH7YEo5k83wXfncyD/IiylLs1SI+YysRu/acugVdjCICZBW9AXBaJ3xp/cAJoPHb8To6A1RGomwCqkBkxCQ52zlAlkRinrlXyW1iaUGxqX82VuITyhGXo1W02Nh0/jD3R0dgTdw5ZpdUCFZNYo/YquxgJS9+CXffvkFBpkl08tJqv2QYzLDXrNX320D3m68zvdZXx8GeK+OqvmBZ7r1ocAjkPcXN7w+6dEKSSnruxBCAmI6C3PRymxdaQ94sojluAbnZuCEllWghzY3/1LutuInJiL0UUZVDK6rYwHuW1rzTtDrovTYAyfQtQxrluEZCYGoJ37PpgYXxR7ZKa/D8ngCZDyAvgCFgPAWVi6IM5EQlISkrCxYQYhC0di5523dF/xSmUsLm45iQpQ5+kwqt2r2Ja1A1odGXIObsOE3vaQxEXyahKDsQAe7JYWYDlbCWpQkDYgWrxRd07gHIkqQbArtssRGWWQae5g7Nrp6BntTinZhvMeFieABQFdnfY9/8OMddzoFbn4HrMd+hv3xPjItIVvYCcgQi37rBzDURiThZSbxXVYXWkR3bEBNjZjURAYiayUzNRJJQp/hT2LlgacxW5ajVyr+/F0v7d4TAuEplmWb65e5CgSdqOtbGXkF1YglL1RYS594L9uCjkyGVIUjnDzn4Ylh9KQa46B6lHgzHtw5+QXqXoRrpN245MTRU0OaewlnZs5h3MQ4QOwJiKMLc/wN51JQ6lUp/VUGenIGHPPpwz7dqqm9TAE04ADQSMX84RaE4ESuIXoyezyCGrHHrZo0f/6VDFpKCEMgGxoxLJAc6/eI4Kd3H0WxfYm+6z7zsBn47sBTMBCOpD+KpvD7w39TtFprz8C0V80esrxBUIJiVx7R0AmS4ewbfkf8DK7Ya+kydjZDezaKRWG1i7FAJQLJWUluI3dwB1lVGbWERoUqMw9z1zOwiTVzFWdRzqajyMUB9ahL72CmYP1W9qBr3J6gOY17eb0h+T/kDWpCBq7oBq7AjvnmP9HmFySQQQiKHMOc9UV9/ZiLiuKMFlzVVETHvnl7Ls38G0bTeggx7qoz+iv6l9dvbvYPKnbuhWTQC1cSDsj2LF0F4m7M11LcIh9S87txpdq/cpJ4B6Q8Uv5Ai0AAKyDqV5amXVp1Yjr1T3i+ijRnNkXSnyijS/rHRlHYpuXUVSciaKdCIEzQPTvabJpV8gkpnJoVLIQ6t+VucDaKon1F8qknWFuJV8Ccm3CqGTBWiKClBqsgz6VRsgQVdagCJNDXcsVvYv9/xSsnL26zJk1nZ1zb7RpUI5clMvIynpKm4V1YWJAE1uKpKSb0Fds/6HKqSy7yI16SrS1TWwg+nepCRTPx+6qdY/VIYa6clJSEq9g5IaVlLsQvM4JKXidknNdkrQFWUi2dx+QYOivNJqy6Bf40B91kCdfhVJSZeRml1Q5/jUatxj/+UE8FiI+AUcgbaEQBVSQ9xg5zAOqoNnkZyejtSk49j2lTPsey1BfLHZWawt9Zn35VEIcAJ4FDL8c45AG0WAxBzbl5IXsCJKsLPrif7TfE1eqm2007xbdSLACaBOWPiHHIF2gMBjxDHtAIF230VOAO3+EeAAcAQ4Au0VAU4A7XXkeb85AhyBdo8AJ4B2/whwADgCHIH2isD/A7TNydJvx9/OAAAAAElFTkSuQmCC"></p>
</div>
<div class="specification">
<p>It is given that <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>9</mn></msub><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msub><mi>u</mi><mn>1</mn></msub></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mtext>Σ</mtext><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mn>9</mn></munderover><msub><mi>u</mi><mi>i</mi></msub></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A game is played in which the arrow attached to the centre of the disc is spun and the sector in which the arrow stops is noted. If the arrow stops in sector <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> the player wins <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> points, otherwise they lose <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> points.</p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> be the number of points won</p>
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mo>(</mo><mi>X</mi><mo>)</mo></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#999;font-size:90%;font-style:italic;">* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.</p>
<p style="color:#999;font-size:90%;font-style:italic;"> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>360</mn><mo>°</mo></math> <strong>A1</strong> </p>
<p> </p>
<p><strong>[1 mark]</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>360</mn><mo>=</mo><mfrac><mn>9</mn><mn>2</mn></mfrac><mfenced><mrow><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><msub><mi>u</mi><mn>9</mn></msub></mrow></mfenced></math> <strong>M1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>360</mn><mo>=</mo><mfrac><mn>9</mn><mn>2</mn></mfrac><mfenced><mrow><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msub><mi>u</mi><mn>1</mn></msub></mrow></mfenced><mo>=</mo><mn>6</mn><msub><mi>u</mi><mn>1</mn></msub></math> <strong>M1A1</strong></p>
<p> </p>
<p><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>360</mn><mo>=</mo><mfrac><mn>9</mn><mn>2</mn></mfrac><mfenced><mrow><mn>2</mn><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mn>8</mn><mi>d</mi></mrow></mfenced></math> <strong>M1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>9</mn></msub><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mn>8</mn><mi>d</mi><mo>⇒</mo><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo><mo>-</mo><mn>12</mn><mi>d</mi></math> <strong>M1</strong></p>
<p>Substitute this value <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>360</mn><mo>=</mo><mfrac><mn>9</mn><mn>2</mn></mfrac><mfenced><mrow><mn>2</mn><msub><mi>u</mi><mn>1</mn></msub><mo>-</mo><mn>8</mn><mo>×</mo><mfrac><msub><mi>u</mi><mn>1</mn></msub><mn>12</mn></mfrac></mrow></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mfrac><mn>9</mn><mn>2</mn></mfrac><mo>×</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo><mn>6</mn><msub><mi>u</mi><mn>1</mn></msub></mrow></mfenced></math> <strong>A1</strong></p>
<p> </p>
<p><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo><mn>60</mn><mo>°</mo></math> <strong>A1</strong></p>
<p> </p>
<p><strong>[4 marks]</strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mo>(</mo><mi>X</mi><mo>)</mo><mo>=</mo><mn>10</mn><mo>×</mo><mfrac><mn>60</mn><mn>360</mn></mfrac><mo>-</mo><mn>2</mn><mo>×</mo><mfrac><mn>300</mn><mn>360</mn></mfrac><mo>=</mo><mn>0</mn></math> <strong>M1A1</strong></p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Iron in the asteroid <em>16 Psyche</em> is said to be valued at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8973</mn></math> quadrillion euros <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtext>EUR</mtext></mfenced></math>, where one quadrillion <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msup><mn>10</mn><mn>15</mn></msup></math>.</p>
</div>
<div class="specification">
<p>James believes the asteroid is approximately spherical with radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>113</mn><mo> </mo><mtext>km</mtext></math>. He uses this information to estimate its volume.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of the iron in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>×</mo><msup><mn>10</mn><mi>k</mi></msup></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>≤</mo><mi>a</mi><mo><</mo><mn>10</mn><mo> </mo><mo>,</mo><mo> </mo><mi>k</mi><mo>∈</mo><mi mathvariant="normal">ℤ</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate James’s estimate of its volume, in <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>km</mtext><mn>3</mn></msup></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The actual volume of the asteroid is found to be <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>074</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mo> </mo><msup><mtext>km</mtext><mn>3</mn></msup></math>.</p>
