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<h2>SL Paper 2</h2><div class="specification">
<p>John purchases a new bicycle for 880 US dollars (USD) and pays for it with a Canadian credit card. There is a transaction fee of 4.2 % charged to John by the credit card company to convert this purchase into Canadian dollars (CAD).</p>
<p>The exchange rate is 1 USD = 1.25 CAD.</p>
</div>
<div class="specification">
<p>John insures his bicycle with a US company. The insurance company produces the following table for the bicycle’s value during each year.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>The values of the bicycle form a geometric sequence.</p>
</div>
<div class="specification">
<p>During the 1st year John pays 120 USD to insure his bicycle. Each year the amount he pays to insure his bicycle is reduced by 3.50 USD.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, in CAD, the total amount John pays for the bicycle.</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 value of the bicycle during the 5th year. <strong>Give your answer to two decimal places</strong>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, in years, when the bicycle value will be less than 50 USD.</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 total amount John has paid to insure his bicycle for the first 5 years.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>John purchased the bicycle in 2008.</p>
<p>Justify why John should not insure his bicycle in 2019.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question">
<p>Consider the expansion of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>3</mn><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup><msup><mo>)</mo><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>∈</mo><msup><mi mathvariant="normal">ℤ</mi><mo>+</mo></msup><mo> </mo></math>.</p>
<p>Given that the coefficient of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>4</mn></msup></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mn>412</mn></math>, find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>.</p>
</div>
<br><hr><br><div class="specification">
<p>A large underground tank is constructed at Mills Airport to store fuel. The tank is in the shape of an isosceles trapezoidal prism, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABCDEFGH</mtext></math>.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext><mo>=</mo><mn>70</mn><mo> </mo><mtext>m</mtext></math> , <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AF</mtext><mo>=</mo><mn>200</mn><mo> </mo><mtext>m</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AD</mtext><mo>=</mo><mn>40</mn><mo> </mo><mtext>m</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BC</mtext><mo>=</mo><mn>40</mn><mo> </mo><mtext>m</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CD</mtext><mo>=</mo><mn>110</mn><mo> </mo><mtext>m</mtext></math>. Angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ADC</mtext><mo>=</mo><mn>60</mn><mo>°</mo></math> and angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BCD</mtext><mo>=</mo><mn>60</mn><mo>°</mo></math>. The tank is illustrated below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>Once construction was complete, a fuel pump was used to pump fuel <strong>into</strong> the empty tank. The amount of fuel pumped into the tank by this pump <strong>each hour</strong> decreases as an arithmetic sequence with terms <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub><mo>,</mo><mo> </mo><msub><mi>u</mi><mn>2</mn></msub><mo>,</mo><mo> </mo><msub><mi>u</mi><mn>3</mn></msub><mo>,</mo><mo> </mo><mo>…</mo><mo>,</mo><mo> </mo><msub><mi>u</mi><mi>n</mi></msub></math>.</p>
<p>Part of this sequence is shown in the table.</p>
<p style="text-align: center;"><img 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cTL5dEYMv60aGfNCGWT1gbttDrUGzBYkc4oIWYF4TYddP6asjL2MuUU6tuAus07kU83m0f0yk6/mjJtU29wQYOerCMNetY1ZWL+pM9PqWPj3qDFNRkuChzVq06rQetchmsNOuj0KDvZmJ0CXtncp29eHU0wNSl9K6pXRGR5inogR1wHPeo8b4opabfckrxdsg801joFAo46HI0VsNRhCY71cVQQYum05EqjQ+ckpt3W9qlrO3wiK8S4Q5Sfax/SjhVY3DnJtWbndNrazk7n2fj3aK/7S0IpVAiIDtPa4XTNpxmBGqTrp0SYYiEW4iP7J9NyBFWUkwL/IrHENpx4OSH2ls7aH3qZrWw+o9OobEQ6QUJM+s3Hy7TePEmETahvqRAzP/Ds/zKtf/SRECHJ9UjoGykmfM7FNWFFfRj+RIfbieDPhF2lrdbLxOdiTrFfZdaIjfMtGdkcJcQGL+kg91tIGDi/KZ2mQc8KGmsdluCow9FYAUsdluBYH8fqQkxMS9oF+nZdkxRSUohxJzikQXffjlRYcTA4ob1kBIdFjx11W+C4RDQ8o87uRtyJ2w4qVAjIDnODdtqnUac8PGsnU6upyLECUo5YeMok3EeR9ijxY9KwHTaP5JmTgXnkcljapoPTZNTQdvJcNoG+WD+WaX33KB6pHPbp+8fJAwdWJAX6RkKIWf9+oW7zXiLKuJxlHWFBJHxe2KBHnbNopGzY/5b2EwHj3hTYukVDGpw+i0Ue+8yczAirL2+lFutnfRtVr9JRWs6XKdv0xmbRciEa9o/oUfSbkKLXUwlnfAqNtU4BgKMOR2MFLHVYgmN9HCsKMdFJcqcW+fpzMj15g+IOMc6AFTQyrB3FYWFgwqaddCzEROfkrqmynSh3ZqFCQHSYGZv5+NbvkUKsjI8i7RqFmPU7MxKUjj7FZRPoixViUhCamU9+mKAs/7SMw+sIp1HksxiNjcoqTcM0Ivn/uM6lAnpc3jw/xBwX4duYeuUVYvbGxp3ad/Pm8eUSnEJjrVMI4KjD0VgBSx2W4Fgfx4pCLBVcppC8/0J0WWEgBY0VYtzJmsymHWgsxNzvAoiNzyNYeSEVhR7VYWbEEKfF9sRInvRbuBAfcjzPGrKcj6KzzqSdM1puRCyTxzfeadVMGUVpB/rCtl0GNm9cfqH8/bzC6kjqM4+YMrlsfPaloG4ma/NsHFFXI3u5vHEq4pO5LLCIS33LbgfC+U3rlVeIjUjT+mnTEn5ckkM01joFAY46HI0VsNRhCY71cawmxOxoSFFHZ86v0vvtn6KpI9uRyM7c2/Fwp8WipsxoE3e+osMz/Cp0mF6/c2VSxseizjpn1OO3CROSx7fpFhmSdy6JQF8sP+fpTVsHZiPEFjOjTu6oUXqj4Ao2iSEdERuXNxkrObZclIQYRsQ8kOfvFDo9vTIHSx2W4FgfxwpCTHR67khC5G/aCXJn6RU0QUKMKO0see1Q0RqxNN2V7TadmbXdci2ZHU0oEiAsAlMh5/XbUybhPhal7TGa6+hNmMA8WpGUMkvXGvFUcKAv1g9+qnFoFi551ogF+pYb9Yzz7mWdqyPCZ/PUJq/vG7FGLF1v9Zb6nY/jdYlcb4X4UV0jlhntzNcr74gY1oh5fgTzdwqdnl6Zg6UOS3Csj2MFIZZ2uNkpGHZWCLXoCcQ36VOTcoQm18ma+Nxp8YiYOScXcrsjcOIpOSp4Au72HVqP9jcrP3KRCqw43eLRlVAfhZDIdNbMTnxaAcR+m2uheSx+ijNdvB7oi/XDZZ8d9Qz3zVfGBdPAuToifPZNiS99SIdnb2OI9uEE1+9UnBb6bG3zaJ8oFz60XLh8hG+ZsuX8pgKfrABMfOPfhXhYxTR+mX/7UAo7cLk+0VjrlAc46nA0VsBShyU41sdxciFmR1vcRcXCWSfMW98O9blO1sTnTksKMXN+3B5dSdrDPnU/432jkr3G7J5Qk3SYYuTHPFlnt2oQebWHIT4WddbWSHqQ6+iTS0F5NGHdfcRWaav5dYV9xD6gL7rf0rNG8rTq0kPaO3L25AryzV/GpUfENs1eXX+2+6RF+39l9pUz1alHmX3EfD4bTmI/Mp19xOQrozi/QojRW+qfPEm36ZAiC/uIpb+BOTxCp6dX6GCpwxIc6+M4uRDT8QlWrgqBIkE4E/9LCNmZ+De/iaKx1il7cNThaKyApQ5LcKyPI4SYDtvrbwVC7PqXsUIO0VgrQIR40IGYWEGd1MEJjvVxhBDTYXv9rUCIXf8yVsghGmsFiBBiOhATK6iTOjjBsT6OEGI6bGEFBEAAAkKtDqDTU0OJqUkllKiTOiB9HCHEdNjCCggoEDinXns32lojfapVwewUTfgamSkmf22SAke9ogRLHZbgWB9HCDEdtrACAhUJDGnQ+3v0NGv8vtMRTyNXTKnO6GisdeiCow5HYwUsdViCY30cIcR02MIKCCgRSDaclXuhKVmehhk01jqUwVGHo7ECljoswbE+jhBiOmxhBQQUCIhNkNc+pk4/2ZRWwfK0TKCx1iENjjocjRWw1GEJjvVxrCjEzHTKMX3RbNB+d5B4WfAeRJ08JFaSTVP/7Ql1L1QNp8YmfUpw0nhpyjM8qrI/V5W4M8xy0Xs7Z+bSW+onG9SuNDp0PsoP3oE/877NURFGXeN3pcq3VIwK779WW2M9/IkOt2/R3dZp9N7aTOp242h+C4HzzlAZWG42vPSQ9k/6eXshYcxmvHYj4VXaevwt9c3r1JT+auPIb+XI1Rm5ubB4jZk3P6bd/5r2NlcjkbNoXjP22Ykn/2GMhv0Tu0H0yuYT+l75BqQ+lub1eb56GfeLh8+btPXOLnXOx1eMeDmCr96GMAwJ4y3IUidr5VjKk6sd2MexmhDz7opfvxDz7r6uXTaTCqpJ42n7P5G9KmKqStyJnFWKVH99Le9oMjKW6yylJRZO/M5QeW3CYxY0I9MdbdvXyIyOEXKVX+nlWzfH11iE3SB+t23esnkF2XvE7xON37v6Hu11fxFBQ8IMadDdp3UetYzeZXtvzBs3RBIBh/VwNK/dbdP75lVvmTIe0uCHF/QsEaXD5J2tRTcCw7OvaP8xv52DBZz7xpFARtHNxD161DmjoRG35j2w8g0TAazGBamLZfpqtGy9NK/E+82Dh/Rbw5nfZzvKyUjMGVHrCrEQhiFhRiUefq0+juE+XIeQPo4QYkUle6UFVVGmxp2vIqaqxB3n1zxcN+9u3UhGVoy4aNDv2j/lR2sYBYumkIae44z95PfHTi7ufI3M2GRHBjAdzZ9o66OPaGsp2+FF0UxHvvHHsFGHXovuZnjlBW/0XtkxYeJ3hN6mnc7PqedRebgdaXq57JE+R/OqrxPa2/w97ZiRLCnEhv+g4+PXoq4lXDIcOAdv6Mfj7+gsM8iT3BTI8NF7VMcxiuNlBZ+pg7f9I5/sQsnPWljSmHpJHiZev43w/5D+0HhAK64QC2EYEsabbvmT9XAs78dVj+HjOLkQs0JF3IlGLy2WIww/iuF7M9z9Z+pmhp3NEG6HDvi9heY9jo0Wddx3BVryorMXL0NOX8KdfV+gyfDKZpMOuzz9IOJH7yhsp8Pr7jSFzR+/mzK5WzPpLm3TwWnBpFEuXok0bT7lQSCjQY++aT6kFcvFvFOy7fA2Q9gizxGfffrG8pa+tulMTBksrjXomeUo/ePjsnED3smZYxmnZUdE7Uu1uc7doU/az+nR2jItLng6bXY188lxxTsgRbpfdL+jQ8tVfwoqdUWO7BRN9XBosZbMMuBrVT7TMsx2juE2fY1MeGxPyEg8/Im6Z0e0kxNizMG0G0/psOO88zRjLukYpQAx1zMCKiQMUSTW3E6TdAWEOkcyHf7vaa/bo07jVlaIZTiZL4bDgxIjfHnhFsQoEhHvOqIrseWWU87H8BP6LFnUFtVLZnh/zIhYIuaa39FZZzcnxEIYhoQJJzU6ZC0cRyd5La/6ONYoxJZpffNBtCeSSdj+ix+YHSaX10cKnbSjsPYW+MXgsiMT6UX2PqTDM7Pw2R8/tSXuaEVnfNj/VzxkHvk5Zg1NJp5ZwFYiTU+1C2Jkh7adfBuhtd1O7l6TIWyXdRGftQe0FQkaaVPwyfkq8jk27jmdtraFaJRpCL45lnGixUJM2gkd1RklxKQ9Ph4l8PjF3knYzafUsS8SX46nxC7OqLObvDB9YZW2Wi+JV1fmkBae4JEr1xcjtL+iL5oP6SavL4s6OyNMR5VdmlDcsAdOqaTR7JH5Len9sXj4JRFMTn5t3tKyWW+0xQvthSdJ2JzAjIRYYjckTOFIR1Imon0TqZc+1OXIHf4JDSLBOEKImZfNt3Zpa/fIs+arKBuxeLpp25qi0aAso7iuub9TFtdh9bXII3lel6WxPKZeRokXMRCe8U3G4ILOc0KsKL5kGBJGpFfxUJ9jRYeuaHQfx8mFmIEwco3YDVpc26XDaLRFjCYt8AgTdyayM0o76FyDKaDbjjgagUsu2EY57chTEXOH9qKHCYRYMAtM26dRJ5iG842KbNPB0VPaMvP9CxvJWgbhjHuYEw8l0nRtcaOZ6bDzjGznaddWCFHKjCyfRBCYqYVobUssCmLeBb72j5JRJsEn52t4XOuvzJfwZZHzkWMZJ2rL344GsZgydW6fuoMh0fBfNPhXZv4k53F8guOKvNl0xaJlKXZtuh6TlnM6cirr1/raLVrZbNF/txuJEJ2gw7FpyE5M8hd5KTuFyeEDhZtLwNfIuGHCvkvxwCNXjhBjQ2Zx/YuntJOMhK43jeBw/qTgkpfkeXlcFIZ/kznBJTtIGXmyYz2OYvTG/C4K/WcBlIha23aH+G/y/lCstStiIc9zem79Lzof4oc/jCpLnpLkOlZUZwoFO/soxBz58ixZcRzzKc/L46Iw8ny1Y12O1Xy5yrF9HGsUYk6jGVVY8yNPhJgVcXw363zK9QYOddsRs8iQ16NGuU2HbW6YjV3usERnlWlIR3XGqV/p6JJM0Dm2nTgLzhJpOqZSoZv6YArR/juMhv0ufdlu02GrkY5EcpicX25i5nuRr8kPfkF08LnooXGTuziTj0wZcGdr8pcI5wKfbflbQcTl59S5nI++ExxX5M2mKzsJkT+b7ih7N2iRw4m6bnfMt2nwTYLPVsE5a8+Ny+XEfnMDf4NG3dhkUim0nQlV+MXXyBQGHnVhcEL7uy/StUiFHZ4wwmKe67y4FE9BeuqHtCuPC+NOp/NT42hGbx5/kswImEwV+c8ZFk/gBe1l5wjmyExRGvI8102uq5x+0Xm+Xv5Tj2UsasPqZdFolfHfMPuUHtk1oL48S1Yyz/K8PC4KI89XO1blWM2VKx3bx7FGISY6NoPNNvCJQLEdkRAWUmSwYPMgtx1xRoilI0Umo9l/7rCKOlOeUhI+e/1LR9s8bsWnbDyPEOOOOQrpSdM1am25+eHvSRqDl3RgHyXna8lnwsgyG8E1I8TK+ipF3Mi4nG+eUhaZtnUkKQebf2ZpwvrKkMUUC25hc+whx/WVvUzXVOEm3TR1K5M/NwG2J8K5+TJRbN64brp2Rnwviss3OyxwzdRHqfVy8nc6gV9qeza54oFFukdIuZgiBp56kIwi5gSpFF8hYQpHOoo6RdfBsO++xjospgzldvjmWpif/mlDaTs5NoK58Wc6jUbb+HqRCMmm7U/DJ0rY7mSfOixN2mXqZREDj5jzjogVxZcMQ8JMxswXS4+jz/r8nPNxnJ0Q406DRz9KlIPtEIUQS6e7Nmin9Zy+NAvLbQfInYqvEzcJszjwdcbmsWxeTOkZxXH9tp0kd+Il0nRtBTFKfoxGIKw16KD9VbRAP8fI+uXegcpEK/jqFUg+tsJfFgzsgptf6zOzNAF9PrL44XJmgyGfHNdX9jLdSyTEcvXa5JM7MB79MlMf95IbklFl7jDy2nbCjPjqa2RGBPdfsvXAuamwN1gj8hOJqQd00Hvj2I7rnSvE4naD7YWESRbru6NuUbruwnPHhRJfVTiy6LLcXJ4jhG2UH+epR9f/4f17UCwAAAaASURBVE/05ePPHREWB4q4jmPkTSNpH9y2wU27xHcdlnwz4DKU37keGeeSfLgMxO/U+OX9T/IewjAkTAlUI4OqcRyZyvW/6OM4OyEmGgk7XcNTC2aROS829pRLTmTIym2H0+W6NO6gfZ24SWCUEEs6Y7tGaJXet0PKHudy4qFEmjlzyd1P9HTjs7jByzESYXixrAizyGI1avTipwl5HyUiMYoY/fir+BoeN+78TCMk1gdKn3mdl+2QU+bx3k8mH2LEyW7KyuWcAznixBUUYrYs5cgP1wNz7kc6bX1M+0ef007oXkZMyDKXnQpfHP/pa2TGxwoIEfk1QjiwifMOPdr1b4Sb77QS8So6/ZAwV3b7ioiRHFFhaJ5Pw/sdfsjJc938Xh9/mn37w+AlPWt9G29C7BNZURnKeuUTvsa/q7B9RcKksF4WCTEPS9t/STbm3uqUDjYcMewyDAnjS3KCc7X9tifw5SpH8XGsJsRsh5Ao+6jT93Rshpq90+ZRhiENTp8li+CdO4NR20OY+mn2AxJ3E2b7ire8UaE4b9aGra+9618jlpleChBi0bz+frz2ioWCrzaoCrEQRmJhvsz77Tu0numEzTRF4r8MFx3zQwjhYiqf9TJx5WiNU/YLYvrXil8ZZpl+vXY7Xuhuy5DrnCPEcmWR95qsiFMaEZO/CfYvajxNHlIhkdZhKaZ8/vnOsehK7aW/L5OOEbh/Tx6JNzc1X9HpcZs60ZPDPnvpOetX7k4+DTPqyNfIjAoffM3T4UVrIl907dN90UakjWZWHGQSMPVuvjd09U1Nxg+TiC1Topui+8VP9A5O6dBuOZT9baZvPkjam3Gb3kbT51d1Q1ceJRO/Q1vfFIQY9zkjGQZytn5NflDbb7uUS0l/ZwdcOHLZ8xxv+p8+jtWEmNkJ+eRJKqYigfI/dLhpxI/o2Exec0LMnHT3yDL7fsl9rQogDfv0/WPeM4t3dBaLTI24iPa9ek1n7Q+i0ZN4hK2EWPB24iwgfD+8xNdcvBJperMbwEi+kiXai83s1/ZjUg6yo/ftI1a0z1qb+tYfj1C11/igbD4D9hEzNUTuZWaedG116FXnE2et1mURYswp7ZxuNj+n/4p+D3zuDu21W7SVEcN8c8Isx32605AGlHnVyiotLj2kvSOzn1YqvIN+U1GSHrvjXHGu+xoZJ8hkX71CjJ/mNU+oPqS958f+rStkirLtKNobLyRMpu0TIkamVeG4No48EyFGAclZY5rde9HJBNezTP3luu2M6AQy4p38zY1Kfq9JJ/0JvtbHskCI2Rsv5jKiv4jyw787l5+5KPvYonoWEmYCcE6UWjk6aRV/LSu4isIXp1D3FR/HikKsbpdhHwQqEjCNYuD73iqmNN3o3NiXHrlisbhMd5uf0xfRyAZ3ADzSJsV7uWz5GplyFhDaEABHvXoAljoswbE+jhBiOmxh5VISiNfApRtNXkonJ3SKR2fLiia++36X1jc/pj0jxFjMsbiToyUlvUNjXRJYQXBwLAAzwWmwnACaJwo4eqBMcMrHEUJsApCIcjUImLUvv9t+Qt9nXqt1NXwP8jIRTqMebMnb4VEvsxZPvu4mGcK3e+7lY4ac8TUyIfEQJksAHLM8qnwDyyr00rjgmLKocuTjCCFWhSjigsBVI5A8TBCJt0jIjVu/Ui6DvkamnAWENgTAUa8egKUOS3CsjyOEmA5bWAGBK0EgfioyFl8X0dPHq/Tb7U/p+DzkdVDjs4jGejyjkBDgGEIpLAxYhnEaFwocxxEKu+7jCCEWxg6hQAAEAgj4GpmAaAjiEABHB0iFr2BZAZ6ICo4CRoVDH0cIsQpAERUEQCBLwNfIZEPgWwgBcAyhFBYGLMM4jQsFjuMIhV33cYQQC2OHUCAAAgEEfI1MQDQEcQiAowOkwlewrABPRAVHAaPCoY8jhFgFoIgKAiCQJeBrZLIh8C2EADiGUAoLA5ZhnMaFAsdxhMKu+zhCiIWxQygQAIEAAr5GJiAagjgEwNEBUuErWFaAJ6KCo4BR4dDHEUKsAlBEBQEQyBLwNTLZEPgWQgAcQyiFhQHLME7jQoHjOEJh130cc0LMBMI/GKAOoA6gDqAOoA6gDqAO1FMHpGzLCDF5AccgAAIgAAIgAAIgAAL1EoAQq5cvrIMACIAACIAACIBAIQEIsUI0uAACIAACIAACIAAC9RKAEKuXL6yDAAiAAAiAAAiAQCGB/wfpEksjMHEVigAAAABJRU5ErkJggg=="></p>
