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<h2>SL Paper 2</h2><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>A large underground tank is constructed at Mills Airport to store fuel. The tank is in the shape of an isosceles trapezoidal prism, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABCDEFGH</mtext></math>.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext><mo>=</mo><mn>70</mn><mo> </mo><mtext>m</mtext></math> , <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AF</mtext><mo>=</mo><mn>200</mn><mo> </mo><mtext>m</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AD</mtext><mo>=</mo><mn>40</mn><mo> </mo><mtext>m</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BC</mtext><mo>=</mo><mn>40</mn><mo> </mo><mtext>m</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CD</mtext><mo>=</mo><mn>110</mn><mo> </mo><mtext>m</mtext></math>. Angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ADC</mtext><mo>=</mo><mn>60</mn><mo>°</mo></math> and angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BCD</mtext><mo>=</mo><mn>60</mn><mo>°</mo></math>. The tank is illustrated below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>Once construction was complete, a fuel pump was used to pump fuel <strong>into</strong> the empty tank. The amount of fuel pumped into the tank by this pump <strong>each hour</strong> decreases as an arithmetic sequence with terms <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub><mo>,</mo><mo> </mo><msub><mi>u</mi><mn>2</mn></msub><mo>,</mo><mo> </mo><msub><mi>u</mi><mn>3</mn></msub><mo>,</mo><mo> </mo><mo>…</mo><mo>,</mo><mo> </mo><msub><mi>u</mi><mi>n</mi></msub></math>.</p>
<p>Part of this sequence is shown in the table.</p>
<p style="text-align: center;"><img 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"></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="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>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>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 pan, in which to cook a pizza, is in the shape of a cylinder. The pan has a diameter of 35 cm and a height of 0.5 cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_11.14.51.png" alt="M17/5/MATSD/SP2/ENG/TZ1/04"></p>
</div>
<div class="specification">
<p>A chef had enough pizza dough to exactly fill the pan. The dough was in the shape of a sphere.</p>
</div>
<div class="specification">
<p>The pizza was cooked in a hot oven. Once taken out of the oven, the pizza was placed in a dining room.</p>
<p>The temperature, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P">
<mi>P</mi>
</math></span>, of the pizza, in degrees Celsius, °C, can be modelled by</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="P(t) = a{(2.06)^{ - t}} + 19,{\text{ }}t \geqslant 0">
<mi>P</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>a</mi>
<mrow>
<mo stretchy="false">(</mo>
<mn>2.06</mn>
<msup>
<mo stretchy="false">)</mo>
<mrow>
<mo>−<!-- − --></mo>
<mi>t</mi>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mn>19</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>t</mi>
<mo>⩾<!-- ⩾ --></mo>
<mn>0</mn>
</math></span></p>
<p>where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> is a constant and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> is the time, in minutes, since the pizza was taken out of the oven.</p>
<p>When the pizza was taken out of the oven its temperature was 230 °C.</p>
</div>
<div class="specification">
<p>The pizza can be eaten once its temperature drops to 45 °C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the volume of this pan.</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 radius of the sphere in cm, correct to one decimal place.</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>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</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>Find the temperature that the pizza will be 5 minutes after it is taken out of the oven.</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>Calculate, to the nearest second, the time since the pizza was taken out of the oven until it can be eaten.</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>In the context of this model, state what the value of 19 represents.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</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="(V = ){\text{ }}\pi \times {{\text{(17.5)}}^2} \times 0.5">
<mo stretchy="false">(</mo>
<mi>V</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>π</mi>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mtext>(17.5)</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>0.5</mn>
</math></span> <strong><em>(A1)(M1)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(A1) </em></strong>for 17.5 (or equivalent) seen.</p>
<p>Award <strong><em>(M1) </em></strong>for correct substitutions into volume of a cylinder formula.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 481{\text{ c}}{{\text{m}}^3}{\text{ }}(481.056 \ldots {\text{ c}}{{\text{m}}^3},{\text{ }}153.125\pi {\text{ c}}{{\text{m}}^3})">
<mo>=</mo>
