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<h2>SL Paper 2</h2><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>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>Let&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>4</mn><mo>-</mo><msup><mi>x</mi><mn>3</mn></msup></math>&nbsp;and&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>ln</mi><mo> </mo><mi>x</mi></math>, for&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>0</mn></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>f</mi><mo>∘</mo><mi>g</mi></mrow></mfenced><mfenced><mi>x</mi></mfenced></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Solve the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>f</mi><mo>∘</mo><mi>g</mi></mrow></mfenced><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>x</mi></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>Hence or otherwise, given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mrow><mn>2</mn><mi>a</mi></mrow></mfenced><mo>=</mo><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mrow><mn>2</mn><mi>a</mi></mrow></mfenced></math>, find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</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 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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>Urvashi wants to model the height of a moving object. She collects the following data showing the height, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
  <mi>h</mi>
</math></span>&nbsp; metres, of the object at time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> seconds.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">She believes the height can be modeled by a quadratic function,&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h\left( t \right) = a{t^2} + bt + c">
  <mi>h</mi>
  <mrow>
    <mo>(</mo>
    <mi>t</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mi>a</mi>
  <mrow>
    <msup>
      <mi>t</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mi>b</mi>
  <mi>t</mi>
  <mo>+</mo>
  <mi>c</mi>
</math></span>, where&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a{\text{,}}\,\,b{\text{,}}\,\,c \in \mathbb{R}">
  <mi>a</mi>
  <mrow>
    <mtext>,</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mspace width="thinmathspace"></mspace>
  <mi>b</mi>
  <mrow>
    <mtext>,</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mspace width="thinmathspace"></mspace>
  <mi>c</mi>
  <mo>∈<!-- ∈ --></mo>
  <mrow>
    <mi mathvariant="double-struck">R</mi>
  </mrow>
</math></span>.</p>
</div>

<div class="specification">
<p>Hence find</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="4a + 2b + c = 34">
  <mn>4</mn>
  <mi>a</mi>
  <mo>+</mo>
  <mn>2</mn>
  <mi>b</mi>
  <mo>+</mo>
  <mi>c</mi>
  <mo>=</mo>
  <mn>34</mn>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down two more equations for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
  <mi>a</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
  <mi>b</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
  <mi>c</mi>
</math></span>.</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>Solve this system of three equations to find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
  <mi>a</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
  <mi>b</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
  <mi>c</mi>
</math></span>.</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>when the height of the object is zero.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the maximum height of the object.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A wind turbine is designed so that the rotation of the blades generates electricity. The turbine is built on horizontal ground and is made up of a vertical tower and three blades.</p>
<p>The point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> is on the base of the tower directly below point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> at the top of the tower. The height of the tower, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext></math>, is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo>&#8202;</mo><mtext>m</mtext></math>. The blades of the turbine are centred at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> and are each of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo>&#8202;</mo><mtext>m</mtext></math>. This is shown in the following diagram.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The end of one of the blades of the turbine is represented by point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> on the diagram. Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> be the height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> above the ground, measured in metres, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> varies as the blade rotates.</p>
</div>

<div class="specification">
<p>Find the</p>
</div>

<div class="specification">
<p>The blades of the turbine complete <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math> rotations per minute under normal conditions, moving at a constant rate.</p>
</div>

<div class="specification">
<p>The height, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>, of point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> can be modelled by the following function. Time, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>, is measured&nbsp;from the instant when the blade <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[BC]</mtext></math> first passes <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[AB]</mtext></math> and is measured in seconds.</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mn>90</mn><mo>-</mo><mn>40</mn><mo>&#8202;</mo><mi>cos</mi><mfenced><mrow><mn>72</mn><mi>t</mi><mo>&#176;</mo></mrow></mfenced><mo>,</mo><mo>&#160;</mo><mi>t</mi><mo>&#8805;</mo><mn>0</mn></math></p>
</div>

<div class="specification">
<p>Looking through his window, Tim has a partial view of the rotating wind turbine. The position&nbsp;of his window means that he cannot see any part of the wind turbine that is <strong>more than</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="bold">100</mn><mo mathvariant="bold">&#160;</mo><mtext mathvariant="bold">m</mtext></math>&nbsp;above the ground. This is illustrated in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>maximum value 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">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>minimum value 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">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the time, in seconds, it takes for the blade <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[BC]</mtext></math> to make one complete rotation under these conditions.</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>Calculate the angle, in degrees, that the blade <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[BC]</mtext></math> turns through in one second.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the amplitude of the function.</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 period of the function.</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 function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>5</mn></math>, clearly labelling the coordinates of the maximum and minimum points.</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 height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> above the ground when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the time, in seconds, that point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> is above a height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo> </mo><mtext>m</mtext></math>, during each complete rotation.</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>At any given instant, find the probability that point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> is visible from Tim’s window.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The wind speed increases. The blades rotate at twice the speed, but still at a constant rate.</p>
<p>At any given instant, find the probability that Tim can see point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> from his window. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The Texas Star is a Ferris wheel at the state fair in Dallas. The Ferris wheel has a diameter of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>61</mn><mo>.</mo><mn>8</mn><mo>&#8202;</mo><mtext>m</mtext></math>. To begin the ride, a passenger gets into a chair at the lowest point on the wheel, which is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>7</mn><mo>&#8202;</mo><mtext>m</mtext></math> above the ground, as shown in the following diagram. A ride consists of multiple revolutions, and the Ferris wheel makes <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn></math> revolutions per minute.</p>
<p style="text-align: center;"><img 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"></p>
<p>The&nbsp;height of a chair above the ground, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>, measured in metres, during a ride on the Ferris wheel can be modelled by the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mo>&#8722;</mo><mi>a</mi><mo>&#8202;</mo><mi>cos</mi><mo>(</mo><mi>b</mi><mi>t</mi><mo>)</mo><mo>+</mo><mi>d</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is the time, in seconds, since a passenger began their ride.</p>
</div>

