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<h2>SL Paper 1</h2><div class="specification">
<p>The ticket prices for a concert are shown in the following table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<ul>
<li>A total of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>600</mn></math> tickets were sold.</li>
<li>The total amount of money from ticket sales was <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>7816</mn></math>.</li>
<li>There were twice as many adult tickets sold as child tickets.</li>
</ul>
<p>Let the number of adult tickets sold be <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>, the number of child tickets sold be <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>, and the number of student tickets sold be <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down three equations that express the information given above.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of each type of ticket sold.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>600</mn></math> <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mi>x</mi><mo>+</mo><mn>10</mn><mi>y</mi><mo>+</mo><mn>12</mn><mi>z</mi><mo>=</mo><mn>7816</mn></math> <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>2</mn><mi>y</mi></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Condone other labelling if clear, e.g. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> (adult), <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> (child) and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math> (student). Accept equivalent, distinct equations e.g. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>y</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>600</mn></math>.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>308</mn><mo>,</mo><mo> </mo><mi>y</mi><mo>=</mo><mn>154</mn><mo>,</mo><mo> </mo><mi>z</mi><mo>=</mo><mn>138</mn></math> <em><strong>A1A1</strong></em></p>
<p> <br><strong>Note:</strong> Award <em><strong>A1</strong></em> for all three correct values seen, <em><strong>A1</strong></em> for correctly labelled as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>,</mo><mo> </mo><mi>y</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math>. <br>Accept answers written in words: e.g. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>308</mn></math> adult tickets.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Many candidates had at least two of the three equations written down correctly. The interpretation of the phrase “twice as many adult tickets sold as child tickets” was enigmatic. Consequently, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo>=</mo><mi>y</mi></math> was a popular but erroneous answer.</p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Too many candidates spent considerable time attempting to solve three equations with three unknowns by hand with pages of working rather than using their GDC.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The strength of earthquakes is measured on the Richter magnitude scale, with values typically between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> is the most severe.</p>
<p>The Gutenberg–Richter equation gives the average number of earthquakes per year, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math>, which have a magnitude of at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math>. For a particular region the equation is</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mi>N</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>M</mi></math>, for some <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>.</p>
<p>This region has an average of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math> earthquakes per year with a magnitude of at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math>.</p>
</div>
<div class="specification">
<p>The equation for this region can also be written as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mfrac><mi>b</mi><msup><mn>10</mn><mi>M</mi></msup></mfrac></math>.</p>
</div>
<div class="specification">
<p>The expected length of time, in years, between earthquakes with a magnitude of at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mi>N</mi></mfrac></math>.</p>
<p>Within this region the most severe earthquake recorded had a magnitude of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>2</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo><</mo><mi>M</mi><mo><</mo><mn>8</mn></math>, find the range for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the expected length of time between this earthquake and the next earthquake of at least this magnitude. Give your answer to the nearest year.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mn>100</mn><mo>=</mo><mi>a</mi><mo>-</mo><mn>3</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>5</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><msup><mn>10</mn><mrow><mn>5</mn><mo>-</mo><mi>M</mi></mrow></msup></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><msup><mn>10</mn><mn>5</mn></msup><msup><mn>10</mn><mi>M</mi></msup></mfrac><mfenced><mrow><mo>=</mo><mfrac><mn>100000</mn><msup><mn>10</mn><mi>M</mi></msup></mfrac></mrow></mfenced></math></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>=</mo><mfrac><mi>b</mi><msup><mn>10</mn><mn>3</mn></msup></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>100000</mn><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><msup><mn>10</mn><mn>5</mn></msup></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>001</mn><mo><</mo><mi>N</mi><mo><</mo><mn>100000</mn><mo> </mo><mo> </mo><mfenced><mrow><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo><</mo><mi>N</mi><mo><</mo><msup><mn>10</mn><mn>5</mn></msup></mrow></mfenced></math> <em><strong>A1A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong></em> for correct endpoints and <em><strong>A1 </strong></em>for correct inequalities/interval notation.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mfrac><msup><mn>10</mn><mn>5</mn></msup><msup><mn>10</mn><mrow><mn>7</mn><mo>.</mo><mn>2</mn></mrow></msup></mfrac><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>0</mn><mo>.</mo><mn>0063095</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p>length of time <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mrow><mn>0</mn><mo>.</mo><mn>0063095</mn><mo>…</mo></mrow></mfrac><mo>=</mo><msup><mn>10</mn><mrow><mn>2</mn><mo>.</mo><mn>2</mn></mrow></msup></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>158</mn></math> years <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Many candidates did not attempt this question. Of those who did attempt the question, most of these candidates arrived at the correct answer to this part with the most common incorrect answer being 103.</p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Those that were successful in part (a) answered this well.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was only answered correctly by the strongest candidates.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This part of the question was a discriminator as correct responses were few and far between.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Let the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> represent the height in centimetres of a cylindrical tin can with diameter <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mtext> cm</mtext></math>.</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mn>640</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>14</mn></math>.</p>
</div>
<div class="specification">
<p>The function <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>h</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> is the inverse function of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the range of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>.</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 <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mn>10</mn></mfenced></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>In the context of the question, interpret your answer to part (b)(i).</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>Write down the range of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>h</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mn>4</mn></mfenced><mo>=</mo><mfrac><mn>640</mn><msup><mn>4</mn><mn>2</mn></msup></mfrac><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mn>14</mn></mfenced><mo>=</mo><mfrac><mn>640</mn><msup><mn>14</mn><mn>2</mn></msup></mfrac><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math> into <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>. This can be implicit from seeing <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>77</mn><mo> </mo><mo>(</mo><mn>3</mn><mo>.</mo><mn>76530</mn><mo>…</mo><mo>)</mo></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo>.</mo><mn>5</mn></math>.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>77</mn><mo>≤</mo><mi>h</mi><mfenced><mi>x</mi></mfenced><mo>≤</mo><mn>40</mn><mo>.</mo><mn>5</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>3</mn><mo>.</mo><mn>76530</mn><mo>…</mo><mo>≤</mo><mi>h</mi><mfenced><mi>x</mi></mfenced><mo>≤</mo><mn>40</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math> <em><strong>A1A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong></em> for both correct endpoints seen, <em><strong>A1</strong></em> for the endpoints in a correct interval.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>10</mn></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mi>x</mi></mfenced><mo>=</mo><msqrt><mfrac><mn>640</mn><mrow><mi>x</mi><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfrac></msqrt></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mn>10</mn></mfenced><mo>=</mo><msqrt><mfrac><mn>640</mn><mrow><mn>10</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfrac></msqrt></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>8</mn><mo>.</mo><mn>21</mn><mo> </mo><mtext>cm</mtext><mo> </mo><mfenced><mrow><mn>8</mn><mo>.</mo><mn>20782</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>a tin that is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mtext>cm</mtext></math> high will have a diameter of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>21</mn><mo> </mo><mtext>cm</mtext><mo> </mo><mo>(</mo><mn>8</mn><mo>.</mo><mn>20782</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>)</mo></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Condone a correct answer expressed as the converse.</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>4</mn><mo>≤</mo><msup><mi>h</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>≤</mo><mn>14</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>≤</mo><mi>y</mi><mo>≤</mo><mn>14</mn></math>. Do not <em><strong>FT</strong></em> in this part.</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Part (a) was reasonably well done. Many candidates were able to find the endpoints but there was some confusion about whether to use strict or weak inequalities. Some candidates wrote their answer as <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo>.</mo><mn>5</mn><mo>≥</mo><mi>y</mi><mo>≥</mo><mn>3</mn><mo>.</mo><mn>77</mn></math> while some others wrote <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo>.</mo><mn>5</mn><mo>≤</mo><mi>y</mi><mo>≤</mo><mn>3</mn><mo>.</mo><mn>77</mn></math>. A few candidates used integer <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> values from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math> to find corresponding values for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>x</mi></mfenced></math> and gave the full list as their final answer. In part (b), the most popular incorrect answer seen was <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>9</mn></math> with weaker candidates simply finding <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mn>10</mn></mfenced></math>. Several candidates equated <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>x</mi></mfenced></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> but missed out <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></math> in their equation. Finding a value of the inverse of a function still proves to be difficult for candidates. There were many candidates who attempted to find an expression for the inverse before substituting <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> and this proved to be difficult for this function. Regardless of what answer candidates derived for part (b), very few of them could write an interpretation of their answer in context. There was significant confusion between the value for the height and value for the diameter. In part (d), there were very few candidates who realized the relationship between the domain of the function and the range of the inverse function. Many candidates simply reverted to their answer to part (a).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Part (a) was reasonably well done. Many candidates were able to find the endpoints but there was some confusion about whether to use strict or weak inequalities. Some candidates wrote their answer as <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo>.</mo><mn>5</mn><mo>≥</mo><mi>y</mi><mo>≥</mo><mn>3</mn><mo>.</mo><mn>77</mn></math> while some others wrote <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo>.</mo><mn>5</mn><mo>≤</mo><mi>y</mi><mo>≤</mo><mn>3</mn><mo>.</mo><mn>77</mn></math>. A few candidates used integer <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> values from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math> to find corresponding values for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>x</mi></mfenced></math> and gave the full list as their final answer. In part (b), the most popular incorrect answer seen was <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>9</mn></math> with weaker candidates simply finding <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mn>10</mn></mfenced></math>. Several candidates equated <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>x</mi></mfenced></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> but missed out <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></math> in their equation. Finding a value of the inverse of a function still proves to be difficult for candidates. There were many candidates who attempted to find an expression for the inverse before substituting <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> and this proved to be difficult for this function. Regardless of what answer candidates derived for part (b), very few of them could write an interpretation of their answer in context. There was significant confusion between the value for the height and value for the diameter. In part (d), there were very few candidates who realized the relationship between the domain of the function and the range of the inverse function. Many candidates simply reverted to their answer to part (a).</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Part (a) was reasonably well done. Many candidates were able to find the endpoints but there was some confusion about whether to use strict or weak inequalities. Some candidates wrote their answer as <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo>.</mo><mn>5</mn><mo>≥</mo><mi>y</mi><mo>≥</mo><mn>3</mn><mo>.</mo><mn>77</mn></math> while some others wrote <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo>.</mo><mn>5</mn><mo>≤</mo><mi>y</mi><mo>≤</mo><mn>3</mn><mo>.</mo><mn>77</mn></math>. A few candidates used integer <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> values from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math> to find corresponding values for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>x</mi></mfenced></math> and gave the full list as their final answer. In part (b), the most popular incorrect answer seen was <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>9</mn></math> with weaker candidates simply finding <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mn>10</mn></mfenced></math>. Several candidates equated <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>x</mi></mfenced></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> but missed out <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></math> in their equation. Finding a value of the inverse of a function still proves to be difficult for candidates. There were many candidates who attempted to find an expression for the inverse before substituting <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> and this proved to be difficult for this function. Regardless of what answer candidates derived for part (b), very few of them could write an interpretation of their answer in context. There was significant confusion between the value for the height and value for the diameter. In part (d), there were very few candidates who realized the relationship between the domain of the function and the range of the inverse function. Many candidates simply reverted to their answer to part (a).</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Part (a) was reasonably well done. Many candidates were able to find the endpoints but there was some confusion about whether to use strict or weak inequalities. Some candidates wrote their answer as <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo>.</mo><mn>5</mn><mo>≥</mo><mi>y</mi><mo>≥</mo><mn>3</mn><mo>.</mo><mn>77</mn></math> while some others wrote <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo>.</mo><mn>5</mn><mo>≤</mo><mi>y</mi><mo>≤</mo><mn>3</mn><mo>.</mo><mn>77</mn></math>. A few candidates used integer <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> values from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math> to find corresponding values for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>x</mi></mfenced></math> and gave the full list as their final answer. In part (b), the most popular incorrect answer seen was <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>9</mn></math> with weaker candidates simply finding <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mn>10</mn></mfenced></math>. Several candidates equated <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>x</mi></mfenced></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> but missed out <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></math> in their equation. Finding a value of the inverse of a function still proves to be difficult for candidates. There were many candidates who attempted to find an expression for the inverse before substituting <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> and this proved to be difficult for this function. Regardless of what answer candidates derived for part (b), very few of them could write an interpretation of their answer in context. There was significant confusion between the value for the height and value for the diameter. In part (d), there were very few candidates who realized the relationship between the domain of the function and the range of the inverse function. Many candidates simply reverted to their answer to part (a).</p>
<div class="question_part_label">b.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>Charlie and Daniella each began a fitness programme. On day one, they both ran <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo> </mo><mtext>m</mtext></math>. On each subsequent day, Charlie ran <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo> </mo><mtext>m</mtext></math> more than the previous day whereas Daniella increased her distance by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>%</mo></math> of the distance ran on the previous day.</p>
</div>
<div class="specification">
<p>Calculate how far</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Charlie ran on day <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math> of his fitness programme.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Daniella ran on day <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math> of her fitness programme.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On day <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> of the fitness programmes Daniella runs more than Charlie for the first time.</p>
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>attempt to find <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>20</mn></msub></math> using an arithmetic sequence<em> </em> <em><strong>(M1)</strong></em></p>
<p>e.g. <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo><mn>500</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>100</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>20</mn></msub><mo>=</mo><mn>500</mn><mo>+</mo><mn>1900</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo>,</mo><mo> </mo><mn>600</mn><mo>,</mo><mo> </mo><mn>700</mn><mo>,</mo><mo> </mo><mo>…</mo></math></p>
<p>(Charlie ran) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2400</mn><mo> </mo><mtext>m</mtext></math> <em> </em> <em><strong>A1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>r</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>1</mn><mo>.</mo><mn>02</mn></math><em> </em> <em><strong>(A1)</strong></em></p>
<p>attempt to find <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>20</mn></msub></math> using a geometric sequence<em> </em> <em><strong>(M1)</strong></em></p>
<p>e.g. <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo><mn>500</mn></math> and a value for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> <strong>OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo>×</mo><msup><mi>r</mi><mn>19</mn></msup></math></strong> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo>,</mo><mo> </mo><mn>510</mn><mo>,</mo><mo> </mo><mn>520</mn><mo>.</mo><mn>2</mn><mo>,</mo><mo> </mo><mo>…</mo></math></p>
<p>(Daniella ran) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>728</mn><mo> </mo><mtext>m </mtext><mfenced><mrow><mn>728</mn><mo>.</mo><mn>405</mn><mo>…</mo></mrow></mfenced></math> <em> </em> <em><strong>A1</strong></em></p>
<p><em><strong><br>[3 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>02</mn><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>></mo><mn>500</mn><mo>+</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>×</mo><mn>100</mn></math><em> </em> <em><strong>(M1)</strong></em></p>
<p>attempt to solve inequality<em> </em> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>></mo><mn>184</mn><mo>.</mo><mn>215</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>185</mn></math> <em> </em> <em><strong>A1</strong></em></p>
<p><em><strong><br>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>a</mi><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></math>. The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> is shown in the diagram. The vertex of the graph has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>,</mo><mo> </mo><mo>−</mo><mn>12</mn><mo>.</mo><mn>5</mn><mo>)</mo></math>. The graph intersects the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis at two points, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>−</mo><mn>2</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>p</mi><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math>.</p>
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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of</p>
<p>(i) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<p>(ii) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<p>(iii) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the axis of symmetry of the graph.</p>
<div class="marks">[1]</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"><mn>3</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>3</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math> seen.</p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>=</mo><mn>4</mn><mi>a</mi><mo>-</mo><mn>2</mn><mi>b</mi><mo>+</mo><mi>c</mi><mo>,</mo><mo> </mo><mo> </mo><mn>0</mn><mo>=</mo><mn>9</mn><mi>a</mi><mo>+</mo><mn>3</mn><mi>b</mi><mo>+</mo><mi>c</mi><mo>,</mo><mo> </mo><mo> </mo><mo>-</mo><mfrac><mn>25</mn><mn>2</mn></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mi>a</mi><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>b</mi><mo>+</mo><mi>c</mi></math> <em><strong>(M1)(A1)</strong></em> </p>
<p>(i) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> <em><strong>A1</strong></em></p>
<p>(ii) <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math> <em><strong>A1</strong></em></p>
<p>(iii) <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>12</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award the <em><strong>(M1)(A1)</strong></em> if at least one correct value is seen. Do not apply <em><strong>FT</strong></em> form part (a) if workings are not shown.</p>
<p><br><strong>METHOD 2</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>12</mn><mo>.</mo><mn>5</mn><mo>=</mo><mi>a</mi><mfenced><mrow><mn>0</mn><mo>.</mo><mn>5</mn><mo>+</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mn>0</mn><mo>.</mo><mn>5</mn><mo>-</mo><mn>3</mn></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p>(i) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>2</mn></math> <em><strong>A1</strong></em></p>
<p> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>=</mo><mn>2</mn><mo>×</mo><msup><mfenced><mn>3</mn></mfenced><mn>2</mn></msup><mo>+</mo><mn>3</mn><mi>b</mi><mo>+</mo><mi>c</mi></math></p>
<p> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>=</mo><mn>2</mn><mo>×</mo><msup><mfenced><mrow><mo>-</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mfenced><mrow><mo>-</mo><mn>2</mn></mrow></mfenced><mi>b</mi><mo>+</mo><mi>c</mi></math> <em><strong>(M1)</strong></em></p>
<p>(ii) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mn>2</mn></math> <em><strong>A1</strong></em></p>
<p>(iii) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mo>-</mo><mn>12</mn></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[5 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"><mi>x</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Do not <em><strong>FT</strong></em> from their part (b), this is a contradiction with the diagram.</p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A factory produces engraved gold disks. The cost <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> of the disks is directly proportional to the cube of the radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> of the disk.</p>
<p>A disk with a radius of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>8</mn><mo> </mo></math>cm costs <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>375</mn><mo> </mo></math>US dollars (USD).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an equation which links <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>.</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, to the nearest USD, the cost of disk that has a radius of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>1</mn><mo> </mo></math>cm.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#999;font-size:90%;font-style:italic;">* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>k</mi><msup><mi>r</mi><mn>3</mn></msup></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>375</mn><mo>=</mo><mi>k</mi><mo>×</mo><mn>0</mn><mo>.</mo><msup><mn>8</mn><mn>3</mn></msup><mo>⇒</mo><mi>k</mi><mo>=</mo><mn>732</mn><mo> </mo><mfenced><mrow><mn>732</mn><mo>.</mo><mn>421</mn><mo>…</mo></mrow></mfenced></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mn>732</mn><msup><mi>r</mi><mn>3</mn></msup></math> <strong>A1</strong></p>
<p> </p>
<p><strong>[3 marks]</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mn>732</mn><mo>.</mo><mn>42</mn><mo>…</mo><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>1</mn><mn>3</mn></msup></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mo>$</mo><mn>975</mn><mo> </mo><mfenced><mrow><mn>974</mn><mo>.</mo><mn>853</mn><mo>…</mo></mrow></mfenced></math> <strong>A1</strong></p>
<p> </p>
<p><strong>Note:</strong> accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>974</mn></math> from use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mn>732</mn><msup><mi>r</mi><mn>3</mn></msup></math> .</p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The height of a baseball after it is hit by a bat is modelled by the function</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mo>-</mo><mn>4</mn><mo>.</mo><mn>8</mn><msup><mi>t</mi><mn>2</mn></msup><mo>+</mo><mn>21</mn><mi>t</mi><mo>+</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> is the height in metres above the ground and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is the time in seconds after the ball was hit.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the height of the ball above the ground at the instant it is hit by the bat.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> when the ball hits the ground.</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>State an appropriate domain for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> in this model.</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"><mn>1</mn><mo>.</mo><mn>2</mn></math> metres <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>.</mo><mn>8</mn><msup><mi>t</mi><mn>2</mn></msup><mo>+</mo><mn>21</mn><mi>t</mi><mo>+</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>=</mo><mn>0</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>t</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>4</mn><mo>.</mo><mn>43</mn><mo> </mo><mi mathvariant="normal">s</mi><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>4</mn><mo>.</mo><mn>431415</mn><mo>…</mo><mo> </mo><mtext>s</mtext></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p> <br><strong>Note:</strong> If both values for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> are seen do not award the<em><strong> A1</strong></em> mark unless the negative is explicitly excluded.<br><br></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>4</mn><mo>.</mo><mn>43</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="[" close="]"><mrow><mn>0</mn><mo>,</mo><mo> </mo><mn>4</mn><mo>.</mo><mn>43</mn></mrow></mfenced></math> <em><strong>A1A1</strong></em></p>
<p> <br><strong>Note:</strong> Award <em><strong>A1</strong></em> for correct endpoints and <em><strong>A1</strong> </em>for expressing answer with correct notation. Award at most <em><strong>A1A0</strong> </em>for use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> instead of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>.<br><br></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>Probably the best answered question on the paper with many correct answers seen.</p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates correctly solved the quadratic equation.</p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Some cases, the lower bound was given as 1.2 from confusing height with time. Often the variable <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> was used in the interval notation which lost a mark.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^2} - 4x - 5">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>4</mn>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>5</mn>
</math></span>. The following diagram shows part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The function can be written in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {\left( {x - h} \right)^2} + k">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mi>h</mi>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>k</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the axis of symmetry of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph of a second function, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span>, is obtained by a reflection of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> in the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis, followed by a translation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 3} \\ 6 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>6</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