<p>Find the percentage error in James’s estimate of the volume.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>97</mn><mo>×</mo><msup><mn>10</mn><mn>18</mn></msup><mo> </mo><mo> </mo><mfenced><mtext>EUR</mtext></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mn>8</mn><mo>.</mo><mn>973</mn><mo>×</mo><msup><mn>10</mn><mn>18</mn></msup></mrow></mfenced></math> <em><strong>(A1)(A1) (C2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>97</mn><mo> </mo><mo>(</mo><mn>8</mn><mo>.</mo><mn>973</mn><mo>)</mo></math>, <em><strong>(A1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>×</mo><msup><mn>10</mn><mn>18</mn></msup></math>. Award <em><strong>(A1)(A0)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>97</mn><mtext>E</mtext><mn>18</mn></math>.<br>Award <em><strong>(A0)(A0)</strong></em> for answers of the type <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8973</mn><mo>×</mo><msup><mn>10</mn><mn>15</mn></msup></math>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><msup><mn>113</mn><mn>3</mn></msup></mrow><mn>3</mn></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in volume of sphere formula.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo> </mo><mn>040</mn><mo> </mo><mn>000</mn><mo> </mo><mfenced><msup><mtext>km</mtext><mn>3</mn></msup></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mn>6</mn><mo>.</mo><mn>04</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mo>,</mo><mo> </mo><mfrac><mrow><mn>5771588</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>,</mo><mo> </mo><mn>6</mn><mo> </mo><mn>043</mn><mo> </mo><mn>992</mn><mo>.</mo><mn>82</mn></mrow></mfenced></math> <em><strong>(A1) (C2) </strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mfrac><mrow><mn>6</mn><mo> </mo><mn>043</mn><mo> </mo><mn>992</mn><mo>.</mo><mn>82</mn><mo>-</mo><mn>6</mn><mo>.</mo><mn>074</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow><mrow><mn>6</mn><mo>.</mo><mn>074</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfrac></mfenced><mo>×</mo><mn>100</mn></math> <em><strong>(M1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution into the percentage error formula (accept a consistent absence of “<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></math>” from all terms).</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>494</mn><mo> </mo><mfenced><mo>%</mo></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>494026</mn><mo>…</mo><mfenced><mo>%</mo></mfenced></mrow></mfenced></math> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2) </strong></em></p>
<p><strong><em><br></em></strong><strong>Note:</strong> Follow through from their answer to part (b). If the final answer is negative, award at most <em><strong>(M1)(A0)</strong></em>.</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><em>Give your answers to this question correct to two decimal places.</em></p>
<p>Gen invests $2400 in a savings account that pays interest at a rate of 4% per year, compounded annually. She leaves the money in her account for 10 years, and she does not invest or withdraw any money during this time.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of her savings after 10 years.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The rate of inflation during this 10 year period is 1.5% per year.</p>
<p>Calculate the real value of her savings after 10 years.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2400{\left( {1.04} \right)^{10}} = {\text{\$}}3552.59">
<mn>2400</mn>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>1.04</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<mtext>$</mtext>
</mrow>
<mn>3552.59</mn>
</math></span> <em><strong> M1A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>real interest rate = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4 - 1.5 = 2.5{\text{% }}">
<mn>4</mn>
<mo>−</mo>
<mn>1.5</mn>
<mo>=</mo>
<mn>2.5</mn>
<mrow>
<mtext>% </mtext>
</mrow>
</math></span> <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2400{\left( {1.025} \right)^{10}} = {\text{\$}}3072.20">
<mn>2400</mn>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>1.025</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<mtext>$</mtext>
</mrow>
<mn>3072.20</mn>
</math></span> <em><strong> M1A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The speed of light is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{300}}\,{\text{000}}">
<mrow>
<mtext>300</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>000</mtext>
</mrow>
</math></span> kilometres per second. The average distance from the Sun to the Earth is 149.6 million km.</p>
</div>
<div class="question">
<p>Calculate the time, <strong>in minutes</strong>, it takes for light from the Sun to reach the Earth.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{149600000}}{{300000 \times 60}}">
<mfrac>
<mrow>
<mn>149600000</mn>
</mrow>
<mrow>
<mn>300000</mn>
<mo>×</mo>
<mn>60</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for dividing the <strong>correct </strong>numerator (which can be presented in a different form such as <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="149.6 \times {10^6}">
<mn>149.6</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mn>6</mn>
</msup>
</mrow>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1.496 \times {10^8}">
<mn>1.496</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mn>8</mn>
</msup>
</mrow>
</math></span>) by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{300}}\,{\text{000}}">
<mrow>
<mtext>300</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>000</mtext>
</mrow>
</math></span> and <strong><em>(M1) </em></strong>for dividing by 60.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 8.31{\text{ }}({\text{minutes}}){\text{ }}(8.31111 \ldots {\text{, 8 minutes 19 seconds}})">
<mo>=</mo>
<mn>8.31</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mrow>
<mtext>minutes</mtext>
</mrow>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>8.31111</mn>
<mo>…</mo>
<mrow>
<mtext>, 8 minutes 19 seconds</mtext>
</mrow>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1) (C3)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>The intensity level of sound, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> measured in decibels (dB), is a function of the sound intensity, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="S">
<mi>S</mi>
</math></span> watts per square metre (W m<sup>−2</sup>). The intensity level is given by the following formula.</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L = 10\,{\text{lo}}{{\text{g}}_{10}}\left( {S \times {{10}^{12}}} \right)">
<mi>L</mi>
<mo>=</mo>
<mn>10</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>S</mi>
<mo>×<!-- × --></mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>12</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="S">
<mi>S</mi>
</math></span> ≥ 0.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An orchestra has a sound intensity of 6.4 × 10<sup>−3 </sup>W m<sup>−2</sup> . Calculate the intensity level, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> of the orchestra.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A rock concert has an intensity level of 112 dB. Find the sound intensity, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="S">
<mi>S</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10\,{\text{lo}}{{\text{g}}_{10}}\left( {6.4 \times {{10}^{ - 3}} \times {{10}^{12}}} \right)">
<mn>10</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>6.4</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>12</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(M1)</strong></em></p>