<div class="specification">
<p>Calculate the value of</p>
</div>

<div class="specification">
<p>A ride on the Ferris wheel lasts for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math> minutes in total.</p>
</div>

<div class="specification">
<p>For exactly one ride on the Ferris wheel, suggest</p>
</div>

<div class="specification">
<p>Big Tex is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>.</mo><mn>7</mn></math>&nbsp;metre-tall cowboy statue that stands on the horizontal ground next to the&nbsp;Ferris wheel.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: center;"><sup><br>[Source: Aline Escobar., n.d. Cowboy. [image online] Available at: <a href="https://thenounproject.com/search/?q=cowboy&i=1080130">https://thenounproject.com/search/?q=cowboy&amp;i=1080130</a><br>This file&nbsp;is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) <br><a href="https://creativecommons.org/licenses/by-sa/3.0/deed.en">https://creativecommons.org/licenses/by-sa/3.0/deed.en</a> [Accessed 13/05/2021]. Source adapted.]</sup></p>
</div>

<div class="specification">
<p>There is a plan to relocate the Texas Star Ferris wheel onto a taller platform which will increase&nbsp;the maximum height of the Ferris wheel to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>65</mn><mo>.</mo><mn>2</mn><mo>&#8202;</mo><mtext>m</mtext></math>. This will change the value of one parameter,&nbsp;<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> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>, found in part (a).</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the number of revolutions of the Ferris wheel per ride.</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>an appropriate domain for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo></math>.</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>an appropriate range for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo></math>.</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>By considering the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo></math>, determine the length of time during one revolution of the Ferris wheel for which the chair is higher than the cowboy statue.</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>Identify which parameter will change.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the new value of the parameter identified in part (e)(i).</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</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>A pan, in which to cook a pizza, is in the shape of a cylinder. The pan has a diameter of 35 cm and a height of 0.5 cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_11.14.51.png" alt="M17/5/MATSD/SP2/ENG/TZ1/04"></p>
</div>

<div class="specification">
<p>A chef had enough pizza dough to exactly fill the pan. The dough was in the shape of a sphere.</p>
</div>

<div class="specification">
<p>The pizza was cooked in a hot oven. Once taken out of the oven, the pizza was placed in a dining room.</p>
<p>The temperature, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P">
  <mi>P</mi>
</math></span>, of the pizza, in degrees Celsius, °C, can be modelled by</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="P(t) = a{(2.06)^{ - t}} + 19,{\text{ }}t \geqslant 0">
  <mi>P</mi>
  <mo stretchy="false">(</mo>
  <mi>t</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mi>a</mi>
  <mrow>
    <mo stretchy="false">(</mo>
    <mn>2.06</mn>
    <msup>
      <mo stretchy="false">)</mo>
      <mrow>
        <mo>−<!-- − --></mo>
        <mi>t</mi>
      </mrow>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>19</mn>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mi>t</mi>
  <mo>⩾<!-- ⩾ --></mo>
  <mn>0</mn>
</math></span></p>
<p>where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
  <mi>a</mi>
</math></span> is a constant and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> is the time, in minutes, since the pizza was taken out of the oven.</p>
<p>When the pizza was taken out of the oven its temperature was 230 °C.</p>
</div>

<div class="specification">
<p>The pizza can be eaten once its temperature drops to 45 °C.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the volume of this pan.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the radius of the sphere in cm, correct to one decimal place.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
  <mi>a</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the temperature that the pizza will be 5 minutes after it is taken out of the oven.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, to the nearest second, the time since the pizza was taken out of the oven until it can be eaten.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the context of this model, state what the value of 19 represents.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<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>At Grande Anse Beach the height of the water in metres is modelled by the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h(t) = p\cos (q \times t) + r">
  <mi>h</mi>
  <mo stretchy="false">(</mo>
  <mi>t</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mi>p</mi>
  <mi>cos</mi>
  <mo>⁡<!-- ⁡ --></mo>
  <mo stretchy="false">(</mo>
  <mi>q</mi>
  <mo>×<!-- × --></mo>
  <mi>t</mi>
  <mo stretchy="false">)</mo>
  <mo>+</mo>
  <mi>r</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> is the number of hours after 21:00 hours on 10 December 2017. The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
  <mi>h</mi>
</math></span> , for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 72">
  <mn>0</mn>
  <mo>⩽<!-- ⩽ --></mo>
  <mi>t</mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mn>72</mn>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_10.10.26.png" alt="M17/5/MATME/SP2/ENG/TZ1/08"></p>
<p>The point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}(6.25,{\text{ }}0.6)">
  <mrow>
    <mtext>A</mtext>
  </mrow>
  <mo stretchy="false">(</mo>
  <mn>6.25</mn>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mn>0.6</mn>
  <mo stretchy="false">)</mo>
</math></span> represents the first low tide and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}(12.5,{\text{ }}1.5)">
  <mrow>
    <mtext>B</mtext>
  </mrow>
  <mo stretchy="false">(</mo>
  <mn>12.5</mn>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mn>1.5</mn>
  <mo stretchy="false">)</mo>
</math></span> represents the next high tide.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>How much time is there between the first low tide and the next high tide?</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the difference in height between low tide and high tide.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>;</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q"> <mi>q</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>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>There are two high tides on 12 December 2017. At what time does the second high tide occur?</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = {x^2} - 1">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>−<!-- − --></mo>
  <mn>1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = {x^2} - 2">
  <mi>g</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>−<!-- − --></mo>
  <mn>2</mn>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
  <mi>x</mi>
  <mo>∈<!-- ∈ --></mo>
  <mrow>
    <mi mathvariant="double-struck">R</mi>
  </mrow>
</math></span>.</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="(f \circ g)(x) = {x^4} - 4{x^2} + 3">
  <mo stretchy="false">(</mo>
  <mi>f</mi>
  <mo>∘</mo>
  <mi>g</mi>
  <mo stretchy="false">)</mo>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>4</mn>
    </msup>
  </mrow>
  <mo>−</mo>
  <mn>4</mn>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>3</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>On the following grid, sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(f \circ g)(x)">
  <mo stretchy="false">(</mo>
  <mi>f</mi>
  <mo>∘</mo>
  <mi>g</mi>
  <mo stretchy="false">)</mo>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant x \leqslant 2.25">
  <mn>0</mn>
  <mo>⩽</mo>
  <mi>x</mi>
  <mo>⩽</mo>
  <mn>2.25</mn>
</math></span>.</p>
<p><img src="images/Schermafbeelding_2017-08-15_om_08.00.33.png" alt="M17/5/MATME/SP2/ENG/TZ2/06.b"></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(f \circ g)(x) = k">
  <mo stretchy="false">(</mo>
  <mi>f</mi>
  <mo>∘</mo>
  <mi>g</mi>
  <mo stretchy="false">)</mo>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mi>k</mi>
</math></span> has exactly two solutions, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant x \leqslant 2.25">
  <mn>0</mn>
  <mo>⩽</mo>
  <mi>x</mi>
  <mo>⩽</mo>
  <mn>2.25</mn>
</math></span>. Find the possible values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
  <mi>k</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</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) = 0.3{x^3} + \frac{{10}}{x} + {2^{ - x}}">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mn>0.3</mn>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>3</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mfrac>
    <mrow>
      <mn>10</mn>
    </mrow>
    <mi>x</mi>
  </mfrac>
  <mo>+</mo>
  <mrow>
    <msup>
      <mn>2</mn>
      <mrow>
        <mo>−<!-- − --></mo>
        <mi>x</mi>
      </mrow>
    </msup>
  </mrow>
</math></span>.</p>
</div>