<p> </p>
<p>Find the coordinates of the vertex of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{ - \left( { - 4} \right)}}{{2\left( 1 \right)}}">
<mfrac>
<mrow>
<mo>−</mo>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>4</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{ - 1 + 5}}{2}">
<mfrac>
<mrow>
<mo>−</mo>
<mn>1</mn>
<mo>+</mo>
<mn>5</mn>
</mrow>
<mn>2</mn>
</mfrac>
</math></span></p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2">
<mi>x</mi>
<mo>=</mo>
<mn>2</mn>
</math></span> (must be an equation with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x =">
<mi>x</mi>
<mo>=</mo>
</math></span>) <em><strong> A1 N2</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> = 2 <em><strong> A1 N1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>(2)</p>
<p>correct substitution <em><strong>(A1)</strong></em></p>
<p><em>eg</em> (2)<sup>2</sup> − 4(2) − 5</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> = −9 <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>valid attempt to complete the square <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span><sup>2</sup> − 4<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> + 4</p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg</em> (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span><sup>2</sup> − 4<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> + 4) − 4 − 5, (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> − 2)<sup>2</sup> − 9</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> = −9 <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p> </p>
<p><strong>METHOD 1</strong> (working with vertex)</p>
<p>vertex of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> is at (2, −9) <em><strong> (A1)</strong></em></p>
<p>correct horizontal reflection <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> = −2, (−2, −9)</p>
<p>valid approach for translation of <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> <strong>or</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> value <em><strong> (M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> − 3, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> + 6, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 2} \\ { - 9} \end{array}} \right) + \left( {\begin{array}{*{20}{c}} { - 3} \\ 6 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−</mo>
<mn>9</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>6</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, one correct coordinate for vertex</p>
<p>vertex of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> is (−5, −3) (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> = −5, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> = −3) <em><strong>A1A1 N1N1</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong> (working with function)</p>
<p>correct approach for horizontal reflection <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>(−<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>)</p>
<p>correct horizontal reflection <em><strong>(A1)</strong></em></p>
<p><em>eg</em> (−<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>)<sup>2</sup> −4(−<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>) − 5, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span><sup>2 </sup>+ 4<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> − 5, (−<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> − 2)<sup>2</sup> − 9</p>
<p>valid approach for translation of <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> <strong>or</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> value <em><strong> (M1)</strong></em></p>
<p><em>eg</em> (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> + 3)<sup>2</sup> + 4(<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> + 3) − 5 + 6, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span><sup>2</sup> + 10<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> + 22, (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> + 5)<sup>2</sup> − 3, one correct coordinate for vertex</p>
<p>vertex of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> is (−5, −3) (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> = −5, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> = −3) <em><strong>A1A1 N1N1</strong></em></p>
<p> </p>
<p><em><strong>[5 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">b.</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>
<br><hr><br><div class="specification">
<p>Sejah placed a baking tin, that contained cake mix, in a preheated oven in order to bake a cake. The temperature in the centre of the cake mix, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T">
<mi>T</mi>
</math></span>, in degrees Celsius (°C) is given by</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="T(t) = 150 - a \times {(1.1)^{ - t}}">
<mi>T</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>150</mn>
<mo>−<!-- − --></mo>
<mi>a</mi>
<mo>×<!-- × --></mo>
<mrow>
<mo stretchy="false">(</mo>
<mn>1.1</mn>
<msup>
<mo stretchy="false">)</mo>
<mrow>
<mo>−<!-- − --></mo>
<mi>t</mi>
</mrow>
</msup>
</mrow>
</math></span></p>
<p>where <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 baking tin was placed in the oven. The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T">
<mi>T</mi>
</math></span> is shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_18.27.39.png" alt="N17/5/MATSD/SP1/ENG/TZ0/12"></p>
</div>
<div class="specification">
<p>The temperature in the centre of the cake mix was 18 °C when placed in the oven.</p>
</div>
<div class="specification">
<p>The baking tin is removed from the oven 15 minutes after the temperature in the centre of the cake mix has reached 130 °C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down what the value of 150 represents in the context of the question.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <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">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total time that the baking tin is in the oven.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>the temperature in the oven <strong><em>(A1)</em></strong></p>
<p><strong>OR</strong></p>
<p>the maximum possible temperature of the cake mix <strong><em>(A1) (C1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A0) </em></strong>for “the maximum temperature”.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="18 = 150 - a( \times 1.1^\circ )">
<mn>18</mn>
<mo>=</mo>
<mn>150</mn>
<mo>−</mo>
<mi>a</mi>
<mo stretchy="false">(</mo>
<mo>×</mo>
<msup>
<mn>1.1</mn>
<mo>∘</mo>
</msup>
<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 correct substitution of 18 and 0. Substitution of 0 can be implied.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(a) = 132">
<mo stretchy="false">(</mo>
<mi>a</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>132</mn>
</math></span> <strong><em>(A1) (C2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="150-132 \times {1.1^{ - t}} = 130">
<mn>150</mn>
<mo>−</mo>
<mn>132</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>1.1</mn>
<mrow>
<mo>−</mo>
<mi>t</mi>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mn>130</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substituting their <em>a </em>and equating to 130. Accept an inequality.</p>
<p>Award <strong><em>(M1) </em></strong>for a sketch of the horizontal line on the graph.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 19.8{\text{ }}(19.7992 \ldots )">
<mi>t</mi>
<mo>=</mo>
<mn>19.8</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>19.7992</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (b).</p>
<p> </p>
<p>34.8 (minutes) (34.7992…, 34 minutes 48 seconds) <strong><em>(A1)</em>(ft) <em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award the final <strong><em>(A1) </em></strong>for adding 15 minutes to their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> value.</p>
<p>In part (c), award <strong><em>(C2) </em></strong>for a final answer of 19.8 with no working.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercept (5, 0) and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept (0, 8).</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) + 3">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>3</mn>
</math></span>.</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>Find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( {4x} \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mn>4</mn>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercept of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( {2x} \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the transformation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( {x + 1} \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept is 11 (accept (0, 11) ) <em><strong>A1 N1</strong></em> </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>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( {4 \times 0} \right) = f\left( 0 \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mn>4</mn>
<mo>×</mo>
<mn>0</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</math></span>, recognizing stretch of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{4}">
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
</math></span> in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-direction</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept is 8 (accept (0, 8) ) <em><strong>A1 N2</strong></em> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercept is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{5}{2}\,\,\left( { = 2.5} \right)">
<mfrac>
<mn>5</mn>
<mn>2</mn>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mn>2.5</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{5}{2}{\text{,}}\,\,\,0} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>5</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> or (2.5, 0) ) <em><strong>A2 N2</strong></em> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct name, correct magnitude <strong>and</strong> direction <em><strong>A1A1 N2</strong></em></p>
<p><em>eg name:</em> translation, (horizontal) shift (do not accept move)</p>
<p><em>eg magnitude and direction</em>: 1 unit to the left, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 1} \\ 0 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, horizontal by –1</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">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A quadratic function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = a{x^2} + bx + c">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>a</mi>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>b</mi>
<mi>x</mi>
<mo>+</mo>
<mi>c</mi>
</math></span>. The points <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(0,{\text{ }}5)">
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>5</mn>
<mo stretchy="false">)</mo>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 4,{\text{ }}5)">
<mo stretchy="false">(</mo>
<mo>−<!-- − --></mo>
<mn>4</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>5</mn>
<mo stretchy="false">)</mo>
</math></span> lie on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<div class="specification">
<p>The <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-coordinate of the minimum of the graph is 3.</p>
</div>
<div class="question">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \frac{b}{{2a}} = - 2">
<mo>−</mo>
<mfrac>
<mi>b</mi>
<mrow>
<mn>2</mn>
<mi>a</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mo>−</mo>
<mn>2</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a{( - 2)^2} - 2b + 5 = 3">
<mi>a</mi>
<mrow>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>2</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>2</mn>
<mi>b</mi>
<mo>+</mo>
<mn>5</mn>
<mo>=</mo>
<mn>3</mn>
</math></span> or equivalent</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a{( - 4)^2} - 4b + 5 = 5">
<mi>a</mi>
<mrow>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>4</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>4</mn>
<mi>b</mi>
<mo>+</mo>
<mn>5</mn>
<mo>=</mo>
<mn>5</mn>
</math></span> or equivalent</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2a( - 2) + b = 0">
<mn>2</mn>
<mi>a</mi>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mi>b</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> or equivalent <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for two of the above equations.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 0.5">
<mi>a</mi>
<mo>=</mo>
<mn>0.5</mn>
</math></span> <strong><em>(A1)</em>(ft)</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = 2">
<mi>b</mi>
<mo>=</mo>
<mn>2</mn>
</math></span> <strong><em>(A1)</em>(ft) <em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award at most <strong><em>(M1)(A1)</em>(ft)<em>(A0) </em></strong>if the answers are reversed.</p>
<p>Follow through from parts (a) and (b).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>The size of a computer screen is the length of its diagonal. Zuzana buys a rectangular computer screen with a size of 68 cm, a height of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> cm and a width of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> cm, as shown in the diagram.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="images/Schermafbeelding_2018-02-12_om_18.05.15.png" alt="N17/5/MATSD/SP1/ENG/TZ0/06"></p>
</div>
<div class="specification">
<p>The ratio between the height and the width of the screen is 3:4.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use this information to write down an equation involving <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use this ratio to write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span><em>.</em></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^2} + {y^2} = {68^2}">
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<msup>
<mi>y</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mn>68</mn>
<mn>2</mn>
</msup>
</mrow>
</math></span> (or 4624 or equivalent) <strong><em>(A1) (C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{y}{x} = \frac{3}{4}">
<mfrac>
<mi>y</mi>
<mi>x</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>3</mn>
<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 a correct equation.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{3}{4}x{\text{ }}(y = 0.75x)">
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mi>x</mi>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>y</mi>
<mo>=</mo>
<mn>0.75</mn>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1) (C2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^2} + {\left( {\frac{3}{4}x} \right)^2} = {68^2}{\text{ }}\left( {{\text{or }}{x^2} + \frac{9}{{16}}{x^2} = 4624{\text{ or equivalent}}} \right)">
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mn>68</mn>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>or </mtext>
</mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mn>9</mn>
<mrow>
<mn>16</mn>
</mrow>
</mfrac>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>4624</mn>
<mrow>
<mtext> or equivalent</mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</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 expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> into their answer to part (a). Accept correct substitution of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 54.4{\text{ (cm), }}y = 40.8{\text{ (cm)}}">
<mi>x</mi>
<mo>=</mo>
<mn>54.4</mn>
<mrow>
<mtext> (cm), </mtext>
</mrow>
<mi>y</mi>
<mo>=</mo>
<mn>40.8</mn>
<mrow>
<mtext> (cm)</mtext>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from parts (a) and (b) as long as <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x > 0">
<mi>x</mi>
<mo>></mo>
<mn>0</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y > 0">
<mi>y</mi>
<mo>></mo>
<mn>0</mn>
</math></span>.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <em>f</em>(<em>x</em>) = <em>ax</em><sup>2</sup> − 4<em>x</em> − <em>c</em>. A horizontal line, <em>L</em> , intersects the graph of<em> f</em> at <em>x</em> = −1 and <em>x</em> = 3.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The equation of the axis of symmetry is <em>x</em> = <em>p</em>. Find <em>p</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, show that <em>a</em> = 2.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong> (using symmetry to find <em>p</em>)</p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{ - 1 + 3}}{2}">
<mfrac>
<mrow>
<mo>−</mo>
<mn>1</mn>
<mo>+</mo>
<mn>3</mn>
</mrow>
<mn>2</mn>
</mfrac>
</math></span>, <img 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"></p>
<p><em>p</em> = 1 <em><strong>A1 N2</strong></em></p>
<p><em><strong>Note:</strong></em> Award no marks if they work backwards by substituting <em>a</em> = 2 into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \frac{b}{{2a}}">
<mo>−</mo>
<mfrac>
<mi>b</mi>
<mrow>
<mn>2</mn>
<mi>a</mi>
</mrow>
</mfrac>
</math></span> to find <em>p</em>.</p>
<p>Do not accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = \frac{2}{a}">
<mi>p</mi>
<mo>=</mo>
<mfrac>
<mn>2</mn>
<mi>a</mi>
</mfrac>
</math></span>.</p>
<p> </p>
<p><strong>METHOD 2</strong> (calculating <em>a</em> first)<br>(i) & (ii) valid approach to calculate <em>a</em> <em><strong> M1</strong></em></p>
<p><em>eg </em> <em>a</em> + 4 − <em>c</em> = <em>a</em>(3<sup>2</sup>) − 4(3) − <em>c</em>, <em>f</em>(−1) = <em>f</em>(3)</p>
<p>correct working <em><strong>A1</strong></em></p>
<p>eg 8<em>a</em> = 16</p>
<p><em>a</em> = 2 <em><strong>AG N0</strong></em></p>
<p>valid approach to find <em>p <strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \frac{b}{{2a}},\,\,\,\frac{4}{{2\left( 2 \right)}}">
<mo>−</mo>
<mfrac>
<mi>b</mi>
<mrow>
<mn>2</mn>
<mi>a</mi>
</mrow>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mn>4</mn>
<mrow>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p><em>p</em> = 1 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>valid approach<strong> <em>M1</em></strong></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \frac{b}{{2a}},\,\,\,\frac{4}{{2a}}">
<mo>−</mo>
<mfrac>
<mi>b</mi>
<mrow>
<mn>2</mn>
<mi>a</mi>
</mrow>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mn>4</mn>
<mrow>
<mn>2</mn>
<mi>a</mi>
</mrow>
</mfrac>
</math></span> (might be seen in (i)), <em>f' </em>(1) = 0</p>
<p>correct equation <em><strong>A1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{4}{{2a}}">
<mfrac>
<mn>4</mn>
<mrow>
<mn>2</mn>
<mi>a</mi>
</mrow>
</mfrac>
</math></span> = 1, 2<em>a</em>(1) − 4 = 0</p>
<p><em>a</em> = 2 <em><strong>AG N0</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong> (calculating <em>a</em> first)<br>(i) & (ii) valid approach to calculate <em>a</em> <em><strong> M1</strong></em></p>
<p><em>eg </em> <em>a</em> + 4 − <em>c</em> = <em>a</em>(3<sup>2</sup>) − 4(3) − <em>c</em>, <em>f</em>(−1) = <em>f</em>(3)</p>
<p>correct working <em><strong>A1</strong></em></p>
<p>eg 8<em>a</em> = 16</p>
<p><em>a</em> = 2 <em><strong>AG N0</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Jashanti is saving money to buy a car. The price of the car, in US Dollars (USD), can be modelled by the equation</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="P = 8500{\text{ }}{(0.95)^t}.">
<mi>P</mi>
<mo>=</mo>
<mn>8500</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>0.95</mn>
<msup>
<mo stretchy="false">)</mo>
<mi>t</mi>
</msup>
</mrow>
<mo>.</mo>
</math></span></p>
<p>Jashanti’s savings, in USD, can be modelled by the equation</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="S = 400t + 2000.">
<mi>S</mi>
<mo>=</mo>
<mn>400</mn>
<mi>t</mi>
<mo>+</mo>
<mn>2000.</mn>
</math></span></p>
<p>In both equations <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> is the time in months since Jashanti started saving for the car.</p>
</div>
<div class="specification">
<p>Jashanti does not want to wait too long and wants to buy the car two months after she started saving. She decides to ask her parents for the extra money that she needs.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the amount of money Jashanti saves per month.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find how long it will take for Jashanti to have saved enough money to buy the car.</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 how much extra money Jashanti needs.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>400 (USD) <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="8500{\text{ }}{(0.95)^t} = 400 \times t + 2000">
<mn>8500</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>0.95</mn>
<msup>
<mo stretchy="false">)</mo>
<mi>t</mi>
</msup>
</mrow>
<mo>=</mo>
<mn>400</mn>
<mo>×</mo>
<mi>t</mi>
<mo>+</mo>
<mn>2000</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for equating <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="8500{(0.95)^t}">
<mn>8500</mn>
<mrow>
<mo stretchy="false">(</mo>
<mn>0.95</mn>
<msup>
<mo stretchy="false">)</mo>
<mi>t</mi>
</msup>
</mrow>
</math></span> to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="400 \times t + 2000">
<mn>400</mn>
<mo>×</mo>
<mi>t</mi>
<mo>+</mo>
<mn>2000</mn>
</math></span> or for comparing the difference between the two expressions to zero or for showing a sketch of both functions.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(t = ){\text{ }}8.64{\text{ (months) }}\left( {8.6414 \ldots {\text{ (months)}}} \right)">
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>8.64</mn>
<mrow>
<mtext> (months) </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>8.6414</mn>
<mo>…</mo>
<mrow>
<mtext> (months)</mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em></strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept 9 months.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="8500{(0.95)^2} - (400 \times 2 + 2000)">
<mn>8500</mn>
<mrow>
<mo stretchy="false">(</mo>
<mn>0.95</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mo stretchy="false">(</mo>
<mn>400</mn>
<mo>×</mo>
<mn>2</mn>
<mo>+</mo>
<mn>2000</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 2">
<mi>t</mi>
<mo>=</mo>
<mn>2</mn>
</math></span> into equation for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P">
<mi>P</mi>
</math></span>, <strong><em>(M1) </em></strong>for finding the difference between a value/expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P">
<mi>P</mi>
</math></span> and a value/expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="S">
<mi>S</mi>
</math></span>. The first <strong><em>(M1) </em></strong>is implied if 7671.25 seen.</p>
<p> </p>
<p>4870 (USD) (4871.25) <strong><em>(A1)</em></strong> <strong><em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept 4871.3.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Olava’s Pizza Company supplies and delivers large cheese pizzas.</p>
<p>The total cost to the customer, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math>, in Papua New Guinean Kina (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>PGK</mtext></math>), is modelled by the function</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mfenced><mi>n</mi></mfenced><mo>=</mo><mn>34</mn><mo>.</mo><mn>50</mn><mi>n</mi><mo>+</mo><mn>8</mn><mo>.</mo><mn>50</mn><mo> </mo><mo>,</mo><mo> </mo><mi>n</mi><mo>≥</mo><mn>2</mn><mo> </mo><mo>,</mo><mo> </mo><mi>n</mi><mo>∈</mo><mi mathvariant="normal">ℤ</mi><mo>,</mo></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>, is the number of large cheese pizzas ordered. This total cost includes a fixed cost for delivery.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State, in the context of the question, what the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>34</mn><mo>.</mo><mn>50</mn></math> represents.</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>State, in the context of the question, what the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>50</mn></math> represents.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the minimum number of pizzas that can be ordered.</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>Kaelani has <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>450</mn><mo> </mo><mtext>PGK</mtext></math>.</p>
<p>Find the maximum number of large cheese pizzas that Kaelani can order from Olava’s Pizza Company.</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>the cost of <strong>each</strong> (large cheese) pizza / <strong>a</strong> pizza / <strong>one</strong> pizza / <strong>per</strong> pizza <em><strong>(A1) (C1)</strong></em><br><br><strong>Note:</strong> Award <em><strong>(A0)</strong></em> for “the cost of (large cheese) pizzas”. Do not accept “the <strong>minimum</strong> cost of a pizza”.</p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the (fixed) delivery cost <em><strong>(A1) (C1)</strong></em><br><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> <em><strong>(A1) (C1)</strong></em><br><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>450</mn><mo>=</mo><mn>34</mn><mo>.</mo><mn>50</mn><mi>n</mi><mo>+</mo><mn>8</mn><mo>.</mo><mn>50</mn></math> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating the cost equation to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>450</mn></math> (may be stated as an inequality).</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>.</mo><mn>8</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>12</mn><mo>.</mo><mn>7971</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></p>
<p><strong><br>Note:</strong> The final answer must be an integer.<br>The final <em><strong>(A1)</strong></em><strong>(ft)</strong> is awarded for rounding their answer <strong>down</strong> to a whole number, provided their unrounded answer is seen.<br><em><strong><br><br>[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">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The price of gas at Leon’s gas station is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>1</mn><mo>.</mo><mn>50</mn></math> per litre. If a customer buys a minimum of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> litres, a discount of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>5</mn></math> is applied.</p>
<p>This can be modelled by the following function, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math>, which gives the total cost when buying a minimum of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> litres at Leon’s gas station.</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>.</mo><mn>50</mn><mi>x</mi><mo>-</mo><mn>5</mn><mo>,</mo><mo> </mo><mi>x</mi><mo>≥</mo><mn>10</mn></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> is the number of litres of gas that a customer buys.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total cost of buying <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn></math> litres of gas at Leon’s gas station.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>L</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>(</mo><mn>70</mn><mo>)</mo></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The price of gas at Erica’s gas station is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>1</mn><mo>.</mo><mn>30</mn></math> per litre. A customer must buy a minimum of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> litres of gas. The total cost at Erica’s gas station is cheaper than Leon’s gas station when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mi>k</mi></math>.</p>
<p>Find the minimum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mfenced><mn>40</mn></mfenced><mo>=</mo><mn>1</mn><mo>.</mo><mn>50</mn><mo>×</mo><mn>40</mn><mo>-</mo><mn>5</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>$</mo><mn>55</mn></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn><mo>=</mo><mn>1</mn><mo>.</mo><mn>50</mn><mi>x</mi><mo>-</mo><mn>5</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>50</mn></math> litres <em><strong>A1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>30</mn><mi>x</mi></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>30</mn><mi>x</mi><mo><</mo><mn>1</mn><mo>.</mo><mn>50</mn><mi>x</mi><mo>-</mo><mn>5</mn></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong></em> for a graph showing two intersecting linear functions, provided one function has a <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-intercept of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> and the other function has a negative <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-intercept.</p>
<p><br>(minimum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo></math>) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>25</mn></math>.</p>
<p><em><strong><br>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The size of the population <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>P</mi><mo>)</mo></math> of migrating birds in a particular town can be approximately modelled by the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>a</mi><mo> </mo><mi>sin</mi><mo>(</mo><mi>b</mi><mi>t</mi><mo>)</mo><mo>+</mo><mi>c</mi><mo>,</mo><mo> </mo><mo> </mo><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi><mo>,</mo><mo> </mo><mi>c</mi><mo>∈</mo><msup><mi mathvariant="normal">ℝ</mi><mo>+</mo></msup></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is measured in months from the time of the initial measurements.</p>
<p>In a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math> month period the maximum population is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2600</mn></math> and occurs when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>3</mn></math> and the minimum population is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>800</mn></math> and occurs when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>9</mn></math>.</p>
<p>This information is shown on the graph below.</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 value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.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"><mi>b</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</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 population first reaches <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2200</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#999;font-size:90%;font-style:italic;">* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2600</mn><mo>-</mo><mn>800</mn></mrow><mn>2</mn></mfrac><mo>=</mo><mn>900</mn></math> <strong>(M1)</strong><strong>A1</strong></p>
<p> </p>
<p><strong>[2 marks]</strong></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"><mfrac><mn>360</mn><mn>12</mn></mfrac><mo>=</mo><mn>30</mn></math> <strong>(M1)</strong><strong>A1</strong></p>
<p> </p>
<p><strong>Note:</strong> Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mn>12</mn></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>524</mn><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>523598</mn><mo>…</mo></mrow></mfenced></math>.</p>
<p> </p>
<p><strong>[2 marks]</strong></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"><mfrac><mrow><mn>2600</mn><mo>+</mo><mn>800</mn></mrow><mn>2</mn></mfrac><mo>=</mo><mn>1700</mn></math> <strong>A1</strong></p>
<p> </p>
<p><strong>[1 mark]</strong></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Solve <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>900</mn><mo> </mo><mi>sin</mi><mfenced><mrow><mn>30</mn><mi>t</mi></mrow></mfenced><mo>+</mo><mn>1700</mn><mo>=</mo><mn>2200</mn></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>12</mn><mo> </mo><mfenced><mrow><mn>1</mn><mo>.</mo><mn>12496</mn><mo>…</mo></mrow></mfenced></math> <strong>A1</strong></p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.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>