<p>= 98.1(dB) (98.06179…) <em><strong>A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="112 = 10\,{\text{lo}}{{\text{g}}_{10}}\left( {S \times {{10}^{12}}} \right)">
<mn>112</mn>
<mo>=</mo>
<mn>10</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>S</mi>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>12</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(M1)</strong></em></p>
<p>0.158 (W m<sup>−2</sup>) (0.158489… (W m<sup>−2</sup>)) <em><strong>A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Sophia pays <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>200</mn></math> into a bank account at the end of each month. The annual interest paid on money in the account is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>1</mn><mo>%</mo></math> which is compounded monthly.</p>
</div>
<div class="specification">
<p>The average rate of inflation per year over the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> years was <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>%</mo></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of her investment after a period of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> years.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an approximation for the real interest rate for the money invested in the account.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the real value of Sophia’s investment at the end of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> years.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#999;font-size:90%;font-style:italic;">* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.</p>
<p>Number of time periods <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>×</mo><mn>5</mn><mo>=</mo><mn>60</mn></math> <strong>(A1)</strong></p>
<p>N = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math><br>I% = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>1</mn></math><br>PV = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math><br>PMT = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math><br>P/Y = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math><br>C/Y = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math><br>Value <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mo>$</mo></mfenced><mn>12</mn><mo>,</mo><mn>961</mn><mo>.</mo><mn>91</mn></math> <strong>(M1)A1</strong></p>
<p> </p>
<p><strong>[3 marks]</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>Real interest rate <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3</mn><mo>.</mo><mn>1</mn><mo>-</mo><mn>2</mn><mo>.</mo><mn>0</mn><mo>=</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>%</mo></math> <strong>(M1)A1</strong></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>1</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>031</mn></mrow><mrow><mn>1</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>02</mn></mrow></mfrac><mo>=</mo><mn>1</mn><mo>.</mo><mn>01078</mn><mo>…</mo></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>08</mn><mo>%</mo></math> (accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>1</mn><mo>%</mo></math>) <strong>A1</strong></p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>N = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math><br>I% = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>1</mn></math><br>PV = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math><br>PMT = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math><br>P/Y = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math><br>C/Y = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mo>$</mo></mfenced><mn>12</mn><mo>,</mo><mn>300</mn><mo> </mo><mo>(</mo><mn>12</mn><mo>,</mo><mn>330</mn><mo>.</mo><mn>33</mn><mo>…</mo><mo>)</mo></math> <strong>(M1)A1</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong>A1</strong> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>12</mn><mo>,</mo><mn>300</mn></math> only.</p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>An arithmetic sequence has <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_1} = {\text{lo}}{{\text{g}}_c}\left( p \right)">
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>=</mo>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<mi>p</mi>
<mo>)</mo>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_2} = {\text{lo}}{{\text{g}}_c}\left( {pq} \right)">
<mrow>
<msub>
<mi>u</mi>
<mn>2</mn>
</msub>
</mrow>
<mo>=</mo>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c > 1">
<mi>c</mi>
<mo>></mo>
<mn>1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p,\,\,q > 0">
<mi>p</mi>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>q</mi>
<mo>></mo>
<mn>0</mn>
</math></span>.</p>
</div>
<div class="question">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = {c^2}">
<mi>p</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = {c^3}">
<mi>q</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>c</mi>
<mn>3</mn>
</msup>
</mrow>
</math></span>. Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum\limits_{n = 1}^{20} {{u_n}} ">
<munderover>
<mo movablelimits="false">∑</mo>
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>20</mn>
</mrow>
</munderover>
<mrow>
<mrow>
<msub>
<mi>u</mi>
<mi>n</mi>
</msub>
</mrow>
</mrow>
</math></span>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><strong>METHOD 1</strong> (finding <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_1}">
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> and <em>d</em>)</p>
<p>recognizing <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum { = {S_{20}}} ">
<mo>∑</mo>
<mrow>
<mo>=</mo>
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mn>20</mn>
</mrow>
</msub>
</mrow>
</mrow>
</math></span> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p>attempt to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_1}">
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> or <em>d</em> using <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{lo}}{{\text{g}}_c}\,{c^k} = k">
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>c</mi>
<mi>k</mi>
</msup>
</mrow>
<mo>=</mo>
<mi>k</mi>
</math></span> <em><strong>(M1)</strong></em><br>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{lo}}{{\text{g}}_c}\,c">
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>c</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{3}}\,{\text{lo}}{{\text{g}}_c}\,c">
<mrow>
<mtext>3</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>c</mi>
</math></span>, correct value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_1}">
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> or <em>d</em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_1}">
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> = 2, <em>d </em>= 3 (seen anywhere) <em><strong> (A1)(A1)</strong></em></p>
<p>correct working <em><strong> (A1)</strong></em><br><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_{20}} = \frac{{20}}{2}\left( {2 \times 2 + 19 \times 3} \right),\,\,{S_{20}} = \frac{{20}}{2}\left( {2 + 59} \right),\,\,10\left( {61} \right)">
