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<h2>HL Paper 1</h2><div class="specification">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - {x^3}">
<mi>y</mi>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
</math></span> is transformed onto the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 33 - 0.08{x^3}">
<mi>y</mi>
<mo>=</mo>
<mn>33</mn>
<mo>−<!-- − --></mo>
<mn>0.08</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
</math></span> by a translation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> units vertically and a stretch parallel to the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis of scale factor <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</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="a">
<mi>a</mi>
</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 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">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The outer dome of a large cathedral has the shape of a hemisphere of diameter 32 m, supported by vertical walls of height 17 m. It is also supported by an inner dome which can be modelled by rotating the curve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 33 - 0.08{x^3}">
<mi>y</mi>
<mo>=</mo>
<mn>33</mn>
<mo>−</mo>
<mn>0.08</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
</math></span> through 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> = 0 and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> = 33, as indicated in the diagram.</p>
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"></p>
<p>Find the volume of the space between the two domes.</p>
<div class="marks">[5]</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="a">
<mi>a</mi>
</math></span> = 33 <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="\frac{1}{{\sqrt[3]{{0.08}}}} = 2.32">
<mfrac>
<mn>1</mn>
<mrow>
<mroot>
<mrow>
<mn>0.08</mn>
</mrow>
<mn>3</mn>
</mroot>
</mrow>
</mfrac>
<mo>=</mo>
<mn>2.32</mn>
</math></span> <em><strong> M1A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>volume within outer dome</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{2}{3}\pi + {16^3} + \pi \times {16^2} \times 17 = 22\,250.85">
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mi>π</mi>
<mo>+</mo>
<mrow>
<msup>
<mn>16</mn>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>π</mi>
<mo>×</mo>
<mrow>
<msup>
<mn>16</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>17</mn>
<mo>=</mo>
<mn>22</mn>
<mspace width="thinmathspace"></mspace>
<mn>250.85</mn>
</math></span> <em><strong> M1A1</strong></em></p>
<p>volume within inner dome</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {\int_0^{33} {\left( {\frac{{33 - y}}{{0.08}}} \right)} ^{\frac{2}{3}}}{\text{d}}y = 3446.92">
<mi>π</mi>
<mrow>
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mrow>
<mn>33</mn>
</mrow>
</msubsup>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>33</mn>
<mo>−</mo>
<mi>y</mi>
</mrow>
<mrow>
<mn>0.08</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>y</mi>
<mo>=</mo>
<mn>3446.92</mn>
</math></span> <em><strong> M1A1</strong></em></p>
<p>volume between = 22 250.85 − 3446.92 = 18 803.93 m<sup>3</sup> <em><strong> A1</strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The 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 given on the following set of axes. The graph passes through the points <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>−</mo><mn>2</mn><mo>,</mo><mo> </mo><mn>6</mn><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>)</mo></math>, and has a horizontal asymptote at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn></math>.</p>
<p><img src="data:image/png;base64,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"></p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>2</mn><mi>f</mi><mo>(</mo><mi>x</mi><mo>−</mo><mn>2</mn><mo>)</mo><mo>+</mo><mn>4</mn></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>g</mi><mo>(</mo><mn>0</mn><mo>)</mo></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>On the same set of axes draw the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>, showing any intercepts and asymptotes.</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>g</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>16</mn></math> <em><strong>M1A1</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><img 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"></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-asymptote <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>y</mi><mo>=</mo><mn>4</mn></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p>concave up decreasing curve and passing through <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>16</mn><mo>)</mo></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;">
<p>This question was not particularly well done. Candidates often failed to apply the transformation of the function correctly and did not understand how to use the algebra of graphical transformations. Others applied the geometry of stretches and translations, often incorrectly. Even if the graph was drawn correctly, some candidates failed to follow the instruction to show the asymptote.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was not particularly well done. Candidates often failed to apply the transformation of the function correctly and did not understand how to use the algebra of graphical transformations. Others applied the geometry of stretches and translations, often incorrectly. Even if the graph was drawn correctly, some candidates failed to follow the instruction to show the asymptote.</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>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="specification">
<p>The number of earthquakes in a given year with a magnitude of at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>2</mn></math> can be modelled by a Poisson distribution, with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math>. The number of earthquakes in one year is independent of the number of earthquakes in any other year.</p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi></math> be the number of years between the earthquake of magnitude <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>2</mn></math> and the next earthquake of at least this magnitude.</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>Find the average number of earthquakes in a year with a magnitude of at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>2</mn></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>Y</mi><mo>></mo><mn>100</mn><mo>)</mo></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><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><strong><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><mn>0</mn><mo>.</mo><mn>00631</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>0063095</mn><mo>…</mo></mrow></mfenced></math></strong> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Do not accept an answer of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn><mo>.</mo><mn>2</mn></mrow></msup></math>.</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mo>></mo><mn>100</mn><mo>⇒</mo></math>no earthquakes in the first <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math> years <strong><em>(M1)</em></strong></p>
<p><br><strong>EITHER</strong></p>
<p>let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> be the number of earthquakes of at least magnitude <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>2</mn></math> in a year</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>~</mo><mtext>Po</mtext><mfenced><mrow><mn>0</mn><mo>.</mo><mn>0063095</mn><mo>…</mo></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>=</mo><mn>0</mn></mrow></mfenced></mrow></mfenced><mn>100</mn></msup></math> <strong><em>(M1)</em></strong></p>
<p><br><strong>OR</strong></p>
<p>let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> be the number of earthquakes in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math> years</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>~</mo><mtext>Po</mtext><mfenced><mrow><mn>0</mn><mo>.</mo><mn>0063095</mn><mo>…</mo><mo>×</mo><mn>100</mn></mrow></mfenced></math> <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>=</mo><mn>0</mn></mrow></mfenced></math></p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>532</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>532082</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mo>></mo><mn>100</mn><mo>⇒</mo></math>no earthquakes in the first <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math> years <strong><em>(M1)</em></strong></p>
<p>let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> be the number of earthquakes in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math> years</p>
<p>since <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> is large and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> is small</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>~</mo><mtext>B</mtext><mfenced><mrow><mn>100</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>0063095</mn><mo>…</mo></mrow></mfenced></math> <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>=</mo><mn>0</mn></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>531</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>531019</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Parts (a), (b), and (c) were accessible to many candidates who earned full marks with the manipulation of logs and indices presenting no problems. Part (d), however, proved to be too difficult for most and very few correct attempts were seen. As in question 9, most candidates relied on calculator notation when using the Poisson distribution. The discipline of defining a random variable in terms of its distribution and parameters helps to conceptualize the problem in terms that aid a better understanding. Most candidates who attempted this question blindly entered values into the Poisson distribution calculator and were unable to earn any marks. There were a couple of correct solutions using a binomial distribution to approximate the given quantity.</p>
<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="question">
<p>The rate, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A">
<mi>A</mi>
</math></span>, of a chemical reaction at a fixed temperature is related to the concentration of two compounds, <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>, by the equation</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = k{B^x}{C^y}">
<mi>A</mi>
<mo>=</mo>
<mi>k</mi>
<mrow>
<msup>
<mi>B</mi>
<mi>x</mi>
</msup>
</mrow>
<mrow>
<msup>
<mi>C</mi>
<mi>y</mi>
</msup>
</mrow>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k \in \mathbb{R}">
<mi>k</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
<p>A scientist measures the three variables three times during the reaction and obtains the following values.</p>
<p><img style="display: block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</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="{\text{log}}\,A = x\,{\text{log}}\,B + y\,{\text{log}}\,C + {\text{log}}\,k">
<mrow>
<mtext>log</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>A</mi>
<mo>=</mo>
<mi>x</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>log</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>B</mi>
<mo>+</mo>
<mi>y</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>log</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>C</mi>
<mo>+</mo>
<mrow>
<mtext>log</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
</math></span> <em><strong>(M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{log}}\,5.74 = x\,{\text{log}}\,2.1 + y\,{\text{log}}\,3.4 + {\text{log}}\,k">
<mrow>
<mtext>log</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>5.74</mn>
<mo>=</mo>
<mi>x</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>log</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>2.1</mn>
<mo>+</mo>
<mi>y</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>log</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>3.4</mn>
<mo>+</mo>
<mrow>
<mtext>log</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{log}}\,2.88 = x\,{\text{log}}\,1.5 + y\,{\text{log}}\,2.4 + {\text{log}}\,k">
<mrow>
<mtext>log</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>2.88</mn>
<mo>=</mo>
<mi>x</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>log</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>1.5</mn>
<mo>+</mo>
<mi>y</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>log</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>2.4</mn>
<mo>+</mo>
<mrow>
<mtext>log</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{log}}\,0.980 = x\,{\text{log}}\,0.8 + y\,{\text{log}}\,1.9 + {\text{log}}\,k">
<mrow>
<mtext>log</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>0.980</mn>
<mo>=</mo>
<mi>x</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>log</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>0.8</mn>
<mo>+</mo>
<mi>y</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>log</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>1.9</mn>
<mo>+</mo>
<mrow>
<mtext>log</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
</math></span> <em><strong>M1A1</strong></em></p>
<p><strong>Note:</strong> Allow any consistent base, allow numerical equivalents.</p>
<p>attempting to solve their system of equations <em><strong>(M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> = 1.53, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> = 0.505 <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> = 0.997 <em><strong>A1</strong></em></p>
<p><em><strong>[6 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> is defined by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{ax + b}}{{cx + d}}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>a</mi>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</mrow>
<mrow>
<mi>c</mi>
<mi>x</mi>
<mo>+</mo>
<mi>d</mi>
</mrow>
</mfrac>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R},\,\,x \ne - \frac{d}{c}">
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>≠<!-- ≠ --></mo>
<mo>−<!-- − --></mo>
<mfrac>
<mi>d</mi>
<mi>c</mi>
</mfrac>
</math></span>.</p>
</div>
<div class="specification">
<p>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> is defined by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = \frac{{2x - 3}}{{x - 2}},\,\,x \in \mathbb{R},\,\,x \ne 2">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>3</mn>
</mrow>
<mrow>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>2</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>≠<!-- ≠ --></mo>
<mn>2</mn>
</math></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the inverse function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}">
<mrow>
<msup>
<mi>f</mi>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span>, stating its domain.</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>Express <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A + \frac{B}{{x - 2}}">
<mi>A</mi>
<mo>+</mo>
<mfrac>
<mi>B</mi>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
</mfrac>
</math></span> where A, B are constants.</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>Sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = g\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>. State the equations of any asymptotes and the coordinates of any intercepts with the axes.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> is defined by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h\left( x \right) = \sqrt x ">
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msqrt>
<mi>x</mi>
</msqrt>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≥ 0.</p>
<p>State the domain and range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h \circ g">
