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<h2>SL Paper 1</h2><div class="specification">
<p>The volume of a hemisphere, <em>V</em>, is given by the formula</p>
<p style="text-align: center;"><em>V</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{4\,{S^3}}}{{243\,\pi }}} ">
<msqrt>
<mfrac>
<mrow>
<mn>4</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>S</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>243</mn>
<mspace width="thinmathspace"></mspace>
<mi>π<!-- π --></mi>
</mrow>
</mfrac>
</msqrt>
</math></span>,</p>
<p>where <em>S</em> is the total surface area.</p>
<p>The total surface area of a given hemisphere is 350 cm<sup>2</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the volume of this hemisphere in cm<sup>3</sup>.</p>
<p>Give your answer correct to <strong>one decimal place</strong>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down your answer to part (a) correct to the nearest integer.</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 your answer to <strong>part (b)</strong> in the form <em>a</em> × 10<sup><em>k</em></sup> , where 1 ≤ <em>a</em> < 10 and <em>k </em>∈<em> </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathbb{Z}">
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the probability distribution of a discrete random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A">
<mi>A</mi>
</math></span>, in terms of an angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta ">
<mi>θ<!-- θ --></mi>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-11_om_09.10.36.png" alt="M17/5/MATME/SP1/ENG/TZ1/10"></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="\cos \theta = \frac{3}{4}"> <mi>cos</mi> <mo></mo> <mi>θ</mi> <mo>=</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </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>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\tan \theta > 0"> <mi>tan</mi> <mo></mo> <mi>θ</mi> <mo>></mo> <mn>0</mn> </math></span>, find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\tan \theta "> <mi>tan</mi> <mo></mo> <mi>θ</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>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{1}{{\cos x}}"> <mi>y</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>cos</mi> <mo></mo> <mi>x</mi> </mrow> </mfrac> </math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 < x < \frac{\pi }{2}"> <mn>0</mn> <mo><</mo> <mi>x</mi> <mo><</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </math></span>. The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y"> <mi>y</mi> </math></span>between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \theta "> <mi>x</mi> <mo>=</mo> <mi>θ</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \frac{\pi }{4}"> <mi>x</mi> <mo>=</mo> <mfrac> <mi>π</mi> <mn>4</mn> </mfrac> </math></span> is rotated 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis. Find the volume of the solid formed.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The diameter of a spherical planet is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>×</mo><msup><mn>10</mn><mn>4</mn></msup><mo> </mo><mtext>km</mtext></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the radius of the planet.</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 volume of the planet can be expressed in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi><mfenced><mrow><mi>a</mi><mo>×</mo><msup><mn>10</mn><mi>k</mi></msup></mrow></mfenced><mo> </mo><msup><mtext>km</mtext><mn>3</mn></msup></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>≤</mo><mi>a</mi><mo><</mo><mn>10</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>∈</mo><mi mathvariant="normal">ℤ</mi></math>.</p>
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}">
<mrow>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> passes through the points <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}(0,{\text{ }}1,{\text{ }}8)">
<mrow>
<mtext>A</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>8</mn>
<mo stretchy="false">)</mo>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}(3,{\text{ }}5,{\text{ }}2)">
<mrow>
<mtext>B</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>5</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>2</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<div class="specification">
<p>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}">
<mrow>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}">
<mrow>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
</mrow>
</math></span> are perpendicular, show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 2">
<mi>p</mi>
<mo>=</mo>
<mn>2</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="\overrightarrow {AB} ">
<mover>
<mrow>
<mi>A</mi>
<mi>B</mi>
</mrow>
<mo>→</mo>
</mover>
</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>Hence, write down a vector equation for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}">
<mrow>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}">
<mrow>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
</mrow>
</math></span>, has equation <strong><em>r</em></strong> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 1 \\ {13} \\ { - 14} \end{array}} \right) + s\left( {\begin{array}{*{20}{c}} p \\ 0 \\ 1 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>13</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−</mo>
<mn>14</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mi>p</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
<p>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}">
<mrow>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}">
<mrow>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
</mrow>
</math></span> are perpendicular, show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 2">
<mi>p</mi>
<mo>=</mo>
<mn>2</mn>
</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>The lines <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}">
<mrow>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}">
<mrow>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> intersect at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C(9,{\text{ }}13,{\text{ }}z)">
<mi>C</mi>
<mo stretchy="false">(</mo>
<mn>9</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>13</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>z</mi>
<mo stretchy="false">)</mo>
</math></span>. Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="z">
<mi>z</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 a unit vector in the direction of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}">
<mrow>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
</mrow>
</math></span>.</p>
<div 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 or otherwise, find one point on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}">
<mrow>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
</mrow>
</math></span> which is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt 5 ">
<msqrt>
<mn>5</mn>
</msqrt>
</math></span> units from C.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The points <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}">
<mrow>
<mtext>A</mtext>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}">
<mrow>
<mtext>B</mtext>
</mrow>
</math></span> have position vectors <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 2} \\ 4 \\ { - 4} \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>2</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>4</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>4</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 6 \\ 8 \\ 0 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>6</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>8</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span> respectively.</p>
<p>Point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{C}}">
<mrow>
<mtext>C</mtext>
</mrow>
</math></span> has position vector <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 1} \\ k \\ 0 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>k</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>. Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{O}}">
<mrow>
<mtext>O</mtext>
</mrow>
</math></span> be the origin.</p>
</div>
<div class="specification">
<p>Find, in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>,</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{OA}}} \bullet \overrightarrow {{\text{OC}}} "> <mover> <mrow> <mtext>OA</mtext> </mrow> <mo>→</mo> </mover> <mo>∙</mo> <mover> <mrow> <mtext>OC</mtext> </mrow> <mo>→</mo> </mover> </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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{OB}}} \bullet \overrightarrow {{\text{OC}}} "> <mover> <mrow> <mtext>OB</mtext> </mrow> <mo>→</mo> </mover> <mo>∙</mo> <mover> <mrow> <mtext>OC</mtext> </mrow> <mo>→</mo> </mover> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}\widehat {\text{O}}{\text{C}} = {\text{B}}\widehat {\text{O}}{\text{C}}"> <mrow> <mtext>A</mtext> </mrow> <mrow> <mover> <mtext>O</mtext> <mo>^</mo> </mover> </mrow> <mrow> <mtext>C</mtext> </mrow> <mo>=</mo> <mrow> <mtext>B</mtext> </mrow> <mrow> <mover> <mtext>O</mtext> <mo>^</mo> </mover> </mrow> <mrow> <mtext>C</mtext> </mrow> </math></span>, show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 7"> <mi>k</mi> <mo>=</mo> <mn>7</mn> </math></span>.</p>
<div class="marks">[8]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the area of triangle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AOC}}"> <mrow> <mtext>AOC</mtext> </mrow> </math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A balloon in the shape of a sphere is filled with helium until the radius is 6 cm.</p>
</div>
<div class="specification">
<p>The volume of the balloon is increased by 40%.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the volume of the balloon.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the radius of the balloon following this increase.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A cylindrical container with a radius of 8 cm is placed on a flat surface. The container is filled with water to a height of 12 cm, as shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_06.17.11.png" alt="M17/5/MATSD/SP1/ENG/TZ2/12"></p>
</div>
<div class="specification">
<p>A heavy ball with a radius of 2.9 cm is dropped into the container. As a result, the height of the water increases to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> cm, as shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_06.18.54.png" alt="M17/5/MATSD/SP1/ENG/TZ2/12.b"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the volume of water in the container.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Emily’s kite ABCD is hanging in a tree. The plane ABCDE is vertical.</p>
<p>Emily stands at point E at some distance from the tree, such that EAD is a straight line and angle BED = 7°. Emily knows BD = 1.2 metres and angle BDA = 53°, as shown in the diagram</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_18.18.28.png" alt="N17/5/MATSD/SP1/ENG/TZ0/10"></p>
</div>
<div class="specification">