</div>
<div class="specification">
<p>At the end of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mtext>nd</mtext></math> hour, the total volume of fuel in the tank was <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>88</mn><mo> </mo><mn>200</mn><mo> </mo><msup><mtext>m</mtext><mn>3</mn></msup></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>, the height of the tank.</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 volume of the tank is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>624</mn><mo> </mo><mn>000</mn><mo> </mo><msup><mtext>m</mtext><mn>3</mn></msup></math>, correct to three significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the common difference, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the amount of fuel pumped into the tank in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>13th</mtext></math> hour.</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>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> such that <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub><mo>=</mo><mn>0</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of hours that the pump was pumping fuel into the tank.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total amount of fuel pumped into the tank in the first <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> hours.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the tank will never be completely filled using this pump.</p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>Two friends Amelia and Bill, each set themselves a target of saving <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>20</mn><mo> </mo><mn>000</mn></math>. They each have <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>9000</mn></math> to invest.</p>
</div>
<div class="specification">
<p>Amelia invests her <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>9000</mn></math> in an account that offers an interest rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>%</mo></math> per annum compounded <strong>annually</strong>.</p>
</div>
<div class="specification">
<p>A third friend Chris also wants to reach the <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>20</mn><mo> </mo><mn>000</mn></math> target. He puts his money in a safe where he does not earn any interest. His system is to add more money to this safe each year. Each year he will add half the amount added in the previous year.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of Amelia’s investment after <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> years to the nearest hundred dollars.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the number of years required for Amelia’s investment to reach the target.</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>Bill invests his <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>9000</mn></math> in an account that offers an interest rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>%</mo></math> per annum compounded <strong>monthly</strong>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> is set to two decimal places.</p>
<p>Find the minimum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> needed for Bill to reach the target after <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> years.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that Chris will never reach the target if his initial deposit is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>9000</mn></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the amount Chris needs to deposit initially in order to reach the target after <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> years. Give your answer to the nearest dollar.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Tommaso plans to compete in a regional bicycle race after he graduates, however he needs to buy a racing bicycle. He finds a bicycle that costs 1100 euro (EUR). Tommaso has 950 EUR and invests this money in an account that pays 5 % interest per year, <strong>compounded monthly</strong>.</p>
</div>
<div class="specification">
<p>The cost of the bicycle, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span>, can be modelled by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C = 20x + 1100">
<mi>C</mi>
<mo>=</mo>
<mn>20</mn>
<mi>x</mi>
<mo>+</mo>
<mn>1100</mn>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> is the number of years since Tommaso invested his money.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the amount that he will have in his account after 3 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>Find the difference between the cost of the bicycle and the amount of money in Tommaso’s account after 3 years. Give your answer correct to two decimal places.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>After <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> complete <strong>months</strong> Tommaso will, for the first time, have enough money in his account to buy the bicycle.</p>
