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<h2>SL Paper 2</h2><div class="specification">
<p>The rate of change of the height <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>h</mi><mo>)</mo></math> of a ball above horizontal ground, measured in metres,&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> seconds after it has been thrown and until it hits the ground, can be modelled by the&nbsp;equation</p>
<p style="padding-left: 60px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>h</mi></mrow><mrow><mo>d</mo><mi>t</mi></mrow></mfrac><mo>=</mo><mn>11</mn><mo>.</mo><mn>4</mn><mo>-</mo><mn>9</mn><mo>.</mo><mn>8</mn><mi>t</mi></math></p>
<p>The height of the ball when&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math>&nbsp;is&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>2</mn><mo> </mo><mtext>m</mtext></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> of the ball at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> at which the ball hits the ground.</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>Hence write down the domain of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the range of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A water container is made in the shape of a cylinder with internal height <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
  <mi>h</mi>
</math></span> cm and internal base radius <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
  <mi>r</mi>
</math></span> cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_08.31.01.png" alt="N16/5/MATSD/SP2/ENG/TZ0/06"></p>
<p>The water container has no top. The inner surfaces of the container are to be coated with a water-resistant material.</p>
</div>

<div class="specification">
<p>The volume of the water container is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.5{\text{ }}{{\text{m}}^3}">
  <mn>0.5</mn>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mrow>
    <msup>
      <mrow>
        <mtext>m</mtext>
      </mrow>
      <mn>3</mn>
    </msup>
  </mrow>
</math></span>.</p>
</div>

<div class="specification">
<p>The water container is designed so that the area to be coated is minimized.</p>
</div>

<div class="specification">
<p>One can of water-resistant material coats a surface area of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2000{\text{ c}}{{\text{m}}^2}">
  <mn>2000</mn>
  <mrow>
    <mtext>&nbsp;c</mtext>
  </mrow>
  <mrow>
    <msup>
      <mrow>
        <mtext>m</mtext>
      </mrow>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a formula for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>, the surface area to be coated.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Express this volume in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{c}}{{\text{m}}^3}"> <mrow> <mtext>c</mtext> </mrow> <mrow> <msup> <mrow> <mtext>m</mtext> </mrow> <mn>3</mn> </msup> </mrow> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span>, an equation for the volume of this water container.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + \frac{{1\,000\,000}}{r}"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}A}}{{{\text{d}}r}}"> <mfrac> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>A</mi> </mrow> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>r</mi> </mrow> </mfrac> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your answer to part (e), find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> which minimizes <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of this minimum area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the least number of cans of water-resistant material that will coat the area in part (g).</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>The cross-sectional view of a tunnel is shown on the axes below. The line <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>[</mo><mtext>AB</mtext><mo>]</mo></math> represents a vertical wall located at the left side of the tunnel. The height, in metres, of the tunnel above the horizontal ground is modelled by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>1</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mo>&nbsp;</mo><mn>0</mn><mo>.</mo><mn>8</mn><msup><mi>x</mi><mn>2</mn></msup><mo>,</mo><mo>&nbsp;</mo><mn>2</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>8</mn></math>, relative to an origin <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">Point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>2</mn><mo>,</mo><mo>&nbsp;</mo><mn>0</mn><mo>)</mo></math>, point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>2</mn><mo>,</mo><mo>&nbsp;</mo><mn>2</mn><mo>.</mo><mn>4</mn><mo>)</mo></math>, and point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>8</mn><mo>,</mo><mo>&nbsp;</mo><mn>0</mn><mo>)</mo></math>.</p>
</div>

<div class="specification">
<p>When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>4</mn></math> the height of the tunnel is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>4</mn><mo> </mo><mtext>m</mtext></math> and when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>6</mn></math> the height of the tunnel is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>2</mn><mo> </mo><mtext>m</mtext></math>. These points are shown as <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext></math> on the diagram, respectively.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>y</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the maximum height of the tunnel.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the trapezoidal rule, with three intervals, to estimate the cross-sectional area of the tunnel.</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 integral which can be used to find the cross-sectional area of the tunnel.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the cross-sectional area of the tunnel.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Hyungmin designs a concrete bird bath. The bird bath is supported by a pedestal.&nbsp;This is shown in the diagram.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">The interior of the bird bath is in the shape of a cone with radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> and a constant&nbsp;slant height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo> </mo><mtext>cm</mtext></math>.</p>
</div>

<div class="specification">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> be the volume of the bird bath.</p>
</div>

<div class="specification">
<p>Hyungmin wants the bird bath to have maximum volume.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an equation in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> that shows this information.</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>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mfrac><mrow><mn>2500</mn><mtext>π</mtext><mi>h</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mfrac><mrow><mtext>π</mtext><msup><mi>h</mi><mn>3</mn></msup></mrow><mn>3</mn></mfrac></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>d</mtext><mi>V</mi></mrow><mrow><mtext>d</mtext><mi>h</mi></mrow></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your answer to <strong>part (c)</strong>, find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> for which <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> is a maximum.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the maximum volume of the bird bath.</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>To prevent leaks, a sealant is applied to the interior surface of the bird bath.</p>
<p>Find the surface area to be covered by the sealant, given that the bird bath has maximum volume.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>A function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = (2x + 2)(5 - {x^2})">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mo stretchy="false">(</mo>
  <mn>2</mn>
  <mi>x</mi>
  <mo>+</mo>
  <mn>2</mn>
  <mo stretchy="false">)</mo>
  <mo stretchy="false">(</mo>
  <mn>5</mn>
  <mo>−<!-- − --></mo>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo stretchy="false">)</mo>
</math></span>.</p>
</div>

<div class="specification">
<p>The graph of the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = {5^x} + 6x - 6">
  <mi>g</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mrow>
    <msup>
      <mn>5</mn>
      <mi>x</mi>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>6</mn>
  <mi>x</mi>
  <mo>−<!-- − --></mo>
  <mn>6</mn>
</math></span> intersects the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <strong>exact </strong>value of each of the zeros of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Expand the expression for <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>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’(x)">
  <msup>
    <mi>f</mi>
    <mo>′</mo>
  </msup>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your answer to part (b)(ii) to find the values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> for which <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> is increasing.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Draw </strong>the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 3 \leqslant x \leqslant 3">
  <mo>−</mo>
  <mn>3</mn>
  <mo>⩽</mo>
  <mi>x</mi>
  <mo>⩽</mo>
  <mn>3</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 40 \leqslant y \leqslant 20">
  <mo>−</mo>
  <mn>40</mn>
  <mo>⩽</mo>
  <mi>y</mi>
  <mo>⩽</mo>
  <mn>20</mn>
</math></span>. Use a scale of 2 cm to represent 1 unit on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis and 1 cm to represent 5 units on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span>-axis.</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>Write down the coordinates of the point of intersection.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>In a company it is found that 25 % of the employees encountered traffic on their way to work. From those who encountered traffic the probability of being late for work is 80 %.</p>
<p>From those who did not encounter traffic, the probability of being late for work is 15 %.</p>
<p>The tree diagram illustrates the information.</p>
<p style="text-align: center;"><img 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"></p>
</div>

<div class="specification">
<p>The company investigates the different means of transport used by their employees in the past year to travel to work. It was found that the three most common means of transport used to travel to work were public transportation (<em>P </em>), car (<em>C </em>) and bicycle (<em>B </em>).</p>
<p>The company finds that 20 employees travelled by car, 28 travelled by bicycle and 19 travelled by public transportation in the last year.</p>
<p>Some of the information is shown in the Venn diagram.</p>
<p style="text-align: center;"><img 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"></p>
</div>