<p>T is a point at the base of the tree. ET is a horizontal line. The angle of elevation of A from E is 41°.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of EB.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the angle of elevation of B from E.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the vertical height of B above the ground.</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 right triangle ABC. Point D lies on AB such that CD bisects AĈB.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p style="text-align: center;">AĈD = <em>θ</em> and AC = 14 cm</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{sin}}\,\theta = \frac{3}{5}"> <mrow> <mtext>sin</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mo>=</mo> <mfrac> <mn>3</mn> <mn>5</mn> </mfrac> </math></span>, find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{cos}}\,\theta "> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</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 value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{cos}}\,2\theta "> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mn>2</mn> <mi>θ</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise, find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{BC}}"> <mrow> <mtext>BC</mtext> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A solid glass paperweight consists of a hemisphere of diameter 6 cm on top of a cuboid with a square base of length 6 cm, as shown in the diagram.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">The height of the cuboid, <em>x </em>cm, is equal to the height of the hemisphere.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>x</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the volume of the paperweight.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>1 cm<sup>3</sup> of glass has a mass of 2.56 grams.</p>
<p>Calculate the mass, in grams, of the paperweight.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A type of candy is packaged in a right circular cone that has volume <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{100 c}}{{\text{m}}^{\text{3}}}">
<mrow>
<mtext>100 c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mrow>
<mtext>3</mtext>
</mrow>
</msup>
</mrow>
</math></span> and vertical height 8 cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_11.14.55.png" alt="M17/5/MATSD/SP1/ENG/TZ1/09"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the radius, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>, of the circular base of the cone.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the slant height, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="l">
<mi>l</mi>
</math></span>, of the cone.</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 curved surface area of the cone.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A solid right circular cone has a base radius of 21 cm and a slant height of 35 cm.<br>A smaller right circular cone has a height of 12 cm and a slant height of 15 cm, and is removed from the top of the larger cone, as shown in the 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>Calculate the radius of the base of the cone which has been removed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the curved surface area of the cone which has been removed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the curved surface area of the remaining solid.</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 triangle ABC, with <em>AB</em> = 6 and <em>AC</em> = 8.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{cos}}\,\hat A = \frac{5}{6}">
<mrow>
<mtext>cos</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mover>
<mi>A</mi>
<mo stretchy="false">^</mo>
</mover>
</mrow>
<mo>=</mo>
<mfrac>
<mn>5</mn>
<mn>6</mn>
</mfrac>
</math></span> find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{sin}}\,\hat A">
<mrow>
<mtext>sin</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mover>
<mi>A</mi>
<mo stretchy="false">^</mo>
</mover>
</mrow>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of triangle ABC.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> passes through points <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}( - 3,{\text{ }}4,{\text{ }}2)">
<mrow>
<mtext>A</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mo>−<!-- − --></mo>
<mn>3</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>4</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>2</mn>
<mo stretchy="false">)</mo>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}( - 1,{\text{ }}3,{\text{ }}3)">
<mrow>
<mtext>B</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mo>−<!-- − --></mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>3</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>3</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<div class="specification">
<p>The line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> also passes through the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{C}}(3,{\text{ }}1,{\text{ }}p)">
<mrow>
<mtext>C</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>p</mi>
<mo stretchy="false">)</mo>
</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="\overrightarrow {{\text{AB}}} = \left( {\begin{array}{*{20}{c}} 2 \\ { - 1} \\ 1 \end{array}} \right)"> <mover> <mrow> <mtext>AB</mtext> </mrow> <mo>→</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find a vector equation for <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.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">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The point D has coordinates <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="({q^2},{\text{ }}0,{\text{ }}q)"> <mo stretchy="false">(</mo> <mrow> <msup> <mi>q</mi> <mn>2</mn> </msup> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>q</mi> <mo stretchy="false">)</mo> </math></span>. Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{DC}}} "> <mover> <mrow> <mtext>DC</mtext> </mrow> <mo>→</mo> </mover> </math></span> is perpendicular to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span>, find the possible values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q"> <mi>q</mi> </math></span>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The position vectors of points P and Q are <strong><em>i</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + ">
<mo>+</mo>
</math></span> 2 <strong><em>j</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - ">
<mo>−<!-- − --></mo>
</math></span> <strong><em>k </em></strong>and 7<strong><em>i</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + ">
<mo>+</mo>
</math></span> 3<strong><em>j</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - ">
<mo>−<!-- − --></mo>
</math></span> 4<strong><em>k </em></strong>respectively.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find a vector equation of the line that passes through P and Q.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The line through P and Q is perpendicular to the vector 2<strong><em>i </em></strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + ">
<mo>+</mo>
</math></span> <em>n</em><strong><em>k</em></strong>. Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n">
<mi>n</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo>-</mo><mn>3</mn><mo>-</mo><mfrac><mn>6</mn><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mi>x</mi><mo>-</mo><mn>3</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>,</mo><mo> </mo><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi><mo>,</mo><mo> </mo><mi>x</mi><mo>≠</mo><mn>1</mn></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>Hence or otherwise, solve the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi>sin</mi><mo> </mo><mn>2</mn><mi>θ</mi><mo>-</mo><mn>3</mn><mo>-</mo><mfrac><mn>6</mn><mrow><mi>sin</mi><mo> </mo><mn>2</mn><mi>θ</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mn>0</mn></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>θ</mi><mo>≤</mo><mi mathvariant="normal">π</mi><mo>,</mo><mo> </mo><mi>θ</mi><mo>≠</mo><mfrac><mi mathvariant="normal">π</mi><mn>4</mn></mfrac></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A lampshade, in the shape of a cone, has a wireframe consisting of a circular ring and four straight pieces of equal length, attached to the ring at points A, B, C and D.</p>
<p>The ring has its centre at point O and its radius is 20 centimetres. The straight pieces meet at point V, which is vertically above O, and the angle they make with the base of the lampshade is 60°.</p>
<p>This information is shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_17.16.13.png" alt="M17/5/MATSD/SP1/ENG/TZ2/03"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of one of the straight pieces in the wireframe.</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 total length of wire needed to construct this wireframe. Give your answer in centimetres correct to the nearest millimetre.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo> </mo><mn>2</mn><mi>x</mi><mo>+</mo><mi>cos</mi><mo> </mo><mn>2</mn><mi>x</mi><mo>-</mo><mn>1</mn><mo>=</mo><mn>2</mn><mo> </mo><mi>sin</mi><mo> </mo><mi>x</mi><mfenced><mrow><mi>cos</mi><mo> </mo><mi>x</mi><mo>-</mo><mi>sin</mi><mo> </mo><mi>x</mi></mrow></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>Hence or otherwise, solve <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo> </mo><mn>2</mn><mi>x</mi><mo>+</mo><mi>cos</mi><mo> </mo><mn>2</mn><mi>x</mi><mo>-</mo><mn>1</mn><mo>+</mo><mi>cos</mi><mo> </mo><mi>x</mi><mo>-</mo><mi>sin</mi><mo> </mo><mi>x</mi><mo>=</mo><mn>0</mn></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo><</mo><mi>x</mi><mo><</mo><mn>2</mn><mi mathvariant="normal">π</mi></math>.</p>
<p> </p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Three airport runways intersect to form a triangle, ABC. The length of AB is 3.1 km, AC is 2.6 km, and BC is 2.4 km.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>A company is hired to cut the grass that grows in triangle ABC, but they need to know the area.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the size, in degrees, of angle BÂC.</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 area, in km<sup>2</sup>, of triangle ABC.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>The following diagram shows a circle with centre O and radius<em> r</em> cm.</p>
<p><img src="data:image/png;base64,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"></p>
<p>The points A and B lie on the circumference of the circle, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}\mathop {\text{O}}\limits^ \wedge {\text{B}}">
<mrow>
<mtext>A</mtext>
</mrow>
<mover>
<mrow>
<mtext>O</mtext>
</mrow>
<mo>∧</mo>
</mover>
<mo></mo>
<mrow>
<mtext>B</mtext>
</mrow>
</math></span> = <em>θ</em>. The area of the shaded sector AOB is 12 cm<sup>2</sup> and the length of arc AB is 6 cm.</p>
<p>Find the value of <em>r</em>.</p>
</div>
<br><hr><br><div class="question">
<p>Solve <span class="mjpage"><math alttext="{\log _2}(2\sin x) + {\log _2}(\cos x) = - 1" xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <msub> <mi>log</mi> <mn>2</mn> </msub> </mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mi>sin</mi> <mo></mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mrow> <msub> <mi>log</mi> <mn>2</mn> </msub> </mrow> <mo stretchy="false">(</mo> <mi>cos</mi> <mo></mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mn>1</mn> </math></span>, for <span class="mjpage"><math alttext="2\pi < x < \frac{{5\pi }}{2}" xmlns="http://www.w3.org/1998/Math/MathML"> <mn>2</mn> <mi>π</mi> <mo><</mo> <mi>x</mi> <mo><</mo> <mfrac> <mrow> <mn>5</mn> <mi>π</mi> </mrow> <mn>2</mn> </mfrac> </math></span>.</p>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a ball attached to the end of a spring, which is suspended from a ceiling.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The height, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> metres, of the ball above the ground at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> seconds after being released can be modelled by the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>4</mn><mo> </mo><mi>cos</mi><mfenced><mrow><mi mathvariant="normal">π</mi><mi>t</mi></mrow></mfenced><mo>+</mo><mn>1</mn><mo>.</mo><mn>8</mn></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>≥</mo><mn>0</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the height of the ball above the ground when it is released.</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 minimum height of the ball above the ground.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the ball takes <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> seconds to return to its initial height above the ground for the first time.</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>For the first 2 seconds of its motion, determine the amount of time that the ball is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>8</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>2</mn><msqrt><mn>2</mn></msqrt></math> metres above the ground.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the rate of change of the ball’s height above the ground when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></math>. Give your answer in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi mathvariant="normal">π</mi><msqrt><mi>q</mi></msqrt><mo> </mo><msup><mi>ms</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>∈</mo><mi mathvariant="normal">ℚ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>∈</mo><msup><mi mathvariant="normal">ℤ</mi><mo>+</mo></msup></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Iron in the asteroid <em>16 Psyche</em> is said to be valued at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8973</mn></math> quadrillion euros <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtext>EUR</mtext></mfenced></math>, where one quadrillion <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msup><mn>10</mn><mn>15</mn></msup></math>.</p>