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>An arithmetic sequence has first term <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math> and common difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>.</mo><mn>5</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>th term of the sequence is zero, find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</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>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mi>n</mi></msub></math> denote the sum of the first <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> terms of the sequence.</p>
<p>Find the maximum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mi>n</mi></msub></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A new café opened and during the first week their profit was $60.</p>
<p>The café’s profit increases by $10 every week.</p>
</div>
<div class="specification">
<p>A new tea-shop opened at the same time as the café. During the first week their profit was also $60.</p>
<p>The tea-shop’s profit increases by 10 % every week.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the café’s <strong>total</strong> profit for the first 12 weeks.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the tea-shop’s <strong>total</strong> profit for the first 12 weeks.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>In this question, give all answers correct to two decimal places.</strong></p>
<p>Sam invests <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>1700</mn></math> in a savings account that pays a nominal annual rate of interest of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>74</mn><mo>%</mo></math>, compounded half-yearly. Sam makes no further payments to, or withdrawals from, this account.</p>
</div>
<div class="specification">
<p>David also invests <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>1700</mn></math> in a savings account that pays an annual rate of interest of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>%</mo></math>, compounded yearly. David makes no further payments or withdrawals from this account.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the amount that Sam will have in his account after <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">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>r</mi></math> required so that the amount in David’s account after <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> years will be equal to the amount in Sam’s 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>Find the interest David will earn over the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> years.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows values of ln <em>x</em> and ln <em>y</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The relationship between ln <em>x</em> and ln <em>y</em> can be modelled by the regression equation ln <em>y</em> = <em>a</em> ln <em>x</em> + <em>b</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>a</em> and of <em>b</em>.</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>Use the regression equation to estimate the value of <em>y</em> when<em> x</em> = 3.57.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The relationship between <em>x</em> and <em>y</em> can be modelled using the formula <em>y</em> = <em>kx<sup>n</sup></em>, where <em>k</em> ≠ 0 , <em>n</em> ≠ 0 , <em>n</em> ≠ 1.</p>
<p>By expressing ln <em>y</em> in terms of ln <em>x</em>, find the value of <em>n</em> and of <em>k</em>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The sum of the first <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> terms of a geometric sequence is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mi>n</mi></msub><mo>=</mo><munderover><mtext>Σ</mtext><mrow><mi>r</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mfrac><mn>2</mn><mn>3</mn></mfrac><msup><mfenced><mfrac><mn>7</mn><mn>8</mn></mfrac></mfenced><mi>r</mi></msup></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the first term of the sequence, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub></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 <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mo>∞</mo></msub></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the least value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> such that <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mo>∞</mo></msub><mo>-</mo><msub><mi>S</mi><mi>n</mi></msub><mo><</mo><mn>0</mn><mo>.</mo><mn>001</mn></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Rosa joins a club to prepare to run a marathon. During the first training session Rosa runs a distance of 3000 metres. Each training session she increases the distance she runs by 400 metres.</p>
</div>
<div class="specification">
<p>A marathon is 42.195 kilometres.</p>
<p>In the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>th training session Rosa will run further than a marathon for the first time.</p>
</div>
<div class="specification">
<p>Carlos joins the club to lose weight. He runs 7500 metres during the first month. The distance he runs increases by 20% each <strong>month</strong>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the distance Rosa runs in the third training session;</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the distance Rosa runs in the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n">