<div class="specification">
<p>Consider a second function, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = 2x - 3">
  <mi>g</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mn>2</mn>
  <mi>x</mi>
  <mo>−<!-- − --></mo>
  <mn>3</mn>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(1)">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mn>1</mn>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 7 \leqslant x \leqslant 4">
  <mo>−</mo>
  <mn>7</mn>
  <mo>⩽</mo>
  <mi>x</mi>
  <mo>⩽</mo>
  <mn>4</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 30 \leqslant y \leqslant 30">
  <mo>−</mo>
  <mn>30</mn>
  <mo>⩽</mo>
  <mi>y</mi>
  <mo>⩽</mo>
  <mn>30</mn>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the vertical asymptote.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-intercept.</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>Write down the possible 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="x &lt; 0">
  <mi>x</mi>
  <mo>&lt;</mo>
  <mn>0</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’(x) &gt; 0">
  <msup>
    <mi>f</mi>
    <mo>′</mo>
  </msup>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>&gt;</mo>
  <mn>0</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 solution of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = g(x)">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mi>g</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">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="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>The diagram shows the straight line <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math>. Points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mfenced><mrow><mo>-</mo><mn>9</mn><mo>,</mo><mo>&nbsp;</mo><mo>-</mo><mn>1</mn></mrow></mfenced></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext><mfenced><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mo>&nbsp;</mo><mn>2</mn></mrow></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> are points on <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math>.</p>
<p style="text-align: center;"><img 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"></p>
</div>

<div class="specification">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> is the midpoint of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AC</mtext></math>.</p>
</div>

<div class="specification">
<p>Line <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub></math> is perpendicular to <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math> and passes through point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math>.</p>
</div>

<div class="specification">
<p>The point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>N</mtext><mfenced><mrow><mi>k</mi><mo>,</mo><mo>&nbsp;</mo><mn>4</mn></mrow></mfenced></math> is on <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the gradient of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub></math>. Give your answer in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi><mi>y</mi><mo>+</mo><mi>d</mi><mo>=</mo><mn>0</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi><mo>,</mo><mo> </mo><mi>d</mi><mo>∈</mo><mi mathvariant="normal">ℤ</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>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">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the distance between points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>N</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>Given that the length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AM</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>45</mn></msqrt></math>, find the area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ANC</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</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) = 2\,{\text{sin}}\left( {3x} \right) + 4">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mn>2</mn>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>sin</mtext>
  </mrow>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mn>3</mn>
      <mi>x</mi>
    </mrow>
    <mo>)</mo>
  </mrow>
  <mo>+</mo>
  <mn>4</mn>
</math></span> for&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="specification">
<p>Let&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = 5f\left( {2x} \right)">
  <mi>g</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mn>5</mn>
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mn>2</mn>
      <mi>x</mi>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
</div>

<div class="specification">
<p>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
  <mi>g</mi>
</math></span> can be written in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = 10\,{\text{sin}}\left( {bx} \right) + c">
  <mi>g</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mn>10</mn>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>sin</mtext>
  </mrow>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mi>b</mi>
      <mi>x</mi>
    </mrow>
    <mo>)</mo>
  </mrow>
  <mo>+</mo>
  <mi>c</mi>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span> ≤ <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> ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m"> <mi>m</mi> </math></span>. Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m"> <mi>m</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g"> <mi>g</mi> </math></span>.</p>
<div class="marks">[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="b"> <mi>b</mi> </math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c"> <mi>c</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the period of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g"> <mi>g</mi> </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>The equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = 12"> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>12</mn> </math></span> has two solutions where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi "> <mi>π</mi> </math></span> ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{{4\pi }}{3}}"> <mrow> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> </mrow> <mn>3</mn> </mfrac> </mrow> </math></span>. Find both solutions.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</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>The diagram below shows a circular clockface with centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>. The clock’s minute hand has a length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mtext>cm</mtext></math>. The clock’s hour hand has a length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo> </mo><mtext>cm</mtext></math>.</p>
<p>At <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>:</mo><mn>00</mn></math> pm the endpoint of the minute hand is at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and the endpoint of the hour hand is at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>&nbsp;</p>
</div>