<mn>481</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>481.056</mn>
<mo>…</mo>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>153.125</mn>
<mi>π</mi>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</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">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{4}{3} \times \pi \times {r^3} = 481.056 \ldots ">
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mo>×</mo>
<mi>π</mi>
<mo>×</mo>
<mrow>
<msup>
<mi>r</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>481.056</mn>
<mo>…</mo>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for equating <strong>their </strong>answer to part (a) to the volume of sphere.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r^3} = \frac{{3 \times 481.056 \ldots }}{{4\pi }}{\text{ }}( = 114.843 \ldots )">
<mrow>
<msup>
<mi>r</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>3</mn>
<mo>×</mo>
<mn>481.056</mn>
<mo>…</mo>
</mrow>
<mrow>
<mn>4</mn>
<mi>π</mi>
</mrow>
</mfrac>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mo>=</mo>
<mn>114.843</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correctly rearranging so <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r^3}">
<mrow>
<msup>
<mi>r</mi>
<mn>3</mn>
</msup>
</mrow>
</math></span> is the subject.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = 4.86074 \ldots {\text{ (cm)}}">
<mi>r</mi>
<mo>=</mo>
<mn>4.86074</mn>
<mo>…</mo>
<mrow>
<mtext> (cm)</mtext>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for correct unrounded answer seen. Follow through from part (a).</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 4.9{\text{ (cm)}}">
<mo>=</mo>
<mn>4.9</mn>
<mrow>
<mtext> (cm)</mtext>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> The final <strong><em>(A1)</em>(ft) </strong>is awarded for rounding their unrounded answer to one decimal place.</p>
<p> </p>
<p><strong><em>[4 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="230 = a{(2.06)^0} + 19">
<mn>230</mn>
<mo>=</mo>
<mi>a</mi>
<mrow>
<mo stretchy="false">(</mo>
<mn>2.06</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>0</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>19</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 211">
<mi>a</mi>
<mo>=</mo>
<mn>211</mn>
</math></span> <strong><em>(A1)(G2)</em></strong></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="(P = ){\text{ }}211 \times {(2.06)^{ - 5}} + 19">
<mo stretchy="false">(</mo>
<mi>P</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>211</mn>
<mo>×</mo>
<mrow>
<mo stretchy="false">(</mo>
<mn>2.06</mn>
<msup>
<mo stretchy="false">)</mo>
<mrow>
<mo>−</mo>
<mn>5</mn>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mn>19</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution into the function, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P(t)">
<mi>P</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
</math></span>. Follow through from part (c). The negative sign in the exponent is required for correct substitution.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 24.7">
<mo>=</mo>
<mn>24.7</mn>
</math></span> (°C) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(24.6878 \ldots ">
<mo stretchy="false">(</mo>
<mn>24.6878</mn>
<mo>…</mo>
</math></span> (°C)) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="45 = 211 \times {(2.06)^{ - t}} + 19">
<mn>45</mn>
<mo>=</mo>
<mn>211</mn>
<mo>×</mo>
<mrow>
<mo stretchy="false">(</mo>
<mn>2.06</mn>
<msup>
<mo stretchy="false">)</mo>
<mrow>
<mo>−</mo>
<mi>t</mi>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mn>19</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for equating 45 to the exponential equation and for correct substitution (follow through for their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> in part (c)).</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(t = ){\text{ }}2.89711 \ldots ">
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>2.89711</mn>
<mo>…</mo>
</math></span> <strong><em>(A1)</em>(ft)<em>(G1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="174{\text{ (seconds) }}\left( {173.826 \ldots {\text{ (seconds)}}} \right)">
<mn>174</mn>
<mrow>
<mtext> (seconds) </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>173.826</mn>
<mo>…</mo>
<mrow>
<mtext> (seconds)</mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award final <strong><em>(A1)</em>(ft) </strong>for converting their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{2.89711}} \ldots ">
<mrow>
<mtext>2.89711</mtext>
</mrow>
<mo>…</mo>
</math></span> minutes into seconds.</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>the temperature of the (dining) room <strong><em>(A1)</em></strong></p>
<p><strong>OR</strong></p>
<p>the lowest final temperature to which the pizza will cool <strong><em>(A1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></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.</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>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>A factory packages coconut water in cone-shaped containers with a base radius of 5.2 cm and a height of 13 cm.</p>