<br><hr><br><div class="specification">
<p>Irina uses a set of coordinate axes to draw her design of a window. The base of the window is on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis, the upper part of the window is in the form of a quadratic curve and the sides are vertical lines, as shown on the diagram. The curve has end points <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>10</mn><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>8</mn><mo>,</mo><mo> </mo><mn>10</mn><mo>)</mo></math> and its vertex is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>4</mn><mo>,</mo><mo> </mo><mn>12</mn><mo>)</mo></math>. Distances are measured in centimetres.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The quadratic curve can be expressed in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>a</mi><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>8</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</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>Hence form two equations in terms of <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>
<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>Hence find the equation of the quadratic curve.</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 area of the shaded region in Irina’s design.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>10</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>64</mn><mi>a</mi><mo>+</mo><mn>8</mn><mi>b</mi><mo>+</mo><mn>10</mn><mo>=</mo><mn>10</mn></math> <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mi>a</mi><mo>+</mo><mn>4</mn><mi>b</mi><mo>+</mo><mn>10</mn><mo>=</mo><mn>12</mn><mo> </mo></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong></em> for each equivalent expression or <em><strong>A1</strong></em> for the use of the axis of symmetry formula to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>=</mo><mfrac><mrow><mo>-</mo><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></math> or from use of derivative. Award <em><strong>A0A1</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>64</mn><mi>a</mi><mo>+</mo><mn>8</mn><mi>b</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>10</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mi>a</mi><mo>+</mo><mn>4</mn><mi>b</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>12</mn><mo> </mo></math>.<br><br></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>8</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>+</mo><mn>10</mn></math> <em><strong>A1</strong></em><em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award<em><strong> A1A0</strong></em> if one term is incorrect, <em><strong>A0A0</strong></em> if two or more terms are incorrect. Award at most <em><strong>A1A0</strong></em> if correct <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> values are seen but answer not expressed as an equation.<br><br></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>recognizing the need to integrate their expression <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>∫</mo><mn>0</mn><mn>8</mn></msubsup><mo>-</mo><mfrac><mn>1</mn><mn>8</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>+</mo><mn>10</mn><mo> </mo><mo>d</mo><mi>x</mi></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct integral, including limits. Condone absence of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>d</mo><mi>x</mi></math>.</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo>.</mo><mn>7</mn><mo> </mo><msup><mtext>cm</mtext><mn>2</mn></msup><mo> </mo><mo> </mo><mfenced><mrow><mfrac><mn>272</mn><mn>3</mn></mfrac><mo>,</mo><mo> </mo><mn>90</mn><mo>.</mo><mn>6666</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Generally, the responses were good for this last question on the paper. The main issue here was to not give the two equations in part (a)(ii) with simplified coefficients of <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>. Several candidates understood what was required but left their answers with <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mn>8</mn></mfenced><mn>2</mn></msup><mi>a</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mn>4</mn></mfenced><mn>2</mn></msup><mi>a</mi></math> un-simplified and lost marks. Some candidates used the coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math> to substitute in the equation with an incorrect equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mi>b</mi><mo>=</mo><mn>0</mn></math>. Candidates were successful at writing the equations in part (a)(iii). In part (b), most candidates realized that they had to use integration to find the area of the shaded region and, for the most part, were able to find a correct value for the area using either the correct equation or their obtained equation from the previous part. A common error was to integrate between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> instead of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math>.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Generally, the responses were good for this last question on the paper. The main issue here was to not give the two equations in part (a)(ii) with simplified coefficients of <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>. Several candidates understood what was required but left their answers with <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mn>8</mn></mfenced><mn>2</mn></msup><mi>a</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mn>4</mn></mfenced><mn>2</mn></msup><mi>a</mi></math> un-simplified and lost marks. Some candidates used the coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math> to substitute in the equation with an incorrect equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mi>b</mi><mo>=</mo><mn>0</mn></math>. Candidates were successful at writing the equations in part (a)(iii). In part (b), most candidates realized that they had to use integration to find the area of the shaded region and, for the most part, were able to find a correct value for the area using either the correct equation or their obtained equation from the previous part. A common error was to integrate between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> instead of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math>.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Generally, the responses were good for this last question on the paper. The main issue here was to not give the two equations in part (a)(ii) with simplified coefficients of <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>. Several candidates understood what was required but left their answers with <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mn>8</mn></mfenced><mn>2</mn></msup><mi>a</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mn>4</mn></mfenced><mn>2</mn></msup><mi>a</mi></math> un-simplified and lost marks. Some candidates used the coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math> to substitute in the equation with an incorrect equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mi>b</mi><mo>=</mo><mn>0</mn></math>. Candidates were successful at writing the equations in part (a)(iii). In part (b), most candidates realized that they had to use integration to find the area of the shaded region and, for the most part, were able to find a correct value for the area using either the correct equation or their obtained equation from the previous part. A common error was to integrate between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> instead of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math>.</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Generally, the responses were good for this last question on the paper. The main issue here was to not give the two equations in part (a)(ii) with simplified coefficients of <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>. Several candidates understood what was required but left their answers with <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mn>8</mn></mfenced><mn>2</mn></msup><mi>a</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mn>4</mn></mfenced><mn>2</mn></msup><mi>a</mi></math> un-simplified and lost marks. Some candidates used the coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math> to substitute in the equation with an incorrect equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mi>b</mi><mo>=</mo><mn>0</mn></math>. Candidates were successful at writing the equations in part (a)(iii). In part (b), most candidates realized that they had to use integration to find the area of the shaded region and, for the most part, were able to find a correct value for the area using either the correct equation or their obtained equation from the previous part. A common error was to integrate between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> instead of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math>.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the curve <em>y</em> = 5<em>x</em><sup>3 </sup>− 3<em>x</em>.</p>
</div>
<div class="specification">
<p>The curve has a tangent at the point P(−1, −2).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}y}}{{{\text{d}}x}}">
<mfrac>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>y</mi>
</mrow>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</mrow>
</mfrac>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the gradient of this tangent at point P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of this tangent. Give your answer in the form <em>y</em> = <em>mx</em> + <em>c</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>15<em>x</em><sup>2</sup> − 3<em><strong> (A1)(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for 15<em>x</em><sup>2</sup>, <em><strong>(A1)</strong></em> for −3. Award at most <em><strong>(A1)</strong></em><em><strong>(A0)</strong></em> if additional terms are seen.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>15 (−1)<sup>2</sup> − 3<em><strong> (M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong> (M1)</strong></em> for substituting −1 into their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}y}}{{{\text{d}}x}}">
<mfrac>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>y</mi>
</mrow>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</mrow>
</mfrac>
</math></span>.</p>
<p> </p>
<p>= 12 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a).</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(<em>y</em> − (−2)) = 12 (<em>x</em> − (−1)) <em><strong> (M1)</strong></em></p>
<p><strong>OR</strong></p>
<p>−2 = 12(−1) + c <em><strong> (M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong> (M1)</strong></em> for point <strong>and</strong> their gradient substituted into the equation of a line.</p>
<p> </p>
<p><em>y</em> = 12<em>x</em> + 10 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (b).</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;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{{x^4}}}{4}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
</mrow>
<mn>4</mn>
</mfrac>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <em>f'</em>(<em>x</em>)</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the gradient of the graph of <em>f</em> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - \frac{1}{2}">
<mi>x</mi>
<mo>=</mo>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <em>x</em>-coordinate of the point at which the <strong>normal</strong> to the graph of <em>f</em> has gradient <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{ - \frac{1}{8}}">
<mrow>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mn>8</mn>
</mfrac>
</mrow>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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><em>x</em><sup>3</sup> <em><strong>(A1) (C1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A0)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4{x^3}}}{4}">
<mfrac>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mn>4</mn>
</mfrac>
</math></span> and not simplified to <em>x</em><sup>3</sup>.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\left( { - \frac{1}{2}} \right)^3}">
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{ - \frac{1}{2}}">
<mrow>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
</math></span> into their derivative.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{ - \frac{1}{8}}">
<mrow>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mn>8</mn>
</mfrac>
</mrow>
</math></span> (−0.125) <em><strong> (A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their part (a).</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><em>x</em><sup>3</sup> = 8 <em><strong>(A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for 8 seen maybe seen as part of an equation <em>y</em> = 8<em>x</em> + <em>c</em>, <em><strong>(M1)</strong></em> for equating their derivative to 8.</p>
<p>(<em>x</em> =) 2 <em><strong>(A1) (C3)</strong></em></p>
<p><strong>Note:</strong> Do not accept (2, 4).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Elvis Presley is an extremely popular singer. Although he passed away in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1977</mn></math>, many of his fans continue to pay tribute by dressing like Elvis and singing his songs.</p>
<p>The number of Elvis impersonators, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mfenced><mi>t</mi></mfenced></math>, can be modelled by the function</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mn>170</mn><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>31</mn><mi>t</mi></msup><mo>,</mo></math></p>
<p style="text-align: left;">where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>, is the number of years since <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1977</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of Elvis impersonators in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1977</mn></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the time taken for the number of Elvis impersonators to reach <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>130</mn><mo> </mo><mn>000</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the number of Elvis impersonators when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>70</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The world population in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2047</mn></math> is projected to be <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo> </mo><mn>500</mn><mo> </mo><mn>000</mn><mo> </mo><mn>000</mn></math> people.</p>
<p>Use this information to explain why the model for the number of Elvis impersonators is unrealistic.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>170</mn></math> <span class="mjpage"> <em><strong>(A1) (C1)</strong></em><br></span></p>
<p><em><strong><span class="mjpage">[1 mark]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>130</mn><mo> </mo><mn>000</mn><mo>=</mo><mn>170</mn><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>31</mn><mi>t</mi></msup></math> <span class="mjpage"> <em><strong>(M1)</strong></em><br></span></p>
<p><span class="mjpage"><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>130</mn><mo> </mo><mn>000</mn></math> to the exponential function.</span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>t</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>24</mn><mo>.</mo><mn>6</mn></math> (<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn><mo>.</mo><mn>5882</mn><mo>…</mo></math> (years)) <em><strong>(A1) (C2)</strong></em></span></p>
<p><em><strong><span class="mjpage">[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>170</mn><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>31</mn><mn>70</mn></msup></math> <span class="mjpage"> <em><strong>(M1)</strong></em><br></span></p>
<p><span class="mjpage"><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mfenced><mi>t</mi></mfenced></math>.</span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>75</mn><mo>×</mo><msup><mn>10</mn><mn>10</mn></msup><mo> </mo><mfenced><mrow><mn>2</mn><mo>.</mo><mn>75067</mn><mo>…</mo><mo>×</mo><msup><mn>10</mn><mn>10</mn></msup><mo>,</mo><mo> </mo><mn>27</mn><mo> </mo><mn>500</mn><mo> </mo><mn>000</mn><mo> </mo><mn>000</mn><mo>,</mo><mo> </mo><mn>27</mn><mo> </mo><mn>506</mn><mo> </mo><mn>771</mn><mo> </mo><mn>343</mn></mrow></mfenced></math> <em><strong>(A1) (C2)</strong></em></span></p>
<p><em><strong><span class="mjpage">[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The number of Elvis impersonators in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2047</mn></math>, is greater than the world population. <em><strong>(R1) (C1)</strong></em></p>
<p><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>75</mn><mo>×</mo><msup><mn>10</mn><mn>10</mn></msup><mo>></mo><mn>9</mn><mo> </mo><mn>500</mn><mo> </mo><mn>000</mn><mo> </mo><mn>000</mn></math> <em><strong>(R1) (C1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(R1)</strong></em> for a correct comparison of <em>their</em> number of impersonators with the world population. Follow through from part (c) if a reasonable argument can be made that the model is unrealistic.<br>Award <em><strong>(R0)</strong></em> if the number of impersonators is not explicitly seen in part (c) or in part (d).</p>
<p><em><strong><span class="mjpage">[1 mark]</span></strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows the graph of the quadratic function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>a</mi><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></math> , with vertex <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>−</mo><mn>2</mn><mo>,</mo><mo> </mo><mn>10</mn></mrow></mfenced></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>k</mi></math> has two solutions. One of these solutions is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>2</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the other solution of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>k</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the table below placing a tick (✔) to show whether the unknown parameters <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> are positive, zero or negative. The row for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> has been completed as an example.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></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>State the values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> for which <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> is decreasing.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>=</mo></mrow></mfenced><mo> </mo><mfenced><mrow><mo>-</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mn>4</mn></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>=</mo></mrow></mfenced><mo> </mo><mfenced><mrow><mo>-</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mn>2</mn><mo>-</mo><mfenced><mrow><mo>-</mo><mn>2</mn></mrow></mfenced></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for correct calculation of the left symmetrical point.</p>
<p><em><strong><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo>-</mo><mn>6</mn></math> (A1) (C2)</strong></em></p>
<p><strong><br></strong><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"> <em><strong>(A1)(A1) (C2)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct row.</p>
<p><em><strong><br></strong></em><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mo>-</mo><mn>2</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≥</mo><mo>-</mo><mn>2</mn></math> <em><strong>(A1)(A1) (C2)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(A1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math> seen as part of an inequality, <em><strong>(A1)</strong></em> for completely correct notation. Award <em><strong>(A1)</strong></em><em><strong>(A1)</strong></em> for correct equivalent statement in words, for example “decreasing when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> is greater than negative <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math>”.</p>
<p><em><strong><br></strong></em><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">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>If a shark is spotted near to Brighton beach, a lifeguard will activate a siren to warn swimmers.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>The sound intensity, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math>, of the siren varies inversely with the square of the distance, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>, from the siren, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>></mo><mn>0</mn></math>.</p>
<p>It is known that at a distance of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn></math> metres from the siren, the sound intensity is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> watts per square metre (<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>W m</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup></math>).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mfrac><mn>9</mn><msup><mi>d</mi><mn>2</mn></msup></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the curve of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math> on the axes below showing clearly the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo>,</mo><mo> </mo><mn>4</mn><mo>)</mo></math>.</p>
<p><img 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"></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>Whilst swimming, Scarlett can hear the siren only if the sound intensity at her location is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>W m</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup></math>.</p>
<p>Find the values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> where Scarlett cannot hear the siren.</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"><mi>I</mi><mo>=</mo><mfrac><mi>k</mi><msup><mi>d</mi><mn>2</mn></msup></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>=</mo><mfrac><mi>k</mi><mrow><mn>1</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup></mrow></mfrac></math> <em><strong>M1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mfrac><mn>9</mn><msup><mi>d</mi><mn>2</mn></msup></mfrac></math> <em><strong>AG</strong></em></p>
<p><strong><br>Note:</strong> The <em><strong>AG</strong> </em>line must be seen for the second <em><strong>M1</strong></em> to be awarded. <br> Award no marks for substituting <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> into <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mfrac><mn>9</mn><msup><mi>d</mi><mn>2</mn></msup></mfrac></math> (i.e., working backwards).</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="padding-left:120px;"><img src="data:image/png;base64,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"> <em><strong>A1A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> for correct general shape (concave up) with no <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math>-intercept, passing through the marked point <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>1</mn><mo>.</mo><mn>5</mn><mo>,</mo><mo> </mo><mn>4</mn></mrow></mfenced></math>; the point must be labelled with either the coordinates or the values <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> axes. Award <em><strong>A1</strong></em> for the curve showing asymptotic behavior (i.e. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math> tends to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math>, as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> tends to infinity), extending to at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>6</mn></math>; the curve must not cross nor veer away from the horizontal asymptote.</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo>≥</mo><mfrac><mn>9</mn><msup><mi>d</mi><mn>2</mn></msup></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for a correct inequality.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>≥</mo><mn>2450</mn><mo> </mo><mfenced><mtext>m</mtext></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mn>2449</mn><mo>.</mo><mn>48</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A0</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>2450</mn></math>.</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 4{x^3} + \frac{3}{{{x^2}}} - 3,{\text{ }}x \ne 0">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>4</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mn>3</mn>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>−<!-- − --></mo>
<mn>3</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>x</mi>
<mo>≠<!-- ≠ --></mo>
<mn>0</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the derivative of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the point on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> at which the gradient of the tangent is equal to 6.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="12{x^2} - \frac{6}{{{x^3}}}">
<mn>12</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mfrac>
<mn>6</mn>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> or equivalent <strong><em>(A1)(A1)(A1) (C3)</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="12{x^2}">
<mn>12</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span>, <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 6">
<mo>−</mo>
<mn>6</mn>
</math></span> and <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{{x^3}}}">
<mfrac>
<mn>1</mn>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^{ - 3}}">
<mrow>
<msup>
<mi>x</mi>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</math></span>. Award at most <strong><em>(A1)(A1)(A0) </em></strong>if additional terms seen.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="12{x^2} - \frac{6}{{{x^3}}} = 6">
<mn>12</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mfrac>
<mn>6</mn>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mn>6</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for equating their derivative to 6.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(1,{\text{ }}4)">
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>4</mn>
<mo stretchy="false">)</mo>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><strong>OR</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 1,{\text{ }}y = 4">
<mi>x</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>y</mi>
<mo>=</mo>
<mn>4</mn>
</math></span> <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>A frequent wrong answer seen in scripts is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(1,{\text{ }}6)">
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>6</mn>
<mo stretchy="false">)</mo>
</math></span> for this answer with correct working award <strong><em>(M1)(A0)(A1) </em></strong>and if there is no working award <strong><em>(C1)</em></strong>.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Maria owns a cheese factory. The amount of cheese, in kilograms, Maria sells in one week, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Q">
<mi>Q</mi>
</math></span>, is given by</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Q = 882 - 45p">
<mi>Q</mi>
<mo>=</mo>
<mn>882</mn>
<mo>−<!-- − --></mo>
<mn>45</mn>
<mi>p</mi>
</math></span>,</p>
<p>where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> is the price of a kilogram of cheese in euros (EUR).</p>
</div>
<div class="specification">
<p>Maria earns <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(p - 6.80){\text{ EUR}}">
<mo stretchy="false">(</mo>
<mi>p</mi>
<mo>−<!-- − --></mo>
<mn>6.80</mn>
<mo stretchy="false">)</mo>
<mrow>
<mtext> EUR</mtext>
</mrow>
</math></span> for each kilogram of cheese sold.</p>
</div>
<div class="specification">
<p>To calculate her weekly profit <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="W">
<mi>W</mi>
</math></span>, in EUR, Maria multiplies the amount of cheese she sells by the amount she earns per kilogram.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down how many kilograms of cheese Maria sells in one week if the price of a kilogram of cheese is 8 EUR.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find how much Maria earns in one week, from selling cheese, if the price of a kilogram of cheese is 8 EUR.</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>Write down an expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="W">
<mi>W</mi>
</math></span> in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>.</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 price, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>, that will give Maria the highest weekly profit.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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>522 (kg) <strong><em>(A1) (C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="522(8 - 6.80)">
<mn>522</mn>
<mo stretchy="false">(</mo>
<mn>8</mn>
<mo>−</mo>
<mn>6.80</mn>
<mo stretchy="false">)</mo>
</math></span> or equivalent <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplying their answer to part (a) by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(8 - 6.80)">
<mo stretchy="false">(</mo>
<mn>8</mn>
<mo>−</mo>
<mn>6.80</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p> </p>
<p>626 (EUR) (626.40) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (a).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(W = ){\text{ }}(882 - 45p)(p - 6.80)">
<mo stretchy="false">(</mo>
<mi>W</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>882</mn>
<mo>−</mo>
<mn>45</mn>
<mi>p</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>p</mi>
<mo>−</mo>
<mn>6.80</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em></strong></p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(W = ) - 45{p^2} + 1188p - 5997.6">
<mo stretchy="false">(</mo>
<mi>W</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mo>−</mo>
<mn>45</mn>
<mrow>
<msup>
<mi>p</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>1188</mn>
<mi>p</mi>
<mo>−</mo>
<mn>5997.6</mn>
</math></span> <strong><em>(A1) (C1)</em></strong></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>sketch of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="W">
<mi>W</mi>
</math></span> with some indication of the maximum <strong><em>(M1)</em></strong></p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 90p + 1188 = 0">
<mo>−</mo>
<mn>90</mn>
<mi>p</mi>
<mo>+</mo>
<mn>1188</mn>
<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 the correct derivative of their part (c) to zero.</p>
<p> </p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(p = ){\text{ }}\frac{{ - 1188}}{{2 \times ( - 45)}}">
<mo stretchy="false">(</mo>
<mi>p</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<mo>−</mo>
<mn>1188</mn>
</mrow>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>45</mn>
<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 into the formula for axis of symmetry.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(p = ){\text{ }}13.2{\text{ (EUR)}}">
<mo stretchy="false">(</mo>
<mi>p</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>13.2</mn>
<mrow>
<mtext> (EUR)</mtext>
</mrow>
</math></span> <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from their part (c), if the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> is such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6.80 < p < 19.6">
<mn>6.80</mn>
<mo><</mo>
<mi>p</mi>
<mo><</mo>
<mn>19.6</mn>
</math></span>.</p>
<p> </p>
<p><strong><em>[2 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>The following function models the growth of a bacteria population in an experiment,</p>