<div class="specification">
<p>Between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>:</mo><mn>00</mn></math> pm and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>:</mo><mn>13</mn></math> pm, the endpoint of the <strong>minute hand</strong> rotates through an angle, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math>, from point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> to point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>. This is illustrated in the diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>A <strong>second</strong> clock is illustrated in the diagram below. The clock face has radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mtext>cm</mtext></math> with&nbsp;minute and hour hands both of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mtext>cm</mtext></math>. The time shown is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>:</mo><mn>00</mn></math> am. The bottom of the&nbsp;clock face is located <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo> </mo><mtext>cm</mtext></math> above a horizontal bookshelf.</p>
<p style="text-align: center;"><img 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"></p>
</div>

<div class="specification">
<p>The height, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> centimetres, of the endpoint of the minute hand above the bookshelf is&nbsp;modelled by the function</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>θ</mi></mfenced><mo>=</mo><mn>10</mn><mo> </mo><mi>cos</mi><mo> </mo><mi>θ</mi><mo>+</mo><mn>13</mn><mo>,</mo><mo>&nbsp;</mo><mi>θ</mi><mo>≥</mo><mn>0</mn><mo>,</mo></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> is the angle rotated by the minute hand from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>:</mo><mn>00</mn></math> am.</p>
</div>

<div class="specification">
<p>The height, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> centimetres, of the endpoint of the <strong>hour hand</strong> above the bookshelf is modelled&nbsp;by the function</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>θ</mi></mfenced><mo>=</mo><mo>-</mo><mn>10</mn><mo> </mo><mi>cos</mi><mfenced><mfrac><mi>θ</mi><mn>12</mn></mfrac></mfenced><mo>+</mo><mn>13</mn><mo>,</mo><mo>&nbsp;</mo><mi>θ</mi><mo>≥</mo><mn>0</mn><mo>,</mo></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> is the angle in degrees rotated by the minute hand from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>:</mo><mn>00</mn></math> am.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the size of angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>B</mtext></math> in degrees.</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 distance between points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</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 size of angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> in degrees.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AC</mtext></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>Calculate the area of the shaded sector,&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AOC</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>Write down the height of the endpoint of the minute hand above the bookshelf&nbsp;at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>:</mo><mn>00</mn></math> am.</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>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mn>160</mn><mo>°</mo></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>Write down the amplitude of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>θ</mi><mo>)</mo></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The endpoints of the minute hand and hour hand meet when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mi>k</mi></math>.</p>
<p>Find the smallest possible 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">i.</div>
</div>
<br><hr><br><div class="specification">
<p>Boris recorded the number of daylight hours on the first day of each month in a northern hemisphere town.</p>
<p>This data was plotted onto a scatter diagram.&nbsp;The points were then joined by a smooth curve, with minimum point <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo>&#160;</mo><mn>8</mn><mo>)</mo></math> and maximum point <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>6</mn><mo>,</mo><mo>&#160;</mo><mn>16</mn><mo>)</mo></math> as shown in the following diagram.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>Let the curve in the diagram be <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is the time, measured in months, since Boris first recorded these values.</p>
<p>Boris thinks that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> might be modelled by a quadratic function.</p>
</div>

<div class="specification">
<p>Paula thinks that a better model is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo>&#8202;</mo><mi>cos</mi><mo>(</mo><mi>b</mi><mi>t</mi><mo>)</mo><mo>+</mo><mi>d</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>&#8805;</mo><mn>0</mn></math>, for specific values of&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo>&#160;</mo><mi>b</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>.</p>
</div>

<div class="specification">
<p>For Paula&rsquo;s model, use the diagram to write down</p>
</div>

<div class="specification">
<p>The true maximum number of daylight hours was <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn></math> hours and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math> minutes.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down one reason why a quadratic function would not be a good model for the number of hours of daylight per day, across a number of years.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the amplitude.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the period.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the equation of the principal axis.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise find the equation of this model in the form:</p>
<p style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo> </mo><mi>cos</mi><mo>(</mo><mi>b</mi><mi>t</mi><mo>)</mo><mo>+</mo><mi>d</mi></math></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the first year of the model, find the length of time when there are more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> hours and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> minutes of daylight per day.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the percentage error in the maximum number of daylight hours Boris recorded in the diagram.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><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>In the month before their IB Diploma examinations, eight male students recorded the number of hours they spent on social media.</p>
<p>For each student, the number of hours spent on social media (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>) and the number of IB Diploma points obtained (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span>) are shown in the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_07.43.52.png" alt="N16/5/MATSD/SP2/ENG/TZ0/01"></p>
</div>