<mi>h</mi>
<mo>∘</mo>
<mi>g</mi>
</math></span>.</p>
<div class="marks">[4]</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>attempt to make <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> the subject of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{{ax + b}}{{cx + d}}">
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>a</mi>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</mrow>
<mrow>
<mi>c</mi>
<mi>x</mi>
<mo>+</mo>
<mi>d</mi>
</mrow>
</mfrac>
</math></span> <em><strong>M1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y\left( {cx + d} \right) = ax + b">
<mi>y</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>c</mi>
<mi>x</mi>
<mo>+</mo>
<mi>d</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>a</mi>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</math></span> <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \frac{{dy - b}}{{a - cy}}">
<mi>x</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>d</mi>
<mi>y</mi>
<mo>−</mo>
<mi>b</mi>
</mrow>
<mrow>
<mi>a</mi>
<mo>−</mo>
<mi>c</mi>
<mi>y</mi>
</mrow>
</mfrac>
</math></span> <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}\left( x \right) = \frac{{dx - b}}{{a - cx}}">
<mrow>
<msup>
<mi>f</mi>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>d</mi>
<mi>x</mi>
<mo>−</mo>
<mi>b</mi>
</mrow>
<mrow>
<mi>a</mi>
<mo>−</mo>
<mi>c</mi>
<mi>x</mi>
</mrow>
</mfrac>
</math></span> <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Do not allow <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = ">
<mi>y</mi>
<mo>=</mo>
</math></span> in place of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}\left( x \right)">
<mrow>
<msup>
<mi>f</mi>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \ne \frac{a}{c},\,\,\,\left( {x \in \mathbb{R}} \right)">
<mi>x</mi>
<mo>≠</mo>
<mfrac>
<mi>a</mi>
<mi>c</mi>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> The final <em><strong>A</strong></em> mark is independent.</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = 2 + \frac{1}{{x - 2}}">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>2</mn>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
</mfrac>
</math></span> <em><strong> A1A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"></p>
<p>hyperbola shape, with single curves in second and fourth quadrants and third quadrant blank, including vertical asymptote <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> <em><strong>A1</strong></em></p>
<p>horizontal asymptote <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 2">
<mi>y</mi>
<mo>=</mo>
<mn>2</mn>
</math></span> <em><strong>A1</strong></em></p>
<p>intercepts <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{3}{2},\,0} \right),\,\left( {0,\,\frac{3}{2}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mn>0</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the domain of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h \circ g">
<mi>h</mi>
<mo>∘</mo>
<mi>g</mi>
</math></span> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \leqslant \frac{3}{2},\,\,x > 2">
<mi>x</mi>
<mo>⩽</mo>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>></mo>
<mn>2</mn>
</math></span> <em><strong>A1A1</strong></em></p>
<p>the range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h \circ g">
<mi>h</mi>
<mo>∘</mo>
<mi>g</mi>
</math></span> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y \geqslant 0,\,\,y \ne \sqrt 2 ">
<mi>y</mi>
<mo>⩾</mo>
<mn>0</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>y</mi>
<mo>≠</mo>
<msqrt>
<mn>2</mn>
</msqrt>
</math></span> <em><strong>A1A1</strong></em></p>
<p><em><strong>[4 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.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>The following table shows the time, in days, from December <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mtext>st</mtext></math> and the percentage of Christmas trees in stock at a shop on the beginning of that day.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>The following table shows the natural logarithm of both <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> on these days to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> decimal places.</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>Use the data in the second table to find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math> for the regression line, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mo> </mo><mi>x</mi><mo>=</mo><mi>m</mi><mo>(</mo><mi>ln</mi><mo> </mo><mi>d</mi><mo>)</mo><mo>+</mo><mi>b</mi></math>.</p>
<p> </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>Assuming that the model found in part (a) remains valid, estimate the percentage of trees in stock when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>25</mn></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"><mi>m</mi><mo>=</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>695</mn><mo> </mo><mo> </mo><mfenced><mrow><mo>-</mo><mn>0</mn><mo>.</mo><mn>695383</mn><mo>…</mo></mrow></mfenced><mo>;</mo><mo> </mo><mi>b</mi><mo>=</mo><mn>4</mn><mo>.</mo><mn>63</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>4</mn><mo>.</mo><mn>62974</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1A1</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"><mi>ln</mi><mo> </mo><mi>x</mi><mo>=</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>695</mn><mfenced><mrow><mi>ln</mi><mo> </mo><mn>25</mn></mrow></mfenced><mo>+</mo><mn>4</mn><mo>.</mo><mn>63</mn></math> <em><strong>M1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mo> </mo><mi>x</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>39288</mn><mo>…</mo></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>10</mn><mo>.</mo><mn>9</mn><mo>%</mo></math> <em><strong>A1</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>Those candidates who did this question were often successful. There were a number, however, who found an equation of a line through two of the points instead of using their technology to find the equation of the regression line. A common problem was to introduce rounding errors at various stages throughout the problem. Some candidates failed to find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> from that of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mo> </mo><mi>x</mi></math>.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Those candidates who did this question were often successful. There were a number, however, who found an equation of a line through two of the points instead of using their technology to find the equation of the regression line. A common problem was to introduce rounding errors at various stages throughout the problem. Some candidates failed to find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> from that of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mo> </mo><mi>x</mi></math>.</p>
<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 defined by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 2{x^3} + 5,{\text{ }} - 2 \leqslant x \leqslant 2">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>2</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>5</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>x</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>2</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the range 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>Find an expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}(x)">
<mrow>
<msup>
<mi>f</mi>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</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 domain and range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}">
<mrow>
<msup>
<mi>f</mi>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</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 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=" - 11 \leqslant f(x) \leqslant 21">
<mo>−</mo>
<mn>11</mn>
<mo>⩽</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>⩽</mo>
<mn>21</mn>
</math></span> <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> <strong><em>A1 </em></strong>for correct end points, <strong><em>A1 </em></strong>for correct inequalities.</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="{f^{ - 1}}(x) = \sqrt[3]{{\frac{{x - 5}}{2}}}">
<mrow>
<msup>
<mi>f</mi>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mroot>
<mrow>
<mfrac>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>5</mn>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<mn>3</mn>
</mroot>
</math></span> <strong><em>(M1)A1</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=" - 11 \leqslant x \leqslant 21,{\text{ }} - 2 \leqslant {f^{ - 1}}(x) \leqslant 2">
<mo>−</mo>
<mn>11</mn>
<mo>⩽</mo>
<mi>x</mi>
<mo>⩽</mo>
<mn>21</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<mn>2</mn>
<mo>⩽</mo>
<mrow>
<msup>
<mi>f</mi>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>⩽</mo>
<mn>2</mn>
</math></span> <strong><em>A1A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = \frac{1}{{{x^2} + 3x + 2}},{\text{ }}x \in \mathbb{R},{\text{ }}x \ne - 2,{\text{ }}x \ne - 1">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>x</mi>
<mo>≠<!-- ≠ --></mo>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>x</mi>
<mo>≠<!-- ≠ --></mo>
<mo>−<!-- − --></mo>
<mn>1</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Express <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^2} + 3x + 2">
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</math></span> in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{(x + h)^2} + k">
<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 class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Factorize <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^2} + 3x + 2">
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</math></span>.</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>Sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>, indicating on it the equations of the asymptotes, the coordinates of the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept and the local maximum.</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>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{x + 1}} - \frac{1}{{x + 2}} = \frac{1}{{{x^2} + 3x + 2}}">
<mfrac>
<mn>1</mn>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</mfrac>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</mfrac>
</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>Hence find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> if <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^1 {f(x){\text{d}}x = \ln (p)} ">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mn>1</mn>
</msubsup>
<mrow>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
<mo>=</mo>
<mi>ln</mi>
<mo></mo>
<mo stretchy="false">(</mo>
<mi>p</mi>
<mo stretchy="false">)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( {\left| x \right|} \right)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mo>|</mo>
<mi>x</mi>
<mo>|</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the area of the region enclosed between the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( {\left| x \right|} \right)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mo>|</mo>
<mi>x</mi>
<mo>|</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis and the lines with equations <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 1">
<mi>x</mi>
<mo>=</mo>
<mo>−</mo>
<mn>1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 1">
<mi>x</mi>
<mo>=</mo>
<mn>1</mn>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^2} + 3x + 2 = {\left( {x + \frac{3}{2}} \right)^2} - \frac{1}{4}">
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
</math></span> <strong><em>A1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^2} + 3x + 2 = (x + 2)(x + 1)">
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
<mo>=</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>A1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-08-08_om_13.58.40.png" alt="M17/5/MATHL/HP1/ENG/TZ1/B11.b/M"></p>
<p><strong><em>A1</em></strong> for the shape</p>
<p><strong><em>A1</em></strong> for the equation <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><strong><em>A1</em></strong> for asymptotes <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 2">
<mi>x</mi>
<mo>=</mo>
<mo>−</mo>
<mn>2</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 1">
<mi>x</mi>
<mo>=</mo>
<mo>−</mo>
<mn>1</mn>
</math></span></p>
<p><strong><em>A1</em></strong> for coordinates <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( { - \frac{3}{2},{\text{ }} - 4} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<mn>4</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p><strong><em>A1</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {0,{\text{ }}\frac{1}{2}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{x + 1}} - \frac{1}{{x + 2}} = \frac{{(x + 2) - (x + 1)}}{{(x + 1)(x + 2)}}">
<mfrac>
<mn>1</mn>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</mfrac>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo>−</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
</mrow>
<mrow>
<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>2</mn>
<mo stretchy="false">)</mo>
</mrow>
</mfrac>
</math></span> <strong><em>M1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{1}{{{x^2} + 3x + 2}}">
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</mfrac>
</math></span> <strong><em>AG</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int\limits_0^1 {\frac{1}{{x + 1}} - \frac{1}{{x + 2}}{\text{d}}x} ">
<munderover>
<mo>∫</mo>
<mn>0</mn>
<mn>1</mn>
</munderover>
<mrow>
<mfrac>
<mn>1</mn>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</mfrac>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</mfrac>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left[ {\ln (x + 1) - \ln (x + 2)} \right]_0^1">
<mo>=</mo>
<msubsup>
<mrow>
<mo>[</mo>
<mrow>
<mi>ln</mi>
<mo></mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo>−</mo>
<mi>ln</mi>
<mo></mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
</mrow>
<mo>]</mo>
</mrow>
<mn>0</mn>
<mn>1</mn>
</msubsup>
</math></span> <strong><em>A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \ln 2 - \ln 3 - \ln 1 + \ln 2">
<mo>=</mo>
<mi>ln</mi>
<mo></mo>
<mn>2</mn>
<mo>−</mo>
<mi>ln</mi>
<mo></mo>
<mn>3</mn>
<mo>−</mo>
<mi>ln</mi>
<mo></mo>
<mn>1</mn>
<mo>+</mo>
<mi>ln</mi>
<mo></mo>
<mn>2</mn>
</math></span> <strong><em>M1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \ln \left( {\frac{4}{3}} \right)">
<mo>=</mo>
<mi>ln</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>M1A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\therefore p = \frac{4}{3}">
<mo>∴</mo>
<mi>p</mi>
<mo>=</mo>
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
</math></span></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-08-08_om_14.20.03.png" alt="M17/5/MATHL/HP1/ENG/TZ1/B11.e/M"></p>
<p>symmetry about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis <strong><em>M1</em></strong></p>
<p>correct shape <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Allow <strong><em>FT </em></strong>from part (b).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\int_0^1 {f(x){\text{d}}x} ">
<mn>2</mn>
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mn>1</mn>
</msubsup>
<mrow>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</mrow>
</math></span> <strong><em>(M1)(A1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 2\ln \left( {\frac{4}{3}} \right)">
<mo>=</mo>
<mn>2</mn>