<p style="text-align: center;"><em>P</em>(<em>t</em>) = <em>A</em> × 2<sup><em>t</em></sup>, <em>t</em> ≥ 0</p>
<p>where <em>A</em> is a constant and t is the time, in hours, since the experiment began.</p>
<p>Four hours after the experiment began, the bacteria population is 6400.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>A</em>.</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>Interpret what <em>A</em> represents in this context.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the time since the experiment began for the bacteria population to be equal to 40<em>A</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>6400 = <em>A</em> × 2<sup>4</sup> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of 4 and 6400 in equation.</p>
<p>(<em>A</em> =) 400 <em><strong>(A1) (C2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the initial population <strong>OR</strong> the population at the start of experiment <strong><em>(A1) (C1)</em></strong></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>40<em>A</em> = <em>A</em> × 2<em><sup>t</sup></em> <strong>OR</strong> 40 × 400 = 400 × 2<em><sup>t</sup></em> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into equation. Follow through with their<em> A</em> from part (a).</p>
<p>40 = 2<em><sup>t</sup></em> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for simplifying.</p>
<p>5.32 (5.32192…) (hours) <strong>OR </strong> 5 hours 19.3 (19.3156…) minutes <em><strong>(A1) (C3)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The cross-section of an arched entrance into the ballroom of a hotel is in the shape of a parabola. This cross-section can be modelled by part of the graph <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>−</mo><mn>1</mn><mo>.</mo><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>.</mo><mn>48</mn><mi>x</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> is the height of the archway, in metres, at a horizontal distance, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> metres, from the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>, in the bottom corner of the archway.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>To prepare for an event, a square-based crate that is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>6</mn><mo> </mo><mtext>m</mtext></math> wide and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>0</mn><mo> </mo><mtext>m</mtext></math> high is to be moved through the archway into the ballroom. The crate must remain upright while it is being moved.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine an equation for the axis of symmetry of the parabola that models the archway.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine whether the crate will fit through the archway. Justify your answer.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo>-</mo><mfrac><mrow><mn>4</mn><mo>.</mo><mn>48</mn></mrow><mrow><mn>2</mn><mfenced><mrow><mo>-</mo><mn>1</mn><mo>.</mo><mn>6</mn></mrow></mfenced></mrow></mfrac></math> <strong>OR </strong>coordinates of maximum point <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>.</mo><mn>4</mn><mo>,</mo><mo> </mo><mn>3</mn><mo>.</mo><mn>136</mn><mo>)</mo></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>4</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>the cart is centred in the archway when it is between</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>6</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>2</mn></math>, <em><strong>A1</strong></em></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>≥</mo><mn>2</mn><mo>.</mo><mn>112</mn><mo> </mo><mfenced><mtext>m</mtext></mfenced></math> (which is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math>) <em><strong>R1</strong></em></p>
<p>the archway is tall enough for the crate <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Do not award <em><strong>R0A1</strong></em>.</p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>the height of the archway is greater or equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>0</mn></math> between</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>557385</mn><mo>…</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>24261</mn><mo>…</mo></math> <em><strong>A1</strong></em></p>
<p>width of this section of archway =</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>.</mo><mn>24261</mn><mo>…</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>557385</mn><mo>…</mo><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>1</mn><mo>.</mo><mn>68522</mn><mo> </mo><mfenced><mtext>m</mtext></mfenced></math> (which is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>6</mn></math>) <em><strong>R1</strong></em></p>
<p>the archway is wide enough for the crate <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Do not award <em><strong>R0A1</strong></em>.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Most candidates were able to substitute into the formula for axis of symmetry or find the vertex of the parabola correctly, both being appropriate methods, but neglected to write an equation from that, even though the question specifically asked for an equation.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Determining a process to see if the crate would fit through the archway proved to be difficult for many candidates. It was common to see the maximum heights compared, the maximum widths compared, or the area of the front surface of the crate compared to the area of the archway opening. Other candidates merely calculated the height at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>6</mn></math>, positioning the corner of the crate at O, and made their conclusion based on this value, without consideration of how the crate would be moving through the archway.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Little Green island originally had no turtles. After 55 turtles were introduced to the island, their population is modelled by</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="N\left( t \right) = a \times {2^{ - t}} + 10{\text{,}}\,\,\,t \geqslant 0{\text{,}}">
<mi>N</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>a</mi>
<mo>×<!-- × --></mo>
<mrow>
<msup>
<mn>2</mn>
<mrow>
<mo>−<!-- − --></mo>
<mi>t</mi>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mn>10</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>t</mi>
<mo>⩾<!-- ⩾ --></mo>
<mn>0</mn>
<mrow>
<mtext>,</mtext>
</mrow>
</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 years since the turtles were introduced.</p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the time, in years, for the population to decrease to 20 turtles.</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>There is a number <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> beyond which the turtle population will not decrease.</p>
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span>. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="55 = a \times {2^0} + 10">
<mn>55</mn>
<mo>=</mo>
<mi>a</mi>
<mo>×</mo>
<mrow>
<msup>
<mn>2</mn>
<mn>0</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>10</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of zero <strong>and</strong> 55 into the function.</p>
<p>45<em><strong> (A1)</strong></em><em><strong> (C2) </strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="45 \times {2^{ - t}} + 10 \leqslant 20">
<mn>45</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>2</mn>
<mrow>
<mo>−</mo>
<mi>t</mi>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mn>10</mn>
<mo>⩽</mo>
<mn>20</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for comparing correct expression involving 20 and their 45. Accept an equation.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 2.17">
<mi>t</mi>
<mo>=</mo>
<mn>2.17</mn>
</math></span> (2.16992…)<em><strong> (A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their part (a), but only if positive.<br><strong>Answer must be in years</strong>; do not accept months for the final <em><strong>(A1)</strong></em>.<em><strong> </strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m =">
<mi>m</mi>
<mo>=</mo>
</math></span>10 <em><strong>(A1)</strong></em></p>
<p>because as the number of years increases the number of turtles approaches 10 <em><strong>(R1)</strong></em><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(R1)</strong></em> for a sketch with an asymptote at approximately <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 10">
<mi>y</mi>
<mo>=</mo>
<mn>10</mn>
</math></span>, <br><strong>OR</strong> for table with values such as 10.003 and 10.001 for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 14">
<mi>t</mi>
<mo>=</mo>
<mn>14</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 15">
<mi>t</mi>
<mo>=</mo>
<mn>15</mn>
</math></span>, for example, <br><strong>OR</strong> when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> approaches large numbers <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> approaches 10. Do not award <em><strong>(A1)(R0)</strong></em>.<em><strong> </strong></em></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">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p>Consider the following graphs of quadratic functions.</p>
<p><img src="images/Schermafbeelding_2017-08-16_om_06.31.16.png" alt="M17/5/MATSD/SP1/ENG/TZ2/15"></p>
<p>The equation of each of the quadratic functions can be written in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = a{x^2} + bx + c">
<mi>y</mi>
<mo>=</mo>
<mi>a</mi>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>b</mi>
<mi>x</mi>
<mo>+</mo>
<mi>c</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a \ne 0">
<mi>a</mi>
<mo>≠</mo>
<mn>0</mn>
</math></span>.</p>
<p>Each of the sets of conditions for the constants <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
<mi>c</mi>
</math></span>, in the table below, corresponds to one of the graphs above.</p>
<p>Write down the number of the corresponding graph next to each set of conditions.</p>
<p> <img src="images/Schermafbeelding_2017-08-16_om_06.39.22.png" alt="M17/5/MATSD/SP1/ENG/TZ2/15_02"></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><img src="images/Schermafbeelding_2017-08-16_om_08.45.18.png" alt="M17/5/MATSD/SP1/ENG/TZ2/15/M"> <strong><em>(A1)(A1)(A1)(A1)(A1)(A1)</em></strong> <strong><em>(C6)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for each correct entry.</p>
<p> </p>
<p><strong><em>[6 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>A factory produces shirts. The cost, <em>C</em>, in Fijian dollars (FJD), of producing<em> x</em> shirts can be modelled by</p>
<p style="text-align: center;"><em>C</em>(<em>x</em>) = (<em>x</em> − 75)<sup>2</sup> + 100.</p>
</div>
<div class="specification">
<p>The cost of production should not exceed 500 FJD. To do this the factory needs to produce at least 55 shirts and at most <em>s</em> shirts.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the cost of producing 70 shirts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>s</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of shirts produced when the cost of production is lowest.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>(70 − 75)<sup>2</sup> + 100 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting in <em>x</em> = 70.</p>
<p>125 <em><strong>(A1) (C2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(<em>s</em> − 75)<sup>2</sup> + 100 = 500 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating <em>C</em>(<em>x</em>) to 500. Accept an inequality instead of =.</p>
<p><strong>OR</strong></p>
<p><img src="data:image/png;base64,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"> <em><strong>(M1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for sketching correct graph(s).</p>
<p>(<em>s</em> =) 95 <em><strong>(A1) (C2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img 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"> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for an attempt at finding the minimum point using graph.</p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{95 + 55}}{2}">
<mfrac>
<mrow>
<mn>95</mn>
<mo>+</mo>
<mn>55</mn>
</mrow>
<mn>2</mn>
</mfrac>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for attempting to find the mid-point between their part (b) and 55.</p>
<p><strong>OR</strong></p>
<p>(<em>C'</em>(<em>x</em>) =) 2<em>x</em> − 150 = 0 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for an attempt at differentiation that is correctly equated to zero.</p>
<p>75 <em><strong>(A1) (C2)</strong></em></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">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph below shows the average savings, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math> thousand dollars, of a group of university graduates as a function of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>, the number of years after graduating from university.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The equation of the model can be expressed in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>a</mi><msup><mi>t</mi><mn>3</mn></msup><mo>+</mo><mi>b</mi><msup><mi>t</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi><mi>t</mi><mo>+</mo><mi>d</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi><mo>,</mo><mo> </mo><mi>c</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> are real constants.</p>
<p>The graph of the model must pass through the following four points.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A negative value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math> indicates that a graduate is expected to be in debt.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down one feature of this graph which suggests a cubic function might be appropriate to model this scenario.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down three simultaneous equations for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</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>Hence, or otherwise, find the values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the model to determine the total length of time, in years, for which a graduate is expected to be in debt after graduating from university.</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><em>Accept any one of the following (or equivalent):</em></p>
<p>one minimum and one maximum point<br>three <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-intercepts or three roots (or zeroes)<br>one point of inflexion <em><strong>R1</strong></em></p>
<p><strong><br>Note:</strong> Do not accept “S shape” as a justification.</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>d</mi><mo>=</mo></mrow></mfenced><mo>-</mo><mn>5</mn></math></em> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>=</mo><mn>8</mn><mi>a</mi><mo>+</mo><mn>4</mn><mi>b</mi><mo>+</mo><mn>2</mn><mi>c</mi></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>=</mo><mn>27</mn><mi>a</mi><mo>+</mo><mn>9</mn><mi>b</mi><mo>+</mo><mn>3</mn><mi>c</mi></math> <em><strong>A2</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A2</strong> </em>if all three equations are correct. <br>Award <em><strong>A1</strong> </em>if at least one is correct. Award <em><strong>A1</strong> </em>for three correct equations that include the letter “<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>”.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>2</mn><mo>,</mo><mo> </mo><mi>b</mi><mo>=</mo><mo>-</mo><mn>12</mn><mo>,</mo><mo> </mo><mi>c</mi><mo>=</mo><mn>18</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>equating found expression to zero <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>=</mo><mn>2</mn><msup><mi>t</mi><mn>3</mn></msup><mo>-</mo><mn>12</mn><msup><mi>t</mi><mn>2</mn></msup><mo>+</mo><mn>18</mn><mi>t</mi><mo>-</mo><mn>5</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>358216</mn><mo>…</mo><mo>,</mo><mo> </mo><mn>1</mn><mo>.</mo><mn>83174</mn><mo>…</mo><mo>,</mo><mo> </mo><mn>3</mn><mo>.</mo><mn>81003</mn><mo>…</mo></math> <em><strong>(A1)</strong></em></p>
<p>(so total time in debt is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>81003</mn><mo>…</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>83174</mn><mo>…</mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>358216</mn><mo>≈</mo></math>)</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>34</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>2</mn><mo>.</mo><mn>33650</mn><mo>…</mo></mrow></mfenced></math> years <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Proved to be difficult with several referring to the shape of the graph, the graph increasing and decreasing, or positive and negative values fitting the context.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>It seemed easy to find the <em>d</em>-value in the function. Most candidates could derive at least one correct equation, but not always three. Many candidates did not write their equations in proper mathematical form, leaving exponents and like terms in their equations. Even those candidates who did not write correct equations in part (ii) were able to correctly find the values of <em>a</em>, <em>b</em>, and <em>c</em> in part (iii) using cubic regression (an off-syllabus method, but still valid and credited full marks). There were some candidates who attempted an analytic method to solve the system of equations which did not usually prove successful.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Some candidates realized they had to find the roots, but then did not know what to do with them. Several candidates selected one of the roots as the answer to the question, usually the largest root, clearly not understanding the relationship between the roots and the length of time in debt. Others found only one root and stated that as the answer.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = {x^2} - 4x + 5">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>4</mn>
<mi>x</mi>
<mo>+</mo>
<mn>5</mn>
</math></span>.</p>
</div>
<div class="specification">
<p>The function can also be expressed in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = {(x - h)^2} + k">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mi>h</mi>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>k</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the axis of symmetry of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span>.</p>
<p>(ii) Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>correct approach <strong><em>(A1)</em></strong></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{ - ( - 4)}}{2},{\text{ }}f'(x) = 2x - 4 = 0,{\text{ (}}{x^2} - 4x + 4) + 5 - 4">
<mfrac>
<mrow>
<mo>−</mo>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>4</mn>
<mo stretchy="false">)</mo>
</mrow>
<mn>2</mn>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>2</mn>
<mi>x</mi>
<mo>−</mo>
<mn>4</mn>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> (</mtext>
</mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>4</mn>
<mi>x</mi>
<mo>+</mo>
<mn>4</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>5</mn>
<mo>−</mo>
<mn>4</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2">
<mi>x</mi>
<mo>=</mo>
<mn>2</mn>
</math></span> (must be an equation) <strong><em>A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h = 2">
<mi>h</mi>
<mo>=</mo>
<mn>2</mn>
</math></span> <strong><em>A1 N1</em></strong></p>
<p>(ii) <strong>METHOD 1</strong></p>
<p>valid attempt to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(2)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
</math></span></p>
<p>correct substitution into <strong>their </strong>function <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{(2)^2} - 4(2) + 5">
<mrow>
<mo stretchy="false">(</mo>
<mn>2</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>4</mn>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>5</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 1">
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</math></span> <strong><em>A1 N2</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>valid attempt to complete the square <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^2} - 4x + 4">
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>4</mn>
<mi>x</mi>
<mo>+</mo>
<mn>4</mn>
</math></span></p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="({x^2} - 4x + 4) - 4 + 5,{\text{ }}{(x - 2)^2} + 1">
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>4</mn>
<mi>x</mi>
<mo>+</mo>
<mn>4</mn>
<mo stretchy="false">)</mo>
<mo>−</mo>
<mn>4</mn>
<mo>+</mo>
<mn>5</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>1</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 1">
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> is of the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = ax + b + \frac{c}{x}">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>a</mi>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
<mo>+</mo>
<mfrac>
<mi>c</mi>
<mi>x</mi>
</mfrac>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
<mi>c</mi>
</math></span> are positive integers.</p>
<p>Part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span> is shown on the axes below. The graph of the function has its local maximum at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 2,{\text{ }} - 2)">
<mo stretchy="false">(</mo>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
</math></span> and its local minimum at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(2,{\text{ }}6)">
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>6</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_11.28.21.png" alt="M17/5/MATSD/SP1/ENG/TZ1/12"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the domain of the function.</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>Draw the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - 6">
<mi>y</mi>
<mo>=</mo>
<mo>−</mo>
<mn>6</mn>
</math></span> on the axes.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of solutions to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = - 6">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mo>−</mo>
<mn>6</mn>
</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 range of values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> for which <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = k">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>k</mi>
</math></span> has no solution.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(x \in \mathbb{R}),{\text{ }}x \ne 0">
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>x</mi>
<mo>≠</mo>
<mn>0</mn>
</math></span> <strong><em>(A2)</em></strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept equivalent notation. Award <strong><em>(A1)(A0) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y \ne 0">
<mi>y</mi>
<mo>≠</mo>
<mn>0</mn>
</math></span>.</p>
<p>Award <strong><em>(A1) </em></strong>for a clear statement that demonstrates understanding of the meaning of domain. For example, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{D}}:( - \infty ,{\text{ }}0) \cup (1,{\text{ }}\infty )">
<mrow>
<mtext>D</mtext>
</mrow>
<mo>:</mo>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mi mathvariant="normal">∞</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo stretchy="false">)</mo>
<mo>∪</mo>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi mathvariant="normal">∞</mi>
<mo stretchy="false">)</mo>
</math></span> should be awarded <strong><em>(A1)(A0)</em></strong>.</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><img src="images/Schermafbeelding_2017-08-15_om_15.32.51.png" alt="M17/5/MATSD/SP1/ENG/TZ1/21.b.i/M"> <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> The command term “Draw” states: “A ruler (straight edge) should be used for straight lines”; do not accept a freehand <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - 6">
<mi>y</mi>
<mo>=</mo>
<mo>−</mo>
<mn>6</mn>
</math></span> line.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>2 <strong><em>(A1)</em>(ft)</strong> <strong><em>(C1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (b)(i).</p>
<p> </p>
<p><strong><em>[1 mark]</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=" - 2 < k < 6">
<mo>−</mo>
<mn>2</mn>
<mo><</mo>
<mi>k</mi>
<mo><</mo>
<mn>6</mn>
</math></span> <strong><em>(A1)(A1)</em></strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for both end points correct and <strong><em>(A1) </em></strong>for correct <strong>strict </strong>inequalities.</p>
<p>Award at most <strong><em>(A1)(A0) </em></strong>if the stated variable is different from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> for example <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 2 < x < 6">
<mo>−</mo>
<mn>2</mn>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mn>6</mn>
</math></span> is <strong><em>(A1)(A0)</em></strong>.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.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>Professor Wei observed that students have difficulty remembering the information presented in his lectures.</p>
<p>He modelled the percentage of information retained, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math>, by the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mn>100</mn><msup><mtext>e</mtext><mrow><mo>-</mo><mi>p</mi><mi>t</mi></mrow></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>≥</mo><mn>0</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is the number of days after the lecture.</p>
<p>He found that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> day after a lecture, students had forgotten <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo>%</mo></math> of the information presented.</p>
</div>
<div class="specification">
<p>Based on his model, Professor Wei believes that his students will always retain some information from his lecture.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use this model to find the percentage of information retained by his students <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn></math> hours after Professor Wei’s lecture.</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>State a mathematical reason why Professor Wei might believe this.</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>Write down one possible limitation of the <strong>domain</strong> of the model.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo>=</mo><mn>100</mn><msup><mtext>e</mtext><mrow><mo>-</mo><mn>1</mn><mo>×</mo><mi>p</mi></mrow></msup></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>5</mn><mo>=</mo><msup><mtext>e</mtext><mrow><mo>-</mo><mn>1</mn><mo>×</mo><mi>p</mi></mrow></msup></math> <em><strong> </strong></em><em><strong>(M1)</strong></em></p>
<p><strong><br>OR</strong></p>
<p><img src="data:image/png;base64,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"></p>
<p> </p>
<p><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>693</mn><mo> </mo><mo> </mo><mo>(</mo><mn>0</mn><mo>.</mo><mn>693147</mn><mo>…</mo><mo>,</mo><mo> </mo><mi>ln</mi><mo> </mo><mn>2</mn><mo>)</mo></math> <em><strong> A1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mo>=</mo><mn>100</mn><msup><mtext>e</mtext><mrow><mo>-</mo><mn>0</mn><mo>.</mo><mn>693147</mn><mo>…</mo><mo>×</mo><mn>1</mn><mo>.</mo><mn>5</mn></mrow></msup></math> <em><strong> </strong></em><em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>35</mn><mo>.</mo><mn>4</mn><mfenced><mo>%</mo></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mn>35</mn><mo>.</mo><mn>3553</mn><mo>…</mo></mrow></mfenced></math> <em><strong> A1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mfenced><mi>t</mi></mfenced><mo>></mo><mn>0</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mfenced><mi>t</mi></mfenced></math> has a horizontal asymptote <em><strong> R1</strong></em></p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>Award <strong>A1</strong> for <strong>one</strong> reasonable limitation of the domain: </em> <em><strong>A1</strong></em></p>
<p style="padding-left:30px;">small values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> produce unrealistic results</p>
<p style="padding-left:30px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mfenced><mn>0</mn></mfenced><mo>=</mo><mn>100</mn><mo>%</mo></math></p>
<p style="padding-left:30px;">large values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> are not possible</p>
<p style="padding-left:30px;">people do not live forever</p>
<p style="padding-left:30px;">model is not valid at small or large values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></p>
<p><em><br>The reason should focus on the domain <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>≥</mo><mn>0</mn></math>. Do not accept answers such as:</em></p>
<p style="padding-left:30px;">recollection varies for different people</p>
<p style="padding-left:30px;">memories are discrete not continuous</p>
<p style="padding-left:30px;">the nature of the information will change how easily it is recalled</p>
<p style="padding-left:30px;">emotional/physical stress can affect recollection/concentration</p>
<p><br><strong>Note:</strong> Do not accept <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>≥</mo><mn>0</mn></math> </em>as this is a limitation that has been given in the question.</p>
<p><em><strong><br>[1 mark]</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>Professor Vinculum investigated the migration season of the Bulbul bird from their natural wetlands to a warmer climate.</p>
<p>He found that during the migration season their population, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P">
<mi>P</mi>
</math></span> could be modelled by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P = 1350 + 400{\left( {1.25} \right)^{ - t}}">
<mi>P</mi>
<mo>=</mo>
<mn>1350</mn>
<mo>+</mo>
<mn>400</mn>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>1.25</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mi>t</mi>
</mrow>
</msup>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> ≥ 0 , where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> is the number of days since the start of the migration season.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the population of the Bulbul birds at the start of the migration season.</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>Find the population of the Bulbul birds after 5 days.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the time taken for the population to decrease below 1400.</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>According to this model, find the smallest possible population of Bulbul birds during the migration season.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>1750 <em><strong>A1</strong></em></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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1350 + 400{\left( {1.25} \right)^{ - 5}}">
<mn>1350</mn>
<mo>+</mo>
<mn>400</mn>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>1.25</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>−</mo>
<mn>5</mn>
</mrow>
</msup>
</mrow>
</math></span> <em><strong>(M1)</strong></em></p>
<p>= 1480 <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Accept 1481.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1400 = 1350 + 400{\left( {1.25} \right)^{ - t}}">
<mn>1400</mn>
<mo>=</mo>
<mn>1350</mn>
<mo>+</mo>
<mn>400</mn>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>1.25</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>−</mo>
<mi>t</mi>
</mrow>
</msup>
</mrow>
</math></span> <em><strong>(M1)</strong></em></p>
<p>9.32 (days (9.31885…) (days)) <em><strong>A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1350 <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Accept 1351 as a valid interpretation of the model as <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P">
<mi>P</mi>