</div>
<div class="specification">
<p>James believes the asteroid is approximately spherical with radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>113</mn><mo> </mo><mtext>km</mtext></math>. He uses this information to estimate its volume.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of the iron in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>×</mo><msup><mn>10</mn><mi>k</mi></msup></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>≤</mo><mi>a</mi><mo><</mo><mn>10</mn><mo> </mo><mo>,</mo><mo> </mo><mi>k</mi><mo>∈</mo><mi mathvariant="normal">ℤ</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>Calculate James’s estimate of its volume, in <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>km</mtext><mn>3</mn></msup></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 actual volume of the asteroid is found to be <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>074</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mo> </mo><msup><mtext>km</mtext><mn>3</mn></msup></math>.</p>
<p>Find the percentage error in James’s estimate of the volume.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the vectors <em><strong>a</strong></em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 0 \\ 3 \\ p \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>p</mi>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span> and <em><strong>b</strong></em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 0 \\ 6 \\ {18} \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>6</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>18</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> for which <em><strong>a</strong></em> and <em><strong>b</strong></em> are</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>parallel.</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>perpendicular.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A cylinder with radius <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> and height <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The sum 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> for this cylinder is 12 cm.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an equation for the area, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A">
<mi>A</mi>
</math></span>, of the <strong>curved</strong> surface in terms 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">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="\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">[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="r">
<mi>r</mi>
</math></span> when the area of the curved surface is maximized.</p>
<div class="marks">[2]</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="\theta ">
<mi>θ<!-- θ --></mi>
</math></span> be an <strong>obtuse</strong> angle such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{sin}}\,\theta = \frac{3}{5}">
<mrow>
<mtext>sin</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>θ<!-- θ --></mi>
<mo>=</mo>
<mfrac>
<mn>3</mn>
<mn>5</mn>
</mfrac>
</math></span>.</p>
</div>
<div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {{\text{e}}^x}\,{\text{sin}}\,x - \frac{{3x}}{4}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mi>x</mi>
</msup>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mfrac>
<mrow>
<mn>3</mn>
<mi>x</mi>
</mrow>
<mn>4</mn>
</mfrac>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{tan}}\,\theta "> <mrow> <mtext>tan</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span> passes through the origin and has a gradient of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{tan}}\,\theta "> <mrow> <mtext>tan</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> </math></span>. 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">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> for 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> ≤ 3. Line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="M"> <mi>M</mi> </math></span> is a tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at point P.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAeoAAAGNCAYAAADenDLYAAAgAElEQVR4Ae3dD3BW5b3g8V8otxVEiwGWEhNl0Ca4xUuCgGwTS7Q0irU3mdDUlY7gBXS8GrqrI2CB1rpXKAJTRkHXrUCB9uJYSibZVZFImVCSOwgIYWWqyRWWf4ayQLSYRS9Dk53n6MGXN++bvO97/j3POd8z45Cc95znz+f34o/nnPM8J6urq6tL2BBAAAEEEEBAS4E+WraKRiGAAAIIIICAJUCi5ouAAAIIIICAxgIkao2DQ9MQQAABBBDIMFFflJM1D0tWVpZkZeXI7ct3S4dl2Snnts+XnJxqqfnwAroIIIAAAggg4FAgw0TdV4ZVviRdf3tP1pSJNLx1UNo6VUv6yICbbpcHCj6Sj/+ftcNh8zgdAQQQQACBaAtkmKi/QOuTK6O/VyByqF0++SIv9xmaJzeOuFVG53w12rL0HgEEEEAAARcEnCVq6StXZQ8ROfSBHD19UUQuyIe1v5Hd3y+XogEOi3ahcxSBAAIIIICA6QIOs2lfuWpg9pcGHc3y+73flp9VXC8OC/6yTH5CAAEEEEAgwgIO82kfuXJgtgyTFjl8/APZvvQtuf7RyXKtw1IjHA+6jgACCCCAwGUCDlNqH+n/9WzpL2dk/wsvSUPpA1JxLfemLxPmFwQQQAABBBwIOEzUIn2uypYbRKTvxFky945rueTtIBicigACCCCAQLyA40Qt8hXJ/emvZMkDo2RAfOn8jgACCCCAAAKOBJwl6o7d8tyaPjJn/ndlmLOSHHWCkxFAAAEEEAirQN+0O9axW5b/4DE5ef9jkttyRr7zs4dkJFOx0mbkBAQQQAABBFIRSH8c3Nkhp1v+j+xr+VS+819nyC0k6VScOQYBBBBAAIGMBLK8eh91TU2NvP/++zJ//vyMGsZJCCCAAAIIICDiSaJubW2VgoICy7exsVGKi4uxRgABBBBAAIEMBFxP1J9++qncd999MmTIEFm9erWMGzdOduzYIf369cugeZyCAAIIIIBAtAXSv0fdi9eWLVukrq5O5syZc+nIFStWXPqZHxBAAAEEEEAgdQFXR9QnTpyQvLw8Wb9+vUybNs16X/XmzZtlypQp0tLSIvn5+am3jCMRQAABBBBAwN171A8++KCcPn1aXnnlFetSd1ZWlnR1dUn8ftwRQAABBBBAIDUB10bU9fX1cuedd8r+/fulsLDQqt1O1PEj7dSaxlEIIIAAAggg4Eqibm9vl7vuuksqKioum45lJ2rFvGHDBpk+fbocP35ccnNzkUcAAQQQQACBFARceZjspZdesqp67LHHklZZVVUl5eXlVsJOehAfIIAAAggggMBlAq6MqJuamuTKK6+8dMnbriF2RK32qUvgR48eZV61DcSfCCCAAAII9CLgSqJOVkd8ok52HPsRQAABBBBAILGAK5e+ExfNXgQQQAABBBBwKkCidirI+QgggAACCHgoQKL2EJeiEUAAAQQQcCpAonYqyPkIIIAAAgh4KECi9hCXohFAAAEEEHAqQKJ2Ksj5CCCAAAIIeChAovYQl6IRQAABBBBwKkCidirI+QgggAACCHgoQKL2EJeiEUAAAQQQcCpAonYqyPkIIIAAAgh4KECi9hCXohFAAAEEEHAqQKJ2Ksj5CCCAAAIIeChAovYQl6IRQAABBBBwKkCidirI+QgggAACCHgoQKL2EJeiEUAAAQQQcCpAonYqyPkIIIAAAgh4KECi7gX3xIkTvRzBxwgggAACCHgnQKLuwfbTTz+VvLw8qaiokKamph6O5CMEEEAAAQS8ESBR9+Dar18/OXv2rEyaNElKSkpI2D1Y8RECCCCAgDcCJOpeXLOzs6W6upqE3YsTHyOAAAIIeCNAok7RlYSdIhSHIYAAAgi4KkCiTpOThJ0mGIcjgAACCDgSIFFnyEfCzhCO0xBAAAEE0hIgUafF1f3gZAm7ubm5+8HsQQABBBBAIE0BEnWaYMkOj0/YRUVFMnfuXGltbU12CvsRQAABBBDoVYBE3StRegfEJuzrrrtOCgoKSNjpEXI0AggggECMAIk6BsPNH2MTtiqXhO2mLmUhgAAC0REgUXsca5Wwly5dKi0tLVZNJGyPwSkeAQQQCJkAidqngObn55OwfbKmGgQQQCBMAiRqn6NJwvYZnOoQQAABwwVI1AEFkIQdEDzVIoAAAoYJkKgDDhgJO+AAUD0CCCCguQCJWpMAkbA1CQTNQAABBDQTIFFrFhAStmYBoTkIIIBAwAIk6oADkKx6EnYyGfYjgAAC0RIgUWsebxK25gGieQgggIDHAiRqj4HdKp6E7ZYk5SCAAAJmCZCozYqXkLANCxjNRQABBBwKkKgdAgZ1Ogk7KHnqRQABBPwVIFH76+16bSRs10kpEAEEENBKgEStVTgybwwJO3M7zkQAAQR0FiBR6xydDNpGws4AjVMQQAABjQVI1BoHx0nTSNhO9DgXAQQQ0EeARK1PLDxpCQnbE1YKRQABBHwTIFH7Rh1sRSTsYP2pHQEEEMhUgESdqZyh55GwDQ0czUYAgcgKkKgjGnoSdkQDT7cRQMA4ARK1cSFzt8EkbHc9KQ0BBBBwW4BE7baooeWRsA0NHM1GAIHQC5CoQx/i9DpIwk7Pi6MRQAABrwVI1F4LG1o+CdvQwNFsBBAInQCJOnQhdbdDJGx3PSkNAQQQSFeARJ2uWESPJ2FHNPB0GwEEAhcgUQceArMakCxhnzhxwqyO0FoEEEDAEAEStSGB0q2Z8Qk7Ly9PVq1aJe3t7bo1lfYggAACRguQqI0OX/CNj03Yx44dk0GDBpGwgw8LLUAAgRAJkKhDFMwguxKbsLdt26Znwu58X9bemSNZWVnd/suZvlz+sL1VOoJEpG4EEEAggQCJOgEKuzIXUAm7trZWGhsbRbuE3WekzNjaJn9rWSNlUiVrWj6Vrq4u6frkPVn1jbek6rtT5NG1B0nWmYefMxFAwAMBErUHqBQpUlxcrG/Cjg/QgJFS+cvnZE3ZWdmwcKPsPtcZfwS/I4AAAoEJkKgDo49GxcYk7D6DZXhhjsjJD+TIXy5EIzj0EgEEjBAgURsRJvMbqX3C7jwjR5rbRIbdKMO/8VXzwekBAgiERoBEHZpQmtERfRL2e7Kj8YPP70d3npTdz/1SFtaLlD5eIeOv5q+FGd8mWolANAT4P1I04qxdL4NP2Adlw8yb5Sr1BPhXcuTWZSKPb/5fsvHx8TJAOy0ahAACURYgUUc5+hr0PbiEHfPUt3ryu229PFF5iwzjb4QG3wqagAACsQL8bylWg58DEwguYQfWZSpGAAEEUhIgUafExEF+CZCw/ZKmHgQQMEWARG1KpCLWTu8Sdqec/+SvckHOS/snn0VMle4igICJAiRqE6MWoTa7mrCtJURz5aqxj0uDvC5zxl4jWXeulVbWN4nQN4quImCeQFaXWkPRo02tqexh8R61mmJ1FmhqapJly5ZJXV2drFy5UqZOnSrZ2dk6N5m2IYAAAo4EGFE74uNkvwVcHWH73XjqQwABBDIQIFFngMYpwQuQsIOPAS1AAAF/BEjU/jhTi0cCvSXs9vZ2qampEXXJ/NNPP/WoFRSLAAIIeCfAPWrvbCk5AAGVkJcsWSKvvfaazJs3T5599tlLrfjWt74lf/rTn7infUmEHxBAwAQBErUJUaKNvQqoBL1jxw5ZsGBBj8e+/PLLMmvWrB6P4UMEEEBAJwEufesUDdqStkBzc7NUVFRISUmJXH311bJ//35paWmR8+fPJyzr3XffTbifnQgggICuAiRqXSNDu3oUUPebFy9eLEVFRTJp0iQrMVdXV0thYaHk5+dLv379ZOHChd3KeP7552XFihWi7l2zIYAAAiYIcOnbhCjRxssEVJJV958PHDggv/vd76zEfNkBX/yikvn06dNl06ZN1p4nnnhCXn/9dSupHz16lHnYidDYhwAC2gmQqLULCQ3qSeDEiRNSWVkpo0ePFjU6ViPn3jaV2NVx6j/7fDUSP3XqFAun9IbH5wggELgAl74DDwENSFXATrLpJGlVtlq5zE7oubm51nStX//611bCb2xslG3btsmgQYNk1apVXBJPNRgchwACvgmQqH2jpiInAuoy9tNPP53WSDpZfSpZqwStLotfeeWVUltba/1Owk4mxn4EEAhSgEQdpD51pyzw1FNPWfekU73c3VvBaqGURYsWyUMPPWQthNLbwim9lcfnCCCAgFcCJGqvZCnXNYENGzZYL+JQK4zZl7DdKPyxxx6zilFPgdsbCduW4E8EENBFgIfJdIkE7UgooOZJqwe/tm7dKmVlZQmPcbLTLl/NvVbTuuI33tYVL8LvCCDgtwCJ2m9x6ktZQN2XnjhxorWgyfz581M+L90D586dKx999JGoVcuSbbEJe/369VJVVeXq6D5ZvexHAAEESNR8B7QVUAuaqAe91NKgbl7yju+wepo8Ly/PeqBMXfruabMTdltbmzz55JMyefJkT9vWU1v4DAEEoiFAoo5GnI3rZW+XpN3ukJqapZ76Vv8wSGUjYaeixDEIIOCGAInaDUXKcFXAr0vesY1Wi6KoudRq2lZvo+rY8+rr6y8tVcoIO1aGnxFAwC0BErVbkpTjmoB6yluNcL2+5B3f4HRH1fb56h8WW7ZssV6vqfaRsG0Z/kQAATcESNRuKFKGawLp3C92rdIvCrJH1eoNXOrlHuluJOx0xTgeAQRSESBRp6LEMb4JqCew1bZ06VLf6oytyI36SdixovyMAAJOBUjUTgU53zUB9YCWeq90sjnNrlXUQ0Gtra1SUFAgx48fF7XUqJONhO1Ej3MRQMAWIFHbEvwZuEBFRYX1bmn1XukgN7fbQcIOMprUjYD5AiRq82MYih6op6fvvPNOOXv2rPW2qyA7ZT/J7fbDbCTsIKNK3QiYK0CiNjd2oWm5SmBqBTL1tLR613TQm2pP//79056qlWq7SdipSnEcAggoAV7KwfcgcAE1tUltapUvHTa1CtrKlSulrq7Ok+ao8tU/SNSIXf3jZMmSJdY/VNRLR1QSZ0MAAQRiBRhRx2rws+8Cuo2mbQD7oTI/LsUzwrbV+RMBBBIJMKJOpMI+3wR0G03bHVdv0iovL5eGhgZ7l2d/MsL2jJaCEQiFACPqUITRzE7oOpq2NdUKaepydKrrf9vnOf2TEbZTQc5HIFwCJOpwxdOo3qgkqO7Puv10tVsI9ippbsypzqRNJOxM1DgHgfAJkKjDF1MjeqT7aNpGfPDBB+W2226TadOm2bt8/5OE7Ts5FSKglQD3qLUKR3Qas3PnTquzujzpnUy+qqrKuvyd7HM/9nMP2w9l6kBAXwFG1PrGJtQtU6t/qVGqDvOme4K2X9QR1OXvRG1jhJ1IhX0IhFeARB3e2GrbM3tNbz+mPrmBoP5Rof5BEeTl70T9IGEnUmEfAuETIFGHL6ba98jttbS97rB6+ltdqn/55Ze9riqj8knYGbFxEgLGCJCojQlVOBrq50IibonZT3/rfgWAhO1WxCkHAb0ESNR6xSP0rVHvex44cKDMnz/fqL6OHz9ennnmGSkrK9O+3SRs7UNEAxFIS4BEnRYXBzsRsB/MCvJ905m2f9WqVXLu3Dmj/oFBws402pyHgF4CJGq94hHq1qhkd+DAAW3v9faE39zcLEVFRXL+/HlR06VM2kjYJkWLtiLQXYBE3d2EPR4IqGTh5asjPWjyZUXa7d+/f78UFhZe9pkpv5CwTYkU7UTgcgEWPLncg988ElAv3xg3bpwUFxd7VIO3xapR9Jw5c6x3VHtbk3els3CKd7aUjICXAiRqL3Up+5KAmuKk3r1s8jZhwgTZtm2byV2w2k7CNj6EdCBiAlz6jljAg+iuaQucJDMyZZpWsvYn288l8WQy7EdADwFG1HrEIdStqKurk5UrV0p2drbR/czNzbUu3+/du9fofsQ3nhF2vAi/I6CXACNqveIRutbYo1ATp2QlCsbixYut3abNA0/Ul2T74kfYpswfT9Yf9iNgugAjatMjqHn7a2trpby8XPLz8zVvaWrNmzhxoqg+hXmLH2EvXLhQ1LKv6hYGGwII+C/AiNp/88jUqEZmKrGtWLHC2Ke944NlL9qi09u04tvo9u+xI+ycnBzr6XdTn95324byEPBDgBG1H8oRrcN+5/SYMWNCI6Dus6srBH/+859D06feOhI7wp40aZKUlJQwwu4Njc8RcFGARO0iJkVdLvDiiy9ar4ZU/6MP06aSVdgeKEslPiqO1dXVol5OQsJORYxjEHBHgETtjiOlxAmot2Spp73Vvc2wbWop0bDfp+4pZuqqAgm7JyE+Q8BdARK1u56U9oVAfX29zJo1S9SUprBtN910k+zZs0fUE+1R3kjYUY4+ffdTgETtp3ZE6lIPH82ePVseeOCBUPY4ivepewokCbsnHT5DwLkAidq5ISXECaiHyNS63mF6iCyui6LeTx3F+9TxDrG/k7BjNfgZAfcESNTuWVLSFwJhfYgsNsBjx46N9H3qWIv4n0nY8SL8joAzAeZRO/Pj7DgB9RBZQUGBhH2esb3imnoCWiUmtuQCau75xo0brdshamqbegsZ87CTe/EJAvECjKjjRfjdkUCYHyKLhbEfknvvvfdid/NzAgFG2AlQ2IVAGgIk6jSwOLRnAfUQmXqdZVgfIovvvRoZ7t+/P343vycRIGEngWE3Ar0IkKh7AeLj1AX27dtnHRzmh8hiNdT7qQ8cOBC7i59TECBhp4DEIQjECJCoYzD40ZnAunXrQrkSWTKVUaNGyerVq0VdSWBLX4CEnb4ZZ0RTgEQdzbi73mv1cJVKWmFciSwZVl5envWRenCOLXMBEnbmdpwZDQESdTTi7Hkvt2/fbr2swn7IyvMKNahArX2tVl87ePCgBq0xvwkkbPNjSA+8ESBRe+MauVJXrVoljzzySOT6PXr0aHn//fcj128vO0zC9lKXsk0UIFGbGDXN2tzc3Gytfa0WAYnalp+fz8InHgWdhO0RLMUaJ0CiNi5k+jX4jTfekEWLFkVy4Y/hw4db/0hRi3qweSNAwvbGlVLNESBRmxMrLVuqEtSCBQvk7rvv1rJ9XjdKjajVduzYMa+rinz5JOzIfwUiC0Cijmzo3em4ejGFegFHYWGhOwUaWIpa+OTw4cMGttzMJpOwzYwbrc5cgESduR1nioh6AUd1dXWkLdR86l27dkXaIIjOk7CDUKfOIARI1EGoh6RONXe6rq5O7rjjjpD0KLNu3HDDDdLQ0JDZyZzlWICE7ZiQAjQXIFFrHiCdm1dbW2vNI47S3OlE8bj++ut5oCwRjM/7SNg+g1OdbwIkat+ow1eRegFHVVVV+DqWZo/sf6jwQFmacB4dTsL2CJZiAxMgUQdGb3bFTU1N1ijytttuM7sjLrWeB8pcgnSxGBK2i5gUFagAiTpQfnMr37FjhzV3Wi2jySbCA2X6fgtI2PrGhpalJkCiTs2Jo2IE1Nuiojx3Oobi0o88UHaJQtsfSNjahoaG9SJAou4FiI+7C+zcuTPyc6fjVYYMGcIDZfEomv5OwtY0MDQrqQCJOikNHyQT2LRpU+TnTsfb2CuUnTlzJv4jftdUIFnCbm1t1bTFNCuqAiTqqEY+w37b752O+tzpRHy88jKRiv774hN2QUGBzJ07V0jY+scuKi0kUUcl0i71M4rvnU6Vjldepiql53GxCfu6664TEraecYpiq0jUUYy6gz5H9b3TqZDl5OTI7t27UzmUYzQWsBP28ePHrVaSsDUOVkSaRqKOSKDd6GaU3zudip+aoqWWVGULh4BayGbp0qXS0tJidYiEHY64mtgLErWJUQuozY2NjZF973Qq5Hl5edZh3NtMRcucY9SDgiRsc+IVxpaSqMMYVQ/6pOZOz549WyZOnOhB6eEoUi3+ol75efr06XB0iF5cJkDCvoyDX3wUIFH7iG1yVfv27bOS0JgxY0zuhudtLy0tlUOHDnleDxUEJ0DCDs4+qjWTqKMa+TT7re69Tps2TVgytGc4dZ/64MGDPR/Ep6EQIGGHIoxGdIJEbUSYgm1ke3u7LFu2TEpKSoJtiAG1s5SoAUFyuYkkbJdBKa6bAIm6Gwk74gX27t0r5eXlUlhYGP8Rv8cJ2EuJqnv6bNESIGFHK95+9pZE7ae2oXW9+OKLUllZaWjr/W22+p+12uw5uP7WTm06CJCwdYhCuNpAog5XPF3vjVoyVN2fZsnQ1GnV1QfuU6fuFdYjSdhhjaz//SJR+29uVI21tbWi1rBWiz+wpSag/gfd1taW2sEcFXoBEnboQ+x5B0nUnhObXcGGDRukqqrK7E743PoJEybIsWPHfK6V6nQXIGHrHiF920ei1jc2gbfMXjL0tttuC7wtJjVg6NCh1lPyJrWZtvonQML2zzosNZGowxJJD/rxxhtvWEuGMnc6PVz15Lfa1LQ2NgSSCZCwk8mwP16ARB0vwu+WgJpetGDBApYMzeD7oP4HrLYzZ85kcDanRE2AhB21iKffXxJ1+maROIMlQ52FmSe/nflF8WwSdhSjnlqfSdSpOUXuqHXr1rFkqIOoq//pdnR0OCiBU6MqQMKOauST95tEndwmsp+oe6urV69myVAH3wD15DdzqR0AcqqQsPkS2AIkaluCPy8JNDQ0sGToJY3MflBPfitHNgScCpCwnQqafz6J2vwYut4DNXeaJUOdsbLmtzM/zu4uQMLubhKVPSTqqEQ6xX6yZGiKUL0clpeXZx3Bmt+9QPFx2gIk7LTJjD+BRG18CN3tAEuGuuOp5p6PGzdOTp8+7U6BlIJAnAAJOw4kxL+SqEMc3Ey6xpKhmaglPqe0tFROnTqV+EP2IuCSAAnbJUiNiyFRaxwcv5tmLxk6duxYv6sOZX2jRo2SXbt2hbJvdEo/ARK2fjFxq0UkarckQ1COvWRodnZ2CHoTfBcGDBggH330UfANoQWREiBhhy/cJOrwxTSjHrFkaEZsPZ6kRtRqPjobAkEI6JmwL8rJmoclKyvr8//uXCutnUl0Oo9Kzcybvzx2eo2cTHJo2HeTqMMe4RT7x5KhKUKlcdjgwYOto9WT9GwIBCWgV8LuK8MqX5Kuv/5R5g4TkXc/kBMdiTL1BfmwdplUrz0oMmyGrHnvr9K1vlLUKVHcSNRRjHqCPrNkaAIUh7vsWwjnz593WBKnI+BcIFHCXrx4cSBvebv4b/tksxoen/xAjvzlQrfOdX74mvy8+gVrBD3s/h/LD0de3e2YKO0gUUcp2kn6ypKhSWBc2D1r1iyWEnXBkSLcE4hN2B9//LEMGjRIVq1a5WPC/kwOH3hPbp1WIcPktLR/cvHyznUeldqfr5TPvqc+v0G+d+s3JdppWoREfflXJJK/sWSod2G/5ppreDmHd7yU7EAgNmEfO3bMx4R9Wg7uuEr+oXys9Jfj8u7R2AcuP7/kPVdmyAMlfycnZYxMHPX5+90ddNX4U0nUxofQeQdYMtS5YbISeDlHMhn26yJgJ+zGxkbZtm2b9wn73L/J22f/XopuvUmK5ZA0Hf6/8vmYulM63n9F5v+PG+TV574jnzTuE7lhvIwecYUuVIG1g0QdGL0eFdtLht5zzz16NChkrVBTtHg5R8iCGtLuFBcXi1qZ0OuEre5P/7F0tIwYer3cfIPIoXePirV+X8deeemfauXmxf8ot3QekrffOiTDpoyRb/YNKXga3SJRp4EVxkPtJUPtB5/C2Mcg+zR8+HDZs2dPkE2gbgTSEvA2Yav70x/Id8dcL337/gcZUXyDSNNhabv4sbzz0i/l9e//VB6+ZaB8/rAZ96ftwJGobYmI/smSod4G3p6i1dra6m1FlI6AywLeJGx1f/oKufWmgSJyjVx/c57IoffkwP98SZ54/Tuy/OGxMkBUMt8th7g/fSmiJOpLFNH7oampyRrt3XbbbdHrvE89tq9UMEXLJ3CqcV3A1YT9xf3pUUPV9ewrJGdEgYislZlTGuX7y/9RbhnQR6TziDS+2sj96ZhIkqhjMKL2444dO2TRokWi3vTE5p2AmqJ1+PBh7yqgZAR8EHCesM/J+3/4F3lD3Z+2Mk8fuXJgtgyTUTJj8wvy+C1qlH1BTja8Kr+tPylSPEJyuD9tRZZE7cMXXMcqWDLUv6ioKVptbW3+VUhNCHgokEnCvvjOcrkx6+ty08y1cnDOWPk7a+nQPjIg90YZM+Np+W8V10ufc9tlXs7XJOe7v5AG1f4NUyQn62GpORk3z9rDvuladFZXV1eXV41T67l6WLxXzY5EufX19bJw4ULZvXt3JPobZCdramqst2gtXbo0yGZQNwKeCKhbaMuWLZO6ujpZuXKlTJ06VexbPp5UGMFCGVFHMOiqy5s2bZJp06ZFtPf+dltN0eJhMn/Nqc0/gUxG2P61Lhw1MaIORxzT6oWaO52XlyfHjx+X3NzctM7l4PQFVJIuKCjg6lL6dJxhoAAjbPeDxojafVPtS9y+fbuUl5eTpH2KlD1Fi7do+QRONYEKMMJ2n59E7b6p9iWqe6Zc9vYvTPb9OqZo+WdOTcELkLDdiwGJ2j1LI0pqbm62HvooLS01or1haSRv0QpLJOlHugIk7HTFuh9Pou5uEuo9ah3fOXPm8FSmz1FWU7TYEIiyAAk78+iTqDO3M+5MNXd69uzZ1v1p4xpveINHjRplTdEyvBs0HwHHAiTs9AlJ1OmbGXvGvn37ZNy4cTJmzBhj+2Bqw9UUrY8+in3vrqk9od0IuCNAwk7dkUSdupXxR65bt856iIwlQ/0P5YgRI2T16tX+V0yNCGgukChhq2dp2L4UYB71lxah/qm9vd16IXxLS4uoF8Wz+Stgz6VWT37zDyV/7anNLAE1D1td9ePvyZdxY0T9pUWof3rttdese9Mk6WDCbLurRWbYEEAguYAaYZOkL/chUV/uEdrfmDutR2hPnz6tR0NoBQIIGCNAojYmVJk3lLnTmdu5eaaaFnfq1Ck3i7DMQAEAABfCSURBVKQsBBCIgACJOgJBZu60HkEeOHAgr7vUIxS0AgGjBEjURoUr/cYydzp9M6/OGDlypBw7dsyr4ikXAQRCKkCiDmlg7W4xd9qWCP5PXncZfAxoAQImCpCoTYxaGm1m7nQaWB4fOnz4cGuddY+roXgEEAiZQN+Q9YfuxAio1yqqRTbU3Gm24AX69+9vNULNabffqBV8q2gBAgjoLsCIWvcIOWif/d5pew6vg6I41QWB3Nxcq5QzZ864UBpFIIBAVARI1CGO9KpVq+SRRx4JcQ/N65paa5251ObFjRYjEKQAiTpIfQ/rVsvw7dmzR8aOHethLRSdroB6DzhzqdNV43gEoi1Aog5p/Hfs2CGLFi3iXqhm8WUutWYBoTkIGCBAojYgSOk2UT2stGDBArn77rvTPZXjPRZgLrXHwBSPQAgFSNQhDGpDQ4P13unCwsIQ9s7sLjGX2uz40XoEghAgUQeh7nGdGzZskOrqao9rofhMBJhLnYka5yAQbQESdcjir957XFdXJ/fcc0/Iehau7qilXdkQQACBVARI1KkoGXRMfX29qLc0saCGnkGz57TzXmo940OrENBRgJXJdIxKhm2yX8Ch3pbFprfA+fPn9W4grUMAAW0EGFFrEwrnDdm5c6f1ENmYMWOcF0YJngmoKx6HDx/2rHwKRgCBcAmQqEMUzxdffFGmTZsm/fr1C1Gv6AoCCCAQbQESdUjibz9EVlFREZIehbcbo0aNkl27doW3g/QMAQRcFSBRu8oZXGHqIbJZs2aJ/eKH4FpCzb0JqLnUbAgggECqAlldXV1dqR6c7nFZWVniYfHpNie0x6uHyNQrFNVDZMXFxaHtZ1g61tzcLEVFRfzdCEtA6QcCHgswovYY2I/i9+3bx0NkfkC7VIf9XmqXiqMYBBAIuQCJOgQBXrZsGQ+RGRTHwYMHW609ceKEQa2mqQggEJQAl76DknepXvUQWUFBgagFNLg/7RKqD8Wo20ItLS1iL4DiQ5VUgQAChgowojY0cHazeYjMljDrz3Hjxsnp06fNajStRQCBQARYmSwQdncqZSUydxyDKKW0tFROnToVRNXUiQAChgkwojYsYLHNZSWyWA3zfu7o6DCv0bQYAQR8FyBR+07uXoWsROaepd8lTZgwQQ4ePOh3tdSHAAIGCpCoDQyaarK9EtnUqVMN7QHNRgABBBBIRYBEnYqShsfwOksNg5JGk0aMGCFqWh0bAggg0JsAD5P1JqTh5+3t7TJ79mxrJTINm0eTUhBg0ZMUkDgEAQQsAUbUBn4RGhoarJXIWC7UwOB90WQWPTE3drQcAb8FSNR+i7tQ34YNG+TJJ590oSSKCEogOzvbqvr8+fNBNYF6EUDAEAEStSGBspvZ1NQkdXV1oubhspktwKInZseP1iPglwCJ2i9pl+pRSXrRokVij8hcKpZiAhBg0ZMA0KkSAQMFeJjMoKCplzioJ4XVGtFs4RBg0ZNwxJFeIOClACNqL3VdLru2tlbKy8t5kYPLrkEVN2rUKBY9CQqfehEwSIARtSHBUut6q4fIVqxYYUiLaWZvAgMGDOjtED5HAAEEhBG1IV8Cta632saMGWNIi2lmbwJDhw4VNdWODQEEEOhJgETdk45Gn6l1vaurq6Vfv34atYqmOBEYMmSI7Nmzx0kRnIsAAhEQIFEbEOTm5mZrStY999xjQGtpYroC6rYGGwIIIJBMgESdTEaj/Rs3bmRKlkbxcKsp+fn5VlHHjx93q0jKQQCBEArwMJnmQWVKluYBonkIIICAxwKMqD0Gdlo8U7KcCup9vppux3up9Y4RrUMgaAFG1EFHoIf61b1L3pLVA1AIPrIvf4egK3QBAQQ8EmBE7RGsG8Vu2bKFt2S5AalxGQMHDpS2tjaNW0jTEEAgaAESddAR6KH+JUuW8JasHnzC8NHIkSPl2LFjYegKfUAAAY8ESNQewTotVr0lS82x5S1ZTiU5HwEEEDBbIKurq6vLqy5kZWWJh8V71Wwtyq2oqJBJkyZZi5xo0SAa4YmAmiNfVFTE3xNPdCkUgXAIkKg1jGNra6sUFBTI2bNneZ2lhvFxs0l2rPkHrZuqlIVAuAS49K1hPFevXi1z5swhSWsYG6+a1N7e7lXRlIsAAoYLMKLWLID2CEu9c5qpO5oFx6PmqFtExNsjXIpFIAQCjKg1C2J9fb3MmjWLJK1ZXGgOAgggEJQAiToo+QT1qsufaoGTBx54IMGn7AqrgFqd7MiRI2HtHv1CAAGHAiRqh4Bunq5evqH+p11cXOxmsZSluYC6xdHR0aF5K2keAggEJcASokHJx9XLcqFxIBH7lUQdsYDTXQTSEGBEnQaWl4fay4WOGTPGy2ooW0OBCRMm8GIODeNCkxDQRYBErUEk1GjaXi60X79+GrSIJiCAAAII6CJAotYgEmo0rbbJkydr0Bqa4LfAgAEDRE3LY0MAAQQSCTCPOpGKj/vUaHrixInWyzcqKyt9rJmqdBGw586zOpkuEaEdCOglwIg64Hjs27ePl28EHAOqRwABBHQWIFEHHJ1ly5bJypUrWS404DgEWf3gwYOt6rn8HWQUqBsBfQW49B1gbNSrLEtKSnj5RoAx0KVqlhHVJRK0AwH9BBhRBxgTRtMB4mtY9fnz5zVsFU1CAIGgBUjUAUVAjabr6upk6tSpAbWAanUSUOu7Hz58WKcm0RYEENBEgEQdUCAYTQcEr2m111xzjaYto1kIIBC0AIk6gAgwmg4A3YAq29raDGglTUQAAb8FSNR+i4sIo+kA0DWvUi0jeuzYMc1bSfMQQCAIARK1z+qMpn0GpzoEEEDAcAEStc8BZDTtM7gh1bGMqCGBopkIBCDAPGof0Zk37SO2YVWxjKhhAaO5CPgowIjaJ2y1pjejaZ+wqQYBBBAIkQCJ2qdgqjdkMW/aJ2wDq7GXET1x4oSBrafJCCDgpQCJ2kvdL8q23ze9efNm1vT2wdvEKrKzs61mszqZidGjzQh4K0Ci9tbXKp33TfuATBUIIIBASAVI1B4H1h5NP/nkk9KvXz+Pa6N4kwXKy8vlyJEjJneBtiOAgAcCJGoPUGOLXLNmjfXr5MmTY3fzMwLdBPLz86Wjo6PbfnYggEC0BfpGu/ve9r69vV1mz54tjY2NjKa9paZ0BBBAILQCjKg9DO1LL70k6nJmcXGxh7VQdFgERo0aJbt27QpLd+gHAgi4JMCI2iXI+GLUAhYLFiyQ/fv3x3/E7wgkFFCrk7EhgAAC8QKMqONFXPp99erVMmfOHCksLHSpRIpBAAEEEIiiAEuIehB1e6nQlpYWUQ8IsSGQikBzc7MUFRVJV1dXKodzDAIIRESAEXXKgb4gJ9/5rcy7PUeysnLk9uW7JdHzubFLhZKkU8blQBHp378/DggggEA3ARJ1N5JEOy7IhzWPyy0/aJCC/94sLWtKpOGtg9LW2f1YtbhJW1ubTJ06tfuH7EEAAQQQQCBNAS59pwDW+WGNPDhusQz+3Zvy7B2Dk56hpmPdddddohY3qaysTHocHyCQSEB9fwYNGiTcMkmkwz4EoivAU9+9xv5j2f/KWll78yPSUpo8SatiNm7cKDk5OcLiJr2ickACAXu97wQfsQsBBCIsQKLuMfid0vHOb+SJOfukbM1yubGHGwVqOpZa3ERNx2Kp0B5R+RABBBBAIA2BHlJPGqWE8tAzsn3eeLlq7OPSICelfuZNkr/8HbmYpK/qXdNMx0qCw+6UBVjvO2UqDkQgMgKMqJOGerDc8ewuabu1WnKmtMualg0yI/+KhEfX19eLmjd9/PjxhJ+zE4FUBVjvO1UpjkMgOgKMqHuM9cfy3tt7RcrukpIbEydpNR1r4cKFsn79esnNze2xND5EAAEEEEAgXQESdU9iF4/Kvs3vyLDC4fKNJFIrVqywHiCrqqrqqSQ+QyAlgYEDB1rT+1I6mIMQQCASAlz67iHMnYcPyFuHbpDv3fpNuTrBcbHrefMAWQIgdqUtMHLkSF7MkbYaJyAQboEk48Rwdzq13l2UUwd3S72MkYmjhnQ7RV3ynjt3Lg+QdZNhBwIIIICAmwKMqJNq2venH0l4f9pegWzt2rVJS+ADBNIVUG/QUldq2BBAAAFbgERtS8T/ad2fbpOy+d/uNn/6xIkTMmXKFNm6dauwSEU8HL87ERg+fLjU1dU5KYJzEUAgZAJc+k4S0M/vT5fIvSXDJR7p6aefllmzZklZWVmSs9mNAAIIIICAOwKMqBM6fiYfNP5RLix7Qn4UN3e6pqaGOdMJzdiJAAIIIOCFQPxg0Ys6zCiz86jUzBwrd649IB/uXiOLXs2Xn/24UAbEtN6+5L1582bmTMe48KN7Anl5eVZh3Kd2z5SSEDBdgERtR7DP1+X6m74h9TMLZdwLIo+u+6ncMeyr9qfWn/Ylb96MdRkLv7gowDQ/FzEpCoGQCPCayxQDqS55qwfI1DKhrECWIhqHZSSQlZXFqy4zkuMkBMIpwIg6hbhyyTsFJA5xTYAXc7hGSUEIhEKARN1LGNXCJuqSt3ozFpe8e8HiY1cEeDGHK4wUgkBoBHjqu5dQbtq0SQ4cOCBvvvlmL0fyMQIIIIAAAu4LkKh7MG1ubpbp06dLY2MjC5v04MRH7gt0dHS4XyglIoCAkQJc+k4Stvb2dnnooYdk5cqVUlxcnOQodiPgvsCECRPk4MGD7hdMiQggYKQAiTpJ2JYsWWK9vnLmzJlJjmA3AggggAAC3gtw6TuB8YYNG2TZsmXWVCzmtSYAYhcCCCCAgG8CjKjjqGPvSzNfOg6HX30RGDp0qDQ0NPhSF5UggID+AiTqmBhxXzoGgx8DExgyZIjs2bMnsPqpGAEE9BIgUX8RDzVfet68eTJ69GjhvrReX1JagwACCERZgHvUX0R/zZo1l+ZLc186yn8l6DsCCCCglwBrfYuIvY53S0uLqFWh2BAIUkBd3enfvz/rfQcZBOpGQCOByF/6bmpqsl62sXXrVpK0Rl/MKDeFKzpRjj59R6C7QKQTtXrZxmOPPWYtalJWVtZdhz0IBCSg1pZXo2o2BBBAILKXvtUT3nfddZeUlpbK0qVL+SYggAACCCCgpUAkE7W6B/iTn/zECsjzzz8vXGrU8rtJoxBAAAEERCRyT33bSVq9EWvHjh0kaf4aIIAAAghoLRC5e9QrVqywpmGpJ70ZSWv93aRxCCCAAAIiEqlEvWrVKqmtrbWmY7E8KN9/BBBAAAETBCKTqFWSVi/bUCNpkrQJX03aiAACCCCgBCJxj1ol6dmzZ1sLSJCk+eIjgAACCJgkEPoRtT2S3r9/PwuamPTNpK0IIIAAApZAqEfUdpLmcjffdgQQQAABUwVCmajVFKynnnrKeqcvSdrUrybtRgABBBBQAqFL1LHzpEnSfMkRQAABBEwXCNU9arV293333WfF5M033+TpbtO/nbQfAQQQQCA886ibm5ulsrJShgwZImpZ0OzsbMKLAAIIIICA8QKhGFGrS9xFRUUybdo0efnll1lxzPivJR1AAAEEELAFjL5Hre5HqyVBFyxYII2NjVJcXGz3iz8RQAABBBAIhYCxibq1tVXmzp1rBeH48ePcjw7F15FOIIAAAgjECxh56Vtd6i4oKJDx48fLK6+8QpKOjyq/I4AAAgiERsCoEbV6qvvpp5+23n61detWKSsrC00g6AgCCCCAAAKJBIwYUat70eqFGnl5eXLNNdeImnpFkk4UTvYhgAACCIRNQPsRdVNTkyxbtkza2tp4YCxs3z76gwACCCDQq4C2I2r7YbGSkhJrfvSOHTt4qrvXcHIAAggggICXAu3t7V4Wn7Bs7RK1naDVw2LXXXednD171pof3a9fv4QdYCcCCCCAAAJ+CKgkPWjQIGvGkXpmyq9Nm0StLnE/+OCD1tPcKkG3tLRIdXU1K4z59U2gHgQQQACBHgXUipfqlckNDQ3WM1NqBpIfW1ZXV1eXVxVlZWVJT8Wrf5Fs375d1Oso1aZWFps6dSrJ2auAUC4CCCCAgGMB9YDzmjVrZPbs2VJeXi5Lly6V/Px8x+UmK8D3EbW6tK2e4K6oqLD+RbJz50555plnRN2DZgSdLEzsRwABBBDQRUDdilX5Sl35VZu6VavymkrgXmyej6hVRw4ePCi7du2yLhfs2bNHZs2aJVVVVTJ27FhGz15ElTIRQAABBHwRUMl5y5YtMmXKFGt0/Ytf/EIKCwtdrTtLRDy79O1qSykMAQQQQAABAwTcXta6b0/3kJ169HaP2mn5nI9AWAX4uxPWyNKvMArYs5Xq6upk/fr1ri9r7fs96jAGiT4hgAACCERPQF32Xrx4sXWPesiQIdY9a/VQtNub9iuTud1hykMAAQQQQMCpQHNzszz00EOinrvavHmztTCX0zKTnc+IOpkM+xFAAAEEEIgTUIueqFcsFxUVSWlpqbUoV2VlZdxR6teLcrLmYVG3sbJyqqXmwwsinSdl94rpkpOVJTcuf0cuJjgr0S7Pn/r28h54og6xD4EwCHCPOgxRpA9hE1CXuidOnGh1S00rTunlUB27ZfkPpspb96+Xf/7rNjk4+TGZMfLqtGhI1GlxcTAC/giQqP1xphYE0hGwp2JNnjxZUl/WWo2sqyVnSpPM2PyavFx5vaR7KTvd49PpUy/HXpCT7/xW5t2eI1lZN8v0FU1ysrOXU/gYAQQQQACBgARUclaXuVNP0qqhfWXoqPFSJsXy/f90bdpJWpUQUKLulI53XpCpTxyWOzceka6/vSnTT/9Spv5qt3QEFACqRQABBBBAwDuBvfL2ex9nVHwwibqzVX4//w8y/mePyh3DvirS51q548nHZfyvlsvvWz/LqCOchECYBHi2I0zRpC+RFug8KrXrWqRw2r/Lb7f+bzmXAUYgibrzg3+VV+uvlYLcAV82+eq/lzvv/1BebTwiXAH/koWfEEAAAQRMFTgn769bJ0enzJMF038g0nxE/nLxqNT8fKO0ppHoAkjUn8kHjW9K/bAbZfg3vhqn/+9S/+q/ygdpdCCuAH5FAAEEEEAgYIHPpHXtjyQrq0p+M/BeefCWbLl67CS5/92ZUjrzNcn9px9KfhrZN4AFTzrkRMthkZvvktwBabQ0YHaqRwABBBBAIDWBKyR/xu+la0bM0VffIc+2dcmzMbtS/ZFMmaoUxyGAAAIIIBCAQACJeoDkFowQefcDOdHBNe4AYk6VGgt0nmySFdNv/nw1o9vnS01rJo+eaNxBmoYAAmkLBJCor5AbS+6Ssvimdp6RI80fS9m935YbA2hVfHP4HQHfBToOSG39V+Q//+Zd6fpbm7z9Dx9KdekS2X6Of9D6HgsqREAjgUBSYp8bvy333rxDtu5t/5Kio01a3h0j95YMD2py95dt4ScEfBf4TA7t/VRuvX+CDFN/K/sMk/Ezp8v9Un/53xPf20WFCCAQtEAgiVr65MuPFv9Qdv/zC7L9pFqo/EPZvuRXsvvxJ+RH+VcEbUL9CAQgcIXcUDpBro35G9n5lyPSXPBj+dH47ADaQ5UIIKCLQMz/FvxsUh8ZcMujsvHZwbL+lq9J1ldmyNaCn8vGx8dLzMxqPxtEXQhoJHBOWrevlZ8uOinzNj4qtzA7QqPY0BQE/BfgpRz+m1MjAskFzm2XeSO/K0tPqkPKZO7m5+RnlSP5B2xyMT5BIPQCAY2oQ+9KBxHITOCLuZZ/a3tb1s0VWTqlSv5LzVFW68tMk7MQCIUAiToUYaQTYRPoM2y8TP/lc7Km7KxsefsQL6sJW4DpDwJpCJCo08DiUAR8FegzXEruLfG1SipDAAH9BDxN1LwBSL+A0yKTBNRyu3+VybfewD1qk8JGWxFwWcDTRO1yWykOgfAKdB6Vmplj5fZ5v5V31JRFuSAnt78gz/5lqswpy2NtgfBGnp4h0KsAibpXIg5AwAeBPtfIfyweLS1Lp8nYnK9JVs6D8i8f3yPrfjNdRjI9y4cAUAUC+gp4Oj1L327TMgQQQAABBMwQYERtRpxoJQIIIIBARAVI1BENPN1GAAEEEDBDgERtRpxoJQIIIIBARAVI1BENPN1GAAEEEDBDgERtRpxoJQIIIIBARAVI1BENPN1GAAEEEDBDgERtRpxoJQIIIIBARAX+PyL7IFQiVO59AAAAAElFTkSuQmCC"></p>