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

<div class="specification">
<p>Ten female students also recorded the number of hours they spent on social media in the month before their IB Diploma examinations. Each of these female students spent between 3 and 30 hours on social media.</p>
<p>The equation of the regression line <em>y </em>on <em>x </em>for these ten female students is</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="y = &nbsp;- \frac{2}{3}x + \frac{{125}}{3}.">
  <mi>y</mi>
  <mo>=</mo>
  <mo>−<!-- − --></mo>
  <mfrac>
    <mn>2</mn>
    <mn>3</mn>
  </mfrac>
  <mi>x</mi>
  <mo>+</mo>
  <mfrac>
    <mrow>
      <mn>125</mn>
    </mrow>
    <mn>3</mn>
  </mfrac>
  <mo>.</mo>
</math></span></p>
<p>An eleventh girl spent 34 hours on social media in the month before her IB Diploma examinations.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On graph paper, draw a scatter diagram for these data. Use a scale of 2 cm to represent 5 hours on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis and 2 cm to represent 10 points 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">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i)     <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar x}">
  <mrow>
    <mrow>
      <mover>
        <mi>x</mi>
        <mo stretchy="false">¯</mo>
      </mover>
    </mrow>
  </mrow>
</math></span>, the mean number of hours spent on social media;</p>
<p>(ii)     <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar y}">
  <mrow>
    <mrow>
      <mover>
        <mi>y</mi>
        <mo stretchy="false">¯</mo>
      </mover>
    </mrow>
  </mrow>
</math></span>, the mean number of IB Diploma points.</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>Plot the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(\bar x,{\text{ }}\bar y)">
  <mo stretchy="false">(</mo>
  <mrow>
    <mover>
      <mi>x</mi>
      <mo stretchy="false">¯</mo>
    </mover>
  </mrow>
  <mo>,</mo>
  <mrow>
    <mtext> </mtext>
  </mrow>
  <mrow>
    <mover>
      <mi>y</mi>
      <mo stretchy="false">¯</mo>
    </mover>
  </mrow>
  <mo stretchy="false">)</mo>
</math></span> on your scatter diagram and label this point M.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> for these eight male students.</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>Draw the regression line, from part (e), on your scatter diagram.</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>Use the given equation of the regression line to estimate the number of IB Diploma points that this girl obtained.</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>Write down a reason why this estimate is not reliable.</p>
<div class="marks">[1]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>The braking distance of a vehicle is defined as the distance travelled from where the brakes&nbsp;are applied to the point where the vehicle comes to a complete stop.</p>
<p>The speed, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s\,{\text{m}}\,{{\text{s}}^{ - 1}}">
  <mi>s</mi>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>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>, and braking distance, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d\,{\text{m}}">
  <mi>d</mi>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>m</mtext>
  </mrow>
</math></span>, of a truck were recorded. This information is&nbsp;summarized in the following table.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>This information was used to create Model A, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
  <mi>d</mi>
</math></span> is a function of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s">
  <mi>s</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s">
  <mi>s</mi>
</math></span> ≥ 0.</p>
<p style="text-align: center;">Model A: <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d\left( s \right) = p{s^2} + qs">
  <mi>d</mi>
  <mrow>
    <mo>(</mo>
    <mi>s</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mi>p</mi>
  <mrow>
    <msup>
      <mi>s</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mi>q</mi>
  <mi>s</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
  <mi>p</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q \in \mathbb{Z}">
  <mi>q</mi>
  <mo>∈<!-- ∈ --></mo>
  <mrow>
    <mi mathvariant="double-struck">Z</mi>
  </mrow>
</math></span></p>
<p>At a speed of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6\,{\text{m}}\,{{\text{s}}^{ - 1}}">
  <mn>6</mn>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>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>, Model A can be represented by the equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6p + q = 2">
  <mn>6</mn>
  <mi>p</mi>
  <mo>+</mo>
  <mi>q</mi>
  <mo>=</mo>
  <mn>2</mn>
</math></span>.</p>
</div>

<div class="specification">
<p>Additional data was used to create Model B, <strong>a revised model</strong> for the braking distance of a truck.</p>
<p style="text-align: center;">Model B:&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d\left( s \right) = 0.95{s^2} - 3.92s">
  <mi>d</mi>
  <mrow>
    <mo>(</mo>
    <mi>s</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mn>0.95</mn>
  <mrow>
    <msup>
      <mi>s</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>−<!-- − --></mo>
  <mn>3.92</mn>
  <mi>s</mi>
</math></span></p>
</div>

<div class="specification">
<p>The actual braking distance at&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="20\,{\text{m}}\,{{\text{s}}^{ - 1}}">
  <mn>20</mn>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>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> is&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="320\,{\text{m}}">
  <mn>320</mn>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>m</mtext>
  </mrow>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a second equation to represent Model A, when the speed is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10\,{\text{m}}\,{{\text{s}}^{ - 1}}">
  <mn>10</mn>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>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 class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
  <mi>p</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
  <mi>q</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of the vertex of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = d\left( s \right)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>d</mi>
  <mrow>
    <mo>(</mo>
    <mi>s</mi>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the values in the table and your answer to part (b), sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = d\left( s \right)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>d</mi>
  <mrow>
    <mo>(</mo>
    <mi>s</mi>
    <mo>)</mo>
  </mrow>
</math></span> for 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s">
  <mi>s</mi>
</math></span> ≤ 10 and −10 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
  <mi>d</mi>
</math></span> ≤ 60, clearly showing the vertex.</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>Hence, identify why Model A may not be appropriate at lower speeds.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Model B to calculate an estimate for the braking distance at a speed of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="20\,{\text{m}}\,{{\text{s}}^{ - 1}}">
  <mn>20</mn>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>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 class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the percentage error in the estimate in part (e).</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>It is found that once a driver realizes the need to stop their vehicle, 1.6 seconds will elapse, on average, before the brakes are engaged. During this reaction time, the vehicle will continue to travel at its original speed.</p>
<p>A truck approaches an intersection with speed <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s\,{\text{m}}\,{{\text{s}}^{ - 1}}">
  <mi>s</mi>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>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>. The driver notices the intersection’s traffic lights are red and they must stop the vehicle within a distance of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="330\,{\text{m}}">
  <mn>330</mn>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>m</mtext>
  </mrow>
</math></span>.</p>
<p style="text-align: center;"><img 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"></p>
<p>Using model B and taking reaction time into account, calculate the maximum possible speed of the truck if it is to stop before the intersection.</p>
<div class="marks">[3]</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{{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 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>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>The depth of water in a port is modelled by the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d(t) = p\cos qt + 7.5">
  <mi>d</mi>
  <mo stretchy="false">(</mo>
  <mi>t</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mi>p</mi>
  <mi>cos</mi>
  <mo>⁡<!-- ⁡ --></mo>
  <mi>q</mi>
  <mi>t</mi>
  <mo>+</mo>
  <mn>7.5</mn>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 12">
  <mn>0</mn>
  <mo>⩽<!-- ⩽ --></mo>
  <mi>t</mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mn>12</mn>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> is the number of hours after high tide.</p>
<p>At high tide, the depth is 9.7 metres.</p>
<p>At low tide, which is 7 hours later, the depth is 5.3 metres.</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>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
  <mi>q</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>Use the model to find the depth of the water 10 hours after high tide.</p>
<div class="marks">[2]</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="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>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = {x^2} + 2x + 1">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>2</mn>
  <mi>x</mi>
  <mo>+</mo>
  <mn>1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = x - 5">
  <mi>g</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mi>x</mi>
  <mo>−<!-- − --></mo>
  <mn>5</mn>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
  <mi>x</mi>
  <mo>∈<!-- ∈ --></mo>
  <mrow>
    <mi mathvariant="double-struck">R</mi>
  </mrow>
</math></span>.</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(8)">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mn>8</mn>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(g \circ f)(x)">
  <mo stretchy="false">(</mo>
  <mi>g</mi>
  <mo>∘</mo>
  <mi>f</mi>
  <mo stretchy="false">)</mo>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Solve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(g \circ f)(x) = 0">
  <mo stretchy="false">(</mo>
  <mi>g</mi>
  <mo>∘</mo>
  <mi>f</mi>
  <mo stretchy="false">)</mo>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mn>0</mn>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>+</mo><mfrac><mn>50</mn><mi>x</mi></mfrac><mo>,</mo><mo>&nbsp;</mo><mo> </mo><mi>x</mi><mo>≠</mo><mn>0</mn><mo>.</mo></math></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mn>1</mn></mfenced></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Solve <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>0</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> has a local minimum at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>.</p>
<p>Find the coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a water wheel with 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>10</mn></math> metres. Water flows&nbsp;into buckets, turning the wheel clockwise at a constant speed.</p>
<p><br>The height, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> metres, of the top of a bucket above the ground <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> seconds after it passes&nbsp;through point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> is modelled by the function</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mn>13</mn><mo>+</mo><mn>8</mn><mo> </mo><mi>cos</mi><mfenced><mrow><mfrac><mi mathvariant="normal">π</mi><mn>18</mn></mfrac><mi>t</mi></mrow></mfenced><mo>-</mo><mn>6</mn><mo> </mo><mi>sin</mi><mfenced><mrow><mfrac><mi mathvariant="normal">π</mi><mn>18</mn></mfrac><mi>t</mi></mrow></mfenced></math>, for&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>≥</mo><mn>0</mn></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
</div>