<div class="specification">
<p>There are 54 employees in the company.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>a</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>b</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee&nbsp;encountered traffic and was late for work.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee&nbsp;was late for work.</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>Use the tree diagram to find the probability that an employee&nbsp;encountered traffic given that they were late for work.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>x</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>y</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of employees who, in the last year, did not travel to work by car, bicycle or public transportation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n\left( {\left( {C \cup B} \right) \cap P'} \right)"> <mi>n</mi> <mrow> <mo>(</mo> <mrow> <mrow> <mo>(</mo> <mrow> <mi>C</mi> <mo>∪</mo> <mi>B</mi> </mrow> <mo>)</mo> </mrow> <mo>∩</mo> <msup> <mi>P</mi> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Sila High School has 110 students. They each take exactly one language class from a choice of English, Spanish or Chinese. The following table shows the number of female and male students in the three different language classes.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>A <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
  <mrow>
    <msup>
      <mi>χ<!-- χ --></mi>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span>&nbsp;test was carried out at the 5 % significance level to analyse the relationship between gender and student choice of language class.</p>
</div>

<div class="specification">
<p>Use your graphic display calculator to write down</p>
</div>

<div class="specification">
<p>The critical value at the 5 % significance level for this test is 5.99.</p>
</div>

<div class="specification">
<p>One student is chosen at random from this school.</p>
</div>

<div class="specification">
<p>Another student is chosen at random from this school.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the null hypothesis, H<sub>0 </sub>, for this test.</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 number of degrees of freedom.</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>the expected frequency of female students who chose to take the Chinese class.</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>State whether or not H<sub>0</sub> should be rejected. Justify your statement.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the student does not take the Spanish class.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that neither of the two students take the Spanish class.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that at least one of the two students is female.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{1}{3}{x^3} + \frac{3}{4}{x^2} - x - 1">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mfrac>
    <mn>1</mn>
    <mn>3</mn>
  </mfrac>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>3</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mfrac>
    <mn>3</mn>
    <mn>4</mn>
  </mfrac>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>−<!-- − --></mo>
  <mi>x</mi>
  <mo>−<!-- − --></mo>
  <mn>1</mn>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right)">
  <msup>
    <mi>f</mi>
    <mo>′</mo>
  </msup>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the gradient of 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> at <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>.</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>Find the equation of the tangent line to 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> at <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>. Give the equation in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="ax + by + d = 0">
  <mi>a</mi>
  <mi>x</mi>
  <mo>+</mo>
  <mi>b</mi>
  <mi>y</mi>
  <mo>+</mo>
  <mi>d</mi>
  <mo>=</mo>
  <mn>0</mn>
</math></span> where, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
  <mi>a</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
  <mi>b</mi>
</math></span>, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d \in \mathbb{Z}">
  <mi>d</mi>
  <mo>∈</mo>
  <mrow>
    <mi mathvariant="double-struck">Z</mi>
  </mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = a\sin bx + c">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mi>a</mi>
  <mi>sin</mi>
  <mo>⁡<!-- ⁡ --></mo>
  <mi>b</mi>
  <mi>x</mi>
  <mo>+</mo>
  <mi>c</mi>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant x \leqslant 12">
  <mn>0</mn>
  <mo>⩽<!-- ⩽ --></mo>
  <mi>x</mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mn>12</mn>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-03_om_16.53.31.png" alt="N16/5/MATME/SP2/ENG/TZ0/10"></p>
<p style="text-align: center;">The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> has a minimum point at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(3,{\text{ }}5)">
  <mo stretchy="false">(</mo>
  <mn>3</mn>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mn>5</mn>
  <mo stretchy="false">)</mo>
</math></span> and a maximum point at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(9,{\text{ }}17)">
  <mo stretchy="false">(</mo>
  <mn>9</mn>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mn>17</mn>
  <mo stretchy="false">)</mo>
</math></span>.</p>
</div>

<div class="specification">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
  <mi>g</mi>
</math></span> is obtained from the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> by a translation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} k \\ 0 \end{array}} \right)">
  <mrow>
    <mo>(</mo>
    <mrow>
      <mtable rowspacing="4pt" columnspacing="1em">
        <mtr>
          <mtd>
            <mi>k</mi>
          </mtd>
        </mtr>
        <mtr>
          <mtd>
            <mn>0</mn>
          </mtd>
        </mtr>
      </mtable>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>. The maximum point on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
  <mi>g</mi>
</math></span> has coordinates <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(11.5,{\text{ }}17)">
  <mo stretchy="false">(</mo>
  <mn>11.5</mn>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mn>17</mn>
  <mo stretchy="false">)</mo>
</math></span>.</p>
</div>

<div class="specification">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
  <mi>g</mi>
</math></span> changes from concave-up to concave-down when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = w">
  <mi>x</mi>
  <mo>=</mo>
  <mi>w</mi>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i)     Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
  <mi>c</mi>
</math></span>.</p>
<p>(ii)     Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = \frac{\pi }{6}">
  <mi>b</mi>
  <mo>=</mo>
  <mfrac>
    <mi>π</mi>
    <mn>6</mn>
  </mfrac>
</math></span>.</p>
<p>(iii)     Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
  <mi>a</mi>
</math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i)     Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
  <mi>k</mi>
</math></span>.</p>
<p>(ii)     Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x)">
  <mi>g</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</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>(i)     Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
  <mi>w</mi>
</math></span>.</p>
<p>(ii)     Hence or otherwise, find the maximum positive rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
  <mi>g</mi>
</math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A hollow chocolate box is manufactured in the form of a right prism with a regular hexagonal&nbsp;base. The height of the prism is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo> </mo><mtext>cm</mtext></math>,&nbsp;and the top and base of the prism have sides of&nbsp;length <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mtext>cm</mtext></math>.</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>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo> </mo><mn>60</mn><mo>°</mo><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></math>, show that the area of the base of the box is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><msqrt><mn>3</mn></msqrt><msup><mi>x</mi><mn>2</mn></msup></mrow><mn>2</mn></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the total external surface area of the box is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1200</mn><mo> </mo><msup><mtext>cm</mtext><mn>2</mn></msup></math>, show that the volume&nbsp;of the box may be expressed as&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mn>300</mn><msqrt><mn>3</mn></msqrt><mi>x</mi><mo>-</mo><mfrac><mn>9</mn><mn>4</mn></mfrac><msup><mi>x</mi><mn>3</mn></msup></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mn>300</mn><msqrt><mn>3</mn></msqrt><mi>x</mi><mo>-</mo><mfrac><mn>9</mn><mn>4</mn></mfrac><msup><mi>x</mi><mn>3</mn></msup></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>16</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>V</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> which maximizes the volume of the box.</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>Hence, or otherwise, find the maximum possible volume of the box.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The box will contain spherical chocolates. The production manager assumes that they can&nbsp;calculate the exact number of chocolates in each box by dividing the volume of the box by&nbsp;the volume of a single chocolate and then rounding down to the nearest integer.</p>
<p>Explain why the production manager is incorrect.</p>
<div class="marks">[1]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{27}}{{{x^2}}} - 16x,\,\,\,x \ne 0">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>27</mn>
    </mrow>
    <mrow>
      <mrow>
        <msup>
          <mi>x</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
  <mo>−<!-- − --></mo>
  <mn>16</mn>
  <mi>x</mi>
  <mo>,</mo>
  <mspace width="thinmathspace"></mspace>
  <mspace width="thinmathspace"></mspace>
  <mspace width="thinmathspace"></mspace>
  <mi>x</mi>
  <mo>≠<!-- ≠ --></mo>
  <mn>0</mn>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <em>y</em> = <em>f </em>(<em>x</em>), for −4 ≤ <em>x</em> ≤ 3 and −50 ≤ <em>y</em> ≤ 100.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the zero of <em>f </em>(<em>x</em>).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the coordinates of the local minimum point.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the equation of the tangent to the graph of <em>y</em> = <em>f </em>(<em>x</em>) at the point (–2, 38.75).</p>
<p>Give your answer in the form <em>y</em> = <em>mx</em> + <em>c</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider a function&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced></math>, for&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≥</mo><mn>0</mn></math>.&nbsp;The derivative of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is given by&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>6</mn><mi>x</mi></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfrac></math>.</p>
</div>