</div>
<div class="specification">
<p>The factory designers are currently investigating whether a cone-shaped container can be replaced with a cylinder-shaped container with the same radius and the same total surface area.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the slant height of the cone-shaped container.</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 slant height of the cone-shaped container.</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 the total surface area of the cone-shaped container is 314 cm<sup>2</sup>, correct to three significant figures.</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 height, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span>, of this cylinder-shaped container.</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>The factory director wants to increase the volume of coconut water sold per container.</p>
<p>State whether or not they should replace the cone-shaped containers with cylinder‑shaped containers. Justify your conclusion.</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><span class="mjpage"><math alttext="\frac{{\pi {{\left( {5.2} \right)}^2} \times 13}}{3}" xmlns="http://www.w3.org/1998/Math/MathML"> <mfrac> <mrow> <mi>π</mi> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mn>5.2</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>×</mo> <mn>13</mn> </mrow> <mn>3</mn> </mfrac> </math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the volume formula for cone.</p>
<p>368 (368.110…) cm<sup><span style="font-size: small;">3</span></sup> <strong><em>(A1)</em><em>(G2)</em></strong></p>
<p><strong>Note:</strong> Accept 117.173…<span class="mjpage"><math alttext="\pi " xmlns="http://www.w3.org/1998/Math/MathML"> <mi>π</mi> </math></span> cm<sup><span style="font-size: small;">3</span></sup> or <span class="mjpage"><math alttext="\frac{{8788}}{{75}}\pi " xmlns="http://www.w3.org/1998/Math/MathML"> <mfrac> <mrow> <mn>8788</mn> </mrow> <mrow> <mn>75</mn> </mrow> </mfrac> <mi>π</mi> </math></span> cm<sup><span style="font-size: small;">3</span></sup>.</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>(slant height<sup>2</sup>) = (5.2)<sup>2</sup> + 13<sup>2</sup> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into the formula.</p>
<p>14.0 (14.0014…) (cm) <strong><em>(A1)</em><em>(G2)</em></strong></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>14.0014… × (5.2) × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi ">
<mi>π</mi>
</math></span> + (5.2)<sup>2</sup> × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi ">
<mi>π</mi>
</math></span> <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution in the curved surface area formula for cone; <em><strong>(M1)</strong></em> for adding the correct area of the base. The addition must be explicitly seen for the second <em><strong>(M1)</strong></em> to be awarded. Do not accept rounded values here as may come from working backwards.</p>
<p>313.679… (cm<sup>2</sup>) <strong><em>(A1)</em></strong></p>
<p><strong>Note:</strong> Use of 3 sf value 14.0 gives an unrounded answer of 313.656….</p>
<p>314 (cm<sup>2</sup>) <strong><em>(AG)</em></strong></p>
<p><strong>Note:</strong> Both the unrounded and rounded answers must be seen for the final <strong><em>(A1)</em></strong> to be awarded.</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>2 × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi ">
<mi>π</mi>
</math></span> × (5.2) × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> + 2 × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi ">
<mi>π</mi>
</math></span> × (5.2)<sup>2</sup> = 314 <em><strong>(M1)(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the curved surface area formula for cylinder; <em><strong>(M1)</strong></em> for adding two correct base areas of the cylinder; <em><strong>(M1)</strong></em> for equating their total cylinder surface area to 314 (313.679…). For this mark to be awarded the areas of the two bases must be added to the cylinder curved surface area and equated to 314. Award at most <em><strong>(M1)(M0)(M0)</strong></em> for cylinder curved surface area equated to 314.</p>
<p>(<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> =) 4.41 (4.41051…) (cm) <strong><em>(A1)(G3)</em></strong></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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi ">
<mi>π</mi>
</math></span> × (5.2)<sup>2</sup> × 4.41051… <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the volume formula for cylinder.</p>
<p>375 (374.666…) (cm<sup>3</sup>) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong>Note</strong>: Follow through from part (d).</p>
<p>375 (cm<sup>3</sup>) > 368 (cm<sup>3</sup>) <strong><em>(R1)</em>(ft)</strong></p>
<p><strong>OR</strong></p>
<p>“volume of cylinder is larger than volume of cone” or similar <strong><em>(R1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from their answer to part (a). The verbal statement should be consistent with their answers from parts (e) and (a) for the <strong><em>(R1)</em></strong> to be awarded.</p>