<p style="text-align: left;">Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="M"> <mi>M</mi> </math></span> is parallel to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span>, find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-coordinate of P.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>4</mn><mo> </mo><mi>sin</mi><mo> </mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>.</mo><mn>5</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>4</mn><mo> </mo><mi>sin</mi><mfenced><mrow><mi>x</mi><mo>-</mo><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mn>2</mn></mfrac></mrow></mfenced><mo>+</mo><mn>2</mn><mo>.</mo><mn>5</mn><mo>+</mo><mi>q</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>></mo><mn>0</mn></math>.</p>
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> is obtained by two transformations of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe these two transformations.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-intercept of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> is at <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mi>r</mi><mo>)</mo></math>.</p>
<p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>≥</mo><mn>7</mn></math>, find the smallest value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>4</mn><mo> </mo><mi>cos</mi><mo> </mo><mi>x</mi><mfenced><mrow><mn>1</mn><mo>-</mo><mn>3</mn><mo> </mo><mi>cos</mi><mo> </mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mo> </mo><msup><mi>cos</mi><mn>2</mn></msup><mo> </mo><mn>2</mn><mi>x</mi><mo>-</mo><msup><mi>cos</mi><mn>3</mn></msup><mo> </mo><mn>2</mn><mi>x</mi></mrow></mfenced></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Expand and simplify <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mi>a</mi><mo>)</mo></mrow><mn>3</mn></msup></math> in ascending powers of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By using a suitable substitution for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>, show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo><mn>3</mn><mo> </mo><mi>cos</mi><mo> </mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mo> </mo><msup><mi>cos</mi><mn>2</mn></msup><mo> </mo><mn>2</mn><mi>x</mi><mo>-</mo><mo> </mo><msup><mi>cos</mi><mn>3</mn></msup><mo> </mo><mn>2</mn><mi>x</mi><mo>=</mo><mn>8</mn><mo> </mo><msup><mi>sin</mi><mn>6</mn></msup><mo> </mo><mi>x</mi></math>.</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>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>∫</mo><mn>0</mn><mi>m</mi></msubsup><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>d</mo><mi>x</mi><mo>=</mo><mfrac><mn>32</mn><mn>7</mn></mfrac><msup><mi>sin</mi><mn>7</mn></msup><mo> </mo><mi>m</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> is a positive real constant.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>It is given that <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>∫</mo><mi>m</mi><mfrac><mi mathvariant="normal">π</mi><mn>2</mn></mfrac></msubsup><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>d</mo><mi>x</mi><mo>=</mo><mfrac><mn>127</mn><mn>28</mn></mfrac></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>m</mi><mo>≤</mo><mfrac><mi mathvariant="normal">π</mi><mn>2</mn></mfrac></math>. Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>AC is a vertical communications tower with its base at C.</p>
<p>The tower has an observation deck, D, three quarters of the way to the top of the tower, A.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-06_om_10.32.25.png" alt="N16/5/MATSD/SP1/ENG/TZ0/11"></p>
<p>From a point B, on horizontal ground 250 m from C, the angle of elevation of D is 48°.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate CD, the height of the observation deck above the ground.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the angle of depression from A to B.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> have coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>1</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>,</mo><mo> </mo><mn>2</mn></mrow></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>9</mn><mo>,</mo><mo> </mo><mi>m</mi><mo>,</mo><mo> </mo><mo>-</mo><mn>6</mn></mrow></mfenced></math> respectively.</p>
</div>
<div class="specification">
<p>The line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math>, which passes through <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>, has equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">r</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>19</mn></mtd></mtr><mtr><mtd><mn>24</mn></mtd></mtr></mtable></mfenced><mo>+</mo><mi>s</mi><mfenced><mtable><mtr><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Express <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mtext>AB</mtext><mo>→</mo></mover></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Consider a unit vector <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">u</mi></math>, such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">u</mi><mo>=</mo><mi>p</mi><mi mathvariant="bold-italic">i</mi><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mi mathvariant="bold-italic">j</mi><mo>+</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi mathvariant="bold-italic">k</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>></mo><mn>0</mn></math>.</p>
<p>Point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> is such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mtext>BC</mtext><mo>→</mo></mover><mo>=</mo><mn>9</mn><mi mathvariant="bold-italic">u</mi></math>.</p>
<p>Find the coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>.</p>
<div class="marks">[8]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><msup><mi>cos</mi><mn>2</mn></msup><mo> </mo><mi>x</mi><mo>+</mo><mn>5</mn><mo> </mo><mi>sin</mi><mo> </mo><mi>x</mi><mo>=</mo><mn>4</mn></math> may be written in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><msup><mi>sin</mi><mn>2</mn></msup><mo> </mo><mi>x</mi><mo>-</mo><mn>5</mn><mo> </mo><mi>sin</mi><mo> </mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>=</mo><mn>0</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>Hence, solve the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><msup><mi>cos</mi><mn>2</mn></msup><mo> </mo><mi>x</mi><mo>+</mo><mn>5</mn><mo> </mo><mi>sin</mi><mo> </mo><mi>x</mi><mo>=</mo><mn>4</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>2</mn><mi mathvariant="normal">π</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>The following diagram shows triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABC</mtext></math>, with <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext><mo>=</mo><mn>10</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BC</mtext><mo>=</mo><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AC</mtext><mo>=</mo><mn>2</mn><mi>x</mi></math>.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mo> </mo><mover><mtext>C</mtext><mo>^</mo></mover><mo>=</mo><mfrac><mn>3</mn><mn>4</mn></mfrac></math>, find the area of the triangle.</p>
<p>Give your answer in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>p</mi><msqrt><mi>q</mi></msqrt></mrow><mn>2</mn></mfrac></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>,</mo><mo> </mo><mi>q</mi><mo>∈</mo><msup><mi mathvariant="normal">ℤ</mi><mo>+</mo></msup></math>.</p>
</div>
<br><hr><br><div class="question">
<p>Find the least positive value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> for which <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mfenced><mrow><mfrac><mi>x</mi><mn>2</mn></mfrac><mo>+</mo><mfrac><mi mathvariant="normal">π</mi><mn>3</mn></mfrac></mrow></mfenced><mo>=</mo><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac></math>.</p>
</div>
<br><hr><br><div class="specification">
<p><strong>In this question, all lengths are in metres and time is in seconds.</strong></p>
<p>Consider two particles, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>1</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>2</mn></msub></math>, which start to move at the same time.</p>
<p>Particle <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>1</mn></msub></math> moves in a straight line such that its displacement from a fixed-point is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mn>10</mn><mo>-</mo><mfrac><mn>7</mn><mn>4</mn></mfrac><msup><mi>t</mi><mn>2</mn></msup></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>≥</mo><mn>0</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the velocity of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>1</mn></msub></math> at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</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>Particle <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>2</mn></msub></math> also moves in a straight line. The position of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>2</mn></msub></math> is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">r</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>6</mn></mtd></mtr></mtable></mfenced><mo>+</mo><mi>t</mi><mfenced><mtable><mtr><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math>.</p>
<p>The speed of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>1</mn></msub></math> is greater than the speed of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>2</mn></msub></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>></mo><mi>q</mi></math>.</p>
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math>.</p>
<div class="marks">[5]</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="\sin \theta = \frac{{\sqrt 5 }}{3}">
<mi>sin</mi>
<mo><!-- --></mo>
<mi>θ<!-- θ --></mi>
<mo>=</mo>
<mfrac>
<mrow>
<msqrt>
<mn>5</mn>
</msqrt>
</mrow>
<mn>3</mn>
</mfrac>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta ">
<mi>θ<!-- θ --></mi>
</math></span> is acute.</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="\cos \theta ">
<mi>cos</mi>
<mo></mo>
<mi>θ</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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\cos 2\theta ">
<mi>cos</mi>
<mo></mo>
<mn>2</mn>
<mi>θ</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A triangular postage stamp, ABC, is shown in the diagram below, such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AB}} = 5{\text{ cm}},{\rm{ B\hat AC}} = 34^\circ ,{\rm{ A\hat BC}} = 26^\circ ">
<mrow>
<mtext>AB</mtext>
</mrow>
<mo>=</mo>
<mn>5</mn>
<mrow>
<mtext> cm</mtext>
</mrow>
<mo>,</mo>
<mrow>
<mrow>
<mi mathvariant="normal">B</mi>
<mrow>
<mover>
<mi mathvariant="normal">A</mi>
<mo stretchy="false">^<!-- ^ --></mo>
</mover>
</mrow>
<mi mathvariant="normal">C</mi>
</mrow>
</mrow>
<mo>=</mo>
<msup>
<mn>34</mn>
<mo>∘<!-- ∘ --></mo>
</msup>
<mo>,</mo>
<mrow>
<mrow>
<mi mathvariant="normal">A</mi>
<mrow>
<mover>
<mi mathvariant="normal">B</mi>
<mo stretchy="false">^<!-- ^ --></mo>
</mover>
</mrow>
<mi mathvariant="normal">C</mi>
</mrow>
</mrow>
<mo>=</mo>
<msup>
<mn>26</mn>
<mo>∘<!-- ∘ --></mo>
</msup>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{A\hat CB}} = 120^\circ ">
<mrow>
<mrow>
<mi mathvariant="normal">A</mi>
<mrow>
<mover>
<mi mathvariant="normal">C</mi>
<mo stretchy="false">^<!-- ^ --></mo>
</mover>
</mrow>
<mi mathvariant="normal">B</mi>
</mrow>
</mrow>
<mo>=</mo>
<msup>
<mn>120</mn>
<mo>∘<!-- ∘ --></mo>