<div class="specification">
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is concave-down when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mi>n</mi></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>''</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>24</mn><mo>-</mo><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mn>2</mn></msup></mfrac></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the least value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</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&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo><mfrac><mrow><mn>6</mn><mi>x</mi></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfrac><mtext>d</mtext><mi>x</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> be the region enclosed by the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>, the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis and the lines <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>3</mn></math>.&nbsp;The area of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19</mn><mo>.</mo><mn>6</mn></math>, correct to three significant figures.</p>
<p>Find&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced></math>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{48}}{x} + k{x^2} - 58">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>48</mn>
    </mrow>
    <mi>x</mi>
  </mfrac>
  <mo>+</mo>
  <mi>k</mi>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>−<!-- − --></mo>
  <mn>58</mn>
</math></span>, where <em>x</em> &gt; 0 and <em>k</em> is a constant.</p>
<p>The graph of the function passes through the point with coordinates (4 , 2).</p>
</div>

<div class="specification">
<p>P is the minimum point of the graph of <em>f </em>(<em>x</em>).</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>k</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your value of <em>k</em> , find <em>f</em> ′(<em>x</em>).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Use your answer</strong> to part (b) to show that the minimum value of <em>f</em>(<em>x</em>) is −22 .</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <em>y</em> = <em>f</em> (<em>x</em>) for 0 &lt; <em>x</em> ≤ 6 and −30 ≤ <em>y</em> ≤ 60.<br>Clearly indicate the minimum point P and the <em>x</em>-intercepts on your graph.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A company performs an experiment on the efficiency of a liquid that is used to detect a nut allergy.</p>
<p>A group of 60 people took part in the experiment. In this group 26 are allergic to nuts. One person from the group is chosen at random.</p>
</div>

<div class="specification">
<p>A second person is chosen from the group.</p>
</div>

<div class="specification">
<p>When the liquid is added to a person’s blood sample, it is expected to turn blue if the person is allergic to nuts and to turn red if the person is not allergic to nuts.</p>
<p>The company claims that the probability that the test result is correct is 98% for people who are allergic to nuts and 95% for people who are not allergic to nuts.</p>
<p>It is known that 6 in every 1000 adults are allergic to nuts.</p>
<p>This information can be represented in a tree diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.31.34.png" alt="N17/5/MATSD/SP2/ENG/TZ0/04.c.d.e.f.g"></p>
</div>

<div class="specification">
<p>An adult, who was not part of the original group of 60, is chosen at random and tested using this liquid.</p>
</div>

<div class="specification">
<p>The liquid is used in an office to identify employees who might be allergic to nuts. The liquid turned blue for <strong>38 </strong><strong>employees</strong>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this person is <strong>not </strong>allergic to nuts.</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 probability that both people chosen are <strong>not </strong>allergic to nuts.</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><strong>Copy </strong>and complete the tree diagram.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this adult is allergic to nuts and the liquid turns blue.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the liquid turns blue.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the tested adult is allergic to nuts given that the liquid turned blue.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the number of employees, from this 38, who are allergic to nuts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>All lengths in this question are in metres.</strong></p>
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = &nbsp;- 0.8{x^2} + 0.5">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mo>−<!-- − --></mo>
  <mn>0.8</mn>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>0.5</mn>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 0.5 \leqslant x \leqslant 0.5">
  <mo>−<!-- − --></mo>
  <mn>0.5</mn>
  <mo>⩽<!-- ⩽ --></mo>
  <mi>x</mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mn>0.5</mn>
</math></span>. Mark uses <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> as a model to create a barrel. The region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis, the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = &nbsp;- 0.5">
  <mi>x</mi>
  <mo>=</mo>
  <mo>−<!-- − --></mo>
  <mn>0.5</mn>
</math></span> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0.5">
  <mi>x</mi>
  <mo>=</mo>
  <mn>0.5</mn>
</math></span> is rotated 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis. This is shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-03_om_15.49.19.png" alt="N16/5/MATME/SP2/ENG/TZ0/06"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the model to find the volume of the barrel.</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>The empty barrel is being filled with water. The volume <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V{\text{ }}{{\text{m}}^3}">
  <mi>V</mi>
  <mrow>
    <mtext> </mtext>
  </mrow>
  <mrow>
    <msup>
      <mrow>
        <mtext>m</mtext>
      </mrow>
      <mn>3</mn>
    </msup>
  </mrow>
</math></span> of water in the barrel after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> minutes is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V = 0.8(1 - {{\text{e}}^{ - 0.1t}})">
  <mi>V</mi>
  <mo>=</mo>
  <mn>0.8</mn>
  <mo stretchy="false">(</mo>
  <mn>1</mn>
  <mo>−</mo>
  <mrow>
    <msup>
      <mrow>
        <mtext>e</mtext>
      </mrow>
      <mrow>
        <mo>−</mo>
        <mn>0.1</mn>
        <mi>t</mi>
      </mrow>
    </msup>
  </mrow>
  <mo stretchy="false">)</mo>
</math></span>. How long will it take for the barrel to be half-full?</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A box of chocolates is to have a ribbon tied around it as shown in the diagram below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The box is in the shape of a cuboid with a height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math> cm. The length and width of the box&nbsp;are <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> cm.</p>
<p style="text-align: left;">After going around the box an extra <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> cm of ribbon is needed to form the bow.</p>
</div>

<div class="specification">
<p>The volume of the box is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>450</mn><msup><mtext> cm</mtext><mn>3</mn></msup></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the total length of the ribbon <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> in terms of <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>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mn>2</mn><mi>x</mi><mo>+</mo><mfrac><mn>300</mn><mi>x</mi></mfrac><mo>+</mo><mn>22</mn></math></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>L</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac></math></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Solve <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>L</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac><mo>=</mo><mn>0</mn></math></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>Hence or otherwise find the minimum length of ribbon required.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the curve <em>y</em> = 2<em>x</em><sup>3</sup>&nbsp;− 9<em>x</em><sup>2</sup> + 12<em>x</em> + 2, for&nbsp;−1 &lt; <em>x</em> &lt; 3</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the curve for −1 &lt; <em>x</em> &lt; 3 and −2 &lt; <em>y</em> &lt; 12.</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>A teacher asks her students to make some observations about the curve.</p>
<p>Three students responded.<br><strong>Nadia</strong> said <em>“The x-intercept of the curve is between −1 and zero”.</em><br><strong>Rick</strong> said <em>“The curve is decreasing when x &lt; 1 ”.</em><br><strong>Paula</strong> said <em>“The gradient of the curve is less than zero between x = 1 and x = 2 ”.</em></p>
<p>State the name of the student who made an <strong>incorrect</strong> observation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{dy}}}}{{{\text{dx}}}}">
  <mfrac>
    <mrow>
      <mrow>
        <mtext>dy</mtext>
      </mrow>
    </mrow>
    <mrow>
      <mrow>
        <mtext>dx</mtext>
      </mrow>
    </mrow>
  </mfrac>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <em>y</em> = 2<em>x</em><sup>3</sup> − 9<em>x</em><sup>2</sup> + 12<em>x</em> + 2 = <em>k</em> has <strong>three</strong> solutions, find the possible values of <em>k</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</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) =&nbsp; - {x^4} + a{x^2} + 5">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mo>−<!-- − --></mo>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>4</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mi>a</mi>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>5</mn>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
  <mi>a</mi>
</math></span> is a constant. Part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span> is shown below.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_17.47.40.png" alt="M17/5/MATSD/SP2/ENG/TZ2/06"></p>
</div>

<div class="specification">
<p>It is known that at the point where <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> the tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span> is horizontal.</p>
</div>