<div class="specification">
<p>A bucket moves around to point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> which is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>06</mn></math> metres above the ground.&nbsp;It takes&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> seconds for the top of this bucket to go from point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> to point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
</div>

<div class="specification">
<p>The chord&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>[</mo><mtext>AB</mtext><mo>]</mo></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn><mo>.</mo><mn>0</mn></math> metres, correct to three significant figures.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> above the ground.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the number of seconds it takes for the water wheel to complete one rotation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the number of rotations the water wheel makes in one hour.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>B</mtext></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>Determine the rate of change of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> when the top of the bucket is at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Scott purchases food for his dog in large bags and feeds the dog the same amount of dog food each day. The amount of dog food left in the bag at the end of each day can be modelled by an arithmetic sequence.</p>
<p>On a particular day, Scott opened a new bag of dog food and fed his dog. By the end of the third day there were <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>115</mn><mo>.</mo><mn>5</mn></math> cups of dog food remaining in the bag and at the end of the eighth day there were <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>108</mn></math> cups of dog food remaining in the bag.</p>
</div>

<div class="specification">
<p>Find the number of cups of dog food</p>
</div>

<div class="specification">
<p>In <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2021</mn></math>, Scott spent <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>625</mn></math> on dog food. Scott expects that the amount he spends on dog food will increase at an annual rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>4</mn><mo>%</mo></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>fed to the dog per day.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>remaining in the bag at the end of the first day.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the number of days that Scott can feed his dog with one bag of food.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the amount that Scott expects to spend on dog food in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2025</mn></math>. Round your answer to the nearest dollar.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mtext>Σ</mtext><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mn>10</mn></munderover><mfenced><mrow><mn>625</mn><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>064</mn><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced></msup></mrow></mfenced></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe what the value in part (d)(i) represents in this context.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Comment on the appropriateness of modelling this scenario with a geometric sequence.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<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^3} - 5{x^2} + 6x - 3 + \frac{1}{x}">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>3</mn>
    </msup>
  </mrow>
  <mo>−<!-- − --></mo>
  <mn>5</mn>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>6</mn>
  <mi>x</mi>
  <mo>−<!-- − --></mo>
  <mn>3</mn>
  <mo>+</mo>
  <mfrac>
    <mn>1</mn>
    <mi>x</mi>
  </mfrac>
</math></span>,&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x > 0">
  <mi>x</mi>
  <mo>&gt;</mo>
  <mn>0</mn>
</math></span></p>
</div>

<div class="specification">
<p>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^3} - 5{x^2} + 6x - 3 + \frac{1}{x}">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>3</mn>
    </msup>
  </mrow>
  <mo>−<!-- − --></mo>
  <mn>5</mn>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>6</mn>
  <mi>x</mi>
  <mo>−<!-- − --></mo>
  <mn>3</mn>
  <mo>+</mo>
  <mfrac>
    <mn>1</mn>
    <mi>x</mi>
  </mfrac>
</math></span>,&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x > 0">
  <mi>x</mi>
  <mo>&gt;</mo>
  <mn>0</mn>
</math></span>, models the path of a river, as shown on the&nbsp;following map, where both axes represent distance and are measured in kilometres. On the&nbsp;same map, the location of a highway is defined by the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = 0.5{\left( 3 \right)^{ - x}} + 1">
  <mi>g</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mn>0.5</mn>
  <mrow>
    <msup>
      <mrow>
        <mo>(</mo>
        <mn>3</mn>
        <mo>)</mo>
      </mrow>
      <mrow>
        <mo>−<!-- − --></mo>
        <mi>x</mi>
      </mrow>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>1</mn>
</math></span>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The origin, O(0, 0) , is the location of the centre of a town called Orangeton.</p>
<p>A straight footpath, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P">
  <mi>P</mi>
</math></span>, is built to connect the centre of Orangeton to the river at the point&nbsp;where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \frac{1}{2}">
  <mi>x</mi>
  <mo>=</mo>
  <mfrac>
    <mn>1</mn>
    <mn>2</mn>
  </mfrac>
</math></span>.</p>
</div>