<mi>n</mi>
</math></span>th training session.</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>Find the 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">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the total distance, in <strong>kilometres</strong>, Rosa runs in the first 50 training sessions.</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>Find the distance Carlos runs in the fifth month of training.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the total distance Carlos runs in the first year.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Helen and Jane both commence new jobs each starting on an annual salary of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>70</mn><mo>,</mo><mn>000</mn></math>. At the start of each new year, Helen receives an annual salary increase of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>2400</mn></math>.</p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><msub><mi>H</mi><mi>n</mi></msub></math> represent Helen’s annual salary at the start of her <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>th year of employment.</p>
</div>
<div class="specification">
<p>At the start of each new year, Jane receives an annual salary increase of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>%</mo></math> of her previous year’s annual salary.</p>
<p>Jane’s annual salary, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><msub><mi>J</mi><mi>n</mi></msub></math>, at the start of her <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>th year of employment is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>J</mi><mi>n</mi></msub><mo>=</mo><mn>70</mn><mo> </mo><mn>000</mn><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>03</mn></mrow></mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup></math>.</p>
</div>
<div class="specification">
<p>At the start of year <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math>, Jane’s annual salary exceeds Helen’s annual salary for the first time.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>H</mi><mi>n</mi></msub><mo>=</mo><mn>2400</mn><mi>n</mi><mo>+</mo><mn>67</mn><mo> </mo><mn>600</mn></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>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>J</mi><mi>n</mi></msub></math> follows a geometric sequence, state the value of the common ratio, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>.</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>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">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math> found in part (c) (i), state Helen’s annual salary and Jane’s annual salary, correct to the nearest dollar.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find Jane’s total earnings at the start of her <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math>th year of employment. Give your answer correct to the nearest dollar.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>An infinite geometric series has first term <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo><mi>a</mi></math> and second term <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>2</mn></msub><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mi>a</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>></mo><mn>0</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the common ratio in terms 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 values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> for which the sum to infinity of the series exists.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</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>a</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mo>∞</mo></msub><mo>=</mo><mn>76</mn></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = {({x^2} + 3)^7}">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>7</mn>
</msup>
</mrow>
</math></span>. Find the term in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^5}">
<mrow>
<msup>
<mi>x</mi>
<mn>5</mn>
</msup>
</mrow>
</math></span> in the expansion of the derivative, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’(x)">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {{\text{e}}^{2\,{\text{sin}}\left( {\frac{{\pi x}}{2}} \right)}}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mn>2</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mi>π<!-- π --></mi>
<mi>x</mi>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</msup>
</mrow>
</math></span>, for <em>x</em> > 0.</p>
<p>The <em>k </em>th maximum point on the graph of <em>f</em> has <em>x</em>-coordinate <em>x<sub>k</sub></em> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k \in {\mathbb{Z}^ + }">
<mi>k</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<msup>
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
<mo>+</mo>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <em>x<sub>k</sub></em><sub> + 1</sub> = <em>x<sub>k</sub></em> + <em>a</em>, find <em>a</em>.</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>Hence find the value of <em>n</em> such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum\limits_{k = 1}^n {{x_k} = 861} "> <munderover> <mo movablelimits="false">∑</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mrow> <msub> <mi>x</mi> <mi>k</mi> </msub> </mrow> <mo>=</mo> <mn>861</mn> </mrow> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The first terms of an infinite geometric sequence, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_n}">
<mrow>
<msub>
<mi>u</mi>
<mi>n</mi>
</msub>
</mrow>
</math></span>, are 2, 6, 18, 54, …</p>