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mn>20</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>20</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>2</mn>
<mo>+</mo>
<mn>19</mn>
<mo>×</mo>
<mn>3</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mn>20</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>20</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mo>+</mo>
<mn>59</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>10</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>61</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum\limits_{n = 1}^{20} {{u_n}} ">
<munderover>
<mo movablelimits="false">∑</mo>
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>20</mn>
</mrow>
</munderover>
<mrow>
<mrow>
<msub>
<mi>u</mi>
<mi>n</mi>
</msub>
</mrow>
</mrow>
</math></span> = 610 <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong> (expressing <em>S</em> in terms of <em>c</em>)</p>
<p>recognizing <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum { = {S_{20}}} ">
<mo>∑</mo>
<mrow>
<mo>=</mo>
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mn>20</mn>
</mrow>
</msub>
</mrow>
</mrow>
</math></span> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p>correct expression for <em>S</em> in terms of <em>c</em> <em><strong>(A1)</strong></em><br><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10\left( {2\,{\text{lo}}{{\text{g}}_c}\,{c^2} + 19\,{\text{lo}}{{\text{g}}_c}\,{c^3}} \right)">
<mn>10</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>19</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>c</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{lo}}{{\text{g}}_c}\,{c^2} = 2,\,\,\,{\text{lo}}{{\text{g}}_c}\,{c^3} = 3">
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>2</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>c</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>3</mn>
</math></span> (seen anywhere) <em><strong>(A1)</strong><strong>(A1)</strong></em></p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_{20}} = \frac{{20}}{2}\left( {2 \times 2 + 19 \times 3} \right),\,\,{S_{20}} = \frac{{20}}{2}\left( {2 + 59} \right),\,\,10\left( {61} \right)">
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mn>20</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>20</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>2</mn>
<mo>+</mo>
<mn>19</mn>
<mo>×</mo>
<mn>3</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mn>20</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>20</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mo>+</mo>
<mn>59</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>10</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>61</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum\limits_{n = 1}^{20} {{u_n}} ">
<munderover>
<mo movablelimits="false">∑</mo>
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>20</mn>
</mrow>
</munderover>
<mrow>
<mrow>
<msub>
<mi>u</mi>
<mi>n</mi>
</msub>
</mrow>
</mrow>
</math></span> = 610 <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><strong>METHOD 3</strong> (expressing <em>S</em> in terms of <em>c</em>)</p>
<p>recognizing <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum { = {S_{20}}} ">
<mo>∑</mo>
<mrow>
<mo>=</mo>
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mn>20</mn>
</mrow>
</msub>
</mrow>
</mrow>
</math></span> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p>correct expression for <em>S</em> in terms of <em>c</em> <em><strong>(A1)</strong></em><br><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10\left( {2\,{\text{lo}}{{\text{g}}_c}\,{c^2} + 19\,{\text{lo}}{{\text{g}}_c}\,{c^3}} \right)">
<mn>10</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>19</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>c</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>correct application of log law <em><strong>(A1)</strong></em><br>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\,{\text{lo}}{{\text{g}}_c}\,{c^2} = \,\,{\text{lo}}{{\text{g}}_c}\,{c^4},\,\,19\,{\text{lo}}{{\text{g}}_c}\,{c^3} = \,\,{\text{lo}}{{\text{g}}_c}\,{c^{57}},\,\,10\,\left( {{\text{lo}}{{\text{g}}_c}\,{{\left( {{c^2}} \right)}^2} + \,\,{\text{lo}}{{\text{g}}_c}\,{{\left( {{c^3}} \right)}^{19}}} \right),\,\,10\,\left( {{\text{lo}}{{\text{g}}_c}\,{c^4} + \,{\text{lo}}{{\text{g}}_c}\,{c^{57}}} \right),\,\,10\left( {{\text{lo}}{{\text{g}}_c}\,{c^{61}}} \right)">
<mn>2</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>c</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>19</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>c</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>=</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>c</mi>
<mrow>
<mn>57</mn>
</mrow>
</msup>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>10</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>c</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mn>19</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>10</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>c</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>+</mo>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>c</mi>
<mrow>
<mn>57</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>10</mn>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>c</mi>
<mrow>
<mn>61</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>correct application of definition of log <em><strong>(A1)</strong></em><br>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{lo}}{{\text{g}}_c}\,{c^{61}} = 61,\,\,{\text{lo}}{{\text{g}}_c}\,{c^4} = 4,\,\,{\text{lo}}{{\text{g}}_c}\,{c^{57}} = 57">
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>c</mi>
<mrow>
<mn>61</mn>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mn>61</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>c</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>4</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>c</mi>
<mrow>
<mn>57</mn>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mn>57</mn>
</math></span></p>
<p>correct working <em><strong>(A1)</strong></em><br>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_{20}} = \frac{{20}}{2}\left( {4 + 57} \right),\,\,10\left( {61} \right)">
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mn>20</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>20</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mn>4</mn>
<mo>+</mo>
<mn>57</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>10</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>61</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum\limits_{n = 1}^{20} {{u_n}} ">
<munderover>
<mo movablelimits="false">∑</mo>
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>20</mn>
</mrow>
</munderover>
<mrow>
<mrow>
<msub>
<mi>u</mi>
<mi>n</mi>
</msub>
</mrow>
</mrow>
</math></span> = 610 <em><strong>A1 N2</strong></em></p>
<p><strong><em>[6 marks]</em></strong></p>