<div class="specification">
<p>There are two other points on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span> at which the tangent is horizontal.</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="y">
  <mi>y</mi>
</math></span>-intercept of the graph.</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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'(x)">
  <msup>
    <mi>f</mi>
    <mo>′</mo>
  </msup>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 8">
  <mi>a</mi>
  <mo>=</mo>
  <mn>8</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(2)">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mn>2</mn>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-coordinates of these two points;</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the intervals where the gradient of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span> is positive.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the range 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>.</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>Write down the number of possible solutions to the equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 5">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mn>5</mn>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = m">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mi>m</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m \in \mathbb{R}">
  <mi>m</mi>
  <mo>∈</mo>
  <mrow>
    <mi mathvariant="double-struck">R</mi>
  </mrow>
</math></span>, has four solutions. Find the possible values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
  <mi>m</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>A theatre set designer is designing a piece of flat scenery in the shape of a hill. The scenery&nbsp;is formed by a curve between two vertical edges of unequal height. One edge is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> metres&nbsp;high and the other is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> metre high. The width of the scenery is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> metres.</p>
<p>A coordinate system is formed with the origin at the foot of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> metres high edge. In this&nbsp;coordinate system the highest point of the cross‐section is at <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>,</mo><mo>&nbsp;</mo><mn>3</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>A set designer wishes to work out an approximate value for the area of the scenery <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>A</mi><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup><mo>&nbsp;</mo><mo>)</mo></math>.</p>
</div>

<div class="specification">
<p>In order to obtain a more accurate measure for the area the designer decides to model the&nbsp;curved edge with the polynomial <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>a</mi><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>b</mi><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi><mi>x</mi><mo>+</mo><mi>d</mi><mo>&nbsp;</mo><mo>&nbsp;</mo><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi><mo>,</mo><mo> </mo><mi>c</mi><mo>,</mo><mo> </mo><mi>d</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> metres is&nbsp;the height of the curved edge a horizontal distance <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mtext>m</mtext></math> from the origin.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>&lt;</mo><mn>21</mn></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By dividing the area between the curve and the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>‐axis into two trapezoids of unequal width show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>&gt;</mo><mn>14</mn><mo>.</mo><mn>5</mn></math>, justifying the direction of the inequality.</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 value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use differentiation to show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mi>a</mi><mo>+</mo><mn>4</mn><mi>b</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn></math>.</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>Determine two other linear equations in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>x</mi></mfenced></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the expression found in (f) to calculate a value for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>The Happy Straw Company manufactures drinking straws.</p>
<p>The straws are packaged in small closed rectangular boxes, each with length 8 cm, width 4 cm&nbsp;and height 3 cm. The information is shown in the diagram.</p>
<p style="text-align: center;"><img 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"></p>
</div>

<div class="specification">
<p>Each week, the Happy Straw Company sells <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> boxes of straws. It is known that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}P}}{{{\text{d}}x}} =&nbsp; - 2x + 220">
  <mfrac>
    <mrow>
      <mrow>
        <mtext>d</mtext>
      </mrow>
      <mi>P</mi>
    </mrow>
    <mrow>
      <mrow>
        <mtext>d</mtext>
      </mrow>
      <mi>x</mi>
    </mrow>
  </mfrac>
  <mo>=</mo>
  <mo>−<!-- − --></mo>
  <mn>2</mn>
  <mi>x</mi>
  <mo>+</mo>
  <mn>220</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> ≥ 0, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P">
  <mi>P</mi>
</math></span> is the weekly profit, in dollars, from the sale of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> thousand boxes.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the surface area of the box in cm<sup>2</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length AG.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of boxes that should be sold each week to maximize the profit.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P\left( x \right)">
  <mi>P</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the least number of boxes which must be sold each week in order to make a profit.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A cafe makes <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> litres of coffee each morning. The cafe&rsquo;s profit each morning, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math>, measured in dollars, is modelled by the following equation</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfrac><mi>x</mi><mn>10</mn></mfrac><mfenced><mrow><msup><mi>k</mi><mn>2</mn></msup><mo>-</mo><mfrac><mn>3</mn><mn>100</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup></mrow></mfenced></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> is a positive constant.</p>
</div>

<div class="specification">
<p>The cafe&rsquo;s manager knows that the cafe makes a profit of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>426</mn></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math> litres of coffee are made in a morning.</p>
</div>

<div class="specification">
<p>The manager of the cafe wishes to serve as many customers as possible.</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"><mfrac><mrow><mo>d</mo><mi>C</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</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>Hence find the maximum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>. Give your answer in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><msup><mi>k</mi><mn>3</mn></msup></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> is a constant.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the model to find how much coffee the cafe should make each morning to maximize its profit.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> against <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>, labelling the maximum point and the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-intercepts with their coordinates.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the maximum amount of coffee the cafe can make that will not result in a loss of money for the morning.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A sector of a circle, centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math> and radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn><mo>&#8202;</mo><mtext>m</mtext></math>, is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>A square field with side <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>&#8202;</mo><mtext>m</mtext></math> has a goat tied to a post in the centre by a rope such that the&nbsp;goat can reach all parts of the field up to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn><mo>&#8202;</mo><mtext>m</mtext></math> from the post.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p style="text-align: center;"><sup>[Source: mynamepong, n.d. Goat [image online] Available at: <a href="https://thenounproject.com/term/goat/1761571/">https://thenounproject.com/term/goat/1761571/</a></sup><br><sup>This file is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)</sup><br><sup><a href="https://creativecommons.org/licenses/by-sa/3.0/deed.en">https://creativecommons.org/licenses/by-sa/3.0/deed.en</a> [Accessed 22 April 2010] Source adapted.]</sup></p>
</div>

<div class="specification">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> be the volume of grass eaten by the goat, in cubic metres, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> be the length of time,&nbsp;in hours, that the goat has been in the field.</p>
<p>The goat eats grass at the rate of&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>V</mi></mrow><mrow><mo>d</mo><mi>t</mi></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn><mo>&#8202;</mo><mi>t</mi><msup><mtext>e</mtext><mrow><mo>-</mo><mi>t</mi></mrow></msup></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AÔB</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the shaded segment.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of a circle with radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>m</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the field that can be reached by the goat.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> at which the goat is eating grass at the greatest rate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>All lengths in this question are in metres.</strong></p>
<p>&nbsp;</p>
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \sqrt {\frac{{4 - {x^2}}}{8}} ">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <msqrt>
    <mfrac>
      <mrow>
        <mn>4</mn>
        <mo>−<!-- − --></mo>
        <mrow>
          <msup>
            <mi>x</mi>
            <mn>2</mn>
          </msup>
        </mrow>
      </mrow>
      <mn>8</mn>
    </mfrac>
  </msqrt>
</math></span>, for −2 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>&nbsp;≤ 2.&nbsp;In the following diagram, the shaded&nbsp;region is enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> and the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">A container can be modelled by rotating this region by 360˚ about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis.</p>
</div>

<div class="specification">
<p>Water can flow in and out of the container.</p>
<p>The volume of water in the container is given by the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( t \right)">
  <mi>g</mi>
  <mrow>
    <mo>(</mo>
    <mi>t</mi>
    <mo>)</mo>
  </mrow>
</math></span>, for 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> ≤ 4 , where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> is measured in hours and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( t \right)">
  <mi>g</mi>
  <mrow>
    <mo>(</mo>
    <mi>t</mi>
    <mo>)</mo>
  </mrow>
</math></span> is measured in m<sup>3</sup>. The rate of change of the volume of water in the container is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g'\left( t \right) = 0.9 - 2.5\,{\text{cos}}\left( {0.4{t^2}} \right)">
  <msup>
    <mi>g</mi>
    <mo>′</mo>
  </msup>
  <mrow>
    <mo>(</mo>
    <mi>t</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mn>0.9</mn>
  <mo>−<!-- − --></mo>
  <mn>2.5</mn>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>cos</mtext>
  </mrow>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mn>0.4</mn>
      <mrow>
        <msup>
          <mi>t</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
</div>