</math></span> = 1350 is an asymptote.</p>
<p><em><strong>[1 mark]</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">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The amount, in milligrams, of a medicinal drug in the body <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> hours after it was injected is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mn>23</mn><mo>(</mo><mn>0</mn><mo>.</mo><mn>85</mn><msup><mo>)</mo><mi>t</mi></msup><mo>,</mo><mo> </mo><mi>t</mi><mo>≥</mo><mn>0</mn></math>. Before this injection, the amount of the drug in the body was zero.</p>
</div>
<div class="specification">
<p>Write down</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the initial dose of the drug.</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>the percentage of the drug that leaves the body each hour.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the amount of the drug remaining in the body <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> hours after the injection.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>23</mn><mo> </mo><mtext>mg</mtext></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[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>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>85</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>23</mn><mo>-</mo><mn>19</mn><mo>.</mo><mn>55</mn></mrow><mn>23</mn></mfrac></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>15</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mfenced><mo>%</mo></mfenced></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>23</mn><msup><mfenced><mrow><mn>0</mn><mo>.</mo><mn>85</mn></mrow></mfenced><mn>10</mn></msup></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>53</mn><mo> </mo><mtext>mg</mtext><mo> </mo><mo> </mo><mfenced><mrow><mn>4</mn><mo>.</mo><mn>52811</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>In an experiment, a number of fruit flies are placed in a container. The population of fruit flies, <em>P</em> , increases and can be modelled by the function</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="P\left( t \right) = 12 \times {3^{0.498t}},\,\,t \geqslant 0,">
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>12</mn>
<mo>×<!-- × --></mo>
<mrow>
<msup>
<mn>3</mn>
<mrow>
<mn>0.498</mn>
<mi>t</mi>
</mrow>
</msup>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>t</mi>
<mo>⩾<!-- ⩾ --></mo>
<mn>0</mn>
<mo>,</mo>
</math></span></p>
<p>where <em>t</em> is the number of days since the fruit flies were placed in the container.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of fruit flies which were placed in the container.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of fruit flies that are in the container after 6 days.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The maximum capacity of the container is 8000 fruit flies.</p>
<p>Find the number of days until the container reaches its maximum capacity.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="12 \times {3^{0.498 \times 0}}">
<mn>12</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>3</mn>
<mrow>
<mn>0.498</mn>
<mo>×</mo>
<mn>0</mn>
</mrow>
</msup>
</mrow>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting zero into the equation.</p>
<p>= 12 <em><strong>(A1) (C2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="12 \times {3^{0.498 \times 6}}">
<mn>12</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>3</mn>
<mrow>
<mn>0.498</mn>
<mo>×</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting 6 into the equation.</p>
<p>320 <em><strong>(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Accept an answer of 319.756… or 319.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="8000 = 12 \times {3^{0.498 \times t}}">
<mn>8000</mn>
<mo>=</mo>
<mn>12</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>3</mn>
<mrow>
<mn>0.498</mn>
<mo>×</mo>
<mi>t</mi>
</mrow>
</msup>
</mrow>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating equation to 8000.<br>Award <em><strong>(M1)</strong></em> for a sketch of P(<em>t</em>) intersecting with the straight line <em>y</em> = 8000.</p>
<p>= 11.9 (11.8848…) <em><strong>(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Accept an answer of 11 or 12.</p>
<p><em><strong>[2 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph of the quadratic function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = c + bx - {x^2}">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>c</mi>
<mo>+</mo>
<mi>b</mi>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> intersects the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis at the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}( - 1,{\text{ }}0)">
<mrow>
<mtext>A</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mo>−<!-- − --></mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span> and has its vertex at the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}(3,{\text{ }}16)">
<mrow>
<mtext>B</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>16</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-06_om_09.57.03.png" alt="N16/5/MATSD/SP1/ENG/TZ0/09"></p>
</div>
<div class="question">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{ - b}}{{2( - 1)}} = 3">
<mfrac>
<mrow>
<mo>−</mo>
<mi>b</mi>
</mrow>
<mrow>
<mn>2</mn>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
</mrow>
</mfrac>
<mo>=</mo>
<mn>3</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 axis of symmetry formula.</p>
<p> </p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b - 2x = 0">
<mi>b</mi>
<mo>−</mo>
<mn>2</mn>
<mi>x</mi>
<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 correctly differentiating and equating to zero.</p>
<p> </p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c + b( - 1) - {( - 1)^2} = 0">
<mi>c</mi>
<mo>+</mo>
<mi>b</mi>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo>−</mo>
<mrow>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>1</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>0</mn>
</math></span> (or equivalent)</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c + b(3) - {(3)^2} = 16">
<mi>c</mi>
<mo>+</mo>
<mi>b</mi>
<mo stretchy="false">(</mo>
<mn>3</mn>
<mo stretchy="false">)</mo>
<mo>−</mo>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>16</mn>
</math></span> (or equivalent) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 1,{\text{ }}0)">
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(3,{\text{ }}16)">
<mo stretchy="false">(</mo>
<mn>3</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>16</mn>
<mo stretchy="false">)</mo>
</math></span> in the original quadratic function.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(b = ){\text{ }}6">
<mo stretchy="false">(</mo>
<mi>b</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>6</mn>
</math></span> <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (a).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>The amount of yeast, <em>g</em> grams, in a sugar solution can be modelled by the function,</p>
<p style="text-align: center;"><em>g</em>(<em>t</em>) = 10 − <em>k</em>(<em>c</em><sup>−<em>t</em></sup>) for <em>t</em> ≥ 0</p>
<p>where <em>t</em> is the time in minutes.</p>
<p>The graph of <em>g</em>(<em>t</em>) is shown.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The initial amount of yeast in this solution is 2 grams.</p>
</div>
<div class="specification">
<p>The amount of yeast in this solution after 3 minutes is 9 grams.</p>
</div>
<div class="question">
<p>Write down the maximum amount of yeast in this solution.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>10 (grams) <em><strong>(A1) (C1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>Consider the quadratic function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = a{x^2} + bx + 22">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>a</mi>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>b</mi>
<mi>x</mi>
<mo>+</mo>
<mn>22</mn>
</math></span>.</p>
<p>The equation of the line of symmetry of the graph <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right){\text{ is }}x = 1.75">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mrow>
<mtext> is </mtext>
</mrow>
<mi>x</mi>
<mo>=</mo>
<mn>1.75</mn>
</math></span>.</p>
</div>
<div class="specification">
<p>The graph intersects the <em>x</em>-axis at the point (−2 , 0).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using only this information, write down an equation in terms of <em>a</em> and <em>b</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using this information, write down a second equation in terms of <em>a</em> and <em>b</em>.</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>Hence find the value of <em>a</em> and of <em>b</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph intersects the <em>x</em>-axis at a second point, P.</p>
<p>Find the <em>x</em>-coordinate of P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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="1.75 = \frac{{ - b}}{{2a}}">
<mn>1.75</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mo>−</mo>
<mi>b</mi>
</mrow>
<mrow>
<mn>2</mn>
<mi>a</mi>
</mrow>
</mfrac>
</math></span> (or equivalent) <em><strong>(A1) (C1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {\left( {1.75} \right)^2}a + 1.75b">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>1.75</mn>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mi>a</mi>
<mo>+</mo>
<mn>1.75</mn>
<mi>b</mi>
</math></span> or for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = {\left( {1.75} \right)^2}a + 1.75b + 22">
<mi>y</mi>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>1.75</mn>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mi>a</mi>
<mo>+</mo>
<mn>1.75</mn>
<mi>b</mi>
<mo>+</mo>
<mn>22</mn>
</math></span> or for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( {1.75} \right) = {\left( {1.75} \right)^2}a + 1.75b + 22">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mn>1.75</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>1.75</mn>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mi>a</mi>
<mo>+</mo>
<mn>1.75</mn>
<mi>b</mi>
<mo>+</mo>
<mn>22</mn>
</math></span>.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\left( { - 2} \right)^2} \times a + \left( { - 2} \right) \times b + 22 = 0">
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>×</mo>
<mi>a</mi>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mi>b</mi>
<mo>+</mo>
<mn>22</mn>
<mo>=</mo>
<mn>0</mn>
</math></span> (or equivalent) <em><strong>(A1) (C1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\left( { - 2} \right)^2} \times a + \left( { - 2} \right) \times b + 22 = 0">
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>×</mo>
<mi>a</mi>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mi>b</mi>
<mo>+</mo>
<mn>22</mn>
<mo>=</mo>
<mn>0</mn>
</math></span> seen.</p>
<p>Award <em><strong>(A0)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = {\left( { - 2} \right)^2} \times a + \left( { - 2} \right) \times b + 22">
<mi>y</mi>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>×</mo>
<mi>a</mi>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mi>b</mi>
<mo>+</mo>
<mn>22</mn>
</math></span>.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>a</em> = −2, <em>b</em> = 7 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from parts (a) and (b).<br>Accept answers(s) embedded as a coordinate pair.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>−2<em>x</em><sup>2</sup> + 7<em>x</em> + 22 = 0 <em><strong> (M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of <em>a</em> and <em>b</em> into equation and setting to zero. Follow through from part (c).</p>
<p>(<em>x </em>=) 5.5 <em><strong> (A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from parts (a) and (b).</p>
<p><strong>OR</strong></p>
<p><em>x</em>-coordinate = 1.75 + (1.75 − (−2)) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct use of axis of symmetry and given intercept.</p>
<p>(<em>x </em>=) 5.5 <em><strong>(A1) (C2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[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 function is defined by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>2</mn><mo>-</mo><mfrac><mn>12</mn><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>7</mn><mo>,</mo><mo> </mo><mi>x</mi><mo>≠</mo><mo>-</mo><mn>5</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the range of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mn>0</mn></mfenced></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>f</mi><mfenced><mrow><mo>-</mo><mn>7</mn></mrow></mfenced><mo>=</mo></mrow></mfenced><mo> </mo><mn>8</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>f</mi><mfenced><mn>7</mn></mfenced><mo>=</mo></mrow></mfenced><mo> </mo><mn>1</mn></math> <em><strong>(A1)</strong></em> </p>
<p>range is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>≤</mo><mn>1</mn><mo>,</mo><mo> </mo><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>≥</mo><mn>8</mn></math> <em><strong>A1</strong></em><em><strong>A1</strong></em> </p>
<p><br><strong>Note:</strong> Award at most <em><strong>A1A1A0</strong></em> if strict inequalities are used.</p>
<p><em><strong><br>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn></math> or sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn></math> <strong><em>(M1)</em></strong></p>
<p><br><strong>OR</strong></p>
<p>finding the correct expression of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mo>-</mo><mn>2</mn><mo>-</mo><mn>5</mn><mi>x</mi></mrow><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac></math> <strong><em>(M1)</em></strong></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mn>0</mn></mfenced><mo>=</mo><mfrac><mrow><mo>-</mo><mn>2</mn><mo>-</mo><mn>5</mn><mfenced><mn>0</mn></mfenced></mrow><mrow><mn>0</mn><mo>-</mo><mn>2</mn></mrow></mfrac></math> <strong><em>(M1)</em></strong><br><br><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>0</mn></math> <strong><em>(M1)</em></strong><br><br><br><strong>THEN</strong><br><br><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mn>0</mn></mfenced><mo>=</mo><mn>1</mn></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows the graph of a function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>, for −4 ≤ <em>x</em> ≤ 2.</p>
<p><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the same axes, sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( { - x} \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Another function, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span>, can be written in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = a \times f\left( {x + b} \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>a</mi>
<mo>×</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>. The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span>.</p>
<p><strong><img 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"></strong></p>
<p>Write down the value of <em>a</em> and of <em>b</em>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><img 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"><em><strong>A2 N2</strong></em><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing horizontal shift/translation of 1 unit <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <em>b </em>= 1, moved 1 right</p>
<p>recognizing vertical stretch/dilation with scale factor 2 <em><strong>(M1)</strong></em></p>
<p><em>eg a</em> = 2, <em>y </em>×(−2)</p>
<p><em>a</em> = −2, <em> b</em> = −1 <em><strong> A1A1 N2N2</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the graph of the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>x</mi><mo>+</mo><mfrac><mn>12</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac><mo>,</mo><mo> </mo><mi>x</mi><mo>≠</mo><mn>0</mn></math>.</p>
<p style="text-align: center;"><img 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KxniPbtJaCdduoBUESwFzsrOCKACBwls8dQdB5cO22dF0+5IIKUNCnLOgFEYD1DtG+WgASQY6edo8zZQPgRAhUJIIKK8Kl6OwFNi9Qc+dQLIkhNlPIsE0AElrND2/YSyDF1VJUigr3oWcERAUTgKJk9hqKLqlJPHRVHRNBjb+o3ZkTQb+5dRK6nZ6WeOiowiMBF9yCIhQQQwUJQrGaTgHbYqaeOKlJEYDPftCoPAUSQhyulFiCgu41qh536Pv1qOiIokECqMEMAEZhJBQ05lECuqaNqByI4NBus3zIBRNBy9jpvu8YGUt91NCJFBJEErz0QQAQ9ZNlpjJotlPquoxEVIogkeO2BACLoIctOY8xxs7mIChFEErz2QAAR9JBlpzFqZ53ygfVDTIhgSIP33gkgAu8ZdhpfnDGU+mZzERciiCR47YEAIughyw5jzDljSLgQgcNOQ0iTBBDBJBp+sEwg54whxY0ILGeftqUmgAhSE6W8IgQ0Y0j3Gcq1IIJcZCnXIgFEYDErtGkvgVz3GIoVI4JIgtceCCCCHrLsMEbtqHPcYyiiQgSRBK89EEAEPWTZWYy6t5B21Jo5lGtBBLnIUq5FAojAYlZo0ywBXTuQe0edu/zZAPkRAoUJIILCwKluO4Gvj4+z3Voitg4RRBK89kAAEfSQZWcx6tYSkkHOBRHkpEvZ1gggAmsZoT17CWgnnevWErFyRBBJ8NoDAUTQQ5YdxRgHinM8jGaICREMafDeOwFE4D3DzuIrMVAsZIjAWcchnFkCiGAWDz9aI1BioFgxIwJrmac9OQkggpx0KTs5gRIDxWo0IkieOgo0TAARGE4OTbtIQDvonFcUxxoRQSTBaw8EEEEPWXYSYxwoznlFcUSFCCIJXnsggAh6yLKTGE9PT8NbV64UiQYRFMFMJUYIIAIjiaAZ+wnkvvX0sAWIYEiD994JIALvGXYU33tXrwY9kKbEgghKUKYOKwQQgZVM0I5ZAk+fPj2fyZPrGcW7lSOCXSJ89kwAEXjOrqPYNFOo5M65ZF2O0kQojRJABI0mrrdml7qQLHJFBJEErz0QQAQ9ZNlBjLkfTbmLCBHsEuGzZwKIwHN2ncQWxwdKXEgWkSGCSILXHggggh6y3HiMcXxAQii1IIJSpKnHAgFEYCELtGGWgMYHdGqo5IIIStKmrtoEEEHtDFD/XgKSQO4nku02AhHsEuGzZwKIwHN2HcRWY3xA2BCBg85DCIsJIILFqFixBoEa4wOKExHUyDZ11iKACGqRp95FBEpfPxAbhQgiCV57IIAIeshywzGWvL/QEBMiGNLgvXcCiMB7hhuOT88d0A651P2FhqgQwZAG770TQATeM9xwfHpQfannD+xiQgS7RPjsmQAi8JzdxmP79MaNoH81FkRQgzp11iKACGqRp969BHQ0oKOCGgsiqEGdOmsRQAS1yFPvLAGNC2hnXOL5xGMNQQRjVPjOKwFE4DWzjcdV47YSQ2SIYEiD994JIALvGW40Pk0bLX1biSEqRDCkwXvvBBCB9ww3GF+cNvrw4cNqrUcE1dBTcQUCiKACdKqcJ3B6ehp0RFBzQQQ16VN3aQKIoDRx6ttLQHcbvfXFrb3r5VwBEeSkS9nWCCACaxnpvD217ja6ix0R7BLhs2cCiMBzdhuMrebVxENciGBIg/feCSAC7xluLD5dSVz7tJCQIYLGOo7z5uaeOIEInHeglsKzclpIzBBBSz3Hf1s1bqZ/uW7AiAj896FmIrRyWkjAEEEz3aaLhuqPJB0tq1/q+hp9TrkggpQ0KWsTASunhRQEItiUSjbOREBHBJparX96el+qBRGkIkk5mwhYOi2kQBDBpnSycUYC+r+iowL1Uf3xlOLooKgI1HD+wYA+QB+gD6TrAykmVxQVQUZJUnTjBCxcRDZEqB0VCwQsEmj+iMAiVNpUn0C8t1CuGRFrIkQEa6ixTW4CjBHkJkz51QjcPjmpfm+h3eARwS4RPtckoKMAZg3VzAB1ZydQ+5bTYwEigjEqfFeLANcR1CJPvUUI6FBXO91aTyKbChIRTJHh+xoEZv9/PD4JH8SJOG9/Hs5+eBaePb4bPv/jb8PlS78Ln539sLfJDBbvRcQKOQloxoP+2rG2IAJrGaE98wR+Co9OPg6vX3ozfHLyv+Hzo/8J9394Nr/J4FdEMIDB27IEdN6z5gPq56JFBHN0+M0kge/vhE9efSVcfvXjcPvRTwc1EREchIuVUxKIt5RIcUFMynapLESQmijl5Sfwbbhz9Ga4/M6X4cHyg4HzZiGC/NmhhgkC1q4dGDYTEQxp8L4JAs++Cbc/1LjA++GrBz8e1GREcBAuVk5FQLfV1c429+1117YXEawlx3Z1CGiM4ChcO/o4/F7jBHe+PagZiOAgXKycioDVQeIYHyKIJHhtgcCzRyfhz386CY9+vh++eue18PrR38Kjs/8Ofzn5Jiw5S4QIWsiyszZqTEA7Wo0RWF0QgdXM0K4hgZ/PboY3Lr0Wfn90Eh6czxL6LpzdfDdcvvRO+OTkftg/cfR5aYhgSJX3RQicnp6ezxayOEgcASCCSILXHggggh6ybCxGi1cS7yJCBLtE+OyZACLwnF2DselhGtrJzl4paaDdiMBAEmhCMQKIoBhqKhKBo+vXz2+eZZ0GIrCeIdqXkgAiSEmTsmYJxCmjlm43PdVgRDBFhu89EkAEHrNqNCbrU0aH2BDBkAbvvRNABN4zbCS++PAZy1NGh6gQwZAG770TQATeM2wkPj1sW7OFWlkQQSuZop0pCCCCFBQpY5aA5buMTjUcEUyR4XuPBBCBx6wai0mPotTtpi1fQLaLDBHsEuGzZwKIwHN2DcQWjwYkg5YWRNBStmjrVgKIYCtBtp8l0OLRgAJCBLNp5UdnBBCBs4RaCqfVowExRASWehJtyU0AEeQm3HH5rR4NKGWIoOOO22HoiKDDpJcIueWjAfFBBCV6CXVYIYAIrGTCWTtaPhpQKhCBsw5JOLMEEMEsHn5cQ6D1owHFjAjWZJ5tWiWACFrNnOF2t340ILSIwHAHo2nJCSCC5Ej7LrC1ewpNZQsRTJHhe48EEIHHrFaMSXcYbemeQlOoEMEUGb73SAAReMxqpZji8wb0FLLWF0TQegZp/yEEEMEhtFh3loCePqZ/HhZE4CGLxLCUACJYSor1ZgnEZxG38PSx2UB++RERLKHEOl4IIAIvmawch8YFND7gZUEEXjJJHEsIIIIllFhnlkCcLqoZQ14WROAlk8SxhAAiWEKJdSYJeLh4bCw4RDBGhe+8EkAEXjNbKK44XVRC8LQgAk/ZJJZ9BBDBPkL8PklAA8PaYXqYLrobJCLYJcJnzwQQgefsZo7to2vX3EwX3UWFCHaJ8NkzAUTgObsZY/M4QDzEhQiGNHjvnQAi8J7hDPFpdpAeRi8ZeF0QgdfMEtcYAUQwRoXvZgno6mEP9xOaCxIRzNHhN28EEIG3jGaOx9sVxFO4EMEUGb73SAAReMxqppjiNQNfHx9nqsFOsYjATi5oSX4CiCA/Yzc1fHrjxvkpIW/XDIwlCBGMUeE7rwQQgdfMJo4rnhLyeM3AGCpEMEaF77wSQAReM5swrnhKSEcEvSyIoJdME6cIIAL6wV4CEoCmi/ZwSijCQASRBK89EEAEPWR5Q4y9nRKKqBBBJMFrDwQQQQ9ZXhljPCXUwyyhXUSIYJcInz0TQASes7sxtp5mCe2iQgS7RPjsmQAi8JzdDbGdnp6e31nUy6MnD0WBCA4lxvotE0AELWcvU9sfPnzo/l5C+9Ahgn2E+N0TAUTgKZuJYtHtpfWv5wUR9Jz9/mJHBP3lfDZiDQxrqqin5w/PBjzxIyKYAMPXLgkgApdpXRdUnCp69+7ddQU42goROEomoewlgAj2IupjhfiMAT2DmCWcD5TDAQK9EEAEvWR6T5xxXKCnq4fnkHBEMEeH37wRQATeMroinjguoNlCLM8JIAJ6Qk8EEEFP2R6JlXGBESiBU0PjVPjWKwFE4DWzC+JiXGAaEkcE02z4xR8BROAvp4si0lgA4wLTqBDBNBt+8UcAEfjL6aKINDtI1wswLjCOCxGMc+FbnwQQgc+8zkal6wS0o+vlaWOzMCZ+RAQTYPjaJQFE4DKt00HpCEA7udsnJ9Mr8QvXEdAHuiKACDpKd3y+QE+PnFybXo4I1pJjuxYJIIIWs7ayzQwOLweHCJazYs32CSCC9nO4KAIGhxdh+nUlRPArCt50QAARdJDk+JAZBoeXJxsRLGfFmu0TQATt53A2gnjlsGTAspwAIljOijXbJ4AI2s/hZATxSWPcUXQS0eQPiGASDT84JIAIHCZVIWmG0HtXr55fPcwdRQ9PMiI4nBlbtEsAEbSbu9mWa4aQRIAEZjFN/ogIJtHwg0MCiMBhUpkhtD2piGA7Q0pohwAiaCdXi1qqK4a1E2OG0CJckyshgkk0/OCQACJwlNR4DyGeObw9qYhgO0NKaIcAImgnV7MtffDgwfmRADOEZjEt/hERLEbFig4IIAIHSWSaaPokIoL0TCnRLgFEYDc3i1oWbySnWULMEFqEbNFKiGARJlZyQgARNJxI7fi5kVyeBCKCPFwp1SYBRGAzL4taJQnwlLFFqA5eCREcjIwNGiaACBpNHtcK5E0cIsjLl9JtEUAEtvKxqDWSgHZUminEkocAIsjDlVJtEkAENvMy2ap4S2muFZhElOQHRJAEI4U0QgARNJIoNZMLxsolCxGUY01N9Qkggvo5WNSCKAEuGFuEa/NKiGAzQgpoiAAiaCBZXDBWPkmIoDxzaqxHABHUY7+o5iiBT2/cWLQ+K6UhgAjScKSUNgggAsN5ihLgquHySUIE5ZlTYz0CiKAe+9maddUwTxibRZT1R0SQFS+FGyOACIwlRM3h1hH1k4II6ueAFpQjgAjKsV5UU5SAbh3x5MmTRduwUnoCiCA9U0q0SwARGMrNUAIaH2CpRwAR1GNPzeUJIILyzCdrPLp+nZvITdIp+wMiKMub2uoSQAR1+f9aOzeR+xWFiTeIwEQaaEQhAoigEOi5auJN5DgdNEep7G+IoCxvaqtLABHU5R+iBLiJXOVE7FSPCHaA8NE1AURQMb1IoCL8PVUjgj2A+NkVAURQKZ1IoBL4hdUigoWgWM0FAURQIY3xTqKcDqoAf2GViGAhKFZzQQARFE4jEigMfGV1iGAlODZrkgAiKJi2KAE9ZYzFNgFEYDs/tC4tAUSQludkaVECGhtgsU8AEdjPES1MRwARpGM5WRISmERj9gdEYDY1NCwDAUSQAeqwSCQwpNHOe0TQTq5o6XYCiGA7w8kSkMAkGvM/IALzKaKBCQkggoQwh0UhgSGN9t4jgvZyRovXE0AE69lNbokEJtE08wMiaCZVNDQBAUSQAOKwiPicYWYHDam09x4RtJczWryeACJYz+7ClkjgApJmv0AEzaaOhq8ggAhWQBvbBAmMUWn3O0TQbu5o+eEEEMHhzC5sgQQuIGn+C0TQfAoJ4AACiOAAWGOrIoExKu1/hwjazyERLCeACJazurBmlMBH164FPXiexQ8BROAnl0SynwAi2M9odA0kMIrFzZeIwE0qCWQBAUSwANLuKkhgl4i/z4jAX06JaJoAIphmM/oLEhjF4u5LROAupQQ0QwARzMDZ/QkJ7BLx+xkR+M0tkV0kgAguMhn9BgmMYnH7JSJwm1oCGyGACEag7H6FBHaJ+P+MCPznmAhfEEAEL1iMvkMCo1jcf4kI3KeYAAcEEMEAxu5bJLBLpJ/PiKCfXBNpCIhgohcggQkwnXyNCDpJNGGeE0AEIx0BCYxA6ewrRNBZwjsPFxHsdAAksAOk04+IoNPEdxo2IhgkHgkMYHT+FhF03gE6Cx8R/JJwJNBZz98TLiLYA4ifXRFABCEEJOCqTycJBhEkwUghjRDoXgRIoJGeWriZiKAwcKqrSqBrESCBqn3PdOWIwHR6aFxiAt2KAAkk7knOikMEzhJKOLMEuhQBEpjtE/wYQr57wD4AAAMPSURBVEAEdIOeCHQnAiTQU/deHysiWM+OLdsj0JUIkEB7HbRWixFBLfLUW4NANyJAAjW6V7t1IoJ2c0fLDyfQhQiePn0a3rt6NXx07VrQexYI7COACPYR4ndPBNyLQDt+CQAJeOq2+WNBBPkZU4MdAq5FgATsdLTWWoIIWssY7d1CwK0IkMCWbsG2iIA+0BMBlyJAAj114TyxIoI8XCnVJgF3IkACNjtaa61CBK1ljPZuIeBKBEhgS1dg2yEBRDCkwXvvBNyIAAl476pl40MEZXlTW10CLkQQJfDWlSvnzxaoi5TaPRBABB6ySAxLCTQvAiSwNNWsdwgBRHAILdZtnUDTIkACrXc/u+1HBHZzQ8vSE2hWBEggfWegxBcEEMELFrzzT6BJESAB/x2zdoSIoHYGqL8kgeZEgARKdo9+60IE/ea+x8ibEgES6LGL1okZEdThTq11CDQjAiRQp4P0Wisi6DXzfcbdjAhufXErcJ1An520RtSIoAZ16qxFoAkRIIFa3aPfehFBv7nvMXLzIkACPXbL+jEjgvo5oAXlCJgWARIo1xGo6WUCiOBlHnzyTcCsCCQB/We8e/eu7wwQnUkCiMBkWmhUJgImRfD18TESyJRwil1GABEs48RaPgiYFMHDhw/DvXv3fBAmiiYJIIIm00ajVxIwKYKVsbAZBJIRQATJUFJQAwQQQQNJoonlCSCC8sypsR4BRFCPPTUbJoAIDCeHpiUngAiSI6VADwQQgYcsEsNSAohgKSnW64oAIugq3d0Hiwi67wIAGCOACMao8J1XAojAa2aJaxMBRLAJHxs3RgARNJYwmluGACIow5labBBABDbyQCuMEUAExhJCc7ISQARZ8VJ4qwQQQauZo91rCCCCNdTYxj0BROA+xQQ4IIAIBjB4CwEIQKBHAoigx6wTMwQgAIEBAUQwgMFbCEAAAj0SQAQ9Zp2YIQABCAwIIIIBDN5CAAIQ6JEAIugx68QMAQhAYEAAEQxg8BYCEIBAjwQQQY9ZJ2YIQAACAwKIYACDtxCAAAR6JPD/B+ajFCxAxsEAAAAASUVORK5CYII="></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the zero of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of the local minimum point.</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>Consider the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>3</mn><mo>-</mo><mi>x</mi></math>.</p>
<p>Solve <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>g</mi><mfenced><mi>x</mi></mfenced></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>=</mo><mi>x</mi><mo>+</mo><mfrac><mn>12</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for equating the function to zero.</p>
<p><em><strong><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo>-</mo><mn>2</mn><mo>.</mo><mn>29</mn><mo> </mo><mo> </mo><mfenced><mrow><mo>-</mo><mn>2</mn><mo>.</mo><mn>28942</mn><mo>…</mo></mrow></mfenced></math> (A1) (C2)</strong></em></p>
<p><em><strong><br></strong></em><strong>Note:</strong> Award <em><strong>(C1)</strong></em> for a correct <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-value given as part of a coordinate pair or alongside an explicitly stated <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-value.</p>
<p><em><strong><br></strong></em><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>.</mo><mn>88</mn><mo>,</mo><mo> </mo><mn>4</mn><mo>.</mo><mn>33</mn></mrow></mfenced></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mfenced><mrow><mn>2</mn><mo>.</mo><mn>88449</mn><mo>…</mo><mo>,</mo><mo> </mo><mn>4</mn><mo>.</mo><mn>32674</mn><mo>…</mo></mrow></mfenced></mfenced></math> <em><strong>(A1)(A1) (C2)</strong></em></p>
<p><strong><br>Note:</strong> Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>88</mn><mo>,</mo><mo> </mo><mi>y</mi><mo>=</mo><mn>4</mn><mo>.</mo><mn>33</mn></math>.</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>-</mo><mi>x</mi><mo>=</mo><mi>x</mi><mo>+</mo><mfrac><mn>12</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac></math> (or equivalent) <em><strong>(M1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for equating the functions or for a sketch of the two functions.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>43</mn><mo> </mo><mo> </mo><mfenced><mrow><mo>-</mo><mn>1</mn><mo>.</mo><mn>43080</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(A1) (C2)</strong></em></p>
<p><strong><br>Note: </strong>Do not award the final <em><strong>(</strong><strong>A1)</strong></em> if the answer is seen as part of a coordinate pair or a <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-value is explicitly stated, unless already penalized in part (a).</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mfrac><mn>3</mn><mi>x</mi></mfrac><mo>,</mo><mo> </mo><mi>x</mi><mo>≠</mo><mn>0</mn></math>.</p>
</div>
<div class="specification">
<p>Line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> is a tangent to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> at the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>,</mo><mo> </mo><mo>−</mo><mn>2</mn><mo>)</mo></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>f</mi><mo>'</mo><mfenced><mi>x</mi></mfenced></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your answer to part (a) to find the gradient of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the number of lines parallel to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> that are tangent to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>. Justify your answer.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>f</mi><mo>'</mo><mfenced><mi>x</mi></mfenced><mo>=</mo></mrow></mfenced><mo> </mo><mn>2</mn><mi>x</mi><mo>+</mo><mfrac><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac></math> <em><strong>A1A1</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>A1</strong> </em>for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi></math>, <em><strong>A1</strong> </em>for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo><mfrac><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3</mn><msup><mi>x</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></math><br> </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>attempt to substitute <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> into their part (a) <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>f</mi><mo>'</mo><mfenced><mn>1</mn></mfenced><mo>=</mo></mrow></mfenced><mo> </mo><mn>2</mn><mfenced><mn>1</mn></mfenced><mo>+</mo><mfrac><mn>3</mn><msup><mn>1</mn><mn>2</mn></msup></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> <em><strong>A1</strong></em><br> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>=</mo><mn>2</mn><mi>x</mi><mo>+</mo><mfrac><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac></math> <em><strong>M1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>686</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>,</mo><mo> </mo><mn>2</mn><mo>.</mo><mn>19</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mo>-</mo><mn>0</mn><mo>.</mo><mn>686140</mn><mo>…</mo><mo>,</mo><mo> </mo><mn>1</mn><mo>,</mo><mo> </mo><mn>2</mn><mo>.</mo><mn>18614</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><br><strong>OR</strong></p>
<p>sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>f</mi><mo>'</mo><mfenced><mi>x</mi></mfenced></math> with line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>5</mn></math> <em><strong>M1</strong></em></p>
<p><img src="data:image/png;base64,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"></p>
<p>three points of intersection marked on this graph <em><strong>A1</strong></em></p>
<p>(and it can be assumed no further intersections occur outside of this window)</p>
<p><br><strong>THEN</strong></p>
<p>there are two other tangent lines to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> that are parallel to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> The final <em><strong>A1</strong> </em>can be awarded provided two solutions other than <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn></math> are shown <strong>OR</strong> three points of intersection are marked on the graph.</p>
<p>Award <em><strong>M1A1A1</strong></em> for an answer of “3 lines” where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> is considered to be parallel with itself (given guide definition of parallel lines), but only if working is shown.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Was reasonably well done, with the stronger candidates able to handle a negative exponent appropriately when finding the derivative. There were a few who confused the notation for derivative with the notation for inverse.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most knew to substitute <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn></math> into the derivative to find the gradient at that point, but some also tried to substitute the <em>y</em>-coordinate for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mo>(</mo><mi>x</mi><mo>)</mo></math>.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>There was a lot of difficulty understanding what approach would help them determine the number of tangents to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> that are parallel to <em>L</em>. Several wrote just an answer, which is not adequate when justification is required.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Dilara is designing a kite <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABCD</mtext></math> on a set of coordinate axes in which one unit represents <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mtext>cm</mtext></math>.</p>
<p>The coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> are <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>2</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo><mo>,</mo><mo> </mo><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>4</mn><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>4</mn><mo>,</mo><mo> </mo><mn>6</mn><mo>)</mo></math> respectively. Point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math> lies on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="[" close="]"><mtext>AC</mtext></mfenced></math> is perpendicular to <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="[" close="]"><mtext>BD</mtext></mfenced></math>. This information is 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 gradient of the line through <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the gradient of the line through <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the line through <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math>. Give your answer in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi><mi>y</mi><mo>+</mo><mi>d</mi><mo>=</mo><mn>0</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> are integers.</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>Write down the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinate of point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfrac><mrow><mn>6</mn><mo>-</mo><mn>0</mn></mrow><mrow><mn>4</mn><mo>-</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mn>3</mn></math> <em><strong>(M1)A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>m</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo> </mo><mo> </mo><mfenced><mrow><mo>-</mo><mn>0</mn><mo>.</mo><mn>333</mn><mo>,</mo><mo> </mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>333333</mn><mo>…</mo></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.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>an equation of line with a correct intercept and either of their gradients from (a) or (b) <em><strong>(M1)</strong></em></p>