<mi>ln</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Do not award <strong><em>FT </em></strong>from part (e).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f'\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>, 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ 5 is shown in the following diagram. The curve intercepts the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis at (1, 0) and (4, 0) and has a local minimum at (3, −1).</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The shaded area enclosed by the curve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f'\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis and the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis is 0.5. Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( 0 \right) = 3">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>3</mn>
</math></span>,</p>
</div>
<div class="specification">
<p>The area enclosed by the curve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f'\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> and the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 1">
<mi>x</mi>
<mo>=</mo>
<mn>1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 4">
<mi>x</mi>
<mo>=</mo>
<mn>4</mn>
</math></span> is 2.5 .</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-coordinate of the point of inflexion on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</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="f\left( 1 \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( 4 \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the curve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>, 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ 5 indicating clearly the coordinates of the maximum and minimum points and any intercepts with the coordinate axes.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>3 <em><strong>A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to use definite integral of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right)">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> <em><strong> (M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^1 {f'\left( x \right){\text{d}}x} = 0.5">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mn>1</mn>
</msubsup>
<mrow>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</mrow>
<mo>=</mo>
<mn>0.5</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( 1 \right) - f\left( 0 \right) = 0.5">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.5</mn>
</math></span> <em><strong> (A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( 1 \right) = 0.5 + 3">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.5</mn>
<mo>+</mo>
<mn>3</mn>
</math></span></p>
<p>= 3.5 <em><strong> A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_1^4 {f'\left( x \right){\text{d}}x} = - 2.5">
<msubsup>
<mo>∫</mo>
<mn>1</mn>
<mn>4</mn>
</msubsup>
<mrow>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</mrow>
<mo>=</mo>
<mo>−</mo>
<mn>2.5</mn>
</math></span> <em><strong> (A1)</strong></em></p>
<p><strong>Note:</strong> <em><strong>(A1)</strong></em> is for −2.5.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( 4 \right) - f\left( 1 \right) = - 2.5">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>−</mo>
<mn>2.5</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( 4 \right) = 3.5 - 2.5">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>3.5</mn>
<mo>−</mo>
<mn>2.5</mn>
</math></span></p>
<p>= 1 <em><strong> A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"> <em><strong> A1A1A1</strong></em></p>
<p><em><strong>A1</strong></em> for correct shape over approximately the correct domain<br><em><strong>A1</strong></em> for maximum and minimum (coordinates or horizontal lines from 3.5 and 1 are required),<br><em><strong>A1</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept at 3</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Roger buys a new laptop for himself at a cost of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>£</mo><mn>495</mn></math>. At the same time, he buys his daughter Chloe a higher specification laptop at a cost of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>£</mo><mn>2200</mn></math>.</p>
<p>It is anticipated that Roger’s laptop will depreciate at a rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>%</mo></math> per year, whereas Chloe’s laptop will depreciate at a rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>%</mo></math> per year.</p>
</div>
<div class="specification">
<p>Roger and Chloe’s laptops will have the same value <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> years after they were purchased.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the value of Roger’s laptop after <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> years.</p>
<div class="marks">[2]</div>
<div class="question_part_label">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">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Comment on the validity of your answer to part (b).</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"><mo>£</mo><mn>495</mn><mo>×</mo><mn>0</mn><mo>.</mo><msup><mn>9</mn><mn>5</mn></msup><mo>=</mo><mo>£</mo><mn>292</mn><mo> </mo><mo> </mo><mo>(</mo><mo>£</mo><mn>292</mn><mo>.</mo><mn>292</mn><mo>…</mo><mo>)</mo></math> <em><strong>(M1)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"><mo>£</mo><mn>495</mn><mo>×</mo><mn>0</mn><mo>.</mo><msup><mn>9</mn><mi>k</mi></msup><mo>=</mo><mn>2200</mn><mo>×</mo><mn>0</mn><mo>.</mo><msup><mn>85</mn><mi>k</mi></msup></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>26</mn><mo>.</mo><mn>1</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>26</mn><mo>.</mo><mn>0968</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em> </p>
<p><em><strong><br></strong></em><strong>Note:</strong> Award<em> <strong>M1A0 </strong></em>for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>-</mo><mn>1</mn></math> in place of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.<em><strong><br><br></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>depreciation rates unlikely to be constant (especially over a long time period) <em><strong>R1</strong></em></p>
<p><br><strong>Note:</strong> Accept reasonable answers based on the magnitude of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> or the fact that “value” depends on factors other than time.</p>
<p><em><strong><br></strong></em><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.</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="g\left( x \right) = 4\,{\text{cos}}\,x + 1">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>4</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cos</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>+</mo>
<mn>1</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a \leqslant x \leqslant \frac{\pi }{2}">
<mi>a</mi>
<mo>⩽<!-- ⩽ --></mo>
<mi>x</mi>
<mo>⩽<!-- ⩽ --></mo>
<mfrac>
<mi>π<!-- π --></mi>
<mn>2</mn>
</mfrac>
</math></span> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a < \frac{\pi }{2}">
<mi>a</mi>
<mo><</mo>
<mfrac>
<mi>π<!-- π --></mi>
<mn>2</mn>
</mfrac>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = - \frac{\pi }{2}"> <mi>a</mi> <mo>=</mo> <mo>−</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </math></span>, sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = g\left( x \right)"> <mi>y</mi> <mo>=</mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>. Indicate clearly the maximum and minimum values of the function.</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>Write down the least value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span> such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g"> <mi>g</mi> </math></span> has an inverse.</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>For the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span> found in part (b), write down the domain of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{g^{ - 1}}"> <mrow> <msup> <mi>g</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </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>For the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span> found in part (b), find an expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{g^{ - 1}}\left( x \right)"> <mrow> <msup> <mi>g</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><img src="data:image/png;base64,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"></p>
<p>concave down and symmetrical over correct domain <em><strong>A1</strong></em></p>
<p>indication of maximum and minimum values of the function (correct range) <em><strong>A1A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span> = 0 <em><strong>A1</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="a"> <mi>a</mi> </math></span> = 0 only if consistent with their graph.</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 \leqslant x \leqslant 5"> <mn>1</mn> <mo>⩽</mo> <mi>x</mi> <mo>⩽</mo> <mn>5</mn> </math></span> <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Allow FT from their graph.</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 4\,{\text{cos}}\,x + 1"> <mi>y</mi> <mo>=</mo> <mn>4</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>x</mi> <mo>+</mo> <mn>1</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 4\,{\text{cos}}\,y + 1"> <mi>x</mi> <mo>=</mo> <mn>4</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>y</mi> <mo>+</mo> <mn>1</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{x - 1}}{4} = {\text{cos}}\,y"> <mfrac> <mrow> <mi>x</mi> <mo>−</mo> <mn>1</mn> </mrow> <mn>4</mn> </mfrac> <mo>=</mo> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>y</mi> </math></span> <em><strong>(M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \Rightarrow y = {\text{arccos}}\left( {\frac{{x - 1}}{4}} \right)"> <mo stretchy="false">⇒</mo> <mi>y</mi> <mo>=</mo> <mrow> <mtext>arccos</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mi>x</mi> <mo>−</mo> <mn>1</mn> </mrow> <mn>4</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \Rightarrow {g^{ - 1}}\left( x \right) = {\text{arccos}}\left( {\frac{{x - 1}}{4}} \right)"> <mo stretchy="false">⇒</mo> <mrow> <msup> <mi>g</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mtext>arccos</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mi>x</mi> <mo>−</mo> <mn>1</mn> </mrow> <mn>4</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>ln</mi><mfenced><mfrac><mn>1</mn><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac></mfenced></math> is defined for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>2</mn><mo>,</mo><mo> </mo><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo></math>. You are not required to state a domain.</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>Solve <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo></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"><mi>y</mi><mo>=</mo><mi>ln</mi><mfenced><mfrac><mn>1</mn><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac></mfenced></math></p>
<p>an attempt to isolate <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> (or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> if switched) <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>e</mtext><mi>y</mi></msup><mo>=</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn><mo>=</mo><msup><mtext>e</mtext><mrow><mo>-</mo><mi>y</mi></mrow></msup></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><msup><mtext>e</mtext><mrow><mo>-</mo><mi>y</mi></mrow></msup><mo>+</mo><mn>2</mn></math></p>
<p>switching <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> (seen anywhere) <em><strong>M1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msup><mtext>e</mtext><mrow><mo>-</mo><mi>x</mi></mrow></msup><mo>+</mo><mn>2</mn></math> <strong><em>A1</em></strong></p>
<p><br><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>x</mi><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>2</mn><mo>.</mo><mn>12</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>2</mn><mo>.</mo><mn>12002</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p><br><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>This question was well answered by most candidates.</p>
<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>It is believed that the power <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math> of a signal at a point <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> km from an antenna is inversely proportional to <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>d</mi><mi>n</mi></msup></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>∈</mo><msup><mi mathvariant="normal">ℤ</mi><mo>+</mo></msup></math>.</p>
<p>The value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math> is recorded at distances of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">m</mi></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo> </mo><mi mathvariant="normal">m</mi></math> and the values of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mi>d</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mi>P</mi></math> are plotted on the graph below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The values of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mi>d</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mi>P</mi></math> are shown in the table 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>Explain why this graph indicates that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math> is inversely proportional to <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>d</mi><mi>n</mi></msup></math>.</p>
<p> </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 the least squares regression line of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mi>P</mi></math> against <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mi>d</mi></math>.</p>
<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>Use your answer to part (b) to write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> to the nearest integer.</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 an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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>a straight line with a negative gradient <strong>A1A1</strong></p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>log</mi><mo> </mo><mi>P</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>.</mo><mn>040</mn><mo>…</mo><mo> </mo><mi>log</mi><mo> </mo><mi>d</mi><mo>-</mo><mn>0</mn><mo>.</mo><mn>12632</mn><mo>…</mo><mo>≈</mo><mo>-</mo><mn>2</mn><mo>.</mo><mn>04</mn><mo> </mo><mi>log</mi><mo> </mo><mi>d</mi><mo>-</mo><mn>0</mn><mo>.</mo><mn>126</mn></math> <strong>A1A1</strong></p>
<p> </p>
<p><strong>Note: A1</strong> for each correct term.</p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>2</mn></math> <strong>A1</strong></p>
<p> </p>
<p><strong>[1 mark]</strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>0</mn><mo>.</mo><mn>126</mn><mo>…</mo></mrow></msup><msup><mi>d</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>≈</mo><mn>0</mn><mo>.</mo><mn>748</mn><msup><mi>d</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></math> <strong>A1</strong></p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The function <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> is defined by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p\left( x \right) = {x^3} + 3{x^2} + 8x - 24"><mi>p</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>−</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mi>x</mi><mo>−</mo><mn>24</mn></math></span> where <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>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the remainder when <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> is divided by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {x - 2} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</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 remainder when <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> is divided by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {x - 3} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>3</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</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>Prove that <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> has only one real zero.</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 transformation that will transform the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = p\left( x \right)"> <mi>y</mi> <mo>=</mo> <mi>p</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> onto the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 8{x^3} + 12{x^2} + 16x - 24"><mi>y</mi><mo>=</mo><mn>8</mn><msup><mi>x</mi><mn>3</mn></msup><mo>−</mo><mn>12</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn><mi>x</mi><mo>−</mo><mn>24</mn></math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span> follows a Poisson distribution with a mean of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