<div class="specification">
<p>The volume of water in the container is increasing only when&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
  <mi>p</mi>
</math></span>&nbsp;&lt; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span>&nbsp;&lt; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
  <mi>q</mi>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the volume of the container.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
  <mi>p</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
  <mi>q</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>During the interval <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
  <mi>p</mi>
</math></span> &lt; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> &lt; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
  <mi>q</mi>
</math></span>, he volume of water in the container increases by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
  <mi>k</mi>
</math></span> m<sup>3</sup>. Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
  <mi>k</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>When <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> = 0, the volume of water in the container is 2.3 m<sup>3</sup>. It is known that the container is never completely full of water during the 4 hour period.</p>
<p> </p>
<p>Find the minimum volume of empty space in the container during the 4 hour period.</p>
<div class="marks">[5]</div>
<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(x) = {x^3} + k{x^2} - 15x + 5">
  <mi>g</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>3</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mi>k</mi>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>−<!-- − --></mo>
  <mn>15</mn>
  <mi>x</mi>
  <mo>+</mo>
  <mn>5</mn>
</math></span>.</p>
</div>

<div class="specification">
<p>The tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = g(x)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>g</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span> at <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> is parallel to the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 21x + 7">
  <mi>y</mi>
  <mo>=</mo>
  <mn>21</mn>
  <mi>x</mi>
  <mo>+</mo>
  <mn>7</mn>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g'(x)">
  <msup>
    <mi>g</mi>
    <mo>′</mo>
  </msup>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</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>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 6">
  <mi>k</mi>
  <mo>=</mo>
  <mn>6</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = g(x)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>g</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span> at <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>. Give your answer in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = mx + c">
  <mi>y</mi>
  <mo>=</mo>
  <mi>m</mi>
  <mi>x</mi>
  <mo>+</mo>
  <mi>c</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your answer to part (a) and the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
  <mi>k</mi>
</math></span>, to find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-coordinates of the stationary points of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = g(x)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>g</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g’( - 1)">
  <msup>
    <mi>g</mi>
    <mo>′</mo>
  </msup>
  <mo stretchy="false">(</mo>
  <mo>−</mo>
  <mn>1</mn>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence justify that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
  <mi>g</mi>
</math></span> is decreasing 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>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span>-coordinate of the local minimum.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) =&nbsp; - 0.5{x^4} + 3{x^2} + 2x">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mo>−<!-- − --></mo>
  <mn>0.5</mn>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>4</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>3</mn>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>2</mn>
  <mi>x</mi>
</math></span>. The following diagram shows part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_06.09.00.png" alt="M17/5/MATME/SP2/ENG/TZ2/08"></p>
<p>&nbsp;</p>
<p>There are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-intercepts at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0">
  <mi>x</mi>
  <mo>=</mo>
  <mn>0</mn>
</math></span> and at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p">
  <mi>x</mi>
  <mo>=</mo>
  <mi>p</mi>
</math></span>. There is a maximum at A where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a">
  <mi>x</mi>
  <mo>=</mo>
  <mi>a</mi>
</math></span>, and a point of inflexion at B where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b">
  <mi>x</mi>
  <mo>=</mo>
  <mi>b</mi>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
  <mi>p</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of A.</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>Write down the rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> at A.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of B.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the the rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> at B.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R">
  <mi>R</mi>
</math></span> be the region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> , the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis, the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b">
  <mi>x</mi>
  <mo>=</mo>
  <mi>b</mi>
</math></span> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a">
  <mi>x</mi>
  <mo>=</mo>
  <mi>a</mi>
</math></span>. The region <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R">
  <mi>R</mi>
</math></span> is rotated 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis. Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The Maxwell Ohm Company is designing a portable Bluetooth speaker. The speaker is in the&nbsp;shape of a cylinder with a hemisphere at each end of the cylinder.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>The dimensions of the speaker, in centimetres, are illustrated in the following diagram where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>&nbsp;is the radius of the hemisphere, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math> is the length of the cylinder, with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>&gt;</mo><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>≥</mo><mn>0</mn></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>The Maxwell Ohm Company has decided that the speaker will have a surface area of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><mo> </mo><msup><mtext>cm</mtext><mn>2</mn></msup></math>.</p>
</div>

<div class="specification">
<p>The quality of sound from the speaker will improve as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> increases.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math>, the volume (cm<sup>3</sup>) of the speaker, in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</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>Write down an equation for the surface area of the speaker in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given the design constraint that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mfrac><mrow><mn>150</mn><mo>-</mo><mn>2</mn><mi mathvariant="normal">π</mi><msup><mi>r</mi><mn>2</mn></msup></mrow><mrow><mi mathvariant="normal">π</mi><mi>r</mi></mrow></mfrac></math>, show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mn>150</mn><mi>r</mi><mo>-</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi><msup><mi>r</mi><mn>3</mn></msup></mrow><mn>3</mn></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>d</mtext><mi>V</mi></mrow><mrow><mtext>d</mtext><mi>r</mi></mrow></mfrac></math>.</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>Using your answer to part (d), show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> is a maximum when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mn>75</mn><mi mathvariant="normal">π</mi></mfrac></msqrt><mo> </mo><mtext>cm</mtext></math>.</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>Find the length of the <strong>cylinder</strong> for which <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> is a maximum.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the maximum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your answer to part (f) to identify the shape of the speaker with the best quality of sound.</p>
<div class="marks">[1]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph of the quadratic function&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>8</mn></mrow></mfenced></math>&nbsp;intersects the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axis at <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>,</mo><mo>&nbsp;</mo><mi>c</mi></mrow></mfenced></math>.</p>
</div>

<div class="specification">
<p>The vertex of the function is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mo>&nbsp;</mo><mo>-</mo><mn>12</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math>.</p>
</div>

<div class="specification">
<p>The equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>12</mn></math> has two solutions. The first solution is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>10</mn></math>.</p>
</div>

<div class="specification">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> be the tangent at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>3</mn></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation for the axis of symmetry of the graph.</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><strong>Use the symmetry</strong> of the graph to show that the second solution is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>4</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>Write down the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-intercepts of the graph.</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>On graph paper, draw 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> for  <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>4</mn></math>  and  <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>14</mn><mo>≤</mo><mi>y</mi><mo>≤</mo><mn>14</mn></math>. Use a scale of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mtext>cm</mtext></math> to represent <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> unit on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mtext>cm</mtext></math> to represent <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> units on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axis.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the tangent <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> on your graph.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>a</mi></mfenced><mo>=</mo><mn>5</mn><mo>.</mo><mn>5</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mfenced><mi>a</mi></mfenced><mo>=</mo><mo>-</mo><mn>6</mn></math>, state whether the function, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>, is increasing or decreasing at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>a</mi></math>. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>Let&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{16}}{x}">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>16</mn>
    </mrow>
    <mi>x</mi>
  </mfrac>
</math></span>. The line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
  <mi>L</mi>
</math></span>&nbsp;is tangent to the graph of&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> at&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 8">
  <mi>x</mi>
  <mo>=</mo>
  <mn>8</mn>
</math></span>.</p>
</div>

<div class="specification">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
  <mi>L</mi>
</math></span> can be expressed in the form <em><strong>r</strong></em>&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left( {\begin{array}{*{20}{c}}  8 \\   2  \end{array}} \right) + t">
  <mo>=</mo>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mtable rowspacing="4pt" columnspacing="1em">
        <mtr>
          <mtd>
            <mn>8</mn>
          </mtd>
        </mtr>
        <mtr>
          <mtd>
            <mn>2</mn>
          </mtd>
        </mtr>
      </mtable>
    </mrow>
    <mo>)</mo>
  </mrow>
  <mo>+</mo>
  <mi>t</mi>
</math></span><em><strong>u</strong></em>.</p>
</div>

