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<h2>SL Paper 2</h2><div class="specification">
<p>Eddie decides to construct a path across his rectangular grass lawn using pairs of tiles.</p>
<p>Each tile is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mtext>cm</mtext></math> wide and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mtext>cm</mtext></math> long. The following diagrams show the path after Eddie has laid one pair and three pairs of tiles. This pattern continues until Eddie reaches the other side of his lawn. When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> pairs of tiles are laid, the path has a width of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>w</mi><mi>n</mi></msub></math> centimetres and a length <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>l</mi><mi>n</mi></msub></math> centimetres.</p>
<p>The following diagrams show this pattern for one pair of tiles and for three pairs of tiles, where the white space around each diagram represents Eddie’s lawn.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The following table shows the values of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>w</mi><mi>n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>l</mi><mi>n</mi></msub></math> for the first three values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>Find the value of</p>
</div>
<div class="specification">
<p>Write down an expression in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> for</p>
</div>
<div class="specification">
<p>Eddie’s lawn has a length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>740</mn><mo> </mo><mtext>cm</mtext></math>.</p>
</div>
<div class="specification">
<p>The tiles cost <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>24</mn><mo>.</mo><mn>50</mn></math> per square metre and are sold in packs of five tiles.</p>
</div>
<div class="specification">
<p>To allow for breakages Eddie wants to have at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>%</mo></math> more tiles than he needs.</p>
</div>
<div class="specification">
<p>There is a fixed delivery cost of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>35</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>w</mi><mi>n</mi></msub></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><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>l</mi><mi>n</mi></msub></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that Eddie needs <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>144</mn></math> tiles.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</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>w</mi><mi>n</mi></msub></math> for this path.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total area of the tiles in Eddie’s path. Give your answer 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></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> is an integer.</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>Find the cost of a single pack of five tiles.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the minimum number of packs of tiles Eddie will need to order.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total cost for Eddie’s order.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</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"><mn>30</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</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"><mn>40</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>arithmetic formula chosen <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>w</mi><mi>n</mi></msub><mo>=</mo><mn>20</mn><mo>+</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>10</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>10</mn><mo>+</mo><mn>10</mn><mi>n</mi></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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>arithmetic formula chosen</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>l</mi><mi>n</mi></msub><mo>=</mo><mn>30</mn><mo>+</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>10</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>20</mn><mo>+</mo><mn>10</mn><mi>n</mi></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>740</mn><mo>=</mo><mn>30</mn><mo>+</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>10</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>740</mn><mo>=</mo><mn>20</mn><mo>-</mo><mn>10</mn><mi>n</mi></math> <em><strong>M1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>72</mn></math> <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>144</mn></math> tiles <em><strong>AG</strong></em></p>
<p><br><strong>Note:</strong> The <em><strong>AG</strong> </em>line must be stated for the final <em><strong>A1</strong> </em>to be awarded.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>w</mi><mn>72</mn></msub><mo>=</mo><mn>730</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>10</mn><mo>×</mo><mn>20</mn></mrow></mfenced><mo>×</mo><mn>144</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>28800</mn></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>88</mn><mo>×</mo><msup><mn>10</mn><mn>4</mn></msup><mo> </mo><mo> </mo><msup><mtext>cm</mtext><mn>2</mn></msup></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Follow through within the question for correctly converting <em>their</em> intermediate value into standard form (but only if the pre-conversion value is seen).</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</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>1</mn></math> square metre <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>100</mn><mo> </mo><mtext>cm</mtext><mo>×</mo><mn>100</mn><mo> </mo><mtext>cm</mtext></math> <em><strong>(M1)</strong></em></p>
<p>(so, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math> tiles) and hence <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> packs of tiles in a square metre <em><strong>(A1)</strong></em></p>
<p>(so each pack is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>$</mo><mn>24</mn><mo>.</mo><mn>50</mn></mrow><mrow><mn>10</mn><mo> </mo><mtext>packs</mtext></mrow></mfrac></math>)</p>
<p><br><strong>OR</strong></p>
<p>area covered by one pack of tiles is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>.</mo><mn>2</mn><mo> </mo><mtext>m</mtext><mo>×</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo> </mo><mtext>m</mtext><mo>×</mo><mn>5</mn><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>0</mn><mo>.</mo><mn>1</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>1</mn></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>2</mn><mo>.</mo><mn>45</mn></math> per pack (of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> tiles) <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>1</mn><mo>.</mo><mn>08</mn><mo>×</mo><mn>144</mn></mrow><mn>5</mn></mfrac><mo> </mo><mfenced><mrow><mo>=</mo><mn>31</mn><mo>.</mo><mn>104</mn></mrow></mfenced></math> <em><strong>(M1)(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong> </em>for correct numerator, <em><strong>M1</strong> </em>for correct denominator.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32</mn></math> (packs of tiles) <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>35</mn><mo>+</mo><mfenced><mrow><mn>32</mn><mo>×</mo><mn>2</mn><mo>.</mo><mn>45</mn></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>113</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>113</mn><mo>.</mo><mn>4</mn></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>In part (a), most candidates were able to find the correct values for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<p>In part (b), most candidates were able to write down the correct expressions for <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>w</mi><mi>n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>l</mi><mi>n</mi></msub></math>.</p>
<p>In part (c)(i), candidates continued to struggle with “show that” questions. Some substituted 144 for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> and worked backwards, however this is never the intention of the question; candidates should progress towards (not “away from”) the given result. Part (ii) was well answered by many candidates.</p>
<p>Part (d) was poorly answered with many candidates multiplying 720 with 730 instead of 10 with 20. However, the majority managed to convert their answer correctly to standard form which gained them a mark for that particular skill.</p>
<p>Part (e) saw very few candidates find the cost of one packet of tiles. The main reason was the failure to convert cm<sup>2</sup> to m<sup>2</sup>.</p>
<p>In part (f), about half of the candidates managed to find the correct number of packets. Some gained a mark for finding 8% or dividing by 5.</p>
<p>In part (g), most candidates could use their answers to parts (e) and (f) to score “follow through” marks and find the total cost of their order.</p>
<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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</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>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>The marks obtained by nine Mathematical Studies SL students in their projects (<em>x</em>) and their final IB examination scores (<em>y</em>) were recorded. These data were used to determine whether the project mark is a good predictor of the examination score. The results are shown in the table.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The equation of the regression line <em>y</em> on <em>x</em> is <em>y</em> = <em>mx</em> + <em>c</em>.</p>
</div>
<div class="specification">
<p>A tenth student, Jerome, obtained a project mark of 17.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar y}">
<mrow>
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</mrow>
</math></span>, the mean examination score.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to write down <em>r </em>, Pearson’s product–moment correlation coefficient.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the exact value of <em>m</em> and of <em>c</em> for these data.</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>Use the regression line <em>y</em> on <em>x</em> to estimate Jerome’s examination score.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Justify whether it is valid to use the regression line y on x to estimate Jerome’s examination score.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>54 <em><strong>(G1)</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.5 <em><strong>(G2)</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>m</em> = 0.875, <em>c</em> = 41.75 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {m = \frac{7}{8}{\text{,}}\,\,c = \frac{{167}}{4}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mfrac>
<mn>7</mn>
<mn>8</mn>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>c</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>167</mn>
</mrow>
<mn>4</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for 0.875 seen. Award <em><strong>(A1)</strong></em> for 41.75 seen. If 41.75 is rounded to 41.8 do not award <em><strong>(A1)</strong></em>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>y</em> = 0.875(17) + 41.75 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong> </em>for correct substitution into their regression line.</p>
<p> </p>
<p>= 56.6 (56.625) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (b)(i).</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the estimate is valid <em><strong>(A1)</strong></em></p>
<p>since this is interpolation <strong>and</strong> the correlation coefficient is large enough <em><strong>(R1)</strong></em></p>
<p><strong>OR</strong></p>
<p>the estimate is not valid <em><strong>(A1)</strong></em></p>
<p>since the correlation coefficient is not large enough <em><strong>(R1)</strong></em></p>
<p><strong>Note:</strong> Do not award <em><strong>(A1)(R0)</strong></em>. The <em><strong>(R1)</strong></em> may be awarded for reasoning based on strength of correlation, but do not accept “correlation coefficient is not strong enough” or “correlation is not large enough”.</p>
<p>Award <em><strong>(A0)</strong></em><em><strong>(R0)</strong></em> for this method if no numerical answer to part (a)(iii) is seen.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.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.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</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">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Scott purchases food for his dog in large bags and feeds the dog the same amount of dog food each day. The amount of dog food left in the bag at the end of each day can be modelled by an arithmetic sequence.</p>
<p>On a particular day, Scott opened a new bag of dog food and fed his dog. By the end of the third day there were <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>115</mn><mo>.</mo><mn>5</mn></math> cups of dog food remaining in the bag and at the end of the eighth day there were <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>108</mn></math> cups of dog food remaining in the bag.</p>
</div>
<div class="specification">
<p>Find the number of cups of dog food</p>
</div>
<div class="specification">
<p>In <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2021</mn></math>, Scott spent <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>625</mn></math> on dog food. Scott expects that the amount he spends on dog food will increase at an annual rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>4</mn><mo>%</mo></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>fed to the dog per day.</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>remaining in the bag at the end of the first day.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the number of days that Scott can feed his dog with one bag of food.</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>Determine the amount that Scott expects to spend on dog food in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2025</mn></math>. Round your answer to the nearest dollar.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mtext>Σ</mtext><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mn>10</mn></munderover><mfenced><mrow><mn>625</mn><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>064</mn><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced></msup></mrow></mfenced></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe what the value in part (d)(i) represents in this context.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Comment on the appropriateness of modelling this scenario with a geometric sequence.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>115</mn><mo>.</mo><mn>5</mn><mo>=</mo><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mfenced><mrow><mn>3</mn><mo>-</mo><mn>1</mn></mrow></mfenced><mo>×</mo><mi>d</mi><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>115</mn><mo>.</mo><mn>5</mn><mo>=</mo><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mn>2</mn><mi>d</mi></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>108</mn><mo>=</mo><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mfenced><mrow><mn>8</mn><mo>-</mo><mn>1</mn></mrow></mfenced><mo>×</mo><mi>d</mi><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>108</mn><mo>=</mo><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mn>7</mn><mi>d</mi></mrow></mfenced></math> <em><strong>(M1)(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong> </em>for attempting to use the arithmetic sequence term formula, <em><strong>A1</strong> </em>for both equations correct. Working for <em><strong>M1</strong> </em>and <em><strong>A1</strong> </em>can be found in parts (i) or (ii).</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>d</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn></math> (cups/day) <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Answer must be written as a positive value to award <em><strong>A1</strong></em>.</p>
<p><br><em><strong>OR</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>d</mi><mo>=</mo></mrow></mfenced><mo> </mo><mfrac><mrow><mn>115</mn><mo>.</mo><mn>5</mn><mo>-</mo><mn>108</mn></mrow><mn>5</mn></mfrac></math> <em><strong>(M1)(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong> </em>for attempting a calculation using the difference between term <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math> and term <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math>; <em><strong>A1</strong> </em>for a correct substitution.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>d</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>1</mn><mo>.</mo><mn>5</mn></math> (cups/day) <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 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><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo></mrow></mfenced><mo> </mo><mn>118</mn><mo>.</mo><mn>5</mn></math> (cups) <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempting to substitute their values into the term formula for arithmetic sequence equated to zero <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>=</mo><mn>118</mn><mo>.</mo><mn>5</mn><mo>+</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>×</mo><mfenced><mrow><mo>-</mo><mn>1</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>n</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>80</mn></math> days <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Follow through from part (a) only if their answer is positive.</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"><mfenced><mrow><msub><mi>t</mi><mn>5</mn></msub><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>625</mn><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>064</mn><mfenced><mrow><mn>5</mn><mo>-</mo><mn>1</mn></mrow></mfenced></msup></math> <em><strong>(M1)(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong> </em>for attempting to use the geometric sequence term formula; <em><strong>A1</strong> </em>for a correct substitution</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>801</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> The answer must be rounded to a whole number to award the final <em><strong>A1</strong></em>.</p>
<p><em><strong><br>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>S</mi><mn>10</mn></msub><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mfenced><mo>$</mo></mfenced><mo> </mo><mn>8390</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>8394</mn><mo>.</mo><mn>39</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>the total cost (of dog food) <em><strong> R1</strong></em></p>
<p>for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> years beginning in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2021</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> years before <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2031</mn></math> <em><strong> R1</strong></em></p>
<p><br><strong>OR</strong></p>
<p>the total cost (of dog food) <em><strong> R1</strong></em></p>
<p>from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2021</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2030</mn></math> (inclusive) <strong>OR</strong> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2021</mn></math> to (the start of) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2031</mn></math> <em><strong> R1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong><br>According to the model, the cost of dog food per year will eventually be too high to keep a dog.</p>
<p><strong>OR</strong><br>The model does not necessarily consider changes in inflation rate.</p>
<p><strong>OR</strong><br>The model is appropriate as long as inflation increases at a similar rate.</p>
<p><strong>OR</strong><br>The model does not account for changes in the amount of food the dog eats as it ages/becomes ill/stops growing.</p>
<p><strong>OR</strong><br>The model is appropriate since dog food bags can only be bought in discrete quantities. <em><strong> R1</strong></em></p>
<p><em><strong><br></strong></em><strong>Note:</strong> Accept reasonable answers commenting on the appropriateness of the model for the specific scenario. There should be a reference to the given context. A reference to the geometric model must be clear: either “model” is mentioned specifically, or other mathematical terms such as “increasing” or “discrete quantities” are seen. Do not accept a contextual argument in isolation, e.g. “The dog will eventually die”.</p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Parts (a) and (b) were mostly well answered, but some candidates ignored the context and did not give the number of dog food cups per day as a positive number. Most candidates considered geometric sequence in part (c) correctly, and used the correct formula for the nth term, although they used an incorrect value for n at times. Some candidates used the finance application incorrectly. The sum in part (d) was calculated correctly by some candidates, although many seemed unfamiliar with sigma notation and with calculating summations using GDC. In part (d), most candidates interpreted correctly that the sum represented the cost of dog food for 10 years but did not identify the specific 10-year period. Part (e) was not answered well – often candidates made very general and abstract statements devoid of any contextual references.</p>
<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>
<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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</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>Sophie is planning to buy a house. She needs to take out a mortgage for $120000. She is considering two possible options.</p>
<p style="padding-left: 90px;">Option 1: Repay the mortgage over 20 years, at an annual interest rate of 5%, compounded annually.</p>
<p style="padding-left: 90px;">Option 2: Pay $1000 every month, at an annual interest rate of 6%, compounded annually, until the loan is fully repaid.</p>
</div>
<div class="specification">
<p>Give a reason why Sophie might choose</p>
</div>
<div class="specification">
<p>Sophie decides to choose option 1. At the end of 10 years, the interest rate is changed to 7%, compounded annually.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the monthly repayment using option 1.</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>Calculate the total amount Sophie would pay, using option 1.</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>Calculate the number of months it will take to repay the mortgage using option 2.</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>Calculate the total amount Sophie would pay, using option 2.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>option 1.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>option 2.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your answer to part (a)(i) to calculate the amount remaining on her mortgage after the first 10 years.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence calculate her monthly repayment for the final 10 years.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>evidence of using Finance solver on GDC <em><strong> M1 </strong></em></p>
<p>Monthly payment = $785 ($784.60) <em><strong> A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="240 \times 785 = {\text{\$}}188000">
<mn>240</mn>
<mo>×</mo>
<mn>785</mn>
<mo>=</mo>
<mrow>
<mtext>$</mtext>
</mrow>
<mn>188000</mn>
</math></span> <em><strong> M1</strong></em><em><strong>A1</strong></em></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="N = 180.7">
<mi>N</mi>
<mo>=</mo>
<mn>180.7</mn>
</math></span> <em><strong> M1</strong></em><em><strong>A1</strong></em></p>
<p>It will take 181 months <em><strong> </strong></em><em><strong>A1</strong></em></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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="181 \times 1000 = {\text{\$ }}181000">
<mn>181</mn>
<mo>×</mo>
<mn>1000</mn>
<mo>=</mo>
<mrow>
<mtext>$ </mtext>
</mrow>
<mn>181000</mn>
</math></span> <em><strong> M1</strong></em><em><strong>A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The monthly repayment is lower, she might not be able to afford $1000 per month. <em><strong> R</strong></em><em><strong>1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the total amount to repay is lower. <em><strong> R</strong></em><em><strong>1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>$74400 (accept $74300) <em><strong> M</strong></em><em><strong>1A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Use of finance solver with <em>N</em> =120, <em>PV</em> = $74400<em>, I</em> = 7% <em><strong>A1 </strong></em></p>
<p>$855 (accept $854 − $856) <em><strong>A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.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.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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{27}}{{{x^2}}} - 16x,\,\,\,x \ne 0">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>27</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>−<!-- − --></mo>
<mn>16</mn>
<mi>x</mi>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>≠<!-- ≠ --></mo>
<mn>0</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <em>y</em> = <em>f </em>(<em>x</em>), for −4 ≤ <em>x</em> ≤ 3 and −50 ≤ <em>y</em> ≤ 100.</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>Use your graphic display calculator to find the zero of <em>f </em>(<em>x</em>).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the coordinates of the local minimum point.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the equation of the tangent to the graph of <em>y</em> = <em>f </em>(<em>x</em>) at the point (–2, 38.75).</p>
<p>Give your answer in the form <em>y</em> = <em>mx</em> + <em>c</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</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 src="data:image/png;base64,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"><em><strong>(A1)(A1)(A1)(A1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for axis labels and some indication of scale; accept <em>y</em> or <em>f</em>(<em>x</em>).</p>
<p>Use of graph paper is not required. If no scale is given, assume the given window for zero and minimum point.</p>
<p>Award <em><strong>(A1)</strong></em> for smooth curve with correct general shape.</p>
<p>Award <em><strong>(A1)</strong></em> for <em>x</em>-intercept closer to <em>y</em>-axis than to end of sketch.</p>
<p>Award <em><strong>(A1)</strong></em> for correct local minimum with <em>x</em>-coordinate closer to <em>y</em>-axis than end of sketch and <em>y</em>-coordinate less than half way to top of sketch.</p>
<p>Award at most <em><strong>(A1)</strong></em><em><strong>(A0)</strong></em><em><strong>(A1)</strong></em><em><strong>(A1)</strong></em> if the sketch intersects the <em>y</em>-axis or if the sketch curves away from the <em>y</em>-axis as<em> x</em> approaches zero.</p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1.19 (1.19055…) <em><strong> (A1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Accept an answer of (1.19, 0).</p>
<p>Do not follow through from an incorrect sketch.</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(−1.5, 36) <em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A0)(A1)</strong></em> if parentheses are omitted.</p>
<p>Accept <em>x</em> = −1.5, <em>y</em> = 36.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>y</em> = −9.25<em>x</em> + 20.3 (<em>y</em> = −9.25<em>x</em> + 20.25) <em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for −9.25<em>x</em>, award <em><strong>(A1)</strong></em> for +20.25, award a maximum of <em><strong>(A0)(A1)</strong></em> if answer is not an equation.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.iii.</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>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>In this question, give all answers to two decimal places.</strong></p>