</msup>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_11.34.31.png" alt="M17/5/MATSD/SP1/ENG/TZ1/13"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of BC.</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 area of the postage stamp.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows triangle ABC, with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AB}} = 3{\text{ cm}}">
<mrow>
<mtext>AB</mtext>
</mrow>
<mo>=</mo>
<mn>3</mn>
<mrow>
<mtext> cm</mtext>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{BC}} = 8{\text{ cm}}">
<mrow>
<mtext>BC</mtext>
</mrow>
<mo>=</mo>
<mn>8</mn>
<mrow>
<mtext> cm</mtext>
</mrow>
</math></span>, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{A\hat BC = }}\frac{\pi }{3}">
<mrow>
<mrow>
<mi mathvariant="normal">A</mi>
<mrow>
<mover>
<mi mathvariant="normal">B</mi>
<mo stretchy="false">^<!-- ^ --></mo>
</mover>
</mrow>
<mi mathvariant="normal">C</mi>
<mo>=</mo>
</mrow>
</mrow>
<mfrac>
<mi>π<!-- π --></mi>
<mn>3</mn>
</mfrac>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-11_om_09.17.57.png" alt="N17/5/MATME/SP1/ENG/TZ0/04"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AC}} = 7{\text{ cm}}">
<mrow>
<mtext>AC</mtext>
</mrow>
<mo>=</mo>
<mn>7</mn>
<mrow>
<mtext> cm</mtext>
</mrow>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The shape in the following diagram is formed by adding a semicircle with diameter [AC] to the triangle.</p>
<p><img src="images/Schermafbeelding_2018-02-11_om_10.50.00.png" alt="N17/5/MATME/SP1/ENG/TZ0/04.b"></p>
<p>Find the exact perimeter of this shape.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>Six equilateral triangles, each with side length 3 cm, are arranged to form a hexagon.<br>This is shown in the following diagram.</p>
<p><img src="data:image/png;base64,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"></p>
<p>The vectors <em><strong>p</strong></em> , <em><strong>q</strong></em> and <em><strong>r</strong></em> are shown on the diagram.</p>
<p>Find <em><strong>p</strong></em>•(<em><strong>p</strong></em> + <em><strong>q</strong></em> + <em><strong>r</strong></em>).</p>
</div>
<br><hr><br><div class="specification">
<p>Point A has coordinates (−4, −12, 1) and point B has coordinates (2, −4, −4).</p>
</div>
<div class="specification">
<p>The line <em>L</em> passes through A and B.</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="\mathop {{\text{AB}}}\limits^ \to = \left( \begin{gathered} \,6 \hfill \\ \,8 \hfill \\ - 5 \hfill \\ \end{gathered} \right)">
<mover>
<mrow>
<mrow>
<mtext>AB</mtext>
</mrow>
</mrow>
<mo stretchy="false">→</mo>
</mover>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mtable rowspacing="3pt" columnspacing="1em" displaystyle="true">
<mtr>
<mtd>
<mspace width="thinmathspace"></mspace>
<mn>6</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mspace width="thinmathspace"></mspace>
<mn>8</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>−</mo>
<mn>5</mn>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
</math></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find a vector equation for <em>L</em>.</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>Point <em>C</em> (<em>k</em> , 12 , −<em>k</em>) is on <em>L</em>. Show that <em>k</em> = 14.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.ii.</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="\mathop {{\text{OB}}}\limits^ \to \, \bullet \mathop {{\text{AB}}}\limits^ \to ">
<mover>
<mrow>
<mrow>
<mtext>OB</mtext>
</mrow>
</mrow>
<mo stretchy="false">→</mo>
</mover>
<mspace width="thinmathspace"></mspace>
<mo>∙</mo>
<mover>
<mrow>
<mrow>
<mtext>AB</mtext>
</mrow>
</mrow>
<mo stretchy="false">→</mo>
</mover>
</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>Write down the value of angle OBA.</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>Point D is also on <em>L</em> and has coordinates (8, 4, −9).</p>
<p>Find the area of triangle OCD.</p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> defined by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>6</mn><mo>+</mo><mn>6</mn><mo> </mo><mi>cos</mi><mo> </mo><mi>x</mi></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>4</mn><mi>π</mi></math>.</p>
<p>The following diagram shows the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbsAAAEuCAYAAAAXwrzuAAAgAElEQVR4Ae2dTY8exdWG8z8idnj8IfA4eOx4xBsFj4kQXgTPWJaCwRrLXmDZjh1evQnCxpgsAhEWZhUUFGcXFmEbpLAOEnss/oDDHzC/oF/dbZ+Z5+np767uro+rpNEz/d19neq6q05XnfpJRoIABCAAAQhETuAnkT8fjwcBCEAAAhDIEDsyAQQgAAEIRE8AsYvexDwgBCAAAQggduQBCEAAAhCInkDUYvfKK7/Kvvzyn9EbkQeEAAQgAIF6AtGK3f37n2TPPPPT7NChA9kPP/y3ngJbIQABCEAgagJRit3333+fC53E7vLlS9m5c2ejNiIPBwEIQAAC9QSiFDuJ29277+eC9+OPP+atu6+//nc9CbZCAAIQgEC0BKITuwcP/paLm0ROLTulxXXRWpIHgwAEIACBSgJRiZ2+zekbnbXiTOz09Grtvf327ypBsAECEIAABOIlEJXYqeel3JeWFsVOQqjemSQIQAACEEiPQFRiVzTfotgVt7EMAQhAAALpEEDs0rE1TwoBCEAgWQKIXbKm58EhAAEIpEMAsUvH1jwpBCAAgWQJIHbJmp4HhwAEIJAOAcQuHVvzpBCAAASSJYDYJWt6HhwCEIBAOgQQu3RszZNCAAIQSJZAkmL3zjt/2AkU/fDhd7nxHz9+nK+z5WRzBA8OAQhAIEICSYqd7ChR06Dzzz77y45ZX3/9N/n6nRX8AwEIQAACURBIVuxkPYndhx/+aceQEjsSBCAAAQjERyBpsXvxxfVMLk0ltfC++eY/8VmYJ4IABCAAgSxpsTt9+tVMrblHjx4ttfDIFxCAAAQgEBeBpMXuypW3MgmefkkQgAAEIBAvgaTFTi7M5547lLfs4jUxTwYBCEAAAkmLnTqnMNSAlwACEIBA/ASSEzt1Svnii3/krks6pMSfwXlCCEAAAiKQlNhp4LjclvpOp04pJAhAAAIQSINAUmKXhkl5SghAAAIQKBJA7IpEWIYABCAAgegIIHbRmZQHggAEIACBIgHErkiEZQhAAAIQiI4AYhedSXkgCEAAAhAoEkDsikRYhgAEIACB6AggdtGZlAeCAAQgAIEiAcSuSIRlCEAAAhCIjgBiF51JeSAIQAACECgSQOyKRFiGAAQgAIHoCCB20ZmUB4IABCAAgSIBxK5IhGUIQAACEIiOAGIXnUl5IAhAAAIQKBJA7IpEWIYABCAAgegIIHbRmZQHggAEIACBIgHErkiEZQhAAAIQiI4AYhedSXkgCEAAAhAoEkDsikRYhgAEIACB6AggdtGZlAeCAAQgAIEiAcSuSIRlCEAAAhCIjgBiF51JeSAIQAACECgSQOyKRFiGAAQgAIHoCCB20ZmUB4IABCAAgSIBxK5IhGUIQAACEIiOAGIXnUl5IAhAAAIQKBJA7IpEWIYABCAAgegIIHbRmZQHggAEIACBIgHErkiEZQhAAAIQiI4AYhedSXkgCEAAAhAoEkDsikRYhgAEIACB6AggdtGZlAeCAAQgAIEiAcSuSIRlCEAAAhCIjgBiF51JeSAIQAACECgSQOyKRFiGAAQgAIHoCCB20ZmUB4IABCAAgSIBxK5IhGUIQAACEIiOAGIXnUl5IAhAAAIQKBJA7IpEWIYABCAAgegIRC929+9/kn355T+zH3/8MTrj8UBhEPj++++zBw/+likv6k////DDf8O4ee4ySgJff/3vPC9+++23UT5f2UNFL3bnzp3NDh06kP+pkCFBYCoCErkzZ17Lnnnmp9mJEz/PNjZO5n9HjhzO19248VtEbypjcJ2cgMpAlYfKkyob1RBIJUUvdjKkWnWqUcvAly9fopWXSu6e8Tnv3fs4z28SuD9/9FH2978/WPr74wcfZOvrJ7IDB1aSKnBmNEnSl1YZKHFTGaiyMEVPVxJiZ7lcNW3Val555VdJGts48DsugevXr+WFyv++/faSwBUFT8uXL13K98XrMK5NUj67hE1lnrwLKgNTTUmJnYxsgqdaDgkCrglI6FZW9pW25srETuskiqpxp+RScs2d85UTMKGjgp9lyYmdsoQJ3t2775fnENZCoAeBO3fey0VLLsoqYataj+D1AM4hjQSszwIdohIVO+UQ1aJVm1avJBIEhhJQPlJ+auO6rBK8s1tb+Te8lF1NQ+3A8bsEVJlXniQ/PWGSZMvOsoM6q+gbXoofa40Bv8MJqNasjiYSqyoha7te31VefnmDPDncLEmfQUMKJHR8C97NBkmLnUROYifRI0GgL4HNzTPZ6urz2Wef/WWw2H366f1sZeXZTC5REgT6EFC5pkoT/RKW6SUtdkJh7qeUBlcuZwGWhhBQzVk16D7f6apae9euXs3PSZ4cYpl0j5X7UpV4vtMt54HkxU44VANSbyUSBLoQUA1a7ss3zp8f3KIrCp/G58mdSYJAFwL6Pof7spwYYve0d6YyCF2/yzMJa8sJKAKKhhm4cF8WxU4D0Sm0yrmztpoAFfdqNojdUzZvv/273M9djYotENglIBeRxEgux6JQuVq23pl0oNrlzn/VBPgkU81GWxC7p3ys8KJ1V59h2PqEwMWL23mnFFfCVnYetRjVWUXhnUgQaCKgTil0tqumhNgtsKF1twCDfysJWLfuIWPqysStbJ3CiR08uJ+hCJXWYIMI2LhhOqVU5wfEboENrbsFGPxbSUAzGagWXSZOrtfRuqs0AxsWCCg/qrJOqiaA2BXY0LorAGFxiYD1drv17ruTiJ3Ek9bdkglYKBCgVVcAUrGI2BXAWOuOMGIFMCzmBNQDUwPIXbfg6s5H647MV0eAVl0dnd1tiN0ui53/1H2X6AM7OPjnKQGrCE3xra4ofrTuyIZlBGjVlVEpX4fYlXCxDggEUC2Bk/CqOVp1JnrWuiPWYcIZsOTRVSmnB2YJmJJViF0JFK3CNVABJtHVFi1lzHF1JmxVvxp3d/z4WqIW4LGLBKxSTli5IpnyZcSunMtOV14G9FYASmy1WlRjRUupErfiegWJ1kB2vicnlvkqHled6QhzWAGnZDViVwJFqyRyCqaK26gCUGKr19ZecDKFT1HAui6fPv1qtrW1mRh9HrdIwL4fEwSjSKZ6GbGrZpOPW5E7k5Q2AXMXqWXVVZxc768hD2rdqbAjpUtAUXVUGSe1J4DY1bCyMVX4xGsgJbBpe/tCplkIXAtX3/MdOXKY+e4SyHd1j6hKOGHk6gjt3YbY7WWytEY+cSITLCFJasHcRXMMN6gSQ3WSIYRYUtlw6WEt4DOt+yUsjQuIXQMi+cTlLqCjSgOoSDd//vlf844pVcIzx3oNQ5Ark+81kWa6hsfSUAOGGzRAKtmM2JVAWVxlHVUoWBappPO/OqaMMTnrUJHUMAQmd00nH9qTmqeBHrlGpP0vYteCFV18W0CKcBf7ZquJVIeKk+vj//jBB3RUiTDPNT2SvtPRaa6JUvl2xK6cy9Ja642Hj3wJS/QLipiigsW1ULk6nzqq3L37fvR24AF3CSg/YvNdHl3+Q+xa0iKTtQQV0W4HDqyMOhP5UNGzeJkRIedRaghQ6a6B02ITYtcCknZRbQr3QUtYEeymb7TqBKLOIENFaazjiagSQUbr8Ah8TukAq2RXxK4EStkq+zBMcOgyOvGt09g6RSsZS6hcnVfj/27evBGfAXiiJQJ0lFvC0WsBseuAjTF3HWAFvKsKFrXqfBpbVyWOukfdK0NjAs5wLW7dPA3YuQWsil0QuwowZasVJ5MQPWVk4lqngmXuoM9V4lZcLzfr/v37GHMXVxbc8zQaV0dwiz1YOq1A7DrgMlcmY1w6QAtw1zfffMOLoM9FYata1pg7gkMHmNFa3jLlTktQDbshdg2AiptxZRaJxLVsLkwFXK4SF9/WExw6rjxYfBo8SkUi/ZYRu47cyHgdgQW2u+wrF6ZvgtZ0PysrzzIdVWB5re3tUsFuS6p+P8Suns+erVbzH+rK/OKLf2TPPXco71zw1Vf/2nMdVsxDYGPjpaBcmCaChA+bJ7+MfVVzYdILfDhpxK4Hw6EfiyVuErqHD7/Lu7erkwFpfgJWsITkwjSxI3zY/PlnjDuQp4HxvW7IInY9OKq33pBemS++uJ4PVu5xaQ4ZkYD1wjQBCe13dfUwrswR88ccp5YLk/Bgbsgjdj04DnFl2vQsjx496nFlDhmTQGi9MItirNkZmAlhzBwy7bnN04AL0w13xK4nx64fjeWy1ODfxb/Hjx/3vDqHuSZgFZgQXZgmepqdQflLhSQpfAKEKHRrQ8SuJ8++vTIVgurKlbd6XpXDxiIQugvTBA9X5lg5ZPrzEnzeLXPEridPczEoEnnbJNelat70vmxLbLr9Qndhmtjhypwuz4x5JZtLERemO8qI3QCWXT8e2/c63JcDoI9wqLkwQ4iFaaJW9UuvzBEyyAynpBeme+iI3QCmXTPk66//BhfmAN5jHaoxk2pxqzJSJSIhrWeA+Vg5Zbrzdq1IT3dn4V4JsRtgO3NltnE1qDWnAlWDyUl+Ebh+/VoQ0/m0FVxiZfqVv7reTZdypeu5U94fsRtofX1Evn//k8azWMQUXJiNqCbfQTOSx+DCNDG0WJlyz5LCI9DVYxTeE85zx4jdQO7qHiyXQ1NSD0wipTRRmn67Ohipxa1Zv00sYvhl2p/p85KrK+LCdEVy+TyI3TKPzkvWa6psbJOGGahFpz9FTaFV1xnv6Afcvn0rD8cUg8AtPoNcmRcvbo/Ojwu4JYAL0y3PxbMhdos0ev6v0GFyPRSTWnNqNUj0iJhSpOPH8tra0eza1atRteokejaDuR+UuYu2BFSODAlF2PY6Ke6H2DmwumYQVnBoUlgErFWuyCOLraIY/rdhLkNn5wjLouHf7blzZ5mRfCQzInYOwFrXdToEOIA54Sk+//yv2erq89EJnYm1PAo3b96YkCiXGkLAxntSQRlCsfpYxK6aTactcleSSTshm31nzV2niCMmDrH9yj2rnqakMAgMnU0ljKec7y4RO0fsh85x5+g2OE1LAlaLDjnwc5M4q4epKmFtxoG2xMZuIxJQGcLnkPEAI3aO2PJh2RHIiU6jWrSEoEkwQt++vn6C+dAmylNDL6P8qHxJGocAYueIK12GHYGc6DSxRU2pEmW5aU+d2piIKpfpS4Dv/n3JtT8OsWvPqnFPBoM2IvJmh9iiplSJHXPceZPlam+EHt21eJxsROycYHxykrbRVBxeklP1IBBr1JQqwVM0lbJxoD3QcchIBKrG6o50uSRPi9g5NLsVomXRVBxehlMNJHDnzntRRk2pEjuiqQzMMCMfbuM9KTfGBY3YOearGhofmR1DdXy6kyfjHnJQFD2iqTjOQI5Ph0fIMdCK0yF2FWD6rqb7cF9y0xxnHYk0yWlRFGJdJprKNHmr71U0c4oEjzQuAcTOMV8GhjoG6vh0ss/Kyr5khM4EfGPjJGGoHOclF6ezyhdjIV3QrD8HYlfPp/NWy7xEU+mMbpIDtrcvRDVRq4lZ06+iqRw7dnQSxlykPQHG57ZnNXRPxG4owZLjGYJQAsWTVakMOSiKnw1BoAXhSUZ8ehsEfp7OHojdCKw1c7n88CS/CFhv2dgmai0KW9Xy6uphhiB4lCUtZB1eoGmMgtiNwJmuxCNAdXDK1IYcFEVPQxA2N884IMkpXBAgaooLiu3Pgdi1Z9VpTwaJdsI1yc6pDTkoip2CXiv+IlNRTZLdGi+iqClyY5KmIYDYjcSZ8D8jge15WnMZxTzLQVHcissMQeiZeUY6jArxSGArTovYVYAZulpd3FWLJvlBwOxRFIDUljUEgQld58+TfOqY3gaI3UjMbQiCOkWQ5ieQyiwHTeLNEIT586LugE5s09sBsRuROUMQRoTb8dQacqCCvkkMYt/OEISOGWek3SkbRgJbc1rErgbO0E3EvBtK0M3x5jJSQR+7mLV5PoYguMlXfc9i348ZctCXYL/jELt+3FodZeO65NIkzUdAUSpWV59H6P7+IGegIQhbW5vzGSTxK9v348QxTP74iN3IyJkFYWTALU7/2mu/zlTAt2n1pLAPsyC0yDQj7kKw+BHh1pwasauB42ITGdsFxWHnUK9YFfApCFmbZ2QIwrD8NPRoKsBDCfY7HrHrx631UXJZKHOT5iFgUSpUwLcRglT2YVqZefIjnzbm4a6rInYjs7chCATgHRl0xelv376V1KzkbcX68qVL2fHjaxXUWD0WATqtjUW2+byIXTOjwXuoFq1xNaTpCaQeIqxK/DR5rdy7dJ6aNk8y5GBa3otXQ+wWaYz0P7W5kcA2nNa6eKc0K3mVuJWt379/XyY3O2kaAublIdDENLyLV0HsikRGWLbvRgTgHQFuzSmti3dZQc+6B/kkthcvbtcQZJNLAny/d0mz+7kQu+7Meh0hlxGDSHuh630QIcKejKurEnb1UD14cH9vvhzYjQA9s7vxcr03YueaaMX5mJG4AsyIq9fWjhIi7OlA8jLB0yS2qoThVhsxEy6cmiEHCzBm+Bexmwi6ongwe/lEsLMsI0RYfavOxO/IkcN0npogWzLkYALIDZdA7BoAudpshS9DEFwRrT+PKhf79j3L2Lqalp0E743z57OXX96oh8nWwQTopDYY4eATIHaDEbY/gdwYKoRJ4xO4cOFNQoQ1CJ3EjtnLx8+LugJDDqbhXHcVxK6OjuNtzF7uGGjN6TSlDyHCml2ZhA6ryUSONtkQGDqoOQLa8zSIXU9wfQ6zrvB9juWY9gTs+4g6YNi3KX6rhU+zl6siRhqHAO/9OFy7nhWx60pswP5Ww6P32wCILQ69d+9jpvRp4cK0CoBChx07drQFWXbpQwCPTh9q7o9B7NwzrT0jvvtaPE42akofdbywwpzf6lad2Njs5YQOc5L99pyEb/V7kMyyArGbGDu9ssYHrrFj6niByNWL3CIfhQ6j85T7vGm9sKlIuGfb9YyIXVdiA/e370mEDhsIsuJwC83GlD7thU6id/r0qxmhwyoy1YDVCgDP+NoBAB0eitg5hNn2VGp56KM1yT0BpvTpJnLWuiN0mPu8qDPy2WIcrn3Oitj1oTbwGMXIo/fbQIgVhzOlTz+xs9BhBD2oyFg9VluHNIYc9IA3wiGI3QhQm06pbyPMXt5Eqft2K1yY0qef4BE6rHueqzvCXOp8sqijNN02xG461jtXso/W1KJ3kDj5x8YzmWuO326ipx6sm5tnnNiCk2S590YB4El+EEDsZrKDPlrT+80tfE3powHSiFw3kTNehA5zmx95x93yHHo2xG4owZ7H65sdtb6e8CoOY0qffiJnYkfosIqM1WM13pse0EY+BLEbGXDV6c3lVrWd9d0IaByTerlqgLQV3vx2Fz+1RjQWlDSMgLw2DDkYxtD10Yida6Itz2edKeip1RJYw26qPKys7EPoOoQJK6sMKHTY8eNrDbTZ3ESAHtdNhKbfjthNz3zniozB2UEx+J/t7Qv5wOiyApx17Vt46smqFjIRP4ZlScbSDuM3xtGI3RhUW56T0GEtQbXYTVP6XLt6lZbdwJadKgYKHUbQgxaZrmIXhhxUgJl5NWI3owEsdBi16GFGsM4ATOnTvgVX19pV6LCbN28MM0rCR1OJ9dP4iN3MdsHdMdwA6gywuvo8rToHrTqJoFrIBw/uH26YRM+gjimKiUnyiwBiN7M9+JA93ACa0ufs1hZi50jsCB3WP09ar2DmrOzPcKwjEbuxyLY8L6HDWoKq2U2tYwUyrnPNsa2bi3N19TBBD2ryXNUmfeskFGAVnXnXI3bz8s97vamwJnRYP0PYd0++13UTsybxV0t5a2uzn1ESPkqeGv2R/COA2HlgE8IK9TfCvXsf54N3mwpvtncTQ7WUVQkjdSOgVh09Wbsxm2pvxG4q0jXXIXRYDZyGTRsbL2UKYIyYdROzJl6EDmvIeCWbzctA7+oSOB6sQuw8MALjcvoZwaLQKIBxU+HN9u5iuL5+gtBhHbIms5J3gDXDrojdDNCLl7RCm9BhRTL1y1ZJUCsEMesuZk3M1GI+dWqj3ghs3SFARKQdFF7+g9h5YhZelO6GuH37FlP6OBpuUCZ8FjqMyUeb8yYV1mZGc++B2M1tgafXxwXS3RBray9kClxcVlCzzk1Lj6AH7fKlOqXQoacdq7n2QuzmIl+4roW84uN2AUzFog3eVesDYXMjbGUcCR1WkQELq9XJjCEHBSieLSJ2HhmEbsvtjWE16bICmnXuxE+hw44dO9reMInuqXdXASJI/hJA7DyyDQNS2xvj+vVrTOkz4vc6qzBoMlyCHtTnS/PKEBiintPcWxG7uS2wcH1CDS3AaPiXKX3ctd5M2Kp+CR1Wnxn53l7Px5etiJ0vlsiyndBhBJGtN4rVpNXqqCqgWe9ODBU67OLF7XqjJLz13Lmzmb7ZkfwmgNh5Zh+GIDQbhCl93AlZm0oBocOq8yRDDqrZ+LYFsfPMIkz82GyQCxfeZEqfCb7XmRBa6DA8DnvzpgU2YCziXja+rUHsPLMIL0+zQdRhgil9pm3dETqsPF8S17aci49rETsPrcJA3mqjWLBdpvSZVuwIHVaeJ5mxpJyLj2sROw+toiEIfPAuNwxT+kwrcubKJHTY3vxoHaUYcrCXjY9rEDsPrcLs5dVGOXmSKX1MgKb+xeOwnC/1nqplRwqDAGLnoZ0sFBY1xmXjWM83pvSZp3VH6LDl/MiQg2Uevi8hdp5aSDVGDVYl7RKwzjtTt2i43hNxVegwDeYnZZlVvJQnSWEQQOw8tRNDEPYa5saN3zKlz4RDDooiT+iw3TxpFS+GHOwy8f0/xM5TC/Ey7TXM2trRTK2LYiHM8nRuTUKHPcmXDDnY+376vgax89hCdAjYNY59xyRE2HTCVlaJUOiwzc0zu4ZJ9D+GHIRneMTOY5sxBGHXOOr5trKyj1bdjG5MiZ86B6kSlrL7jiEHu+9lSP8hdh5biyEIu8YhRNi8LTpr5VnosJQ7ZjDkYPe9DOk/xM5ja5nrjiEIWd6aIESYH4K3sXEy6aAHDDnwuNCsuTXErgaOD5sYgpBlhAjzQ+SsdXf50qVkZy9nyIEPpWK/e0Ds+nGb7CiGIGTZnTvv5ZEqrLDld17xsyEI8jykluglHa7FETvPbWcvV4oFi5mGEGHziltZ5WJl5dlM365SSww5CNfiiF0Atjt06ED25Zf/DOBO3d+ifbdUIOKyQpd18whhqrOX611MUeTdv9nTnxGxm5555ytqCIL+UkwSeYYczCNodRWJFGcvtyEHKXtZQi6DELsArKcCXzXKFNP29oVMAYjrCl62TS+GKQ5BUKxaZjkItxRC7AKwnbny1CsxtaTAwww5mF7M2lQgVPCrA1Uq6ZVXfpXU88ZmV8QuEIum+KIx5MBPkTMhTGkIglU4Ux5MH0hRWXmbiF0lGr82pOhCYciB32KX0hCElD8l+FUS9r8bxK4/u0mPTPHjOEMO/BY7tfBSmQUh5U5ikxZ0I14MsRsRrutTpxRp3dxGDDnwW/BSGYKQ8vAf1+XYXOdD7OYi3+O6KQ1oZciB3yJn3+1SmAXBAjukPNNDj+LKu0MQO+9MUn1DKb10DDkIQ+xSGIKgSqY6iJHCJoDYBWa/VCZ0ZchBGGKnFp7GQd68eSOwN6n97ab0+aA9lfD2ROwCs1kKH8qtBatWg7nL+PVX/K5dvZqtrb0Q2JvU7nZT7BjWjkx4eyF2gdkshS7Qt2/fYpaDmWck71K5+PTT+/l8gzHOu5jikJ/AisTWt4vYtUblx44pzKelVoJaC10KXPadt+V35MjhTMIQW0oxmENsNrTnQeyMREC/Mc+UbG4jDVhGwOYVsC783zh/Pjt1aiOgt6j5Vm34S4wt1uanj28PxC5Am2qKkVgDQ+vZVlefR+gCcmNKFGOMphLzexZgsTf4lhG7wQinP0HMNc6NjZcytRK6tCrY148WYGwTuqozmIYdkOIggNgFascYvyXY90gNVEbA/BCwLnZQNBWNj4whWV4k8HMM1nzyDIhdoLaUiyW2ubWImhKewC2KYUzRVFLo9Rxo0df7thG73ujmPTBGV6ZaBWodLBag/B+WAMYS9AAX5rzl2xhXR+zGoDrROWObPFMFJRO1hiVuxcqIoqlcvLg90RswzmXMhanWHSkeAohdwLbULNGxuDKJmhK2yJnoqbKiUG8hJ8uLEj1SPAQQu4BtaWPSYhgHdP36tTzGohWa/IYpfjEEhlYPTLkxSXERQOwCt2csrkwCP4cpbmWVktADQzN3XeCFYsXtI3YVYEJZHYMr09xGBH6OQ/Dkyjx4cH8or9DSfVpexIW5hCWKBcQucDPG4Mq8ceO3BH4OLGJKWYvO1llgaAlHaAkXZmgWa3+/iF17Vt7uGborUy5MAj/H0aozwVOeDHGOO1yY3hZzg28MsRuMcP4ThDzA3NxGag1YQclv+MKnyktorkzLi7gw5y/TxrgDxG4MqhOfM+QB5rgwwxe2sspJiK5MXJgTF1wTXw6xmxj4WJdTrMwQg9biwoxT7CSAobkycWGOVTr5cV7Ezg87DL6LEKcjMbcRLsw4BS8kV6aipSiCDy7MwUWRtydA7Lw1TbcbM1dmSD3g5MLc2DjJt7qIemIuujRDGmCuQeQMJO9W5oS2N2IXmsVq7je04LUMJI+zRbcoeCEMMFdrLpYA1jXFQ/KbELuIskBIrhhzYTKQPG7B0wBz392DNp0PLsyICsOSR0HsSqCEukovaygf2TWdj2r9i60A/o9P+MyV6fMMAufOnQ2yc1eo5dRc943YzUV+pOuqR6Z6ZvqczG3EdD7xiVtZhUVzFG5tbXqZJUP81u0lyABuCrELwEhdbvHbb7/N3UZ6iX1NquWvrOzLcGGmIXY2g7mPeTLEXsy+vte+3xdi57uFetyf7+HDNjZeYkbySHtglrXstG5l5dlMwuJb8v1d8Y1XyPeD2IVsvYp797m2am6jP37wAd/rEhK8N86fz44fX0vZUgEAAAhuSURBVKvIsfOsjiGI+jzkwrwqYhem3Wrv2r6J+dgp4PbtW9nq6vMIXUJCp5adhQ+Tm92XFML3bV9YxXAfiF0MVix5Br3I6mXmW9LYusuXLiF2iYmdBG99/YRXMyGo57KPrlXf3tlY7gexi8WShefwsaOKja0jPFgaHVOK3+98GnMnr4fv4/8KrzSLAwkgdgMB+ny4Pr77FBz6zJnXGFuXYIvORE+9b/fv35f54F5nbJ3PJdc494bYjcPVi7NaRxUfIkNYxxR1Q7fCj9/0Wngac/fznx+b9f2wvOjT98NZgSRyccQuYkNbRBUfvkvQMSU9YSurzPz5o49y9+GcQiNvh7wepLQIIHaR29uHF1uiS8cUxM7ETzNd3Lx5Y5Y3z6cK4CwAEr4oYhe58c1lM+d3EusMQMQUBE+CZx1VlDenTj659qd+9tSvh9glkAPUupszXuba2gtETEm4Y4q16BZ/V1cPZ3fvvj/52+dbp63JASR8QcQuAePbMIQ5vpNYq47hBrTqFsVOYy0PHtw/6czglhfnaFEmUMx4/4iInfcmcnOD6mo9xyDz1177NbOR06rb0wPXhiHcv/+Jmwze4ixzvQMtbo1dJiCA2E0A2YdLzNG6s2sSB5NW3WKrzv7XMISp4mVaXpzDu+HD+889ZBlil1AumLpmq0Hk6nlnhRu/iN5iHrB4mVN0npo67ydUrATzqIhdMKYafqNT1m7tWrTqELhFgSv+P0XrzvIirbrhZUjIZ0DsQrZej3tXDXeKnpmnTm3QquNbXWOr3lp3Y367o1XXo6CI8BDELkKj1j2SzeE1puvIer3RqqNVV2zJlS2rdaegA2OEtaNVV1capLUNsUvL3vnTatydpjcZo3DROdfWjjKujlZdY6vOhE89MzWT+RitO3kx1LIjQQCxSzAPWMikMQb13rv3cbaysi+frNMKM35p4TXlAY2705Q7LsfAmYeBb3XTF3LffPOf3J6y6Vdf/Su/gddf/02+7osv/jH9DWX0xpwFug8XVdgkZUSXBYG5SK9dvdq6Vt9UCLI9HaE8cuRwtrW16eT1sAqdvBik+QhcufJWPq3XO+/8IXv48Lv5bgSxm5X97BeXe0fhk1y5M9UpRedDoNIRKJe21jdeVcBcfE+W12IsV/3sL25AN6BW3WLrbs5bx405J/2Zry2XkQoEF7XfO3fey92XmsLFZQHIudISzjfOn8/DiA1xZ1qnlK+//vfMbxiXFwHEboJ8IMikegL2XWNIbdrOoWj2iFNa4uTa3uqssr5+Inv55Y36jFux1dyXly9fqtiD1VMS+PDDP2Uvvrie6XfuRMtubgt4cH25fFQx0De3rknH7N+/j96X9L50VtGRd0B5qs+cd+p96dI13/V9YP9dAnJhSuRUgTl9+tV8g/6fKyF2c5H37Lo2HKFM8OQWKuvIon0VuZ6QYLTmXLfwbM67MsFTvlN+LH5rrsvDnr1uUd+O9cRU70ulR48e5ZVpCZ7+tyRXtVrgZWWO7ePyF7FzSTPwc1lhYS5NZULVktXq05++71nG1PcQDQSW0Km25rqw43wIaFHwVDiq5baYHy2vWt61/Bn4q5jM7ZtXaYwxlkWIiF2RSOLLlvlUeBw7dnSnYLEC5uDBA9nvf/9/+XpFvkCUEKUx84AETy7Nzc0zuSvM8uHi7y9/+Yuliljir3Bwj69WuirV+ivzILl6IMTOFcmIzqMM97OfHdkjdFbAyHV56913ETq+002SBxQ/8xe/+J/K/KhCckjvzYhe3aAfRa07lTGqcBdd1C4ezInYWSHI7xN3HxzgQB4gD5AH+ucBeZZcJydi5/qmXJ1PmY3Uj4B14S57YalF92PKUcMILH4/XsyXY7q+ht0xR3chYC07CZ23LbsuDzTlvojdMNo2fm6xYLEOAcPOzNEQ6E5AnU/USWoxP47RAuh+ZxwxhIAqKzZkZMyKCy27IVZK4Fi14hRHU7UuerolYHDPH3ExP45ZMHqOIZrbsw5xKl/GaM0tgkLsFmnwPwQgAAEITEJAFRfG2TlCjRvTEUhOAwEIQCBwArTsAjcgtw8BCEAAAs0EELtmRuwBAQhAAAKBE0DsAjfg2Ldvce70S4LA1ARsPrTFHpj2v2ItzjXr9dQcuN5wAojdcIZRn0EzDKtw0S8JAnMRkLBZ5HzdgwIKK9Cw8iaCN5dVwrouYheWvSa928ePH2fPPXcoL1Q0JxUJAnMRuHLlrSWxs/uw/GnL/EKgigBiV0WG9flsBmrRqeasGrRcSiQIzEGgTuwWW3xz3BvXDIMAYheGnWa5SxUiDx9+l19bNWgVOCQIzEGgTOy0DjfmHNYI85qIXZh2G/2u1SFlscasFp4ET65NEgSmJmDCJnFb/ONb8tSWCPd6iF24thv1zlWIaFJWS9Yrk84ARoTfKQmUteyURyV8NiP2lPfDtcIjgNiFZ7PR79g6pizWoO1/CpbR8XOBEgJlYqfdrMVHJawEGquWCCB2SzhYEAG16MrcQ1ov0VO3bxIEpiRQJXbWukPsprRGmNdC7MK022h3LSHTt7myQeTahttoNPScuIaAvh8vfkPWrlb5YlhMDTg27RBA7HZQ8I96Xpq7Ur+LQw3k2lzcpv/prEKeGZtAXQQV5UG1+PA0jG2FOM6P2MVhR54CAhCAAARqCCB2NXDYBAEIQAACcRBA7OKwI08BAQhAAAI1BBC7GjhsggAEIACBOAggdnHYkaeAAAQgAIEaAohdDRw2QQACEIBAHAQQuzjsyFNAAAIQgEANAcSuBg6bIAABCEAgDgKIXRx25CkgAAEIQKCGAGJXA4dNEIAABCAQB4GoxS4OE/EUEIAABCAwlABiN5Qgx0MAAhCAgPcEEDvvTcQNQgACEIDAUAL/D2MozWzBpwZmAAAAAElFTkSuQmCC"></p>
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> touches the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis at 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>, as shown. The shaded region is enclosed by the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> and the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis, between the points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
</div>
<div class="specification">
<p>The right cone in the following diagram has a total surface area of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mi mathvariant="normal">π</mi></math>, equal to the shaded area in the previous diagram.</p>
<p>The cone has a base radius of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math>, height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>, and slant height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinates of <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">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the area of the shaded region is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mi mathvariant="normal">π</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</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>Hence, find the volume of the cone.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A calculator fits into a cuboid case with height 29 mm, width 98 mm and length 186 mm.</p>
</div>
<div class="question">
<p>Find the volume, in cm<sup>3</sup>, of this calculator case.</p>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a circle 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"><mi>r</mi></math>.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">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> lie on the circumference of the circle, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>B</mtext><mo>=</mo><mn>1</mn><mo> </mo><mtext>radian</mtext></math>.</p>
<p style="text-align: left;">The perimeter of the shaded region is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</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>r</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the exact area of the <strong>non-shaded</strong> region.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{lo}}{{\text{g}}_9}\left( {{\text{cos}}\,2x + 2} \right) = {\text{lo}}{{\text{g}}_3}\sqrt {{\text{cos}}\,2x + 2} ">
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mn>9</mn>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>cos</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mn>3</mn>
</msub>
</mrow>
<msqrt>
<mrow>
<mtext>cos</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</msqrt>
</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>Hence or otherwise solve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{lo}}{{\text{g}}_3}\left( {{\text{2}}\,{\text{sin}}\,x} \right) = {\text{lo}}{{\text{g}}_9}\left( {{\text{cos}}\,2x + 2} \right)">
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mn>3</mn>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>2</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mn>9</mn>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>cos</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 < x < \frac{\pi }{2}">
<mn>0</mn>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mfrac>
<mi>π</mi>
<mn>2</mn>
</mfrac>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{sin}}\,x = \frac{1}{3}">
<mrow>
<mtext>sin</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 < x < \frac{\pi }{2}">
<mn>0</mn>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mfrac>
<mi>π</mi>
<mn>2</mn>
</mfrac>
</math></span>, find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{cos}}\,4x">
<mrow>
<mtext>cos</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>4</mn>
<mi>x</mi>
</math></span>.</p>
</div>
<br><hr><br><div class="specification">
<p><strong>Note: In this question, distance is in metres and time is in seconds.</strong></p>
<p>Two particles <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{P_1}">
<mrow>
<msub>
<mi>P</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{P_2}">
<mrow>
<msub>
<mi>P</mi>
<mn>2</mn>
</msub>
</mrow>
</math></span> start moving from a point A at the same time, along different straight lines.</p>
<p>After <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> seconds, the position of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{P_1}">
<mrow>
<msub>
<mi>P</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> is given by <strong><em>r</em></strong> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 4 \\ { - 1} \\ 3 \end{array}} \right) + t\left( {\begin{array}{*{20}{c}} 1 \\ 2 \\ { - 1} \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>4</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>t</mi>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>Two seconds after leaving A, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{P_1}">
<mrow>
<msub>
<mi>P</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> is at point B.</p>
</div>
<div class="specification">
<p>Two seconds after leaving A, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{P_2}">
<mrow>
<msub>
<mi>P</mi>
<mn>2</mn>
</msub>
</mrow>
</math></span> is at point C, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{AC}}} = \left( {\begin{array}{*{20}{c}} 3 \\ 0 \\ 4 \end{array}} \right)">
<mover>
<mrow>
<mtext>AC</mtext>
</mrow>
<mo>→<!-- → --></mo>