<div class="specification">
<p>The direction vector of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x">
  <mi>y</mi>
  <mo>=</mo>
  <mi>x</mi>
</math></span> is&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}}  1 \\   1  \end{array}} \right)">
  <mrow>
    <mo>(</mo>
    <mrow>
      <mtable rowspacing="4pt" columnspacing="1em">
        <mtr>
          <mtd>
            <mn>1</mn>
          </mtd>
        </mtr>
        <mtr>
          <mtd>
            <mn>1</mn>
          </mtd>
        </mtr>
      </mtable>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the gradient of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <em><strong>u</strong></em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the acute angle between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x"> <mi>y</mi> <mo>=</mo> <mi>x</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {f \circ f} \right)\left( x \right)"> <mrow> <mo>(</mo> <mrow> <mi>f</mi> <mo>∘</mo> <mi>f</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, write down <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>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise, find the obtuse angle formed by the tangent line to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 8"> <mi>x</mi> <mo>=</mo> <mn>8</mn> </math></span> and the tangent line to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at <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>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.iii.</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) = 4 - 2{{\text{e}}^x}">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mn>4</mn>
  <mo>−<!-- − --></mo>
  <mn>2</mn>
  <mrow>
    <msup>
      <mrow>
        <mtext>e</mtext>
      </mrow>
      <mi>x</mi>
    </msup>
  </mrow>
</math></span>. The following diagram shows part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-intercept of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <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>The region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</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 rotated 360º about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis. Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \,\,{\text{sin}}\,\left( {{e^x}} \right)">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mspace width="thinmathspace"></mspace>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>sin</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mrow>
        <msup>
          <mi>e</mi>
          <mi>x</mi>
        </msup>
      </mrow>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span> for 0&nbsp;≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>&nbsp;≤ 1.5.&nbsp;The following diagram shows the graph of&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img 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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <em>x</em>-intercept of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>, the<em> y</em>-axis and the <em>x</em>-axis is rotated 360° about the <em>x</em>-axis.</p>
<p>Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <em>g</em>(<em>x</em>) = −(<em>x</em> − 1)<sup>2</sup> + 5.</p>
</div>

<div class="specification">
<p>Let <em>f</em>(<em>x</em>) = x<sup>2</sup>. The following diagram shows part of the graph of <em>f</em>.</p>
<p><img src="data:image/png;base64,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"></p>
<p>The graph of <em>g</em> intersects the graph of <em>f</em> at <em>x</em> = −1 and <em>x</em> = 2.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of the vertex of the graph of <em>g</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the grid above, sketch the graph of g for −2 ≤ <em>x</em> ≤ 4.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the region enclosed by the graphs of <em>f</em> and <em>g</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Haruka has an eco-friendly bag in the shape of a cuboid with width 12 cm, length 36 cm and height of 9 cm. The bag is made from five rectangular pieces of cloth and is open at the top.</p>
<p>&nbsp;</p>
<p style="text-align: center;"><img 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"></p>
</div>

<div class="specification">
<p>Nanako decides to make her own eco-friendly bag in the shape of a cuboid such that the surface area is minimized.</p>
<p>The width of Nanako’s bag is <em>x </em>cm, its length is three times its width and its height is <em>y </em>cm.</p>
<p>&nbsp;</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">The volume of Nanako’s bag is 3888 cm<sup>3</sup>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the area of cloth, in cm<sup>2</sup>, needed to make Haruka’s bag.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the volume, in cm<sup>3</sup>, of the bag.</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 this value to write down, and simplify, the equation in<em> x</em> and <em>y</em> for the volume of Nanako’s bag.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down and simplify an expression in <em>x</em> and <em>y</em> for the area of cloth, <em>A</em>, used to make Nanako’s bag.</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>Use your answers to parts (c) and (d) to show that</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = 3{x^2} + \frac{{10368}}{x}">
  <mi>A</mi>
  <mo>=</mo>
  <mn>3</mn>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mfrac>
    <mrow>
      <mn>10368</mn>
    </mrow>
    <mi>x</mi>
  </mfrac>
</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>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}A}}{{{\text{d}}x}}">
  <mfrac>
    <mrow>
      <mrow>
        <mtext>d</mtext>
      </mrow>
      <mi>A</mi>
    </mrow>
    <mrow>
      <mrow>
        <mtext>d</mtext>
      </mrow>
      <mi>x</mi>
    </mrow>
  </mfrac>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your answer to part (f) to show that the width of Nanako’s bag is 12 cm.</p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The cloth used to make Nanako’s bag costs 4 Japanese Yen (JPY) per cm<sup>2</sup>.</p>
<p>Find the cost of the cloth used to make Nanako’s bag.</p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^2}{{\text{e}}^{3x}}">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mrow>
    <msup>
      <mrow>
        <mtext>e</mtext>
      </mrow>
      <mrow>
        <mn>3</mn>
        <mi>x</mi>
      </mrow>
    </msup>
  </mrow>
</math></span>,&nbsp;&nbsp;<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 <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>.</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>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> has a horizontal tangent line at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0"> <mi>x</mi> <mo>=</mo> <mn>0</mn> </math></span> and at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a"> <mi>x</mi> <mo>=</mo> <mi>a</mi> </math></span>. Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <em>f</em>(<em>x</em>) = ln <em>x</em> − 5<em>x</em> , for <em>x</em> &gt; 0 .</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <em>f '</em>(<em>x</em>).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <em>f "</em>(<em>x</em>).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Solve<em> f '</em>(<em>x</em>)<em> = f "</em>(<em>x</em>).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>In this question distance is in centimetres and time is in seconds.</strong></p>
<p>Particle A is moving along a straight line such that its displacement from a point P, after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> seconds, is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{s_{\text{A}}} = 15 - t - 6{t^3}{{\text{e}}^{ - 0.8t}}">
  <mrow>
    <msub>
      <mi>s</mi>
      <mrow>
        <mtext>A</mtext>
      </mrow>
    </msub>
  </mrow>
  <mo>=</mo>
  <mn>15</mn>
  <mo>−<!-- − --></mo>
  <mi>t</mi>
  <mo>−<!-- − --></mo>
  <mn>6</mn>
  <mrow>
    <msup>
      <mi>t</mi>
      <mn>3</mn>
    </msup>
  </mrow>
  <mrow>
    <msup>
      <mrow>
        <mtext>e</mtext>
      </mrow>
      <mrow>
        <mo>−<!-- − --></mo>
        <mn>0.8</mn>
        <mi>t</mi>
      </mrow>
    </msup>
  </mrow>
</math></span>, 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> ≤ 25. This is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>Another particle, B, moves along the same line, starting at the same time as particle A. The velocity of particle B is given by&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{B}}} = 8 - 2t">
  <mrow>
    <msub>
      <mi>v</mi>
      <mrow>
        <mtext>B</mtext>
      </mrow>
    </msub>
  </mrow>
  <mo>=</mo>
  <mn>8</mn>
  <mo>−<!-- − --></mo>
  <mn>2</mn>
  <mi>t</mi>
</math></span>, 0&nbsp;≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span>&nbsp;≤ 25.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the initial displacement of particle A from point 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 value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> when particle A first reaches point P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> when particle A first changes direction.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total distance travelled by particle A in the first 3 seconds.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that particles A and B start at the same point, find the displacement function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{s_{\text{B}}}"> <mrow> <msub> <mi>s</mi> <mrow> <mtext>B</mtext> </mrow> </msub> </mrow> </math></span> for particle B.</p>
<div class="marks">[5]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the other value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> when particles A and B meet.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>Note: In this question, distance is in metres and time is in seconds.</strong></p>
<p>A particle P moves in a straight line for five seconds. Its acceleration at time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 3{t^2} - 14t + 8">
  <mi>a</mi>
  <mo>=</mo>
  <mn>3</mn>
  <mrow>
    <msup>
      <mi>t</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>−<!-- − --></mo>
  <mn>14</mn>
  <mi>t</mi>
  <mo>+</mo>
  <mn>8</mn>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 5">
  <mn>0</mn>
  <mo>⩽<!-- ⩽ --></mo>
  <mi>t</mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mn>5</mn>
</math></span>.</p>
</div>