<p> </p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The following diagram shows [AB], with length 2 cm. The line is divided into an infinite number of line segments. The diagram shows the first three segments.</p>
<p><img src="images/Schermafbeelding_2018-02-12_om_09.33.46.png" alt="N17/5/MATME/SP1/ENG/TZ0/10.a"></p>
<p>The length of the line segments are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p{\text{ cm}},{\text{ }}{p^2}{\text{ cm}},{\text{ }}{p^3}{\text{ cm}},{\text{ }} \ldots "> <mi>p</mi> <mrow> <mtext> cm</mtext> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <msup> <mi>p</mi> <mn>2</mn> </msup> </mrow> <mrow> <mtext> cm</mtext> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <msup> <mi>p</mi> <mn>3</mn> </msup> </mrow> <mrow> <mtext> cm</mtext> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo>…</mo> </math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 < p < 1"> <mn>0</mn> <mo><</mo> <mi>p</mi> <mo><</mo> <mn>1</mn> </math></span>.</p>
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = \frac{2}{3}"> <mi>p</mi> <mo>=</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The following diagram shows [CD], with length <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b{\text{ cm}}"> <mi>b</mi> <mrow> <mtext> cm</mtext> </mrow> </math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b > 1"> <mi>b</mi> <mo>></mo> <mn>1</mn> </math></span>. Squares with side lengths <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k{\text{ cm}},{\text{ }}{k^2}{\text{ cm}},{\text{ }}{k^3}{\text{ cm}},{\text{ }} \ldots "> <mi>k</mi> <mrow> <mtext> cm</mtext> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <msup> <mi>k</mi> <mn>2</mn> </msup> </mrow> <mrow> <mtext> cm</mtext> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <msup> <mi>k</mi> <mn>3</mn> </msup> </mrow> <mrow> <mtext> cm</mtext> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo>…</mo> </math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 < k < 1"> <mn>0</mn> <mo><</mo> <mi>k</mi> <mo><</mo> <mn>1</mn> </math></span>, are drawn along [CD]. This process is carried on indefinitely. The diagram shows the first three squares.</p>
<p><img src="images/Schermafbeelding_2018-02-12_om_09.48.48.png" alt="N17/5/MATME/SP1/ENG/TZ0/10.b"></p>
<p>The <strong>total</strong> sum of the areas of all the squares is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{9}{{16}}"> <mfrac> <mn>9</mn> <mrow> <mn>16</mn> </mrow> </mfrac> </math></span>. Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b"> <mi>b</mi> </math></span>.</p>
<div class="marks">[9]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>infinite sum of segments is 2 (seen anywhere) <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p + {p^2} + {p^3} + \ldots = 2,{\text{ }}\frac{{{u_1}}}{{1 - r}} = 2"> <mi>p</mi> <mo>+</mo> <mrow> <msup> <mi>p</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mi>p</mi> <mn>3</mn> </msup> </mrow> <mo>+</mo> <mo>…</mo> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mrow> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> </mrow> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mi>r</mi> </mrow> </mfrac> <mo>=</mo> <mn>2</mn> </math></span></p>
<p>recognizing GP <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math>ratio is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p,{\text{ }}\frac{{{u_1}}}{{1 - r}},{\text{ }}{u_n} = {u_1} \times {r^{n - 1}},{\text{ }}\frac{{{u_1}({r^n} - 1)}}{{r - 1}}"> <mi>p</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mrow> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> </mrow> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mi>r</mi> </mrow> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <msub> <mi>u</mi> <mi>n</mi> </msub> </mrow> <mo>=</mo> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> </mrow> <mo>×</mo> <mrow> <msup> <mi>r</mi> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mrow> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> </mrow> <mo stretchy="false">(</mo> <mrow> <msup> <mi>r</mi> <mi>n</mi> </msup> </mrow> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>r</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </math></span></p>
<p>correct substitution into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_\infty }"> <mrow> <msub> <mi>S</mi> <mi mathvariant="normal">∞</mi> </msub> </mrow> </math></span> formula (may be seen in equation) <strong><em>A1</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{p}{{1 - p}}"> <mfrac> <mi>p</mi> <mrow> <mn>1</mn> <mo>−</mo> <mi>p</mi> </mrow> </mfrac> </math></span></p>
<p>correct equation <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{p}{{1 - p}} = 2,{\text{ }}p = 2 - 2p"> <mfrac> <mi>p</mi> <mrow> <mn>1</mn> <mo>−</mo> <mi>p</mi> </mrow> </mfrac> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>p</mi> <mo>=</mo> <mn>2</mn> <mo>−</mo> <mn>2</mn> <mi>p</mi> </math></span></p>
<p>correct working leading to answer <strong><em>A1</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3p = 2,{\text{ }}2 - 3p = 0"> <mn>3</mn> <mi>p</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>2</mn> <mo>−</mo> <mn>3</mn> <mi>p</mi> <mo>=</mo> <mn>0</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = \frac{2}{3}{\text{ (cm)}}"> <mi>p</mi> <mo>=</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <mrow> <mtext> (cm)</mtext> </mrow> </math></span> <strong><em>AG N0</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing infinite geometric series with squares <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{k^2} + {k^4} + {k^6} + \ldots ,{\text{ }}\frac{{{k^2}}}{{1 - {k^2}}}"> <mrow> <msup> <mi>k</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mi>k</mi> <mn>4</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mi>k</mi> <mn>6</mn> </msup> </mrow> <mo>+</mo> <mo>…</mo> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mrow> <mrow> <msup> <mi>k</mi> <mn>2</mn> </msup> </mrow> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mrow> <msup> <mi>k</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </math></span></p>
<p>correct substitution into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_\infty } = \frac{9}{{16}}"> <mrow> <msub> <mi>S</mi> <mi mathvariant="normal">∞</mi> </msub> </mrow> <mo>=</mo> <mfrac> <mn>9</mn> <mrow> <mn>16</mn> </mrow> </mfrac> </math></span> (must substitute into formula) <strong><em>(A2)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{k^2}}}{{1 - {k^2}}} = \frac{9}{{16}}"> <mfrac> <mrow> <mrow> <msup> <mi>k</mi> <mn>2</mn> </msup> </mrow> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mrow> <msup> <mi>k</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mn>9</mn> <mrow> <mn>16</mn> </mrow> </mfrac> </math></span></p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="16{k^2} = 9 - 9{k^2},{\text{ }}25{k^2} = 9,{\text{ }}{k^2} = \frac{9}{{25}}"> <mn>16</mn> <mrow> <msup> <mi>k</mi> <mn>2</mn> </msup> </mrow> <mo>=</mo> <mn>9</mn> <mo>−</mo> <mn>9</mn> <mrow> <msup> <mi>k</mi> <mn>2</mn> </msup> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>25</mn> <mrow> <msup> <mi>k</mi> <mn>2</mn> </msup> </mrow> <mo>=</mo> <mn>9</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <msup> <mi>k</mi> <mn>2</mn> </msup> </mrow> <mo>=</mo> <mfrac> <mn>9</mn> <mrow> <mn>25</mn> </mrow> </mfrac> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = \frac{3}{5}"> <mi>k</mi> <mo>=</mo> <mfrac> <mn>3</mn> <mn>5</mn> </mfrac> </math></span> (seen anywhere) <strong><em>A1</em></strong></p>