<p><strong>replace</strong> with the cylinder containers <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note</strong>: Do not award <strong><em>(A1)</em>(ft)<em>(R0)</em></strong>. <strong>Follow through</strong> from their <strong>incorrect</strong> volume for the cylinder <strong>in this question part</strong> but only if substitution in the volume formula shown.</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 archaeological site is to be made accessible for viewing by the public. To do this, archaeologists built two straight paths from point A to point B and from point B to point C as shown in the following diagram. The length of path AB is 185 m, the length of path BC is 250 m, and 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> is 125°.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The archaeologists plan to build two more straight paths, AD and DC. For the paths to go around the site, angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}\mathop {\text{A}}\limits^ \wedge {\text{D}}">
<mrow>
<mtext>B</mtext>
</mrow>
<mover>
<mrow>
<mtext>A</mtext>
</mrow>
<mo>∧<!-- ∧ --></mo>
</mover>
<mo><!-- --></mo>
<mrow>
<mtext>D</mtext>
</mrow>
</math></span> is to be made equal to 85° and angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}\mathop {\text{C}}\limits^ \wedge {\text{D}}">
<mrow>
<mtext>B</mtext>
</mrow>
<mover>
<mrow>
<mtext>C</mtext>
</mrow>
<mo>∧<!-- ∧ --></mo>
</mover>
<mo><!-- --></mo>
<mrow>
<mtext>D</mtext>
</mrow>
</math></span> is to be made equal to 70° as shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the size of angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{C}}\mathop {\text{A}}\limits^ \wedge {\text{D}}">
<mrow>
<mtext>C</mtext>
</mrow>
<mover>
<mrow>
<mtext>A</mtext>
</mrow>
<mo>∧</mo>
</mover>
<mo></mo>
<mrow>
<mtext>D</mtext>
</mrow>
</math></span>.</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 size of angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}\mathop {\text{C}}\limits^ \wedge {\text{D}}">
<mrow>
<mtext>A</mtext>
</mrow>
<mover>
<mrow>
<mtext>C</mtext>
</mrow>
<mo>∧</mo>
</mover>
<mo></mo>
<mrow>
<mtext>D</mtext>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(CAD =) 53.1° (53.0521…°) <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from their part (b)(i) only if working seen.</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>(ACD = ) 70° − (180° − 125° − 31.9478°…) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for subtracting their angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}\mathop {\text{C}}\limits^ \wedge {\text{B}}">
<mrow>
<mtext>A</mtext>
</mrow>
<mover>
<mrow>
<mtext>C</mtext>
</mrow>
<mo>∧</mo>
</mover>
<mo></mo>
<mrow>
<mtext>B</mtext>
</mrow>
</math></span> from 70°.</p>
<p><strong>OR</strong></p>
<p>(ADC =) 360 − (85 + 70 + 125) = 80</p>
<p>(ACD =) 180 − 80 − 53.0521... <em><strong>(M1)</strong></em></p>
<p>46.9° (46.9478…°) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong>Note:</strong> Follow through from part (b)(i).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</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>A sector of a circle, centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math> and radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>m</mtext></math>, is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbsAAADfCAYAAABve33mAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAACN2SURBVHhe7d0LVFV12j/w78tyWROOr6mpkRGp5IhW6KtY6qRmguNrrmNarziKVGCmxghjmVKO4d0xcSgvr5fCu2OpZ1k5ilrYaBk6ZKkUUUZYDJWSQzCVy/95//vZZ2+5eIADnMve+3w/a7ng/M6Fc8H98Pv9nv08//F/ChAREVlYkPaViIjIshjsiIjI8hjsiIjI8hjsiIjI8hjsiIjI8hjsiIjI8hjsiIjI8hjsiMi3SuxICO2I0NBpsJdcUQbOw55wl3I5Bum55c7bUB0cKC/IRmbaZuTK21erMhRkZyIt8xTqvJmheO93gcGOiMhMSvZi+pDxmLP7e23AlSvK3xSzMSTuOez+waGNBTYGOyLys1thW/8xiooOILlXC22MyLMY7IjIiy6jJHcrUod1RWhoR3RLyMDhTy9q1+lcLV1Vv9/V+xaUadcrHCXI3ZyKYer1DyLVfhYF9mnO2yfYUaLc5EruckSqlzfgcOZkdJPHSc2G+ijV7i//opCQfhAF5TITkpmR/lgbkH04Awnd5DZdMWzOYZQ4lOd3Yk3lWKpdu58rlY8VmX4Yn1R9rNStyC25rN1OyOu2Iz0hyvmza95GloCjpiFLvi9dDlsneczcGsuU8vOmIyrJrl4qTR+JTlXfW3nd9uXac5B/ynu3+YTympxXu1aGgqvPu7bnrigvQHZmlfd0WCoyswtQuSDpxufqgqMkF/b0x9XPz/mzM5Fdz31qYrAjIi9xoDx3DeJtM7E5r0Idqchaikfj/uQ8WNfBUbANk6rcT6j3HbkM2WVyVL6E3L88CVvqRuSp136IzUmxeGrNKfXSNbL+hEfnvAl5tOvatsQN+BkFm/5Y5f6iGFnpj2LkonedwVCn3Dfu0aXIUp9KBfIypyB+0iTEj55fObZ5Jv74eoHyiutWmj4RMVUfS7nf7196T/t5+vs1DelZxeqIfhvb4KdhL64RWBpFe9+SlmvPQSjvXeooDJ5iR7HLF+BAWfYyjLz6vIX2vOLXIFcP8o4i2Gf8HnFzqryneRsxJ+5RLMq+oF6s/3N1ofwE/hIfi6T0A8pPFfKzn0PcyOcb9J4w2BGRl5Ti5K6d6oEvOHoRDuYVoagwB5viezqvrlU5Tr25HacQguEZ76Gw6GsUHn8Zw4OVqyq+QOG3ygGu7BR2rT2hDIQgOu0A8uQ2OemIQm37WD0RvylHeaxPsT/2DjS7koc3VxxRnthoZBw/h6KiczieMRrqjzhdiG+rHXf1+56BPbmPclk52GZdRFSNsVNHP8F36u3rEDwCaQfzqv+8t3LxuUzNHAV4fe5K5f1SXtOMncgp/BpFeYeRMUF5vyp2YdZKJSh2sGF9zsuIlsdqnQL7ua9xKrkXmsnlq5qhg20FcjJs6qXWyXtxTlsidhTYMTdded+CYzBj10nl+Rch7/DLmBARjIp9y7DyXWdQqu7f+PzDD5RXGIzItMPq51GUtwfJyn2QtxO7TpYqt1EC4rvrMWufEqSveY2F2Lz8TRQ43Phcr3EZxYe2YK3ySxQRv9H5nhTl4WDaCARX7Meav35UZdZYNwY7IvKOK0X48K1C5ZvumDRlFLq2UA43QSEYNOVx58G6Vi3QK/mAclA7hD+2+gh77Rvw/GMzsU/9s/4CfvjxChzfFuK0XG49FlPGd1fuoTx0h4GYMnmo3OharQfDNiBEOeC1QIcOyq2b9ULyKeXAeWIaWuXsgz3zBTyWtMs5cygqxY9Vg13kaEy4T+7bEl163qkGqMqxVrhr4G/RWr1h/YIfGouHurZUvmuOkHsGo79zWOX44n3sPqU8A3lNU/qhgxydW3SF7Snn+1Wx+23k1jb7ccvP+OLYQSXYKD9i0lRM6dNBef7KOxI+Ak+p71shdh88U31Wq2qGX9/YVvmqBPQ5IzE8dQPsh75Bl4VHlIB1FAsGyXWX8W3hF+r7V+012v6CTyQ47o1HeFD9n+u1yvDZiX8oj6v8gZE5EVFhsowZgaHqLF0Ze+cs/unmW8JgR0ReFo7bQ67Xvle0DUX3OqODvh8WgSFxTyIp6U/Vlr2E48dSFMk3vTsh5Oq0ppny0J1cB57Q1vh11aOdowQnMh5Ht4jBiEuahqSqS281tWul3TcIN7RsheuqjTWMcwnVNdevSaG/XxWluPTvpgS7K/jxB5m5tUbv22+qMhusfN8qvr2kzONquh7hcS9i14wYJdDLEuKflM9kGqbaeiNs2Hxkq/t2+mPX9Rrr/1yv9RMufVvH3lzNP0zqwGBHRN4RFIwbQ2UeVIAvi392jokLRTgrK1+1cXyJ/fPSkVURgujkZVhpP4nCc3uRrEaxtrjx180Q9OvWCJWLJ8+h+OqE4Iry0Ofg8qFrBCfHF/sxb9kBVATHIHnFethzzuGcPcUZKGsGRh9x/ZoU+vsV3BqtbmjKE9NnaKU4+eX3VZJaKt+34PatXAeqoA7ok7RBmaWdQ459PTIyliE5OgTIW4Mn1T1H/bGBXy6UuQiYCjc+12v9Cq3ayyyxNaIz3ldmhbKMWeXfqRT0cnU3FxjsiMg7gtog7M6blG/OYu2qPciXRAZHMbJXbag7QeW7T3BUlvNwC7oPHIYHe7XGd0f34UCVKBbUPgx3Shwt3YFVW86q+zaOkiNYteagen3druC7syfV5TzcdjcGRkejV7sLOGp/x3Wg9JGgm7tjsOyDyWta9Z4zO7I8H/aXnO9X8EP3o1dL5ZCtz/RKz6HogqulP1E5Wys9WwTnnKs5br6rLyJkbO1KrDpRAockxRS8iZfU9y0MDw3tAQkt1TjykTlSsiejkJBZgBa9hsFmG4aB3W9Rr3bOBpujfVhn5x7k7h3YnS+zMUm4yXBmZnabg+yCM/V+rtdqgVvCb1O+liJrzUbnLFISYSZLtmpXjMzMV36KexjsiMhL2uK+qTPUBISKrFkYGhGK0LAoxGV+qF1fi3bdMCBSDpsnkG7roRzUOiEqbo22zKjt7bS8B/EzByqXi5E1JwYRygE1LGopijuGqbeqWzO0694bkfJt3lLYaj6vBiyNeVSLuxH77AQlGCmvadkjzv2piCFI2qw8r+DRWDS1X41AZEdSVJiLUw9qyJqGKPXUg3+jReQYPCsJQhUHsGx0b4SFhiJiyDR1OTF4+AxMvc85O6smKBxj5k51Pi/tvQ4N7QGbJLooAXLC+AGQ3b+W9yVg0XBltlfxJuYMjVBuozy2banyuQUjYtKD6B3eo/7P9RrXI3zMdC0ZZg3iojopn1U/JKmJMMPwWPTtbgcxBjsi8pqgkOGYu3WJmu0ngqOfwaubXqg7QSWoK+LWvooZskwmIiZigf3vOJgmwa0Q73z8jfLXvHMfyb5gojpTcWYXrkfaiHC5VK+g8HFYu+s5RKtPSzkYT1gC+/F9SJODcek/8PGXVZZdfaY5Ogx6Bpn2l51LhCrtub3zZ9hCmjuHmvVA7LrK594B/w+unm2zyHFYp+6zCVmcVIKJJAjNXQd7Rop2f9ETExbswTurbAhxGRGClNnc5BrPS6F8LmmbXsUsNUFFERQK27Kt2JSmfSZClokztiPzD33Qwq3P1YUWffCHzO3ISNZfi/Kw8nu0d17le+KG//g/hfY9EZE5XMlFeu+RSC9VgkHyFryerBxMZYl07hPqDE3S7U9ek5JPgYzBjohM6AKyU22I2yynNtTUB8n2V5Hcq5V2mUjmp0REptMWg2a9Wn3JTBEcnYIM+2r8gYGOauDMjoiILI8zOyIisjwGOyIisjwGOyIisjzu2RlAaWkpLl6s7PH11VeFKC93XTMuPz8f//rXv7RLlSIiItCihevGl927d9e+A2644Qbccouz8gERUaBgsPOygoIC9evZs2fVrxKsLl68gM8//wInT+aoYw3xm990uyZY/fhjOXJyjmuX3BcaehvuuedeNG/eHFFRUerY7bffrgbEjh074le/+pU6RkRkdgx2HqDPzCSg/fOf/0RhYSGOHTuKoqKvtFtUqhqsunXrpn6VoNKhQwf1e9Gy5X8q/66pUNcov/zyC77/vrLL1qVL/8IPPziL0RUVnUdFRXmdwXLs2Fi0adMWXbt2VQNh27ZtOTMkItNhsGugb775Bl999RXOnTuH06dPY/v2rdo1lYYMeQDt2rVTgkQb3HxzCK6//jrcdFM7XHed2hzE0L7++rz69csvv8RPP/2kBm55nd999606rhs27Hfo2bMXwsO74LbbwpSv7pVpIiLyBwa7OsjB/rPPPlMP9q4Cmx7UZMlPZmZmCWiNJYFQZobFxd+4DIJ6ALz77ruVGexv0Lq12ruDiMjvGOyqkOXITz/9FB999BEOHTqEEyc+0K4BoqLuQefOndClSzjat2+vBDZpXUJlZWVKwPtOmel+oQbAw4cPadc49wQffHAk/uu/eqFbtwgufxKR3wR8sJPAJjOUd989gv37/6aNOmdtsqcm+1RWn7F5mswAS0pKkJ//GY4ff//q7K937ygMHTpUnfn17NmTCTBE5DMBF+z02ZsEt1WrVmqjzplbVFQfNbh17HirNkqe8P3336unU0jw27vXro0Cv/vdcDz88MOc9RGR1wVEsJMAl5v7D7z22mv429/2qWPt2rVXZm9D0KPHnbj11ls5c/Mhmfnl5eXh2LFjyh8en6hjffr0xahRozB48GAGPiLyOMsGO1cBTtL++/fvryZRcM/NGGTP77PP8nHkyLtXT39g4CMiT7NUsJPsSTm/rWqAk+XJgQPvwx13dPXYuWvkHRL4ioqK1H1UfblTD3zDhw9ndicRNZolgp0cHCW46XtwnMGZn6sZn+zxTZwYz+QWImqwhgW7smyk9n0C/5iktcHXhv1Blin37duH3bt3q2W39D243r17M8HEYiTwSVZn1T2+WbNS8cADD/BkdiJySwOC3WUU25/GkKRdqAh+DJs+mItBLX3fNKHmLE5OEejXr7960GOSifV9/vnnOHNGTvDfpl723WzvCkrs0xGVVJlNWk1wDJIXTMSI6AEIb8FmIkRG436wc+Qj0zYDR9tdRlZWBSZssmPBoLbald6l78WtXr1GPdFbn8Xdf/8Q7sMFKKn5efr0x3jjjTfU2V5oaCgmT57i/b099f/BSMxptwQ5621QK5qWF+DwusWYln4AGP4yDq+yIYTxjshQ3Ax2DpRlz0Xf5Z1gX9kK6dHTcGSg9/9T60uVq1evwvnzRepe3MMPP8JZHFUjs7233z58tXrLzJmzEB0d7aUlzvOwJ/w3kpBWGeyEHgRP9Uba4Q2ID79eu4KIjMDNUFWK3IMfYuBj9yP81gEY+1AYKva9hqwvftau9ywJcitXrkRk5F2YPftZ3HHHHXjxxeV44YU09OjRg4GOqunSpQsmTXoC69ZtQGzsOCxZskiZ+Q9Wgt7Mqy2WvC6oDcLuZDIUkVG5FewcBW9i+e6eGHt/R+UOrdFr6P0IxknsPvaVMufzHDkwLV68SA1ycsCSA5ccwORAxqQTqo8sadtso7Bp0xZMm/aUOtOToDdmzGi899572q28oQwF9gws3lyI4OEPI7ozZ3VERuPGMuYl5KY/gbk3psEe39UZHctPIH3MeKR/9T8eSVSRIPfKKxuwdesW9bIEOe7HUVPJvl5OzgfYuXOnWp8zKqovUlL+iH79+mm3aAxtGTPL2ROwGj8mbhFR3eoPdurpBuOxuUK7XE1YkxJVZLnyz39eqga59u07YMSIEWrnbAY58iQJevIH1Wuv7VSTWSToPf/8HLUgdcO52LNzlCB37zasmrUcWRiBNPtSxHfl7zCRkdQT7H5GQebjGFmQiA8WDELV/76OgkzYhjyHgglbrrmuPhLktm/fri5VCpnJSQo59+LI2/7+93evzvRiY3+PhISEBiay1JKgoidxxb2Cisj5OGyPRzgneESGUcd/RwfK819TAtIFTBrd+5pgFhQ+BI9Ft0bF5hexxJ6Pcm28LnIKwZYtW67Zk5N9FgY68oXf/vY+LFv2YrU9vVmznlX/ACMi66o12F3JXYEBQ2chq+Is0m39kGA/r10jqu5bfIjNSUMQkWBHifNKl+x2O4YOfUDNrhw50nY1yHHJknxN/rCqGvRkGV3+AFu9erX6B1mdykvw5de/aBd0l1GSux1LFv8VFQjB8MfuR2fO6ogMxf2TyhtJKp6kpaWpJ4NLtRM56ZeZlWQkUo5MTk6X4tNycvqMGc8of4jZtGt19VRQUQRHp2DB+AcRPSjcr6X0iOhaXgt2VZNPpOLJE09MVs+RIzIq6bP317/uVAtPSxLLokWLWXuTyCK8EuxeeeUVzJ07R/1elonkwME9OTKLM2fO4H//d42axDJ69Bg8/fQzCAkJ0a4lIjPyeLA7evQoxo0bq10iMr933jmCzp07a5eIyIy8MrNbtGgRgoKC1HJN5B2hoR1RVPS1dqnhmnr/QDB79mxERERg/Pjx2ggRmZVXcsamT5+Offve8l1dQiIPk8QqKTA9evRobYSIzMwrwU76isnmfmpqqjZCZB5y+kFS0lPq7y87ohNZg9fOBpL6g1KNXs6vIzKTXbt2oX//AY0sJ0ZERuTV8+y++eYb3HtvX5w69bF3G2oGIO7ZeQd/Z4msyat1Hm655RYsXLgYy5Yt00aIjE36KGZkvMxAR2QxXi9qJBv8x44dVTf8iYxMet5JUsq11VOIyOy8Huxkgz8j4yUsWLCg/rqDRH4iv5tSEFp+T4nIerwe7IRs9EuyyoEDB7QRImPJzMzE8OH/zfJgRBblk2AnZsyYgaSkaWoCAJGRyPmgO3ZsR2JiojZCRFbjs2AnG/6y8S8JAERGsnz5cjz//PNMSiGyMJ8FOxETE6MmAEgiAJERHDp0UP36wAND1a9EZE0+DXaSrCIJAJIIwGQV8jdpQzVv3jykpKRoI0RkVT4NdkISACQRQKpUEPnTunXrMHZsLJNSiAKAz4OdkESAdevWslA0+Y387kmx8vj4eG2EiKzMq+XC6iI1M+VUhNWrV2sj1BBS7qupArlc2COPPIJJkxK5V0cUIPwW7MSTTz6J0aMf4gGnEVjbsvHkD62cnBwsXLhQGyEiq/NrsJOlpISEx7F//wG2UmkgBrvGkaSUyMi78P77H6i1W4koMPhlz04niQGSIJCRkaGNEHmXFCWX4uQMdESBxa/BTkiCALuaky9IMXIpSs7u40SBx+/BTpYvpXoFu5qTN8l5nXKOpxQl55I5UeDxe7ATkqDSpk0bdjUnr5HMXylGzu7jRIHJrwkqVUmB6HHjYrFnj501Ct3ABBX3sfs4ERliZickYSAxcZJa1YLqx0DnPnYfJyLDBDshiQOSrMKu5uQpevdxKUJORIHLMMuYOjk4rVixAhs3bmQiATWJJKUMGxaD9es3sP4lUYAz1MxO9OvXj13NySOk2Di7jxORMNzMTuhVLphQQI2lV+dhwhMRCcPN7IQcnCShQKpdEDWGdB9PTk5hoCMilSGDnWBXc2os6T5+8eJF2Gw2bYSIAp0hlzF1kpWZlPQUC0WT25iUQkSuGHZmJ6TaBbuau+aJfnZWJEXF2X2ciGoydLATeldzqYJBVBd2Hyei2hg+2EmCgSQazJ8/Xxshck2KiUtRcS55E1FNhg92QhINJOFAEg+IXJEi4lJMnF3vicgVQyeoVMWu5tWxEHQlOS9z1Cgbtm3bzqasROSSKWZ2QhIOJFklMzNTGyFykuLhUkScgY6IamOaYCeSkpKwY8d2djWnq+T0FElKYfdxIqqLqYKdLF9KAoJUxyDSu48vWrSYS9tEVCdTBTuhJyCwqznp3celeDgRUV1Mk6BSFYv8MkGFxcKJqCFMGezEli1b1BPNZ86cqY1QIJk9ezaioqJY/5KI3GK6ZUyd3tWcySqBh93HiaihTDuzE+xqHnj0Qs8ZGS+ptVOJiNxh2pmdYFfzwCNFwfv3H8BAR0QNYuqZnZB9u3vv7ctEhQAgn/W4cbHsPk5EDWbqmZ2Qqhnsah4YpBg4u48TUWOYPtgJvau5VNMga2L3cSJqCtMvY+rY1dy62H2ciJrKEjM7IQkLkrhg+q7mjmJkz3kQoZHLkXtFG3MhkDqVS/FvKQLOQEdEjWWZYCdmzJiB2bOfNXFX88so3rsET2Z+qF0mOY9Sin9LEXAiosayVLCTxAVJVlm5cqU2Yi6O4n1Im3sGt90RrI2QFP1m93EiaipLBTshCQySrCInnJtK+VlsmmNH11fSMTnsOm0wsOnFvtl9nIiaynLBTkjbl1mznlUTG8zhEnLX/RlHBzyNxF43amOBTQo9p6cvR0pKijZCRNR4lgx25upq7kB57has+mEC5sd1RwttNNDp3ceZlEJEnmDJYCcSExNN0dXcUfIOlq4CpjwzGB0s+2k0jHxm7D5ORJ5kmfPsXJETkXft2o3Vq1drI0ZzBSX26YhKqq0RbWtEZ7yF9bZbtcuVrNrPTpaeJ06ciOnTp7MpKxF5jKXnEnpigwQ9Y2qGDraX1aBV+e99ZES3VuJcCuznPnYZ6KyM3ceJyBssv3AmCQ7z5s1TEx7I2OQzSkqahqlTp2ojRESeYflgJwkOY8fGqgkPVmLFJUwp5r1w4WK1uDcRkSdZes9Ox9qKxie1TeWUETbiJSJvCIhgJ/Su5jt37tRGyCjYfZyIvC1gkt31ruZ6VQ4yDnYfJyJvC5iZnWBXc+PhZ0JEvhBQpzFL4oMkQLCruXFI0W4p3s1AR0TeFFDBTkhVjmPHjrKruQHIPqoU7Wb3cSLyNmMHOzcbmaocRbBPjlIrizj/dcXIzHw4tKt1kukniRCS+WeeQtHWI++9FOuWz4GIyNsMHOwa0sjUgfJTdqwpHA97XpFWiSQfe+O7unyBkgghySpSrYP8g93HiciXDBvsGtTI1PE1Dq19C2GTbYhs4d5Lkq7mUq3DrF3NZfZqVnr3cSnWTUTkC8YMdg1qZOpA2bvrMWvfWexLGoNJ6a8hu6BMu652Zu9qbmZ693EmpRCRrxgw2DW0kWkQWg5KwydF55Bjn4sBFzYhbsgDSMg8i3LtFrWJiYkxZ1dzE9OLcrP7OBH5ksGCXVMamTZHh17DEb9gKw6m9cKxOc9hXe4l7TrXJFnFfF3NzUsKPUtRbnYfJyJfM1Sw80wj05boGpeMmZF52HjkHOpL4tS7mksVD/IuKcYtRbmZlEJEvmagYHcF3x3fg8ysxbBFhGqnD9yLpKxSZUqwHLZOdyHBfl67bT2C2iDszpu0C/WTRIl169Yavqu5mendx+Pj47URIiLfMVCw82AjU8dFFJ6+BRMHdlIetX6SKJGcnKImTpB3pKamqkkp7GhARP5gsD27RnCUIPcNO97ILXGeQF6eD/vzz2LH4BlI7NVKvYk79Coexu1qbl5SfFvOa2RSChH5iwmD3XnYE+5CaOg02EtkR86BshMbMNXWG2Gy9DlmEy4NXYrXk/s0MMGlsqs5k1U8h93HicgIAqrrgTtWr16NsrIyzJw5UxsxJtnTNEO38tmzZyMiIgLjx4/XRoiIfM/8y5geJgkUkkhh9GQVMwQ6KbYtRbel+DYRkT8x2NUgCRSSSCEJFdR4shQs5zBK0W0mpRCRvzHYuSCJFG3atGFX8yaQItuSlMLu40RkBNyzq4UUiB43LhZ79thZw7GB2H2ciIyGM7taSFfzxMRJatUPahh2Hycio2Gwq4MkVkiyCruau0/vPi5FtomIjILLmPWQg/eKFSuwceNGJlrUQ5JShg2Lwfr1G1j/kogMhTO7evTr149dzd0kxbTZfZyIjIgzOzdIFZDIyLsMlXBhtJPK5bzEhITHmdBDRIbEmZ0b5OAtCRfLli3TRqgmKaItxbQZ6IjIiBjs3MSu5rWT4tkXL168WkybiMhouIzZAJKVmZT0FPbvP+D3ZBWjLGMyKYWIzIAzuwaQaiDsal5dZmYmu48TkeEx2DWQ3tVcqoQEOklK2bFjO7uPE5HhMdg1kCRgSCLG/PnztZHAxe7jRGQWDHaNIIkYkpARyF3NpUi2FMtm93EiMgMmqDSSfl6Zv5JV/JmgIucdjhplw7Zt29UaokRERseZXSNJQoYkq0iCRqCR4thSJJuBjojMgjO7JgjEtHsjnX5BROQuzuyaQA72kqAh1UMCgd59fNGixQx0RGQqDHZNpCdoBEJXc737uBTHJiIyEy5jekAgFEE2YjFsIiJ3cWbnAbJfZ/Wu5lIEm93HicisGOw8RO9qLrM8q2H3cSIyOy5jepAVu5rrGacZGS+ptUGJiMyIMzsPsmJXcyl63b//AAY6IjI1zuw8TApE33tvX68ncviigoq8lnHjYtl9nIhMjzM7D5OqIlbpar5y5Up2HyciS2Cw8wK9q7lUGzErKXItr4Hdx4nIChjsvECSU6T9jZTVkgQPs5HnPG/ePLVaChGRFTDYeYkkdEhihxm7mktxaylyze7jRGQVTFDxIr3qyPvvf+DxDgHeSlDxd+siIiJv4MzOiySxQ5JVJNHDLKSoNbuPE5HVMNh5mSR4SKKHnHBudHoxa3YfJyKrYbDzAUn0mDXrWUMnq8iSa3r6cqSkpGgjRETWwWDnA2boaq53H2dSChFZEYOdjyQmJmLHju0eKxTtyeQUeU5SxFqKWRMRWRGDnY9IsooRu5rL0qqcE8ju40RkZQx2PqQnfkh1EqNg93EiCgQ8z87HjNTV3JvnARIRGQlndj4mCSBjx8Yaoqu5FKteuHAxAx0RWR6DnR/Ex8f7vau5FKmW8/+YlEJEgYDBzg8kEUQSQiQxxB8kKUXO/ZOfz6QUIgoEDHZ+onc116uW+JIUp5afze7jRBQomKDiR03pat7YQtC+6qRORGQknNn5kSSGSIKIL7uaS1FqKU7NQEdEgYTBzs8kQeTYsaM+6WouxajZfZyIAhGDnZ9JgkhGxktqwog3C0XLY0sxanYfJ6JAxGBnAJIoIgkjUs3EW9h9nIgCGRNUDKKh1UwakqBipKotRET+wJmdQUgQ8lZXc737OAMdEQUqBjsDiYmJ8XhXc73oNLuPE1Eg4zKmwehLjvv3H6izuok7y5iyNDpqlA3r12/gXh0RBTTO7AxG72ouVU6aSopNS9FpBjoiCnSc2RmQJ2Zk7s4QiYgCAWd2BiSJJMnJKU3qai5FniUphYGOiIjBzrD0KieN6WouxaXlvD0mpRAROXEZ08AasxSpL4Fu27adTVmJiDSc2RmY7NdJgklGRoY2Uj8pKp2YOImBjoioCgY7g2tIV3MpJi1Fpdl9nIioOgY7g5PlS0k0qa+rud59XIpKMymFiKg6BjsTkESTNm3a1NnVXIpIs/s4EZFrTFAxCekwPm5c7NVizlUrqLD7OBFR3TizMwlJOJHEE6mKUhO7jxMR1Y3BzkQk8USSVap2Nde7j0sRaSIico3LmCYjwW3FihU4fvw95OcXYNiwGBZ6JiKqB2d2JtOvXz81EUVIsWh2Hyciqh9ndiakdzW/9dZQvPHGm9yrIyKqB4OdSW3cuFE9n+6RRx7RRoiIqDYMdkREZHncsyMiIstjsCMiIstjsDOT8gJk716OhG4d1Qoq8q9bwnLszi5AuXYTIiK6FoOdKThQnr8ZCX0G48l9zRC7N08tFVZUeBJbB17E2rgRGDPnMEoc2s2JiKgaJqiYQfkJpI8Zj3RMhf31aejVourfKJdRbH8aQ5L247bkLXg9uQ9aaNcQEZETZ3aG9zMKXl+B9DwgcmwMIqsFOtEcIfePwkPBFchb+wZOlnF6R0RUE4Od4X2Ps0dPK19vwp1hbVx/YC07o0//1kDF2ziYW6oNEhGRjsHO6Bz/xqXvflG+CUbbltc7x2pVhm8v/aR9T0REOgY7owu6Aa3aXad8U4ELZT87x2p1M7qH3qh9T0REOgY7w7sJ3QfcqXz9HqcLL8LljlzZFzhxrFSZ/PVFzy43aINERKRjsDO869E5+mEMD67AqSWrsLf4sjauu4zit/dgd0UwImf+Hve15EdKRFQTj4wmEBQyEsvsixCNXZg1Zw0OF5Q5r3CUIHfzC3hMTjuIX4W1cV35gRIRucDz7EzEUZKLt/bvwso5G5GnjQVHp2DB+AcRPSic59cREdWCwY6IiCyPq15ERGR5DHZERGR5DHZERGR5DHZERGR5DHZERGR5DHZERGR5DHZERGRxwP8HBzDbq2Z7EREAAAAASUVORK5CYII="></p>