<p>e.g. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>x</mi><mo>+</mo><mn>4</mn></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mn>4</mn><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mfenced><mrow><mi>x</mi><mo>-</mo><mn>0</mn></mrow></mfenced></math></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting either of their gradients from parts (a) or (b) and point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>3</mn><mo>,</mo><mo> </mo><mn>3</mn><mo>)</mo></math> into equation of a line.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>3</mn><mi>y</mi><mo>-</mo><mn>12</mn><mo>=</mo><mn>0</mn></math> or any integer multiple <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>12</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This question was overall well done by most candidates. In part (a) calculating the gradient was correctly done with few errors noted where candidates swapped the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> coordinates in the gradient formula. Some candidates left their answer as <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>6</mn><mn>3</mn></mfrac></math> which resulted in a loss of the final mark. There was some confusion with the gradient of a line and the gradient of the perpendicular line in part (a). Some candidates found the perpendicular gradient in part (a). Although many candidates were able to write an appropriate equation of the line through <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>BD</mi></math>, several did not express their answer in the required form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi><mi>y</mi><mo>+</mo><mi>d</mi><mo>=</mo><mn>0</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> are integers. Many final answers were given as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>x</mi><mo>+</mo><mn>4</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>x</mi><mo>-</mo><mn>4</mn><mo>=</mo><mn>0</mn></math>. In part (d), writing the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinate of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">D</mi></math> was well done by most candidates. Some candidates wrote a coordinate pair rather than just the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinate as required.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was overall well done by most candidates. In part (a) calculating the gradient was correctly done with few errors noted where candidates swapped the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> coordinates in the gradient formula. Some candidates left their answer as <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>6</mn><mn>3</mn></mfrac></math> which resulted in a loss of the final mark. There was some confusion with the gradient of a line and the gradient of the perpendicular line in part (a). Some candidates found the perpendicular gradient in part (a). Although many candidates were able to write an appropriate equation of the line through <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>BD</mi></math>, several did not express their answer in the required form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi><mi>y</mi><mo>+</mo><mi>d</mi><mo>=</mo><mn>0</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> are integers. Many final answers were given as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>x</mi><mo>+</mo><mn>4</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>x</mi><mo>-</mo><mn>4</mn><mo>=</mo><mn>0</mn></math>. In part (d), writing the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinate of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">D</mi></math> was well done by most candidates. Some candidates wrote a coordinate pair rather than just the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinate as required.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was overall well done by most candidates. In part (a) calculating the gradient was correctly done with few errors noted where candidates swapped the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> coordinates in the gradient formula. Some candidates left their answer as <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>6</mn><mn>3</mn></mfrac></math> which resulted in a loss of the final mark. There was some confusion with the gradient of a line and the gradient of the perpendicular line in part (a). Some candidates found the perpendicular gradient in part (a). Although many candidates were able to write an appropriate equation of the line through <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>BD</mi></math>, several did not express their answer in the required form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi><mi>y</mi><mo>+</mo><mi>d</mi><mo>=</mo><mn>0</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> are integers. Many final answers were given as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>x</mi><mo>+</mo><mn>4</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>x</mi><mo>-</mo><mn>4</mn><mo>=</mo><mn>0</mn></math>. In part (d), writing the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinate of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">D</mi></math> was well done by most candidates. Some candidates wrote a coordinate pair rather than just the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinate as required.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was overall well done by most candidates. In part (a) calculating the gradient was correctly done with few errors noted where candidates swapped the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> coordinates in the gradient formula. Some candidates left their answer as <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>6</mn><mn>3</mn></mfrac></math> which resulted in a loss of the final mark. There was some confusion with the gradient of a line and the gradient of the perpendicular line in part (a). Some candidates found the perpendicular gradient in part (a). Although many candidates were able to write an appropriate equation of the line through <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>BD</mi></math>, several did not express their answer in the required form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi><mi>y</mi><mo>+</mo><mi>d</mi><mo>=</mo><mn>0</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> are integers. Many final answers were given as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>x</mi><mo>+</mo><mn>4</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>x</mi><mo>-</mo><mn>4</mn><mo>=</mo><mn>0</mn></math>. In part (d), writing the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinate of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">D</mi></math> was well done by most candidates. Some candidates wrote a coordinate pair rather than just the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinate as required.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = p{x^2} + qx - 4p">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>p</mi>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>q</mi>
<mi>x</mi>
<mo>−</mo>
<mn>4</mn>
<mi>p</mi>
</math></span>, where <em>p</em> ≠ 0. Find Find the number of roots for the equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = 0">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
</math></span>.</p>
<p>Justify your answer.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><strong>METHOD 1</strong></p>
<p>evidence of discriminant <em><strong>(M1)</strong></em><br><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{b^2} - 4ac,\,\,\Delta ">
<mrow>
<msup>
<mi>b</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>4</mn>
<mi>a</mi>
<mi>c</mi>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi mathvariant="normal">Δ</mi>
</math></span></p>
<p>correct substitution into discriminant <em><strong>(A1)</strong></em><br><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{q^2} - 4p\left( { - 4p} \right)">
<mrow>
<msup>
<mi>q</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>4</mn>
<mi>p</mi>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>4</mn>
<mi>p</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>correct discriminant <em><strong>A1</strong></em><br><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{q^2} + 16{p^2}">
<mrow>
<msup>
<mi>q</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>16</mn>
<mrow>
<msup>
<mi>p</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="16{p^2} > 0\,\,\,\,\left( {{\text{accept}}\,\,{p^2} > 0} \right)">
<mn>16</mn>
<mrow>
<msup>
<mi>p</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>></mo>
<mn>0</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>accept</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>p</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>></mo>
<mn>0</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong> A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{q^2} \geqslant 0\,\,\,\,\left( {{\text{do not accept}}\,\,{q^2} > 0} \right)">
<mrow>
<msup>
<mi>q</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>⩾</mo>
<mn>0</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>do not accept</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>q</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>></mo>
<mn>0</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong> A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{q^2} + 16{p^2} > 0">
<mrow>
<msup>
<mi>q</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>16</mn>
<mrow>
<msup>
<mi>p</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>></mo>
<mn>0</mn>
</math></span> <em><strong> A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> has 2 roots <em><strong>A1 N0</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><em>y</em>-intercept = −4<em>p</em> (seen anywhere) <em><strong>A1</strong></em></p>
<p>if <em>p</em> is positive, then the <em>y</em>-intercept will be negative <em><strong>A1</strong></em></p>
<p>an upward-opening parabola with a negative <em>y</em>-intercept <em><strong> R1</strong></em><br><em>eg</em> sketch that must indicate<em> p</em> > 0.</p>
<p>if <em>p</em> is negative, then the y-intercept will be positive <em><strong>A1</strong></em></p>
<p>a downward-opening parabola with a positive y-intercept <em><strong> R1</strong></em><br><em>eg</em> sketch that must indicate <em>p</em> > 0.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> has 2 roots <em><strong>A2 N0</strong></em></p>
<p><em><strong>[7 marks]</strong></em></p>
<p> </p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>Gabriella purchases a new car.</p>
<p>The car’s value in dollars, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V">
<mi>V</mi>
</math></span>, is modelled by the function</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="V(t) = 12870 - k{(1.1)^t},{\text{ }}t \geqslant 0">
<mi>V</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>12870</mn>
<mo>−<!-- − --></mo>
<mi>k</mi>
<mrow>
<mo stretchy="false">(</mo>
<mn>1.1</mn>
<msup>
<mo stretchy="false">)</mo>
<mi>t</mi>
</msup>
</mrow>
<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="t">
<mi>t</mi>
</math></span> is the number of years since the car was purchased and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> is a constant.</p>
</div>
<div class="specification">
<p>After two years, the car’s value is $9143.20.</p>
</div>
<div class="specification">
<p>This model is defined for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant n">
<mn>0</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>t</mi>
<mo>⩽<!-- ⩽ --></mo>
<mi>n</mi>
</math></span>. At <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n">
<mi>n</mi>
</math></span> years the car’s value will be zero dollars.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, and simplify, an expression for the car’s value when Gabriella purchased it.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n"> <mi>n</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="12870 - k{(1.1)^0}"> <mn>12870</mn> <mo>−</mo> <mi>k</mi> <mrow> <mo stretchy="false">(</mo> <mn>1.1</mn> <msup> <mo stretchy="false">)</mo> <mn>0</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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V(t)"> <mi>V</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 12870 - k"> <mo>=</mo> <mn>12870</mn> <mo>−</mo> <mi>k</mi> </math></span> <strong><em>(A1) (C2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="12870 - 3080"> <mn>12870</mn> <mo>−</mo> <mn>3080</mn> </math></span> <strong>OR</strong> 9790 for a final answer.</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="9143.20 = 12870 - k{(1.1)^2}"> <mn>9143.20</mn> <mo>=</mo> <mn>12870</mn> <mo>−</mo> <mi>k</mi> <mrow> <mo stretchy="false">(</mo> <mn>1.1</mn> <msup> <mo stretchy="false">)</mo> <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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V(t)"> <mi>V</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(k = ){\text{ }}3080"> <mo stretchy="false">(</mo> <mi>k</mi> <mo>=</mo> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mn>3080</mn> </math></span> <strong><em>(A1) (C2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="12870 - 3080{(1.1)^n} = 0"> <mn>12870</mn> <mo>−</mo> <mn>3080</mn> <mrow> <mo stretchy="false">(</mo> <mn>1.1</mn> <msup> <mo stretchy="false">)</mo> <mi>n</mi> </msup> </mrow> <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 correct substitution into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V(t)"> <mi>V</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </math></span>.</p>
<p> </p>
<p><strong>OR</strong></p>
<p><img src="images/Schermafbeelding_2017-03-07_om_07.33.35.png" alt="N16/5/MATSD/SP1/ENG/TZ0/15.c/M"> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for a correctly shaped curve with some indication of scale on the vertical axis.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(n = ){\text{ }}15.0{\text{ }}(15.0033 \ldots )"> <mo stretchy="false">(</mo> <mi>n</mi> <mo>=</mo> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mn>15.0</mn> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mn>15.0033</mn> <mo>…</mo> <mo stretchy="false">)</mo> </math></span> <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (b).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Natasha carries out an experiment on the growth of mould. She believes that the growth can be modelled by an exponential function</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>A</mi><msup><mtext>e</mtext><mrow><mi>k</mi><mi>t</mi></mrow></msup></math>,</p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math> is the area covered by mould in <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>mm</mtext><mtext>2</mtext></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is the time in days since the start of the experiment and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> are constants.</p>
<p>The area covered by mould is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>112</mn><mo> </mo><msup><mtext>mm</mtext><mn>2</mn></msup></math> at the start of the experiment and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>360</mn><mo> </mo><msup><mtext>mm</mtext><mn>2</mn></msup></math> after <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> days.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>A</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>112</mn></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>112</mn><msup><mtext>e</mtext><mrow><mn>5</mn><mi>k</mi></mrow></msup><mo>=</mo><mn>360</mn></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct equation.</p>
<p><br><strong>EITHER</strong></p>
<p>graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>112</mn><msup><mtext>e</mtext><mrow><mn>5</mn><mi>k</mi></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>360</mn></math> with indication of point of intersection <em><strong>(M1)</strong></em></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>k</mi><mo>=</mo></mrow></mfenced><mo> </mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mi>ln</mi><mfenced><mfrac><mn>360</mn><mn>112</mn></mfrac></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct rearranging and use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>log</mi></math>.</p>
<p> </p>
<p><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>k</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>0</mn><mo>.</mo><mn>234</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>233521</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(</strong><strong>M1)(M1)(A0)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>233</mn></math>.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>In part (a), there were some problems for a few candidates to identify the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>. Many answers were left as <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>112</mn><msup><mi mathvariant="normal">e</mi><mrow><mi>k</mi><mfenced><mn>0</mn></mfenced></mrow></msup></mfrac></math> and thus scored no marks. Those candidates who could identify the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> were generally able to find a correct solution. Most candidates were able to substitute into the given formula, and many were able to find a correct solution to the resulting equation. The exponential function did not seem to have put candidates off. In several responses the use of logs was seen or implied in the candidates' work; this topic is off syllabus and candidates are expected to use technology (and not logs) to solve such problems. However, very few candidates showed workings between the substitution and the final answer, which was to their detriment in the awarding of marks for their method whenever an incorrect answer was seen. A few candidates did not seem to understand the function notation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mfenced><mi>t</mi></mfenced></math>. In part (b) a few candidates wrote <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>360</mn><mfenced><mn>5</mn></mfenced></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mfenced><mi>t</mi></mfenced></math> and multiplied the two values.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (a), there were some problems for a few candidates to identify the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>. Many answers were left as <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>112</mn><msup><mi mathvariant="normal">e</mi><mrow><mi>k</mi><mfenced><mn>0</mn></mfenced></mrow></msup></mfrac></math> and thus scored no marks. Those candidates who could identify the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> were generally able to find a correct solution. Most candidates were able to substitute into the given formula, and many were able to find a correct solution to the resulting equation. The exponential function did not seem to have put candidates off. In several responses the use of logs was seen or implied in the candidates' work; this topic is off syllabus and candidates are expected to use technology (and not logs) to solve such problems. However, very few candidates showed workings between the substitution and the final answer, which was to their detriment in the awarding of marks for their method whenever an incorrect answer was seen. A few candidates did not seem to understand the function notation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mfenced><mi>t</mi></mfenced></math>. In part (b) a few candidates wrote <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>360</mn><mfenced><mn>5</mn></mfenced></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mfenced><mi>t</mi></mfenced></math> and multiplied the two values.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The coordinates of point A are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(6,{\text{ }} - 7)">
<mo stretchy="false">(</mo>
<mn>6</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−<!-- − --></mo>
<mn>7</mn>
<mo stretchy="false">)</mo>
</math></span> and the coordinates of point B are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 6,{\text{ }}2)">
<mo stretchy="false">(</mo>
<mo>−<!-- − --></mo>
<mn>6</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>2</mn>
<mo stretchy="false">)</mo>
</math></span>. Point M is the midpoint of AB.</p>
</div>
<div class="specification">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}">
<mrow>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> is the line through A and B.</p>
</div>
<div class="specification">
<p>The line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}">
<mrow>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
</mrow>
</math></span> is perpendicular to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}">
<mrow>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> and passes through M.</p>
</div>
<div class="question">
<p>Write down, 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>, the equation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}">
<mrow>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
</mrow>
</math></span>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{4}{3}x - \frac{5}{2}{\text{ }}(y = 1.33 \ldots x - 2.5)">
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mi>x</mi>
<mo>−</mo>
<mfrac>
<mn>5</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>y</mi>
<mo>=</mo>
<mn>1.33</mn>
<mo>…</mo>
<mi>x</mi>
<mo>−</mo>
<mn>2.5</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft) <em>(C1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from parts (c)(i) and (a). Award <strong><em>(A0) </em></strong>if final answer is not written 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><strong><em>[1 mark]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>The intensity level of sound, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> measured in decibels (dB), is a function of the sound intensity, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="S">
<mi>S</mi>
</math></span> watts per square metre (W m<sup>−2</sup>). The intensity level is given by the following formula.</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L = 10\,{\text{lo}}{{\text{g}}_{10}}\left( {S \times {{10}^{12}}} \right)">
<mi>L</mi>
<mo>=</mo>
<mn>10</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>S</mi>
<mo>×<!-- × --></mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>12</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="S">
<mi>S</mi>
</math></span> ≥ 0.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An orchestra has a sound intensity of 6.4 × 10<sup>−3 </sup>W m<sup>−2</sup> . Calculate the intensity level, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> of the orchestra.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A rock concert has an intensity level of 112 dB. Find the sound intensity, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="S">
<mi>S</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10\,{\text{lo}}{{\text{g}}_{10}}\left( {6.4 \times {{10}^{ - 3}} \times {{10}^{12}}} \right)">
<mn>10</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>6.4</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>12</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(M1)</strong></em></p>
<p>= 98.1(dB) (98.06179…) <em><strong>A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="112 = 10\,{\text{lo}}{{\text{g}}_{10}}\left( {S \times {{10}^{12}}} \right)">
<mn>112</mn>
<mo>=</mo>
<mn>10</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>S</mi>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>12</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(M1)</strong></em></p>
<p>0.158 (W m<sup>−2</sup>) (0.158489… (W m<sup>−2</sup>)) <em><strong>A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The pH of a solution measures its acidity and can be determined using the formula pH <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>−</mo><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mi>C</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> is the concentration of hydronium ions in the solution, measured in moles per litre. A lower pH indicates a more acidic solution.</p>
<p>The concentration of hydronium ions in a particular type of coffee is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>3</mn><mo>×</mo><mn>10</mn><msup><mrow></mrow><mrow><mo>-</mo><mn>5</mn></mrow></msup></math> moles per litre.</p>
</div>
<div class="specification">
<p>A different, unknown, liquid has <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> times the concentration of hydronium ions of the coffee in part (a).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the pH of the coffee.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine whether the unknown liquid is more or less acidic than the coffee. Justify your answer mathematically.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(pH =)<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mo>-</mo><msub><mi>log</mi><mn>10</mn></msub><mfenced><mrow><mn>1</mn><mo>.</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>5</mn></mrow></msup></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>89</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>4</mn><mo>.</mo><mn>88605</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>calculating pH</p>
<p>(pH =)<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mo>-</mo><msub><mi>log</mi><mn>10</mn></msub><mfenced><mrow><mn>10</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>5</mn></mrow></msup></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>89</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>3</mn><mo>.</mo><mn>88605</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p>(<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>89</mn><mo><</mo><mn>4</mn><mo>.</mo><mn>89</mn></math>, therefore) the unknown liquid is more acidic (than coffee). <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Follow through within the part for the final <em><strong>A1</strong></em>. A correct conclusion must be supported by a mathematical justification linking the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math>-value to the pH level to earn the final <em><strong>A1</strong></em>; a comparison of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math>-values only earns <em><strong>M0A0A0</strong></em>.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>referencing the graph</p>
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mfenced><mi>x</mi></mfenced></math> shows that as the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> increases, the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> decreases. <em><strong>M1</strong></em></p>
<p>Since the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math>-value (<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-value) of the unknown liquid is larger than that of the coffee, the pH level (<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-value) is lower. <em><strong>R1</strong></em></p>
<p>The unknown liquid is more acidic (than coffee). <em><strong>A1</strong></em></p>
<p><strong><br>Note:</strong> Follow through within the part for the final <em><strong>A1</strong></em>. A correct conclusion must be supported by a mathematical justification linking the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math>-value to the pH level to earn the final <em><strong>A1</strong></em>; a comparison of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math>-values only earns <em><strong>M0R0A0</strong></em>.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Evaluation of logarithms was well done, although the notation when substituting into the logarithmic formula was not always correct, with several candidates including a multiplication sign between the base and the argument. Even when the substitution was done correctly, some candidates still used multiplication, so not fully understanding logarithmic notation.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Several candidates multiplied their answer to part (a) by 10 rather than multiplying the C-value by 10, and several attempted to compare the C-values rather than calculating the pH of the unknown liquid. Most were able to make a correct contextual interpretation of their result.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows part of the graph of a function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>. The graph passes through point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}(1,{\text{ }}3)">
<mrow>
<mtext>A</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>3</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_06.22.37.png" alt="M17/5/MATSD/SP1/ENG/TZ2/13"></p>
</div>
<div class="specification">
<p>The tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span> at A has equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - 2x + 5">
<mi>y</mi>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>5</mn>
</math></span>. Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span> be the normal to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span> at A.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(1)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span>. Give your answer in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="ax + by + d = 0">
<mi>a</mi>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
<mi>y</mi>
<mo>+</mo>
<mi>d</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d \in \mathbb{Z}">
<mi>d</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">Z</mi>
</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>Draw the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span> on the diagram above.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>3 <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 3">
<mi>y</mi>
<mo>=</mo>
<mn>3</mn>
</math></span></p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3 = 0.5(1) + c">
<mn>3</mn>
<mo>=</mo>
<mn>0.5</mn>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mi>c</mi>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><strong>OR</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y - 3 = 0.5(x - 1)">
<mi>y</mi>
<mo>−</mo>
<mn>3</mn>
<mo>=</mo>
<mn>0.5</mn>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−</mo>
<mn>1</mn>
<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 correct gradient, <strong><em>(A1) </em></strong>for correct substitution of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}(1,{\text{ }}3)">
<mrow>
<mtext>A</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>3</mn>
<mo stretchy="false">)</mo>
</math></span> in the equation of line.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x - 2y + 5 = 0">
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
<mi>y</mi>
<mo>+</mo>
<mn>5</mn>
<mo>=</mo>
<mn>0</mn>
</math></span> or any integer multiple <strong><em>(A1)</em>(ft)</strong> <strong><em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft) </strong>for their equation correctly rearranged in the indicated form.</p>
<p>The candidate’s answer <strong>must </strong>be an equation for this mark.</p>