<p>valid approach with segments and CD (may be seen earlier) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = k,{\text{ }}{S_\infty } = b"> <mi>r</mi> <mo>=</mo> <mi>k</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <msub> <mi>S</mi> <mi mathvariant="normal">∞</mi> </msub> </mrow> <mo>=</mo> <mi>b</mi> </math></span></p>
<p>correct expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b"> <mi>b</mi> </math></span> in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span> (may be seen earlier) <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = \frac{k}{{1 - k}},{\text{ }}b = \sum\limits_{n = 1}^\infty {{k^n},{\text{ }}b = k + {k^2} + {k^3} + \ldots } "> <mi>b</mi> <mo>=</mo> <mfrac> <mi>k</mi> <mrow> <mn>1</mn> <mo>−</mo> <mi>k</mi> </mrow> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>b</mi> <mo>=</mo> <munderover> <mo movablelimits="false">∑</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi mathvariant="normal">∞</mi> </munderover> <mrow> <mrow> <msup> <mi>k</mi> <mi>n</mi> </msup> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>b</mi> <mo>=</mo> <mi>k</mi> <mo>+</mo> <mrow> <msup> <mi>k</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mi>k</mi> <mn>3</mn> </msup> </mrow> <mo>+</mo> <mo>…</mo> </mrow> </math></span></p>
<p>substituting <strong>their</strong> value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span> into <strong>their</strong> formula for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b"> <mi>b</mi> </math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\frac{3}{5}}}{{1 - \frac{3}{5}}},{\text{ }}\frac{{\left( {\frac{3}{5}} \right)}}{{\left( {\frac{2}{5}} \right)}}"> <mfrac> <mrow> <mfrac> <mn>3</mn> <mn>5</mn> </mfrac> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mfrac> <mn>3</mn> <mn>5</mn> </mfrac> </mrow> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>3</mn> <mn>5</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>2</mn> <mn>5</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = \frac{3}{2}"> <mi>b</mi> <mo>=</mo> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </math></span> <strong><em>A1 N3</em></strong></p>
<p><strong><em>[9 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Tommaso and Pietro have each been given <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1500</mn></math> euro to save for college.</p>
<p>Pietro invests his money in an account that pays a nominal annual interest rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>75</mn><mo>%</mo></math>, <strong>compounded half-yearly</strong>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the amount Pietro will have in his account after <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> years. Give your answer correct to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> decimal places.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Tommaso wants to invest his money in an account such that his investment will increase to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn></math> times the initial amount in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> years. Assume the account pays a nominal annual interest of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>%</mo></math> <strong>compounded quarterly</strong>.</p>
<p>Determine the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD</strong> <strong>1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>5</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>10</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>%</mo><mo>=</mo><mn>2</mn><mo>.</mo><mn>75</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>%</mo><mo>=</mo><mn>2</mn><mo>.</mo><mn>75</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>V</mi><mo>=</mo><mo>-</mo><mn>1500</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>V</mi><mo>=</mo><mo>-</mo><mn>1500</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>M</mi><mi>T</mi><mo>=</mo><mn>0</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>M</mi><mi>T</mi><mo>=</mo><mn>0</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>1</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>2</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>2</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>2</mn></math> <em><strong>(M1)(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award<em><strong> M1</strong></em> for an attempt to use a financial app in their technology, <em><strong>A1</strong></em> for all entries correct.</p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1500</mn><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mrow><mn>2</mn><mo>.</mo><mn>75</mn></mrow><mrow><mn>2</mn><mo>×</mo><mn>100</mn></mrow></mfrac></mrow></mfenced><mrow><mn>2</mn><mo>×</mo><mn>5</mn></mrow></msup></math> <em><strong>(M1)(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1719</mn><mo>.</mo><mn>49</mn></math> euro <em><strong>A1</strong></em></p>
<p><em><strong><br>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD</strong> <strong>1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>5</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>20</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>V</mi><mo>=</mo><mo>±</mo><mn>1500</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>V</mi><mo>=</mo><mo>±</mo><mn>1500</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>V</mi><mo>=</mo><mo>∓</mo><mn>2250</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>V</mi><mo>=</mo><mo>∓</mo><mn>2250</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>M</mi><mi>T</mi><mo>=</mo><mn>0</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>M</mi><mi>T</mi><mo>=</mo><mn>0</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>1</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>4</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>4</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>/</mo><mi>Y</mi><mo>=</mo><mn>4</mn></math> <em><strong>(M1)(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award<em><strong> M1</strong></em> for an attempt to use a financial app in their technology, <em><strong>A1</strong></em> for all entries correct. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>V</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>V</mi></math> must have opposite signs.</p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1500</mn><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mi>r</mi><mrow><mn>4</mn><mo>×</mo><mn>100</mn></mrow></mfrac></mrow></mfenced><mrow><mn>4</mn><mo>×</mo><mn>5</mn></mrow></msup><mo>=</mo><mn>2250</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mi>r</mi><mrow><mn>4</mn><mo>×</mo><mn>100</mn></mrow></mfrac></mrow></mfenced><mrow><mn>4</mn><mo>×</mo><mn>5</mn></mrow></msup><mo>=</mo><mn>1</mn><mo>.</mo><mn>5</mn></math> <em><strong>(M1)(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong></em> for substitution in compound interest formula,<em><strong> A1</strong></em> for correct substitution and for equating to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2250</mn></math> (if using LHS equation) or to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn></math> (if using RHS equation).</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>8</mn><mo>.</mo><mn>19</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>8</mn><mo>.</mo><mn>19206</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><em><strong><br></strong></em><strong>Note: </strong>Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>8</mn><mo>.</mo><mn>19</mn><mo>%</mo></math>.</p>