<div class="specification">
<p>When <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 0">
  <mi>t</mi>
  <mo>=</mo>
  <mn>0</mn>
</math></span>, the velocity of P is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3{\text{ m}}\,{{\text{s}}^{ - 1}}">
  <mn>3</mn>
  <mrow>
    <mtext>&nbsp;m</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <msup>
      <mrow>
        <mtext>s</mtext>
      </mrow>
      <mrow>
        <mo>−<!-- − --></mo>
        <mn>1</mn>
      </mrow>
    </msup>
  </mrow>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 0"> <mi>a</mi> <mo>=</mo> <mn>0</mn> </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>Hence or otherwise, find all possible values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> for which the velocity of P is decreasing.</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 an expression for the velocity of P at time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span>.</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 total distance travelled by P when its velocity is increasing.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle P moves along a straight line. Its velocity <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{P}}}{\text{ m}}\,{{\text{s}}^{ - 1}}">
  <mrow>
    <msub>
      <mi>v</mi>
      <mrow>
        <mtext>P</mtext>
      </mrow>
    </msub>
  </mrow>
  <mrow>
    <mtext>&nbsp;m</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <msup>
      <mrow>
        <mtext>s</mtext>
      </mrow>
      <mrow>
        <mo>−<!-- − --></mo>
        <mn>1</mn>
      </mrow>
    </msup>
  </mrow>
</math></span> after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> seconds is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{P}}} = \sqrt t \sin \left( {\frac{\pi }{2}t} \right)">
  <mrow>
    <msub>
      <mi>v</mi>
      <mrow>
        <mtext>P</mtext>
      </mrow>
    </msub>
  </mrow>
  <mo>=</mo>
  <msqrt>
    <mi>t</mi>
  </msqrt>
  <mi>sin</mi>
  <mo>⁡<!-- ⁡ --></mo>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mfrac>
        <mi>π<!-- π --></mi>
        <mn>2</mn>
      </mfrac>
      <mi>t</mi>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 8">
  <mn>0</mn>
  <mo>⩽<!-- ⩽ --></mo>
  <mi>t</mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mn>8</mn>
</math></span>. The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{P}}}">
  <mrow>
    <msub>
      <mi>v</mi>
      <mrow>
        <mtext>P</mtext>
      </mrow>
    </msub>
  </mrow>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_10.04.21.png" alt="M17/5/MATME/SP2/ENG/TZ1/07"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the first value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> at which P changes direction.</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 <strong>total </strong>distance travelled by P, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 8"> <mn>0</mn> <mo>⩽</mo> <mi>t</mi> <mo>⩽</mo> <mn>8</mn> </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>A second particle Q also moves along a straight line. Its velocity, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{Q}}}{\text{ m}}\,{{\text{s}}^{ - 1}}"> <mrow> <msub> <mi>v</mi> <mrow> <mtext>Q</mtext> </mrow> </msub> </mrow> <mrow> <mtext>&nbsp;m</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <msup> <mrow> <mtext>s</mtext> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></span> after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> seconds is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{Q}}} = \sqrt t "> <mrow> <msub> <mi>v</mi> <mrow> <mtext>Q</mtext> </mrow> </msub> </mrow> <mo>=</mo> <msqrt> <mi>t</mi> </msqrt> </math></span> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 8"> <mn>0</mn> <mo>⩽</mo> <mi>t</mi> <mo>⩽</mo> <mn>8</mn> </math></span>. After <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span> seconds Q has travelled the same total distance as P.</p>
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle P starts from a point A and moves along a horizontal straight line. Its velocity <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v{\text{ cm}}\,{{\text{s}}^{ - 1}}">
  <mi>v</mi>
  <mrow>
    <mtext>&nbsp;cm</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <msup>
      <mrow>
        <mtext>s</mtext>
      </mrow>
      <mrow>
        <mo>−<!-- − --></mo>
        <mn>1</mn>
      </mrow>
    </msup>
  </mrow>
</math></span> after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> seconds is given by</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="v(t) = \left\{ {\begin{array}{*{20}{l}} { - 2t + 2,}&amp;{{\text{for }}0 \leqslant t \leqslant 1} \\ {3\sqrt t + \frac{4}{{{t^2}}} - 7,}&amp;{{\text{for }}1 \leqslant t \leqslant 12} \end{array}} \right.">
  <mi>v</mi>
  <mo stretchy="false">(</mo>
  <mi>t</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mrow>
    <mo>{</mo>
    <mrow>
      <mtable columnalign="left" rowspacing="4pt" columnspacing="1em">
        <mtr>
          <mtd>
            <mrow>
              <mo>−<!-- − --></mo>
              <mn>2</mn>
              <mi>t</mi>
              <mo>+</mo>
              <mn>2</mn>
              <mo>,</mo>
            </mrow>
          </mtd>
          <mtd>
            <mrow>
              <mrow>
                <mtext>for&nbsp;</mtext>
              </mrow>
              <mn>0</mn>
              <mo>⩽<!-- ⩽ --></mo>
              <mi>t</mi>
              <mo>⩽<!-- ⩽ --></mo>
              <mn>1</mn>
            </mrow>
          </mtd>
        </mtr>
        <mtr>
          <mtd>
            <mrow>
              <mn>3</mn>
              <msqrt>
                <mi>t</mi>
              </msqrt>
              <mo>+</mo>
              <mfrac>
                <mn>4</mn>
                <mrow>
                  <mrow>
                    <msup>
                      <mi>t</mi>
                      <mn>2</mn>
                    </msup>
                  </mrow>
                </mrow>
              </mfrac>
              <mo>−<!-- − --></mo>
              <mn>7</mn>
              <mo>,</mo>
            </mrow>
          </mtd>
          <mtd>
            <mrow>
              <mrow>
                <mtext>for&nbsp;</mtext>
              </mrow>
              <mn>1</mn>
              <mo>⩽<!-- ⩽ --></mo>
              <mi>t</mi>
              <mo>⩽<!-- ⩽ --></mo>
              <mn>12</mn>
            </mrow>
          </mtd>
        </mtr>
      </mtable>
    </mrow>
    <mo fence="true" stretchy="true" symmetric="true"></mo>
  </mrow>
</math></span></p>
<p>The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
  <mi>v</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-03_om_16.40.29.png" alt="N16/5/MATME/SP2/ENG/TZ0/09"></p>
</div>

<div class="specification">
<p>P is at rest when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 1">
  <mi>t</mi>
  <mo>=</mo>
  <mn>1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = p">
  <mi>t</mi>
  <mo>=</mo>
  <mi>p</mi>
</math></span>.</p>
</div>