<mi>λ</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6{\text{P}}\left( {X = 3} \right) = 3{\text{P}}\left( {X = 2} \right) - 2{\text{P}}\left( {X = 1} \right) + 3{\text{P}}\left( {X = 0} \right)">
<mn>6</mn>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo>=</mo>
<mn>3</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>3</mn>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo>=</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mn>2</mn>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
<mi>λ</mi>
</math></span>.</p>
<div class="marks">[6]</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="p\left( 2 \right) = 8 - 12 + 16 - 24">
<mi>p</mi>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>8</mn>
<mo>−</mo>
<mn>12</mn>
<mo>+</mo>
<mn>16</mn>
<mo>−</mo>
<mn>24</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong></em> for a valid attempt at remainder theorem or polynomial division.</p>
<p>= −12 <em><strong>A1</strong></em></p>
<p>remainder = −12</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="p\left( 3 \right) = 27 - 27 + 24 - 24">
<mi>p</mi>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>27</mn>
<mo>−</mo>
<mn>27</mn>
<mo>+</mo>
<mn>24</mn>
<mo>−</mo>
<mn>24</mn>
</math></span> = 0 <em><strong>A1</strong></em> </p>
<p>remainder = 0</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="x = 3">
<mi>x</mi>
<mo>=</mo>
<mn>3</mn>
</math></span> (is a zero) <span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: italic;font-variant: normal;font-weight: bold;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">A1</span></p>
<p><strong>Note:</strong> Can be seen anywhere.</p>
<p><strong>EITHER</strong></p>
<p>factorise to get <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {x - 3} \right)\left( {{x^2} + 8} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>3</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>8</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(M1)A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^2} + 8 \ne 0">
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>8</mn>
<mo>≠</mo>
<mn>0</mn>
</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>) (or equivalent statement) <em><strong>R1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>R1</strong> </em>if correct two complex roots are given.</p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p'\left( x \right) = 3{x^2} - 6x + 8">
<msup>
<mi>p</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>6</mn>
<mi>x</mi>
<mo>+</mo>
<mn>8</mn>
</math></span> <span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: italic;font-variant: normal;font-weight: bold;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">A1</span></p>
<p>attempting to show <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p'\left( x \right) \ne 0">
<msup>
<mi>p</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>≠</mo>
<mn>0</mn>
</math></span> <em><strong>M1</strong></em></p>
<p><em>eg</em> discriminant = 36 – 96 < 0, completing the square</p>
<p>no turning points<em><strong> R1</strong></em></p>
<p><strong>THEN</strong></p>
<p>only one real zero (as the curve is continuous) <em><strong>AG</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>new graph is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = p\left( {2x} \right)"> <mi>y</mi> <mo>=</mo> <mi>p</mi> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(M1)</strong></em></p>
<p>stretch parallel to the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis (with <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> invariant), scale factor 0.5 <em><strong>A</strong><strong>1</strong></em></p>
<p><strong>Note:</strong> Accept “horizontal” instead of “parallel to the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis”.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{6{\lambda ^3}{e^{ - \lambda }}}}{6} = \frac{{3{\lambda ^2}{e^{ - \lambda }}}}{2} - 2\lambda {e^{ - \lambda }} + 3{e^{ - \lambda }}">
<mfrac>
<mrow>
<mn>6</mn>
<mrow>
<msup>
<mi>λ</mi>
<mn>3</mn>
</msup>
</mrow>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mo>−</mo>
<mi>λ</mi>
</mrow>
</msup>
</mrow>
</mrow>
<mn>6</mn>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>3</mn>
<mrow>
<msup>
<mi>λ</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mo>−</mo>
<mi>λ</mi>
</mrow>
</msup>
</mrow>
</mrow>
<mn>2</mn>
</mfrac>
<mo>−</mo>
<mn>2</mn>
<mi>λ</mi>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mo>−</mo>
<mi>λ</mi>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mo>−</mo>
<mi>λ</mi>
</mrow>
</msup>
</mrow>
</math></span> <em><strong>M1A1</strong></em></p>
<p><strong>Note:</strong> Allow factorials in the denominator for <em><strong>A1</strong></em>.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2{\lambda ^3} - 3{\lambda ^2} + 4\lambda - 6 = 0">
<mn>2</mn>
<mrow>
<msup>
<mi>λ</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>λ</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>4</mn>
<mi>λ</mi>
<mo>−</mo>
<mn>6</mn>
<mo>=</mo>
<mn>0</mn>
</math></span> <em><strong>A</strong><strong>1</strong></em></p>
<p><strong>Note:</strong> Accept any correct cubic equation without factorials and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{e^{ - \lambda }}}">
<mrow>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mo>−</mo>
<mi>λ</mi>
</mrow>
</msup>
</mrow>
</mrow>
</math></span>.</p>
<p><strong>EITHER</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4\left( {2{\lambda ^3} - 3{\lambda ^2} + 4\lambda - 6} \right) = 8{\lambda ^3} - 12{\lambda ^2} + 16\lambda - 24 = 0">
<mn>4</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mrow>
<msup>
<mi>λ</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>λ</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>4</mn>
<mi>λ</mi>
<mo>−</mo>
<mn>6</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>8</mn>
<mrow>
<msup>
<mi>λ</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>12</mn>
<mrow>
<msup>
<mi>λ</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>16</mn>
<mi>λ</mi>
<mo>−</mo>
<mn>24</mn>
<mo>=</mo>
<mn>0</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\lambda = 3">
<mn>2</mn>
<mi>λ</mi>
<mo>=</mo>
<mn>3</mn>
</math></span> <em><strong>(A1)</strong></em></p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {2\lambda - 3} \right)\left( {{\lambda ^2} + 2} \right) = 0">
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mi>λ</mi>
<mo>−</mo>
<mn>3</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>λ</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
</math></span> <em><strong>(M1)(A1)</strong></em></p>
<p><strong>THEN</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
<mi>λ</mi>
</math></span> = 1.5 <em><strong>A</strong><strong>1</strong></em></p>
<p><em><strong>[6 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>It is believed that two variables, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> are related. Experimental values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> are obtained. A graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,m">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>m</mi>
</math></span> against <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> shows a straight line passing through (2.1, 7.3) and (5.6, 2.4).</p>
</div>
<div class="specification">
<p>Hence, find</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the straight line, giving your answer in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,m = ap + b">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>m</mi>
<mo>=</mo>
<mi>a</mi>
<mi>p</mi>
<mo>+</mo>
<mi>b</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a{\text{,}}\,\,b \in \mathbb{R}">
<mi>a</mi>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>b</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>a formula for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</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">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 0">
<mi>p</mi>
<mo>=</mo>
<mn>0</mn>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>gradient = −1.4 <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,m - 7.3 = - 1.4\left( {p - 2.1} \right)">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>m</mi>
<mo>−</mo>
<mn>7.3</mn>
<mo>=</mo>
<mo>−</mo>
<mn>1.4</mn>
<mrow>
<mo>(</mo>
<mrow>
<mi>p</mi>
<mo>−</mo>
<mn>2.1</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>M1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,m = - 1.4p + 10.24">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>m</mi>
<mo>=</mo>
<mo>−</mo>
<mn>1.4</mn>
<mi>p</mi>
<mo>+</mo>
<mn>10.24</mn>
</math></span> <em><strong>A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m = {e^{ - 1.4p + 10.24}}\,\,\left( { = 28000{e^{ - 1.4p}}} \right)">
<mi>m</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mo>−</mo>
<mn>1.4</mn>
<mi>p</mi>
<mo>+</mo>
<mn>10.24</mn>
</mrow>
</msup>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mn>28000</mn>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mo>−</mo>
<mn>1.4</mn>
<mi>p</mi>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>A1</strong></em></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>28000 <em><strong>A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="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 an expression for the inverse function<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><msup><mi>f</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo></math>. The domain is not required.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the range of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><msup><mi>f</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo></math>.</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"><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>interchanging <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>,</mo><mo> </mo><mi>y</mi></math> at any stage <em><strong>(A1)</strong></em> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>2</mn><mo>-</mo><mfrac><mn>12</mn><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>12</mn><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfrac><mo>=</mo><mn>2</mn><mo>-</mo><mi>y</mi></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>12</mn><mrow><mn>2</mn><mo>-</mo><mi>y</mi></mrow></mfrac><mo>=</mo><mi>x</mi><mo>+</mo><mn>5</mn></math> <em><strong>(A1)</strong></em> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>12</mn><mrow><mn>2</mn><mo>-</mo><mi>y</mi></mrow></mfrac><mo>-</mo><mn>5</mn><mo>=</mo><mi>x</mi></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo> </mo><msup><mi>f</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo></mrow></mfenced><mo> </mo><mfrac><mn>12</mn><mrow><mn>2</mn><mo>-</mo><mi>x</mi></mrow></mfrac><mo>-</mo><mn>5</mn><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mfrac><mrow><mn>2</mn><mo>+</mo><mn>5</mn><mi>x</mi></mrow><mrow><mn>2</mn><mo>-</mo><mi>x</mi></mrow></mfrac></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>
<div class="question" style="padding-left: 20px;">
<p>range is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>≤</mo><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mi>x</mi></mfenced><mo>≤</mo><mn>7</mn><mo>,</mo><mo> </mo><mo> </mo><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mi>x</mi></mfenced><mo>≠</mo><mo>-</mo><mn>5</mn></math> <em><strong>A1</strong></em></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>Consider the functions <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> defined by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {\text{ln}}\left| x \right|">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mrow>
<mo>|</mo>
<mi>x</mi>
<mo>|</mo>
</mrow>
</math></span>, <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> \ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left\{ 0 \right\}">
<mrow>
<mo>{</mo>
<mn>0</mn>
<mo>}</mo>
</mrow>
</math></span>, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = {\text{ln}}\left| {x + k} \right|">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mrow>
<mo>|</mo>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mi>k</mi>
</mrow>
<mo>|</mo>
</mrow>
</math></span>, <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> \ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left\{ { - k} \right\}">
<mrow>
<mo>{</mo>
<mrow>
<mo>−<!-- − --></mo>
<mi>k</mi>
</mrow>
<mo>}</mo>
</mrow>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k \in \mathbb{R}">
<mi>k</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k > 2">
<mi>k</mi>
<mo>></mo>
<mn>2</mn>
</math></span>.</p>
</div>
<div class="specification">
<p>The graphs of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> intersect at the point P .</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the transformation by which <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right)"> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> is transformed to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right)"> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </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>State the range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g"> <mi>g</mi> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graphs of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)"> <mi>y</mi> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = g\left( x \right)"> <mi>y</mi> <mo>=</mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> on the same axes, clearly stating the points of intersection with any axes.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The tangent to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)"> <mi>y</mi> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> at P passes through the origin (0, 0).</p>
<p>Determine 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">[7]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>translation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span> units to the left (or equivalent) <em><strong>A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>range is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {g\left( x \right) \in } \right)\mathbb{R}"> <mrow> <mo>(</mo> <mrow> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>∈</mo> </mrow> <mo>)</mo> </mrow> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> </math></span> <em><strong>A1</strong></em></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><img 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"></p>
<p>correct shape of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)"> <mi>y</mi> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> <em><strong>A1</strong></em></p>
<p>their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right)"> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> translated <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span> units to left (possibly shown by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - k"> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mi>k</mi> </math></span> marked on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis) <em><strong>A1</strong></em></p>