<p>Bryan decides to purchase a new car with a price of €14 000, but cannot afford the full amount. The car dealership offers two options to finance a loan.</p>
<p><strong>Finance option A:</strong></p>
<p>A 6 year loan at a nominal annual interest rate of 14 % <strong>compounded quarterly</strong>. No deposit required and repayments are made each quarter.</p>
</div>
<div class="specification">
<p><strong>Finance option B:</strong></p>
<p>A 6 year loan at a nominal annual interest rate of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> % <strong>compounded monthly</strong>. Terms of the loan require a 10 % deposit and monthly repayments of €250.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the repayment made each quarter.</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>Find the total amount paid for the car.</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 interest paid on the loan.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the amount to be borrowed for this option.</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 annual interest rate, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State which option Bryan should choose. Justify your answer.</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>Bryan’s car depreciates at an annual rate of 25 % per year.</p>
<p>Find the value of Bryan’s car six years after it is purchased.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>N = 24<br>I % = 14<br>PV = −14000<br>FV = 0<br>P/Y = 4<br>C/Y = 4 <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong> </em>for an attempt to use a financial app in their technology, award <em><strong>A1</strong> </em>for all entries correct. Accept PV = 14000.</p>
<p>(€)871.82 <em><strong>A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>4 × 6 × 871.82 <em><strong>(M1)</strong></em></p>
<p>(€) 20923.68 <em><strong>A1</strong></em></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>20923.68 − 14000 <em><strong>(M1)</strong></em></p>
<p>(€) 6923.68 <em><strong>A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.9 × 14000 (= 14000 − 0.10 × 14000) <em><strong>M1</strong></em></p>
<p>(€) 12600.00 <em><strong>A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>N = 72</p>
<p>PV = 12600</p>
<p>PMT = −250</p>
<p>FV = 0</p>
<p>P/Y = 12</p>
<p>C/Y = 12 <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong></em> for an attempt to use a financial app in their technology, award <em><strong>A1</strong> </em>for all entries correct. Accept PV = −12600 provided PMT = 250.</p>
<p>12.56(%) <em><strong>A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>EITHER</strong></em></p>
<p>Bryan should choose Option A <em><strong>A1</strong></em></p>
<p>no deposit is required <em><strong>R1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>R1</strong></em> for stating that no deposit is required. Award <em><strong>A1</strong> </em>for the correct choice from that fact. Do not award <em><strong>R0A1</strong></em>.</p>
<p><em><strong>OR</strong></em></p>
<p>Bryan should choose Option B <em><strong>A1</strong></em></p>
<p>cost of Option A (6923.69) > cost of Option B (72 × 250 − 12600 = 5400) <em><strong>R1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>R1</strong> </em>for a correct comparison of costs. Award <em><strong>A1</strong></em> for the correct choice from that comparison. Do not award <em><strong>R0A1</strong></em>.</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="14\,000{\left( {1 - \frac{{25}}{{100}}} \right)^6}">
<mn>14</mn>
<mspace width="thinmathspace"></mspace>
<mn>000</mn>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mrow>
<mn>25</mn>
</mrow>
<mrow>
<mn>100</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>6</mn>
</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.<br>Award <em><strong>A1</strong> </em>for correct substitutions.</p>
<p>= (€)2491.70 <em><strong>A1</strong></em></p>
<p><em><strong>OR</strong></em></p>
<p>N = 6</p>
<p>I% = −25</p>
<p>PV = ±14 000</p>
<p>P/Y = 1</p>
<p>C/Y = 1 <em><strong>(A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>A1</strong> </em>for PV = ±14 000, <em><strong>M1</strong> </em>for other entries correct.</p>
<p>(€)2491.70 <em><strong>A1</strong></em></p>
<p><em><strong>[3 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;">
[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">a.iii.</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>
<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>
<br><hr><br><div class="specification">
<p>Paul wants to buy a car. He needs to take out a loan for $7000. The car salesman offers him a loan with an interest rate of 8%, compounded annually. Paul considers two options to repay the loan.</p>
<p style="padding-left: 180px;">Option 1: Pay $200 each month, until the loan is fully repaid</p>
<p style="padding-left: 180px;">Option 2: Make 24 equal monthly payments.</p>
</div>
<div class="specification">
<p>Use option 1 to calculate</p>
</div>
<div class="specification">
<p>Use option 2 to calculate</p>
</div>
<div class="specification">
<p>Give a reason why Paul might choose</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the number of months it will take for Paul to repay the loan.</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>the total amount that Paul has to pay.</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>the amount Paul pays each month.</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>the total amount that Paul has to pay.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>option 1.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>option 2.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>evidence of using Finance solver on GDC <em><strong>M1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N = 39.8">
<mi>N</mi>
<mo>=</mo>
<mn>39.8</mn>
</math></span> <em><strong>A1</strong></em></p>
<p>It will take 40 months <em><strong>A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="40 \times 200 = {\text{\$}}8000">
<mn>40</mn>
<mo>×</mo>
<mn>200</mn>
<mo>=</mo>
<mrow>
<mtext>$</mtext>
</mrow>
<mn>8000</mn>
</math></span> <em><strong>M1A1</strong></em></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>Monthly payment = $316 ($315.70) <em><strong>M1A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="24 \times 315.7 = {\text{\$}}7580{\text{ }}\left( {{\text{\$}}7576.80} \right)">
<mn>24</mn>
<mo>×</mo>
<mn>315.7</mn>
<mo>=</mo>
<mrow>
<mtext>$</mtext>
</mrow>
<mn>7580</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>$</mtext>
</mrow>
<mn>7576.80</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>M1A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The monthly repayment is lower, he might not be able to afford $316 per month. <em><strong>R1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the total amount to repay is lower. <em><strong>R1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.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.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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</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 $60.</p>
<p>The tea-shop’s profit increases by 10 % every week.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the café’s profit during the 11th week.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the café’s <strong>total</strong> profit for the first 12 weeks.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the tea-shop’s profit during the 11th week.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the tea-shop’s <strong>total</strong> profit for the first 12 weeks.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the <em>m</em>th week the tea-shop’s <strong>total</strong> profit exceeds the café’s <strong>total</strong> profit, for the first time since they both opened.</p>
<p>Find the value of <em>m</em>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>60 + 10 × 10 <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into the arithmetic sequence formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p>= ($) 160 <em><strong>(A1)(G3)</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{12}}{2}\left( {2 \times 60 + 11 \times 10} \right)">
<mfrac>
<mrow>
<mn>12</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>60</mn>
<mo>+</mo>
<mn>11</mn>
<mo>×</mo>
<mn>10</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting the arithmetic series formula, <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct substitution. Follow through from their first term and common difference in part (a).</p>
<p>= ($) 1380 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>60 × 1.1<sup>10</sup> <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting the geometric progression <em>n</em>th term formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p>= ($) 156 (155.624…) <em><strong>(A1)(G3)</strong></em></p>
<p><strong>Note:</strong> Accept the answer if it rounds correctly to 3 sf, as per the accuracy instructions.</p>
<p><em><strong>[3 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{60\left( {{{1.1}^{12}} - 1} \right)}}{{1.1 - 1}}">
<mfrac>
<mrow>
<mn>60</mn>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mrow>
<mn>1.1</mn>
</mrow>
<mrow>
<mn>12</mn>
</mrow>
</msup>
</mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mn>1.1</mn>
<mo>−</mo>
<mn>1</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting the geometric series formula, <strong><em>(A1)</em>(ft)</strong> for correct substitution. Follow through from part (c) for their first term and common ratio.</p>
<p>= ($)1280 (1283.05…) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{60\left( {{{1.1}^n} - 1} \right)}}{{1.1 - 1}} > \frac{n}{2}\left( {2 \times 60 + \left( {n - 1} \right) \times 10} \right)">
<mfrac>
<mrow>
<mn>60</mn>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mrow>
<mn>1.1</mn>
</mrow>
<mi>n</mi>
</msup>
</mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mn>1.1</mn>
<mo>−</mo>
<mn>1</mn>
</mrow>
</mfrac>
<mo>></mo>
<mfrac>
<mi>n</mi>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>60</mn>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>n</mi>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mn>10</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(M1)</strong></em><em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted geometric and arithmetic series formula with <em>n</em> (accept other variable for “<em>n</em>”), <em><strong>(M1)</strong></em> for comparing their expressions consistent with their part (b) and part (d).</p>
<p><strong>OR</strong></p>
<p><img 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"> <em><strong>(M1)</strong></em><em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for two curves with approximately correct shape drawn in the first quadrant, <em><strong>(M1)</strong></em> for one point of intersection with approximate correct position.</p>
<p>Accept alternative correct sketches, such as</p>
<p><img src="data:image/png;base64,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"></p>
<p>Award <em><strong>(M1)</strong></em> for a curve with approximate correct shape drawn in the 1<sup>st</sup> (or 4<sup>th</sup>) quadrant and all above (or below) the <em>x</em>-axis, <em><strong>(M1)</strong></em> for one point of intersection with the x-axis with approximate correct position.</p>
<p>17 <em><strong>(A2)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em></p>
<p><strong>Note:</strong> Follow through from parts (b) and (d).<br>An answer of 16 is incorrect. Award at most <em><strong>(M1)(M1)(A0)(A0)</strong></em> with working seen. Award <em><strong>(G0)</strong></em> if final answer is 16 without working seen.</p>
<p><em><strong>[4 marks]</strong></em></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>The admissions team at a new university are trying to predict the number of student applications they will receive each year.</p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> be the number of years that the university has been open. The admissions team collect the following data for the first two years.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>It is assumed that the number of students that apply to the university each year will follow a geometric sequence, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math>.</p>
</div>
<div class="specification">
<p>In the first year there were <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mn>380</mn></math> places at the university available for applicants. The admissions team announce that the number of places available will increase by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>600</mn></math> every year.</p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math> represent the number of places available at the university in year <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>.</p>
</div>
<div class="specification">
<p>For the first <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> years that the university is open, all places are filled. Students who receive a place each pay an <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>80</mn></math> acceptance fee.</p>
</div>
<div class="specification">
<p>When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>k</mi></math>, the number of places available will, for the first time, exceed the number of students applying.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the percentage increase in applications from the first year to the second year.</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 common ratio of the sequence.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of student applications the university expects to receive when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>11</mn></math>. Express your answer to the nearest integer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></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>Calculate the total amount of acceptance fees paid to the university in 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">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether, for all <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>></mo><mi>k</mi></math>, the university will have places available for all applicants. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</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"><mfrac><mrow><mn>12</mn><mo> </mo><mn>669</mn><mo>-</mo><mn>12</mn><mo> </mo><mn>300</mn></mrow><mrow><mn>12</mn><mo> </mo><mn>300</mn></mrow></mfrac><mo>×</mo><mn>100</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>%</mo></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><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>03</mn></math> <em><strong>A1</strong></em></p>
<p> <br><strong>Note:</strong> Follow through from part (a).</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></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"><mfenced><mrow><msub><mi>u</mi><mi>n</mi></msub><mo>=</mo></mrow></mfenced><mo> </mo><mn>12</mn><mo> </mo><mn>300</mn><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>03</mn><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>u</mi><mn>11</mn></msub><mo>=</mo></mrow></mfenced><mo> </mo><mn>12</mn><mo> </mo><mn>300</mn><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>03</mn><mn>10</mn></msup></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16530</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Answer must be to the nearest integer. Do not accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16500</mn></math>. </p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>v</mi><mi>n</mi></msub><mo>=</mo></mrow></mfenced><mo> </mo><mn>10380</mn><mo>+</mo><mn>600</mn><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>600</mn><mi>n</mi><mo>+</mo><mn>9780</mn></math> <em><strong>M1A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong></em> for substituting into arithmetic sequence formula, <em><strong>A1</strong></em> for correct substitution.</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"><mn>80</mn><mo>×</mo><mfrac><mn>10</mn><mn>2</mn></mfrac><mfenced><mrow><mn>2</mn><mfenced><mn>10380</mn></mfenced><mo>+</mo><mn>9</mn><mfenced><mn>600</mn></mfenced></mrow></mfenced></math> <em><strong>(M1)(M1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for multiplying by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math> and <em><strong>(M1)</strong></em> for substitution into sum of arithmetic sequence formula.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>10</mn><mo> </mo><mn>500</mn><mo> </mo><mn>000</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mo>$</mo><mn>10</mn><mo> </mo><mn>464</mn><mo> </mo><mn>000</mn></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo> </mo><mn>300</mn><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>03</mn><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup><mo><</mo><mn>10</mn><mo> </mo><mn>380</mn><mo>+</mo><mn>600</mn><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced></math> or equivalent <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating their expressions from parts (b) and (c).</p>
<p><br><strong>EITHER</strong></p>
<p>graph showing <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>12</mn><mo> </mo><mn>300</mn><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>03</mn><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>10</mn><mo> </mo><mn>380</mn><mo>+</mo><mn>600</mn><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p>graph showing <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>12</mn><mo> </mo><mn>300</mn><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>03</mn><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>-</mo><mfenced><mrow><mn>10</mn><mo> </mo><mn>380</mn><mo>+</mo><mn>600</mn><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p>list of values including, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi>u</mi><mrow><mi>n</mi><mo>=</mo></mrow></msub></mfenced><mo> </mo><mn>17537</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi>v</mi><mrow><mi>n</mi><mo>=</mo></mrow></msub></mfenced><mo> </mo><mn>17580</mn></math> <em><strong>(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>.</mo><mn>4953</mn><mo>…</mo></math> from graphical method or solving numerical equality <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for a valid attempt to solve.</p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>k</mi><mo>=</mo></mrow></mfenced><mn>13</mn></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>this will not guarantee enough places. <strong><em>A1</em></strong></p>
<p><strong>EITHER</strong></p>
<p>A written statement that <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub><mo>></mo><msub><mi>v</mi><mi>n</mi></msub></math>, with range of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>. <em><strong>R1 </strong></em></p>
<p><em>Example:</em> “when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>24</mn></math> (or greater), the number of applications will exceed the number of places again” (“<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub><mo>></mo><msub><mi>v</mi><mi>n</mi></msub><mo>,</mo><mo> </mo><mi>n</mi><mo>≥</mo><mn>24</mn></math>”).</p>
<p><strong><br>OR</strong></p>
<p>exponential growth will always exceed linear growth <em><strong>R1</strong></em></p>
<p><br><strong>Note:</strong> Accept an equivalent sketch. Do not award <em><strong>A1R0</strong></em>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>The percentage increase proved more difficult than anticipated, with many using an incorrect denominator. Part (b) was accessible with many candidates earning at least three marks. The expression for the general term of the arithmetic sequence was found in part (c). A surprising number of candidates found the acceptance fees paid in the tenth year, rather than the required total acceptance fees found in the first ten years. Most candidates were able to earn one mark for multiplying their value by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math>. In part (e), candidates were usually able to find the first point of intersection of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math>, but did not always realize the answer must be an integer. Part (f) required candidates to support their answer through a comparison of growth rates, or by finding a range of values/single data point where <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub><mo>></mo><msub><mi>v</mi><mi>n</mi></msub></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>></mo><mi>k</mi></math>. Though the answer "<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> is geometric, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math> is arithmetic", inferred some understanding, this was insufficient justification and required a description that went a little bit further. It is recommended that teachers provide opportunities for candidates to explore the more advanced features of the GDC. An inappropriate choice of calculator window made it difficult for candidates to assess and appreciate the behaviour of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math>.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The percentage increase proved more difficult than anticipated, with many using an incorrect denominator. Part (b) was accessible with many candidates earning at least three marks. The expression for the general term of the arithmetic sequence was found in part (c). A surprising number of candidates found the acceptance fees paid in the tenth year, rather than the required total acceptance fees found in the first ten years. Most candidates were able to earn one mark for multiplying their value by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math>. In part (e), candidates were usually able to find the first point of intersection of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math>, but did not always realize the answer must be an integer. Part (f) required candidates to support their answer through a comparison of growth rates, or by finding a range of values/single data point where <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub><mo>></mo><msub><mi>v</mi><mi>n</mi></msub></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>></mo><mi>k</mi></math>. Though the answer "<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> is geometric, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math> is arithmetic", inferred some understanding, this was insufficient justification and required a description that went a little bit further. It is recommended that teachers provide opportunities for candidates to explore the more advanced features of the GDC. An inappropriate choice of calculator window made it difficult for candidates to assess and appreciate the behaviour of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math>.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The percentage increase proved more difficult than anticipated, with many using an incorrect denominator. Part (b) was accessible with many candidates earning at least three marks. The expression for the general term of the arithmetic sequence was found in part (c). A surprising number of candidates found the acceptance fees paid in the tenth year, rather than the required total acceptance fees found in the first ten years. Most candidates were able to earn one mark for multiplying their value by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math>. In part (e), candidates were usually able to find the first point of intersection of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math>, but did not always realize the answer must be an integer. Part (f) required candidates to support their answer through a comparison of growth rates, or by finding a range of values/single data point where <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub><mo>></mo><msub><mi>v</mi><mi>n</mi></msub></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>></mo><mi>k</mi></math>. Though the answer "<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> is geometric, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math> is arithmetic", inferred some understanding, this was insufficient justification and required a description that went a little bit further. It is recommended that teachers provide opportunities for candidates to explore the more advanced features of the GDC. An inappropriate choice of calculator window made it difficult for candidates to assess and appreciate the behaviour of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math>.</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The percentage increase proved more difficult than anticipated, with many using an incorrect denominator. Part (b) was accessible with many candidates earning at least three marks. The expression for the general term of the arithmetic sequence was found in part (c). A surprising number of candidates found the acceptance fees paid in the tenth year, rather than the required total acceptance fees found in the first ten years. Most candidates were able to earn one mark for multiplying their value by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math>. In part (e), candidates were usually able to find the first point of intersection of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math>, but did not always realize the answer must be an integer. Part (f) required candidates to support their answer through a comparison of growth rates, or by finding a range of values/single data point where <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub><mo>></mo><msub><mi>v</mi><mi>n</mi></msub></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>></mo><mi>k</mi></math>. Though the answer "<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> is geometric, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math> is arithmetic", inferred some understanding, this was insufficient justification and required a description that went a little bit further. It is recommended that teachers provide opportunities for candidates to explore the more advanced features of the GDC. An inappropriate choice of calculator window made it difficult for candidates to assess and appreciate the behaviour of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math>.</p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The percentage increase proved more difficult than anticipated, with many using an incorrect denominator. Part (b) was accessible with many candidates earning at least three marks. The expression for the general term of the arithmetic sequence was found in part (c). A surprising number of candidates found the acceptance fees paid in the tenth year, rather than the required total acceptance fees found in the first ten years. Most candidates were able to earn one mark for multiplying their value by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math>. In part (e), candidates were usually able to find the first point of intersection of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math>, but did not always realize the answer must be an integer. Part (f) required candidates to support their answer through a comparison of growth rates, or by finding a range of values/single data point where <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub><mo>></mo><msub><mi>v</mi><mi>n</mi></msub></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>></mo><mi>k</mi></math>. Though the answer "<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> is geometric, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math> is arithmetic", inferred some understanding, this was insufficient justification and required a description that went a little bit further. It is recommended that teachers provide opportunities for candidates to explore the more advanced features of the GDC. An inappropriate choice of calculator window made it difficult for candidates to assess and appreciate the behaviour of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math>.