<p> </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><img src="images/Schermafbeelding_2017-08-16_om_08.26.38.png" alt="M17/5/MATSD/SP1/ENG/TZ2/13.c/M"> <strong><em>(M1)(A1)</em>(ft)</strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>M1) </em></strong>for a straight line, with positive gradient, passing through <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(1,{\text{ }}3)">
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>3</mn>
<mo stretchy="false">)</mo>
</math></span>, <strong><em>(A1)</em>(ft) </strong>for line (or extension of their line) passing approximately through 2.5 or their intercept with the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the straight lines <em>L</em><sub>1</sub> and <em>L</em><sub>2 </sub>. <em>R</em> is the point of intersection of these lines.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The equation of line <em>L</em><sub>1</sub> is <em>y</em> = <em>ax</em> + 5.</p>
</div>
<div class="specification">
<p>The equation of line <em>L</em><sub>2</sub> is <em>y</em> = −2<em>x</em> + 3.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>a</em>.</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 coordinates of <em>R</em>.</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>Line <em>L</em><sub>3</sub> is parallel to line <em>L</em><sub>2</sub> and passes through the point (2, 3).</p>
<p>Find the equation of line <em>L</em><sub>3</sub>. Give your answer in the form <em>y</em> = <em>mx</em> + <em>c</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>0 = 10<em>a</em> + 5 <em><strong>(M1)</strong></em></p>
<p>Note: Award <em><strong>(M1)</strong></em> for correctly substituting any point from <em>L</em><sub>1</sub> into the equation.</p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0 - 5}}{{10 - 0}}">
<mfrac>
<mrow>
<mn>0</mn>
<mo>−</mo>
<mn>5</mn>
</mrow>
<mrow>
<mn>10</mn>
<mo>−</mo>
<mn>0</mn>
</mrow>
</mfrac>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituting any two points on <em>L</em><sub>1</sub> into the gradient formula.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \frac{5}{{10}}\left( { - \frac{1}{2},\,\, - 0.5} \right)">
<mo>−</mo>
<mfrac>
<mn>5</mn>
<mrow>
<mn>10</mn>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mo>−</mo>
<mn>0.5</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1) (C2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( { - 1.33,\,\,5.67} \right)\,\,\left( {\left( { - \frac{4}{3},\,\,\frac{{17}}{{13}}} \right),\,\,\left( { - 1\frac{1}{3},\,\,5\frac{2}{3}} \right),\,\,\left( { - 1.33333 \ldots ,\,\,5.66666 \ldots } \right)} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>1.33</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>5.67</mn>
</mrow>
<mo>)</mo>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>17</mn>
</mrow>
<mrow>
<mn>13</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>1</mn>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>5</mn>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>1.33333</mn>
<mo>…</mo>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>5.66666</mn>
<mo>…</mo>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note: </strong>Award <em><strong>(A1)</strong></em> for <em>x</em>-coordinate and <em><strong>(A1)</strong></em> for <em>y</em>-coordinate. Follow through from their part (a). Award <em><strong>(A1)</strong></em><em><strong>(A0)</strong></em> if brackets are missing. Accept <em>x</em> = −1.33, <em>y</em> = 5.67.</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>3 = −2(2) + <em>c</em> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituting –2 and the given point into the equation of a line.</p>
<p><em>y</em> = −2<em>x</em> + 7 <em><strong>(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A0)</strong></em> if the equation is not written in the form <em>y</em> = <em>mx</em> + <em>c</em>.</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">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>In this question, give your answers to the nearest whole number.</strong></p>
<p><br>Criselda travelled to Kota Kinabalu in Malaysia. At the airport, she saw the following information at the Currency Exchange counter.</p>
<p style="text-align: center;"><img 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47dlpEHGWKrjdIlOc608EqcvtUxtt252NBmDdS1I7eX6K8CXOp3c28bS5gV7S6b2hv7OEgBxHH3OCWEclAFqSCZpzP8VNhBuv2uGlXvQEzIuywqBRJOG35XYu1tsOjkYkPVkNa0Iz9FrU5EFlK/1b3Ue2pWKWQPs169lkthumvH1YmSQgilZV1K94KAICAInAoCQiinokmRQxAQBASBlhEQQmlZAdK9ICAICAKngoAQyqloUuQQBAQBQaBlBIRQWlaAdC8ICAKCwKkgIIRyKpoUOQQBQUAQaBkBIZSWFSDdCwKCgCBwKgjUJhRVUP4KBmIDYgNiA2IDVTYQIkf56ZUQKnJPENgBAeWE8qdZBATz48C7YPmilGaVIr2dJgLiR83rVTBvFnMObyGUZvUgvXUAAc7ZOiB6ayIK5s1Cz+EthNKsHqS3DiDAOVsHRG9NRMG8Weg5vIVQmtWD9NYBBDhn64DorYkomDcLPYe3EEqzepDeOoAA52wdEL01EQXzZqHn8BZCaVYP0lsHEOCcrQOityaiYN4s9BzeQijN6kF66wACnLN1QPTWRBTMm4Wew1sIpVk9SG8dQIBztg6I3pqIgnmz0HN4C6E0qwfprQMIcM7WAdFbE1EwbxZ6Du89EMoDLGcpjJJz95MtvQFMbmYg/x1us0qW3o4DAc7ZGh9d6b/DPYdklMJs+bDlUNz/e382msE3XftPSJMziKIejGbrLdvbf/F2MUcsQj/V0ofBZAqLdbZ/oVtskcN7R0JZwXxyCTHz+1/xZQr3p4VjiyqUrr8XBDhna3T82SdIL8kkj/po7xVMtyIVIZRq3VURiiKZGHqjO2ifdqul2OYpZ+M7EEoG69kYespQ4wTGd0vIuWMFi3SY348uYDD9vM04pawg8N0jwDlbk4Jliwn0NYn0YTi9176Z3adwGecBrj+ZG3+tMyohlGqUkFD81RqNkUOYrk5nds3Z+A6E8hmmgwuIonO4TD95xvkZpsMfYHT9niz1QqAHDPXbDEZnyugvYXL7BhLlALFSxgpmox5E0RkkkxuY6BSbI6xsOYN0lJjVUgy9wQSmi5Wzg2UKiXKws9cw/f03l6LrDeBqhmRoivupApXCmy70DMM6qh4TMZBsDpN+DFH0FCaLr65f+dQ5BDhnaw6IDFbTofGF55Au8yQVAPpsBFGSwtIOyE9b+2magJ9CyJ9tg41/aBfzCixsPCN6sLFoBDNUjYfnsccZDu/HE8pqCgM92yFAVZpRCPSAoVoFkHzkmQJ+bQiF3Mf87foORj0VzOkzRUQvIL03+WJUol9GfafkwKYKDHnZ547MlNjWAPoTWBCeqYREHp4kApyzNSmstccogjgZwbWZEJXHQGbRnm+4lHXAT70AWG632TvtYh6KbUr+B1hOX+XZGhoXMBbpuIY4eW0ceZzh8H48oQRBQXBCVw8wXSRgqJZQYugNb2GZZbBe/gVrIISCOeD1X7Bcf4X79AXEKk+py6uGcW+H5C5xvNE5JJOP+WrDpgBwqUpmdvElTOZqhfNg2o8g0kbhysSDKeRroK+wmDxlVmshLOTeKSPAOVuzMn+B2ehJaZJVIhcbuFxqDNYfTQbgCYxmXwAg4KdCKESdGNu8CS0SdG8IaTBbwq9QAI47znA2fsSEgkEe9eYIxZ00Uc/IMh4VSK84M0BCoauRklMgMUTgyAL7J1dcnWFbmO7C76SofOweApyzNY/EChbTX1161/oFmWihLdtnNCjGkO+1CKFU624DoRQmuwCAsahqhaI6RN1gXDmiOMPZ+OMJBYWNDpXy8vcikFDQyFHFG5SJSqulROwjgiJpYV94RRJTaa+/bL66koSwqlxPHgHO2doVXJFLCpNB36xajH+hXwQJBf1ACKVadxiD/EkwQLb8AGNvv7c2odjJ8vHFGc7GH08odnYf2pRXy+0X3vnrEOhuRWADuE15+USFwf4MkvRPol8M7v59UkR9RMdBgtGP/TG58VSTA12OvoVrfTgB0wNev/K1cwhwztYcEGjXgZU2+gHuP9aaGAqhVOsO8S4TSjBdiDqgsQhXH6gX3eHxxhnOxncgFLKZxx4bpqsJBN0tt7PlLQzNZvrjCcWRQIR7KzYvTPoPKdGSIhqCU2Bk91ConOTon3VEkyLA1Fq15cnTDiDAOVtzohOfiMjeSLaEuzGehDQrFBvI3B6kO16MWQIhlGrdYWzDOEJK2/0oMuHFWBThJJRs3hcIhaS9cAV5JHGGs/EdCEWBhpvfNO/qPsfJFcztG6LUyF0ZNTD19/GEAgDbnPKis4ISoajjWtwLYY4Ic3Oh8hDiIrYkH7uJAOdsjaLB+YT2N2rLZMKEQctc5ZRXXY0hoZTjGsa34klSfMUgVN4npeOMM5yN70goCnD/DHv+ouMoDfz0ynoBt/ZdkT4Mrj7A7Pr57oSieKDwHoo6KjmG261PVhgD8t9DiRMIyeOOZuJMrq4BSrlTRoBztsZl9u1YEUXwZ5F8H1Y/0fIbeYdMVijVuqsilMA7cZDBeuG/C/cfuGZ+yuYY4wxn43sglGqoT/cpWaYeyTL0dLH+viTjnO37kuL7Gu3pYn6ccYbDWwhla79xszUFaiQ/L7M1gqdegXO2U5e7TflOD/PjjjMc3kIoW3sB2biPVNruTn5VeWsMT7sC52ynLXW70p0e5scdZzi8hVDa9QPp/QQR4JztBEU9GpEE82ZVweEthNKsHqS3DiDAOVsHRG9NRMG8Weg5vIVQmtWD9NYBBDhn64DorYkomDcLPYe3EEqzepDeOoAA52wdEL01EQXzZqHn8BZCaVYP0lsHEOCcrQOityaiYN4s9BzeQijN6kF66wACnLN1QPTWRBTMm4Wew1sIpVk9SG8dQIBztg6I3pqIgnmz0HN4C6E0qwfprQMIcM7WAdFbE1EwbxZ6Du8SoaiC8lcwEBsQGxAbEBuosoEQhZUIJVRI7gkCgkB9BJQTyp9mERDMjwPvguWLUppVivR2mgiIHzWvV8G8Wcw5vIVQmtWD9NYBBDhn64DorYkomDcLPYe3EEqzepDeOoAA52wdEL01EQXzZqHn8BZCaVYP0lsHEOCcrQOityaiYN4s9BzeQijN6kF66wACnLN1QPTWRBTMm4Wew1sIpVk9SG8dQIBztg6I3pqIgnmz0HN4C6E0qwfprQMIcM7WAdFbE1EwbxZ6Dm8hlGb1IL11AAHO2TogemsiCubNQs/hLYTSrB6ktw4gwDlbB0RvTUTBvFnoObx3J5T1AqbpLzBK+jCYfq4p1QoW0wkMerH7mZfeACbTBaxtC59hOriAqD+BRWZvdvjDV1hMnjq86E/klLCrC5OH8WoKgziG/mQOB4N8fQej/g+Q3j+YQT7AcvbW2QLKsvodZn98LQui7O16BEmMP4sRQ2/wBm5m9/Dl/b/g/SoD0HLg88BV9ZG+h8Xak1LV649h5t8vj6LyDudslZX2/DBbfoBxcp7bS28I6WK1oYcM1ovfYIR1oj4Mru5gWYCoTpkN3RzoceuYZ0u4GycQa7/swyCdk1jGC50t7+Bq0Nd6ipN/wt0S/ULVof+vvG/HT2GyCPgH39Ven3B470Yo2RwmT55C8kwZ7kVNQvkCs9ETKIKnDDWFQe8MeqO7WorYKzrfRWOGUOIhTFXQtH92wa5pQlEyPCOElcF6NoZefAmTuQl42RJmVwPoRb7DZLCeX0ESKwKZwNQGSCX/FCbKKQvYoDN67ShCmqj2I4hovxrPB7hPf4D+jjbIOZtV2aE/rP8L6dV/cjLAQFfApjyA7P4djMe/GZJ9gOXdP3OsCRZ1ypRbbuZOu5h/gf9Jrw0ZIHY14qGaXPWewHB6Dxk8wHL6Cno9OqEx/kknj/i55Yk2h/duhGJsJVtMoF+XUPTsMQS2CQAbDL8Z8zzGXjhCycea3adwGXvBc6MYzRKKHuMZIUQ1IenHEA+mUJw/q8A+hisyA8vli/kJR/YJ0stLMmtjCEVjguQUQVRwYMhXN2cvyApqI4ilApyzlQoe5MZX+OP9f+CezjlYn8MBBOqAb291ymB7zV/bxDz74wO8tytuJXvuV2W7prjk+BbLqHp/cxOu1XsYvbwtrRJX05fw5JBZBDpM5jOHd+OEUp98QsHuAgbpv+F2hEvLc0jGH4qA2xmuWiKeQzJKIR393UudqTRLSpb3EcTJGG7trBcN4hru0mE+m9Vt4QwOUfbb6cNgMiWpFNNO8gpem1SCNaD1gsihZt1vYVZY7mIfePUdHO/jFcdMg3O98dm0og48NOXl1/dxwklAAq9fG52wE4KAAxlCKQV1JVIh5WVsgW07xyBb/AY3loSqCEWVV6T1AuKIyqvuq3HSVVTe9jb/cs62TRv7LKt9zifOjR2gbskEoFSnTplSpYPcOCrMtV3/HUazL7ysusyZIw9d0uBpVh/Z8g/4w0+/6nrPyMSJ7+KQTzi8GycU0DNJlSJTwTclqQtffBNEcGmng51KUyQwvltCBjjLpAHBT6etYD65zPOa2I6q56dZ1nNIVcrEljF9RzH0hmaGsP4Ik+Qc4svUzP5MO1HfLFkBoFQG28Eya1gu15BjcAG9QWrIx4yz0uk3EYp5bmXYYnxYp0AodXDCoI04ZbBe/hVOWWpH+JuXFsWgrlYK/h4asQeje0vG5BH/EcfGr9ryyU1E9K5aKzo13z7/hHM2vsahnpi9yuQfMK2crIT6z3E4s/b+2DKhevu/dxyYY/r1uYsJjKjhiXU9m31SqROmwz3f5vBunlCUy5KNKDWwfCXxC6RVm/KFYIfohEjHCyA6kMUkaOR1isHJV6Rp1wvwhbSSmWH4ez55GUzpmXYKM2vTV+GeAkWlf/wZC8qprjUJBdvdZnxBQqmDE+KG8tLxFj/nDuTpRhdZwcKuAnNiuZqpCQP+wT6iQGoMcSOHO5Q9aXmwXqhP07adpBRn4fxYcUzVV87Zqmvt+SnKpv2r/iaxG4XSf1I9y9apnU1lXIuH/NQ+5sbXNd4q44CTxZDUnG1y97ENFQOee5MyfNbslcO7FUKxousTYilc2xQWznRVCaOgYLDDFmgZowwMqFgEAzG2g/dVauwmhTRNIcVNWrsRnLdbJB0MXiboa4cNBNICMdDxYcehe+oZdx/rbUkojxmfrkNXfJr9K3Da5AA4dk437rndWC85JPbBEIpuAldjVB9Yb3tCyU+J0bZwnPWunLPVq73fUm7ydg6X6SdC1FX9KDx/goRsyJdL1ylTrnWoO0eDOUm5u2yGLzVnm9x9U1/FlicvvUM5ftvNfOfwbpdQqOx4GsUL6jYNFQp2hSDMBVxz3xIKpspMmkURys0dzG+HEHt9VxHKN+4ggiYU3GgOkYS5pwOnfxQQZ9cUGPzMyec9N3KGl9RIisz4ChjXwWmDA+DQMI1UIntbwHxQKQM8uuo24HNZqrABKMu7eWxsuxwZ+8NlvnPOxhQ//O2CTdbobn0H48FbmPv5e1q1Thla/sCfjwvzTb4aslcFULXNKnt9UjrAcmBgmeY5vI+HUNTACwHNC8aFZyglLWOUUQpaHqGYFUQxVeUrMm+3ilAyLuiY9vN3Oej4imMutY2P2esmI1V90RMi6p2SwCy7anwU41o4+bhxg2d0ky3g5mZRnjXjPhtOAvRYVFrrCZuC2Z5QcP8mMHPndMuJ593nnM0r1uDX3HZq2Vz2CW7Gv1aTSZ0yDUqnujo2zLU9lmIRAUXbtL+n6MUqUjxPeR9HuqsK74YJpQowJBRMUXjBmAY7C3SoDNY3hfzgFAwWZlzeCsWujrApvSox7QcDLkBwDwUDo26HCa5mtcU7vRkjY6R5QCWyP2Z8FONaONUlFJyRkfEpLNQYL38KvEjo2wmmtALHfAu6oQRaNTa6+qLn/vPGSliaPupeji245enU/uaUV3YP0/HPxQ389Ue4mnxwx7rrlKkL1B7LHRfmue1VH2jIbbzo796kkOKjfOVI0l1qWBzeDROKOgmlXuY5815OU/fVMdpL6OOpqkI6C8nGy+/7ZWBF1xQAAA2gSURBVKDGKS9DMC6/uYLF7di8eY0BzxCVOiqMx5L1Ca4L8h4EBjk8wVVxyqtAKBQD3LgzG9Nx1fsPHKGoo73qTfMLSCYfyQmrR4yPEkotnKqCNvUGTLV5MzJNejHEyQhSuxGP8uALX9iOefFLpQr9E2H2ZcUahGLLqnZeFYOn7srI5OsMh1Hjyjlbjaq7F9F6UycI8Rh6jls/uSqsOvKJD1nx4UnHUiqW+FydMrtL8KgW2sPcrHR7A8DDJNnyFob95+5lXSUR6oXuS218sdFBoSY5x5LuUqPi8N6RUDDwkr2AOo6onLrw8xkmSNzMyDslodUHMW6NtVdGKw7ftMbTY5P8fRMyrsLPUph3VWbzdyRFZNrtDeCNPTAQ+ikK/z2N8Hso/kpHD73wHor/focu4f1jCKXk8KruCK4LJ+Sw6pbjo4SifID+fEcQpy0IxRyOKMzIMOVFg7whDHROlASv2XIGN77t6LH9AjdISloOYpMeZhqvgq1h6+qqdE9Sh/RRzc+cs9WsvmMxclReyR0nMEqpX+XNFwjFTB7UuMt/cUWuXhw1P+VSKocTsR2HvkP19jAnq12NS/7uW+mdshChFHys6l005fsDNt27A2yPrsrhvSOhPHo8DVbMyaEQyDb2HiCqjXWkwCYEdBCjb8pvqtDGc0VG3/Wb8m2A1n6fXIBrf2SnOQIO75MilDz3TVJQ6vdx9G8SkaV9Lf0KodSCaetCKiX5d+/t4K0bOWAFlb44gd/yOiBCx9o0F+COdbzf+7g4vE+KUADKv2JczM/XVaMQSl2kti5X+rXhrVs4XAW1OjmRXxs+HEjH2TIX4I5ztN//qDi8T4xQvn9FiQTfPwKcs33/kh2vBIJ5s7rh8BZCaVYP0lsHEOCcrQOityaiYN4s9BzeQijN6kF66wACnLN1QPTWRBTMm4Wew1sIpVk9SG8dQIBztg6I3pqIgnmz0HN4C6E0qwfprQMIcM7WAdFbE1EwbxZ6Dm8hlGb1IL11AAHO2TogemsiCubNQs/hLYTSrB6ktw4gwDlbB0RvTUTBvFnoObxLhKIKyl/BQGxAbEBsQGygygZCFFYilFAhuScICAL1EVBOKH+aRUAwPw68C5YvSmlWKdLbaSIgftS8XgXzZjHn8BZCaVYP0lsHEOCcrQOityaiYN4s9BzeQijN6kF66wACnLN1QPTWRBTMm4Wew1sIpVk9SG8dQIBztg6I3pqIgnmz0HN4C6E0qwfprQMIcM7WAdFbE1EwbxZ6Dm8hlGb1IL11AAHO2TogemsiCubNQs/hLYTSrB6ktw4gwDlbB0RvTUTBvFnoObyFUJrVg/TWAQQ4Z+uA6K2JKJg3Cz2HtxBKs3qQ3jqAAOdsHRC9NREF82ah5/AWQmlWD9JbBxDgnK0DorcmomDeLPQc3rsTynoB0/QXGCV9GEw/b5ZK/b/d8QVT9issJk8h6k9gkZGmVB+TAfTs74zF0BtMYLpYkULlj9liAn1bh/4uTx8Gkyks1rSTcv3ynQxW0yHE0VOYLL4CQBP/9/wXmI2ewWW6gLnCpiCPh6PGlsqJ43yA5ewtDHpxXr83gMl0AevV7zD7g8hRaJu2o/BKA3gr+RMYzb6UoerwHc7Z2oIku0/hMkZbqDmK7BOklxfQn8yh5CWsndVs+wDFjgrzKuyo7OsF3I4SiLXfqZj2FmbLB1rCfDZxxvpnHNZLoOahbnF470Yo2RwmT55C8uwcosgLbpwk2xLK+g5GvQtIxh9gaS17BYt0CL3oSWUwywklMK71HNJBH6LeGGZbkUrzhKJloASrMO/HEF+mcG/xoGCrMb6EJzYQZLCejaEXX8Jkbgg4W8LsShG0F2S0bnxjXcFiOjFkdA7J5COsSXc6WPW3xZE0cIIfOWdrRVQd3JR/erquHMwD3KcvII58W1CV8BmZcFD7rGz3cA+PB3PEJ4QdkT/7BDfjn+HWTIqz5QcYJ+fBmJRPCAjeW+mS9LnHjxzeuxGKGSAbuEMCbEUoJoDHQ5iu/OiZs3Y8mAK3TqkcV91ZREGGhglFj9Fb+SGhsHJ7hMKWV4Y/hiu90jJCBgnFPFt/hIky+BKJKz304TL9VJ7JFrDrzhfO2ZpHQK1uX8CPg2dkVb1pFGoC8hMkP/4ISRwIimqC138Z8MdN7R72+XFgvgE7AkH2xwd4f19cjYTjldJhwmR0SIMNf+TwPnJCMSmwIKFsRjCsIKwXJqtsOYO0sAylqbXNhFKsH0EUJzC6XbhZvQ7a55C8fgVJrGYdgRWUGaIevy87SxBULrJCMeWDqzGb8jJ1qwgFAOxMyZuR6nF693A0XbxyztYsFia4jf4D94U07YZRKMJIfoLZ/S0MSoSC9q/SM28gVWnTDc019fgoMK/ErgYSocm2vhdBpNLU6ftHpOlr9PuIIhzeR04oJIg9AtBqQgHIn5NUgE6vnUFveGvSayuYTy4hjl9AqmcT6FBYx+Q2MZjq+hckLYSpOSwPANZAXsFU5UvXf8EymHbLybS0AtuWUGiKAvdOOAPaQCiA5OQvuXU9IiPXfkfuc87WqPgY3NbfvH2/qlGo2fAPeRo5ZAtW/5h+UcSSHkWQax/zDdhVwY7PFOZnGGvUTTOhtnsniliGkG7YO8bmDnnl8D56QlE528KGsgJXzfqvbwKbxEUI6xEKrhCM8vx9FZODzgN7FaGYZ/6KwndM/T2CElEUhw558D4rb75tTSiqYSQ2Ewh6A7iaLcspKn+s/pjwEIK/qtJjCoy1VL8bNzhna056EtzAt1luFLiiuctXHVW2oPbgbt6YfbUYeiNTh2u6gfvtYr4FdiwWSk8voR/EUsXAf8FE7fuq+OfHKLbNwz3g8P4OCAVByWC9eA+pPlGmcvkqOPZhOL0vB0ZTZTtC4fZkDNHoVYjvnN4KRferlP8O0jSFNHVOZ0/LVDkqiqquuhySHXnwKEJR9RV+U2eUUWB2uXFsRl6fUAzRbCRJIsYpf+ScrRmZVXD7GYZ2T8u3WWYU6zsYD2/cQY+NtqBzoDAd9iHyJ1FMF4e83Srmj8HOB8OuKP29YlrwAZbTV9Ar+R8t08xnDu/viFCKQNlTEZhuKj7W3+oRiknVsIHaEIp2Gj994BGK3bhWx2yvIU3fwWz+rpiLruOoavR7JxQESBHLbzDSG+ze7HLT2AxG5RNDHBljn926cs7WCAp+cKu1QvkCs/Frk9Y1o9xkCygMZ6f4vKFre5jvgJ3FRrXxyp3CtPdDH47D1zi8myeUyvSIF6BDeNp7m2de1YRi6ltC4hRVd4XCpMx8x/S/W3m8D6yjbsJIjeO5OxWSLeDmZlFexeFxUis/kljgZI8ZGm7Kl48sc9h5MnXkK+dshxcffQL3OAJXqm8ckLa1QFmbu6/YH9P+/My8l4UNNn9tDfNdsNMwPcD9zc9whUf6N0Kn/PtZORW+sd5+C3B4N08oVekRn2z87wVMfEIoPNRfKgml1DZDCLX3UMJBNR8DCdJ1CaU0PpTPyM2lGdR4n//DHetU7Vz+FHjfxshLA0zV2OzqK/DuDztWHHO3rpyztYMCkkwFKYQGVmULtPxqCsMhf3SfFj3k56PCvC52an94+jOMC2n7Fcyv3sL70msSiN5nmA5fO//G2w1fObxbIBQ8udWHwdWde1kR3xotbDipfPAYepH/ZjumbZ4+ag8lW97B1aAPcXIFc3rCaqdTXuaFJnIijKaWtt5DMSc8gvsSJrjHydi+GOX2SJ6SU2Yqz21ehExGkNqNeDzo8KSIX9AR6IuNzJ6VrrdlwGrYAZrsjnO2Jsfg+goTSr7aDEwOsGLAFtSR+JubmfVZnXYejPLTilivpetRYR7ADvTE9IIcYPAOytjVYOR+KUQffnjn3p7PlnA3HsLLAgG1AziH946EYtIvITAq5cw32K/t+x75Bvtg8i8Hnq0fKpufg7+xAdIWLnzIVweBpbw+JRY+0118j0T1s8V7KFrh+FMKEcQ6iP8XbgcX7lRXyNgKo3Zf9Pi5lUjp52jy/q79dwMw5eWXL5z0CuiR6lTjRQzbDVFv9uufo6ErncLz7n3hnK0dJPZJKLcwxJ/vqfChNuQ8KsxDPl4gFHybPhCb6K8TZPf5oQfti+eQjH7deLK1Kew5vHcklKaG39F+tBF6b8ofHRSKjORNeaoWztloGfm8XwQE8/3iuak1Dm8hlE3ItfrcpPyOePavUyfyW14FK+GcrVBIvuwVAcF8r3BubIzDWwhlI3RtF1AvqalfGz7G38pSqxP5tWHfQjhn88vJ9/0hIJjvD8s6LXF4C6HUQU/KCAJbIMA52xZNSNEtERDMtwRsx+Ic3kIoOwIr1QUBHwHO2fxy8n1/CAjm+8OyTksc3kIoddCTMoLAFghwzrZFE1J0SwQE8y0B27E4h7cQyo7ASnVBwEeAcza/nHzfHwKC+f6wrNMSh7cQSh30pIwgsAUCnLNt0YQU3RIBwXxLwHYszuEthLIjsFJdEPAR4JzNLyff94eAYL4/LOu0xOEthFIHPSkjCGyBAOdsWzQhRbdEQDDfErAdi3N4lwhFFZS/goHYgNiA2IDYQJUNhDipQCihAnJPEBAEBAFBQBCog4AQSh2UpIwgIAgIAoLARgSEUDZCJAUEAUFAEBAE6iAghFIHJSkjCAgCgoAgsBGB/weiPKf2gQBQvAAAAABJRU5ErkJggg=="></p>
<p>This means the Currency Exchange counter would <strong>buy</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>USD</mtext></math> from a traveller and in exchange return <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>MYR</mtext></math> at a rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mtext>USD</mtext><mo>=</mo><mn>4</mn><mo>.</mo><mn>25</mn><mo> </mo><mtext>MYR</mtext></math>. There is no commission charged.</p>
<p>Criselda changed <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>460</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>SGD</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>MYR</mtext></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the amount of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>MYR</mtext></math> that Criselda received.</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>While in Kota Kinabalu, Criselda spent <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>440</mn><mo> </mo><mtext>MYR</mtext></math>. She returned to the Currency Exchange counter and changed the remainder of her <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>MYR</mtext></math> into <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>USD</mtext></math>.</p>
<p>Calculate the amount of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>USD</mtext></math> she received.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>460</mn><mo>×</mo><mn>3</mn><mo>.</mo><mn>07</mn></math> <span class="mjpage"> <em><strong>(A1)(M1)</strong></em><br></span></p>
<p><span class="mjpage"><strong>Note:</strong> Award<em><strong> (A1)</strong></em> for selecting <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>07</mn></math> as the exchange rate, <em><strong>(M1)</strong></em> for multiplying <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>460</mn></math> by an exchange rate from the table.<br></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1412</mn><mo> </mo><mfenced><mtext>MYR</mtext></mfenced></math> <em><strong>(A1)</strong></em><em><strong> (C3)</strong></em><br></span></p>
<p><span class="mjpage"><strong>Note:</strong> Do not award the final<em><strong> (A1)</strong></em> if the answer is to the wrong level of accuracy.</span></p>
<p><em><strong><span class="mjpage">[3 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>1412</mn><mo>-</mo><mn>440</mn></mrow><mrow><mn>4</mn><mo>.</mo><mn>45</mn></mrow></mfrac></math> <span class="mjpage"> <em><strong>(M1)(M1)</strong></em><br></span></p>
<p><span class="mjpage"><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct subtraction or for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>972</mn><mo> </mo><mfenced><mrow><mn>972</mn><mo>.</mo><mn>2</mn></mrow></mfenced></math> or <em>their</em> correct difference seen. Award <em><strong>(M1)</strong></em> for dividing by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>45</mn></math>. Follow through from part (a).<br></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>218</mn><mo> </mo><mfenced><mtext>USD</mtext></mfenced></math> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em><br></span></p>
<p><span class="mjpage"><strong>Note:</strong> Do not award the final<em><strong> (A1)</strong></em> if the answer is to the wrong level of accuracy.</span></p>
<p><em><strong><span class="mjpage">[3 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the graph of the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{3}{x} - 2,\,\,\,x \ne 0">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>3</mn>
<mi>x</mi>
</mfrac>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>≠<!-- ≠ --></mo>
<mn>0</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the vertical asymptote.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the horizontal asymptote.</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 value of <em>x</em> for which <em>f</em>(<em>x</em>) = 0 .</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><em>x</em> = 0 <em><strong>(A1)(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <em>x </em>= “a constant” <em><strong>(A1)</strong></em> for = 0. Award <em><strong>(A0)(A0)</strong></em> for an answer of “0”.</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><em>f</em>(<em>x</em>) = −2 (<em>y</em> = −2) <em><strong>(</strong><strong>A1)(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for y = “a constant” <em><strong>(A1)</strong></em> for = −2. Award <em><strong>(A0)(A0)</strong></em> for an answer of “−2”.</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="\frac{3}{x} - 2 = 0">
<mfrac>
<mn>3</mn>
<mi>x</mi>
</mfrac>
<mo>−</mo>
<mn>2</mn>
<mo>=</mo>
<mn>0</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating <em>f</em>(<em>x</em>) to 0.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {x = } \right)\frac{3}{2}\,\,\,\,\,\left( {1.5} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>=</mo>
</mrow>
<mo>)</mo>
</mrow>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>1.5</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong> (A1) (C2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows part of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mi>k</mi><mi>x</mi></mfrac></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>0</mn><mo>,</mo><mo> </mo><mi>k</mi><mo>></mo><mn>0</mn></math>.</p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>p</mi><mo>,</mo><mo> </mo><mfrac><mi>k</mi><mi>p</mi></mfrac></mrow></mfenced></math> be any point on the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>. Line <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math> is the tangent to the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>Line <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math> intersects the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mfenced><mrow><mn>2</mn><mi>p</mi><mo>,</mo><mo> </mo><mn>0</mn></mrow></mfenced></math> and the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axis at point B.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mfenced><mi>p</mi></mfenced></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mi>x</mi><mo>+</mo><msup><mi>p</mi><mn>2</mn></msup><mi>y</mi><mo>-</mo><mn>2</mn><mi>p</mi><mi>k</mi><mo>=</mo><mn>0</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AOB</mtext></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is translated by <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd></mtr></mtable></mfenced></math> to give the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math>.<br>In the following diagram:</p>
<ul>
<li>point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Q</mtext></math> lies on the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math>
</li>
<li>points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext></math> lie on the vertical asymptote of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math>
</li>
<li>points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math> lie on the horizontal asymptote of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math>
</li>
<li>point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>G</mtext></math> lies on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>FG</mtext></math> is parallel to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DC</mtext></math>.</li>
</ul>
<p>Line <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub></math> is the tangent to the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Q</mtext></math>, and passes through <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math>.</p>
<p><img src="data:image/png;base64,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"></p>
<p>Given that triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>EDF</mtext></math> and rectangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CDFG</mtext></math> have equal areas, find the gradient of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>.</p>
<div class="marks">[6]</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"><mi>f</mi><mo>'</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>-</mo><mi>k</mi><msup><mi>x</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></math> <em><strong> (A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mfenced><mi>p</mi></mfenced><mo>=</mo><mo>-</mo><mi>k</mi><msup><mi>p</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mo>-</mo><mfrac><mi>k</mi><msup><mi>p</mi><mn>2</mn></msup></mfrac></mrow></mfenced></math> <em><strong> A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to use point and gradient to find equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math> <em><strong>M1</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mfrac><mi>k</mi><mi>p</mi></mfrac><mo>=</mo><mo>-</mo><mi>k</mi><msup><mi>p</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><mfenced><mrow><mi>x</mi><mo>-</mo><mi>p</mi></mrow></mfenced><mo>,</mo><mo> </mo><mo> </mo><mfrac><mi>k</mi><mi>p</mi></mfrac><mo>=</mo><mo>-</mo><mfrac><mi>k</mi><msup><mi>p</mi><mn>2</mn></msup></mfrac><mfenced><mi>p</mi></mfenced><mo>+</mo><mi>b</mi></math></p>
<p>correct working leading to answer <em><strong> A1</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>p</mi><mn>2</mn></msup><mi>y</mi><mo>-</mo><mi>k</mi><mi>p</mi><mo>=</mo><mo>-</mo><mi>k</mi><mi>x</mi><mo>+</mo><mi>k</mi><mi>p</mi><mo>,</mo><mo> </mo><mo> </mo><mi>y</mi><mo>-</mo><mfrac><mi>k</mi><mi>p</mi></mfrac><mo>=</mo><mo>-</mo><mfrac><mi>k</mi><msup><mi>p</mi><mn>2</mn></msup></mfrac><mi>x</mi><mo>+</mo><mfrac><mi>k</mi><mi>p</mi></mfrac><mo>,</mo><mo> </mo><mo> </mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mi>k</mi><msup><mi>p</mi><mn>2</mn></msup></mfrac><mi>x</mi><mo>+</mo><mfrac><mrow><mn>2</mn><mi>k</mi></mrow><mi>p</mi></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mi>x</mi><mo>+</mo><msup><mi>p</mi><mn>2</mn></msup><mi>y</mi><mo>-</mo><mn>2</mn><mi>p</mi><mi>k</mi><mo>=</mo><mn>0</mn></math> <em><strong> AG N0</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1 – area of a triangle</strong></p>
<p>recognizing <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> <em><strong>(M1)</strong></em></p>
<p>correct working to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-coordinate of null<em><strong> (A1)</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>p</mi><mn>2</mn></msup><mi>y</mi><mo>-</mo><mn>2</mn><mi>p</mi><mi>k</mi><mo>=</mo><mn>0</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-coordinate of null at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi>k</mi></mrow><mi>p</mi></mfrac></math> (may be seen in area formula) <em><strong> A1</strong></em></p>
<p>correct substitution to find area of triangle<em><strong> (A1)</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mfenced><mrow><mn>2</mn><mi>p</mi></mrow></mfenced><mfenced><mfrac><mrow><mn>2</mn><mi>k</mi></mrow><mi>p</mi></mfrac></mfenced><mo>,</mo><mo> </mo><mo> </mo><mi>p</mi><mo>×</mo><mfenced><mfrac><mrow><mn>2</mn><mi>k</mi></mrow><mi>p</mi></mfrac></mfenced></math></p>
<p>area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AOB</mtext><mo>=</mo><mn>2</mn><mi>k</mi></math> <em><strong> A1 N3</strong></em></p>
<p> </p>
<p><strong>METHOD 2 – integration</strong></p>
<p>recognizing to integrate <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math> between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>p</mi></math> <em><strong>(M1)</strong></em></p>
<p><em>eg </em> <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>∫</mo><mn>0</mn><mrow><mn>2</mn><mi>p</mi></mrow></msubsup><msub><mi>L</mi><mrow><mn>1</mn><mo> </mo></mrow></msub><mo>d</mo><mi>x</mi><mo> </mo><mo>,</mo><mo> </mo><msubsup><mo>∫</mo><mn>0</mn><mrow><mn>2</mn><mi>p</mi></mrow></msubsup><mo>-</mo><mfrac><mi>k</mi><msup><mi>p</mi><mn>2</mn></msup></mfrac><mi>x</mi><mo>+</mo><mfrac><mrow><mn>2</mn><mi>k</mi></mrow><mi>p</mi></mfrac></math></p>
<p>correct integration of <strong>both</strong> terms <em><strong> A1</strong></em></p>
<p><em>eg </em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mrow><mi>k</mi><msup><mi>x</mi><mn>2</mn></msup></mrow><mrow><mn>2</mn><msup><mi>p</mi><mn>2</mn></msup></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><mi>k</mi><mi>x</mi></mrow><mi>p</mi></mfrac><mo> </mo><mo>,</mo><mo> </mo><mo>-</mo><mfrac><mi>k</mi><mrow><mn>2</mn><msup><mi>p</mi><mn>2</mn></msup></mrow></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mfrac><mrow><mn>2</mn><mi>k</mi></mrow><mi>p</mi></mfrac><mi>x</mi><mo>+</mo><mi>c</mi><mo> </mo><mo>,</mo><mo> </mo><msubsup><mfenced open="[" close="]"><mrow><mo>-</mo><mfrac><mi>k</mi><mrow><mn>2</mn><msup><mi>p</mi><mn>2</mn></msup></mrow></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mfrac><mrow><mn>2</mn><mi>k</mi></mrow><mi>p</mi></mfrac><mi>x</mi></mrow></mfenced><mn>0</mn><mrow><mn>2</mn><mi>p</mi></mrow></msubsup></math></p>
<p>substituting limits into <strong>their</strong> integrated function and subtracting (in either order) <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mrow><mi>k</mi><msup><mfenced><mrow><mn>2</mn><mi>p</mi></mrow></mfenced><mn>2</mn></msup></mrow><mrow><mn>2</mn><msup><mi>p</mi><mn>2</mn></msup></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><mi>k</mi><mfenced><mrow><mn>2</mn><mi>p</mi></mrow></mfenced></mrow><mi>p</mi></mfrac><mo>-</mo><mfenced><mn>0</mn></mfenced><mo>,</mo><mo> </mo><mo>-</mo><mfrac><mrow><mn>4</mn><mi>k</mi><msup><mi>p</mi><mn>2</mn></msup></mrow><mrow><mn>2</mn><msup><mi>p</mi><mn>2</mn></msup></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>4</mn><mi>k</mi><mi>p</mi></mrow><mi>p</mi></mfrac></math></p>
<p>correct working<em><strong> (A1)</strong></em></p>
<p><em>eg </em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mi>k</mi><mo>+</mo><mn>4</mn><mi>k</mi></math></p>
<p>area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AOB</mtext><mo>=</mo><mn>2</mn><mi>k</mi></math> <em><strong> A1 N3</strong></em></p>
<p> </p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>Note:</strong> In this question, the second <em><strong>M</strong></em> mark may be awarded independently of the other marks, so it is possible to award <em><strong>(M0)(A0)M1(A0)(A0)A0</strong></em>.</p>
<p> </p>
<p>recognizing use of transformation <em><strong>(M1)</strong></em></p>
<p><em>eg</em> area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AOB</mtext></math> = area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DEF</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mi>k</mi><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac><mo>+</mo><mn>3</mn><mo>,</mo></math> gradient of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub><mo>=</mo></math> gradient of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext><mfenced><mrow><mn>4</mn><mo>,</mo><mo> </mo><mn>3</mn></mrow></mfenced><mtext>, 2p+4, </mtext></math> one correct shift</p>
<p>correct working<em><strong> (A1)</strong></em></p>
<p><em>eg</em> area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DEF</mtext><mo>=</mo><mn>2</mn><mi>k</mi><mo>,</mo><mo> </mo><mtext>CD</mtext><mo>=</mo><mn>3</mn><mo>,</mo><mo> </mo><mtext>DF</mtext><mo>=</mo><mn>2</mn><mi>p</mi><mo>,</mo><mo> </mo><mtext>CG</mtext><mo>=</mo><mn>2</mn><mi>p</mi><mo>,</mo><mo> </mo><mtext>E</mtext><mfenced><mrow><mn>4</mn><mo>,</mo><mo> </mo><mfrac><mrow><mn>2</mn><mi>k</mi></mrow><mi>p</mi></mfrac><mo>+</mo><mn>3</mn></mrow></mfenced><mo>,</mo><mo> </mo><mtext>F</mtext><mfenced><mrow><mn>2</mn><mi>p</mi><mo>+</mo><mn>4</mn><mo>,</mo><mo> </mo><mn>3</mn></mrow></mfenced><mo>,</mo><mo> </mo><mtext>Q</mtext><mfenced><mrow><mi>p</mi><mo>+</mo><mn>4</mn><mo>,</mo><mo> </mo><mfrac><mi>k</mi><mi>p</mi></mfrac><mo>+</mo><mn>3</mn></mrow></mfenced><mo>,</mo></math> </p>
<p>gradient of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub><mo>=</mo><mo>-</mo><mfrac><mi>k</mi><msup><mi>p</mi><mn>2</mn></msup></mfrac><mo>,</mo><mo> </mo><mi>g</mi><mo>'</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>-</mo><mfrac><mi>k</mi><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mn>2</mn></msup></mfrac><mo>,</mo></math> area of rectangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CDFG</mtext><mo>=</mo><mn>2</mn><mi>k</mi></math></p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>ED</mtext><mo>×</mo><mtext>DF</mtext></mrow><mn>2</mn></mfrac><mo>=</mo><mtext>CD</mtext><mo>×</mo><mtext>DF</mtext><mo>,</mo><mo> </mo><mn>2</mn><mi>p</mi><mo>·</mo><mn>3</mn><mo>=</mo><mn>2</mn><mi>k</mi><mo> </mo><mo>,</mo><mo> </mo><mtext>ED</mtext><mo>=</mo><mn>2</mn><mtext>CD</mtext><mo> </mo><mo>,</mo><mo> </mo><msubsup><mo>∫</mo><mn>4</mn><mrow><mn>2</mn><mi>p</mi><mo>+</mo><mn>4</mn></mrow></msubsup><msub><mi>L</mi><mn>2</mn></msub><mo> </mo><mtext>d</mtext><mi>x</mi><mo>=</mo><mn>4</mn><mi>k</mi></math></p>