<p>asymptote included and marked as <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - k"> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mi>k</mi> </math></span> <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right)"> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> intersects <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 1"> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mn>1</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 1"> <mi>x</mi> <mo>=</mo> <mn>1</mn> </math></span> <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right)"> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> intersects <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - k - 1"> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mi>k</mi> <mo>−</mo> <mn>1</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - k + 1"> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </math></span> <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right)"> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> intersects <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y"> <mi>y</mi> </math></span>-axis at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = {\text{ln}}\,k"> <mi>y</mi> <mo>=</mo> <mrow> <mtext>ln</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>k</mi> </math></span> <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Do not penalise candidates if their graphs “cross” as <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \to \pm \infty "> <mi>x</mi> <mo stretchy="false">→</mo> <mo>±</mo> <mi mathvariant="normal">∞</mi> </math></span>.</p>
<p><strong>Note:</strong> Do not award <em><strong>FT</strong> </em>marks from the candidate’s part (a) to part (c).</p>
<p><em><strong>[6 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>at P <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\left( {x + k} \right) = {\text{ln}}\left( { - x} \right)"> <mrow> <mtext>ln</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>+</mo> <mi>k</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mtext>ln</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>attempt to solve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x + k = - x"> <mi>x</mi> <mo>+</mo> <mi>k</mi> <mo>=</mo> <mo>−</mo> <mi>x</mi> </math></span> (or equivalent) <em><strong>(M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - \frac{k}{2} \Rightarrow y = {\text{ln}}\left( {\frac{k}{2}} \right)\,\,"> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mfrac> <mi>k</mi> <mn>2</mn> </mfrac> <mo stretchy="false">⇒</mo> <mi>y</mi> <mo>=</mo> <mrow> <mtext>ln</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mi>k</mi> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math></span> (or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = {\text{ln}}\left| {\frac{k}{2}} \right|"> <mi>y</mi> <mo>=</mo> <mrow> <mtext>ln</mtext> </mrow> <mrow> <mo>|</mo> <mrow> <mfrac> <mi>k</mi> <mn>2</mn> </mfrac> </mrow> <mo>|</mo> </mrow> </math></span>) <em><strong>A1</strong></em></p>
<p>P<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( { - \frac{k}{2},\,\,{\text{ln}}\frac{k}{2}} \right)"> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mfrac> <mi>k</mi> <mn>2</mn> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mtext>ln</mtext> </mrow> <mfrac> <mi>k</mi> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> (or P<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( { - \frac{k}{2},\,\,{\text{ln}}\left| {\frac{k}{2}} \right|} \right)"> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mfrac> <mi>k</mi> <mn>2</mn> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mtext>ln</mtext> </mrow> <mrow> <mo>|</mo> <mrow> <mfrac> <mi>k</mi> <mn>2</mn> </mfrac> </mrow> <mo>|</mo> </mrow> </mrow> <mo>)</mo> </mrow> </math></span>)</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to differentiate <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\left( { - x} \right)"> <mrow> <mtext>ln</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\left| x \right|"> <mrow> <mtext>ln</mtext> </mrow> <mrow> <mo>|</mo> <mi>x</mi> <mo>|</mo> </mrow> </math></span> <em><strong>(M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{1}{x}"> <mfrac> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>y</mi> </mrow> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </math></span> <em><strong>A1</strong></em></p>
<p>at P, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{ - 2}}{k}"> <mfrac> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>y</mi> </mrow> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mo>−</mo> <mn>2</mn> </mrow> <mi>k</mi> </mfrac> </math></span> <em><strong>A1</strong></em></p>
<p>recognition that tangent passes through origin <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \Rightarrow \frac{y}{x} = \frac{{{\text{d}}y}}{{{\text{d}}x}}"> <mo stretchy="false">⇒</mo> <mfrac> <mi>y</mi> <mi>x</mi> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>y</mi> </mrow> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> </mrow> </mfrac> </math></span> <em><strong>(M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{ln}}\left| {\frac{k}{2}} \right|}}{{ - \frac{k}{2}}} = \frac{{ - 2}}{k}"> <mfrac> <mrow> <mrow> <mtext>ln</mtext> </mrow> <mrow> <mo>|</mo> <mrow> <mfrac> <mi>k</mi> <mn>2</mn> </mfrac> </mrow> <mo>|</mo> </mrow> </mrow> <mrow> <mo>−</mo> <mfrac> <mi>k</mi> <mn>2</mn> </mfrac> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mo>−</mo> <mn>2</mn> </mrow> <mi>k</mi> </mfrac> </math></span> <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\left( {\frac{k}{2}} \right)\, = 1"> <mrow> <mtext>ln</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mi>k</mi> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace"></mspace> <mo>=</mo> <mn>1</mn> </math></span> <em><strong>(A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \Rightarrow k = 2{\text{e}}"> <mo stretchy="false">⇒</mo> <mi>k</mi> <mo>=</mo> <mn>2</mn> <mrow> <mtext>e</mtext> </mrow> </math></span> <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> For candidates who explicitly differentiate <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\left( {x} \right)"> <mrow> <mtext>ln</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </math></span> (rather than <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\left( { - x} \right)"> <mrow> <mtext>ln</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\left| x \right|"> <mrow> <mtext>ln</mtext> </mrow> <mrow> <mo>|</mo> <mi>x</mi> <mo>|</mo> </mrow> </math></span>, award <em><strong>M0A0A1M1A1A1A1</strong></em>.</p>
<p><em><strong>[7 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question">
<p>The graph of the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>ln</mi><mo> </mo><mi>x</mi></math> is translated by <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>a</mi></mtd></mtr><mtr><mtd><mi>b</mi></mtd></mtr></mtable></mfenced></math> so that it then passes through the points <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><msup><mtext>e</mtext><mn>3</mn></msup><mo>,</mo><mo> </mo><mn>1</mn><mo>+</mo><mi>ln</mi><mo> </mo><mn>2</mn><mo>)</mo></math> .</p>
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>new function is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow></mfenced><mo>+</mo><mi>b</mi><mfenced><mrow><mo>=</mo><mi>ln</mi><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow></mfenced><mo>+</mo><mi>b</mi></mrow></mfenced></math> <em><strong> (M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mn>0</mn></mfenced><mo>=</mo><mi>ln</mi><mfenced><mrow><mo>-</mo><mi>a</mi></mrow></mfenced><mo>+</mo><mi>b</mi><mo>=</mo><mn>1</mn></math> <em><strong> A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><msup><mtext>e</mtext><mn>3</mn></msup></mfenced><mo>=</mo><mi>ln</mi><mfenced><mrow><msup><mtext>e</mtext><mn>3</mn></msup><mo>-</mo><mi>a</mi></mrow></mfenced><mo>+</mo><mi>b</mi><mo>=</mo><mn>1</mn><mo>+</mo><mi>ln</mi><mo> </mo><mn>2</mn></math> <em><strong> A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mfenced><mrow><mo>-</mo><mi>a</mi></mrow></mfenced><mo>=</mo><mi>ln</mi><mfenced><mrow><msup><mtext>e</mtext><mn>3</mn></msup><mo>-</mo><mi>a</mi></mrow></mfenced><mo>-</mo><mi>ln</mi><mo> </mo><mn>2</mn></math> <em><strong> (M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mfenced><mrow><mo>-</mo><mi>a</mi></mrow></mfenced><mo>=</mo><mi>ln</mi><mfenced><mfrac><mrow><msup><mtext>e</mtext><mn>3</mn></msup><mo>-</mo><mi>a</mi></mrow><mn>2</mn></mfrac></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>a</mi><mo>=</mo><mfrac><mrow><msup><mtext>e</mtext><mn>3</mn></msup><mo>-</mo><mi>a</mi></mrow><mn>2</mn></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mi>a</mi><mo>=</mo><msup><mtext>e</mtext><mn>3</mn></msup><mo>-</mo><mi>a</mi></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><msup><mtext>e</mtext><mn>3</mn></msup><mtext> </mtext><mfenced><mrow><mo>=</mo><mo>-</mo><mn>20</mn><mo>.</mo><mn>0855</mn><mo>…</mo></mrow></mfenced></math> <em><strong> A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>1</mn><mo>-</mo><mi>ln</mi><mo> </mo><msup><mtext>e</mtext><mn>3</mn></msup><mo>=</mo><mn>1</mn><mo>-</mo><mn>3</mn><mo>=</mo><mo>-</mo><mn>2</mn></math> <em><strong> (M1)A1</strong></em></p>
<p> </p>
<p><em><strong>[7 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>Adesh wants to model the cooling of a metal rod. He heats the rod and records its temperature as it cools.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>He believes the temperature can be modeled by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T\left( t \right) = a{{\text{e}}^{bt}} + 25">
<mi>T</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>a</mi>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mi>b</mi>
<mi>t</mi>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mn>25</mn>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a{\text{,}}\,\,b \in \mathbb{R}">
<mi>a</mi>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>b</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>Hence</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\left( {T - 25} \right) = bt + {\text{ln}}\,a">
<mrow>
<mtext>ln</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>T</mi>
<mo>−</mo>
<mn>25</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>b</mi>
<mi>t</mi>
<mo>+</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<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 equation of the regression line of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\left( {T - 25} \right)">
<mrow>
<mtext>ln</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>T</mi>
<mo>−</mo>
<mn>25</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<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">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>predict the temperature of the metal rod after 3 minutes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\left( {T - 25} \right) = {\text{ln}}\left( {a{{\text{e}}^{bt}}} \right)">
<mrow>
<mtext>ln</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>T</mi>
<mo>−</mo>
<mn>25</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>a</mi>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mi>b</mi>
<mi>t</mi>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>M1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\left( {T - 25} \right) = {\text{ln}}\,a + {\text{ln}}\left( {{{\text{e}}^{bt}}} \right)">
<mrow>
<mtext>ln</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>T</mi>
<mo>−</mo>
<mn>25</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>a</mi>
<mo>+</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mi>b</mi>
<mi>t</mi>
</mrow>
</msup>
</mrow>
</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="{\text{ln}}\left( {T - 25} \right) = bt + {\text{ln}}\,a">
<mrow>
<mtext>ln</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>T</mi>
<mo>−</mo>
<mn>25</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>b</mi>
<mi>t</mi>
<mo>+</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>a</mi>
</math></span> <em><strong>AG</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="{\text{ln}}\left( {T - 25} \right) = - 0.00870t + 3.89">
<mrow>
<mtext>ln</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>T</mi>
<mo>−</mo>
<mn>25</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>−</mo>
<mn>0.00870</mn>
<mi>t</mi>
<mo>+</mo>
<mn>3.89</mn>
</math></span> <em><strong>M1A1A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = - 0.00870">
<mi>b</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.00870</mn>
</math></span> <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = {e^{3.89...}} = 49.1">
<mi>a</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mn>3.89...</mn>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mn>49.1</mn>
</math></span> <em><strong>M1A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T\left( {180} \right) = 49.1{e^{ - 0.00870\left( {180} \right)}} + 25 = 35.2">
<mi>T</mi>
<mrow>
<mo>(</mo>
<mrow>
<mn>180</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>49.1</mn>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mo>−</mo>
<mn>0.00870</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>180</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mn>25</mn>
<mo>=</mo>
<mn>35.2</mn>
</math></span> <em><strong>M1A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="question">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^4} - 6{x^2} - 2x + 4">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>6</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>4</mn>
</math></span>, <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>.</p>
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> is translated two units to the left to form the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>.</p>
<p>Express <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a{x^4} + b{x^3} + c{x^2} + dx + e">
<mi>a</mi>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>b</mi>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>c</mi>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>d</mi>
<mi>x</mi>
<mo>+</mo>
<mi>e</mi>
</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="c">
<mi>c</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
<mi>d</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="e \in \mathbb{Z}">
<mi>e</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
</math></span>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p 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="g\left( x \right) = f\left( {x + 2} \right)\left( { = {{\left( {x + 2} \right)}^4} - 6{{\left( {x + 2} \right)}^2} - 2\left( {x + 2} \right) + 4} \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>4</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>6</mn>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>4</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>M1</strong></em></p>
<p>attempt to expand <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{{\left( {x + 2} \right)}^4}}">
<mrow>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>4</mn>
</msup>
</mrow>
</mrow>
</math></span> <em><strong>M1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\left( {x + 2} \right)^4} = {x^4} + 4\left( {2{x^3}} \right) + 6\left( {{2^2}{x^2}} \right) + 4\left( {{2^3}x} \right) + {2^4}">
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mn>4</mn>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>4</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>6</mn>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mn>2</mn>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>4</mn>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mn>2</mn>
<mn>3</mn>
</msup>