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The percentage increase proved more difficult than anticipated, with many using an incorrect denominator. Part (b) was accessible with many candidates earning at least three marks. The expression for the general term of the arithmetic sequence was found in part (c). A surprising number of candidates found the acceptance fees paid in the tenth year, rather than the required total acceptance fees found in the first ten years. Most candidates were able to earn one mark for multiplying their value by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math>. In part (e), candidates were usually able to find the first point of intersection of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math>, but did not always realize the answer must be an integer. Part (f) required candidates to support their answer through a comparison of growth rates, or by finding a range of values/single data point where <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub><mo>></mo><msub><mi>v</mi><mi>n</mi></msub></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>></mo><mi>k</mi></math>. Though the answer "<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> is geometric, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math> is arithmetic", inferred some understanding, this was insufficient justification and required a description that went a little bit further. It is recommended that teachers provide opportunities for candidates to explore the more advanced features of the GDC. An inappropriate choice of calculator window made it difficult for candidates to assess and appreciate the behaviour of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math>.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The percentage increase proved more difficult than anticipated, with many using an incorrect denominator. Part (b) was accessible with many candidates earning at least three marks. The expression for the general term of the arithmetic sequence was found in part (c). A surprising number of candidates found the acceptance fees paid in the tenth year, rather than the required total acceptance fees found in the first ten years. Most candidates were able to earn one mark for multiplying their value by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math>. In part (e), candidates were usually able to find the first point of intersection of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math>, but did not always realize the answer must be an integer. Part (f) required candidates to support their answer through a comparison of growth rates, or by finding a range of values/single data point where <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub><mo>></mo><msub><mi>v</mi><mi>n</mi></msub></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>></mo><mi>k</mi></math>. Though the answer "<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> is geometric, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math> is arithmetic", inferred some understanding, this was insufficient justification and required a description that went a little bit further. It is recommended that teachers provide opportunities for candidates to explore the more advanced features of the GDC. An inappropriate choice of calculator window made it difficult for candidates to assess and appreciate the behaviour of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math>.</p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The percentage increase proved more difficult than anticipated, with many using an incorrect denominator. Part (b) was accessible with many candidates earning at least three marks. The expression for the general term of the arithmetic sequence was found in part (c). A surprising number of candidates found the acceptance fees paid in the tenth year, rather than the required total acceptance fees found in the first ten years. Most candidates were able to earn one mark for multiplying their value by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math>. In part (e), candidates were usually able to find the first point of intersection of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math>, but did not always realize the answer must be an integer. Part (f) required candidates to support their answer through a comparison of growth rates, or by finding a range of values/single data point where <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub><mo>></mo><msub><mi>v</mi><mi>n</mi></msub></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>></mo><mi>k</mi></math>. Though the answer "<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> is geometric, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math> is arithmetic", inferred some understanding, this was insufficient justification and required a description that went a little bit further. It is recommended that teachers provide opportunities for candidates to explore the more advanced features of the GDC. An inappropriate choice of calculator window made it difficult for candidates to assess and appreciate the behaviour of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>n</mi></msub></math>.</p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>Boris recorded the number of daylight hours on the first day of each month in a northern hemisphere town.</p>
<p>This data was plotted onto a scatter diagram. The points were then joined by a smooth curve, with minimum point <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>8</mn><mo>)</mo></math> and maximum point <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>6</mn><mo>,</mo><mo> </mo><mn>16</mn><mo>)</mo></math> as shown in the following diagram.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>Let the curve in the diagram be <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is the time, measured in months, since Boris first recorded these values.</p>
<p>Boris thinks that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> might be modelled by a quadratic function.</p>
</div>
<div class="specification">
<p>Paula thinks that a better model is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo> </mo><mi>cos</mi><mo>(</mo><mi>b</mi><mi>t</mi><mo>)</mo><mo>+</mo><mi>d</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>≥</mo><mn>0</mn></math>, for specific values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>.</p>
</div>
<div class="specification">
<p>For Paula’s model, use the diagram to write down</p>
</div>
<div class="specification">
<p>The true maximum number of daylight hours was <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn></math> hours and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math> minutes.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down one reason why a quadratic function would not be a good model for the number of hours of daylight per day, across a number of years.</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>the amplitude.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the period.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the equation of the principal axis.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise find the equation of this model in the form:</p>
<p style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo> </mo><mi>cos</mi><mo>(</mo><mi>b</mi><mi>t</mi><mo>)</mo><mo>+</mo><mi>d</mi></math></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the first year of the model, find the length of time when there are more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> hours and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> minutes of daylight per day.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the percentage error in the maximum number of daylight hours Boris recorded in the diagram.</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><strong>EITHER<br></strong>annual cycle for daylight length <em><strong>R1</strong></em></p>
<p><strong>OR<br></strong>there is a minimum length for daylight (cannot be negative) <em><strong>R1</strong></em></p>
<p><strong>OR<br></strong>a quadratic could not have a maximum and a minimum or equivalent <em><strong>R1</strong></em></p>
<p><br><strong>Note:</strong> Do not accept “Paula's model is better”.</p>
<p><br><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></strong> <em><strong>A1</strong></em></p>
<p><br><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math></strong> <em><strong>A1</strong></em></p>
<p><br><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>12</mn></math></strong> <em><strong>A1A1</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>A1</strong></em> “<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo></math> (a constant)” and <em><strong>A1</strong> </em>for that constant being <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mo>-</mo><mn>4</mn><mo> </mo><mi>cos</mi><mo>(</mo><mn>30</mn><mi>t</mi><mo>)</mo><mo>+</mo><mn>12</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mo>-</mo><mn>4</mn><mo> </mo><mi>cos</mi><mo>(</mo><mo>-</mo><mn>30</mn><mi>t</mi><mo>)</mo><mo>+</mo><mn>12</mn></math> <em><strong>A1A1A1</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>A1</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>30</mn></math> (or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mn>30</mn></math>), <em><strong>A1</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><mn>4</mn></math>, and <em><strong>A1</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>12</mn></math>. Award at most <em><strong>A1A1A0</strong></em> if extra terms are seen or form is incorrect. Award at most <em><strong>A1A1A0</strong></em> if <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> is used instead of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>.</p>
<p> </p>
<p><em><strong>[3 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"><mn>10</mn><mo>.</mo><mn>5</mn><mo>=</mo><mo>-</mo><mn>4</mn><mo> </mo><mi>cos</mi><mo>(</mo><mn>30</mn><mi>t</mi><mo>)</mo><mo>+</mo><mn>12</mn></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>t</mi><mn>1</mn></msub><mo>=</mo><mn>2</mn><mo>.</mo><mn>26585</mn><mo>…</mo><mo>,</mo><mo> </mo><mo> </mo><msub><mi>t</mi><mn>2</mn></msub><mo>=</mo><mn>9</mn><mo>.</mo><mn>73414</mn><mo>…</mo></math> <em><strong>(A1)(A1)</strong></em></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>t</mi><mn>1</mn></msub><mo>=</mo><mfrac><mn>1</mn><mn>30</mn></mfrac><msup><mi>cos</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfrac><mn>3</mn><mn>8</mn></mfrac></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>t</mi><mn>2</mn></msub><mo>=</mo><mn>12</mn><mo>-</mo><msub><mi>t</mi><mn>1</mn></msub></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>.</mo><mn>73414</mn><mo>…</mo><mo>-</mo><mn>2</mn><mo>.</mo><mn>26585</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>47</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>7</mn><mo>.</mo><mn>46828</mn><mo>…</mo></mrow></mfenced></math> months (<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>622356</mn><mo>…</mo></math> years) <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>M1A1A1A0</strong></em> for an unsupported answer of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>46</mn></math>. If there is only one intersection point, award <em><strong>M1A1A0A0</strong></em>.</p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">d.</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>16</mn><mo>-</mo><mfenced><mrow><mn>16</mn><mo>+</mo><mstyle displaystyle="true"><mfrac><mn>14</mn><mn>60</mn></mfrac></mstyle></mrow></mfenced></mrow><mrow><mn>16</mn><mo>+</mo><mstyle displaystyle="true"><mfrac><mn>14</mn><mn>60</mn></mfrac></mstyle></mrow></mfrac></mfenced><mo>×</mo><mn>100</mn><mo>%</mo></math> <em><strong>(M1)(M1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>M1</strong> </em>for correct values and absolute value signs, <em><strong>M1</strong> </em>for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>×</mo><mn>100</mn></math>.</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>.</mo><mn>44</mn><mo>%</mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>1</mn><mo>.</mo><mn>43737</mn><mo>…</mo><mo>%</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Part (a) indicated a lack of understanding of quadratic functions and the cyclical nature of daylight hours. Some candidates seemed to understand the limitations of a quadratic model but were not always able to use appropriate mathematical language to explain the limitations clearly.</p>
<p>In part (b), many candidates struggled to write down the amplitude, period, and equation of the principal axis.</p>
<p>In part (c), very few candidates recognized that it would be a negative cosine graph here and most did not know how to find the “<em>b</em>” value even if they had originally found the period in part (b). Some candidates used the regression features in their GDC to find the equation of the model; this is outside the SL syllabus but is a valid approach and earned full credit.</p>
<p>In part (d), very few candidates were awarded “follow through” marks in this part. Some substituted 10.5 into their equation rather that equate their equation to 10.5 and attempt to solve it using their GDC to graph the equations or using the “solver” function.</p>
<p>Part (e) was perhaps the best answered part in this question. However, due to premature rounding, many candidates did not gain full marks. A common error was to write the true number of daylight hours as 16.14.</p>
<p> </p>
<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>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</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>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>
<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>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em> one correct value</p>
<p>−0.453620, 6.14210</p>
<p><em>a</em> = −0.454, <em>b</em> = 6.14 <em><strong>A1A1 N3</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>correct substitution <em><strong> (A1)</strong></em></p>
<p><em>eg </em>−0.454 ln 3.57 + 6.14</p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg </em> ln <em>y</em> = 5.56484</p>
<p>261.083 (260.409 from 3 sf)</p>
<p><em>y</em> = 261, (<em>y</em> = 260 from 3sf) <em><strong>A1 N3</strong></em></p>
<p><strong>Note:</strong> If no working shown, award <em><strong>N1</strong></em> for 5.56484.<br>If no working shown, award <em><strong>N2</strong> </em>for ln <em>y</em> = 5.56484.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>valid approach for expressing ln <em>y</em> in terms of ln <em>x</em> <em><strong>(M1)</strong></em></p>
<p><em>eg </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,y = {\text{ln}}\,\left( {k{x^n}} \right),\,\,{\text{ln}}\,\left( {k{x^n}} \right) = a\,{\text{ln}}\,x + b">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>y</mi>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>x</mi>
<mi>n</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>x</mi>
<mi>n</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</math></span></p>
<p>correct application of addition rule for logs <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,k + {\text{ln}}\,\left( {{x^n}} \right)">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>+</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mi>n</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>correct application of exponent rule for logs <em><strong>A1</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,k + n\,{\text{ln}}\,x">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>+</mo>
<mi>n</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
</math></span></p>
<p>comparing one term with regression equation (check <em><strong>FT</strong></em>) <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = a,\,\,b = {\text{ln}}\,k">
<mi>n</mi>
<mo>=</mo>
<mi>a</mi>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>b</mi>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
</math></span></p>
<p>correct working for <em>k</em> <strong>(A1)</strong></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,k = 6.14210,\,\,\,k = {e^{6.14210}}">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>=</mo>
<mn>6.14210</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mn>6.14210</mn>
</mrow>
</msup>
</mrow>
</math></span></p>
<p>465.030</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = - 0.454,\,\,k = 465">
<mi>n</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.454</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>=</mo>
<mn>465</mn>
</math></span> (464 from 3sf) <em><strong>A1A1 N2N2</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{e^{{\text{ln}}\,y}} = {e^{a\,{\text{ln}}\,x + b}}">
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>y</mi>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</mrow>
</msup>
</mrow>
</math></span></p>
<p>correct use of exponent laws for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{e^{a\,{\text{ln}}\,x + b}}">
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</mrow>
</msup>
</mrow>
</math></span> <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{e^{a\,{\text{ln}}\,x}} \times {e^b}">
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mi>e</mi>
<mi>b</mi>
</msup>
</mrow>
</math></span></p>
<p>correct application of exponent rule for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a\,{\text{ln}}\,x">
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
</math></span> <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,{x^a}">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>x</mi>
<mi>a</mi>
</msup>
</mrow>
</math></span></p>
<p>correct equation in<em> y</em> <em><strong>A1</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = {x^a} \times {e^b}">
<mi>y</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mi>a</mi>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mi>e</mi>
<mi>b</mi>
</msup>
</mrow>
</math></span></p>
<p>comparing one term with equation of model (check <em><strong>FT</strong></em>) <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = {e^b},\,\,n = a">
<mi>k</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>e</mi>
<mi>b</mi>
</msup>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>n</mi>
<mo>=</mo>
<mi>a</mi>
</math></span></p>
<p>465.030</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = - 0.454,\,\,k = 465">
<mi>n</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.454</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>=</mo>
<mn>465</mn>
</math></span> (464 from 3sf) <em><strong>A1A1 N2N2</strong></em></p>
<p> </p>
<p><strong>METHOD 3</strong></p>
<p>valid approach for expressing ln <em>y</em> in terms of ln <em>x</em> (seen anywhere) <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,y = {\text{ln}}\,\left( {k{x^n}} \right),\,\,{\text{ln}}\,\left( {k{x^n}} \right) = a\,{\text{ln}}\,x + b">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>y</mi>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>x</mi>
<mi>n</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>x</mi>
<mi>n</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</math></span></p>
<p>correct application of exponent rule for logs (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,\left( {{x^a}} \right) + b">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mi>a</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>b</mi>
</math></span></p>
<p>correct working for <em>b</em> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = {\text{ln}}\,\left( {{e^b}} \right)">
<mi>b</mi>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>e</mi>
<mi>b</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>correct application of addition rule for logs <em><strong>A1</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,\left( {{e^b}{x^a}} \right)">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>e</mi>
<mi>b</mi>
</msup>
</mrow>
<mrow>
<msup>
<mi>x</mi>
<mi>a</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>comparing one term with equation of model (check <em><strong>FT</strong></em>) <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = {e^b},\,\,n = a">
<mi>k</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>e</mi>
<mi>b</mi>
</msup>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>n</mi>
<mo>=</mo>
<mi>a</mi>
</math></span></p>
<p>465.030</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = - 0.454,\,\,k = 465">
<mi>n</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.454</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
<mo>=</mo>
<mn>465</mn>
</math></span> (464 from 3sf) <em><strong>A1A1 N2N2</strong></em></p>
<p><em><strong>[7 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>Abdallah owns a plot of land, near the river Nile, in the form of a quadrilateral ABCD.</p>
<p>The lengths of the sides are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AB}} = {\text{40 m, BC}} = {\text{115 m, CD}} = {\text{60 m, AD}} = {\text{84 m}}">
<mrow>
<mtext>AB</mtext>
</mrow>
<mo>=</mo>
<mrow>
<mtext>40 m, BC</mtext>
</mrow>
<mo>=</mo>
<mrow>
<mtext>115 m, CD</mtext>
</mrow>
<mo>=</mo>
<mrow>
<mtext>60 m, AD</mtext>
</mrow>
<mo>=</mo>
<mrow>
<mtext>84 m</mtext>
</mrow>
</math></span> and angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{B\hat AD}} = 90^\circ ">
<mrow>
<mrow>
<mi mathvariant="normal">B</mi>
<mrow>
<mover>
<mi mathvariant="normal">A</mi>
<mo stretchy="false">^<!-- ^ --></mo>
</mover>
</mrow>
<mi mathvariant="normal">D</mi>
</mrow>
</mrow>
<mo>=</mo>
<msup>
<mn>90</mn>
<mo>∘<!-- ∘ --></mo>
</msup>
</math></span>.</p>
<p>This information is shown on the diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.24.18.png" alt="N17/5/MATSD/SP2/ENG/TZ0/03"></p>
</div>
<div class="specification">
<p>The formula that the ancient Egyptians used to estimate the area of a quadrilateral ABCD is</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{area}} = \frac{{({\text{AB}} + {\text{CD}})({\text{AD}} + {\text{BC}})}}{4}">
<mrow>
<mtext>area</mtext>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<mtext>AB</mtext>
</mrow>
<mo>+</mo>
<mrow>
<mtext>CD</mtext>
</mrow>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mrow>
<mtext>AD</mtext>
</mrow>
<mo>+</mo>
<mrow>
<mtext>BC</mtext>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
<mn>4</mn>
</mfrac>
</math></span>.</p>
<p>Abdallah uses this formula to estimate the area of his plot of land.</p>
</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="{\text{BD}} = 93{\text{ m}}">
<mrow>
<mtext>BD</mtext>
</mrow>
<mo>=</mo>
<mn>93</mn>
<mrow>
<mtext> m</mtext>
</mrow>
</math></span> correct to the nearest metre.</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 angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{B\hat CD}}">
<mrow>
<mrow>
<mi mathvariant="normal">B</mi>
<mrow>
<mover>
<mi mathvariant="normal">C</mi>
<mo stretchy="false">^</mo>
</mover>
</mrow>
<mi mathvariant="normal">D</mi>
</mrow>
</mrow>
</math></span>.</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 area of ABCD.</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>Calculate Abdallah’s estimate for the area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the percentage error in Abdallah’s estimate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.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 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="{\text{B}}{{\text{D}}^2} = {40^2} + {84^2}">
<mrow>
<mtext>B</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>D</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mn>40</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<msup>
<mn>84</mn>
<mn>2</mn>
</msup>
</mrow>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into Pythagoras.</p>
<p>Accept correct substitution into cosine rule.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{BD}} = 93.0376 \ldots ">
<mrow>
<mtext>BD</mtext>
</mrow>
<mo>=</mo>
<mn>93.0376</mn>
<mo>…</mo>
</math></span> <strong><em>(A1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 93">
<mo>=</mo>
<mn>93</mn>
</math></span> <strong><em>(AG)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Both the rounded and unrounded value must be seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p> </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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\cos C = \frac{{{{115}^2} + {{60}^2} - {{93}^2}}}{{2 \times 115 \times 60}}{\text{ }}({93^2} = {115^2} + {60^2} - 2 \times 115 \times 60 \times \cos C)">
<mi>cos</mi>
<mo></mo>
<mi>C</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msup>
<mrow>
<mn>115</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<msup>
<mrow>
<mn>60</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mrow>
<msup>
<mrow>
<mn>93</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>115</mn>
<mo>×</mo>
<mn>60</mn>
</mrow>
</mfrac>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mn>93</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mn>115</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<msup>
<mn>60</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>2</mn>
<mo>×</mo>
<mn>115</mn>
<mo>×</mo>
<mn>60</mn>
<mo>×</mo>
<mi>cos</mi>
<mo></mo>
<mi>C</mi>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution into cosine 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=" = 53.7^\circ {\text{ }}(53.6679 \ldots ^\circ )">
<mo>=</mo>
<msup>
<mn>53.7</mn>
<mo>∘</mo>
</msup>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>53.6679</mn>
<msup>
<mo>…</mo>
<mo>∘</mo>
</msup>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></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="\frac{1}{2}(40)(84) + \frac{1}{2}(115)(60)\sin (53.6679 \ldots )">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo stretchy="false">(</mo>
<mn>40</mn>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mn>84</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo stretchy="false">(</mo>
<mn>115</mn>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mn>60</mn>
<mo stretchy="false">)</mo>
<mi>sin</mi>
<mo></mo>
<mo stretchy="false">(</mo>
<mn>53.6679</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(M1)(M1)(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into right-angle triangle area. Award <strong><em>(M1) </em></strong>for substitution into area of triangle formula and <strong><em>(A1)</em>(ft) </strong>for correct substitution.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 4460{\text{ }}{{\text{m}}^2}{\text{ }}(4459.30 \ldots {\text{ }}{{\text{m}}^2})">
<mo>=</mo>
<mn>4460</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>4459.30</mn>
<mo>…</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Follow through from part (b).</p>
<p> </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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{(40 + 60)(84 + 115)}}{4}">
<mfrac>
<mrow>
<mo stretchy="false">(</mo>
<mn>40</mn>
<mo>+</mo>
<mn>60</mn>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mn>84</mn>
<mo>+</mo>
<mn>115</mn>
<mo stretchy="false">)</mo>
</mrow>
<mn>4</mn>
</mfrac>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution in the area formula used by ‘Ancient Egyptians’.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 4980{\text{ }}{{\text{m}}^2}{\text{ }}(4975{\text{ }}{{\text{m}}^2})">
<mo>=</mo>
<mn>4980</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>4975</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)(G2)</em></strong></p>