<p> Accept a trial and error method which leads to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>8</mn><mo>.</mo><mn>19</mn></math>.<br><em><strong><br><br>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Charlie and Daniella each began a fitness programme. On day one, they both ran <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo> </mo><mtext>m</mtext></math>. On each subsequent day, Charlie ran <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo> </mo><mtext>m</mtext></math> more than the previous day whereas Daniella increased her distance by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>%</mo></math> of the distance ran on the previous day.</p>
</div>
<div class="specification">
<p>Calculate how far</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Charlie ran on day <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math> of his fitness programme.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Daniella ran on day <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math> of her fitness programme.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On day <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> of the fitness programmes Daniella runs more than Charlie for the first time.</p>
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>attempt to find <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>20</mn></msub></math> using an arithmetic sequence<em> </em> <em><strong>(M1)</strong></em></p>
<p>e.g. <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo><mn>500</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>100</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>20</mn></msub><mo>=</mo><mn>500</mn><mo>+</mo><mn>1900</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo>,</mo><mo> </mo><mn>600</mn><mo>,</mo><mo> </mo><mn>700</mn><mo>,</mo><mo> </mo><mo>…</mo></math></p>
<p>(Charlie ran) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2400</mn><mo> </mo><mtext>m</mtext></math> <em> </em> <em><strong>A1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>r</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>1</mn><mo>.</mo><mn>02</mn></math><em> </em> <em><strong>(A1)</strong></em></p>
<p>attempt to find <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>20</mn></msub></math> using a geometric sequence<em> </em> <em><strong>(M1)</strong></em></p>
<p>e.g. <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo><mn>500</mn></math> and a value for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> <strong>OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo>×</mo><msup><mi>r</mi><mn>19</mn></msup></math></strong> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo>,</mo><mo> </mo><mn>510</mn><mo>,</mo><mo> </mo><mn>520</mn><mo>.</mo><mn>2</mn><mo>,</mo><mo> </mo><mo>…</mo></math></p>
<p>(Daniella ran) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>728</mn><mo> </mo><mtext>m </mtext><mfenced><mrow><mn>728</mn><mo>.</mo><mn>405</mn><mo>…</mo></mrow></mfenced></math> <em> </em> <em><strong>A1</strong></em></p>
<p><em><strong><br>[3 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>02</mn><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>></mo><mn>500</mn><mo>+</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>×</mo><mn>100</mn></math><em> </em> <em><strong>(M1)</strong></em></p>
<p>attempt to solve inequality<em> </em> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>></mo><mn>184</mn><mo>.</mo><mn>215</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>185</mn></math> <em> </em> <em><strong>A1</strong></em></p>
<p><em><strong><br>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Katya approximates <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math>, correct to four decimal places, by using the following expression.</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn>6</mn><mo>+</mo><mstyle displaystyle="true"><mfrac><mn>13</mn><mn>16</mn></mfrac></mstyle></mrow></mfrac></math></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate Katya’s approximation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math>, correct to four decimal places.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the percentage error in using Katya’s four decimal place approximation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math>, compared to the exact value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math> in your calculator.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi><mo>≈</mo><mn>3</mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn>6</mn><mo>+</mo><mstyle displaystyle="true"><mfrac><mn>13</mn><mn>16</mn></mfrac></mstyle></mrow></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3</mn><mo>.</mo><mn>14678</mn><mo>…</mo><mo> </mo><mfenced><mrow><mfrac><mn>343</mn><mn>109</mn></mfrac><mo>,</mo><mo> </mo><mn>3</mn><mfrac><mn>16</mn><mn>109</mn></mfrac></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3</mn><mo>.</mo><mn>1468</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> for correct rounding to 4 decimal places. Follow through within this part.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mfrac><mrow><mn>3</mn><mo>.</mo><mn>1468</mn><mo>-</mo><mi mathvariant="normal">π</mi></mrow><mi mathvariant="normal">π</mi></mfrac></mfenced><mo>×</mo><mn>100</mn></math> <em><strong>(M1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>M1</strong></em> for substitution of their final answer in part (a) into the percentage error formula. Candidates should use the exact value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math> from their GDC.</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>166</mn><mo> </mo><mfenced><mo>%</mo></mfenced><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>165754</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = \frac{{\cos x + \sin y}}{{\sqrt {{w^2} - z} }}">
<mi>p</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>cos</mi>
<mo><!-- --></mo>
<mi>x</mi>
<mo>+</mo>
<mi>sin</mi>
<mo><!-- --></mo>
<mi>y</mi>
</mrow>
<mrow>
<msqrt>