<p>The first terms of a second infinite geometric sequence, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_n}">
<mrow>
<msub>
<mi>v</mi>
<mi>n</mi>
</msub>
</mrow>
</math></span>, are 2, −6, 18, −54, …</p>
<p>The terms of a third sequence, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{w_n}">
<mrow>
<msub>
<mi>w</mi>
<mi>n</mi>
</msub>
</mrow>
</math></span>, are defined as <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{w_n} = {u_n} + {v_n}">
<mrow>
<msub>
<mi>w</mi>
<mi>n</mi>
</msub>
</mrow>
<mo>=</mo>
<mrow>
<msub>
<mi>u</mi>
<mi>n</mi>
</msub>
</mrow>
<mo>+</mo>
<mrow>
<msub>
<mi>v</mi>
<mi>n</mi>
</msub>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>The finite series, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum\limits_{k = 1}^{225} {{w_k}} ">
<munderover>
<mo movablelimits="false">∑<!-- ∑ --></mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>225</mn>
</mrow>
</munderover>
<mrow>
<mrow>
<msub>
<mi>w</mi>
<mi>k</mi>
</msub>
</mrow>
</mrow>
</math></span> , can also be written in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum\limits_{k = 0}^m {4{r^k}} ">
<munderover>
<mo movablelimits="false">∑<!-- ∑ --></mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>m</mi>
</munderover>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>r</mi>
<mi>k</mi>
</msup>
</mrow>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the first three <strong>non-zero</strong> terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{w_n}"> <mrow> <msub> <mi>w</mi> <mi>n</mi> </msub> </mrow> </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 value of <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">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="question">
<p>Consider the expansion of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mfrac><mi>k</mi><mi>x</mi></mfrac></mrow></mfenced><mn>9</mn></msup></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>></mo><mn>0</mn></math>.</p>
<p>The coefficient of the term in <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>6</mn></msup></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6048</mn></math>. Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</p>
</div>
<br><hr><br><div class="specification">
<p>The first term of an infinite geometric sequence is 4. The sum of the infinite sequence is 200.</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>Find the sum of the first 8 terms.</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 least value of <em>n</em> for which <em>S</em><sub><em>n</em></sub> > 163.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The first two terms of a geometric sequence are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_1} = 2.1">
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>=</mo>
<mn>2.1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_2} = 2.226">
<mrow>
<msub>
<mi>u</mi>
<mn>2</mn>
</msub>
</mrow>
<mo>=</mo>
<mn>2.226</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <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>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_{10}}"> <mrow> <msub> <mi>u</mi> <mrow> <mn>10</mn> </mrow> </msub> </mrow> </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 the least value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n"> <mi>n</mi> </math></span> such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_n} > 5543"> <mrow> <msub> <mi>S</mi> <mi>n</mi> </msub> </mrow> <mo>></mo> <mn>5543</mn> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p>Consider a geometric sequence where the first term is 768 and the second term is 576.</p>
<p>Find the least value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n"> <mi>n</mi> </math></span> such that the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n"> <mi>n</mi> </math></span>th term of the sequence is less than 7.</p>
</div>
<br><hr><br><div class="specification">
<p>On 1st January 2020, Laurie invests $<em>P</em> in an account that pays a nominal annual interest rate of 5.5 %, compounded <strong>quarterly</strong>.</p>
<p>The amount of money in Laurie’s account <strong>at the end of each year</strong> follows a geometric sequence with common ratio, <em>r</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>r</em>, giving your answer to four significant figures.</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>Laurie makes no further deposits to or withdrawals from the account.</p>
<p>Find the year in which the amount of money in Laurie’s account will become double the amount she invested.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>In an arithmetic sequence, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_1} = 1.3">
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>=</mo>
<mn>1.3</mn>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_2} = 1.4">
<mrow>
<msub>
<mi>u</mi>
<mn>2</mn>
</msub>
</mrow>
<mo>=</mo>
<mn>1.4</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_k} = 31.2">
<mrow>
<msub>
<mi>u</mi>
<mi>k</mi>
</msub>
</mrow>
<mo>=</mo>
<mn>31.2</mn>
</math></span>.</p>
</div>
<div class="specification">
<p>Consider the terms, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_n}">
<mrow>
<msub>
<mi>u</mi>
<mi>n</mi>
</msub>
</mrow>
</math></span>, of this sequence such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n">
<mi>n</mi>
</math></span> ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>.</p>
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="F">
<mi>F</mi>
</math></span> be the sum of the terms for which <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n">
<mi>n</mi>