<p> </p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\frac{{4975 - 4459.30 \ldots }}{{4459.30 \ldots }}} \right| \times 100">
<mrow>
<mo>|</mo>
<mrow>
<mfrac>
<mrow>
<mn>4975</mn>
<mo>−</mo>
<mn>4459.30</mn>
<mo>…</mo>
</mrow>
<mrow>
<mn>4459.30</mn>
<mo>…</mo>
</mrow>
</mfrac>
</mrow>
<mo>|</mo>
</mrow>
<mo>×</mo>
<mn>100</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into percentage error formula.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 11.6{\text{ }}(\% ){\text{ }}(11.5645 \ldots )">
<mo>=</mo>
<mn>11.6</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi mathvariant="normal">%</mi>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>11.5645</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Follow through from parts (c) and (d)(i).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.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.</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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>On her first day in a hospital, Kiri receives <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> milligrams (mg) of a therapeutic drug. The amount of the drug Kiri receives increases by the same amount, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
<mi>d</mi>
</math></span>, each day. On the seventh day, she receives 21 mg of the drug, and on the eleventh day she receives 29 mg.</p>
</div>
<div class="specification">
<p>Kiri receives the drug for 30 days.</p>
</div>
<div class="specification">
<p>Ted is also in a hospital and on his first day he receives a 20 mg antibiotic injection. The amount of the antibiotic Ted receives decreases by 50 % each day. On the second day, Ted receives a 10 mg antibiotic injection, on the third day he receives 5 mg, and so on.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an equation, in terms 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> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
<mi>d</mi>
</math></span>, for the amount of the drug that she receives on the seventh day.</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 an equation, in terms 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> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
<mi>d</mi>
</math></span>, for the amount of the drug that she receives on the eleventh day.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
<mi>d</mi>
</math></span> and the 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>.</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 amount of the drug, in mg, that she receives.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the amount of antibiotic, in mg, that Ted receives on the fifth day.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The daily amount of antibiotic Ted receives will first be less than 0.06 mg on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> th day. 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">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the total amount of antibiotic, in mg, that Ted receives during the first <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> days.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(amount taken in the 7th day): <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_1} + 6d = 21">
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>+</mo>
<mn>6</mn>
<mi>d</mi>
<mo>=</mo>
<mn>21</mn>
</math></span> <strong><em>(A1)</em></strong></p>
<p><strong>Note:</strong> Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_1} + \left( {7 - 1} \right)d = 21">
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>7</mn>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mi>d</mi>
<mo>=</mo>
<mn>21</mn>
</math></span>. The equations do not need to be simplified. They should be given in terms 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> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
<mi>d</mi>
</math></span> for the marks to be awarded.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(amount taken in the 11th day): <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_1} + 10d = 29">
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>+</mo>
<mn>10</mn>
<mi>d</mi>
<mo>=</mo>
<mn>29</mn>
</math></span> <strong><em>(A1)</em></strong></p>
<p><strong>Note:</strong> Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_1} + \left( {11 - 1} \right)d = 29">
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>11</mn>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mi>d</mi>
<mo>=</mo>
<mn>29</mn>
</math></span>. The equations do not need to be simplified. They should be given in terms 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> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
<mi>d</mi>
</math></span> for the marks to be awarded.</p>
<p><em><strong>[1 mark]</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="{u_1}">
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> =) 9 <strong><em>(A1)</em>(ft)</strong></p>
<p>(<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
<mi>d</mi>
</math></span> =) 2 <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from part (a), but only if values are positive and <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> < 21.</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_{30}} = } \right)\frac{{30}}{2}\left( {2 \times 9 + \left( {30 - 1} \right) \times 2} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mn>30</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
</mrow>
<mo>)</mo>
</mrow>
<mfrac>
<mrow>
<mn>30</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>9</mn>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>30</mn>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(M1)</em></strong><strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for substitution in the sum of an arithmetic sequence formula; <strong><em>(A1)</em>(ft)</strong> for their correct substitution.</p>
<p>1140 (mg) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p><strong>Note:</strong> Follow through from their <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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
<mi>d</mi>
</math></span> from part (b).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>20 × (0.5)<sup>4</sup> <strong><em>(M1)</em></strong><strong><em>(A1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for substitution into the geometric sequence formula, <strong><em>(A1)</em></strong> for correct substitution.</p>
<p>1.25 (mg) <strong><em>(A1)</em><em>(G3)</em></strong></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="20 \times {\left( {0.5} \right)^{k - 1}} < 0.06">
<mn>20</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.5</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mi>k</mi>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
<mo><</mo>
<mn>0.06</mn>
</math></span> <strong><em>(M1)(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for correct substitution into the geometric sequence formula; <strong><em>(M1)</em></strong> for comparing their expression to 0.06. Accept an equation instead of inequality.</p>
<p>(<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> =) 10 (10th day) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p><strong>Note:</strong> Follow through from part (d)(i), if 0 < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> < 1. Follow through answers must be rounded up for final mark.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.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{{20\left( {1 - {{0.5}^{10}}} \right)}}{{1 - 0.5}}">
<mfrac>
<mrow>
<mn>20</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mrow>
<msup>
<mrow>
<mn>0.5</mn>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mn>0.5</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)(A1)(ft)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for substitution into sum of a geometric sequence formula, <strong><em>(A1)(ft)</em></strong> for correct substitution.<br> Follow through from their <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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> in part (d)(i), if 0 < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> < 1. Follow through from their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> in part (d)(ii) but only if <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> is a positive integer.</p>
<p>40.0 (39.9609…) (mg) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.iii.</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>
<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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A water container is made in the shape of a cylinder with internal height <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> cm and internal base radius <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_08.31.01.png" alt="N16/5/MATSD/SP2/ENG/TZ0/06"></p>
<p>The water container has no top. The inner surfaces of the container are to be coated with a water-resistant material.</p>
</div>
<div class="specification">
<p>The volume of the water container is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.5{\text{ }}{{\text{m}}^3}">
<mn>0.5</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>The water container is designed so that the area to be coated is minimized.</p>
</div>
<div class="specification">
<p>One can of water-resistant material coats a surface area of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2000{\text{ c}}{{\text{m}}^2}">
<mn>2000</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a formula for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>, the surface area to be coated.</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>Express this volume in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{c}}{{\text{m}}^3}"> <mrow> <mtext>c</mtext> </mrow> <mrow> <msup> <mrow> <mtext>m</mtext> </mrow> <mn>3</mn> </msup> </mrow> </math></span>.</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>Write down, in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span>, an equation for the volume of this water container.</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>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + \frac{{1\,000\,000}}{r}"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </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>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}A}}{{{\text{d}}r}}"> <mfrac> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>A</mi> </mrow> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>r</mi> </mrow> </mfrac> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your answer to part (e), find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> which minimizes <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of this minimum area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the least number of cans of water-resistant material that will coat the area in part (g).</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</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="(A = ){\text{ }}\pi {r^2} + 2\pi rh"> <mo stretchy="false">(</mo> <mi>A</mi> <mo>=</mo> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mi>h</mi> </math></span> <strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for either <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {r^2}"> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </math></span> <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi rh"> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mi>h</mi> </math></span> seen. Award <strong><em>(A1) </em></strong>for two correct terms added together.</p>
<p> </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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="500\,000"> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </math></span> <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Units <strong>not </strong>required.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></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="500\,000 = \pi {r^2}h"> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mi>h</mi> </math></span> <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {r^2}h"> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mi>h</mi> </math></span> equating to their part (b).</p>
<p>Do not accept unless <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V = \pi {r^2}h"> <mi>V</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mi>h</mi> </math></span> is explicitly defined as their part (b).</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + 2\pi r\left( {\frac{{500\,000}}{{\pi {r^2}}}} \right)"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> <strong><em>(A1)</em>(ft)<em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{{500\,000}}{{\pi {r^2}}}}"> <mrow> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </mrow> </math></span> seen.</p>
<p>Award <strong><em>(M1) </em></strong>for correctly substituting <strong>only</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{{500\,000}}{{\pi {r^2}}}}"> <mrow> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </mrow> </math></span> into a <strong>correct </strong>part (a).</p>
<p>Award <strong><em>(A1)</em>(ft)<em>(M1) </em></strong>for rearranging part (c) to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi rh = \frac{{500\,000}}{r}"> <mi>π</mi> <mi>r</mi> <mi>h</mi> <mo>=</mo> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span> and substituting for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi rh"> <mi>π</mi> <mi>r</mi> <mi>h</mi> </math></span> in expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + \frac{{1\,000\,000}}{r}"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span> <strong><em>(AG)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>The conclusion, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + \frac{{1\,000\,000}}{r}"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span>, must be consistent with their working seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p>Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{10^6}"> <mrow> <msup> <mn>10</mn> <mn>6</mn> </msup> </mrow> </math></span> as equivalent to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{1\,000\,000}"> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> </math></span>.</p>
<p> </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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi r - \frac{{{\text{1}}\,{\text{000}}\,{\text{000}}}}{{{r^2}}}"> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mo>−</mo> <mfrac> <mrow> <mrow> <mtext>1</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> </mrow> <mrow> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </math></span> <strong><em>(A1)(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi r"> <mn>2</mn> <mi>π</mi> <mi>r</mi> </math></span>, <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{{r^2}}}"> <mfrac> <mn>1</mn> <mrow> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r^{ - 2}}"> <mrow> <msup> <mi>r</mi> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </math></span>, <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - {\text{1}}\,{\text{000}}\,{\text{000}}"> <mo>−</mo> <mrow> <mtext>1</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> </math></span>.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi r - \frac{{1\,000\,000}}{{{r^2}}} = 0"> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mo>−</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for equating their part (e) to zero.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r^3} = \frac{{1\,000\,000}}{{2\pi }}"> <mrow> <msup> <mi>r</mi> <mn>3</mn> </msup> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </math></span> <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \sqrt[3]{{\frac{{1\,000\,000}}{{2\pi }}}}"> <mi>r</mi> <mo>=</mo> <mroot> <mrow> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mn>3</mn> </mroot> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for isolating <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span>.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>sketch of derivative function <strong><em>(M1)</em></strong></p>
<p>with its zero indicated <strong><em>(M1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(r = ){\text{ }}54.2{\text{ }}({\text{cm}}){\text{ }}(54.1926 \ldots )"> <mo stretchy="false">(</mo> <mi>r</mi> <mo>=</mo> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mn>54.2</mn> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mrow> <mtext>cm</mtext> </mrow> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mn>54.1926</mn> <mo>…</mo> <mo stretchy="false">)</mo> </math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {(54.1926 \ldots )^2} + \frac{{1\,000\,000}}{{(54.1926 \ldots )}}"> <mi>π</mi> <mrow> <mo stretchy="false">(</mo> <mn>54.1926</mn> <mo>…</mo> <msup> <mo stretchy="false">)</mo> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>54.1926</mn> <mo>…</mo> <mo stretchy="false">)</mo> </mrow> </mfrac> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution of their part (f) into the given equation.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 27\,700{\text{ }}({\text{c}}{{\text{m}}^2}){\text{ }}(27\,679.0 \ldots )"> <mo>=</mo> <mn>27</mn> <mspace width="thinmathspace"></mspace> <mn>700</mn> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mrow> <mtext>c</mtext> </mrow> <mrow> <msup> <mrow> <mtext>m</mtext> </mrow> <mn>2</mn> </msup> </mrow> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mn>27</mn> <mspace width="thinmathspace"></mspace> <mn>679.0</mn> <mo>…</mo> <mo stretchy="false">)</mo> </math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{27\,679.0 \ldots }}{{2000}}"> <mfrac> <mrow> <mn>27</mn> <mspace width="thinmathspace"></mspace> <mn>679.0</mn> <mo>…</mo> </mrow> <mrow> <mn>2000</mn> </mrow> </mfrac> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for dividing their part (g) by 2000.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 13.8395 \ldots "> <mo>=</mo> <mn>13.8395</mn> <mo>…</mo> </math></span> <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes: </strong>Follow through from part (g).</p>
<p> </p>
<p>14 (cans) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Final <strong><em>(A1) </em></strong>awarded for rounding up their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="13.8395 \ldots "> <mn>13.8395</mn> <mo>…</mo> </math></span> to the next integer.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">h.</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>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>The Tower of Pisa is well known worldwide for how it leans.</p>
<p>Giovanni visits the Tower and wants to investigate how much it is leaning. He draws a diagram showing a non-right triangle, ABC.</p>
<p>On Giovanni’s diagram the length of AB is 56 m, the length of BC is 37 m, and angle ACB is 60°. AX is the perpendicular height from A to BC.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>Giovanni’s tourist guidebook says that the actual horizontal displacement of the Tower, BX, is 3.9 metres.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Giovanni’s diagram to show that angle ABC, the angle at which the Tower is leaning relative to the<br>horizontal, is 85° to the nearest degree.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Giovanni's diagram to calculate the length of AX.</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>Use Giovanni's diagram to find the length of BX, the horizontal displacement of the Tower.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the percentage error on Giovanni’s diagram.</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>Giovanni adds a point D to his diagram, such that BD = 45 m, and another triangle is formed.</p>
<p><img 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"></p>
<p>Find the angle of elevation of A from D.</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="\frac{{{\text{sin BAC}}}}{{37}} = \frac{{{\text{sin 60}}}}{{56}}"> <mfrac> <mrow> <mrow> <mtext>sin BAC</mtext> </mrow> </mrow> <mrow> <mn>37</mn> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mtext>sin 60</mtext> </mrow> </mrow> <mrow> <mn>56</mn> </mrow> </mfrac> </math></span> <em><strong>(M1)</strong></em><em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting the sine rule formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p>angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}\mathop {\text{A}}\limits^ \wedge {\text{C}}"> <mrow> <mtext>B</mtext> </mrow> <mover> <mrow> <mtext>A</mtext> </mrow> <mo>∧</mo> </mover> <mo></mo> <mrow> <mtext>C</mtext> </mrow> </math></span> = 34.9034…° <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A0)</strong></em> if unrounded answer does not round to 35. Award <em><strong>(G2)</strong></em> if 34.9034… seen without working.</p>
<p>angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}\mathop {\text{B}}\limits^ \wedge {\text{C}}"> <mrow> <mtext>A</mtext> </mrow> <mover> <mrow> <mtext>B</mtext> </mrow> <mo>∧</mo> </mover> <mo></mo> <mrow> <mtext>C</mtext> </mrow> </math></span> = 180 − (34.9034… + 60) <em><strong>(M1)</strong></em></p>
<p>Note: Award <em><strong>(M1)</strong></em> for subtracting their angle BAC + 60 from 180.</p>
<p>85.0965…° <em><strong>(A1)</strong></em></p>
<p>85° <em><strong>(AG)</strong></em></p>
<p><strong>Note:</strong> Both the unrounded and rounded value must be seen for the final <em><strong>(A1)</strong></em> to be awarded. If the candidate rounds 34.9034...° to 35° while substituting to find angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}\mathop {\text{B}}\limits^ \wedge {\text{C}}"> <mrow> <mtext>A</mtext> </mrow> <mover> <mrow> <mtext>B</mtext> </mrow> <mo>∧</mo> </mover> <mo></mo> <mrow> <mtext>C</mtext> </mrow> </math></span>, the final <em><strong>(A1)</strong></em> can be awarded but <strong>only</strong> if both 34.9034...° and 35° are seen.<br>If 85 is used as part of the workings, award at most <em><strong>(M1)(A0)(A0)(M0)(A0)(AG)</strong></em>. This is the reverse process and not accepted.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>sin 85… × 56 <em><strong>(M1)</strong></em></p>
<p>= 55.8 (55.7869…) (m) <em><strong>(A1)</strong></em><em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in trigonometric ratio.</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="\sqrt {{{56}^2} - 55.7869{ \ldots ^2}} ">
<msqrt>
<mrow>
<msup>
<mrow>
<mn>56</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>55.7869</mn>
<mrow>
<msup>
<mo>…</mo>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the Pythagoras theorem formula. Follow through from part (a)(ii).</p>
<p><strong>OR</strong></p>
<p>cos(85) × 56 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in trigonometric ratio.</p>
<p>= 4.88 (4.88072…) (m) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Accept 4.73 (4.72863…) (m) from using their 3 s.f answer. Accept equivalent methods.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\frac{{4.88 - 3.9}}{{3.9}}} \right| \times 100">
<mrow>
<mo>|</mo>
<mrow>
<mfrac>
<mrow>
<mn>4.88</mn>
<mo>−</mo>
<mn>3.9</mn>
</mrow>
<mrow>
<mn>3.9</mn>
</mrow>
</mfrac>
</mrow>
<mo>|</mo>
</mrow>
<mo>×</mo>
<mn>100</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into the percentage error formula.</p>
<p>= 25.1 (25.1282) (%) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a)(iii).</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="{\text{ta}}{{\text{n}}^{ - 1}}\left( {\frac{{55.7869 \ldots }}{{40.11927 \ldots }}} \right)">
<mrow>
<mtext>ta</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>n</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>55.7869</mn>
<mo>…</mo>
</mrow>
<mrow>
<mn>40.11927</mn>
<mo>…</mo>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for their 40.11927… seen. Award <em><strong>(M1)</strong></em> for correct substitution into trigonometric ratio.</p>
<p><strong>OR</strong></p>
<p>(37 − 4.88072…)<sup>2</sup> + 55.7869…<sup>2</sup></p>
<p>(AC =) 64.3725…</p>
<p>64.3726…<sup>2</sup> + 8<sup>2</sup> − 2 × 8 × 64.3726… × cos120</p>
<p>(AD =) 68.7226…</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{sin 120}}}}{{68.7226 \ldots }} = \frac{{{\text{sin A}}\mathop {\text{D}}\limits^ \wedge {\text{C}}}}{{64.3725 \ldots }}">
<mfrac>
<mrow>
<mrow>
<mtext>sin 120</mtext>
</mrow>
</mrow>
<mrow>
<mn>68.7226</mn>
<mo>…</mo>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mtext>sin A</mtext>
</mrow>
<mover>
<mrow>
<mtext>D</mtext>
</mrow>
<mo>∧</mo>
</mover>
<mo></mo>
<mrow>
<mtext>C</mtext>
</mrow>
</mrow>
<mrow>
<mn>64.3725</mn>
<mo>…</mo>
</mrow>
</mfrac>
</math></span> <em><strong>(A1)</strong></em><strong>(ft)<em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for their correct values seen, <em><strong>(M1)</strong></em> for correct substitution into the sine formula.</p>
<p>= 54.3° (54.2781…°) <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></p>
<p><strong>Note:</strong> Follow through from part (a). Accept equivalent methods.</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.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">a.iii.</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 following table shows the average body weight, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>, and the average weight of the brain, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>, of seven species of mammal. Both measured in kilograms (kg).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_10.57.27.png" alt="M17/5/MATSD/SP2/ENG/TZ1/01"></p>
</div>
<div class="specification">
<p>The average body weight of grey wolves is 36 kg.</p>
</div>
<div class="specification">
<p>In fact, the average weight of the brain of grey wolves is 0.120 kg.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the range of the average body weights for these seven species of mammal.</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>For the data from these seven species calculate <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>, the Pearson’s product–moment correlation coefficient;</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>For the data from these seven species describe the correlation between the average body weight and the average weight of the brain.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>, in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = mx + c">
<mi>y</mi>
<mo>=</mo>
<mi>m</mi>
<mi>x</mi>
<mo>+</mo>
<mi>c</mi>
</math></span>.</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>Use your regression line to estimate the average weight of the brain of grey wolves.</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 percentage error in your estimate in part (d).</p>
<div class="marks">[2]</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="529 - 3">
<mn>529</mn>
<mo>−</mo>
<mn>3</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 526{\text{ (kg)}}">
<mo>=</mo>
<mn>526</mn>
<mrow>
<mtext> (kg)</mtext>
</mrow>
</math></span> <strong><em>(A1)(G2)</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.922{\text{ }}(0.921857 \ldots )">
<mn>0.922</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>0.921857</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(very) strong, positive <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (b)(i).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 0.000986x + 0.0923{\text{ }}(y = 0.000985837 \ldots x + 0.0923391…)">
<mi>y</mi>
<mo>=</mo>
<mn>0.000986</mn>
<mi>x</mi>
<mo>+</mo>
<mn>0.0923</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>y</mi>
<mo>=</mo>
<mn>0.000985837</mn>
<mo>…</mo>
<mi>x</mi>
<mo>+</mo>
<mn>0.0923391</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.000986x">
<mn>0.000986</mn>
<mi>x</mi>
</math></span>, <strong><em>(A1) </em></strong>for 0.0923.</p>