<div class="specification">
<p>When <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = q">
  <mi>t</mi>
  <mo>=</mo>
  <mi>q</mi>
</math></span>, the acceleration of P is zero.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the initial velocity of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P"> <mi>P</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">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="p"> <mi>p</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) &nbsp; &nbsp; Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q"> <mi>q</mi> </math></span>.</p>
<p>(ii) &nbsp; &nbsp; Hence, find the <strong>speed </strong>of P when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = q"> <mi>t</mi> <mo>=</mo> <mi>q</mi> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) &nbsp; &nbsp; Find the total distance travelled by P between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 1"> <mi>t</mi> <mo>=</mo> <mn>1</mn> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = p"> <mi>t</mi> <mo>=</mo> <mi>p</mi> </math></span>.</p>
<p>(ii) &nbsp; &nbsp; Hence or otherwise, find the displacement of P from A when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = p"> <mi>t</mi> <mo>=</mo> <mi>p</mi> </math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle moves along a straight line so that its velocity,&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
  <mi>v</mi>
</math></span> m s<sup>−1</sup>, after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> seconds is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v\left( t \right) = {1.4^t} - 2.7">
  <mi>v</mi>
  <mrow>
    <mo>(</mo>
    <mi>t</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mrow>
    <msup>
      <mn>1.4</mn>
      <mi>t</mi>
    </msup>
  </mrow>
  <mo>−<!-- − --></mo>
  <mn>2.7</mn>
</math></span>, for 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> ≤ 5.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find when the particle is at rest.</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 acceleration of the particle when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 2">
  <mi>t</mi>
  <mo>=</mo>
  <mn>2</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total distance travelled by the particle.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The function&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{1}{3}{x^3} + \frac{1}{2}{x^2} + kx + 5">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mfrac>
    <mn>1</mn>
    <mn>3</mn>
  </mfrac>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>3</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mfrac>
    <mn>1</mn>
    <mn>2</mn>
  </mfrac>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mi>k</mi>
  <mi>x</mi>
  <mo>+</mo>
  <mn>5</mn>
</math></span>&nbsp;has a local maximum and a local minimum. The local maximum is at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x =&nbsp; - 3">
  <mi>x</mi>
  <mo>=</mo>
  <mo>−<!-- − --></mo>
  <mn>3</mn>
</math></span>.</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="k = - 6">
  <mi>k</mi>
  <mo>=</mo>
  <mo>−</mo>
  <mn>6</mn>
</math></span>.</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>Find the coordinates of the local <strong>minimum</strong>.</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 interval where the gradient of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right)">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
</math></span> is negative.</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>Determine the equation of the normal at <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> in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = mx + c">
  <mi>y</mi>
  <mo>=</mo>
  <mi>m</mi>
  <mi>x</mi>
  <mo>+</mo>
  <mi>c</mi>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Let&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f''\left( x \right) = \left( {{\text{cos}}\,2x} \right)\left( {{\text{sin}}\,6x} \right)">
  <msup>
    <mi>f</mi>
    <mo>″</mo>
  </msup>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mrow>
        <mtext>cos</mtext>
      </mrow>
      <mspace width="thinmathspace"></mspace>
      <mn>2</mn>
      <mi>x</mi>
    </mrow>
    <mo>)</mo>
  </mrow>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mrow>
        <mtext>sin</mtext>
      </mrow>
      <mspace width="thinmathspace"></mspace>
      <mn>6</mn>
      <mi>x</mi>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>, for 0&nbsp;≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>&nbsp;≤ 1.</p>
</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''}">
  <mrow>
    <msup>
      <mi>f</mi>
      <mo>″</mo>
    </msup>
  </mrow>
</math></span> on the grid below:</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-coordinates of the points of inflexion of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> for which the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> is concave-down.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The population of fish in a lake is modelled by the function</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( t \right) = \frac{{1000}}{{1 + 24{{\text{e}}^{ - 0.2t}}}}">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>t</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>1000</mn>
    </mrow>
    <mrow>
      <mn>1</mn>
      <mo>+</mo>
      <mn>24</mn>
      <mrow>
        <msup>
          <mrow>
            <mtext>e</mtext>
          </mrow>
          <mrow>
            <mo>−<!-- − --></mo>
            <mn>0.2</mn>
            <mi>t</mi>
          </mrow>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span>, 0&nbsp;≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span>&nbsp;≤ 30 , where&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> is measured in months.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the population of fish at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> = 10.</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 rate at which the population of fish is increasing at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> = 10.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> for which the population of fish is increasing most rapidly.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle P moves along a straight line. The velocity <em>v</em> m s<sup>−1</sup> of P after <em>t</em> seconds is given by <em>v</em> (<em>t</em>) = 7 cos <em>t</em> − 5<em>t </em><sup>cos <em>t</em></sup>, for 0 ≤ <em>t</em> ≤ 7.</p>
<p>The following diagram shows the graph of <em>v</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the initial velocity of 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 maximum speed of P.</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 number of times that the acceleration of P is 0 m s<sup>−2</sup> .</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the acceleration of P when it changes direction.</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>Find the total distance travelled by P.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 6 - \ln ({x^2} + 2)">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mn>6</mn>
  <mo>−<!-- − --></mo>
  <mi>ln</mi>
  <mo>⁡<!-- ⁡ --></mo>
  <mo stretchy="false">(</mo>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>2</mn>
  <mo stretchy="false">)</mo>
</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>. The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> passes through the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(p,{\text{ }}4)">
  <mo stretchy="false">(</mo>
  <mi>p</mi>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mn>4</mn>
  <mo stretchy="false">)</mo>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p > 0">
  <mi>p</mi>
  <mo>&gt;</mo>
  <mn>0</mn>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
  <mi>p</mi>
</math></span>.</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>The following diagram shows part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>.</p>
<p><img src="images/Schermafbeelding_2018-02-12_om_13.30.18.png" alt="N17/5/MATME/SP2/ENG/TZ0/05.b"></p>
<p>The region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x =&nbsp; - p">
  <mi>x</mi>
  <mo>=</mo>
  <mo>−</mo>
  <mi>p</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p">
  <mi>x</mi>
  <mo>=</mo>
  <mi>p</mi>
</math></span> is rotated 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis. Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = {({x^2} + 3)^7}">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mrow>
    <mo stretchy="false">(</mo>
    <mrow>
      <msup>
        <mi>x</mi>
        <mn>2</mn>
      </msup>
    </mrow>
    <mo>+</mo>
    <mn>3</mn>
    <msup>
      <mo stretchy="false">)</mo>
      <mn>7</mn>
    </msup>
  </mrow>
</math></span>. Find the term in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^5}">
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>5</mn>
    </msup>
  </mrow>
</math></span> in the expansion of the derivative, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’(x)">
  <msup>
    <mi>f</mi>
    <mo>′</mo>
  </msup>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<br><hr><br><div class="question">
<p><strong>Note:</strong> &nbsp; &nbsp; <strong>In this question, distance is in metres and time is in seconds.</strong></p>
<p>&nbsp;</p>
<p>A particle moves along a horizontal line starting at a fixed point A. The velocity <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v"> <mi>v</mi> </math></span> of the particle, at time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span>, is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v(t) = \frac{{2{t^2} - 4t}}{{{t^2} - 2t + 2}}"> <mi>v</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mrow> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mn>4</mn> <mi>t</mi> </mrow> <mrow> <mrow> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mn>2</mn> <mi>t</mi> <mo>+</mo> <mn>2</mn> </mrow> </mfrac> </math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 5"> <mn>0</mn> <mo>⩽</mo> <mi>t</mi> <mo>⩽</mo> <mn>5</mn> </math></span>. The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v"> <mi>v</mi> </math></span></p>
<p><img src="images/Schermafbeelding_2017-08-15_om_08.18.11.png" alt="M17/5/MATME/SP2/ENG/TZ2/07"></p>
<p>There are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span>-intercepts at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(0,{\text{ }}0)"> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mrow> <mtext>&nbsp;</mtext> </mrow> <mn>0</mn> <mo stretchy="false">)</mo> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(2,{\text{ }}0)"> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mrow> <mtext>&nbsp;</mtext> </mrow> <mn>0</mn> <mo stretchy="false">)</mo> </math></span>.</p>
<p>Find the maximum distance of the particle from A during the time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 5"> <mn>0</mn> <mo>⩽</mo> <mi>t</mi> <mo>⩽</mo> <mn>5</mn> </math></span> and justify your answer.</p>
</div>
<br><hr><br>