</mrow>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mrow>
<msup>
<mn>2</mn>
<mn>4</mn>
</msup>
</mrow>
</math></span> <em><strong>(A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = {x^4} + 8{x^3} + 24{x^2} + 32x + 16">
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>8</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>24</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>32</mn>
<mi>x</mi>
<mo>+</mo>
<mn>16</mn>
</math></span> <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = {x^4} + 8{x^3} + 24{x^2} + 32x + 16 - 6\left( {{x^2} + 4x + 4} \right) - 2x - 4 + 4">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>8</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>24</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>32</mn>
<mi>x</mi>
<mo>+</mo>
<mn>16</mn>
<mo>−</mo>
<mn>6</mn>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>4</mn>
<mi>x</mi>
<mo>+</mo>
<mn>4</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mn>2</mn>
<mi>x</mi>
<mo>−</mo>
<mn>4</mn>
<mo>+</mo>
<mn>4</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = {x^4} + 8{x^3} + 18{x^2} + 6x - 8">
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>8</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>18</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>6</mn>
<mi>x</mi>
<mo>−</mo>
<mn>8</mn>
</math></span> <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> For correct expansion of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( {x - 2} \right) = {x^4} - 8{x^3} + 18{x^2} - 10x">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>8</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>18</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>10</mn>
<mi>x</mi>
</math></span> award max <em><strong>M0M1(A1)A0A1</strong></em>.</p>
<p><em><strong>[5 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{{1 - 3x}}{{x - 2}}">
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mn>3</mn>
<mi>x</mi>
</mrow>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
</mfrac>
</math></span>, showing clearly any asymptotes and stating the coordinates of any points of intersection with the axes.</p>
<p><img src="images/Schermafbeelding_2018-02-07_om_17.42.06.png" alt="N17/5/MATHL/HP1/ENG/TZ0/06.a"></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise, solve the inequality <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\frac{{1 - 3x}}{{x - 2}}} \right| < 2">
<mrow>
<mo>|</mo>
<mrow>
<mfrac>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mn>3</mn>
<mi>x</mi>
</mrow>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
</mfrac>
</mrow>
<mo>|</mo>
</mrow>
<mo><</mo>
<mn>2</mn>
</math></span>.</p>
<div class="marks">[5]</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 src="images/Schermafbeelding_2018-02-07_om_17.44.18.png" alt="N17/5/MATHL/HP1/ENG/TZ0/06.a/M"></p>
<p>correct vertical asymptote <strong><em>A1</em></strong></p>
<p>shape including correct horizontal asymptote <strong><em>A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{1}{3},{\text{ }}0} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {0,{\text{ }} - \frac{1}{2}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \frac{1}{3}">
<mi>x</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - \frac{1}{2}">
<mi>y</mi>
<mo>=</mo>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> marked on the axes.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p><img src="images/Schermafbeelding_2018-02-07_om_18.03.17.png" alt="N17/5/MATHL/HP1/ENG/TZ0/06.b/M"></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1 - 3x}}{{x - 2}} = 2">
<mfrac>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mn>3</mn>
<mi>x</mi>
</mrow>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>2</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \Rightarrow x = 1">
<mo stretchy="false">⇒</mo>
<mi>x</mi>
<mo>=</mo>
<mn>1</mn>
</math></span> <strong><em>A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \left( {\frac{{1 - 3x}}{{x - 2}}} \right) = 2">
<mo>−</mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mn>3</mn>
<mi>x</mi>
</mrow>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>2</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award this <strong><em>M1 </em></strong>for the line above or a correct sketch identifying a second critical value.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \Rightarrow x = - 3">
<mo stretchy="false">⇒</mo>
<mi>x</mi>
<mo>=</mo>
<mo>−</mo>
<mn>3</mn>
</math></span> <strong><em>A1</em></strong></p>
<p>solution is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 3 < x < 1">
<mo>−</mo>
<mn>3</mn>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mn>1</mn>
</math></span> <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {1 - 3x} \right| < 2\left| {x - 2} \right|,{\text{ }}x \ne 2">
<mrow>
<mo>|</mo>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mn>3</mn>
<mi>x</mi>
</mrow>
<mo>|</mo>
</mrow>
<mo><</mo>
<mn>2</mn>
<mrow>
<mo>|</mo>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>|</mo>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>x</mi>
<mo>≠</mo>
<mn>2</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - 6x + 9{x^2} < 4({x^2} - 4x + 4)">
<mn>1</mn>
<mo>−</mo>
<mn>6</mn>
<mi>x</mi>
<mo>+</mo>
<mn>9</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo><</mo>
<mn>4</mn>
<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>
</math></span> <strong><em>(M1)A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - 6x + 9{x^2} < 4{x^2} - 16x + 16">
<mn>1</mn>
<mo>−</mo>
<mn>6</mn>
<mi>x</mi>
<mo>+</mo>
<mn>9</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo><</mo>
<mn>4</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>16</mn>
<mi>x</mi>
<mo>+</mo>
<mn>16</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="5{x^2} + 10x - 15 < 0">
<mn>5</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>10</mn>
<mi>x</mi>
<mo>−</mo>
<mn>15</mn>
<mo><</mo>
<mn>0</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^2} + 2x - 3 < 0">
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mi>x</mi>
<mo>−</mo>
<mn>3</mn>
<mo><</mo>
<mn>0</mn>
</math></span> <strong><em>A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(x + 3)(x - 1) < 0">
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<mn>3</mn>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo><</mo>
<mn>0</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p>solution is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 3 < x < 1">
<mo>−</mo>
<mn>3</mn>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mn>1</mn>
</math></span> <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>METHOD 3</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 2 < \frac{{1 - 3x}}{{x - 2}} < 2">
<mo>−</mo>
<mn>2</mn>
<mo><</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mn>3</mn>
<mi>x</mi>
</mrow>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
</mfrac>
<mo><</mo>
<mn>2</mn>
</math></span></p>
<p>consider <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1 - 3x}}{{x - 2}} < 2">
<mfrac>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mn>3</mn>
<mi>x</mi>
</mrow>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
</mfrac>
<mo><</mo>
<mn>2</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Also allow consideration of “>” or “=” for the awarding of the <strong><em>M </em></strong>mark.</p>
<p> </p>
<p>recognition of critical value at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 1">
<mi>x</mi>
<mo>=</mo>
<mn>1</mn>
</math></span> <strong><em>A1</em></strong></p>
<p>consider <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 2 < \frac{{1 - 3x}}{{x - 2}}">
<mo>−</mo>
<mn>2</mn>
<mo><</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mn>3</mn>
<mi>x</mi>
</mrow>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Also allow consideration of “>” or “=” for the awarding of the <strong><em>M </em></strong>mark.</p>
<p> </p>
<p>recognition of critical value at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 3">
<mi>x</mi>
<mo>=</mo>
<mo>−</mo>
<mn>3</mn>
</math></span> <strong><em>A1</em></strong></p>
<p>solution is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 3 < x < 1">
<mo>−</mo>
<mn>3</mn>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mn>1</mn>
</math></span> <strong><em>A1</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<p><strong><em> </em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the graphs of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \left| x \right|">
<mi>y</mi>
<mo>=</mo>
<mrow>
<mo>|</mo>
<mi>x</mi>
<mo>|</mo>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - \left| x \right| + b">
<mi>y</mi>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mrow>
<mo>|</mo>
<mi>x</mi>
<mo>|</mo>
</mrow>
<mo>+</mo>
<mi>b</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b \in {\mathbb{Z}^ + }">
<mi>b</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<msup>
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
<mo>+</mo>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graphs on the same set of axes.</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 the graphs enclose a region of area 18 square units, find the value of <em>b</em>.</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><img src="images/Schermafbeelding_2017-08-08_om_11.15.31.png" alt="M17/5/MATHL/HP1/ENG/TZ1/A6.a/M"></p>
<p>graphs sketched correctly (condone missing <em>b</em>) <strong><em>A1A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{b^2}}}{2} = 18">
<mfrac>
<mrow>
<mrow>
<msup>
<mi>b</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mn>2</mn>
</mfrac>
<mo>=</mo>
<mn>18</mn>
</math></span> <strong><em>(M1)A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = 6">
<mi>b</mi>
<mo>=</mo>
<mn>6</mn>
</math></span> <strong><em>A1</em></strong></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>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{2 - 3{x^5}}}{{2{x^3}}},\,\,x \in \mathbb{R},\,\,x \ne 0">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mo>−<!-- − --></mo>
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>5</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>2</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
<mo>,</mo>
<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>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> has a local maximum at A. Find the coordinates of A.</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>Show that there is exactly one point of inflexion, B, on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The coordinates of B can be expressed in the form B<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {{2^a},\,b \times {2^{ - 3a}}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mn>2</mn>
<mi>a</mi>
</msup>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mi>b</mi>
<mo>×</mo>
<mrow>
<msup>
<mn>2</mn>
<mrow>
<mo>−</mo>
<mn>3</mn>
<mi>a</mi>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> where <em>a</em>, <em>b</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \in \mathbb{Q}">
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">Q</mi>
</mrow>
</math></span>. Find the value of <em>a</em> and the value of <em>b</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> showing clearly the position of the points A and B.</p>
<div class="marks">[4]</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>attempt to differentiate <em><strong> (M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right) = - 3{x^{ - 4}} - 3x">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>−</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mrow>
<mo>−</mo>
<mn>4</mn>
</mrow>
</msup>
</mrow>
<mo>−</mo>
<mn>3</mn>
<mi>x</mi>
</math></span> <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong> </em>for using quotient or product rule award <em><strong>A1</strong> </em>if correct derivative seen even in unsimplified form, for example <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right) = \frac{{ - 15{x^4} \times 2{x^3} - 6{x^2}\left( {2 - 3{x^5}} \right)}}{{{{\left( {2{x^3}} \right)}^2}}}">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mo>−</mo>
<mn>15</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>2</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>6</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mo>−</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>5</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \frac{3}{{{x^4}}} - 3x = 0">
<mo>−</mo>
<mfrac>
<mn>3</mn>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>−</mo>
<mn>3</mn>
<mi>x</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> <em><strong>M1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \Rightarrow {x^5} = - 1 \Rightarrow x = - 1">
<mo stretchy="false">⇒</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>5</mn>
</msup>
</mrow>
<mo>=</mo>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">⇒</mo>
<mi>x</mi>
<mo>=</mo>
<mo>−</mo>
<mn>1</mn>
</math></span> <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}\left( { - 1,\, - \frac{5}{2}} \right)">
<mrow>
<mtext>A</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>1</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mo>−</mo>
<mfrac>
<mn>5</mn>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>A1</strong></em></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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f''\left( x \right) = 0">
<msup>
<mi>f</mi>
<mo>″</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
</math></span> <em><strong>M1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f''\left( x \right) = 12{x^{ - 5}} - 3\left( { = 0} \right)">
<msup>
<mi>f</mi>
<mo>″</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>12</mn>
<mrow>
<msup>
<mi>x</mi>
<mrow>
<mo>−</mo>
<mn>5</mn>
</mrow>
</msup>
</mrow>
<mo>−</mo>
<mn>3</mn>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> for correct derivative seen even if not simplified.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \Rightarrow x = \sqrt[5]{4}\left( { = {2^{\frac{2}{5}}}} \right)">
<mo stretchy="false">⇒</mo>
<mi>x</mi>
<mo>=</mo>
<mroot>
<mn>4</mn>
<mn>5</mn>
</mroot>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mrow>
<msup>
<mn>2</mn>
<mrow>
<mfrac>
<mn>2</mn>
<mn>5</mn>
</mfrac>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>A1</strong></em></p>
<p>hence (at most) one point of inflexion <em><strong>R1</strong></em></p>
<p><strong>Note:</strong> This mark is independent of the two <em><strong>A1</strong> </em>marks above. If they have shown or stated their equation has only one solution this mark can be awarded.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f''\left( x \right)">
<msup>
<mi>f</mi>
<mo>″</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> changes sign at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \sqrt[5]{4}\left( { = {2^{\frac{2}{5}}}} \right)">
<mi>x</mi>
<mo>=</mo>
<mroot>
<mn>4</mn>
<mn>5</mn>
</mroot>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mrow>
<msup>
<mn>2</mn>
<mrow>
<mfrac>
<mn>2</mn>
<mn>5</mn>
</mfrac>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>R1</strong></em></p>
<p>so exactly one point of inflexion</p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \sqrt[5]{4} = {2^{\frac{2}{5}}}\left( { \Rightarrow a = \frac{2}{5}} \right)">
<mi>x</mi>
<mo>=</mo>
<mroot>
<mn>4</mn>
<mn>5</mn>
</mroot>
<mo>=</mo>
<mrow>
<msup>
<mn>2</mn>
<mrow>
<mfrac>
<mn>2</mn>
<mn>5</mn>
</mfrac>
</mrow>
</msup>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mo stretchy="false">⇒</mo>
<mi>a</mi>
<mo>=</mo>
<mfrac>
<mn>2</mn>
<mn>5</mn>
</mfrac>
</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="f\left( {{2^{\frac{2}{5}}}} \right) = \frac{{2 - 3 \times {2^2}}}{{2 \times {2^{\frac{6}{5}}}}} = - 5 \times {2^{ - \frac{6}{5}}}\left( { \Rightarrow b = - 5} \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mn>2</mn>