<div class="specification">
<p>Bridges are located where the highway crosses the river.</p>
</div>

<div class="specification">
<p>A straight road is built from the centre of Orangeton, due north, to connect the town to&nbsp;the highway.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the domain 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.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the distance from the centre of Orangeton to the point at which the road meets the highway.</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>This straight road crosses the highway and then carries on due north.</p>
<p>State whether the straight road will ever cross the river. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>Note: In this question, distance is in millimetres.</strong></p>
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = x + a\sin \left( {x - \frac{\pi }{2}} \right) + a">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mi>x</mi>
  <mo>+</mo>
  <mi>a</mi>
  <mi>sin</mi>
  <mo>⁡<!-- ⁡ --></mo>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mi>x</mi>
      <mo>−<!-- − --></mo>
      <mfrac>
        <mi>π<!-- π --></mi>
        <mn>2</mn>
      </mfrac>
    </mrow>
    <mo>)</mo>
  </mrow>
  <mo>+</mo>
  <mi>a</mi>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \geqslant 0">
  <mi>x</mi>
  <mo>⩾<!-- ⩾ --></mo>
  <mn>0</mn>
</math></span>.</p>
</div>

<div class="specification">
<p>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 origin. Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_k}">
  <mrow>
    <msub>
      <mrow>
        <mtext>P</mtext>
      </mrow>
      <mi>k</mi>
    </msub>
  </mrow>
</math></span> be any point on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-coordinate <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2k\pi ">
  <mn>2</mn>
  <mi>k</mi>
  <mi>π<!-- π --></mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k \in \mathbb{N}">
  <mi>k</mi>
  <mo>∈<!-- ∈ --></mo>
  <mrow>
    <mi mathvariant="double-struck">N</mi>
  </mrow>
</math></span>. A straight line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
  <mi>L</mi>
</math></span> passes through all the points <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_k}">
  <mrow>
    <msub>
      <mrow>
        <mtext>P</mtext>
      </mrow>
      <mi>k</mi>
    </msub>
  </mrow>
</math></span>.</p>
</div>

<div class="specification">
<p>Diagram 1 shows a saw. The length of the toothed edge is the distance AB.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_15.10.11.png" alt="N17/5/MATME/SP2/ENG/TZ0/10.d_01"></p>
<p>The toothed edge of the saw can be modelled using the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
  <mi>L</mi>
</math></span>. Diagram 2 represents this model.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_15.11.17.png" alt="N17/5/MATME/SP2/ENG/TZ0/10.d_02"></p>
<p>The shaded part on the graph is called a tooth. A tooth is represented by 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> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
  <mi>L</mi>
</math></span>, between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_k}">
  <mrow>
    <msub>
      <mrow>
        <mtext>P</mtext>
      </mrow>
      <mi>k</mi>
    </msub>
  </mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_{k + 1}}">
  <mrow>
    <msub>
      <mrow>
        <mtext>P</mtext>
      </mrow>
      <mrow>
        <mi>k</mi>
        <mo>+</mo>
        <mn>1</mn>
      </mrow>
    </msub>
  </mrow>
</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="f(2\pi ) = 2\pi ">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mn>2</mn>
  <mi>π</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mn>2</mn>
  <mi>π</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_0}">
  <mrow>
    <msub>
      <mrow>
        <mtext>P</mtext>
      </mrow>
      <mn>0</mn>
    </msub>
  </mrow>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_1}">
  <mrow>
    <msub>
      <mrow>
        <mtext>P</mtext>
      </mrow>
      <mn>1</mn>
    </msub>
  </mrow>
</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>Find the equation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
  <mi>L</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>Show that the distance between the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-coordinates of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_k}">
  <mrow>
    <msub>
      <mrow>
        <mtext>P</mtext>
      </mrow>
      <mi>k</mi>
    </msub>
  </mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_{k + 1}}">
  <mrow>
    <msub>
      <mrow>
        <mtext>P</mtext>
      </mrow>
      <mrow>
        <mi>k</mi>
        <mo>+</mo>
        <mn>1</mn>
      </mrow>
    </msub>
  </mrow>
</math></span> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi ">
  <mn>2</mn>
  <mi>π</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A saw has a toothed edge which is 300 mm long. Find the number of complete teeth on this saw.</p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The Voronoi diagram below shows four supermarkets represented by points with coordinates&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mo>(</mo><mn>0</mn><mo>,</mo><mo>&#160;</mo><mn>0</mn><mo>)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext><mo>(</mo><mn>6</mn><mo>,</mo><mo>&#160;</mo><mn>0</mn><mo>)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext><mo>(</mo><mn>0</mn><mo>,</mo><mo>&#160;</mo><mn>6</mn><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext><mo>(</mo><mn>2</mn><mo>,</mo><mo>&#160;</mo><mn>2</mn><mo>)</mo></math>. The vertices <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>X</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Y</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Z</mtext></math> are also shown. All distances&nbsp;are measured in kilometres.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>The equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>(XY)</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>2</mn><mo>&#8722;</mo><mi>x</mi></math> and the equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>(YZ)</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>3</mn><mo>.</mo><mn>5</mn></math>.</p>
</div>

<div class="specification">
<p>The coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Y</mtext></math> are <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>&#8722;</mo><mn>1</mn><mo>,</mo><mo>&#160;</mo><mn>3</mn><mo>)</mo></math> and the coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Z</mtext></math> are <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>7</mn><mo>,</mo><mo>&#160;</mo><mn>7</mn><mo>)</mo></math>.</p>
</div>