<mrow>
<msup>
<mi>w</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mi>z</mi>
</msqrt>
</mrow>
</mfrac>
</math></span>,</p>
<p>where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 36^\circ ,{\text{ }}y = 18^\circ ,{\text{ }}w = 29">
<mi>x</mi>
<mo>=</mo>
<msup>
<mn>36</mn>
<mo>∘<!-- ∘ --></mo>
</msup>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>y</mi>
<mo>=</mo>
<msup>
<mn>18</mn>
<mo>∘<!-- ∘ --></mo>
</msup>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>w</mi>
<mo>=</mo>
<mn>29</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="z = 21.8">
<mi>z</mi>
<mo>=</mo>
<mn>21.8</mn>
</math></span>.</p>
</div>
<div class="question">
<p>Write your answer to <strong>part (b)(ii) </strong>in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a \times {10^k}">
<mi>a</mi>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mi>k</mi>
</msup>
</mrow>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 \leqslant a < 10,{\text{ }}k \in \mathbb{Z}">
<mn>1</mn>
<mo>⩽</mo>
<mi>a</mi>
<mo><</mo>
<mn>10</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>k</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
</math></span>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3.91 \times {10^{ - 2}}">
<mn>3.91</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note</strong><strong>: </strong>Answer should be consistent with their answer to part (b)(ii). Award <strong><em>(A1)</em>(ft) </strong>for 3.91, and <strong><em>(A1)</em>(ft) </strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{10^{ - 2}}">
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</math></span>. Follow through from part (b)(ii).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p style="text-align: left;">Inspectors are investigating the carbon dioxide emissions of a power plant. Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> be the rate, in tonnes per hour, at which carbon dioxide is being emitted and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> be the time in hours since the inspection began.</p>
<p>When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> is plotted against <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>, the total amount of carbon dioxide produced is represented by the area between the graph and the horizontal <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>-axis.</p>
<p>The rate, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math>, is measured over the course of two hours. The results are shown in the following table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the trapezoidal rule with an interval width of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>4</mn></math> to estimate the total amount of carbon dioxide emitted during these two hours.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The real amount of carbon dioxide emitted during these two hours was <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn></math> tonnes.</p>
<p>Find the percentage error of the estimate found in part (a).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>attempt at using trapezoidal rule formula <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mfenced><mfrac><mrow><mn>2</mn><mo>-</mo><mn>0</mn></mrow><mn>5</mn></mfrac></mfenced><mfenced><mrow><mn>30</mn><mo>+</mo><mn>50</mn><mo>+</mo><mn>2</mn><mfenced><mrow><mn>50</mn><mo>+</mo><mn>60</mn><mo>+</mo><mn>40</mn><mo>+</mo><mn>20</mn></mrow></mfenced></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p>(total carbon =) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>84</mn></math> tonnes <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mfrac><mrow><mn>84</mn><mo>-</mo><mn>72</mn></mrow><mn>72</mn></mfrac></mfenced><mo>×</mo><mn>100</mn><mo>%</mo></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of final answer in part (a) into percentage error formula.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>16</mn><mo>.</mo><mn>7</mn><mo>%</mo><mo> </mo><mo> </mo><mfenced><mrow><mn>16</mn><mo>.</mo><mn>6666</mn><mo>…</mo><mo>%</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Although there were successful attempts at using the trapezoidal rule formula, there was quite a bit of confusion among candidates as to which values were to be substituted. It seemed that a significant number of candidates were approaching it with some confusion due to a lack of practice of using the trapezoidal rule formula. Calculation of percentage error in part (b) was generally well done by most candidates.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Although there were successful attempts at using the trapezoidal rule formula, there was quite a bit of confusion among candidates as to which values were to be substituted. It seemed that a significant number of candidates were approaching it with some confusion due to a lack of practice of using the trapezoidal rule formula. Calculation of percentage error in part (b) was generally well done by most candidates.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>A triangular field <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABC</mtext></math> is such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext><mo>=</mo><mn>56</mn><mo> </mo><mtext>m</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BC</mtext><mo>=</mo><mn>82</mn><mo> </mo><mtext>m</mtext></math>, each measured correct to the nearest metre, and the angle at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>105</mn><mo>°</mo></math>, measured correct to the nearest <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>°</mo></math>.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>Calculate the maximum possible area of the field.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>attempt to find any relevant maximum value<em> </em> <em><strong>(M1)</strong></em></p>
<p>largest sides are <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>56</mn><mo>.</mo><mn>5</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>82</mn><mo>.</mo><mn>5</mn></math><em> </em> <em><strong>(A1)</strong></em></p>
<p>smallest possible angle is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>102</mn><mo>.</mo><mn>5</mn></math><em> </em> <em><strong>(A1)</strong></em></p>
<p>attempt to substitute into area of a triangle formula<em> </em> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>56</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>82</mn><mo>.</mo><mn>5</mn><mo>×</mo><mi>sin</mi><mo> </mo><mfenced><mrow><mn>102</mn><mo>.</mo><mn>5</mn><mo>°</mo></mrow></mfenced></math></p>
<p><em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2280</mn><mo> </mo><mfenced><msup><mtext>m</mtext><mn>2</mn></msup></mfenced><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>2275</mn><mo>.</mo><mn>37</mn><mo>…</mo></mrow></mfenced></math> A1</strong></em></p>
<p><em><strong><br>[5 marks]</strong></em></p>
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<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
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