</div>
<div class="specification">
<p>A square field with side <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo> </mo><mtext>m</mtext></math> has a goat tied to a post in the centre by a rope such that the goat can reach all parts of the field up to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>m</mtext></math> from the post.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p style="text-align: center;"><sup>[Source: mynamepong, n.d. Goat [image online] Available at: <a href="https://thenounproject.com/term/goat/1761571/">https://thenounproject.com/term/goat/1761571/</a></sup><br><sup>This file is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)</sup><br><sup><a href="https://creativecommons.org/licenses/by-sa/3.0/deed.en">https://creativecommons.org/licenses/by-sa/3.0/deed.en</a> [Accessed 22 April 2010] Source adapted.]</sup></p>
</div>
<div class="specification">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> be the volume of grass eaten by the goat, in cubic metres, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> be the length of time, in hours, that the goat has been in the field.</p>
<p>The goat eats grass at the rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>V</mi></mrow><mrow><mo>d</mo><mi>t</mi></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn><mo> </mo><mi>t</mi><msup><mtext>e</mtext><mrow><mo>-</mo><mi>t</mi></mrow></msup></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AÔB</mtext></math>.</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 area of the shaded segment.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of a circle with radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>m</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the field that can be reached by the goat.</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>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> at which the goat is eating grass at the greatest rate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mtext>AÔB</mtext><mo>=</mo></mrow></mfenced><mo> </mo><mtext>arccos</mtext><mfenced><mfrac><mn>4</mn><mrow><mn>4</mn><mo>.</mo><mn>5</mn></mrow></mfrac></mfenced><mo>=</mo><mn>27</mn><mo>.</mo><mn>266</mn><mo>…</mo></math> <em><strong>(M1)(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AÔB</mtext><mo>=</mo><mn>54</mn><mo>.</mo><mn>532</mn><mo>…</mo><mo>≈</mo><mn>54</mn><mo>.</mo><mn>5</mn><mo>°</mo></math> (<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>951764</mn><mo>…</mo><mo>≈</mo><mn>0</mn><mo>.</mo><mn>952</mn></math> radians) <em><strong>A1</strong> </em></p>
<p> </p>
<p><strong>Note:</strong> Other methods may be seen; award <em><strong>(M1)(A1)</strong></em> for use of a correct trigonometric method to find an appropriate angle and then <em><strong>A1</strong> </em>for the correct answer.</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>finding area of triangle</p>
<p><strong>EITHER</strong></p>
<p>area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>4</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup><mo>×</mo><mi>sin</mi><mfenced><mrow><mn>54</mn><mo>.</mo><mn>532</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong> </em>for correct substitution into formula.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>8</mn><mo>.</mo><mn>24621</mn><mo>…</mo><mo>≈</mo><mn>8</mn><mo>.</mo><mn>25</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup></math> <em><strong>(A1)</strong></em></p>
<p><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext><mo>=</mo><mn>2</mn><mo>×</mo><msqrt><mn>4</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup><mo>-</mo><msup><mn>4</mn><mn>2</mn></msup></msqrt><mo>=</mo><mn>4</mn><mo>.</mo><mn>1231</mn><mo>…</mo></math></p>
<p>area triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>4</mn><mo>.</mo><mn>1231</mn><mo>…</mo><mo>×</mo><mn>4</mn></mrow><mn>2</mn></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>8</mn><mo>.</mo><mn>24621</mn><mo>…</mo><mo>≈</mo><mn>8</mn><mo>.</mo><mn>25</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup></math> <em><strong>(A1)</strong></em></p>
<p> </p>
<p>finding area of sector</p>
<p><strong>EITHER</strong></p>
<p>area of sector <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>54</mn><mo>.</mo><mn>532</mn><mo>…</mo></mrow><mn>360</mn></mfrac><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><mn>4</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>9</mn><mo>.</mo><mn>63661</mn><mo>…</mo><mo>≈</mo><mn>9</mn><mo>.</mo><mn>64</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup></math> <em><strong>(A1)</strong></em></p>
<p><strong>OR</strong></p>
<p>area of sector <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>0</mn><mo>.</mo><mn>9517641</mn><mo>…</mo><mo>×</mo><mn>4</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>9</mn><mo>.</mo><mn>63661</mn><mo>…</mo><mo>≈</mo><mn>9</mn><mo>.</mo><mn>64</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup></math> <em><strong>(A1)</strong></em></p>