<p>Award a maximum of <strong><em>(A1)(A0) </em></strong>if the answer is not an equation in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = mx + c">
<mi>y</mi>
<mo>=</mo>
<mi>m</mi>
<mi>x</mi>
<mo>+</mo>
<mi>c</mi>
</math></span>.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.000985837 \ldots (36) + 0.0923391 \ldots ">
<mn>0.000985837</mn>
<mo>…</mo>
<mo stretchy="false">(</mo>
<mn>36</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>0.0923391</mn>
<mo>…</mo>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substituting 36 into their equation.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.128{\text{ (kg) }}\left( {0.127829 \ldots {\text{ (kg)}}} \right)">
<mn>0.128</mn>
<mrow>
<mtext> (kg) </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.127829</mn>
<mo>…</mo>
<mrow>
<mtext> (kg)</mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(</em></strong><strong><em>A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (c). The final <strong><em>(A1) </em></strong>is awarded only if their answer is positive.</p>
<p> </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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\frac{{0.127829 \ldots - 0.120}}{{0.120}}} \right| \times 100">
<mrow>
<mo>|</mo>
<mrow>
<mfrac>
<mrow>
<mn>0.127829</mn>
<mo>…</mo>
<mo>−</mo>
<mn>0.120</mn>
</mrow>
<mrow>
<mn>0.120</mn>
</mrow>
</mfrac>
</mrow>
<mo>|</mo>
</mrow>
<mo>×</mo>
<mn>100</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for their correct substitution into percentage error formula.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6.52{\text{ }}(\% ){\text{ }}\left( {6.52442...{\text{ }}(\% )} \right)">
<mn>6.52</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi mathvariant="normal">%</mi>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>6.52442...</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi mathvariant="normal">%</mi>
<mo stretchy="false">)</mo>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (d). Do not accept a negative answer.</p>
<p> </p>
<p><strong><em>[2 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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</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>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>
<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>valid approach to find maxima <em><strong>(M1)</strong></em></p>
<p><em>eg</em> one correct value of <em>x<sub>k</sub></em>, sketch of <em>f</em></p>
<p>any two correct consecutive values of <em>x<sub>k</sub></em> <em><strong>(A1)(A1)</strong></em></p>
<p><em>eg x</em><sub>1</sub> = 1, <em>x</em><sub>2</sub> = 5</p>
<p><em>a</em> = 4 <em><strong>A1 N3</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing the sequence <em>x</em><sub>1,<sup> </sup></sub> <em>x</em><sub>2</sub><sub>,<sup> </sup></sub> <em>x</em><sub>3, …,</sub> <em>x</em><sub>n</sub> is arithmetic <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <em>d</em> = 4</p>
<p>correct expression for sum<em> <strong>(A1)</strong><br></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{n}{2}\left( {2\left( 1 \right) + 4\left( {n - 1} \right)} \right)">
<mfrac>
<mi>n</mi>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>4</mn>
<mrow>
<mo>(</mo>
<mrow>
<mi>n</mi>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>valid attempt to solve for <em>n</em> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> graph, 2<em>n</em><sup>2</sup> − <em>n</em> − 861 = 0</p>
<p><em>n</em> = 21 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[4 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><strong>Give your answers to parts (b), (c) and (d) to the nearest whole number.</strong></p>
<p>Harinder has 14 000 US Dollars (USD) to invest for a period of five years. He has two options of how to invest the money.</p>
<p><strong>Option A:</strong> Invest the full amount, in USD, in a fixed deposit account in an American bank.</p>
<p>The account pays a nominal annual interest rate of <em>r </em>% , <strong>compounded yearly</strong>, for the five years. The bank manager says that this will give Harinder a return of 17<em> </em>500 USD.</p>
</div>
<div class="specification">
<p><strong>Option B:</strong> Invest the full amount, in Indian Rupees (INR), in a fixed deposit account in an Indian bank. The money must be converted from USD to INR before it is invested.</p>
<p>The exchange rate is 1 USD = 66.91 INR.</p>
</div>
<div class="specification">
<p>The account in the Indian bank pays a nominal annual interest rate of 5.2 % <strong>compounded monthly</strong>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of <em>r</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>Calculate 14 000 USD in INR.</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 amount of this investment, in INR, in this account after five years.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Harinder chose option B. At the end of five years, Harinder converted this investment back to USD. The exchange rate, at that time, was 1 USD = 67.16 INR.</p>
<p>Calculate how much <strong>more</strong> money, in USD, Harinder earned by choosing option B instead of option A.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</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="17500 = 14000{\left( {1 + \frac{r}{{100}}} \right)^5}">
<mn>17500</mn>
<mo>=</mo>
<mn>14000</mn>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<mi>r</mi>
<mrow>
<mn>100</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>5</mn>
</msup>
</mrow>
</math></span> <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into the compound interest formula, <em><strong>(A1)</strong></em> for correct substitution. Award at most <em><strong>(M1)(A0)</strong></em> if not equated to 17500.</p>
<p>OR</p>
<p><em>N</em> = 5</p>
<p><em>PV</em> = ±14000</p>
<p><em>FV</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \mp ">
<mo>∓</mo>
</math></span>17500</p>
<p><em>P</em>/<em>Y</em> = 1</p>
<p><em>C</em>/<em>Y</em> = 1 <em><strong>(A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <em>C</em>/<em>Y</em> = 1 seen, <em><strong>(M1)</strong></em> for <strong>all</strong> other correct entries. <em>FV</em> and <em>PV</em> must have opposite signs.</p>
<p>= 4.56 (%) (4.56395… (%)) <em><strong>(A1) (G3)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>14000 × 66.91 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for multiplying 14000 by 66.91.</p>
<p>936740 (INR) <em><strong>(A1) (G2)</strong></em></p>
<p><strong>Note:</strong> Answer must be given to the nearest whole number.</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="936740 \times {\left( {1 + \frac{{5.2}}{{12 \times 100}}} \right)^{12 \times 5}}">
<mn>936740</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<mrow>
<mn>5.2</mn>
</mrow>
<mrow>
<mn>12</mn>
<mo>×</mo>
<mn>100</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mn>12</mn>
<mo>×</mo>
<mn>5</mn>
</mrow>
</msup>
</mrow>
</math></span> <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into the compound interest formula, <em><strong>(A1)</strong></em><strong>(ft)</strong> for their correct substitution.</p>
<p><strong>OR </strong></p>
<p><em>N</em> = 60</p>
<p><em>I</em>% = 5.2</p>
<p><em>PV</em> = ±936740</p>
<p><em>P</em>/<em>Y</em>= 12</p>
<p><em>C</em>/<em>Y</em>= 12 <em><strong>(A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <em>C</em>/<em>Y </em>= 12 seen, <em><strong>(M1)</strong></em> for <strong>all</strong> other correct entries.</p>
<p><strong>OR </strong></p>
<p><em>N</em> = 5</p>
<p><em>I</em>% = 5.2</p>
<p><em>PV</em> = ±936740</p>
<p><em>P</em>/<em>Y</em>= 1</p>
<p><em>C</em>/<em>Y</em>= 12 <em><strong>(A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <em>C</em>/<em>Y </em>= 12 seen, <em><strong>(M1)</strong></em> for <strong>all</strong> other correct entries</p>
<p>= 1214204 (INR) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G3)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (b). Answer must be given to the nearest whole number.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1214204}}{{67.16}}">
<mfrac>
<mrow>
<mn>1214204</mn>
</mrow>
<mrow>
<mn>67.16</mn>
</mrow>
</mfrac>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for dividing their (c) by 67.16.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{{1214204}}{{67.16}}} \right) - 17500 = 579">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>1214204</mn>
</mrow>
<mrow>
<mn>67.16</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mn>17500</mn>
<mo>=</mo>
<mn>579</mn>
</math></span> (USD) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong> (G3)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for finding the difference between their conversion and 17500. Answer must be given to the nearest whole number. Follow through from part (c).</p>
<p><em><strong>[3 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;">
[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>
<br><hr><br><div class="specification">
<p><strong>Give your answers in parts (a), (d)(i), (e) and (f) to the nearest dollar.</strong></p>
<p>Daisy invested <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>37</mn><mo> </mo><mn>000</mn></math> Australian dollars (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AUD</mtext></math>) in a fixed deposit account with an annual interest rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>4</mn><mo>%</mo></math> compounded <strong>quarterly</strong>.</p>
</div>
<div class="specification">
<p>After <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> months, the amount of money in the fixed deposit account has appreciated to more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo> </mo><mn>000</mn><mo> </mo><mtext>AUD</mtext></math>.</p>
</div>
<div class="specification">
<p>Daisy is saving to purchase a new apartment. The price of the apartment is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn><mo> </mo><mn>000</mn><mo> </mo><mtext>AUD</mtext></math>.</p>
<p>Daisy makes an initial payment of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>%</mo></math> and takes out a loan to pay the rest.</p>
</div>
<div class="specification">
<p>The loan is for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> years, compounded monthly, with equal monthly payments of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1700</mn><mo> </mo><mtext>AUD</mtext></math> made by Daisy at the end of each month.</p>
</div>
<div class="specification">
<p>For this loan, find</p>
</div>
<div class="specification">
<p>After <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> years of paying off this loan, Daisy decides to pay the <strong>remainder</strong> in one final payment.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of Daisy’s investment after <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</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 minimum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>∈</mo><mi mathvariant="normal">ℕ</mi></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>Write down the amount of the loan.</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>the amount of interest paid by Daisy.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the annual interest rate of the loan.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the amount of Daisy’s final payment.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find how much money Daisy saved by making one final payment 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">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<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><mn>2</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>V</mi><mo>=</mo><mo>-</mo><mn>37</mn><mo> </mo><mn>000</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>%</mo><mo>=</mo><mn>6</mn><mo>.</mo><mn>4</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>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, award<em><strong> A1</strong></em> for all entries correct.<br><br><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>8</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>V</mi><mo>=</mo><mo>-</mo><mn>37</mn><mo> </mo><mn>000</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>%</mo><mo>=</mo><mn>6</mn><mo>.</mo><mn>4</mn></math><br><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> <em><strong>(M1)(A1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>M1</strong></em> for an attempt to use a financial app in their technology, award<em><strong> A1</strong></em> for all entries correct.</p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>V</mi><mo>=</mo><mn>37</mn><mo> </mo><mn>000</mn><mo>×</mo><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mrow><mn>6</mn><mo>.</mo><mn>4</mn></mrow><mrow><mn>100</mn><mo>×</mo><mn>4</mn></mrow></mfrac></mrow></mfenced><mrow><mn>4</mn><mo>×</mo><mn>2</mn></mrow></msup></math> <em><strong>(M1)(A1)</strong></em></p>
<p><br><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><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>42</mn><mo> </mo><mn>010</mn><mo> </mo><mtext>AUD</mtext></math><em><strong> A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)(A1)A0</strong></em> for unsupported <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>42009</mn><mo>.</mo><mn>87</mn></math>.</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>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>V</mi><mo>=</mo><mo>-</mo><mn>37</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>50</mn><mo> </mo><mn>000</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>%</mo><mo>=</mo><mn>6</mn><mo>.</mo><mn>4</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>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, award<em><strong> A1</strong></em> for all entries correct. The final mark can still be awarded for the correct number of months (multiple of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math>).<br><br><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>V</mi><mo>=</mo><mo>-</mo><mn>37</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>50</mn><mo> </mo><mn>000</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>%</mo><mo>=</mo><mn>6</mn><mo>.</mo><mn>4</mn></math><br><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> <em><strong>(M1)(A1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>M1</strong></em> for an attempt to use a financial app in their technology, award<em><strong> A1</strong></em> for all entries correct.</p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo> </mo><mn>000</mn><mo><</mo><mn>37</mn><mo> </mo><mn>000</mn><mo>×</mo><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mrow><mn>6</mn><mo>.</mo><mn>4</mn></mrow><mrow><mn>100</mn><mo>×</mo><mn>4</mn></mrow></mfrac></mrow></mfenced><mrow><mn>4</mn><mo>×</mo><mi>n</mi></mrow></msup></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo> </mo><mn>000</mn><mo><</mo><mn>37</mn><mo> </mo><mn>000</mn><mo>×</mo><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mrow><mn>6</mn><mo>.</mo><mn>4</mn></mrow><mrow><mn>100</mn><mo>×</mo><mn>4</mn></mrow></mfrac></mrow></mfenced><mi>n</mi></msup></math> <em><strong>(M1)(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong></em> for the correct inequality, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo> </mo><mn>000</mn></math> and substituted compound interest formula. Allow an equation. Award <em><strong>A1</strong></em> for correct substitution.</p>
<p> </p>
<p><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>4</mn><mo>.</mo><mn>74</mn><mo> </mo><mo> </mo><mfenced><mtext>years</mtext></mfenced><mo> </mo><mfenced><mrow><mn>4</mn><mo>.</mo><mn>74230</mn><mo>…</mo></mrow></mfenced></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>18</mn><mo>.</mo><mn>9692</mn><mo>…</mo><mo> </mo><mo> </mo><mfenced><mtext>quarters</mtext></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>57</mn></math> months<em><strong> A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong></em> for rounding their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> to the correct number of months. The final answer must be a multiple of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math>. Follow through within this part.</p>
<p><em><strong><br>[4 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>150</mn><mo> </mo><mn>000</mn><mo> </mo><mtext>AUD</mtext></math><em><strong> A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</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"><mn>120</mn><mo>×</mo><mn>1700</mn><mo>-</mo><mn>150</mn><mo> </mo><mn>000</mn></math><em><strong> (M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>54</mn><mo> </mo><mn>000</mn><mo> </mo><mtext>AUD</mtext></math><em><strong> A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</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>P</mi><mi>V</mi><mo>=</mo><mo>-</mo><mn>150</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><mn>1700</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 or an attempt to use an annuity formula or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>V</mi><mo>=</mo><mn>0</mn></math> seen. If a compound interest formula is equated to zero, award <em><strong>M1</strong></em>, otherwise award <em><strong>M0</strong></em> for a substituted compound interest formula. <br>Award <em><strong>A1</strong></em> for all entries correct in financial app or correct substitution in annuity formula, but award <em><strong>A0</strong></em> for a substituted compound interest formula. Follow through marks in part (d)(ii) are contingent on working seen.</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>46</mn><mo> </mo><mfenced><mo>%</mo></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mn>6</mn><mo>.</mo><mn>45779</mn><mo>…</mo></mrow></mfenced></math><em><strong> A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.ii.</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>60</mn></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>46</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>6</mn><mo>.</mo><mn>45779</mn><mo>…</mo></mrow></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>V</mi><mo>=</mo><mo>-</mo><mn>150</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><mn>1700</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 or an attempt to use an annuity formula. Award <em><strong>(M0)</strong></em> for a substituted compound interest formula. Award <em><strong>A1</strong></em> for all entries correct. Follow through marks in part (e) are contingent on working seen.</p>
<p> </p>
<p><em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>V</mi><mo>=</mo><mn>86973</mn><mo> </mo><mtext>AUD</mtext></math> A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>204</mn><mo> </mo><mn>000</mn><mo>-</mo><mfenced><mrow><mn>60</mn><mo>×</mo><mn>1700</mn><mo>+</mo><mn>86973</mn></mrow></mfenced></math> </strong></em><strong>OR </strong><em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>204</mn><mo> </mo><mn>000</mn><mo>-</mo><mn>188</mn><mo> </mo><mn>973</mn></math></strong></em><strong> </strong><em><strong>(M1)(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong></em> for <em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo>×</mo><mn>1700</mn></math></strong></em>. Award <em><strong>M1</strong></em> for subtracting their <em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>60</mn><mo>×</mo><mn>1700</mn><mo>+</mo><mn>86973</mn></mrow></mfenced></math> </strong></em>from their <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>204</mn><mo> </mo><mn>000</mn><mo>)</mo></math>. Award at most <em><strong>M1M0</strong></em> for their <em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>204</mn><mo> </mo><mn>000</mn><mo>-</mo><mfenced><mrow><mn>60</mn><mo>×</mo><mn>1700</mn></mrow></mfenced></math></strong></em> or <em><strong>M0M0</strong></em> for their <em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>204</mn><mo> </mo><mn>000</mn><mo>-</mo><mfenced><mn>86973</mn></mfenced></math></strong></em>. Follow through from parts (d)(i) and (e). Follow through marks in part (f) are contingent on working seen.</p>
<p> </p>
<p><em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>15</mn><mo> </mo><mn>027</mn><mo> </mo><mtext>AUD</mtext></math> A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">f.</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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</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>
<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>correct substitution into infinite sum <em><strong>(A1)</strong></em><br><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="200 = \frac{4}{{1 - r}}"> <mn>200</mn> <mo>=</mo> <mfrac> <mn>4</mn> <mrow> <mn>1</mn> <mo>−</mo> <mi>r</mi> </mrow> </mfrac> </math></span></p>
<p><em>r </em>= 0.98 (exact) <em><strong>A1 N2</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>correct substitution <em><strong>(A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4\left( {1 - {{0.98}^8}} \right)}}{{1 - 0.98}}"> <mfrac> <mrow> <mn>4</mn> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow> <msup> <mrow> <mn>0.98</mn> </mrow> <mn>8</mn> </msup> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mn>0.98</mn> </mrow> </mfrac> </math></span></p>
<p>29.8473</p>
<p>29.8 <em><strong>A1 N2</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>attempt to set up inequality (accept equation) <em><strong>(M1)</strong></em><br><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4\left( {1 - {{0.98}^n}} \right)}}{{1 - 0.98}} > 163,\,\,\frac{{4\left( {1 - {{0.98}^n}} \right)}}{{1 - 0.98}} = 163"> <mfrac> <mrow> <mn>4</mn> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow> <msup> <mrow> <mn>0.98</mn> </mrow> <mi>n</mi> </msup> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mn>0.98</mn> </mrow> </mfrac> <mo>></mo> <mn>163</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mfrac> <mrow> <mn>4</mn> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow> <msup> <mrow> <mn>0.98</mn> </mrow> <mi>n</mi> </msup> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mn>0.98</mn> </mrow> </mfrac> <mo>=</mo> <mn>163</mn> </math></span></p>
<p>correct inequality for <em>n</em> (accept equation) or crossover values <em><strong>(A1)</strong></em><br><em>eg n</em> > 83.5234, <em>n</em> = 83.5234, <em>S</em><sub><em>83</em></sub> = 162.606 <strong>and </strong><em>S</em><sub><em>84</em></sub> = 163.354</p>
<p><em>n</em> = 84 <em><strong>A1 N1</strong></em></p>
<p><strong><em>[3 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>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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>3800 m <strong><em>(A1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3000 + (n - 1)400{\text{ m}}">
<mn>3000</mn>
<mo>+</mo>
<mo stretchy="false">(</mo>
<mi>n</mi>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mn>400</mn>
<mrow>
<mtext> m</mtext>
</mrow>
</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="2600 + 400n{\text{ m}}">
<mn>2600</mn>
<mo>+</mo>
<mn>400</mn>
<mi>n</mi>
<mrow>
<mtext> m</mtext>
</mrow>
</math></span> <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution into arithmetic sequence formula, <strong><em>(A1) </em></strong>for correct substitution.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></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="3000 + (k - 1)400 > 42195">
<mn>3000</mn>
<mo>+</mo>
<mo stretchy="false">(</mo>
<mi>k</mi>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mn>400</mn>
<mo>></mo>
<mn>42195</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for their correct inequality. Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3 + (k - 1)0.4 > 42.195">
<mn>3</mn>
<mo>+</mo>
<mo stretchy="false">(</mo>
<mi>k</mi>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mn>0.4</mn>
<mo>></mo>
<mn>42.195</mn>
</math></span>.</p>
<p>Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = ">
<mo>=</mo>
</math></span> <strong>OR </strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \geqslant ">
<mo>⩾</mo>
</math></span>. Award <strong><em>(M0) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3000 + (k - 1)400 > 42.195">
<mn>3000</mn>
<mo>+</mo>
<mo stretchy="false">(</mo>
<mi>k</mi>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mn>400</mn>
<mo>></mo>
<mn>42.195</mn>
</math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(k = ){\text{ }}99">
<mo stretchy="false">(</mo>
<mi>k</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>99</mn>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (a)(ii), but only if <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> is a positive integer.</p>
<p> </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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{50}}{2}\left( {2 \times 3000 + (50 - 1)(400)} \right)">
<mfrac>
<mrow>
<mn>50</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>3000</mn>
<mo>+</mo>
<mo stretchy="false">(</mo>
<mn>50</mn>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mn>400</mn>
<mo stretchy="false">)</mo>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(M1)(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution into sum of an arithmetic series formula, <strong><em>(A1)</em>(ft) </strong>for correct substitution.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="640\,000{\text{ m}}">
<mn>640</mn>
<mspace width="thinmathspace"></mspace>
<mn>000</mn>
<mrow>
<mtext> m</mtext>
</mrow>
</math></span> <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="640\,000">
<mn>640</mn>
<mspace width="thinmathspace"></mspace>
<mn>000</mn>
</math></span> seen.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 640{\text{ km}}">
<mo>=</mo>
<mn>640</mn>
<mrow>
<mtext> km</mtext>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for correctly converting their answer in metres to km; this can be awarded independently from previous marks.</p>
<p> </p>
<p><strong><em>OR</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{50}}{2}\left( {2 \times 3 + (50 - 1)(0.4)} \right)">
<mfrac>
<mrow>
<mn>50</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>3</mn>
<mo>+</mo>
<mo stretchy="false">(</mo>
<mn>50</mn>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mn>0.4</mn>
<mo stretchy="false">)</mo>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(M1)(A1)</em>(ft)<em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution into sum of an arithmetic series formula, <strong><em>(A1)</em>(ft) </strong>for correct substitution, <strong><em>(A1) </em></strong>for correctly converting 3000 m and 400 m into km.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 640{\text{ km}}">
<mo>=</mo>
<mn>640</mn>
<mrow>
<mtext> km</mtext>
</mrow>
</math></span> <strong><em>(A1)(G3)</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7500 \times {1.2^{5 - 1}}">
<mn>7500</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>1.2</mn>
<mrow>
<mn>5</mn>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span> <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution into geometric series 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=" = 15\,600{\text{ m }}(15\,552{\text{ m}})">
<mo>=</mo>
<mn>15</mn>
<mspace width="thinmathspace"></mspace>
<mn>600</mn>
<mrow>
<mtext> m </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>15</mn>
<mspace width="thinmathspace"></mspace>
<mn>552</mn>
<mrow>
<mtext> m</mtext>
</mrow>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)(G3)</em></strong></p>
<p><strong><em>OR</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7.5 \times {1.2^{5 - 1}}">
<mn>7.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>1.2</mn>
<mrow>
<mn>5</mn>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span> <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution into geometric series 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=" = 15.6{\text{ km}}">
<mo>=</mo>
<mn>15.6</mn>