</math></span> is not a multiple of 3.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the exact value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_k}">
<mrow>
<msub>
<mi>S</mi>
<mi>k</mi>
</msub>
</mrow>
</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>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="F = 3240">
<mi>F</mi>
<mo>=</mo>
<mn>3240</mn>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An infinite geometric series is given as <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_\infty } = a + \frac{a}{{\sqrt 2 }} + \frac{a}{2} + \ldots ">
<mrow>
<msub>
<mi>S</mi>
<mi mathvariant="normal">∞</mi>
</msub>
</mrow>
<mo>=</mo>
<mi>a</mi>
<mo>+</mo>
<mfrac>
<mi>a</mi>
<mrow>
<msqrt>
<mn>2</mn>
</msqrt>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mi>a</mi>
<mn>2</mn>
</mfrac>
<mo>+</mo>
<mo>…</mo>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a \in {\mathbb{Z}^ + }">
<mi>a</mi>
<mo>∈</mo>
<mrow>
<msup>
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
<mo>+</mo>
</msup>
</mrow>
</math></span>.</p>
<p>Find the largest value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_\infty } < F">
<mrow>
<msub>
<mi>S</mi>
<mi mathvariant="normal">∞</mi>
</msub>
</mrow>
<mo><</mo>
<mi>F</mi>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>All answers in this question should be given to four significant figures.</strong></p>
<p><br>In a local weekly lottery, tickets cost <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>2</mn></math> each.</p>
<p>In the first week of the lottery, a player will receive <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mi>D</mi></math> for each ticket, with the probability distribution shown in the following table. For example, the probability of a player receiving <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>10</mn></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>03</mn></math>. The grand prize in the first week of the lottery is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>1000</mn></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAgMAAABXCAYAAACZW0afAAATqklEQVR4Ae2dgdHUNhOG08c/aSBDA5lUECoIFYQKQgWhg1BBqCBUECoIHdABHdw/D8kyy6Lz2e8n29Ldq5kb+2yvtHr2lbS274PvLi4mYAImYAImYAIPTeC7h+69O28CJmACJmACJnBxMmARmIAJmIAJmMCDE/gmGfj++/9d/DEDa8AasAasAWvgvjWQ859mMpAv8P78BBjQLtsJmNt2ZliYm7lpBDQr660PNycDGseprDxYtHCZm7lpBDQr683cNAKaVdWbkwGN41RWNehTOX+is+amwTc3c9MIaFbWWx9uTgY0jlNZebBo4TI3c9MIaFbWm7lpBDSrqjcnAxrHqaxq0Kdy/kRnzU2Db27mphHQrKy3PtycDGgcp7LyYNHCZW7mphHQrKw3c9MIaFZVb04GNI5TWdWgT+X8ic6amwbf3MxNI6BZWW99uDkZ0DhOZeXBooXL3MxNI6BZWW/mphHQrKrenAxoHKeyqkGfyvkTnTU3Db65mZtGQLOy3vpwczKgcZzKyoNFC5e5mZtGQLOy3sxNI6BZVb05GdA4TmVVgz6V8yc6a24afHMzN42AZrWX3l6//v3y7NkPX/55/pcvf718/Pjx8ubNH5qjohVt0jafnqVyczLQk+6gddWgD+rmcG6ZmxYSczM3jYBm1Vtvnz59ujx//vPnz7t3f31x6sOHfy4vXvzSfVH+0sCVHXyhj04GrgDy4fUEeg+W9S3PfaW5afEzN3PTCGhWvfXG4vvTTz9eSApa5dWr31qHdz2GT04GdkX8GJX3HiyPQc3/4Y4aZ+tNI2du53PjSQBxOPpVwK2eOxm4RcjnVxHwJLMK0zcXmds3SFYdMLdVmL65yNy+QbLqQE9u3PVT3/v3f69qm+SBVwfY8TQBW97xv33751e/N+D3B1FINLiWNrDFhm0u8UqCczwRcDKQ6XhfJoCgXLYTMLftzLAwN3PTCGhWPfXGokt9LMa58MqA4/nDNfG9PsJnsY+nC2y5jiQhnjzwPWziGAkEhbayPef5IWNcn/16yj4+5OIfEGYad7pfg36n3ezeLXPTkJqbuWkENKueeos7dRbgVmFBZmGOEklCLPxxPLb5LxIiwYjFP77XOuLJQdTBluTAyUAm4n2JQM/BIjkwqZG5aYEzN3PTCGhWPfUWd/HXfiQYi3t4WhfyOB6vCbiefXyMxf9WMsCizxOKXPyaINPwvkyg52CRnZjQ0Ny0oJmbuWkENKueeotH9NTZ+t3AmmSA1wHYx9OFuvjX7zWhIBngSUAuJAP1dwX5vLJfufk1wX+PYABz7VGPAnokmxr0EXxjwMQjObZ8H62MyI3JCL/4mNt1xaCnYMVkW8uI+htFbyxEobG6KD0CN+7geRXAJ68J6Igxl18TwANW+TqSiHwsfpQYTwbiSUEkG7WOSBZoi8J1tEmd9YlB1fWW79SXi5OB/36wAZgIVgZ0D/s16CP0CVEzWVMYSD1F3qt/o3GDU0w6aJWJ2tza0c4LWisZGFF/I+gta6xF9lG4oZl4CkBc4sNde/zQjzEYx1msYz6DG9dxjgU9kgP24Rs2bCMxiGMxvvNx6oU7SQWJQ69Cm7k4GbhcPj/OqRlwhjT7fg362f1B8Dm7xh/4x0A4279ofzRuebLBx5hY4g4j/D57Owq34FOTgVH1NwK3peTS3M4eWX3br3pzMnC5fM7o6kTbF/u5tdWgn+vN5XO2HI/Awhcy6Xoszp21HY1b5RB3Jk4GKpl/v19LBtBZ1doI+jtbb8ELP+IJQL4TNbe2zmY9WvX2kMkAkyhiBwaTAPvxY49ZA7vkdw360rVHnOMpQP21LsnYaE9nRuNWY8OjxNGY4eMo3GJxq08GRtXfSNwYjzy9Y36MYm5B4j62VW8PlwzE3VTcGcSjrzph3Ee4/+1FDfrZfavv1/AnJp+zfcvtj8Yt+8Y+E3W8v6znzvw+CrdrycCo+huFW2injklzCzL3sa16e6hkgAW/Zrs8EcjZ732E+ete1KB/ffb4b9xhMNHkwpOC0e5yR+OWefFqYFTdjsLtWjIwqv5G4RY6ix++xY2SuQWZ+9hWvT1UMtB6CsArAo7fc6lBP7uvrXePrWNn+zkat+DB5DxqIoCPo3C7lgy0tNY6FryP2o7CLfqLzvApkoEWo9axsD9qOxq3o/r91HYqt4dKBlj48yQak0X+kcxTAY9oX4N+to+RlGU/eGIzWlI2Gjd4jZ4I4OMo3GJ8x2IWehtVf6NwC048GWCxj2JuQeI+tlVvD5cMkBBQeCzN595/PEhfa9BHkDKPHGPx55VBxGUE38KHEbmh2dbiFj6PsB2FWyQDrWR/RP2dzQ1eoa34kXVl90jcYEFM6mftjUvYj/rj9Kq3h0oG4h9yIJjs82F/1GD1mthr0HvV+5R6mGRIAPCNu4866Tyl7l62I3FjYgle+JU/o/2IcARuPAHMjOoYH1F/Z3NjHAYz+LXG5CNyg0t+ohzaipuZXvPN0fVUvT1UMnA07FHaq0Efxa/R/TA3LULmZm4aAc1qb72x+OdkAC95QsKN5MylcnMyMHM0V/peg77S7OEvMzdNAuZmbhoBzWpvvbWSgXg6EK9VNM/PtarcnAycG49DWq9BP6TRO2jE3LQgmpu5aQQ0q7311koG8pMBXkHxKiH+PBp/eJ3Ca4T8m7T4DQvn8yf+zBqb/Kpm79cQlZuTAU1/U1nVoE/l/InOmpsG39zMTSOgWe2tN5IBFvV4CsCiT5ss4vEjQb5zXZT4Nxo4Hr9XYXGPOtiSULD4R6ENfrhJwQbbPX8PRP25OBnINO50vwb9TrvZvVvmpiE1N3PTCGhWe+stXgnQTnzyXXskBPkYPYmEIJKB3DuSAJKBSA5Y9KPuvCXx2KvQTi5OBjKNO92vQb/TbnbvlrlpSM3N3DQCmtXeemu9JsieXksG4p++r8kACzw/PoynANRFIsGTgSNL5eZk4Ej6J7VVg36SG9M1a25ayMzN3DQCmtXeeuuZDLDo4299/M93EoR4UhAkcsIQx3ptKzcnA73IDlxPDfrArg7lmrlp4TA3c9MIaFZ764079vxuv3rJD//wob4mqO/943u+jsWf72zjNwTURyER4FXDXqVyczKwF+mB6q1BH8i1oV0xNy085mZuGgHNai+9xeN/6o9P6849znFnH38ZEAt/nOM75+N73oYNi7//mkDTgK1WEkB4LtsJmNt2ZliYm7lpBDQr660PNz8Z0DhOZeXBooXL3MxNI6BZWW/mphHQrKrenAxoHKeyqkGfyvkTnTU3Db65mZtGQLOy3vpwczKgcZzKyoNFC5e5mZtGQLOy3sxNI6BZVb05GdA4TmVVgz6V8yc6a24afHMzN42AZmW99eHmZEDjOJWVB4sWLnMzN42AZmW9mZtGQLOqenMyoHGcyqoGfSrnT3TW3DT45mZuGgHNynrrw83JgMZxKisPFi1c5mZuGgHNynozN42AZlX15mRA4ziVVQ36VM6f6Ky5afDNzdw0ApqV9daHWzMZAK4/ZmANWAPWgDVgDdyvBnIa0UwG8