<p> </p>
<p><strong>THEN</strong></p>
<p>area of segment <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>9</mn><mo>.</mo><mn>63661</mn><mo>…</mo><mo>-</mo><mn>8</mn><mo>.</mo><mn>24621</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>.</mo><mn>39</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup><mo> </mo><mo> </mo><mfenced><mrow><mn>1</mn><mo>.</mo><mn>39040</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong> </em></p>
<p> </p>
<p><em><strong>[5 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"><mi mathvariant="normal">π</mi><mo>×</mo><mn>4</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>63</mn><mo>.</mo><mn>6</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>63</mn><mo>.</mo><mn>6172</mn><mo>…</mo><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup></mrow></mfenced></math> <em><strong>A1</strong> </em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p style="padding-left:90px;"><img src="data:image/png;base64,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"></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>39040</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo> </mo><mo> </mo><mo> </mo><mo>(</mo><mn>5</mn><mo>.</mo><mn>56160</mn><mo>)</mo></math> <em><strong>(A1)</strong></em></p>
<p>subtraction of four segments from area of circle <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>58</mn><mo>.</mo><mn>1</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>58</mn><mo>.</mo><mn>055</mn><mo>…</mo><mo> </mo></mrow></mfenced></math> <em><strong>A1</strong> </em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mfenced><mrow><mn>0</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>4</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup><mo>×</mo><mi>sin</mi><mo> </mo><mn>54</mn><mo>.</mo><mn>532</mn><mo>…</mo></mrow></mfenced><mo>+</mo><mn>4</mn><mfenced><mrow><mfrac><mrow><mn>35</mn><mo>.</mo><mn>4679</mn></mrow><mn>360</mn></mfrac><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><mn>4</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo> </mo><mo> </mo><mn>32</mn><mo>.</mo><mn>9845</mn><mo>…</mo><mo>+</mo><mn>25</mn><mo>.</mo><mn>0707</mn></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>58</mn><mo>.</mo><mn>1</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>58</mn><mo>.</mo><mn>055</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">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>V</mi></mrow><mrow><mo>d</mo><mi>t</mi></mrow></mfrac></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>V</mi></mrow><mrow><mo>d</mo><mi>t</mi></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>110363</mn><mo>…</mo></math> <strong>OR </strong>attempt to find where <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mo>d</mo><mn>2</mn></msup><mi>V</mi></mrow><mrow><mo>d</mo><msup><mi>t</mi><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mn>0</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn></math> hour <em><strong>A1</strong> </em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Part (a)(i) proved to be difficult for many candidates. About half of the candidates managed to correctly find the angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mi>O</mi><mo>^</mo></mover><mi>B</mi></math>. A variety of methods were used: cosine to find half of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mi>O</mi><mo>^</mo></mover><mi>B</mi></math> then double it; sine to find angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mi>O</mi><mo>^</mo></mover><mi>B</mi></math> , then find half of A<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mi>O</mi><mo>^</mo></mover><mi>B</mi></math> and double it; Pythagoras to find half of AB and then sine rule to find half of angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mi>O</mi><mo>^</mo></mover><mi>B</mi></math> then double it; Pythagoras to find half of AB, then double it and use cosine rule to find angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mi>O</mi><mo>^</mo></mover><mi>B</mi></math> . Many candidates lost a mark here due to premature rounding of an intermediate value and hence the final answer was not correct (to three significant figures).</p>
<p>In part (a)(ii) very few candidates managed to find the correct area of the shaded segment and include the correct units. Some only found the area of the triangle or the area of the sector and then stopped.</p>
<p>In part (b)(i), nearly all candidates managed to find the area of a circle.</p>
<p>In part (b)(ii), finding the area of the field reached by the goat proved troublesome for most of the candidates. It appeared as if the candidates did not fully understand the problem. Very few candidates realized the connection to part (a)(ii).</p>
<p>Part (c) was accessed by only a handful of candidates. The candidates could simply have graphed the function on their GDC to find the greatest value, but most did not realize this.</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.</div>
</div>
<br><hr><br><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>