<mrow>
<mtext> km</mtext>
</mrow>
</math></span> <strong><em>(A1)(G3)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{7500({{1.2}^{12}} - 1)}}{{1.2 - 1}}">
<mfrac>
<mrow>
<mn>7500</mn>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mrow>
<mn>1.2</mn>
</mrow>
<mrow>
<mn>12</mn>
</mrow>
</msup>
</mrow>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
</mrow>
<mrow>
<mn>1.2</mn>
<mo>−</mo>
<mn>1</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for substitution into sum of a geometric series formula, <strong><em>(A1) </em></strong>for correct substitutions. Follow through from their ratio (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>) in part (d). If <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r < 1">
<mi>r</mi>
<mo><</mo>
<mn>1</mn>
</math></span> (distance does not increase) or the final answer is unrealistic (<em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = 20">
<mi>r</mi>
<mo>=</mo>
<mn>20</mn>
</math></span>), do not award the final <em><strong>(A1)</strong></em>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 297\,000{\text{ m }}(296\,853 \ldots {\text{ m}},{\text{ }}297{\text{ km}})">
<mo>=</mo>
<mn>297</mn>
<mspace width="thinmathspace"></mspace>
<mn>000</mn>
<mrow>
<mtext> m </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>296</mn>
<mspace width="thinmathspace"></mspace>
<mn>853</mn>
<mo>…</mo>
<mrow>
<mtext> m</mtext>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>297</mn>
<mrow>
<mtext> km</mtext>
</mrow>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)(G2)</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.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>
<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>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>
<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>1.042 × 880 × 1.25 <strong>OR</strong> (880 + 0.042 × 880) × 1.25 <em><strong> (M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for multiplying 880 by 1.042 and <em><strong>(M1)</strong></em> for multiplying 880 by 1.25.</p>
<p>1150 (CAD) (1146.20 (CAD)) <em><strong> (A1)(G2)</strong></em></p>
<p><strong>Note:</strong> Accept 1146.2 (CAD)</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{{704}}{{880}}">
<mfrac>
<mrow>
<mn>704</mn>
</mrow>
<mrow>
<mn>880</mn>
</mrow>
</mfrac>
</math></span> <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{563.20}}{{704}}">
<mfrac>
<mrow>
<mn>563.20</mn>
</mrow>
<mrow>
<mn>704</mn>
</mrow>
</mfrac>
</math></span> <em><strong> (M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly dividing sequential terms to find the common ratio, or 0.8 seen.</p>
<p>880(0.8)<sup>5−1</sup> <em><strong> (M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into geometric sequence formula.</p>
<p>360.45 (USD) <em><strong> (A1)(G3)</strong></em></p>
<p><strong>Note:</strong> Do not award the final <em><strong>(A1)</strong></em> if the answer is not correct to 2 decimal places. Award at most <em><strong>(M0)(M1)(A0)</strong></em> if <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = 1.25">
<mi>r</mi>
<mo>=</mo>
<mn>1.25</mn>
</math></span>.</p>
<p><strong><em>[3 marks]</em></strong></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="880{\left( {0.8} \right)^{n - 1}} < 50">
<mn>880</mn>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.8</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
<mo><</mo>
<mn>50</mn>
</math></span> <em><strong> (M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into geometric sequence formula and (in)equating to 50. Accept weak or strict inequalities. Accept an equation. Follow through from their common ratio in part (b). Accept a sketch of their GP with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 50">
<mi>y</mi>
<mo>=</mo>
<mn>50</mn>
</math></span> as a valid method.</p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_{13}} = 60.473">
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mn>13</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mn>60.473</mn>
</math></span> <strong>AND</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_{14}} = 48.379">
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mn>14</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mn>48.379</mn>
</math></span> <em><strong> (M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_{13}}">
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mn>13</mn>
</mrow>
</msub>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_{14}}">
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mn>14</mn>
</mrow>
</msub>
</mrow>
</math></span> <strong>both</strong> seen. If the student states <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_{14}} = 48.379 < 50">
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mn>14</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mn>48.379</mn>
<mo><</mo>
<mn>50</mn>
</math></span>, without <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_{13}} = 60.473">
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mn>13</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mn>60.473</mn>
</math></span> seen, this is not sufficient to award <em><strong>(M1)</strong></em>.</p>
<p>14 or “14th year” or “after the 13th year” <strong> <em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong>Note:</strong> The context of the question requires the final answer to be an integer. Award at most <em><strong>(M1)(A0)</strong></em> for a final answer of 13.9 years. Follow through from their 0.8 in part (b).</p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{5}{2}\left( {\left( {2 \times 120} \right) + \left( { - 3.5\left( {5 - 1} \right)} \right)} \right)">
<mfrac>
<mn>5</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>120</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>3.5</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>5</mn>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong> (M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into arithmetic series formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p>565 (USD) <strong> <em>(A1)</em><em>(G2)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</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>
<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,iVBORw0KGgoAAAANSUhEUgAAAncAAAEjCAYAAABQPSceAAAgAElEQVR4Ae2d3Ysc2Zmn5z8pQe3ClqAW985eaBjQsNAsNXVRCDEMBt30ohZIBg99YWaWqULNmr7xGEp0jZmGgSFFaxo8De0q2hiD3SZpDMKUSBiYxoiEuWjsIlmEEUWxI4omeZdfZp7MyMiIyMjM+Dgn4jlQUmZkxIlznjfixO99z0f8kZEgAAEIQAACEIAABBpD4I8aUxMqAgEIQAACEIAABCBgiDsuAghAAAIQgAAEINAgAoi7BhmTqkAAAhCAAAQgAAHEHdcABCAAAQhAAAIQaBABxF2DjElVIAABCEAAAhCAAOKOawACEIAABCAAAQg0iADirkHGpCoQgAAEIAABCEAAccc1AAEIQAACEIAABBpEAHHXIGNSFQhAAAIQqInANz178q0btr315/akd2Vm39jg9Lu2vXXDtu+f2qCmYoV92qFd9b+0nxwf2smIaUZtrvrW/ezY/urDnn2TsZufPxV/rSDu/LQ0pYIABCAAgZAIIO6Kt9YC07RTXFnv+M9HQvqPjxF3ooS4S7tW2A4BCEAAAhDISyC3EMmbIftZbqaIu/jVgriLE+E7BCAAAQhAIJPApfW/OLEHO+qGvWG790/sV7/9Ime37Pyx4+OP7aw3sOH0nOqO/IU9uX9r3K27d2jPen17EY9ODU7tgbp9v/WBnf3iA9vX56179rT/xsxieei3nXftyWnPBpMTfdM7tj8eHf9D6/42er7Hdta/NLvq26+O37XdUb4HdvTx+fTYaVGnH35nZ/ffsu2tt+zBZ7+x3ulxhM9H9mJwPd1z9GHSjeoYbm8d2FGna/2rSeFc3UbnHnPe/tax9Rb6XN15J/uM9ndd4zrTpfW7n85Ybt20/cOOdVW/rKTydQ4nTJV3ynHDwVxdt7du2YPjX8zqMTrHMpundcvKhl17engwvg7SypBQD8RdAhQ2QQACEIAABJIJXNvF6XsTwRMVFO6zExZJD+yMY3fes7OLsQAaXpzao4lwHI3Zk2DZ+bY9eGcs9qZdj0kCaOexdS+HlpjHSPjcskenX4+E5FTcRQWU+7z3nh05cem2bd22o+6rZCyWJLIckxu2fdCxvlOvV1/Z04W8J/vunVhPAi+pbiuLu0t72XmYYqu79qT3OqUur613fHciqCJ1EAdXvtGR6fvtPjy1i1F989g86VqxdBvuPLSnL7PFKeIuxbRshgAEIAABCCwQuOza0Uh43bT9x1+MI1nDgb340EW4MsTd8KU9Pbhp21szYTETYe64N9bv3JtE7D6w7ijidW2DrovM3bBFcXfT9o/PTdM4hldX9v/M5THbbsOv7ezhvDicibtb9qDzlV0p2tc7mUardu8/s5cSWlfn9mRP5Y6cewFMRNztTSJ/FhU237WzgcJurmwSrDORMhx8Ye+PzhEp84bdssN+x+6MhKmrnwBdWPfxJBI2J9QiFZqeNyJmpwxu2p3Oy5E4nuV/YO93L8bbpvWYHJvL5kni7pV1D2/bKBI4so3KNxOru4ddy5J3iLuIPfkIAQhAAAIQyCIwe6A7sTLZeyr6nEhLemBP9lVX3uendnb6T3Y0EU3bLio2FQMzETE+yj3sIwJrGt1yXbHxkl/boPdzOzv9LNK1d8OcMJiKu0m0b3R0krCxPGPanLiLlXtaxgmv1PoN7bL7eBxlcxG6aVkc03j93Pek8kVEZDRqqEMWbOXymfwfEcLjbtYf29npqf10rus8w76x7EZfs2yeNLN6WvdY5NBFUaM2Szgf4i4BCpsgAAEIQAACSQQSBZF2nD6MnRBJevjPIi/T7lb3sHZLqEzziUSNRgVJEDBOOC086Id29fLZdMxb/Fwu8jetixNTifXQxoRzj8oU/ceJu7fswenvZj9M6zMRd9PvjlN018kYwK3l+86O0qek8iVtmxw1LUOsrJFMh4NzezYd6xYRWNOo5Cz/7KVuctg8Sdw5206vj0gZRttizkWk7PqIuIsB4SsEIAABCEAgjcAscheLli1EgxbF3exYTR74bBwJmgqNidhJjWxlRO6i4kwFj+Sxf/hPdva5JlHMxEit4i5SNte9OWbtUeRuzviakPG5nZ3+eDYpYxQJjNg3HhmMHJ/L5knibuF6imSa4yPiLgckdoEABCAAAQiMCETEyWpj7iLiZTp5IjqWzkWyIt2JeznH3MXF3VQYzCZPzMa0zbp1a4ncBTDmbjYOcjaWzqLjBydiLirc3Jg7m04WUff0b+2162rOtHlEKE4XvJ6J+enYx8h4Qde1nnZXIu7SyLAdAhCAAAQgsEAgOkkg3lWm706kLT6wZ6Ihetxt29/TEiKzbtjE/bJmy8bF3dyYMXeum/Y/994ejWlzwqAecade1NkEjXiX8dxs1KmQntQhXs+pbSKCeNRl6WyQPps1Oqllms30Q9ZxM8FslrHfRJgn2nIrbvPFa2W0lE1a13pkIsq0yLEPiLsYEL5CAAIQgAAEsgnMr1uWf507TXD4ZDaJYrR+3e/sYvKaMie64mvUjfLvXyy+hcGNy0oQPfNjxiZr1F1M1sWbjNGrTdwJ7rJ17kYGuLbB+UezsYNps1vVEz14bifT5VVms5HXXudutD5eZ2Yrica9Q3va7Y9mJU+vj8R17k6tN13XL4/Nk8SdzhBf526ypuKyNfoYczc1Dx8gAAEIQAACHhCYjY3bnnblRaNd6ZMAPCg8RfCEAJE7TwxBMSAAAQhAAAKjaE1krbmFbsuo4AMXBFIIIO5SwLAZAhCAAAQgUA8BdeWdzmZnjsaRpbz+qp4CclbPCSDuPDcQxYMABCAAAQhAAAKrEEDcrUKLfSEAAQhAAAIQgIDnBBB3nhuI4kEAAhCAAAQgAIFVCCDuVqHFvhCAAAQgAAEIQMBzAog7zw1E8SAAAQhAAAIQgMAqBBB3q9BiXwhAAAIQgAAEIOA5AcSd5waieBCAAAQgAAEIQGAVAoi7VWixLwQgAAEIQAACEPCcAOLOcwNRPAhAAAIQgAAEILAKAcTdKrTYFwIQgAAEIAABCHhOAHHnuYEoHgQgAAEIQAACEFiFAOJuFVrsCwEIQAACEIAABDwngLjz3EAUDwIQgAAEIAABCKxCAHG3Ci32hQAEIAABCEAAAp4TQNx5biCKBwEIQAACEIAABFYhgLhbhRb7QgACEIAABCAAAc8JIO48NxDFgwAEIAABCEAAAqsQQNytQot9IQCBCgi8su7hbdveupHxd8+e9t9UUBZOAQEIQCA8Aoi78GxGiSHQDgKXXTvauWG7h127jNZ4eGHdx+/YUfdVdCufIRAogaFd9b+0nxy/a7tTh+bAjjo/s97gwr48/c389R9oLSl2tQQQd9Xy5mwQgEBeAmnizsyG/U/tBHGXlyT7eUvg0l52HtrulsRc1/pXw0lJL63f7djR3s1F58bbulAwnwgg7nyyBmWBAARmBBLF3Rv7995viWTMKPEpWALXdnH6nu1u3bUnvdeJtRhenNqjux3rO82XuBcbIbBIAHG3yIQtEICADwSSxN3VuZ0cf4m488E+lGEzAknX90KOb6z/+S8Qdwtc2LCMAOJuGSF+hwAE6iEwefjFJ1YsjMGrp3ScFQIbEBjaZfex7W7dZuzoBhQ5NJ0A4i6dDb9AAAJ1EkiKbFx9Zc86z4nc1WkXzl0AATcjPFncDfsduzOdXKFZ4zftTuel0TtbAPqWZIG4a4mhqSYEgiOQJO6MMXfB2ZECJxDIFnfjA15b7/iube88tu4lsi4BIpsyCCDuMuDwEwQgUCOBRHFXY3k4NQQKI/DG+p17SyJyk30Qd4VRb1NGiLs2WZu6QiAkAoi7kKxFWVckMO163Tux3nQJlGgmiLsoDT6vRgBxtxov9oYABKoigLirijTnqYXApNt166btH5/b1UIZEHcLSNiQmwDiLjcqdoQABKoh4MYjRV8/ljzwvJrycBYIlERg9LaVg1H37P5hx7p99y4WvbWia08PDxhzVxL6pmeLuGu6hakfBCAAAQh4TODaBr2fx14/dsO2d961J5/93HqDa4/LTtF8JYC489UylAsCEIAABCAAAQisQQBxtwY0DoEABCAAAQhAAAK+EkDc+WoZygUBCNh//Md/WL/f5w8GjboGfv3rX4+ubW5xCJRFAHFXFlnyhQAE1ibw+9//3j76h48s/uoxvkcnmfA55Ovhb/76r9e+PzgQAssIIO6WEeJ3CECgMgLPnz+37zx6NBJ1+l/fSRAImYAiz85R+R9/9mf2z8+e2YsXL0bXuH4jQaAMAoi7MqiSJwQgkJvAH/7wh9EDTw8+RWL0IOShlxsfO3pKYJmjcvi3f2v6I0GgDAKIuzKokicEILCUgATc3/3gByNB9+2//Es7Oz1lHNJSauzgM4FVHBVd/3JmcGR8tmi4ZUPchWs7Sg6B4AhogsQvf/lLk5jTg02RC7pegzMjBY4RWNdRkXOje4EEgaIJIO6KJkp+EIDAAgFFNNTdqq5X/emztpEgECqBJEflX//1X1eqju4BOTk4OCthY+ccBBB3OSCxCwQgsB4BPbQUndMDTBEKfddDkQSBUAm4mdxFOSpydIjehXo1+FtuxJ2/tqFkEAiSgKIRGj/nul7V9cS4oiBNSaEjBMpyVFz0TsMVSBAoigDiriiS5AOBlhOQgFMUQlE6RTUk8Oh6bflFEXj1q3JUdK/oniGqHfgF41HxEXceGYOiQCA0AnoYKaLB2nShWY7yZhGo2lHRfeQcoqxy8RsE8hJA3OUlxX4QgMCUgCIaWoxVDyRF6hSx01gkEgRCJRB3VKqeyU30LtQrx89yI+78tAulgoCXBDQbMLo2ncYJ0ZXkpakoVE4CvjgqLnonp4kEgU0JIO42JcjxEGg4AT104mvTrbrkQ8MRUb0ACegajs7k9sFR0RAHRcIZqxrgBeVZkRF3nhmE4kDAFwJuyQc3QUIRBR46vliHcqxDIARHRbPMNcyBBIFNCCDuNqHHsRBoIIGylnxoICqqFAiBkBwVoneBXFSeFxNx57mBKB4EqiCgiJwb0O0mSLA2XRXkOUeZBKKOimZ063sIY0QVvdPYVhIE1iWAuFuXHMdBoAEEoks+6IHC2nQNMGrLq9AER0X3pZwsHKyWX8wbVB9xtwE8DoVAiAQUuVAEw71BouolH0JkRpn9JyAhFJ3JHbqjovtSfyQIrEMAcbcONY6BQIAEFNHQQG2tTac/1qYL0IgUeY5Akx0VondzpubLigQQdysCY3cIhEbAxyUfQmNIef0i0BZHRZE7jRUkQWBVAoi7VYmxPwQCIKCIhrqlXNeruqtYmy4Aw1HETAJtc1QkYjX2TsMoSBBYhQDibhVa7AsBzwmEtOSD5ygpnicEkhyVNk000PAJOWkkCKxCAHG3Ci32hYCnBOTZq/tGXr5b8sHTolIsCOQiIAEnYaNrWmNE27qINtG7XJcLO8UIIO5iQPgKgVAIqNHXA08PPj0A9SBsU0QjFDtRztUI4Kgs8nL3uaKYJAjkIYC4y0OJfSDgEQEJuPiSDzT6HhmIoqxMAEclG5nubzlxGkdLgkAeAoi7PJTYBwI1E1DjrhebuwkSrE1Xs0E4fSEEcFTyY5Swk8DDkcvPrM17Iu7abH3q7j0BRTTU3apGXX/6rG0kCIRKIMlRYSb3cmsSvVvOiD1mBBB3MxZ88p7A0K76v7An92+Nxphtbx3Y0cfnNhjGC35tg94ndrR307a3btmDD58n7GM2HJzbs8ODUV679z+yF4PreEa1fde4I0XnNJZO0Tp9x2OvzRycuAACbiY3jsr6MBW9V5uAg7c+w7Ycibhri6UbUM/hxc/t5MNfWP9Kau7aBucf2YOdm7Z/fG5X0/oN7ap3Yvt7H1hXYm14Yd3Hd2P7mNnVuT3Zu2vvdy9sqLy6H9j+3on1RnlPM6v0gxrs+Np0TJCo1AScrAQCOCrFQpWzpwg+CQJZBBB3WXT4zSMCb+zfv/yNXcxF6d5Yv3PPtnceW/dy8sPwpT09eNuOuq9mZb/s2tHOPXvafzPZNj5u97Brl9O9Xln38G2703lpc6eY/l7eBwk4NdZuyQcJPDzz8niTc/kEcFTKYyyxTPSuPL5NyRlx1xRLtrIeQ7vsPrbdiLgb9jt2Zysq5AQmJtxGAvCtmJCb5HXQsX4F6k5drGqkWZuulRduYyuNo1KNaRW904x5EgTSCCDu0siwPQACY0H2xw9PJxG9hEjeqBYSd7dteyLcxgLw9nx0zybibkEYFotBEQ23ZpW8b0XsNBaJBIFQCcQdFWZyl29JiWi1HwzbKJ91qGdA3IVqOco9ici9a096ryc05kXcDFF0e5qIS9s+y2WTT5oNGF2bTgOjmSCxCVGOrZsAjkq9FpCI1h8JAkkEEHdJVNgWAAFNnPiRPZibTBEVcdEqRLenibi07dF8Vvss8RZfm44lH1ZjyN7+EdA1HJ3JjaNSj42I3tXDPZSzIu5CsRTlnCdwdW4nh5/Yy7nZrX50y7olH9wEiba+E3PeYHwLmQCOip/Wk8jWuF0SBOIEEHdxInz3n8Dwa/vph5/GhN242KPxdJEJFqOt8QkUSTNqbSIMN5hQwZIP/l86lHA1Ajgqq/Gqem91jcuJVNtDgkCUAOIuSoPP/hPQunUf/uN4DTtX2quv7Fnn+XhZkyThVuJSKG7JBy3M6iZIMMjZGYb/QyUQdVQUGdJ3xoj6aU1NytLsWRIEogQQd1EafPabwNVLO5u8UUJCavZ3M7KsSTWLGEvAubXp1LCyNp3flw6lW04AR2U5Ix/3IHrno1XqLxPirn4bUII8BIZf29lD99qxqLDT5/i6du7tFfot7RVlev3YczsZvcrspu0ffmK9Ja8fU+RCEQyJOQlLjXehOySP8djHZwJyVKIzuXFUfLZWctnc8kpEV5P5tHEr4q6NVqfOKxGQZ+waT3W/sjbdSvjY2UMCOCoeGmWDIsmeapskzEkQEAHEHdcBBFIIsORDChg2B0tAjoqcEwkBHJVgzZhYcAk72ZToXSKe1m1E3LXO5FQ4i4AaRjWSrutV3VWsTZdFjN9CIICjEoKVNisj0bvN+DXtaMRd0yxKfdYiwJIPa2HjII8JJDkqzOT22GAFFE0LSms8sCK0pHYTQNy12/6tr70mRGipBzWIbsmH1kMBQNAEojO51U3HItpBm3PlwqvXQV3vpHYTQNy12/6trL28Wjc+RaJODSERjVZeCo2qNI5Ko8y5dmV0HRC9WxtfYw5E3DXGlFRkGYGkJR8YfLyMGr/7TCA6kxtHxWdLVVs2Re80XpjUXgKIu/bavhU1l3jTOBQ3QYK16Vph9sZXEkel8SbeqIK6PiT26ZHYCGPQByPugjYfhU8jkLTkA4OM02ixPQQCSY4KM7lDsFw9ZZQjqz9SOwkg7tpp98bWWuNN1KDJa1W0TlE7ul4ba+5WVMzN5I6uTYej0grTb1RJoncb4Qv+YMRd8CakAhJv8bXp6I7gugidQNxR0XccldCtWm355ehqFQBS+wgg7tpn88bUWAJOM10VpVNUQwKPiEZjzNvKiuj6xVFppelLqbSuJ7WPcgxI7SKAuGuXvYOvrSIXaqhYmy54U1KBCAEclQgMPhZKQA6whqiQ2kUAcdcuewdbW3mgWoxVETp5omqwNBaJBIFQCcQdFXWhEWEJ1Zr+lpvonb+2KbNkiLsy6ZL3xgQ0G1DrNbkJEuqyYtzRxljJoEYCOCo1wm/pqZ1jTNvZngsAcdceWwdTUzVA8bXpWPIhGPNR0BQCcUeFmdwpoNhcOAG1qW5ccuGZk6GXBBB3XpqlnYWKL/nAOzHbeR00qdY4Kk2yZth1Ua+HBB7Ru7DtmLf0iLu8pNivNAIaZxRdm07faYBKw03GFRBwjoqbyY2jUgF0TpFJgOhdJp7G/Yi4a5xJw6iQxh05T9JNkGBtujBsRynTCUQdFc3oxlFJZ8Uv1RPQUAC1t2p/Sc0mgLhrtn29qx1LPnhnEgq0IQEclQ0BcnilBLQsilYbIDWbAOKu2fb1onbqDlAEQ42KvEaWfPDCLBRiQwJRR0XXtiLRREQ2hMrhpRNQW0z0rnTMtZ8AcVe7CZpbAD3o3BR8DeRlbbrm2rotNcNRaYulm11POSNaYorUXAKIu+batraaacmH6AQJlnyozRScuCACclTknMhJwVEpCCrZ1EZAUWdF7xjnXJsJSj8x4q50xO04gSIa6pZyXa/yClmbrh22b3ItcVSabN12100OuP5IzSSAuGumXSurFUs+VIaaE1VEAEelItCcplYCRO9qxV/6yRF3pSNu5gk0KFdLPSi0z5IPzbRx22qFo9I2i1NfRe7UfpOaRwBx1zybllYjlnwoDS0Z10ggyVGpsTicGgKVEVCbLgdd9wCpWQQQd82yZym1UfheY+jUCLglH9R1RYJAqASiM7l1XWuyBIPLQ7Um5d6EgK59teukZhFA3DXLnoXVRuJNs1zdBAmF7/HuCsNLRjURwFGpCTyn9ZYA0TtvTbNRwRB3G+Fr3sG60eNLPmgbCQKhEsBRCdVylLsqAm49UnpkqiJe/nkQd+UzDuIMisopOue6XlmbLgizUcgMAjgqGXD4CQIRAhJ1Wr9Ry1mRmkEAcdcMO65VC93Q8bXpGHe0FkoO8ohA3FHRdyISHhmIonhJQM8CCTzuFS/Ns3KhEHcrIwv/AAk4db0qSue8Nbpew7drm2ug6xdHpc1XAHXflADRu00J+nU84s4ve5RWGt24imDE16Yr7YRkDIEKCOCoVACZU7SGgIbjyOnH2Q/f5Ii78G2YWQPdpG6wrFvyQYu1kiAQKgEclVAtR7lDIKAVEtSzQwqbAOIubPulll7vxGRtulQ8/BAgARyVAI1GkYMjoB4eonfBmW2hwIi7BSThblBEI742nUQeCQIhE4g7KszkDtmalD0EAoreKThACpcA4i5c201L7t6JqckR+lM3rPdjJi67drRzY+Qhykuc/d20O52XNnS1Gw6s9/Gh7WufnXft5Hww+83tw/+NI4Cj0jiTUqGACGgsq9pkVk8IyGixoiLuYkBC+hrukg9Du+w+tt05UecE3j172n8zMcNr6x1/2/Yff2GDodlw8IW9v/dte9J7HZKZKOsKBJyjogdLMI7KCvVjVwiEQkDrnuqPFCYBxF1gdlNEzq1HpAegBr6G5129su7xiXUH1/P0Fc2727H+JGw37Hfszs5j6166ON5EFB7M9pnPgG+hEgjXUQmVOOWGQDYBonfZfHz/FXHnu4Um5dON1pi16Yb/1/r/fhkj/8b6nXciXbL6fs+240Ju1J0bje7FsuFrMASa4agEg5uCQmBlAorcafksUngEEHce28wt+aDBrYrS6UZThKORafjSnt79np1dTKJ5+n5w03YPuzYnA0fiLjYur5FAmlupqKOia1uRaO/HiDbXHNQMAqkEdF/q2dPY505qzcP/od3ibvi1nT28HYkW+WFQ3VBubTqNO1LErulr06kL9i+iQi5NxKVt98N0lCKFQKsclRQGbIZAiAT0/JETRgqLQKvF3WhMlwb1x7v+arKhlnxQdE6ekm6m9iz5oC7Y79pR99WMfJqIS9s+O5JPHhGQo6KHg5vJ3QZHxSP8FAUCGxMgercxwloyaLG400zMv7EfHr9nu1v1jeFSRCP+TszWrU036pL9fmTihJnRLVtLg1DUSdvrqBRFkHwg4A8B56DpeUUKg0B7xZ0iQJqZ+Xq83trC2K6S7ceSDzPAC12yo5/GEyridhlHW+sT47NS8ylOAEclToTvEGgGAd3bir4rEEEKg0BLxV20G/CVdQ9v2/bckhvlGU8DUzX7SF2v+l/f2+0NRW0xz30k5ObswlIo84T8+Iaj4ocdKAUEyiTgluBq9/OqTMLF5t1Ocacuv4c/st7VeP20cTTo9vyYrwI5a8yCuzEk6hTiDm9tugKBRLNK6pKd/s4ixlMUHn5IclQ8LCZFggAECiBA9K4AiBVm0UJxp+jP9+0v5l5xNVl24+GpXbj1cgswggSc3s/nJkhI4OH1zIMd9p/Zo+Nzu5rfPPs2HNiLD98dv81i79Ce9Xj92AxO9Z+iM7lxVKrnzxkhUCcBF6RQO0Dym0ALxd2kG3bpq6/WM5zEm2a5tmJtuvUQcVSABHBUAjQaRYZACQT0bFPvE8lvAq0Td8mD982GF6f2aGf9xXHlybgZRW5tOrwbvy9+SpdNAEclmw+/QqCNBDQcQ1F7nm9+W79l4k5juA4jL6aPGmcS0VtxzTtd6O1cmy7Kjs9NIoCj0iRrUhcIFE+A6F3xTIvOsUXi7toG3Q9sf272ZRTneOmN7a2btv/4CxtkjL1TRENjD1zXq8bVMUEiypLPIRKIOyr6zhjREC1JmSFQLgGtY6noHc+9cjlvkntLxJ0TbjdGF+T2wqLF8d9vJC6N8m//9m/2/f/z/VEef3rrT+yjf/gHe/HixegC10XOHwxCvAZyOyqjt4O4e2jx/937x/aTbj99cswmLRXHQgACXhFQj5X+SH4SaIm42xy+IhgSdPJW+INBk66B//Kf/rN9+i//knMMzWStwZiDNByc27PDA9veumUPOl8h8DZvcsgBAl4TkCNL9M5fEyHuctrGTQFf1k3lwtVa2JUEAd8J6HpebeX5ZHE3qufklXFVLQjuO1vKB4GmEyB656+FEXc5bJP3Aaj93Dg8wtU5wLKLFwTyOi7jwiLuvDAahYCABwQUxFD0TuNzSX4RQNzlsIcuXF3Ay6J2ekhGu+u44HPAZZfaCTjn5Z+fPctRlhRxNxxY7+ND26dbNgdDdoFAcwhoCTAFNUh+EUDc5bBHnmnfWj5C3VtRcafjlgnCHKdnFwiUTsA5MMvXrnLiLnnc5e5h1y5LLy0ngAAEfCGgNoPonS/WmJUDcTdjkfgp70NP3ktU2LnPiuaRIBACgTxOjJkTd/fm1oscDnp2djx+Tdzu/Wf2cvLe5hDqTRkhAIHNCLjoHcGMzTgWeYuL9JwAAB5dSURBVDTibgnN7zx6tPRVK27WkBN00f8VzVseDVlSCH6GQAUE8jkyyeJuXDy3pND6b3qpoJqcAgIQKJiAG9pBMKNgsBtkh7jLgOdEm/7PShJv2sf9Sdy5z/ofbyaLHr/5REDOTPZkoCxx5367YXTP+mRVygKB8gmsNjGr/PK0/QyIu4wrYN1p3hJ3JAiESEDOiHNOksvvBNx8t+x432u7OH3PdreI3CWzYysEmkuA6J1ftkXcpdjDTfHWw27VhLhblRj7+0Qg26lJEXeaLXt6bA92btj23gfWHVz7VCXKAgEIVEDARe8YilQB7CWnQNylAHIDRFN+ztyMuMvEw4+eE0iN3i15/dj21oEddX5mPYSd5xameBAoj0C+iVnlnZ+cxwQQdwlXwqZTuxF3CVDZFBSBv/vBD1i7KiiLUVgI+EEg38QsP8ra5FIg7hKsu0nUTtkh7hKgsikoAps6OEFVlsJCAAKFEiB6VyjOtTJD3MWwuUGhv/zlL2O/5P+KuMvPij39JbCpk+NvzSgZBCBQJgH3jvV1xqyXWa425Y24i1nbDQjdZPkSxF0MKl+DJOCid5s4OkFWnEJDAAIbE8iemLVx9mSwhADiLgZIiw5vuhAj4i4Gla/BEijC2Qm28hQcAhBYm0DqxKy1c+TAVQgg7iK03EDQTaJ2yg5xF4HKx6AJuGEKmzo8QUOg8BCAwFoEiN6tha2QgxB3EYxFDQJF3EWg8jF4AkTvgjchFYBALQTcerEKnJCqJYC4m/B2UbsiFl9E3FV7EXO2cgm46N0/P3tW7onIHQIQaBwBJmbVY1LE3YS7wse6CItIiLsiKJKHTwSKdH58qhdlgQAEyiXgJmYRvSuXczx3xJ2ZFT3wE3EXv8z43gQCRQ1baAIL6gABCOQn4KJ3m45nz39G9kTcmVnRgz4Rd9xYTSRA9K6JVqVOECiXgNqN7zx6NJpoOIveuXdU3xht1zNze+um3em8tKGKk/Sqw4OO9Uc/llvepuTeenHnQsZFLraIuGvK7UE94gTUSMsZIkEAAhBII6DnqsboamkxPQ8VudPkisX0yrqHt207Ubg5AXjPnvbfLB7KlkwCrRd3LlycSWnFHxF3KwJj92AIFD2EIZiKU1AIQGApAb2ZQu+l1jNQwzg00z67KxZxtxTqmju0Wty5qN0sVLwmxdhhiLsYEL42ikDRwxgaBYfKQKBlBCTe9BYbiTk9+9Q+SOTlS4i7fJxW36vV4k5hY12QRSfEXdFEyc8nAkTvfLIGZYFAPQTUzaqeL3W96k+fFTBZLSHuVuOVf+/Wiju3dlcZ781E3OW/ANkzTALqeinDMQqTBqWGQHsIqKdL0Tk959QG6Ht212sWm4m4G02oiE6uiH5mzF0WwbTfWivuylx1H3GXdrmxvSkEyhrS0BQ+1AMCTSKg+13PTNf1qihdMZMQidyVdZ20VtwpjKyLtYyEuCuDKnn6RqCMyUi+1ZHyQKDNBCTgdJ/rmeaemat3vWYRRNxl0dnkt1aKO4WRdbGuH0rORo64y+bDr80g4KJ3ZQxtaAYhagGB8AjouahnpFubTl2w+l5OQtyVw9WsleJOoWV5I2UlxF1ZZMnXNwJlDm/wra6UBwJNJiBnLd/adEVSQNwVSTOaV+vEnYvaFRtajiK1UVRwfgvfINBMAm5iUllDHJpJjVpBwB8CWrYkOkFCkfiyerUWa424W2RSzJbWiTtdxGVG7WQWInfFXJzkEgYBondh2IlSQsARkHhbf206l8sm/7u3T0RnxfL6sU2Ixo9tlbiran0uxF38MuN7kwm46J26dEgQgIC/BNzadHpGaYKE7tkye7H8JdH8krVK3Clqp7+yE+KubMLk7xuBKoY7+FZnygOBUAjo/nRdr5oooe/Vdb2GQqlZ5WyNuHMz+4pZmyf7IkDcZfPh12YSKHuiUjOpUSsIlENAzzw3ZELPJA1HquL5V05tyHVVAq0Rd7qw9fCpIiHuqqDMOXwjQPTON4tQnjYSkIDTG2T0HNIzTwKPrtf2XQmtEHcuaqeHTxUJcVcFZc7hIwF1+VQx9MHHulMmCNRFQF2ser5JzOn5o3uwquddXXXmvNkEWiHuNGi0qqidcCPusi86fm0ugaomLTWXIDWDQH4CClyoV0qTI/Snz5o0QYJA48Wdm8lX5Sr6iDturDYTUNSA6F2brwDqXjaBetemK7t25F8EgcaLOzegtMqZQYi7Ii5N8giVANG7UC1HuX0moGeYnmeu61Xj6pgg4bPF6i1b48Wde9lxlZgRd1XS5lw+EtCDR+PvSBCAwGYEJODU3arnCmvTbcayTUc3Wty52XtVRu108SDu2nQLUdckAlVPYkoqA9sgEDIBPb/kIOl54tamC7k+lL1aAo0Wdwpfy+OpOiHuqibO+XwkoHuvyolMPjKgTBBYhYCcIk0AVIROzxHdQ3S9rkKQfR2Bxoo7F7XTzVJ1QtxVTZzz+UiA6J2PVqFMPhKQgIuvTVd1j5OPXCjT+gQaK+40W6+OqJ1Mgbhb/4LkyGYRcFGIzR9U13Zx+p7tHnSsP5xnNByc27PDg9F9t3v/I3sxuJ7fgW8Q8JCA7gmt4uAmSOiZpVmwJAgUQaCR4k5ekARWXeFsxF0RlyZ5NIGAHmBFTGoaXpzao50bth0Xd1fn9mTvrr3fvbChXdug+4Ht751Y7yqmAJsAkzo0goDWoVPgQfeF/vS5jh6mRsCkEqkEahd340b7nj3tv4kV8toGvU/saO+mbW/dsgcfPrdBzva67nW2EHcxU/K11QQ2Xo5IAu7+9+zo/q2YuHtj/c492z3s2uWU8CvrHr5tdzovLWdzMT2SDxAok4CGCunZpOeDonX6vnlEu8wSk3fIBOoVd8Ov7ezhLdveiou7oV31Tmx/7wPrqotleGHdx3dt//jcrpbQduN86oraqXiZ4u6bnj351o1xF9LcQ2lJxfgZAoES2Cx699p6x9+zJ72+dQ9vz4u74Ut7evBWTMgN7bL7OLH7NlB8FDtgAnoesTZdwAYMuOg1ijs12u/Z/z58x3bj4m7UaL9tR91XM7SXXTvaiYvA2c/uk0Lcdc/QyxR3KuhI1N6OPZRcDfgfAs0joLFFui9W636Sk/cjezBy6hSRmxd3w37H7mzdnm8nbCLu4m1K85BSI48JKLigZ5GueTcsYbVr3+PKUbQgCNQk7lyj/Ru7kJcda4jHjXZcyC3vbnFRO4W760xLxd3g1B7E6lxneTk3BKogIKdLD7zcadQd+6PJ+Lm4uEsTcWnbc5+VHSGwFgFFqPXscWvTqQu27mfRWhXhoEYQqEfcTRvtb8ZdKHNCZzyOZnvnsXUvo6Nm4o37In/NzKs7aqdSZYu7ycNnoX6L9WELBJpEQA+6/NG719b78Id2duFmvsbv/zQRl7a9SSSpi08EFFRws8J1fcuB0aQJEgTqJFCDuHNjaF6rfzJB3MUbcYcnbfv4983G9bhzFPN/tribiNf7pzYo5nTkAoFgCMj50npe2UmR/X+090+/jkyKWLz/6ZbNpsiv5RLQsiXRCRIaesAEiXKZk3t+AhWLu3ijXZy423hGXn5mS/fMFne/s7P7t8bj7YYD6318aPtbCUs8LD0LO0AgPAL5limaCDndF4l/Nyf3jyZUxMbm2sR5ii+ZEh4qSuwhAYk31qbz0DAUaYFAteLu6txOHn9uF9Pe1iRxt163rBu0ulDDGjZkirvRxBANAu+PJpQcnX5l/dPv2mI3dA0F55QQqIDAeksVLUbubCLkWAqlAqO1/BRubTq17XrWqBuWCRItvyg8r36F4s4JuTRvfBa9GnW3xMekJS57MKa72lie8i2SJe7GXUnv2A+Pv2d/Nep2urLe8Z/PL/FQfhE5AwRqI5AvehcvXpK4MzMWMY6D4nuBBPRscV2vmiih73S9FgiYrEojUKG4S6qDE3yxmbErLoWy8iy8pKIUuC1d3E2ikls3bPfh6TiCmSFaCywSWUHAKwJ6YOphmT+liDuN3B08txMtcLx10/YPP7Eerx/Lj5U9FwgoIueG+agt1wSJOtdNXSggGyCQg4Cf4s40Ni/fIsa+Re3EPF3cTR5QO+9NZwEmDwrPYTl2gUDABHxZtihghBS9YAIScJrso/ZbAQMJPLpeC4ZMdpUR8FTcqf7XNjj/yB7ofZJbB3b08Xni68cUAVg++64ynqMTpYq70dspJoPBR3tOIpfxLuhqi8vZIFALAUVEfFi6qJbKc1IvCKiLVQECXYdqt/U80XcSBEInULO42wzfemN3NjtnnqPTxN04Shftgp5E8u7/o511fszLzvPAZZ/GECB61xhTBlcRXXtyLjQ5Qn/6zNp0wZmRAmcQCFrcycvSn28pWdwlRem0LMpbtr332M76s1ef+1YfygOBsgi4xV8ZpF4WYfKNEmBtuigNPjeZQLDiznn9ull9S8nizrdSUh4I1E9Aos6nZYzqJ0IJiiaga0zj51zXq4bxMEGiaMrk5xuBYMWdz+N1EHe+XeaUx2cCbmYi0TufrRRe2STg9JxQe8zadOHZjxJvRiBIceeidr4OfEXcbXZRcnS7CBC9a5e9y66tngtaZkftsFubruxzkj8EfCMQpLjTOB2fZ9kh7ny7zCmP7wT0SifdN3LcSBBYlYCuGzd+U9eRInZ0va5Kkf2bRCA4cReCl4+4a9ItQl2qIiCHTQ9lEgTyEpCAi69NR/d+Xnrs12QCwYm7EMbnIO6afMtQt7IIqDuN6F1ZdJuTr8SbIr1ugoRWTPBxYl1ziFOTEAkEJ+50Q0vg+ZwQdz5bh7L5TED3t2+LkvvMq01l0zp0iuxG16ajG79NVwB1XYVAUOIuFM8ecbfKJci+EJgRUDeb7h/GS82YtP2T2n1F53RdSPzrO12vbb8qqP8yAkGJO93YIYzJQdwtu+z4HQLpBHxdnDy9xPxSNAFF5Fibrmiq5NcmAsGIO42pkGgKIQyPuGvTLURdiyZA9K5oouHkJ9vLgVcb6ha3DqHND4cwJW0LgWDEnbz5UMbiIO7acvtQz7II6H7XGmWk5hNQF6u6Wt3adLK9vpMgAIH1CQQh7kLz5BF361+QHAkBEVC0RvcRD/nmXg+ycXxtOk2aIEEAApsTCELcKWInby6UhLgLxVKU02cC6p7TOFtSswhoiI3ac7WTsq+WNWGCRLNsTG3qJ+C9uHMe/Oeff14/rZwlQNzlBMVuEMgg4O59oncZkAL5ibXpAjEUxWwMAe/Fnbz3//7Wfxt5efL2QlgiAXHXmPuDitRM4O9PTuxPb/0JkZ2a7bDu6d3adGoTNUFC3bAS7SQIQKBcAl6Lu6jnLlHnQvkSfD6H8RF35V605N58Arq/3azJb+3+V+8XLm++RVaroaKtrr3WRAl997nNXq127A0B/wl4Le7cOkdRjBqvoXEa8gI1VsPHhLjz0SqUKRQCusfdWwgkCkJ45WAobMssp5xxZyu1gRLnIfS0lMmEvCFQFwFvxZ28PLfOURyOflN4Xw2IvEPfPELEXdxifIfAcgK6j91L4HV/u/ta/6e1BctzZY+yCUjAObvJ8ZbAo+u1bOrkD4FsAt6KO+cBugY+qRpqVFwUzycPEXGXZC22QSCdgMZmZd3LitLrvkI0pDOs8he1y4qqymbOydZ3EgQg4AcBb8Wd8wCXYVIj47xGXxoXxN0yq/E7BGYEdN8qMrcsCq82QV19pPoISFzLBq7bXJ9Zm64+e3BmCKQR8FLcqbFf1UtXpE/H+ND4I+7SLje2Q2CegIvI5blv12kX5s/Gt3UJsDbduuQ4DgL1EPBS3K3robvGP8+DokzciLsy6ZJ3UwjoPtW9ovs2b1LboEg9qXwC6hWR0yzmspO4+zT8pXwCnAEC4RLwTtzJQ1RDsu7YGj0o1GVQp8BD3IV7Q1DyagisI+xUMokL3V+IjPLsJLbOPmpLWZuuPNbkDIGyCHgn7jTuZlPP3D0A6hJ4iLuyLlfybQIBN9N9lYhdtN5qI/RHKpaA7KE16dR+ubXpij0DuUEAAlUR8ErcOVFWhFeuhkqNlB4kVSfEXdXEOV8oBNx9ua6wUz2LbCdC4VZWOdVDojZSETq1W3KIi2h/yyov+UIAAvkIeCXuFLEr0iMv4kGSD+P8Xoi7eR58g4AIOFGmcVybJrUTii6R1iMgW6i9VVulMXWySdayU+udhaMgAIG6CHgj7uRBqqHRmLsik/NKq5yuj7gr0oLk1QQCur+LHAvr2otNIoBN4LpKHSTeNDvZTZCQQC66vV2lPOwLAQiUR8AbcafuADU6ZSQ1Ysq7Ks8UcVeGFckzZAKKsumvyHuwzDYjZNbxssuxFSuJayewJY5JEIBAcwl4Ie7K9sJd1KCq8XeIu+beMNRsdQLq8pOoKDp6Xna7sXpN/TpCUU05tmqP5Nzqe5Hi2q/aUhoIQCBKwAtx59ZSihas6M9uiZUqBgsj7oq2HvmFSkCCTveDugPLSG7YBaJlTFeC17Wn4s7adGVcdeQJAf8J1C7u1CjLq1eDVHZSQ1dF9yzirmxLkn8oBNQVq+hRWanK9qOsOhSRr5xWdb2q7XHtqYQeCQIQaCeB2sWd67KpwvN23bNlC0nEXTtvJmo9T8DNVi+6O3b+LDZyDCVoqmhD4ueu87vqK8YS0GpzJKL1nQQBCECgdnGnSFrZYitq5irEJOIuSpzPbSTgImpVjHN156qyHanTpnJSXXe02hpF7MoW0HXWl3NDAAKrE6hV3DnPvsruAz0IJCjVIJaVEHdlkSXfUAhU4URFWWhMn+67KtuS6Pmr+Kxxw9EJEqqz2jMSBCAAgTiBWsVd2SIrXln3vWxRibhzpPm/jQTqiqTV1Z6UaWOxZG26MgmTNwSaSaA2cedmr9blaZfZHYy4a+bNQq3yEZAYqWMMXNlOW77aF7OXulmjEyTUDVtXW1lMjcgFAhCokkBt4k7dC5q9Wk66tkH3A9vfumHbex9Yd3C9cBrXbbTwQwEbEHcFQCSLYAmUF0Fbfl/r3OW1K+WbRALVdb1qooS+0/VaPnfOAIGmEahF3Ll3TC5dc244sN7nP7Yn92/Z9tZtO+q+ivC/tkHvEzvau2nbW7fswYfPbTCc/Dx8aU8f/sh6V9/YVe9H9qjz0txPLgM1mBJhajyLToi7oomSXygE3L2dGWUq8b5251/atngEVKycs6m2QxG7kMrvEUqKAgEITAjUIu7kWcs7zUrDwXM7uX/Ldu8f20+6fbua23loV70T23dRueGFdR/ftf3j8/F+OcSdslMjWoaXj7ibMxZfWkRA95QiTmmpivtabcuy9iWtfFVul4BT+6P2wg0TyRTFVRaOc0EAAkETqFzcqfFSY5b5wuqrc3uyd3s+GhfFLPF28PZ8JO+ya0c79+xp/42ZLe++UXZu3F/R3R6Iu6ix+NwmAhprlxoNr+i+9jl6p7ZGfCTm1E5IhKbyatOFQ10hAIFCCVQu7uTZq2FLT6+td3zXdh+e2kW8L3Vy0LDfsTtbTsi5nF5Z9/Btu5PQBev2SPo/82GUdECObYi7HJDYpXEEsp2lau9riaasCGLV8OXUqu1Te6M/fWZtuqqtwPkg0B4ClYo7F7XL8lTHwu3AjjqfTMba3bDd+yf2q/7lxCpvrN+5Z9s7j617GVV/Ene3bfugY/3o5iW2VLdI0V2ziLsl0Pm5kQQkWNK6Q6u+r/O0NVUYQYJXTNQmyKllbboqqHMOCECgUnHnBg2nY58It71De9YbjCdBXH1lTzWhYu/EeldSbWkiLm17+tn0i4SmPOkiE+KuSJrkFQoBN25ssbzV39cqw/JegsWSFrFFXa9q61zXq5xHJkgUQZY8IACBvAQqE3dq8CSi1Oilp7FA2z3smovTad+x139z0uWaJuLStqefTb84D7/ILhLEXTZzfm0eAXcfJYuY6u/r6L2d1VNQpCVUdwlK3f9q61ibrki65AUBCKxCoDJx56J2mZMXRhMlblpc3Nnc9mK7ZQXLdZesAi5rX8RdFh1+ayIBN94usW5z929kj7ntxd/XOpN7B2tmuxMp0jofJR41vk/3vVubbp18OAYCEIBAUQQqE3cSUGpos1NK9G30EHhrOlliFMmLj7mL7ZN9nvlfNSZGHndRCXFXFEnyCYWAnLe08XapQyli92zR97XY5esxWJ2yIpVOOOp+V/uRHLVcPW+OgAAEILApgUrEnTxbNYBqELPT0C67j2135z07u4i8VWJumRP10y5bCiX7LPFfsx9M8b0Xv6teatjdn+rqPuv/MqMGi6VhCwSqJ6BxZekOUj33taOQq9fA7bzkf93PqqvucTfGkPt7CTR+hgAEKidQibhTI5je8MfqPPzazh5q8eJn9lITKIYDe/HhQ7vjFige7b5kEeNYlsu+OvG5bL+03zVeT4190p/G3tD4p5Fje1MIqDtSIio11XBfu7JsGr3T8ZrlqnZM97gilOqGJkEAAhDwlUDp4s6NxVketYsguurbr47ftd2RYDqwo4/PZ68Wm+52bYPzj+zBjkRV2j7TnTM/yBtXo71JknhNEnd6KJAg0HQCuvaXCp6K7+socxe9W6UdktOm+1oOmv70eZXjo+fnMwQgAIEqCZQu7uTlpo/FqbKq6edSg62H0yYzZl10ICrw5OmTINAGArru5ST5nPL2ICiSrzZLddIx+k703WfLUjYIQCBOoFRx5yJivjf6glLEw0lRuqi4C6He8QuC7xBYlUARztGq51xnfzf8Iin6pm2K7rmuV9amW4cwx0AAAr4QKFXcqYH0PWrnDFGEuFNe7uEQSr1d/fkfAusScE7cusdXeVw8eqeyuyEV6nqVwEsSf1WWkXNBAAIQ2JRAaeLOefPylkNIRYk796DjARGC1SljEQTcNV9EXmXn4cYAf/rpp9O16eSIhdJOlc2H/CEAgWYQKE3cOW842k3J5+QZtXCBC9dA9deA2qhNxtk24xFALSAAgSYSKE3cqdGUR88fDLgGuAZ8uwaYINHExxl1ggAEHIHSxJ07Af9DAAIQgAAEIAABCFRHAHFXHWvOBAEIQAACEIAABEonkEPcTd73mvIGhtECwp1T6/YvSy8sJ4AABCBQHoFrG/R+bj+ZLqB+w7b3Du3p5z0bfNO3n37et2F5JydnCEAAAoURyCHuJucavd/1pt3pvIw0cJfW73bsaO+mbW/dsgedr+yqsKKREQQgAIGKCIxec/iu7e68a09Oe7M34gwH1js9tgc78bavonJxGghAAAJrENhQ3E3OePWVPb1/y7a37tqT3us1isEhEIAABOoicG0Xp+/Zbmr7NX6X9Z3DrtE/UZeNOC8EILAKgWLEnZkNL07tkd7zetCxPn0Xq9igvfte9a17+mN7cv/AjrqvEjgM7ar/pZ19dmwPvvXYupdJF5a60j6ZRY8/fD6LuiTkyCYILBAY9UrcsN1M8fbKvjz9DeJuAR4bIAABHwkUJu5s+NKeHqh79p497b/xsa6UyScCul7u3rMH7yjieztR3A37HfuLd961/yWnYSdJ3I0jKvt7H1h3cC0Pw7qP79r+8TnDA3yytddleWP9zj3b3qLb1WszUTgIQGAlAsWJO3MTL5If1CuVip1bQ0AC7k6KuBtDmDx8k8TdyKF4e14YjqIwOBituYA2rijt1sYIyQACEPCOAOLOO5O0q0CbiLvxsXEhp4f127GJP+1iSm1XIYC4W4UW+0IAAmEQKE7c0S0bhsU9K+X64i4tojd5WDP20zNL+1oc1y1Lj4OvFqJcEIDA6gQKE3duQsXuw1O7SBr3vnrZOKIFBNYXd2kiLm17C2BSxbUIjK/BZRMq1sqagyAAAQjUQqAYccdSKLUYrwknRdw1wYqh18F1zWYs5aT17r7sM1EndFNTfgi0hMCG4i66iPGBvd+9iCxw3BKCVHMjAuuLO7plNwLPwfMEpg7qgR11uta/ct0PWo6na886P7OX023zh/INAhCAgG8Ecog759XesO2kV5BpRffPfm49LUVBgsCKBNYXd2ajY+OzaEdjP99iQsWKdmB3LdY5sN7n/zRZM3HS3rnXjzmtBygIQAACARDIIe4CqAVFDJbAJuJuvLYiS6EEa3wKDgEIQAACpRBA3JWClUzzEthI3BmLGOflzH4QgAAEINAeAoi79tjas5omdPfHly+ZvBZqNhwg6S0C1zY4/8ge6C0WWwd29PE5rx/zzNIUBwIQgAAEqiWAuKuWN2eDAAQgAAEIQAACpRJA3JWKl8whAAEIQAACEIBAtQQQd9Xy5mwQgAAEIAABCECgVAKIu1LxkjkEIAABCEAAAhColgDirlrenA0CEIAABCAAAQiUSgBxVypeMocABCAAAQhAAALVEkDcVcubs0EAAhCAAAQgAIFSCSDuSsVL5hCAAAQgAAEIQKBaAv8fGyf7iA9SqEgAAAAASUVORK5CYII="></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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"></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>