gXen58Ag9llOwFz284MC3MzN42AZmW99eHmZEDjOJWVB4sWLnMzN42AZmW9mZtGQLOqenMyoHGcyqoGfSrnT3TW3DT45mZuGgHNynrrw83JgMZxKisPFi1c5mZuGgHNynozN42AZlX15mRA4ziVVQ36VM6f6Ky5afDNzdw0ApqV9daHm5MBjeNUVh4sWrjMzdw0ApqV9WZuGgHNqurNyYDGcSqrGvSpnD/RWXPT4JubuWkENCvrrQ83JwMax6msPFi0cJmbuWkENCvrzdw0AppV1ZuTAY3jVFY16FM5f6Kz5qbBNzdz0whoVtZbH25OBjSOU1l5sGjhMjdz0whoVtabuWkENKuqt9OTgXfv/mr+08fPn/984dxSef3698vbt39+ueTly1+bdb148cvl/fu/v1y35w7+APnZsx++NINfR7X/pdG0U4OeTnXfJWY//fTjZwb0+1aBF6zwEbtWzN+8+eOruPL9iHIktyP6c1QbR3LbqrePHz9emA/wkS3fc8l6ZA768OGffHrX/T255TG0Zvzc4rqF47Vx3QtmT26xhqz1+amcYHCrTdrgGvTYs1RupycD0TkWhBBpFtq1RZSB3Bqor1799nmgxzm2QKTjQD2ikKTUhZDv1/qyt0816Hu1R9yIY3AmRsTjWuE6fIu4x/eIXdj1HgRR763tUdxu+THb+aO4bdUbHNES45OC7rK2GJ+hxU+fPn1OFlgUjip7cSPBoR/wol/sc+xaWcN1iSPjl7FPCY7MC9S7R+nFjbkq/EYLt3x+KidY3GqTNugfn6zVHhwrtyGTATqKoHA2gpM7z2COQZuPs38tg2IAEFzEuXchaHWw0e4tce3lVw36Xu3APscrYlgX92ifOMIkF77n2LKfv+dr994/itve/Ti6/qO4bdUbOqp6Y164pq94SnAUv7241T7SX45dK7e43uJYecY8UI9fa3/r8R7cwsd8wwYHPtfKUzltaZO2HjYZIAAM3AogMqXWAsOCizAi889B5Bjn4q41n+u5Hz60kg58WLpT7ulHrqvHYMn1XduvCznXtY6FPZNDjQnX59gyaXENH9jtNaGET3l7FLfc5j3sH8Wtpa3WsWBKopqTVY7XCT2uZYvWZtcbixvxyItcaxHK/W4xzMe2cqTubJ/b6rHfQ2/EGR9zaR3L51t9ysducWrV3zpGmw+dDMSiXwfvNVgAi8fMWfgRPOwQTb1jj/NP2Ubd1M9+TWCibtrmmlaiENfsse0xWG75FfGqfGGxlABxngHEBIXgW8kadZNIoQX6kpOFW3495fwR3BT/6H+wwMclvkr9T7U5gpuiNxLLygpdte6SGcet409ls2S/B7eYc+AVJW5Y6ljl/BquWzjmOvcatz24oYsa71hPMrtg2IPTljYfLhmgwxTEGpNdXRw4zqdVsK/ZXVy39GSAoCCoa58qkqiTbbRJAoLfXMtE0iqRpdc+ta7teazHYLnlDwOddmrfWOwjrq06YMY12BKjpcK1OfNeurbHuSO4bfUzNMQYgAcT+rXxsLXuXtcfwU3RG9qpGuN7nTNCj/TjSLZ7cIsbFbQShX3aas1Ta7iu5Rjt0U5NwuJcj20PbsxRxD2XSAZaSUwPTlvabF2bfVX2K7ehfjOAc/FhUW1lrhy/NkAR6bWFJwZ4HhQKwGwTAy2LhXby93x9ZJOtQZiv671fg967fuqLvtVkgHgtTQTEmAmZuOHn0rW0Q+zrhL5Hf6jzCG5bfEe7aPwWoy117nHtEdwUvaHFqh1YcrwW6uccfWnNQ/X6Ht/34Ibv1JvnvWDX6lecWxrHWzjSLmM2t9+DVa6jBzdiXZOBYAeTWnpw2tLmwyUDaxZJhNhKBuKOqSXwOAf8XiUm5uwzA6jeZeT2QkDZJp/fa7/HYFnjG32vfWsdi7oqL77ja60jrmfLZF4n9Hy+5/5R3Nb6DBd82nNiXevL0nVHcWtpq3UsfGXeqHNH61hc3xrjcW6P7R7cYu5jG6V1LM6xbTHMx1rMWseoizm3tZjm9p6634MbY4s+5tI6ls9nJnE8H2sxycda9beOUbeTgSCctsCsGRynWSBaEyVCJIHgc02UCBbbax9sa4mFK54CRDtLCce1R0u17t7fewyWNT4hWOITJSadYBTHY8v1lS3H+Fwr1J8ntmvX9Th+FLe1vqKtygu213S9tt7e1x3FbaveWhNtnrxbHDg/u97QDH2Pwn7VUZxje4vrWo5HJAL420NvMTfnWDPXLM1FT+W0pU3aaq17OW5b9yu3IV4TbMnAW0JkMmTQ5sABOhZ5IPaeMCMZYEtbkaTgH99bJWyOvrOrQW/51uNYFTdMlpIjWOEbW0okVPGd+vKTHhK+pfp69CHXcRS33ObSfiS8MWHB5kgeS77lc0dx26o3fMwLIzyXJlh0iIaPKntxox/0m3knxlgeV7V/a7je4kib1JNLjOt8rMd+L255cWeuZk1ZWjd6cFrbJjpcSuAUjpXb6clALJA4xmdpcNJhgsN1ITQEFrZ1S117CZCBRf20SaD4TrCWJg8mn5ywKAFUbPDxqBKDiDZrXyPWbKPk+NW7tLieuvLkE7Z7b4/ktqYvaD80h297aXuNL0vXHMltq94yQ8ZqnuyXtLjU317n9uSW+1Z1E0lmvklZ4kp/lzgy7ulL/eyVuPbkhiaoj/kmz1P0mbHHJ5encIp6ltrkGubFzDLHKepQtpXb6cmA0gnEu5ewFH/W2BDAW5nmmnqUa2rQlToe0cbctKibm7lpBDQr660PtymTAbpONhWPSzUUx1qRwCw9mtvTGw8Wja65mZtGQLOy3sxNI6BZVb1NmwzQfZ4OnLXAbsHPY7MzE5ca9C2+P/K15qZF39zMTSOgWVlvfbhNnQxoCB7PyoNFi7m5mZtGQLOy3sxNI6BZVb05GdA4TmVVgz6V8yc6a24afHMzN42AZmW99eHmZEDjOJWVB4sWLnMzN42AZmW9mZtGQLOqenMyoHGcyqoGfSrnT3TW3DT45mZuGgHNynrrw83JgMZxKisPFi1c5mZuGgHNynozN42AZlX15mRA4ziVVQ36VM6f6Ky5afDNzdw0ApqV9daHWzMZAK4/ZmANWAPWgDVgDdyvBnIa8U0ykE963wRMwARMwARM4P4JOBm4/xi7hyZgAiZgAiawSMDJwCIenzQBEzABEzCB+yfwf/b98goawkesAAAAAElFTkSuQmCC"></p>
</div>
<div class="specification">
<p>If nobody wins the grand prize in the first week, the probabilities will remain the same, but the value of the grand prize will be <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>2000</mn></math> in the second week, and the value of the grand prize will continue to double each week until it is won. All other prize amounts will remain the same.</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>c</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>Determine whether this lottery is a fair game in the first week. Justify your answer.</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>Given that the grand prize is not won and the grand prize continues to double, write an expression in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> for the value of the grand prize in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mtext>th</mtext></math> week of the lottery.</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>The <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mtext>th</mtext></math> week is the first week in which the player is expected to make a profit. Ryan knows that if he buys a lottery ticket in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mtext>th</mtext></math> week, his expected profit is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mi>p</mi></math>.</p>
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Gemma and Kaia started working for different companies on January 1st 2011.</p>
<p>Gemma’s starting annual salary was <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>45</mn><mo> </mo><mn>000</mn></math>, and her annual salary increases <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>%</mo></math> on January 1st each year after 2011.</p>
</div>
<div class="specification">
<p>Kaia’s annual salary is based on a yearly performance review. Her salary for the years 2011, 2013, 2014, 2018, and 2022 is shown in the following table.</p>
<p style="text-align: left;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find Gemma’s annual salary for the year 2021, 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>Assuming Kaia’s annual salary can be approximately modelled by the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi></math>, show that Kaia had a higher salary than Gemma in the year 2021, according to the model.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br>