<div class="specification">
<p>A town planner believes that the larger the area of the Voronoi cell <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>XYZ</mtext></math>, the more people will&nbsp;shop at supermarket <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the midpoint of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[BD]</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>(XZ)</mtext></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>X</mtext></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>Determine the exact length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[YZ]</mtext></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>Given that the exact length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[XY]</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>32</mn></msqrt></math>, find the size of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>XŶZ</mtext></math> in degrees.</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>Hence find the area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>XYZ</mtext></math>.</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>State one criticism of this interpretation.</p>
<div class="marks">[1]</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>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = 12\,\,{\text{cos}}\,x - 5\,\,{\text{sin}}\,x,\,\, - \pi&nbsp; \leqslant x \leqslant 2\pi ">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mn>12</mn>
  <mspace width="thinmathspace"></mspace>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>cos</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mi>x</mi>
  <mo>−<!-- − --></mo>
  <mn>5</mn>
  <mspace width="thinmathspace"></mspace>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>sin</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mi>x</mi>
  <mo>,</mo>
  <mspace width="thinmathspace"></mspace>
  <mspace width="thinmathspace"></mspace>
  <mo>−<!-- − --></mo>
  <mi>π<!-- π --></mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mi>x</mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mn>2</mn>
  <mi>π<!-- π --></mi>
</math></span>,&nbsp;be a periodic function with&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = f\left( {x + 2\pi } \right)">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mi>x</mi>
      <mo>+</mo>
      <mn>2</mn>
      <mi>π<!-- π --></mi>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span></p>
<p>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 src="data:image/png;base64,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"></p>
<p style="text-align: left;">There is a maximum point at A. The minimum value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> is −13 .</p>
</div>

<div class="specification">
<p>A ball on a spring is attached to a fixed point O. The ball is then pulled down and released, so that it moves back and forth vertically.</p>
<p style="text-align: center;"><img 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"></p>
<p>The distance, <em>d</em> centimetres, of the centre of the ball from O at time <em>t</em> seconds, is given by</p>
<p style="padding-left: 90px;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d\left( t \right) = f\left( t \right) + 17,\,\,0 \leqslant t \leqslant 5.">
  <mi>d</mi>
  <mrow>
    <mo>(</mo>
    <mi>t</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>t</mi>
    <mo>)</mo>
  </mrow>
  <mo>+</mo>
  <mn>17</mn>
  <mo>,</mo>
  <mspace width="thinmathspace"></mspace>
  <mspace width="thinmathspace"></mspace>
  <mn>0</mn>
  <mo>⩽<!-- ⩽ --></mo>
  <mi>t</mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mn>5.</mn>
</math></span></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>, write down the amplitude.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>, write down the period.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, write <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> in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p\,\,{\text{cos}}\,\left( {x + r} \right)"> <mi>p</mi> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>+</mo> <mi>r</mi> </mrow> <mo>)</mo> </mrow> </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 the maximum speed of the ball.</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 first time when the ball’s speed is changing at a rate of 2 cm s<sup>−2</sup>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">e.</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 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 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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>At an amusement park, a Ferris wheel with diameter 111 metres rotates at a constant speed. The bottom of the wheel is <em>k</em> metres above the ground. A seat starts at the bottom of the wheel.</p>
<p style="text-align: center;"><img 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"></p>
<p>The wheel completes one revolution in 16 minutes.</p>
</div>

<div class="specification">
<p>After&nbsp;<em>t</em>&nbsp;minutes, the height of the seat above ground is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h\left( t \right) = 61.5 + a\,{\text{cos}}\left( {\frac{\pi }{8}t} \right)">
  <mi>h</mi>
  <mrow>
    <mo>(</mo>
    <mi>t</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mn>61.5</mn>
  <mo>+</mo>
  <mi>a</mi>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>cos</mtext>
  </mrow>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mfrac>
        <mi>π<!-- π --></mi>
        <mn>8</mn>
      </mfrac>
      <mi>t</mi>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>, for 0&nbsp;≤&nbsp;<em>t</em>&nbsp;≤ 32.</p>
</div>

<div class="question">
<p>Find when the seat is 30 m above the ground for the third time.</p>
</div>
<br><hr><br><div class="specification">
<p>A new concert hall was built with <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math> seats in the first row. Each subsequent row of the hall&nbsp;has two more seats than the previous row. The hall has a total of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math> rows.</p>
</div>

<div class="specification">
<p>Find:</p>
</div>

<div class="specification">
<p>The concert hall opened in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2019</mn></math>. The average number of visitors per concert during that year&nbsp;was <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>584</mn></math>. In <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2020</mn></math>, the average number of visitors per concert increased by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>2</mn><mo>%</mo></math>.</p>
</div>

<div class="specification">
<p>The concert organizers use this data to model future numbers of visitors. It is assumed that&nbsp;the average number of visitors per concert will continue to increase each year by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>2</mn><mo>%</mo></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the number of seats in the last row.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the total number of seats in the concert hall.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the average number of visitors per concert in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2020</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the first year in which this model predicts the average number of visitors per&nbsp;concert will exceed the total seating capacity of the concert hall.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>It is assumed that the concert hall will host <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math> concerts each year.</p>
<p>Use the average number of visitors per concert per year to predict the <strong>total</strong> number of&nbsp;people expected to attend the concert hall from when it opens until the end of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2025</mn></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows the graph of a function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 6 \leqslant x \leqslant&nbsp; - 2">
  <mo>−<!-- − --></mo>
  <mn>6</mn>
  <mo>⩽<!-- ⩽ --></mo>
  <mi>x</mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mo>−<!-- − --></mo>
  <mn>2</mn>
</math></span>.</p>
<p>The points <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 6,{\text{ }}6)">
  <mo stretchy="false">(</mo>
  <mo>−<!-- − --></mo>
  <mn>6</mn>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mn>6</mn>
  <mo stretchy="false">)</mo>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 2,{\text{ }}6)">
  <mo stretchy="false">(</mo>
  <mo>−<!-- − --></mo>
  <mn>2</mn>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mn>6</mn>
  <mo stretchy="false">)</mo>
</math></span> lie on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>. There is a minimum point at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 4,{\text{ }}0)">
  <mo stretchy="false">(</mo>
  <mo>−<!-- − --></mo>
  <mn>4</mn>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mn>0</mn>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<p><img src="data:image/png;base64,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"></p>
</div>

<div class="question">
<p>Write down the range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>.</p>
</div>
<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 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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>