<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"><mi>sin</mi><mo> </mo><mn>60</mn><mo>°</mo><mo>=</mo><mfrac><mi>h</mi><mn>40</mn></mfrac></math><strong> OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tan</mi><mo> </mo><mn>60</mn><mo>°</mo><mo>=</mo><mfrac><mi>h</mi><mn>20</mn></mfrac></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitutions in trig ratio.</p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>20</mn><mn>2</mn></msup><mo>+</mo><msup><mi>h</mi><mn>2</mn></msup><mo>=</mo><msup><mn>40</mn><mn>2</mn></msup><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfenced><msqrt><msup><mn>40</mn><mn>2</mn></msup><mo>-</mo><msup><mn>20</mn><mn>2</mn></msup></msqrt></mfenced></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitutions in Pythagoras’ theorem.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>h</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>34</mn><mo>.</mo><mn>6</mn><mo> </mo><mfenced><mtext>m</mtext></mfenced><mo> </mo><mo> </mo><mfenced><mrow><msqrt><mn>1200</mn></msqrt><mo>,</mo><mo> </mo><mn>20</mn><msqrt><mn>3</mn></msqrt><mo>,</mo><mo> </mo><mn>34</mn><mo>.</mo><mn>6410</mn><mo>…</mo></mrow></mfenced></math> <strong><em>(A1)</em><em>(G2)</em></strong></p>
<p><br><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><mn>1</mn><mn>2</mn></mfrac><mfenced><mrow><mn>70</mn><mo>+</mo><mn>110</mn></mrow></mfenced><mfenced><mrow><mn>34</mn><mo>.</mo><mn>6410</mn><mo>…</mo></mrow></mfenced><mo>×</mo><mn>200</mn></math><strong> </strong> <strong><em>(M1)(M1)</em></strong></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for their correctly substituted area of trapezium formula, provided all substitutions are positive. Award <em><strong>(M1)</strong></em> for multiplying by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math>. Follow through from part (a).</p>
<p><br><strong>OR</strong></p>
<p><strong><br></strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>×</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>20</mn><mo>×</mo><mn>34</mn><mo>.</mo><mn>6410</mn><mo>…</mo><mo>+</mo><mn>70</mn><mo>×</mo><mn>34</mn><mo>.</mo><mn>6410</mn><mo>…</mo></mrow></mfenced><mo>×</mo><mn>200</mn></math><strong> </strong> <strong><em>(M1)(M1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for the addition of correct areas for two triangles and one rectangle. Award <em><strong>(M1)</strong></em> for multiplying by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math>. Follow through from part (a).</p>
<p><br><strong>OR</strong></p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn><mo>×</mo><mn>34</mn><mo>.</mo><mn>6410</mn><mo>…</mo><mo>×</mo><mn>200</mn><mo>+</mo><mn>2</mn><mo>×</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>34</mn><mo>.</mo><mn>6410</mn><mo>…</mo><mo>×</mo><mn>20</mn><mo>×</mo><mn>200</mn></math><strong> </strong> <strong><em>(M1)(M1)</em></strong></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution in volume of cuboid formula. Award <em><strong>(M1)</strong></em> for correctly substituted volume of triangular prism(s). Follow through from part (a).</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>623538</mn><mo>…</mo></math> <strong><em>(A1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>624000</mn><mo> </mo><mfenced><msup><mtext>m</mtext><mn>3</mn></msup></mfenced></math> <em><strong> (AG)</strong></em></p>
<p><strong><br>Note:</strong> Both an unrounded answer that rounds to the given answer and the rounded value must be seen for the <em><strong>(A1)</strong></em> to be awarded.</p>
<p><br><em><strong>[3 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><mrow><mi>d</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mo>-</mo><mn>1800</mn></math><strong> </strong> <strong><em>(A1)</em></strong></p>
<p><br><em><strong>[1 mark]</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"><mfenced><mrow><msub><mi>u</mi><mn>13</mn></msub><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mo> </mo><mn>45000</mn><mo>+</mo><mfenced><mrow><mn>13</mn><mo>-</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mo>-</mo><mn>1800</mn></mrow></mfenced></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><strong><br>Note:</strong> Award <strong><em>(M1)</em></strong> for correct substitutions in arithmetic sequence formula.<br><strong>OR</strong><br>Award <strong><em>(M1)</em></strong> for a correct <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>4</mtext><mtext>th</mtext></msup></math> term seen as part of list.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>23400</mn><mo> </mo><mo> </mo><mfenced><msup><mtext>m</mtext><mn>3</mn></msup></mfenced></math> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong><br>Note:</strong> Follow through from part (c) for their value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>.</p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</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>45000</mn><mo>+</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mo>-</mo><mn>1800</mn></mrow></mfenced></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><strong><br>Note:</strong> Award <strong><em>(M1)</em></strong> for their correct substitution into arithmetic sequence formula, equated to zero.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>n</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mo> </mo><mn>26</mn></math> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong><br>Note:</strong> Follow through from part (c). Award at most <em><strong>(M1)(A0)</strong></em> if their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> is not a positive integer.</p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math><strong> </strong> <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong><br>Note:</strong> Follow through from part (e)(i), but only if their final answer in (e)(i) is positive. If their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> in part (e)(i) is not an integer, award <em><strong>(A1)</strong></em><strong>(ft)</strong> for the nearest lower integer.</p>
<p><br><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>S</mi><mn>8</mn></msub><mo>=</mo></mrow></mfenced><mo> </mo><mfrac><mn>8</mn><mn>2</mn></mfrac><mfenced><mrow><mn>2</mn><mo>×</mo><mn>45000</mn><mo>+</mo><mfenced><mrow><mn>8</mn><mo>-</mo><mn>1</mn></mrow></mfenced><mo>×</mo><mfenced><mrow><mo>-</mo><mn>1800</mn></mrow></mfenced></mrow></mfenced></math><strong> </strong> <em><strong>(M1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitutions in arithmetic series formula. If a list method is used, award <em><strong>(M1)</strong></em> for the addition of their <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> correct terms.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>310</mn><mo> </mo><mn>000</mn><mo> </mo><mfenced><msup><mtext>m</mtext><mn>3</mn></msup></mfenced><mo> </mo><mfenced><mrow><mn>309</mn><mo> </mo><mn>600</mn></mrow></mfenced></math> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><br><strong>Note:</strong> Follow through from part (c). Award at most <em><strong>(M1)(A0)</strong></em> if their final answer is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>624</mn><mo> </mo><mn>000</mn></math>.</p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>S</mi><mn>25</mn></msub><mo>=</mo></mrow></mfenced><mo> </mo><mfrac><mn>25</mn><mn>2</mn></mfrac><mfenced><mrow><mn>2</mn><mo>×</mo><mn>45000</mn><mo>+</mo><mfenced><mrow><mn>25</mn><mo>-</mo><mn>1</mn></mrow></mfenced><mo>×</mo><mfenced><mrow><mo>-</mo><mn>1800</mn></mrow></mfenced></mrow></mfenced><mo> </mo><mo> </mo><mo>,</mo><mo> </mo><mo> </mo><mfenced><mrow><msub><mi>S</mi><mn>25</mn></msub><mo>=</mo></mrow></mfenced><mo> </mo><mfrac><mn>25</mn><mn>2</mn></mfrac><mfenced><mrow><mn>45000</mn><mo>+</mo><mn>1800</mn></mrow></mfenced></math><strong> </strong> <em><strong>(M1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitutions into arithmetic series formula.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mn>25</mn></msub><mo>=</mo><mn>585000</mn><mo> </mo><mfenced><msup><mtext>m</mtext><mn>3</mn></msup></mfenced></math> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)(A1)</strong></em> for correctly finding <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mn>26</mn></msub><mo>=</mo><mn>585000</mn><mo> </mo><mfenced><msup><mtext>m</mtext><mn>3</mn></msup></mfenced></math>, provided working is shown e.g. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>S</mi><mn>26</mn></msub><mo>=</mo></mrow></mfenced><mo> </mo><mfrac><mn>26</mn><mn>2</mn></mfrac><mfenced><mrow><mn>2</mn><mo>×</mo><mn>45000</mn><mo>+</mo><mfenced><mrow><mn>26</mn><mo>-</mo><mn>1</mn></mrow></mfenced><mo>×</mo><mfenced><mrow><mo>-</mo><mn>1800</mn></mrow></mfenced></mrow></mfenced></math> , <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>S</mi><mn>26</mn></msub><mo>=</mo></mrow></mfenced><mo> </mo><mfrac><mn>26</mn><mn>2</mn></mfrac><mfenced><mrow><mn>45000</mn><mo>+</mo><mn>0</mn></mrow></mfenced></math>. Follow through from part (c) and either their (e)(i) or (e)(ii). If <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo><</mo><mn>0</mn></math> and their final answer is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>624</mn><mo> </mo><mn>000</mn></math>, award at most <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(R0)</strong></em>. If <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>></mo><mn>0</mn></math>, there is no maximum, award at most <em><strong>(M1)(A0)(R0)</strong></em>. Award no marks if their number of terms is not a positive integer.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>585000</mn><mo> </mo><mfenced><msup><mtext>m</mtext><mn>3</mn></msup></mfenced><mo><</mo><mn>624000</mn><mo> </mo><mfenced><msup><mtext>m</mtext><mn>3</mn></msup></mfenced></math> <em><strong>(R1)</strong></em></p>
<p>Hence it will never be filled <em><strong>(AG)</strong></em></p>
<p><br><strong>Note:</strong> The <em><strong>(AG)</strong></em> line must be seen. If it is omitted do not award the final <em><strong>(R1)</strong></em>. Do not follow through within the part.<br>For unsupported <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi>S</mi><mn>25</mn></msub></mfenced><mo>=</mo><mn>585000</mn></math> seen, award at most <em><strong>(G1)(R1)(AG)</strong></em>. Working must be seen to follow through from parts (c) and (e)(i) or (e)(ii).</p>
<p><br><strong>OR</strong></p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>S</mi><mi>n</mi></msub><mo>=</mo></mrow></mfenced><mo> </mo><mfrac><mi>n</mi><mn>2</mn></mfrac><mfenced><mrow><mn>2</mn><mo>×</mo><mn>45000</mn><mo>+</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>×</mo><mfenced><mrow><mo>-</mo><mn>1800</mn></mrow></mfenced></mrow></mfenced></math><strong> </strong> <em><strong>(M1)</strong></em></p>
<p><em><strong><br></strong></em><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution into arithmetic series formula, with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>.</p>
<p><br>Maximum of this function <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>585225</mn><mo> </mo><mfenced><msup><mtext>m</mtext><mn>3</mn></msup></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>Note:</strong> Follow through from part (c). Award at most <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(R0)</strong></em> if their final answer is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>624</mn><mo> </mo><mn>000</mn></math>. Award at most <em><strong>(M1)(A0)(R0)</strong></em> if their common difference is not <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>–</mo><mn>1800</mn></math>. Award at most <em><strong>(M1)(A0)(R0)</strong></em> if <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>585</mn><mo> </mo><mn>225</mn></math> is not explicitly identified as the maximum of the function.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>585225</mn><mo> </mo><mfenced><msup><mtext>m</mtext><mn>3</mn></msup></mfenced><mo><</mo><mn>624000</mn><mo> </mo><mfenced><msup><mtext>m</mtext><mn>3</mn></msup></mfenced></math> <em><strong>(R1)</strong></em><br><br>Hence it will never be filled <em><strong>(AG)</strong></em></p>
<p><br><strong>Note:</strong> The <em><strong>(AG)</strong></em> line must be seen. If it is omitted do not award the final <em><strong>(R1)</strong></em>. Do not follow through within the part.</p>
<p><br><strong>OR</strong></p>
<p><br>sketch with concave down curve <strong>and</strong> labelled <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>624000</mn></math> horizontal line<strong> </strong> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Accept a label of “tank volume” instead of a numerical value. Award <em><strong>(M0)</strong></em> if the line and the curve intersect.</p>
<p><br>curve explicitly labelled as <strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>S</mi><mi>n</mi></msub><mo>=</mo></mrow></mfenced><mo> </mo><mfrac><mi>n</mi><mn>2</mn></mfrac><mfenced><mrow><mn>2</mn><mo>×</mo><mn>45000</mn><mo>+</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>×</mo><mfenced><mrow><mo>-</mo><mn>1800</mn></mrow></mfenced></mrow></mfenced></math> </strong>or equivalent <em><strong>(A1)<br></strong></em><strong><br>Note:</strong> Award <em><strong>(A1)</strong></em> for a written explanation interpreting the sketch. Accept a comparison of values, e.g <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>585225</mn><mo> </mo><mfenced><msup><mtext>m</mtext><mn>3</mn></msup></mfenced><mo><</mo><mn>624000</mn><mo> </mo><mfenced><msup><mtext>m</mtext><mn>3</mn></msup></mfenced></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>585225</mn></math> is the graphical maximum. Award at most <em><strong>(M1)(A0)(R0)</strong></em> if their common difference is not <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>–</mo><mn>1800</mn></math>.</p>
<p><br>the line and the curve do not intersect <em><strong>(R1)</strong></em></p>
<p>hence it will never be filled <em><strong>(AG)</strong></em></p>
<p><br><strong>Note:</strong> The <em><strong>(AG)</strong></em> line must be seen. If it is omitted do not award the final <em><strong>(R1)</strong></em>. Do not follow through within the part.</p>
<p><br><strong>OR</strong></p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>624000</mn><mo>=</mo><mfrac><mi>n</mi><mn>2</mn></mfrac><mfenced><mrow><mn>2</mn><mo>×</mo><mn>45000</mn><mo>+</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>×</mo><mfenced><mrow><mo>-</mo><mn>1800</mn></mrow></mfenced></mrow></mfenced></math><strong> </strong> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correctly substituted arithmetic series formula equated to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>624000</mn><mo> </mo><mo>(</mo><mn>623538</mn><mo>)</mo></math>.</p>
<p><br>Demonstrates there is no solution <em><strong>(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for a correct working that the discriminant is less than zero <strong>OR</strong> correct working indicating there is no real solution in the quadratic formula.</p>
<p><br>There is no (real) solution (to this equation) <em><strong>(</strong><strong>R1)</strong></em></p>
<p>hence it will never be filled <em><strong>(AG)</strong></em></p>
<p><br><strong>Note:</strong> At most <em><strong>(M1)(A0)(R0)</strong></em> for their correctly substituted arithmetic series formula <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>624000</mn><mo>,</mo><mo> </mo><mn>623538</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>622800</mn></math> with a statement "no solution". Follow through from their part (b).</p>
<p><em><strong><br>[3 marks]</strong></em></p>
<div class="question_part_label">g.</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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="question">
<p>The sum of an infinite geometric sequence is 33.25. The second term of the sequence is 7.98. Find the possible values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>.</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 substitution into formula for infinite geometric series <strong><em>(A1)</em></strong></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="33.25 = \frac{{{u_1}}}{{1 - r}}">
<mn>33.25</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
</mrow>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mi>r</mi>
</mrow>
</mfrac>
</math></span></p>
<p>correct substitution into formula for <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> (seen anywhere) <strong><em>(A1)</em></strong></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7.98 = {u_1}r">
<mn>7.98</mn>
<mo>=</mo>
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
<mi>r</mi>
</math></span></p>
<p>attempt to express <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> in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> (or vice-versa) <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_1} = \frac{{7.98}}{r}">
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>7.98</mn>
</mrow>
<mi>r</mi>
</mfrac>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_1} = 33.25\left( {1 - r} \right)">
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>=</mo>
<mn>33.25</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mi>r</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \frac{{7.98}}{{{u_1}}}">
<mi>r</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>7.98</mn>
</mrow>
<mrow>
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
</mrow>
</mfrac>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \frac{{33.25 - {u_1}}}{{33.25}}">
<mi>r</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>33.25</mn>
<mo>−</mo>
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
</mrow>
<mrow>
<mn>33.25</mn>
</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="\frac{{\left( {\frac{{7.98}}{r}} \right)}}{{1 - r}} = 33.25">
<mfrac>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>7.98</mn>
</mrow>
<mi>r</mi>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mi>r</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mn>33.25</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="33.25\left( {1 - r} \right) = \frac{{7.98}}{r}">
<mn>33.25</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mi>r</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>7.98</mn>
</mrow>
<mi>r</mi>
</mfrac>
</math></span>, (0.4, 19.95), (0.6, 13.3), <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{u_1}}}{{1 - \frac{{7.98}}{{{u_1}}}}} = 33.25">
<mfrac>
<mrow>
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
</mrow>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mrow>
<mn>7.98</mn>
</mrow>
<mrow>
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
</mrow>
</mfrac>
</mrow>
</mfrac>
<mo>=</mo>
<mn>33.25</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = 0.4\,\,\,\,\left( { = \frac{2}{5}} \right)">
<mi>r</mi>
<mo>=</mo>
<mn>0.4</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mfrac>
<mn>2</mn>
<mn>5</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = 0.6\,\,\,\,\left( { = \frac{3}{5}} \right)">
<mi>r</mi>
<mo>=</mo>
<mn>0.6</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mfrac>
<mn>3</mn>
<mn>5</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>A1A1</em></strong> <strong><em>N3</em></strong></p>
<p> </p>
<p><em><strong>[6 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>Maegan designs a decorative glass face for a new Fine Arts Centre. The glass face is made up of small triangular panes. The <strong>first</strong> three levels of the glass face are illustrated in the following diagram.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mtext>st</mtext></math> level, at the bottom of the glass face, has <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> triangular panes. The <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mtext>nd</mtext></math> level has <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math> triangular panes, and the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mtext>rd</mtext></math> level has <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math> triangular panes. Each additional level has <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> more triangular panes than the level below it.</p>
</div>
<div class="specification">
<p>Maegan has <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn></math> triangular panes to build the decorative glass face and does not want it to have any incomplete levels.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of triangular panes in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mtext>th</mtext></math> level.</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>Show that the total number of triangular panes, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mi>n</mi></msub></math>, in the first <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> levels is given by:</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mi>n</mi></msub><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>n</mi></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><strong>Hence</strong>, find the total number of panes in a glass face with <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math> levels.</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 maximum number of <strong>complete</strong> levels that Maegan can build.</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>Each triangular pane has an area of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>84</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup></math>.</p>
<p>Find the <strong>total</strong> area of the decorative glass face, if the maximum number of complete levels were built. Express your area to the nearest <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>m</mtext><mn>2</mn></msup></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</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>u</mi><mn>12</mn></msub><mo>=</mo><mn>5</mn><mo>+</mo><mfenced><mrow><mn>12</mn><mo>-</mo><mn>1</mn></mrow></mfenced><mo>×</mo><mfenced><mn>2</mn></mfenced></math> <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted arithmetic sequence formula, <em><strong>(A1)</strong></em> for correct substitutions.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn></math> <strong><em>(A1)</em><em>(G3)</em></strong></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"><msub><mi>S</mi><mi>n</mi></msub><mo>=</mo><mfrac><mi>n</mi><mn>2</mn></mfrac><mfenced><mrow><mn>2</mn><mo>×</mo><mn>5</mn><mo>+</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mfenced><mn>2</mn></mfenced></mrow></mfenced></math> <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted arithmetic sequence formula, <em><strong>(A1)</strong></em> for correct substitutions.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mi>n</mi></msub><mo>=</mo><mfrac><mi>n</mi><mn>2</mn></mfrac><mfenced><mrow><mn>8</mn><mo>+</mo><mn>2</mn><mi>n</mi></mrow></mfenced></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mi>n</mi></msub><mo>=</mo><mi>n</mi><mfenced><mrow><mn>5</mn><mo>+</mo><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for evidence of expansion and simplification, or division by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> leading to the final answer.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mi>n</mi></msub><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>n</mi></math> <em><strong>(AG)</strong></em></p>
<p><strong>Note:</strong> The final line must be seen, with no incorrect working, for the final <em><strong>(M1)</strong></em> to be awarded.</p>
<p><em><strong>[3 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><mrow><msub><mi>S</mi><mn>18</mn></msub><mo>=</mo></mrow></mfenced><msup><mn>18</mn><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>×</mo><mn>18</mn></math> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted formula for <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mi>n</mi></msub></math>.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>S</mi><mn>18</mn></msub><mo>=</mo></mrow></mfenced><mo> </mo><mn>396</mn></math> <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> The use of “hence” in the question paper means that the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mi>n</mi></msub></math> formula (from part (b)) must be used.</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"><mn>1000</mn><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>n</mi></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn><mo>=</mo><mfrac><mi>n</mi><mn>2</mn></mfrac><mfenced><mrow><mn>10</mn><mo>+</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></mrow></mfenced></math> (or equivalent) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mi>n</mi></msub></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn></math> or for equating the correctly substituted sum of arithmetic sequence formula to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn></math>.</p>
<p><strong>OR</strong></p>
<p>a sketch of the graphs <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mi>n</mi></msub><mo>=</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>n</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mi>n</mi></msub><mo>=</mo><mn>1000</mn></math> intersecting <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for a sketch of a quadratic and a horizontal line with at least one point of intersection.</p>
<p><strong>OR</strong></p>
<p>a sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>n</mi><mo>-</mo><mn>1000</mn></math> intersecting the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for a sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>n</mi><mo>-</mo><mn>1000</mn></math> with at least one <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-intercept.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>n</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>29</mn><mo>.</mo><mn>6859</mn><mo>…</mo></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>+</mo><mn>2</mn><msqrt><mn>251</mn></msqrt></math> <em><strong>(A1)</strong></em></p>
<p><strong>Note</strong>: Award <em><strong>(A1)</strong> </em>for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>29</mn><mo>.</mo><mn>6859</mn><mo>…</mo></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>+</mo><mn>2</mn><msqrt><mn>251</mn></msqrt></math> seen. Can be implied by a correct final answer.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>n</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>29</mn></math> <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></p>
<p><strong>Note:</strong> Do not accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math>. Award a maximum of <em><strong>(M1)(A1)(A0)</strong></em> if two final answers are given. Follow though from their unrounded answer.</p>
<p><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mn>30</mn></msub><mo>=</mo><mn>1020</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mn>29</mn></msub><mo>=</mo><mn>957</mn></math> <em><strong>(A2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A2)</strong></em> for both “crossover” values seen. Do not split this <em><strong>(A2)</strong></em> mark.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>n</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>29</mn></math> <em><strong>(A1)</strong></em><strong><em>(G2)</em></strong></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>A</mi><mo>=</mo></mrow></mfenced><mo> </mo><mfenced><mrow><msup><mn>29</mn><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>×</mo><mn>29</mn></mrow></mfenced><mo>×</mo><mfenced><mrow><mn>1</mn><mo>.</mo><mn>84</mn></mrow></mfenced></math> <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution to find the total number of triangular panes. Award <em><strong>(M1)</strong></em> for multiplying their number of panes by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>84</mn></math>.</p>