<mrow>
<mfrac>
<mn>2</mn>
<mn>5</mn>
</mfrac>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mo>−</mo>
<mn>3</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>2</mn>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>2</mn>
<mrow>
<mfrac>
<mn>6</mn>
<mn>5</mn>
</mfrac>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mo>−</mo>
<mn>5</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>2</mn>
<mrow>
<mo>−</mo>
<mfrac>
<mn>6</mn>
<mn>5</mn>
</mfrac>
</mrow>
</msup>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mo stretchy="false">⇒</mo>
<mi>b</mi>
<mo>=</mo>
<mo>−</mo>
<mn>5</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(M1)A1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong> </em>for the substitution of their value for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"><em><strong>A1A1A1A1</strong></em></p>
<p><em><strong>A1</strong></em> for shape for <em>x</em> < 0<br><em><strong>A1 </strong></em>for shape for <em>x</em> > 0<br><em><strong>A1 </strong></em>for maximum at A<br><em><strong>A1 </strong></em>for POI at B.</p>
<p><strong>Note:</strong> Only award last two <em><strong>A1</strong></em>s if A and B are placed in the correct quadrants, allowing for follow through.</p>
<p><em><strong>[4 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.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>A rational function is defined by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = a + \frac{b}{{x - c}}">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>a</mi>
<mo>+</mo>
<mfrac>
<mi>b</mi>
<mrow>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mi>c</mi>
</mrow>
</mfrac>
</math></span> where the parameters <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a,{\text{ }}b,{\text{ }}c \in \mathbb{Z}">
<mi>a</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>b</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>c</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}\backslash \{ c\} ">
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
<mi mathvariant="normal">∖<!-- ∖ --></mi>
<mo fence="false" stretchy="false">{</mo>
<mi>c</mi>
<mo fence="false" stretchy="false">}</mo>
</math></span>. The following diagram represents 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>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-02-28_om_09.42.27.png" alt="N16/5/MATHL/HP1/ENG/TZ0/03"></p>
<p>Using the information on the graph,</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>state the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> and 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">[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="b">
<mi>b</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 style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 1">
<mi>a</mi>
<mo>=</mo>
<mn>1</mn>
</math></span> <strong><em>A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c = 3">
<mi>c</mi>
<mo>=</mo>
<mn>3</mn>
</math></span> <strong><em>A1</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>use the coordinates of <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> on the graph <strong><em>M1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(1) = 0 \Rightarrow 1 + \frac{b}{{1 - 3}} = 0 \Rightarrow b = 2">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0</mn>
<mo stretchy="false">⇒</mo>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<mi>b</mi>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mn>3</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0</mn>
<mo stretchy="false">⇒</mo>
<mi>b</mi>
<mo>=</mo>
<mn>2</mn>
</math></span> <strong><em>A1</em></strong></p>
<p><strong><em>[2 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="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graphs of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{x}{2} + 1">
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mi>x</mi>
<mn>2</mn>
</mfrac>
<mo>+</mo>
<mn>1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \left| {x - 2} \right|">
<mi>y</mi>
<mo>=</mo>
<mrow>
<mo>|</mo>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>|</mo>
</mrow>
</math></span> on the following axes.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAcwAAAGrCAYAAABNKqdkAAAgAElEQVR4Ae3dD3CUdZ7n8U8HakQ3IBOxzgRYUHKIc6LeBNEbODfCGqBUxoUVlBGjoCXrHzhSQhZ0ZmpHVwZMwcJIlTNKJDCyykkKZtdxQM2xU7AzIO2fYWokGZyBg6Sp02Vj7BtYDvq56pA/nU53CPDr7t/ze96pStH9dPfv9/29vg/PJ0//SUKe53niCwEEEEAAAQR6FMjr8VZuRAABBBBAAIFWAQKTHQEBBBBAAIFeCBCYvUDiLggggAACCBCY7APmBCK1Kg+FFIp/375K4Wjs7NgtdaosGq25tYfVtsXcnIyEAAIIZEmAwMwSdCCmKZymGu+E6tfdK+38lT5pOnV22fnXatJDw3S0+UQgGFgkAgi4KUBgutnXHK6qn665caxG6HMd/+r02TryrtCQ4v+iO268SuxwOWwNUyOAwEUJcPy6KD4enEogr3+BRuiI9h/+99abY40/18q9t+j+/zow1d3ZhgACCPhCgMD0RZv8VWRe/4G6qqPkZn20uUFl371Lg9nbOlS4gAAC/hPgEOa/ntlf8Z8N1FWFn2n3H/63jtS9qi3D7tc9g79mf91UiAACCPQgQGD2gMNNFyhw2eW68jLpTx9V6x923qin7hnGa5cXSMnDEEDAHgEC055euFNJ3p+pYESh1Pc2Pbp4ogrZy9zpLStBIMACHMoC3PyMLn3IE/rpD+/XqHx2sYw6MzgCCGRNgKNZ1qiDMlGzwqvflBY9pQmFvG4ZlK6zTgSCINA3CItkjZkWaFa46gHdHZmm14Yc0u9uq9DCUQMyPSnjI4AAAlkV4Awzq9yuTnZaX35+TJEP63Xstr/RghI+b+lqp1kXAkEWCPH3MIPc/syt/ejRo9qwYYMWLlyoSy+9NHMTMTICCCCQJQGeks0SdJCmOX78uIYOHdq65AEDBujJJ58M0vJZKwIIOCrAU7KONjZXyzpx4oQqKys7pn/qqaf00ksvdVznAgIIIOBXAQLTr52zsO54WM6fP1+vvvpqR3U333yzCM0ODi4ggICPBQhMHzfPptITw3LRokUdpdXW1qo9NOOX+UIAAQT8KsCbfvzaOcvqXrx4sV588UU98sgjWrNmjS677LLWCj3PU/wNQNOmTdMHH3ygXbt2ady4cZZVTzkIIIDAuQUIzHMbcY9zCMRfo4w/7doelvF3xYZCodZHxQMz/kVongORmxFAwHoBnpK1vkX+KDAxLFNVPGTIEK1atSrVTWxDAAEEfCHAGaYv2mR/kfGPkhQUFHQUmnyG2X5D8v3at/MvAgggYLsAgWl7h3xaX7rA9OlyKBsBBBDgzxSyDyCAAAIIINAbAV7D7I0S90EAAQQQCLwAgRn4XQAABBBAAIHeCBCYvVHiPggggAACgRcgMAO/C5wnQCyi8LZNqiofrVBojCrrvjjPAbg7Aggg4E8BAtOffctJ1bHIbq16uEx31zZpePkWfeXt0/IJg3JSC5MigAAC2Rbgz3tlW9yv80X3auWsBdo/9WWFF4xTIT9q+bWT1I0AAhcowOcwLxAuWA9rVrjqAd396Rx98Mo0De5FWPI5zGDtIawWgSAI9OLQFwQG1tiTQKyhVksX/T/NHvd/9Y8Px1+7DKmofJXebWjp6WHchgACCDglQGA61c5MLOakDu76hXaU3qRv3PiXqqjZL++r/Xpe1Sp7bJ3C0VjrpPEQTfzORCWMiQACCORSgMDMpb4v5o7qaP0fVDh2kv6qpPDsr4bKv14PPbNQZTtf1NLNDTobmb5YDEUigAACFyxAYF4wXUAeGPtChz5u6rbYvOJvaWaZtL++SVFJ8T/jlfjd7QFsQAABBHwuQGD6vIEZLz9vkIbfVKTIx4d0rNup5GUafW2R8jNeBBMggAACuRcgMHPfA8srKNCYSWUq3P+hfhs51VlrtEn1+7+pmeOH8xv8O1W4hAACDgsQmA4318zS8jSg9DG9NOVf9OTSf9SB+Jt8YhHtXfe6Pq54WjNG9jMzDaMggAAClgsQmJY3yIry8oZp2uotqhldpwn9+yjU5yFtKXhM6yvG8nSsFQ2iCAQQyIYAv7ggG8oBnINfXBDAprNkBBwX4AzT8QazPAQQQAABMwIEphlHRkEAAQQQcFyAwHS8wSwPAQQQQMCMAIFpxpFREEAAAQQcFyAwHW8wy0MAAQQQMCNAYJpxZBQEEEAAAccFCEzHG8zyEEAAAQTMCBCYZhwZBQEEEEDAcQEC0/EGszwEEEAAATMCBKYZR0ZBAAEEEHBcgMB0vMEsDwEEEEDAjACBacaRURBAAAEEHBcgMB1vMMtDAAEEEDAjQGCacWQUBBBAAAHHBQhMxxvM8hBAAAEEzAgQmGYcGQUBBBBAwHEBAtPxBrM8BBBAAAEzAgSmGUdGQQABBBBwXIDAdLzBLA8BBBBAwIwAgWnGkVEQQAABBBwXIDAdbzDLQwABBBAwI0BgmnFkFAQQQAABxwUITMcbzPIQQAABBMwIEJhmHBkFAQQQQMBxAQLT8QazPAQQQAABMwIEphnHAIwSU0vdUhWFQgq1f0+qVkMsAEtniQgggIAkApPdoHcCsSN67/V/UqTj3oUqm/ktFbMHdYhwAQEE3Bbo6/byWJ0ZgZiiH9Xqx4NW60tvggaYGZRREEAAAV8JcH7gq3blqtjj2rv5de1YsVx/X12ruoaWXBXCvAgggEDOBEKe53k5m52JfSEQa6jWlGvnakdHtWVavGW1vjttlPI7tnW9EH+dM/7F7tXVhWsIIOBfAc4w/du7rFWeN3KOtnuezjTt09Z1i1WqHVox/Wm9HG7uqKHjjUBtbwjquIELCCCAgCMCnGE60shsLiMWeVfPzirX+rE/1YHlZ1/TbD+jTK6DM8xkEa4jgIBfBTjD9Gvnclh3XuFE/e13H5I2vqd9LWc/VxIPxsTvHJbH1AgggEBGBHiXbEZYXR80T/lDijV6tDQkn5+5XO8260MAgbMCHO3YEy5AIKbo0f+jksqpGskedAF+PAQBBPwowOHOj13Las2nFAn/XNvCEZ198vWUInt/or/fWaKnSgdltRImQwABBHIpQGDmUt8vc3/5gf5hTJH6hEIqKl+j3dEJ+u4P7lAhe49fOkidCCBgQIB3yRpAZIjuAu3vmuVdst1t2IIAAv4U4BzBn32jagQQQACBLAsQmFkGZzoEEEAAAX8KEJj+7BtVI4AAAghkWYDAzDI40yGAAAII+FOAwPRn36gaAQQQQCDLAgRmlsGZDgEEEEDAnwIEpj/7RtUIIIAAAlkWIDCzDM50CCCAAAL+FCAw/dk3qkYAAQQQyLIAgZllcKZDAAEEEPCnAIHpz75RNQIIIIBAlgUIzCyDMx0CCCCAgD8FCEx/9o2qEUAAAQSyLEBgZhmc6RBAAAEE/ClAYPqzb1SNAAIIIJBlAQIzy+BMhwACCCDgTwEC0599o2oEEEAAgSwLEJhZBmc6BBBAAAF/ChCY/uwbVSOAAAIIZFmAwMwyONMhgAACCPhTgMD0Z9+oGgEEEEAgywIEZpbBmQ4BBBBAwJ8CBKY/+0bVCCCAAAJZFiAwswzuwnSxxlrNLZqh6oaTLiyHNSCAAAK9EiAwe8XEnToEYoe19XvfV3WkYwsXEEAAgUAIEJiBaLOpRTYrvPJF7R50gwpNDck4CCCAgE8ECEyfNCr3ZcYUDW/QGj2giknDcl8OFSCAAAJZFiAwswzu2+mi+/TyGmn+vDHq79tFUDgCCCBw4QIE5oXbBeiRzQq/vEma/6BK8lPvMqFQSInfAcJhqQggEBCB1Ee/gCyeZfZGIP5U7Bvacs1CVZQM7M0DuA8CCCDgpACB6WRbDS4quk+vbCnUE/cMU087i+d5Svw2WAFDIYAAAlYIhLz4UY4vBFIKxNRS96xGTVymtJ8iKVun+nfmaGRSmsafno1/sXulhGUjAgj4UIDA9GHTcltye4ge1PP1GzRnZL+U5RCYKVnYiAACPhZIOi/w8UooHQEEEEAAgQwKEJgZxGVoBBBAAAF3BHhK1p1eWrUSnpK1qh0UgwACBgQ4wzSAyBAIIIAAAu4LEJju95gVIoAAAggYECAwDSAyBAIIIICA+wIEpvs9ZoUIIIAAAgYECEwDiAyBAAIIIOC+AIHpfo9ZIQIIIICAAQEC0wAiQyCAAAIIuC9AYLrfY1aIAAIIIGBAgMA0gMgQCCCAAALuCxCY7veYFSKAAAIIGBAgMA0gMgQCCCCAgPsCBKb7PWaFCCCAAAIGBAhMA4gMgQACCCDgvgCB6X6PWSECCCCAgAEBAtMAIkMggAACCLgvQGC632NWiAACCCBgQIDANIDIEAgggAAC7gsQmO73mBUigAACCBgQIDANIDIEAggggID7AgSm+z1mhQgggAACBgQITAOIDIEAAggg4L4Agel+j1khAggggIABAQLTACJDIIAAAgi4L0Bgut9jVogAAgggYECAwDSAGIQhYpHdWlU+WqFQSKHbl6q2oSUIy2aNCCCAQIcAgdlBwYW0AtFPtHVHH9332n55Z5q0Z2qjniz9oepaYmkfwg0IIICAawIEpmsdNb6ek/ps3wndMvtWFcb3lrxCjZ1brtnaoe37jhufjQERQAABWwUITFs7Y01d/TSi9FYNTthTYscO6eNrv6MZYwusqZJCEEAAgUwL9M30BIzvkkCLGure0rqaiCo3LVJJfkKKurRM1oIAAgikECAwU6CwKYVAS50qR03Uikj8tjLp29M1dtoo5bfdNf5mIL4QQAABlwU4RXC5uybXNmCCljd5OtO0R+sXSyum36sFtYfF235MIjMWAgjYLEBg2twdC2vLKxyr8mWrta7s3/TOns8UbavR8zwlfltYOiUhgAACFyVAYF4UX0AfnDdc42eOD+jiWTYCCARVgMAMaucvat1RHa3/UlNuGdHxGuZFDceDEUAAAR8IEJg+aFJOS4wdVu3cMbq9cqPCkVOSTilSt1bLj83SorKhYgfKaXeYHAEEsijA8S6L2L6cKu/r+sa4G1W/4kGNKbpEoaJH9XrzXVr/WrlG8bESX7aUohFA4MIEQl78nRp8IWBYoP1jJuxehmEZDgEEcibAGWbO6JkYAQQQQMBPAgSmn7pFrQgggAACORMgMHNGz8QIIIAAAn4SIDD91C1qRQABBBDImQCBmTN6JkYAAQQQ8JMAgemnblErAggggEDOBAjMnNEzMQIIIICAnwQITD91i1oRQAABBHImQGDmjJ6JEUAAAQT8JEBg+qlb1IoAAgggkDMBAjNn9EyMAAIIIOAnAQLTT92iVgQQQACBnAkQmDmjZ2IEEEAAAT8JEJh+6ha1IoAAAgjkTIDAzBk9EyOAAAII+EmAwPRTt6gVAQQQQCBnAgRmzuiZGAEEEEDATwIEpp+6Ra0IIIAAAjkTIDBzRs/ECCCAAAJ+EiAw/dQtakUAAQQQyJkAgZkzeiZGAAEEEPCTAIHpp25RKwIIIIBAzgQIzJzRMzECCCCAgJ8ECEw/dYtaEUAAAQRyJkBg5ozeTxO3qOHdVSovCikUCil0e6VqwhHF/LQEakUAAQQuUoDAvEhA9x9+So3bNupt3am1TZ68M03aM/WYlox5VCvDze4vnxUigAACbQIhz/M8NBBIKxD7o3b+sq9uKx2qjp+uYgdUPWWCnr3ppzqwfIIGpHhw/Ew0/sXulQKHTQgg4EuBvr6smqKzJ5B3tUpLk6bLG6ThNxUlbeQqAggg4LYAgel2fzO4uis05ZYRym+bof2MMoMTMjQCCCCQU4GOZ9lyWgWT+0ug5Tfa/vFkPV6W8DStv1ZAtQgggMB5CxCY500W9Ac0K/yTn+nKFx5WSX7n7hN/rTLxO+hKrB8BBNwT6Dziubc2VmRcIKZo+A1tLnhE80oGGh+dARFAAAGbBXiXrM3dsay2WOPPtfq9P9ej5dd3vHaZrsT21zR5l2w6IbYjgIDfBDjD9FvHclRvLFKn1Zv76b7Z7WEZU/TAW6re+UWOKmJaBBBAILsCBGZ2vX04W0zRhlotmfWAKiomqqhP22/7CfVR/+s2S0Xt75P14dIoGQEEEDgPAT5Wch5YQbxrrHGrFpROV3UkxerLJmt8cb8UN7AJAQQQcE+A1zDd66kVK+I1TCvaQBEIIGBQgKdkDWIyFAIIIICAuwIEpru9ZWUIIIAAAgYFCEyDmAyFAAIIIOCuAIHpbm9ZGQIIIICAQQEC0yAmQyGAAAIIuCtAYLrbW1aGAAIIIGBQgMA0iMlQCCCAAALuChCY7vaWlSGAAAIIGBQgMA1iMhQCCCCAgLsCBKa7vWVlCCCAAAIGBQhMg5gMhQACCCDgrgCB6W5vWRkCCCCAgEEBAtMgJkMhgAACCLgrQGC621tWhgACCCBgUIDANIjJUAgggAAC7goQmO72lpUhgAACCBgUIDANYjIUAggggIC7AgSmu71lZQgggAACBgUITIOYDIUAAggg4K4Agelub1kZAggggIBBAQLTICZDIYAAAgi4K0BguttbVoYAAgggYFCAwDSIyVAIIIAAAu4KEJju9paVIYAAAggYFCAwDWK6PVSLGuq26a2qchVX1qnF7cWyOgQQQKCbAIHZjYQN3QVOqqF6of6uZr3mL9qgP3W/A1sQQAAB5wUITOdbbGKB/TRyzjq9/toyPV9WaGJAxkAAAQR8J0Bg+q5lFIwAAgggkAuBvrmYlDndEwiFQu4tihUhgAACCQKcYSZgcBEBBBBAAIF0ApxhppNh+3kJeJ7X5f6ccXbh4AoCCDggwBmmA01kCQgggAACmRcgMDNvzAwIIIAAAg4IEJgONJElIIAAAghkXoDAzLwxMyCAAAIIOCBAYDrQxMwvIaaWuqUq6nOd5u6IKLJioi4PzVB1w8nMT80MCCCAgCUCIS/57Y2WFEYZ/hZof5csu5e/+0j1CCDQKcAZZqcFlxBAAAEEEEgrQGCmpeEGBBBAAAEEOgUIzE4LLiGAAAIIIJBWgMBMS8MNCCCAAAIIdAoQmJ0WXEIAAQQQQCCtAIGZloYbEEAAAQQQ6BQgMDstuIQAAggggEBaAQIzLQ03IIAAAggg0ClAYHZacAkBBBBAAIG0AgRmWhpuQAABBBBAoFOAwOy04BICCCCAAAJpBQjMtDTcgAACCCCAQKcAgdlpwSUEEEAAAQTSChCYaWm4AQEEEEAAgU4BArPTgksIIIAAAgikFSAw09JwAwIIIIAAAp0CBGanBZcQQAABBBBIK0BgpqXhBgQQQAABBDoFCMxOCy4hgAACCCCQVoDATEvDDQgggAACCHQKEJidFlxCAAEEEEAgrQCBmZaGGxBAAAEE/CZw4sQJxb8z8UVgZkKVMRFAAAEEsi4QD8r58+e3fmciNAnMrLeUCRFAAAEEMinw6quvZiQ0+2ayaMZGAAEEEEAgWwKXXnqp1qxZo6uvvlrPPPOMPv/8c7300ksaMmSIkRI4wzTCyCAIIIAAAjYIxENz6dKl+tGPfqRt27Zp2rRpOnr0aEJpR1RbXqxQKKRQ6C5VhZulWER7V5WrKBRScVVYpxPunXgx5Hmel7iBywiYEIjvjPEvdi8TmoyBAAIXIhA/u3zqqad08803q7a2tsuZZqyxVo/ePF3vzH5DNVcd0JEpCzVn1ICep4kH5sV8xY+JfGPAPsA+wD7APmD7PlBfX58Qd5977y8u8aTrvTlbDnlnEm5Jd5GnZHv+eYJbEUAAAQQcEfj1r3+dsJICjZlUpkJdp3HX/yf1JgyNvekn6E+98RRkwn4otb4+EN8S9P0iUYV9JFHj7GVMMOkuYO74sXv3bo0fP751iu3bt6usrCxhutP6qrlF0i69ueuQHho56pyh2ZtQTZiAiwgggAACCNgvkBiWu3btSgpLKdb4z3ru7Ut0f6m0v75J0V4sicDsBRJ36SoQi+xVTeWk1rPIovK12hs51fUOXEMAAQRyKJAcluPGjetaTeywtj63R2U/+L4emz1ekY3vaV/jr7Vq6TY1xrreNfEagZmoweVzC0T3auWsH6h+UrXOeP+hcPkXqpy1VuFoD3vZuUflHggggIARgQ0bNrQ+DRt/Z+xHH32kLmF5Oqyq4pBCE38sVTyjaYPzVXTjf1NpZL2eW9OkO5fercE9pCIfKzHSoqAMclIN1Q+qtH6eDiyfoLNvwP5CdZXf1vJr1+mdOZ2vAfDaVFD2CdaJgD0Cx48f1+TJk1sLSv4YiYkqe8hSE8MzhlMCsUPa9eaHGn1tkfI7FhZ/p9lfaP+b/6qDnGR2qHABAQSyL1BQUND6ectMhGV8NQRm9nvq2xljB/9Vb+4YqJuGD+q+4+z4hXYdPOnbtVE4Agi4IRD/NXimfhVesgiBmSzC9TQCMUWPHtR+XaNrh3SeX6a5M5sRQAAB5wQyFJin1Fj7pIomVashcE/Ttajh3VUqL4r/nsKQQrdXqiYcUeAYnPuvcqELiinasF1V5aPbfnflJFXW7FWEHaINNMjHitT7VCwS1ra3qs4eQ4qWqq4lSDtL0vGzqFxV7zb06iMfqTXNbs1IYMY/3/K9J9cqYrZWH4x2So3bNupt3am1TZ68M03aM/WYlox5VCvjv+DX1195yh9SrNH6g+qP9uYTS75erLHiY42/0CtvS1PXfiLP+w817ZmqY0vu0ayVe605CBhb7AUMFNxjRSqsU4rsXauHSx5S7aGhKt/5pbymFzRhQEYO06kKyPG2+A9PS1Va/lv9Rd2Xrb/05Ez4AR1/4WE9V/dFjms7O735TsQ/drD0lxp0x/VWLDCrRcQa9fvLp2rBHSPPvikmr1BjFyzR82UfauXmDxX/nRJ+/sor/pZmll2StIRTOnbooCJlkzW+uF/SbUG/elJ//H2BZiyYpJH58f9qX1Ph2Ll65vnx2rlyq/YG6swhxb4Q5GNFN46YouG1mnXPXt20dYdee3qmJow8xy8C7zaGzzfE/qDtP66VZn9Hf932S9DzCv+7Hpo9WBu3/8aK46fhwGxW+OVN0vzHNemq5AOrz5vZm/LzrlZp6dCub4jJG6ThNxX15tH23ydvuMbPTN55ozpa36iymd9SseG9yX6Qc1XYTyNKb036XNfXdNXwYhWe66HO3x7wY0Vyf6P79PLTr+ual36gBWMLux5Dku/r6vW2Y2Vk7yf6fcfnuuPHlz9p9qQb2j7GltvFGzzExX9C2qA1mqV5JQW5XZV1s1+hKbeMSPgohnUF9rKgfho542lV7F2pH9Y1KqZTitSt1XN7/1ovzBgZzP/kvZRLvttlU8bo2tazzuRbgnCdY0XXLp9Uw+YqLdJEjYv9Tz3c+v6H0Sqv2q6GjuDo+gg3rxVo7IzvqHRnhe5+YqMORE8qUrde269aov9ROsiKJZsLzPhPSGuk+fPGOBAMBnvT8htt/3iyHi9LOvM0OEVWh8ofq4pNS3RlzWT1CQ3XrO3XqGrTEyoJ7MH/fPWPa9/2Rs17fELSmef5juPj+3Os6Nq8ts83l469XjeOm6+apjP66tOnpZUP67GX9wXote485Zc8oU17XtId7z6k6/pfo4cO3aVlC8ep0FxSdbU/z2uGymhW+JU6XfPCPA6cXRrQrPBPfqYrX3jYKZe8wnFaWLNfntek/7V8tkoKv9Zl1VxJJxA/s9qkmiuf0LySgenu5Ph2jhXdGhxtUv3+gRo7aUrb/6U85Y+aefa17kVV2twQpM8391X/gUM0umKZFpdKO+Yu0LOtz2Z1U8vJhh4C84hqy4vb3grf9hGJ+Mckkr6Lqz5Qc/gNbRl2v+4Z7OKB87QitfO6rTvZIVRcpfDpxB7GD45vaHPBIwE+OCZ6cFnRfXpl89e1JLDPwpz9P+HuseLC9vHYsUP6uNtHCvqpePxklQXqXekxRQ9s1IKVZ3R/xd9q+fsf6P0l0rKJj9nzKYN0f1m699vb/2p1ur82XuiVrfu0V3/Nuvdz2n/PM0ff9lau3+99ZX+pGamw/S+vZ2RwPw565pC3deUb3qdf9ebvuvtxgb2pmWNFSqUv3/cWF3Y/Tp6pX+eV6V5vXf2JlA9zbuOZT711ZSOS8uLfvX0v3umpbJ1Xb8F/nR7OMHv709IgTVi+r/UzM/E/Fnz2+3O9v7hEKlun+jNN2p7wS7l7O6qf7xeL1Gn15n66b/b1ba/nxn9yekvVO+34LJGfbX1Ze6xRdavfUf/7/kqj2l/rjf5WNdW7rXirfPZMOVaktB5wgybNLtL+3b9L+IUWbb9ZK0gf12p9avpPSUQD9J+/eYM17yo3EJhJ6wv01fhvdanVklkPqKJioor6tD+F3Uf9r9ssFfEr5QK3e0QPqHbJHE2s+BtNLLqk86n9/mXapCt4g1zgdohUCx6k0vlLNeWd72vp+t+2vsknFvmV1tUcVsUL0zQyKEfpAd/UjIpvasezL2r9gbZPrUd/p7dqfqUpj0204mNrQWlFqr3U+LZY41YtKJ2uFTu7vSAhBeknReOyPh0wdli1C+7V9BU7UixgvGaOH85HcVLIBHFT3uB7tHpnlUb/y/3qHwqpz6yfqWB+lSoC9eawgSqpeEX7lg3SxusuP/vD5cgXdfyBH2v1tGFW/F/h72EG8X9nFtbM38PMAjJTIIBAVgU4w8wqN5MhgAACCPhVgMD0a+eoGwEEEEAgqwIEZla5mQwBBBBAwK8CBKZfO0fdCCCAAAJZFSAws8rNZAgggAACfhUgMP3aOepGAAEEEMiqAIGZVW4mQwABBBDwqwCB6dfOUTcCCCCAQFYFCMyscjMZAggggIBfBQhMv3aOuhFAAAEEsipAYGaVm8kQQAABBPwqQGD6tXNZr7tFDXXb9FZVuYor6wL2Z6myjs2ECCBgoQCBaWFT7CvppBqqF+rvatZr/qINSv6LdfbVS0UIIICAeQEC07ypgyP208g56/T6a8v0fFmhg+tjSQgggMC5BQjMcxtxDwQQQAABBKz4m5y0AQEEEEAAAesFOMO0vkUUiAACCCBggwCBaUMXqLqgRhYAAApbSURBVAEBBBBAwHoBAtP6FmWiwCOqLS9WKBTq8bu4KqzTvZw+eaxePoy7IYAAAr4R6OubSinUoMBQTas5KK/G4JAMhQACCDguQGA63uBsLc/zvC5Txc84+UIAAQRcEuApWZe6yVoQQAABBDImQGBmjNalgWNqqVuqoj7Xae6OiCIrJury0AxVN5x0aZGsBQEEEOhRIOQlP5fW4925EYHeCbQ/Jcvu1Tsv7oUAAvYLcIZpf4+oEAEEEEDAAgEC04ImUAICCCCAgP0CBKb9PaJCBBBAAAELBAhMC5pACQgggAAC9gsQmPb3iAoRQAABBCwQIDAtaAIlIIAAAgjYL0Bg2t8jKkQAAQQQsECAwLSgCZSAAAIIIGC/AIFpf4+oEAEEEEDAAgEC04ImUAICCCCAgP0CBKb9PaJCBBBAAAELBAhMC5pACQgggAAC9gsQmPb3iAoRQAABBCwQIDAtaAIlIIAAAgjYL0Bg2t8jKkQAAQQQsECAwLSgCZSAAAIIIGC/AIFpf4+oEAEEEEDAAgEC04ImUAICCCCAgP0CBKb9PaJCBBBAAAELBAhMC5pACQgggAAC9gsQmPb3iAoRQAABBCwQIDAtaAIlIIAAAgjYL0Bg2t8jKkQAAQQQsECAwLSgCZSAAAIIIGC/AIFpf4+oEAEEEEDAAgEC04ImUAICCCCAgP0CBKb9PaJCBBBAAAELBAhMC5pACQgggAAC9gsQmPb3iAoRQAABBCwQIDAtaIL9JbSo4d1VKi8KKRQKKXR7pWrCEcXsL5wKEUAAAWMCBKYxSlcHOqXGbRv1tu7U2iZP3pkm7Zl6TEvGPKqV4WZXF826EEAAgW4CIc/zvG5b2YBAu0Dsj9r5y766rXSoOn66ih1Q9ZQJevamn+rA8gka0H7fhH/jZ6LxL3avBBQuIoCArwX6+rp6is+8QN7VKi1NmiZvkIbfVJS0kasIIICA2wIdJw1uL5PVmRe4QlNuGaF88wMzIgIIIGClAIFpZVssL6rlN9r+8WQ9XpbwNK3lJVMeAgggcLECBObFCgbu8c0K/+RnuvKFh1WS37n7tL57Nv4O2rbvwLGwYAQQcF6g84jn/FJZYKfAEdWWF3eEW3vIJf9bXBXW6c4HSYopGn5Dmwse0bySgV1u4QoCCCDgugDvknW9wwbXF2v8uVa/9+d6tPz6c752GQ/f+BfvkjXYAIZCAIGcCnCGmVN+/0wei9Rp9eZ+um92e1jGFD3wlqp3fuGfRVApAgggcBECBOZF4AXjoTFFG2q1ZNYDqqiYqKI+7a9T9lH/6zZLRbxPNhj7AatEAAE+h8k+0KNArHGrFpROV3Ukxd3KJmt8cb8UN7AJAQQQcE+A1zDd66kVK+I1TCvaQBEIIGBQgKdkDWIyFAIIIICAuwIEpru9ZWUIIIAAAgYFCEyDmAyFAAIIIOCuAIHpbm9ZGQIIIICAQQEC0yAmQyGAAAIIuCtAYLrbW1aGAAIIIGBQgMA0iMlQCCCAAALuChCY7vaWlSGAAAIIGBQgMA1iMhQCCCCAgLsCBKa7vWVlCCCAAAIGBQhMg5gMhQACCCDgrgCB6W5vWRkCCCCAgEEBAtMgJkMhgAACCLgrQGC621tWhgACCCBgUIDANIjJUAgggAAC7goQmO72lpUhgAACCBgUIDANYjIUAggggIC7AgSmu71lZQgggAACBgUITIOYDIUAAggg4K4Agelub1kZAggggIBBAQLTICZDIYAAAgi4K0BguttbVoYAAgggYFCAwDSIyVAIIIAAAu4KEJju9paVIYAAAggYFCAwDWIyFAIIIICAuwIEpru9ZWUIIIAAAgYFCEyDmAyFAAIIIOCuAIHpbm9ZGQIIIICAQQEC0yCmy0PFIru1qny0QqGQQrcvVW1Di8vLZW0IIIBANwECsxsJG7oJRD/R1h19dN9r++WdadKeqY16svSHqmuJdbsrGxBAAAFXBQhMVztrbF0n9dm+E7pl9q0qjO8teYUaO7dcs7VD2/cdNzYLAyGAAAK2CxCYtnco5/X104jSWzU4YU+JHTukj6/9jmaMLch5dRSAAAIIZEugb7YmYh4XBFrUUPeW1tVEVLlpkUryE1LUheWxBgQQQKAHAQKzBxxuShBoqVPlqIlaEYlvK5O+PV1jp41SfsJduIgAAgi4LMApgsvdNbm2ARO0vMnTmaY9Wr9YWjH9Xi2oPaz2t/20vns2/g7atm+TUzMWAgggYIMAgWlDF7JewxHVlhd3hFt7yCX/W1wV1umk2vIKx6p82WqtK/s3vbPnM0WTbucqAggg4KoAT8m62tke1zVU02oOyqvp8U7pb8wbrvEzx0v1nXfxPK/zitQaxl02cAUBBBDwuQBnmD5vYG7Kj+po/ZeacssIXsPMTQOYFQEEciBAYOYA3VdTxg6rdu4Y3V65UeHIKUmnFKlbq+XHZmlR2VCxA/mqmxSLAAIXIcDx7iLwAvHQvK/rG+NuVP2KBzWm6BKFih7V6813af1r5RrFx0oCsQuwSAQQOCsQ8pJffEIGAQMC8TcQxb/YvQxgMgQCCFghwBmmFW2gCAQQQAAB2wUITNs7RH0IIIAAAlYIEJhWtIEiEEAAAQRsFyAwbe8Q9SGAAAIIWCFAYFrRBopAAAEEELBdgMC0vUPUhwACCCBghQCBaUUbKAIBBBBAwHYBAtP2DlEfAggggIAVAgSmFW2gCAQQQAAB2wUITNs7RH0IIIAAAlYIEJhWtIEiEEAAAQRsFyAwbe8Q9SGAAAIIWCFAYFrRBopAAAEEELBdgMC0vUPUhwACCCBghQCBaUUbKAIBBBBAwHYBAtP2DlEfAggggIAVAgSmFW2gCAQQQAAB2wUITNs7RH0IIIAAAlYIEJhWtIEiEEAAAQRsFyAwbe8Q9SGAAAIIWCFAYFrRBopAAAEEELBdgMC0vUPUhwACCCBghQCBaUUbKAIBBBBAwHYBAtP2DlEfAggggIAVAgSmFW2gCAQQQAAB2wUITNs7RH0IIIAAAlYIEJhWtIEiEEAAAQRsFyAwbe8Q9SGAAAIIWCFAYFrRBopAAAEEELBdgMC0vUMW1hdrrNXcohmqbjhpYXWUhAACCGRGgMDMjKu7o8YOa+v3vq/qiLtLZGUIIIBAKgECM5UK29IINCu88kXtHnSDCtPcg80IIICAqwIEpqudNb6umKLhDVqjB1QxaZjx0RkQAQQQsF2AwLS9Q7bUF92nl9dI8+eNUX9baqIOBBBAIIsCBGYWsf07VbPCL2+S5j+okvzUu0woFFLit3/XSuUIIIBAaoHUR7/U92VrIAXiT8W+oS3XLFRFycBACrBoBBBAIC5AYAZyPzii2vLiLmeEiWeH7ZeLq8I6Hd2nV7YU6ol7hvW4s3iep1TfgeRl0Qgg4KRAyIsf5fhCIKVATC11z2rUxGVK+ymSsnWqf2eORvKjV0pBNiKAgDsCBKY7vczSStpD9KCer9+gOSP7ZWlepkEAAQRyK8B5QW79mR0BBBBAwCcCBKZPGkWZCCCAAAK5FeAp2dz6MzsCCCCAgE8E/j9ppHiV862q5AAAAABJRU5ErkJggg=="></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>Solve the equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{x}{2} + 1 = \left| {x - 2} \right|">
<mfrac>
<mi>x</mi>
<mn>2</mn>
</mfrac>
<mo>+</mo>
<mn>1</mn>
<mo>=</mo>
<mrow>
<mo>|</mo>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>|</mo>
</mrow>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><img 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"></p>
<p>straight line graph with correct axis intercepts <em><strong>A1</strong></em></p>
<p>modulus graph: V shape in upper half plane <em><strong>A1</strong></em></p>
<p>modulus graph having correct vertex and <em>y</em>-intercept <em><strong>A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD</strong> <strong>1</strong></p>
<p>attempt to solve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{x}{2} + 1 = x - 2">
<mfrac>
<mi>x</mi>
<mn>2</mn>
</mfrac>
<mo>+</mo>
<mn>1</mn>
<mo>=</mo>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 6">
<mi>x</mi>
<mo>=</mo>
<mn>6</mn>
</math></span> <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 6">
<mi>x</mi>
<mo>=</mo>
<mn>6</mn>
</math></span> using the graph.</p>
<p>attempt to solve (algebraically) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{x}{2} + 1 = 2 - x">
<mfrac>
<mi>x</mi>
<mn>2</mn>
</mfrac>
<mo>+</mo>
<mn>1</mn>
<mo>=</mo>
<mn>2</mn>
<mo>−</mo>
<mi>x</mi>
</math></span> <em><strong>M1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \frac{2}{3}">
<mi>x</mi>
<mo>=</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</math></span> <em><strong> A1</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<p> </p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\left( {\frac{x}{2} + 1} \right)^2} = {\left( {x - 2} \right)^2}">
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>x</mi>
<mn>2</mn>
</mfrac>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span> <em><strong>M1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{x^2}}}{4} + x + 1 = {x^2} - 4x + 4">
<mfrac>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mn>4</mn>
</mfrac>
<mo>+</mo>
<mi>x</mi>
<mo>+</mo>
<mn>1</mn>
<mo>=</mo>
<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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 = \frac{{3{x^2}}}{4} - 5x + 3">
<mn>0</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mn>4</mn>
</mfrac>
<mo>−</mo>
<mn>5</mn>
<mi>x</mi>
<mo>+</mo>
<mn>3</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3{x^2} - 20x + 12 = 0">
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>20</mn>
<mi>x</mi>
<mo>+</mo>
<mn>12</mn>
<mo>=</mo>
<mn>0</mn>
</math></span></p>
<p>attempt to factorise (or equivalent) <em><strong>M1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {3x - 2} \right)\left( {x - 6} \right) = 0">
<mrow>
<mo>(</mo>
<mrow>
<mn>3</mn>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>6</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \frac{2}{3}">
<mi>x</mi>
<mo>=</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</math></span> <em><strong> A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 6">
<mi>x</mi>
<mo>=</mo>
<mn>6</mn>
</math></span> <em><strong>A1</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="question">
<p>A function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mi>p</mi><msup><mtext>e</mtext><mrow><mi>q</mi><mo> </mo><mi>cos</mi><mfenced><mrow><mi>r</mi><mi>t</mi></mrow></mfenced></mrow></msup><mo>,</mo><mo> </mo><mi>p</mi><mo>,</mo><mo> </mo><mi>q</mi><mo>,</mo><mo> </mo><mi>r</mi><mo>∈</mo><msup><mi mathvariant="normal">ℝ</mi><mo>+</mo></msup></math>. Part of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is shown.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>The points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> have coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>6</mn><mo>.</mo><mn>5</mn><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext><mo>(</mo><mn>5</mn><mo>.</mo><mn>2</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>2</mn><mo>)</mo></math>, and lie on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>.</p>
<p>The point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> is a local maximum and the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> is a local minimum.</p>
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>, of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math> and of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>substitute coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mn>0</mn></mfenced><mo>=</mo><mi>p</mi><msup><mtext>e</mtext><mrow><mi>q</mi><mo> </mo><mi>cos</mi><mfenced><mn>0</mn></mfenced></mrow></msup><mo>=</mo><mn>6</mn><mo>.</mo><mn>5</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>5</mn><mo>=</mo><mi>p</mi><msup><mtext>e</mtext><mi>q</mi></msup></math> <em><strong>(A1)</strong></em></p>
<p><br>substitute coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mrow><mn>5</mn><mo>.</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mi>p</mi><msup><mtext>e</mtext><mrow><mi>q</mi><mo> </mo><mi>cos</mi><mfenced><mrow><mn>5</mn><mo>.</mo><mn>2</mn><mi>r</mi></mrow></mfenced></mrow></msup><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn></math></p>
<p><br><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mfenced><mi>t</mi></mfenced><mo>=</mo><mo>-</mo><mi>p</mi><mi>q</mi><mi>r</mi><mo> </mo><mi>sin</mi><mfenced><mrow><mi>r</mi><mi>t</mi></mrow></mfenced><msup><mtext>e</mtext><mrow><mi>q</mi><mo> </mo><mi>cos</mi><mfenced><mrow><mi>r</mi><mi>t</mi></mrow></mfenced></mrow></msup></math> <em><strong>(M1)</strong></em></p>
<p>minimum occurs when <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>p</mi><mi>q</mi><mi>r</mi><mo> </mo><mi>sin</mi><mfenced><mrow><mn>5</mn><mo>.</mo><mn>2</mn><mi>r</mi></mrow></mfenced><msup><mtext>e</mtext><mrow><mi>q</mi><mo> </mo><mi>cos</mi><mfenced><mrow><mn>5</mn><mo>.</mo><mn>2</mn><mi>r</mi></mrow></mfenced></mrow></msup><mo>=</mo><mn>0</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mfenced><mrow><mi>r</mi><mi>t</mi></mrow></mfenced><mo>=</mo><mn>0</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>×</mo><mn>5</mn><mo>.</mo><mn>2</mn><mo>=</mo><mi mathvariant="normal">π</mi></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>OR</strong></p>
<p>minimum value occurs when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mfenced><mrow><mi>r</mi><mi>t</mi></mrow></mfenced><mo>=</mo><mo>-</mo><mn>1</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>×</mo><mn>5</mn><mo>.</mo><mn>2</mn><mo>=</mo><mi mathvariant="normal">π</mi></math> <em><strong>(A1)</strong></em></p>
<p><strong><br>OR</strong></p>
<p>period <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mo>×</mo><mn>5</mn><mo>.</mo><mn>2</mn><mo>=</mo><mn>10</mn><mo>.</mo><mn>4</mn></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow><mrow><mn>10</mn><mo>.</mo><mn>4</mn></mrow></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>r</mi><mo>=</mo><mfrac><mi mathvariant="normal">π</mi><mrow><mn>5</mn><mo>.</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>604152</mn><mo>…</mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>604</mn></mrow></mfenced></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><mi>p</mi><mo> </mo><msup><mtext>e</mtext><mrow><mo>-</mo><mi>q</mi></mrow></msup></math> <em><strong>(A1)</strong></em></p>
<p>eliminate <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>e</mtext><mrow><mn>2</mn><mi>q</mi></mrow></msup><mo>=</mo><mfrac><mrow><mn>6</mn><mo>.</mo><mn>5</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>2</mn></mrow></mfrac></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>2</mn><mo>=</mo><mfrac><msup><mi>p</mi><mn>2</mn></msup><mrow><mn>6</mn><mo>.</mo><mn>5</mn></mrow></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>74</mn><mo> </mo><mfenced><mrow><mn>1</mn><mo>.</mo><mn>74062</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>14017</mn><mo>…</mo><mo> </mo><mo> </mo><mfenced><mrow><mn>1</mn><mo>.</mo><mn>14</mn></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[8 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p>This was a challenging question and suitably positioned at the end of the examination. Candidates who attempted it were normally able to substitute points A and B into the given equation. Some were able to determine the first derivative. Only a few candidates were able to earn significant marks for this question.</p>
</div>
<br><hr><br><div class="question">
<p>It is believed that two variables, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
<mi>v</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span> are related by the equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = k{w^n}">
<mi>v</mi>
<mo>=</mo>
<mi>k</mi>
<mrow>
<msup>
<mi>w</mi>
<mi>n</mi>
</msup>
</mrow>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k{\text{,}}\,\,n \in \mathbb{R}">
<mi>k</mi>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>n</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>. Experimental values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
<mi>v</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span> are obtained. A graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,v">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>v</mi>
</math></span> against <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,w">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>w</mi>
</math></span> shows a straight line passing through (−1.7, 4.3) and (7.1, 17.5).</p>
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n">
<mi>n</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="{\text{ln}}\,v = n\,{\text{ln}}\,w + {\text{ln}}\,k">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>v</mi>
<mo>=</mo>
<mi>n</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>w</mi>
<mo>+</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>k</mi>
</math></span> <em><strong>M1A1</strong></em></p>
<p>gradient <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{17.5 - 4.3}}{{7.1 + 1.7}}{\text{ }}\left( { = 1.5} \right)">
<mo>=</mo>
<mfrac>
<mrow>
<mn>17.5</mn>
<mo>−</mo>
<mn>4.3</mn>
</mrow>
<mrow>
<mn>7.1</mn>
<mo>+</mo>
<mn>1.7</mn>
</mrow>
</mfrac>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mn>1.5</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>M1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = 1.5">
<mi>n</mi>
<mo>=</mo>
<mn>1.5</mn>
</math></span> <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 1.5 \times 1.7 + 4.3{\text{ }}\left( { = 6.85} \right)">
<mo>=</mo>
<mn>1.5</mn>
<mo>×</mo>
<mn>1.7</mn>
<mo>+</mo>
<mn>4.3</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mn>6.85</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>M1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = {e^{6.85}} = 944">
<mi>k</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mn>6.85</mn>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mn>944</mn>
</math></span> <em><strong>M1A1</strong></em></p>
<p><em><strong>[7 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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>a</mi><mo> </mo><mi>cos</mi><mo> </mo><mfenced><mrow><mi>b</mi><mfenced><mrow><mi>x</mi><mo>-</mo><mi>c</mi></mrow></mfenced></mrow></mfenced><mo>,</mo><mo> </mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>∈</mo><msup><mi mathvariant="normal">ℝ</mi><mo>+</mo></msup></math>.</p>
<p>Part of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math> is shown below. Point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> is a local maximum and has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>1</mn><mo>,</mo><mo> </mo><mn>3</mn></mrow></mfenced></math> and point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> is a local minimum with coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>,</mo><mo> </mo><mo>-</mo><mn>3</mn></mrow></mfenced></math>.</p>
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"></p>
</div>
<div class="question">
<p>Write down a sequence of transformations that will transform the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>cos</mi><mo> </mo><mi>x</mi></math> onto the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>Vertical stretch, scale factor <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math> <strong>A1</strong></p>
<p>Horizontal stretch, scale factor <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mi mathvariant="normal">π</mi></mfrac><mo>≈</mo><mn>0</mn><mo>.</mo><mn>318</mn></math> <strong>A1</strong></p>
<p>Horizontal translation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> unit to the right <strong>A1</strong></p>
<p> </p>
<p><strong>Note:</strong> The vertical stretch can be at any position in the order of transformations. If the order of the final two transformations are reversed the horizontal translation is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math> units to the right.</p>
<p> </p>
<p><strong>[3 marks]</strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br>