<p>correct working<em> <strong>(A1)</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ED</mtext><mo>=</mo><mn>6</mn><mo>,</mo><mo> </mo><mtext>E</mtext><mfenced><mrow><mn>4</mn><mo>,</mo><mo> </mo><mn>9</mn></mrow></mfenced><mo>,</mo><mo> </mo><mi>k</mi><mo>=</mo><mn>3</mn><mi>p</mi><mo>,</mo><mo> </mo><mtext>gradient</mtext><mo>=</mo><mfrac><mrow><mn>3</mn><mo>-</mo><mfenced><mrow><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mi>k</mi></mrow><mi>p</mi></mfrac></mstyle><mo>+</mo><mn>3</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mn>2</mn><mi>p</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mo>-</mo><mn>4</mn></mrow></mfrac><mo>,</mo><mo> </mo><mfrac><mrow><mo>-</mo><mn>6</mn></mrow><mfenced><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mi>k</mi></mrow><mn>3</mn></mfrac></mstyle></mfenced></mfrac><mo>,</mo><mo> </mo><mo>-</mo><mfrac><mn>9</mn><mi>k</mi></mfrac></math></p>
<p>correct expression for gradient (in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>)<em><strong> (A1)</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>6</mn></mrow><mrow><mn>2</mn><mi>p</mi></mrow></mfrac><mo>,</mo><mo> </mo><mfrac><mrow><mn>9</mn><mo>-</mo><mn>3</mn></mrow><mrow><mn>4</mn><mo>-</mo><mfenced><mrow><mn>2</mn><mi>p</mi><mo>+</mo><mn>4</mn></mrow></mfenced></mrow></mfrac><mo>,</mo><mo> </mo><mo>-</mo><mfrac><mrow><mn>3</mn><mi>p</mi></mrow><msup><mi>p</mi><mn>2</mn></msup></mfrac><mo>,</mo><mo> </mo><mfrac><mrow><mn>3</mn><mo>-</mo><mfenced><mrow><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mfenced><mrow><mn>3</mn><mi>p</mi></mrow></mfenced></mrow><mi>p</mi></mfrac></mstyle><mo>+</mo><mn>3</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mn>2</mn><mi>p</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mstyle displaystyle="true"><mo>-</mo></mstyle><mstyle displaystyle="true"><mn>4</mn></mstyle></mrow></mfrac><mo>,</mo><mo> </mo><mo>-</mo><mfrac><mn>9</mn><mrow><mn>3</mn><mi>p</mi></mrow></mfrac></math></p>
<p>gradient of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>3</mn><mi>p</mi></mfrac><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mo>-</mo><mn>3</mn><msup><mi>p</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></mfenced></math> <em><strong> A1 N3</strong></em></p>
<p><em><strong>[6 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">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>M-Line is a company that prints and sells custom designs on T-shirts. For each order, they charge an initial design fee and then an additional fee for each printed T-shirt.</p>
<p>M-Line charges <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="M">
<mi>M</mi>
</math></span> euros per order. This charge is modelled by the linear function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="M\left( x \right) = 5x + 40">
<mi>M</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>5</mn>
<mi>x</mi>
<mo>+</mo>
<mn>40</mn>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> is the number of T-shirts in the order.</p>
</div>
<div class="specification">
<p>EnYear is another company that prints and sells T-shirts. The price, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
<mi>N</mi>
</math></span> euros, that they charge for an order can be modelled by the linear function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N\left( x \right) = 9x">
<mi>N</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>9</mn>
<mi>x</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> is the number of T-shirts in the order.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the initial design fee charged for each order.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total amount charged for an order of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="94"> <mn>94</mn> </math></span> T-shirts.</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>Write down the number of T-shirts in an order for which EnYear charged <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="63"> <mn>63</mn> </math></span> euros.</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>An order of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span> T-shirts will be charged the same price by both M-Line and EnYear.</p>
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="40"> <mn>40</mn> </math></span> (euros) <em><strong>(A1) (C1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {M\left( {94} \right) = } \right)5\left( {94} \right) + 40"> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mrow> <mo>(</mo> <mrow> <mn>94</mn> </mrow> <mo>)</mo> </mrow> <mo>=</mo> </mrow> <mo>)</mo> </mrow> <mn>5</mn> <mrow> <mo>(</mo> <mrow> <mn>94</mn> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>40</mn> </math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="94"> <mn>94</mn> </math></span> into given function.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="510"> <mn>510</mn> </math></span> (euros) <em><strong>(A1) (C2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7"> <mn>7</mn> </math></span> (T-shirts) <em><strong>(A1) (C1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="9p = 5p + 40"> <mn>9</mn> <mi>p</mi> <mo>=</mo> <mn>5</mn> <mi>p</mi> <mo>+</mo> <mn>40</mn> </math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating the given functions. Accept a sketch showing both functions.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {p = } \right)\,\,10"> <mrow> <mo>(</mo> <mrow> <mi>p</mi> <mo>=</mo> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>10</mn> </math></span> (T-shirts) <em><strong>(A1) (C2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[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>Jean-Pierre jumps out of an airplane that is flying at constant altitude. Before opening his parachute, he goes through a period of freefall.</p>
<p>Jean-Pierre’s vertical speed during the time of freefall, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math>, in <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>m s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, is modelled by the following function.</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mi>K</mi><mo>-</mo><mn>60</mn><mfenced><mrow><mn>1</mn><mo>.</mo><msup><mn>2</mn><mrow><mo>-</mo><mi>t</mi></mrow></msup></mrow></mfenced><mo> </mo><mo>,</mo><mo> </mo><mi>t</mi><mo>≥</mo><mn>0</mn></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>, is the number of seconds after he jumps out of the airplane, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math> is a constant. A sketch of Jean-Pierre’s vertical speed against time is shown below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">Jean-Pierre’s initial vertical speed is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo> </mo><msup><mtext>m s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the context of the model, state what the horizontal asymptote represents.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find Jean-Pierre’s vertical speed after <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> seconds. Give your answer in <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>km</mtext><mo> </mo><msup><mtext>h</mtext><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> .</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>=</mo><mi>K</mi><mo>-</mo><mn>60</mn><mfenced><mrow><mn>1</mn><mo>.</mo><msup><mn>2</mn><mn>0</mn></msup></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted function equated to zero.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>K</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>60</mn></math> <em><strong>(A1) (C2)</strong></em></p>
<p><em><strong><br></strong></em><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the (vertical) speed that Jean-Pierre is approaching (as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> increases) <em><strong>(A1) (C1)<br></strong></em><strong>OR<br></strong>the limit of the (vertical) speed of Jean-Pierre <em><strong>(A1) (C1)</strong></em></p>
<p><em><strong><br></strong></em><strong>Note: </strong>Accept “maximum speed” or “terminal speed”.</p>
<p><em><strong><br></strong></em><em><strong>[1 mark]</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>S</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>60</mn><mo>-</mo><mn>60</mn><mfenced><mrow><mn>1</mn><mo>.</mo><msup><mn>2</mn><mrow><mo>-</mo><mn>10</mn></mrow></msup></mrow></mfenced></math> <em><strong>(M1)<br></strong></em></p>
<p><strong><br></strong><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted function.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>S</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>50</mn><mo>.</mo><mn>3096</mn><mo>…</mo><mo> </mo><mfenced><msup><mtext>m s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></mfenced></math> <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong><br>Note: </strong>Follow through from part (a).</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>181</mn><mo> </mo><mfenced><msup><mtext>km h</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mn>181</mn><mo>.</mo><mn>114</mn><mo>…</mo><mo> </mo><mfenced><msup><mtext>km h</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></mfenced></mrow></mfenced></math> <em><strong>(A1)</strong></em><strong>(ft) <em> (C3)</em></strong></p>
<p><br><strong>Note:</strong> Award the final <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct conversion of their speed to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>km</mtext><mo> </mo><msup><mtext>h</mtext><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>.</p>
<p><em><strong><br></strong></em><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Three towns, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> are represented as coordinates on a map, where the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> axes represent the distances east and north of an origin, respectively, measured in kilometres.</p>
<p>Town <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> is located at <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>−</mo><mn>6</mn><mo>,</mo><mo> </mo><mo>−</mo><mn>1</mn><mo>)</mo></math> and town <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> is located at <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>8</mn><mo>,</mo><mo> </mo><mn>6</mn><mo>)</mo></math>. A road runs along the perpendicular bisector of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[AB]</mtext></math>. This information is 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 equation of the line that the road follows.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Town <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> is due north of town <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and the road passes through town <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>.</p>
<p>Find the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-coordinate of town <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>midpoint <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>,</mo><mo> </mo><mn>2</mn><mo>.</mo><mn>5</mn><mo>)</mo></math> <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>m</mi><mrow><mi>A</mi><mi>B</mi></mrow></msub><mo>=</mo><mfrac><mrow><mn>6</mn><mo>-</mo><mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mn>8</mn><mo>-</mo><mfenced><mrow><mo>-</mo><mn>6</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math> <em><strong>(M1)A1</strong></em></p>
<p><br><strong>Note:</strong> Accept equivalent gradient statements including using midpoint.</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>m</mi><mo>⊥</mo></msub><mo>=</mo><mo>-</mo><mn>2</mn></math> <em><strong>M1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong> </em>for finding the negative reciprocal of their gradient.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mn>2</mn><mo>.</mo><mn>5</mn><mo>=</mo><mo>-</mo><mn>2</mn><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>2</mn><mi>x</mi><mo>+</mo><mfrac><mn>9</mn><mn>2</mn></mfrac></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>-</mo><mn>9</mn><mo>=</mo><mn>0</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>substituting <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>6</mn></math> into their equation from part (a) <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>2</mn><mfenced><mrow><mo>-</mo><mn>6</mn></mrow></mfenced><mo>+</mo><mfrac><mn>9</mn><mn>2</mn></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>16</mn><mo>.</mo><mn>5</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1A0</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>6</mn><mo>,</mo><mo> </mo><mn>16</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math> as their final answer.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>A large proportion of candidates seemed to be well drilled into finding the gradient of a line and the subsequent gradient of the normal. But without finding the coordinates of the midpoint of AB, no more marks were gained.</p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates worked out the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> correctly (or “correct” following the value they found in part (a)) but then incorrectly gave their answer as a coordinate pair.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph of a quadratic function has <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept 10 and <strong>one </strong>of its <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercepts is 1.</p>
<p>The <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-coordinate of the vertex of the graph is 3.</p>
<p>The equation of the quadratic function is in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = a{x^2} + bx + c">
<mi>y</mi>
<mo>=</mo>
<mi>a</mi>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>b</mi>
<mi>x</mi>
<mo>+</mo>
<mi>c</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
<mi>c</mi>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the second <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercept of the function.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>10 <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(0,{\text{ }}10)">
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>10</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3 = \frac{{ - b}}{{2a}}">
<mn>3</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mo>−</mo>
<mi>b</mi>
</mrow>
<mrow>
<mn>2</mn>
<mi>a</mi>
</mrow>
</mfrac>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 = a{(1)^2} + b(1) + c">
<mn>0</mn>
<mo>=</mo>
<mi>a</mi>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>b</mi>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mi>c</mi>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10 = a{(6)^2} + b(6) + c">
<mn>10</mn>
<mo>=</mo>
<mi>a</mi>
<mrow>
<mo stretchy="false">(</mo>
<mn>6</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>b</mi>
<mo stretchy="false">(</mo>
<mn>6</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mi>c</mi>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 = a{(5)^2} + b(5) + c">
<mn>0</mn>
<mo>=</mo>
<mi>a</mi>
<mrow>
<mo stretchy="false">(</mo>
<mn>5</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>b</mi>
<mo stretchy="false">(</mo>
<mn>5</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mi>c</mi>
</math></span> <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for each of the above equations, provided they are not equivalent, up to a maximum of <strong><em>(M1)(M1)</em></strong>. Accept equations that substitute their 10 for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
<mi>c</mi>
</math></span>.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>sketch graph showing given information: intercepts <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(1,{\text{ }}0)">
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(0,{\text{ }}10)">
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>10</mn>
<mo stretchy="false">)</mo>
</math></span> and line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 3">
<mi>x</mi>
<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="y = a(x - 1)(x - 5)">
<mi>y</mi>
<mo>=</mo>
<mi>a</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−</mo>
<mn>5</mn>
<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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(x - 1)(x - 5)">
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−</mo>
<mn>5</mn>
<mo stretchy="false">)</mo>
</math></span> seen.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 2">
<mi>a</mi>
<mo>=</mo>
<mn>2</mn>
</math></span> <strong><em>(A1)</em>(ft)</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = - 12">
<mi>b</mi>
<mo>=</mo>
<mo>−</mo>
<mn>12</mn>
</math></span> <strong><em>(A1)</em>(ft)</strong> <strong><em>(C4)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (a).</p>
<p>If it is not clear which is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> and which is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span> award at most <strong><em>(A0)(A1)(ft)</em></strong>.</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>5 <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> intersects the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis at point A and the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis at point B, as shown on the diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_17.18.01.png" alt="M17/5/MATSD/SP1/ENG/TZ2/04"></p>
<p>The length of line segment OB is three times the length of line segment OA, where O is the origin.</p>
</div>
<div class="specification">
<p>Point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{(2, 6)}}">
<mrow>
<mtext>(2, 6)</mtext>
</mrow>
</math></span> lies on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the gradient of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</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">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-coordinate of point A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 3">
<mo>−</mo>
<mn>3</mn>
</math></span> <strong><em>(A1)(A1)</em></strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(A1) </em></strong>for 3 and <strong><em>(A1) </em></strong>for a negative value.</p>
<p>Award <strong><em>(A1)(A0) </em></strong>for either <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3x">
<mn>3</mn>
<mi>x</mi>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 3x">
<mo>−</mo>
<mn>3</mn>
<mi>x</mi>
</math></span>.</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="6 = - 3(2) + c">
<mn>6</mn>
<mo>=</mo>
<mo>−</mo>
<mn>3</mn>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mi>c</mi>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><strong>OR</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(y - 6) = - 3(x - 2)">
<mo stretchy="false">(</mo>
<mi>y</mi>
<mo>−</mo>
<mn>6</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mo>−</mo>
<mn>3</mn>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
<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 substitution of their gradient from part (a) into a correct equation with the coordinates <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(2,{\text{ }}6)">
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>6</mn>
<mo stretchy="false">)</mo>
</math></span> correctly substituted.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - 3x + 12">
<mi>y</mi>
<mo>=</mo>
<mo>−</mo>
<mn>3</mn>
<mi>x</mi>
<mo>+</mo>
<mn>12</mn>
</math></span> <strong><em>(A1)(</em>ft)</strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(A1)(</em>ft) </strong>for their correct equation. Follow through from part (a).</p>
<p>If no method seen, award <strong><em>(A1)(A0) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - 3x">
<mi>y</mi>
<mo>=</mo>
<mo>−</mo>
<mn>3</mn>
<mi>x</mi>
</math></span>.</p>
<p>Award <strong><em>(A1)(A0) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 3x + 12">
<mo>−</mo>
<mn>3</mn>
<mi>x</mi>
<mo>+</mo>
<mn>12</mn>
</math></span>.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 = - 3x + 12">
<mn>0</mn>
<mo>=</mo>
<mo>−</mo>
<mn>3</mn>
<mi>x</mi>
<mo>+</mo>
<mn>12</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substitution of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 0">
<mi>y</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> in their equation from part (b).</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(x = ){\text{ }}4">
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>4</mn>
</math></span> <strong><em>(A1)</em>(ft)</strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Follow through from their equation from part (b). Do not follow through if no method seen. Do not award the final <strong><em>(A1) </em></strong>if the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> is negative or zero.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A potter sells <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> vases per month.</p>
<p>His monthly profit in Australian dollars (AUD) can be modelled by</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="P\left( x \right) = - \frac{1}{5}{x^3} + 7{x^2} - 120{\text{,}}\,\,x \geqslant 0.">
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mfrac>
<mn>1</mn>
<mn>5</mn>
</mfrac>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>7</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>120</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>⩾<!-- ⩾ --></mo>
<mn>0.</mn>
</math></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P">
<mi>P</mi>
</math></span> if no vases are sold.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Differentiate <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P\left( x \right)">
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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>−120 (AUD) <em><strong>(A1) (C1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \frac{3}{5}{x^2} + 14x">
<mo>−</mo>
<mfrac>
<mn>3</mn>
<mn>5</mn>
</mfrac>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>14</mn>
<mi>x</mi>
</math></span> <em><strong>(A1)(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct term. Award at most <em><strong>(A1)(A0)</strong></em> for extra terms seen.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>In this question, give all answers to two decimal places.</strong></p>
<p>Karl invests 1000 US dollars (USD) in an account that pays a nominal annual interest of 3.5%, <strong>compounded quarterly</strong>. He leaves the money in the account for 5 years.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the amount of money he has in the account after 5 years.</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>Write down the amount of <strong>interest</strong> he earned after 5 years.</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>Karl decides to donate this <strong>interest</strong> to a charity in France. The charity receives 170 euros (EUR). The exchange rate is 1 USD = <em>t</em> EUR.</p>
<p>Calculate the value of <em>t</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1000{\left( {1 + \frac{{3.5}}{{4 \times 100}}} \right)^{4 \times 5}}">
<mn>1000</mn>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<mrow>
<mn>3.5</mn>
</mrow>
<mrow>
<mn>4</mn>
<mo>×</mo>
<mn>100</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mn>4</mn>
<mo>×</mo>
<mn>5</mn>
</mrow>
</msup>
</mrow>
</math></span> <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution in compound interest formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p><strong>OR </strong></p>
<p><em>N</em> = 5</p>
<p><em>I</em> = 3.5</p>
<p><em>PV</em> = 1000</p>
<p><em>P</em>/<em>Y</em> = 1</p>
<p><em>C</em>/<em>Y</em> = 4</p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <em>C</em>/<em>Y</em> = 4 seen, <em><strong>(M1)</strong></em> for other correct entries.</p>
<p><strong>OR</strong></p>
<p><em>N</em> = 5 × 4</p>
<p><em>I</em> = 3.5</p>
<p><em>PV</em> = 1000</p>
<p><em>P</em>/<em>Y</em> = 1</p>
<p><em>C</em>/<em>Y</em> = 4</p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <em>C</em>/<em>Y</em> = 4 seen, <em><strong>(M1)</strong></em> for other correct entries.</p>
<p>= 1190.34 (USD) <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution in compound interest formula, <em><strong>(A1)</strong></em> for correct substitution.</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>190.34 (USD) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C4)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for subtraction of 1000 from their part (a)(i). Follow through from (a)(i).</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{170}}{{190.34}}">
<mfrac>
<mrow>
<mn>170</mn>
</mrow>
<mrow>
<mn>190.34</mn>
</mrow>
</mfrac>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for division of 170 by their part (a)(ii).</p>
<p>= 0.89 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their part (a)(ii).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider a function <em>f </em>(<em>x</em>) , for −2 ≤ <em>x</em> ≤ 2 . The following diagram shows the graph of <em>f</em>.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="question">
<p>On the grid above, sketch the graph of <em>f </em><sup>−1</sup>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><img 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"><strong>A1</strong><strong>A1A1A1 N4</strong></p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> for evidence of approximately correct reflection in <em>y</em> = <em>x</em> with correct curvature.</p>
<p>(<em>y</em> = <em>x</em> does not need to be explicitly seen)</p>
<p>Only if this mark is awarded, award marks as follows:</p>
<p><em><strong>A1</strong></em> for both correct invariant points in circles,</p>
<p><em><strong>A1</strong></em> for the three other points in circles,</p>
<p><em><strong>A1</strong></em> for correct domain.</p>
<p><em><strong>[4 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 1 + {{\text{e}}^{ - x}}">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>1</mn>
<mo>+</mo>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mi>x</mi>
</mrow>
</msup>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = 2x + b">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span> is a constant.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(g \circ f)(x)">
<mo stretchy="false">(</mo>
<mi>g</mi>
<mo>∘</mo>
<mi>f</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {\lim }\limits_{x \to + \infty } (g \circ f)(x) = - 3">
<munder>
<mrow>
<mo form="prefix">lim</mo>
</mrow>
<mrow>
<mi>x</mi>
<mo stretchy="false">→</mo>
<mo>+</mo>
<mi mathvariant="normal">∞</mi>
</mrow>
</munder>
<mo></mo>
<mo stretchy="false">(</mo>
<mi>g</mi>
<mo>∘</mo>
<mi>f</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mo>−</mo>
<mn>3</mn>
</math></span>, find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>attempt to form composite <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(1 + {{\text{e}}^{ - x}})">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>+</mo>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mi>x</mi>
</mrow>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</math></span></p>
<p>correct function <strong><em>A1 N2</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(g \circ f)(x) = 2 + b + 2{{\text{e}}^{ - x}},{\text{ }}2(1 + {{\text{e}}^{ - x}}) + b">
<mo stretchy="false">(</mo>
<mi>g</mi>
<mo>∘</mo>
<mi>f</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>2</mn>
<mo>+</mo>
<mi>b</mi>
<mo>+</mo>
<mn>2</mn>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mi>x</mi>
</mrow>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>2</mn>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>+</mo>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mi>x</mi>
</mrow>
</msup>
</mrow>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mi>b</mi>
</math></span></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>evidence of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {\lim }\limits_{x \to \infty } (2 + b + 2{{\text{e}}^{ - x}}) = 2 + b + \mathop {\lim }\limits_{x \to \infty } (2{{\text{e}}^{ - x}})">
<munder>
<mrow>
<mo form="prefix">lim</mo>
</mrow>
<mrow>
<mi>x</mi>
<mo stretchy="false">→</mo>
<mi mathvariant="normal">∞</mi>
</mrow>
</munder>
<mo></mo>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo>+</mo>
<mi>b</mi>
<mo>+</mo>
<mn>2</mn>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mi>x</mi>
</mrow>
</msup>
</mrow>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>2</mn>
<mo>+</mo>
<mi>b</mi>
<mo>+</mo>
<munder>
<mrow>
<mo form="prefix">lim</mo>
</mrow>
<mrow>
<mi>x</mi>
<mo stretchy="false">→</mo>
<mi mathvariant="normal">∞</mi>
</mrow>
</munder>
<mo></mo>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mi>x</mi>
</mrow>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2 + b + 2{{\text{e}}^{ - \infty }}">
<mn>2</mn>
<mo>+</mo>
<mi>b</mi>
<mo>+</mo>
<mn>2</mn>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mi mathvariant="normal">∞</mi>
</mrow>
</msup>
</mrow>
</math></span>, graph with horizontal asymptote when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \to \infty ">
<mi>x</mi>
<mo stretchy="false">→</mo>
<mi mathvariant="normal">∞</mi>
</math></span></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>M0 </em></strong>if candidate clearly has incorrect limit, such as <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \to 0,{\text{ }}{{\text{e}}^\infty },{\text{ }}2{{\text{e}}^0}">
<mi>x</mi>
<mo stretchy="false">→</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mi mathvariant="normal">∞</mi>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>2</mn>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mn>0</mn>
</msup>
</mrow>
</math></span>.</p>
<p> </p>
<p>evidence that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{e}}^{ - x}} \to 0">
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mi>x</mi>
</mrow>
</msup>
</mrow>
<mo stretchy="false">→</mo>
<mn>0</mn>
</math></span> (seen anywhere) <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {\lim }\limits_{x \to \infty } ({{\text{e}}^{ - x}}) = 0,{\text{ }}1 + {{\text{e}}^{ - x}} \to 1,{\text{ }}2(1) + b = - 3,{\text{ }}{{\text{e}}^{{\text{large negative number}}}} \to 0">
<munder>
<mrow>
<mo form="prefix">lim</mo>
</mrow>
<mrow>
<mi>x</mi>
<mo stretchy="false">→</mo>
<mi mathvariant="normal">∞</mi>
</mrow>
</munder>
<mo></mo>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mi>x</mi>
</mrow>
</msup>
</mrow>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>1</mn>
<mo>+</mo>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mi>x</mi>
</mrow>
</msup>
</mrow>
<mo stretchy="false">→</mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>2</mn>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mi>b</mi>
<mo>=</mo>
<mo>−</mo>
<mn>3</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mrow>
<mtext>large negative number</mtext>
</mrow>
</mrow>
</msup>
</mrow>
<mo stretchy="false">→</mo>
<mn>0</mn>
</math></span>, graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = {{\text{e}}^{ - x}}">
<mi>y</mi>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mi>x</mi>
</mrow>
</msup>
</mrow>
</math></span> or</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 2{{\text{e}}^{ - x}}">
<mi>y</mi>
<mo>=</mo>
<mn>2</mn>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mi>x</mi>
</mrow>
</msup>
</mrow>
</math></span> with asymptote <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 0">
<mi>y</mi>
<mo>=</mo>
<mn>0</mn>
</math></span>, graph of composite function with asymptote <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - 3">
<mi>y</mi>
<mo>=</mo>
<mo>−</mo>
<mn>3</mn>
</math></span></p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2 + b = - 3">
<mn>2</mn>
<mo>+</mo>
<mi>b</mi>
<mo>=</mo>
<mo>−</mo>
<mn>3</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = - 5">
<mi>b</mi>
<mo>=</mo>
<mo>−</mo>
<mn>5</mn>
</math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br>