<p><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>A</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>957</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>84</mn></math> <em><strong>(A1)</strong></em><strong>(ft)<em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for their <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>957</mn></math> seen. Award <em><strong>(M1)</strong></em> for multiplying their number of panes by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>84</mn></math>. Follow through from part (d).</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>A</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>1760</mn><mo>.</mo><mn>88</mn><mo> </mo><mfenced><msup><mtext>m</mtext><mn>2</mn></msup></mfenced></math> <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>A</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>1761</mn><mo> </mo><mfenced><msup><mtext>m</mtext><mn>2</mn></msup></mfenced></math> <em><strong>(A1)</strong></em><strong>(ft)<em>(G3)</em></strong></p>
<p><em><strong>[4 marks]</strong></em></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>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>
<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) <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>u</mi><mn>1</mn></msub><msub><mi>u</mi><mn>2</mn></msub></mfrac><mo>,</mo><mo> </mo><mfrac><mstyle displaystyle="true"><mfrac><mn>1</mn><mn>4</mn></mfrac><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mi>a</mi></mstyle><mi>a</mi></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mi>a</mi><mo>-</mo><mn>3</mn></math> <em><strong>A1 N2</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>recognizing <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mrow><mo> </mo><mi>r</mi><mo> </mo></mrow></mfenced><mo><</mo><mn>1</mn></math> (must be in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>) <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mrow><mfrac><mn>1</mn><mn>4</mn></mfrac><mi>a</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo><</mo><mn>1</mn><mo>,</mo><mo> </mo><mo> </mo><mo>-</mo><mn>1</mn><mo>≤</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mi>a</mi><mo>-</mo><mn>3</mn><mo>≤</mo><mn>1</mn><mo>,</mo><mo> </mo><mo> </mo><mo>-</mo><mn>4</mn><mo><</mo><mi>a</mi><mo>-</mo><mn>12</mn><mo><</mo><mn>4</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo><</mo><mi>a</mi><mo><</mo><mn>16</mn></math> <em><strong>A2 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct equation <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>a</mi><mrow><mn>1</mn><mo>-</mo><mfenced><mrow><mstyle displaystyle="true"><mfrac><mn>1</mn><mn>4</mn></mfrac></mstyle><mi>a</mi><mo>-</mo><mn>3</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mn>76</mn><mo> </mo><mo>,</mo><mo> </mo><mi>a</mi><mo>=</mo><mn>76</mn><mfenced><mrow><mn>4</mn><mo>-</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mi>a</mi></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mn>76</mn><mn>5</mn></mfrac><mo> </mo><mfenced><mrow><mo>=</mo><mn>15</mn><mo>.</mo><mn>2</mn></mrow></mfenced></math> (exact) <em><strong>A2 N3</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>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 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">[4]</div>
<div class="question_part_label">a.</div>
</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>
<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>attempt to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
<mi>d</mi>
</math></span> <em><strong>(M1)</strong></em></p>
<p>eg 1.4 − 1.3 , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_1} - {u_2}">
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>−</mo>
<mrow>
<msub>
<mi>u</mi>
<mn>2</mn>
</msub>
</mrow>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1.4 = 1.3 + \left( {2 - 1} \right)d">
<mn>1.4</mn>
<mo>=</mo>
<mn>1.3</mn>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mi>d</mi>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d = 0.1">
<mi>d</mi>
<mo>=</mo>
<mn>0.1</mn>
</math></span> (may be seen in expression for <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>) <em><strong>(A1)</strong></em></p>
<p>correct equation <em><strong>(A1)</strong></em></p>
<p>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1.3 + \left( {k - 1} \right) \times 0.1 = 31.2">
<mn>1.3</mn>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>k</mi>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mn>0.1</mn>
<mo>=</mo>
<mn>31.2</mn>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.1k = 30">
<mn>0.1</mn>
<mi>k</mi>
<mo>=</mo>
<mn>30</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 300">
<mi>k</mi>
<mo>=</mo>
<mn>300</mn>
</math></span> <em><strong>A1 N3</strong></em></p>
<p style="text-align: start;"><em><strong><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[4 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{300}}{2}\left( {1.3 + 31.2} \right)">
<mfrac>
<mrow>
<mn>300</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mn>1.3</mn>
<mo>+</mo>
<mn>31.2</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{300}}{2}\left[ {2\left( {1.3} \right) + \left( {300 - 1} \right)\left( {0.1} \right)} \right]">
<mfrac>
<mrow>
<mn>300</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mrow>
<mo>[</mo>
<mrow>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>1.3</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>300</mn>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.1</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>]</mo>
</mrow>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{300}}{2}\left[ {2.6 + 299\left( {0.1} \right)} \right]">
<mfrac>
<mrow>
<mn>300</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mrow>
<mo>[</mo>
<mrow>
<mn>2.6</mn>
<mo>+</mo>
<mn>299</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.1</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>]</mo>
</mrow>
</math></span> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_k} = 4875">
<mrow>
<msub>
<mi>S</mi>
<mi>k</mi>
</msub>
</mrow>
<mo>=</mo>
<mn>4875</mn>
</math></span> <em><strong>A1 N2</strong></em></p>
<p style="text-align: start;"><em><strong><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing need to find the sequence of multiples of 3 (seen anywhere) <em><strong>(M1)</strong></em></p>
<p><em>eg </em> first term is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_3}">
<mrow>
<msub>
<mi>u</mi>
<mn>3</mn>
</msub>
</mrow>
</math></span> (= 1.5) (accept notation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_1} = 1.5">
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>=</mo>
<mn>1.5</mn>
</math></span>) ,</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d = 0.1 \times 3">
<mi>d</mi>
<mo>=</mo>
<mn>0.1</mn>
<mo>×</mo>
<mn>3</mn>
</math></span> (= 0.3) , 100 terms (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = 100">
<mi>n</mi>
<mo>=</mo>
<mn>100</mn>
</math></span>), last term is 31.2</p>
<p>(accept notation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_{100}} = 31.2">
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mn>100</mn>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mn>31.2</mn>
</math></span>) , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_3} + {u_6} + {u_9} + \ldots ">
<mrow>
<msub>
<mi>u</mi>
<mn>3</mn>
</msub>
</mrow>
<mo>+</mo>
<mrow>
<msub>
<mi>u</mi>
<mn>6</mn>
</msub>
</mrow>
<mo>+</mo>
<mrow>
<msub>
<mi>u</mi>
<mn>9</mn>
</msub>
</mrow>
<mo>+</mo>
<mo>…</mo>
</math></span> (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="F = {u_3} + {u_6} + {u_9} + \ldots ">
<mi>F</mi>
<mo>=</mo>
<mrow>
<msub>
<mi>u</mi>
<mn>3</mn>
</msub>
</mrow>
<mo>+</mo>
<mrow>
<msub>
<mi>u</mi>
<mn>6</mn>
</msub>
</mrow>
<mo>+</mo>
<mrow>
<msub>
<mi>u</mi>
<mn>9</mn>
</msub>
</mrow>
<mo>+</mo>
<mo>…</mo>
</math></span>)</p>
<p>correct working for sum of sequence where n is a multiple of 3 <em><strong>A2</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{100}}{2}\left( {1.5 + 31.2} \right)">
<mfrac>
<mrow>
<mn>100</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mn>1.5</mn>
<mo>+</mo>
<mn>31.2</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="50\left( {2 \times 1.5 + 99 \times 0.3} \right)">
<mn>50</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>1.5</mn>
<mo>+</mo>
<mn>99</mn>
<mo>×</mo>
<mn>0.3</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> , 1635</p>
<p>valid approach (seen anywhere) <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_k} - \left( {{u_3} + {u_6} + \ldots } \right)">
<mrow>
<msub>
<mi>S</mi>
<mi>k</mi>
</msub>
</mrow>
<mo>−</mo>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msub>
<mi>u</mi>
<mn>3</mn>
</msub>
</mrow>
<mo>+</mo>
<mrow>
<msub>
<mi>u</mi>
<mn>6</mn>
</msub>
</mrow>
<mo>+</mo>
<mo>…</mo>
</mrow>
<mo>)</mo>
</mrow>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_k} - \frac{{100}}{2}\left( {1.5 + 31.2} \right)">
<mrow>
<msub>
<mi>S</mi>
<mi>k</mi>
</msub>
</mrow>
<mo>−</mo>
<mfrac>
<mrow>
<mn>100</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mn>1.5</mn>
<mo>+</mo>
<mn>31.2</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> , <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>
<mo>−</mo>
</math></span> (their sum for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {{u_3} + {u_6} + \ldots } \right)">
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msub>
<mi>u</mi>
<mn>3</mn>
</msub>
</mrow>
<mo>+</mo>
<mrow>
<msub>
<mi>u</mi>
<mn>6</mn>
</msub>
</mrow>
<mo>+</mo>
<mo>…</mo>
</mrow>
<mo>)</mo>
</mrow>
</math></span>)</p>
<p>correct working (seen anywhere) <em><strong>A1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_k} - 1635">
<mrow>
<msub>
<mi>S</mi>
<mi>k</mi>
</msub>
</mrow>
<mo>−</mo>
<mn>1635</mn>
</math></span> , 4875 − 1635</p>
<p><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> <em><strong>AG N0</strong></em></p>
<p style="text-align: start;"><em><strong><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[5 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">attempt to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> <em><strong>(M1)</strong></em><br></span></p>
<p style="text-align: start;"><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> dividing consecutive terms<br></span></p>
<p style="text-align: start;"><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">correct value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> (seen anywhere, including in formula)<br></span></p>
<p style="text-align: start;"><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{\sqrt 2 }}">
<mfrac>
<mn>1</mn>
<mrow>
<msqrt>
<mn>2</mn>
</msqrt>
</mrow>
</mfrac>
</math></span> , 0.707106… , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{a}{{0.293 \ldots }}">
<mfrac>
<mi>a</mi>
<mrow>
<mn>0.293</mn>
<mo>…</mo>
</mrow>
</mfrac>
</math></span></span></p>
<p style="text-align: start;"><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">correct working (accept equation) <em><strong> (A1)</strong></em><br></span></p>
<p style="text-align: start;"><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{a}{{1 - \frac{1}{{\sqrt 2 }}}} < 3240">
<mfrac>
<mi>a</mi>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msqrt>
<mn>2</mn>
</msqrt>
</mrow>
</mfrac>
</mrow>
</mfrac>
<mo><</mo>
<mn>3240</mn>
</math></span></span></p>
<p style="text-align: start;"><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">correct working <em><strong>A1</strong></em><br></span></p>
<p style="text-align: start;"> </p>
<p style="text-align: start;"><span style="font-size: 10.5pt;"><strong><span style="font-family: Verdana, sans-serif;color: black;">METHOD 1 (analytical)</span></strong></span></p>
<p style="text-align: start;"><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3240 \times \left( {1 - \frac{1}{{\sqrt 2 }}} \right)">
<mn>3240</mn>
<mo>×</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msqrt>
<mn>2</mn>
</msqrt>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a < 948.974">
<mi>a</mi>
<mo><</mo>
<mn>948.974</mn>
</math></span> , 948.974</span></p>
<p style="text-align: start;"><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><strong>METHOD 2 (using table, must find both <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> values)</strong><br></span></p>
<p style="text-align: start;"><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 948">
<mi>a</mi>
<mo>=</mo>
<mn>948</mn>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_\infty } = 3236.67 \ldots ">
<mrow>
<msub>
<mi>S</mi>
<mi mathvariant="normal">∞</mi>
</msub>
</mrow>
<mo>=</mo>
<mn>3236.67</mn>
<mo>…</mo>
</math></span> <strong>AND </strong> when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 949">
<mi>a</mi>
<mo>=</mo>
<mn>949</mn>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{S_\infty } = 3240.08 \ldots ">
<mrow>
<msub>
<mi>S</mi>
<mi mathvariant="normal">∞</mi>
</msub>
</mrow>
<mo>=</mo>
<mn>3240.08</mn>
<mo>…</mo>
</math></span></span></p>
<p style="text-align: start;"><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 948">
<mi>a</mi>
<mo>=</mo>
<mn>948</mn>
</math></span> <em><strong>A1 N2</strong></em></span></p>
<p style="text-align: start;"><em><strong><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[5 marks]</span></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;">
[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>
<br><hr><br><div class="specification">
<p>A new concert hall was built with <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math> seats in the first row. Each subsequent row of the hall has two more seats than the previous row. The hall has a total of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math> rows.</p>
</div>
<div class="specification">
<p>Find:</p>
</div>
<div class="specification">
<p>The concert hall opened in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2019</mn></math>. The average number of visitors per concert during that year was <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>584</mn></math>. In <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2020</mn></math>, the average number of visitors per concert increased by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>2</mn><mo>%</mo></math>.</p>
</div>
<div class="specification">
<p>The concert organizers use this data to model future numbers of visitors. It is assumed that the average number of visitors per concert will continue to increase each year by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>2</mn><mo>%</mo></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the number of seats in the last row.</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>the total number of seats in the concert hall.</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 average number of visitors per concert in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2020</mn></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>Determine the first year in which this model predicts the average number of visitors per concert will exceed the total seating capacity of the concert hall.</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>It is assumed that the concert hall will host <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math> concerts each year.</p>
<p>Use the average number of visitors per concert per year to predict the <strong>total</strong> number of people expected to attend the concert hall from when it opens until the end of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2025</mn></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>recognition of arithmetic sequence with common difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> <em><strong>(M1)</strong></em> </p>
<p>use of arithmetic sequence formula <em><strong>(M1)</strong></em> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>+</mo><mn>2</mn><mfenced><mrow><mn>20</mn><mo>-</mo><mn>1</mn></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>52</mn></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of arithmetic series formula <em><strong>(M1)</strong></em> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>14</mn><mo>+</mo><mn>52</mn></mrow><mn>2</mn></mfrac><mo>×</mo><mn>20</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>660</mn></math> <strong><em>A1</em></strong></p>
<p> </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><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>584</mn><mo>+</mo><mfenced><mrow><mn>584</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>012</mn></mrow></mfenced></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>584</mn><mo>×</mo><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>012</mn></mrow></mfenced><mn>1</mn></msup></math> <em><strong>(M1)</strong></em> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>591</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>591</mn><mo>.</mo><mn>008</mn></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>M0A0</strong></em> if incorrect <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> used in part (b), and <em><strong>FT</strong></em> with their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> in parts (c) and (d).<br><br></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>recognition of geometric sequence <em><strong>(M1)</strong></em> </p>
<p>equating their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>th geometric sequence term to their <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>660</mn></math> <em><strong>(M1)</strong></em> </p>
<p><br><strong>Note:</strong> Accept inequality.<br><br><strong><br>METHOD 1<br></strong></p>
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>600</mn><mo>=</mo><mn>584</mn><mo>×</mo><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>012</mn></mrow></mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></msup></math> <strong><em>A1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn><mo>=</mo></mrow></mfenced><mo> </mo><mn>10</mn><mo>.</mo><mn>3</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>10</mn><mo>.</mo><mn>2559</mn><mo>…</mo></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>11</mn><mo>.</mo><mn>3</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>11</mn><mo>.</mo><mn>2559</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2030</mn></math> <strong><em>A1</em></strong></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>600</mn><mo>=</mo><mn>584</mn><mo>×</mo><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>012</mn></mrow></mfenced><mi>x</mi></msup></math> <strong><em>A1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>10</mn><mo>.</mo><mn>3</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>10</mn><mo>.</mo><mn>2559</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2030</mn></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>11<sup>th</sup> term <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>658</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>657</mn><mo>.</mo><mn>987</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(M1)A1</strong></em> </p>
<p>12<sup>th</sup> term <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>666</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>666</mn><mo>.</mo><mn>883</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(M1)A1</strong></em> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2030</mn></math> <strong><em>A1</em></strong></p>
<p><br><strong>Note:</strong> The last mark can be awarded if both their 11<sup>th</sup> and 12<sup>th</sup> correct terms are seen.<br><br></p>
<p><em><strong>[5 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"><mn>7</mn></math> seen <em><strong>(A1)</strong></em> </p>
<p><br><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>584</mn><mfenced><mfrac><mrow><mn>1</mn><mo>.</mo><msup><mn>012</mn><mn>7</mn></msup><mo>-</mo><mn>1</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>012</mn><mo>-</mo><mn>1</mn></mrow></mfrac></mfenced></math> <em><strong>(M1)</strong></em> </p>
<p>multiplying their sum by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math> <em><strong>(M1)</strong></em> </p>
<p><br><strong>OR</strong></p>
<p>sum of the number of visitors for their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> and their seven years <em><strong>(M1)</strong></em> </p>
<p>multiplying their sum by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math> <em><strong>(M1)</strong></em> </p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>29</mn><mo> </mo><mn>200</mn><mfenced><mfrac><mrow><mn>1</mn><mo>.</mo><msup><mn>012</mn><mn>7</mn></msup><mo>-</mo><mn>1</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>012</mn><mo>-</mo><mn>1</mn></mrow></mfrac></mfenced></math> <em><strong>(M1)</strong></em><em><strong>(M1)</strong></em> </p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>212000</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>211907</mn><mo>.</mo><mn>3</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p><br><strong>Note:</strong> Follow though from their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> from part (b).<br><br></p>
<p><em><strong>[4 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;">
[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>
<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>
<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>
<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>attempt to add corresponding terms <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2 + 2{\text{,}}\,\,6 + \left( { - 6} \right){\text{,}}\,\,2{\left( 3 \right)^{n - 1}} + \,2{\left( { - 3} \right)^{n - 1}}">
<mn>2</mn>
<mo>+</mo>
<mn>2</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>6</mn>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>2</mn>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mspace width="thinmathspace"></mspace>
<mn>2</mn>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span></p>
<p>correct value for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{w_5}">
<mrow>
<msub>
<mi>w</mi>
<mn>5</mn>
</msub>
</mrow>
</math></span> <em><strong>(A1) </strong></em></p>
<p><em>eg</em> 324</p>
<p>4, 36, 324 (accept 4 + 36 + 324) <em><strong> A1 N3</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>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4 \times {r^1} = 36">
<mn>4</mn>
<mo>×</mo>
<mrow>
<msup>
<mi>r</mi>
<mn>1</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>36</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4 \times {9^{n - 1}}">
<mn>4</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>9</mn>
<mrow>
<mi>n</mi>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = 9">
<mi>r</mi>
<mo>=</mo>
<mn>9</mn>
</math></span> (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum\limits_{k = 0}^m {4 \times {9^k}} ">
<munderover>
<mo movablelimits="false">∑</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>m</mi>
</munderover>
<mrow>
<mn>4</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>9</mn>
<mi>k</mi>
</msup>
</mrow>
</mrow>
</math></span>; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> may be incorrect) <em><strong> A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition that 225 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> consists of 113 non-zero terms <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum\limits_1^{113} {} ">
<munderover>
<mo movablelimits="false">∑</mo>
<mn>1</mn>
<mrow>
<mn>113</mn>
</mrow>
</munderover>
<mrow>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum\limits_0^{112} {} ">
<munderover>
<mo movablelimits="false">∑</mo>
<mn>0</mn>
<mrow>
<mn>112</mn>
</mrow>
</munderover>
<mrow>
</mrow>
</math></span>, 113</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m = 112">
<mi>m</mi>
<mo>=</mo>
<mn>112</mn>
</math></span> (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum\limits_{k = 0}^112 {4 \times {r^k}} ">
<munderover>
<mo movablelimits="false">∑</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mn>1</mn>
</munderover>
<mn>12</mn>
<mrow>
<mn>4</mn>
<mo>×</mo>
<mrow>
<msup>
<mi>r</mi>
<mi>k</mi>
</msup>
</mrow>
</mrow>
</math></span>; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> may be incorrect) <em><strong> A1 N2</strong></em></p>
<p><em><strong>[2 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;">
[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="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>
<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>attempt 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{{576}}{{768}},{\text{ }}\frac{{768}}{{576}},{\text{ }}0.75"> <mfrac> <mrow> <mn>576</mn> </mrow> <mrow> <mn>768</mn> </mrow> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mrow> <mn>768</mn> </mrow> <mrow> <mn>576</mn> </mrow> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0.75</mn> </math></span></p>
<p>correct expression for <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> <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="768{(0.75)^{n - 1}}"> <mn>768</mn> <mrow> <mo stretchy="false">(</mo> <mn>0.75</mn> <msup> <mo stretchy="false">)</mo> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></span></p>
<p><strong>EITHER (solving inequality)</strong></p>
<p>valid approach (accept equation) <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="{u_n} < 7"> <mrow> <msub> <mi>u</mi> <mi>n</mi> </msub> </mrow> <mo><</mo> <mn>7</mn> </math></span></p>
<p>valid approach to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n"> <mi>n</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="768{(0.75)^{n - 1}} = 7,{\text{ }}n - 1 > {\log _{0.75}}\left( {\frac{7}{{768}}} \right)"> <mn>768</mn> <mrow> <mo stretchy="false">(</mo> <mn>0.75</mn> <msup> <mo stretchy="false">)</mo> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mo>=</mo> <mn>7</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo>></mo> <mrow> <msub> <mi>log</mi> <mrow> <mn>0.75</mn> </mrow> </msub> </mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>7</mn> <mrow> <mn>768</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span>, sketch</p>
<p>correct value</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="n = 17.3301"> <mi>n</mi> <mo>=</mo> <mn>17.3301</mn> </math></span> <strong><em>(A1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = 18"> <mi>n</mi> <mo>=</mo> <mn>18</mn> </math></span> (must be an integer) <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong>OR (table of values)</strong></p>
<p>valid approach <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="{u_n} > 7"> <mrow> <msub> <mi>u</mi> <mi>n</mi> </msub> </mrow> <mo>></mo> <mn>7</mn> </math></span>, one correct crossover value</p>
<p>both crossover values, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_{17}} = 7.69735"> <mrow> <msub> <mi>u</mi> <mrow> <mn>17</mn> </mrow> </msub> </mrow> <mo>=</mo> <mn>7.69735</mn> </math></span> <strong>and</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_{18}} = 5.77301"> <mrow> <msub> <mi>u</mi> <mrow> <mn>18</mn> </mrow> </msub> </mrow> <mo>=</mo> <mn>5.77301</mn> </math></span> <strong><em>A2</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = 18"> <mi>n</mi> <mo>=</mo> <mn>18</mn> </math></span> (must be an integer) <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong>OR (sketch of functions)</strong></p>
<p>valid approach <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>sketch of appropriate functions</p>
<p>valid approach <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>finding intersections or roots (depending on function sketched)</p>
<p>correct value</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="n = 17.3301"> <mi>n</mi> <mo>=</mo> <mn>17.3301</mn> </math></span> <strong><em>(A1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = 18"> <mi>n</mi> <mo>=</mo> <mn>18</mn> </math></span> (must be an integer) <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[6 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
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