</mover>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>4</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 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>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{AB}}} "> <mover> <mrow> <mtext>AB</mtext> </mrow> <mo>→</mo> </mover> </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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\overrightarrow {{\text{AB}}} } \right|"> <mrow> <mo>|</mo> <mrow> <mover> <mrow> <mtext>AB</mtext> </mrow> <mo>→</mo> </mover> </mrow> <mo>|</mo> </mrow> </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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\cos {\rm{B\hat AC}}"> <mi>cos</mi> <mo></mo> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mrow> <mover> <mi mathvariant="normal">A</mi> <mo stretchy="false">^</mo> </mover> </mrow> <mi mathvariant="normal">C</mi> </mrow> </mrow> </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>Hence or otherwise, find the distance between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{P_1}"> <mrow> <msub> <mi>P</mi> <mn>1</mn> </msub> </mrow> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{P_2}"> <mrow> <msub> <mi>P</mi> <mn>2</mn> </msub> </mrow> </math></span> two seconds after they leave A.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A ladder on a fire truck has its base at point B which is 4 metres above the ground. The ladder is extended and its other end rests on a vertical wall at point C, 16 metres above the ground. The horizontal distance between B and C is 9 metres.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the angle of elevation from B to C.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second truck arrives whose ladder, when fully extended, is 30 metres long. The base of this ladder is also 4 metres above the ground. For safety reasons, the maximum angle of elevation that the ladder can make is 70º.</p>
<p>Find the maximum height on the wall that can be reached by the ladder on the second truck.</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="\mathop {{\text{OA}}}\limits^ \to = \left( \begin{gathered} 2 \hfill \\ 1 \hfill \\ 3 \hfill \\ \end{gathered} \right)">
<mover>
<mrow>
<mrow>
<mtext>OA</mtext>
</mrow>
</mrow>
<mo stretchy="false">→<!-- → --></mo>
</mover>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mtable rowspacing="3pt" columnspacing="1em" displaystyle="true">
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{AB}}}\limits^ \to = \left( \begin{gathered} 1 \hfill \\ 3 \hfill \\ 1 \hfill \\ \end{gathered} \right)">
<mover>
<mrow>
<mrow>
<mtext>AB</mtext>
</mrow>
</mrow>
<mo stretchy="false">→<!-- → --></mo>
</mover>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mtable rowspacing="3pt" columnspacing="1em" displaystyle="true">
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
</math></span>, where O is the origin. <em>L</em><sub>1</sub> is the line that passes through A and B.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find a vector equation for <em>L</em><sub>1</sub>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The vector <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( \begin{gathered} 2 \hfill \\ p \hfill \\ 0 \hfill \\ \end{gathered} \right)">
<mrow>
<mo>(</mo>
<mtable rowspacing="3pt" columnspacing="1em" displaystyle="true">
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>p</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
</math></span> is perpendicular to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{AB}}}\limits^ \to ">
<mover>
<mrow>
<mrow>
<mtext>AB</mtext>
</mrow>
</mrow>
<mo stretchy="false">→</mo>
</mover>
</math></span>. Find the value of <em>p</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A park in the form of a triangle, ABC, is shown in the following diagram. AB is 79 km and BC is 62 km. Angle A<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {\text{B}}\limits^ \wedge ">
<mover>
<mrow>
<mtext>B</mtext>
</mrow>
<mo>∧<!-- ∧ --></mo>
</mover>
</math></span>C is 52°.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of side AC in km.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the area of the park.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The vectors <strong><em>a</em></strong> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 4 \\ 2 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>4</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span> and <strong><em>b</em></strong> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} {k + 3} \\ k \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>3</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>k</mi>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span> are perpendicular to each other.</p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <strong><em>c</em></strong> = <strong><em>a</em></strong> + 2<strong><em>b</em></strong>, find <strong><em>c</em></strong>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Two fixed points, A and B, are 40 m apart on horizontal ground. Two straight ropes, AP and BP, are attached to the same point, P, on the base of a hot air balloon which is vertically above the line AB. The length of BP is 30 m and angle BAP is 48°.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>Angle APB is acute.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram, draw and label with an <em>x</em> the angle of depression of B from P.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the size of angle APB.</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 the angle of depression of B from P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A line, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}">
<mrow>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span>, has equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \left( {\begin{array}{*{20}{c}} { - 3} \\ 9 \\ {10} \end{array}} \right) + s\left( {\begin{array}{*{20}{c}} 6 \\ 0 \\ 2 \end{array}} \right)">
<mi>r</mi>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>3</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>9</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>10</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>6</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>. Point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {15{\text{,}}\,\,9{\text{,}}\,\,c} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>15</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>9</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>c</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> lies on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}">
<mrow>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span>.</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="c"> <mi>c</mi> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second line, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}"> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> </math></span>, is parallel to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}"> <mrow> <msub> <mi>L</mi> <mn>1</mn> </msub> </mrow> </math></span> and passes through (1, 2, 3).</p>
<p>Write down a vector equation for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}"> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the functions <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msqrt><mn>3</mn></msqrt><mi>sin</mi><mo> </mo><mi>x</mi><mo>+</mo><mi>cos</mi><mo> </mo><mi>x</mi></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>2</mn><mi>x</mi></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>f</mi><mo>∘</mo><mi>g</mi><mo>)</mo><mo>(</mo><mi>x</mi><mo>)</mo></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Solve the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>f</mi><mo>∘</mo><mi>g</mi><mo>)</mo><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo> </mo><mi>cos</mi><mo> </mo><mn>2</mn><mi>x</mi></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mi>π</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>Consider the vectors <em><strong>a</strong></em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 3 \\ {2p} \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mi>p</mi> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span> and <em><strong>b</strong></em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} {p + 1} \\ 8 \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mi>p</mi> <mo>+</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>8</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span>.</p>
<p>Find the possible values of <em>p</em> for which <strong><em>a</em></strong> and <strong><em>b</em></strong> are parallel.</p>
</div>
<br><hr><br><div class="specification">
<p>Consider the graph of the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = 2\,{\text{sin}}\,x">
<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>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
</math></span>, 0 ≤ <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="2\pi ">
<mn>2</mn>
<mi>π<!-- π --></mi>
</math></span> . The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> intersects the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - 1">
<mi>y</mi>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mn>1</mn>
</math></span> exactly twice, at point A and point B. This is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question">
<p>Consider the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = 2\,{\text{sin}}\,px"> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>2</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>sin</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>p</mi> <mi>x</mi> </math></span>, 0 ≤ <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="2\pi "> <mn>2</mn> <mi>π</mi> </math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span> > 0.</p>
<p>Find the greatest value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span> such that the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g"> <mi>g</mi> </math></span> does not intersect the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - 1"> <mi>y</mi> <mo>=</mo> <mo>−</mo> <mn>1</mn> </math></span>.</p>
</div>
<br><hr><br><div class="specification">
<p>A buoy is floating in the sea and can be seen from the top of a vertical cliff. A boat is travelling from the base of the cliff directly towards the buoy.</p>
<p>The top of the cliff is 142 m above sea level. Currently the boat is 100 metres from the buoy and the angle of depression from the top of the cliff to the boat is 64°.</p>
<p><img 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"></p>
</div>
<div class="question">
<p>Draw and label the angle of depression on the diagram.</p>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABC</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AC</mtext><mo>=</mo><mn>15</mn><mo> </mo><mtext>cm</mtext><mo>,</mo><mo> </mo><mtext>BC</mtext><mo>=</mo><mn>10</mn><mo> </mo><mtext>cm</mtext></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>B</mtext><mo>^</mo></mover><mtext>C</mtext><mo>=</mo><mi>θ</mi></math>.</p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo> </mo><mtext>C</mtext><mover><mtext>A</mtext><mo>^</mo></mover><mtext>B</mtext><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>3</mn></mfrac></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>B</mtext><mo>^</mo></mover><mtext>C</mtext></math> is acute, find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo> </mo><mi>θ</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mo> </mo><mfenced><mrow><mn>2</mn><mo>×</mo><mtext>C</mtext><mover><mtext>A</mtext><mo>^</mo></mover><mtext>B</mtext></mrow></mfenced></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>The magnitudes of two vectors, <em><strong>u</strong></em> and <em><strong>v</strong></em>, are 4 and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt 3 "> <msqrt> <mn>3</mn> </msqrt> </math></span> respectively. The angle between <em><strong>u</strong></em> and <em><strong>v</strong></em> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\pi }{6}"> <mfrac> <mi>π</mi> <mn>6</mn> </mfrac> </math></span>.</p>
<p>Let <em><strong>w</strong></em> = <em><strong>u</strong></em> − <em><strong>v</strong></em>. Find the magnitude of <em><strong>w</strong></em>.</p>
</div>
<br><hr><br><div class="specification">
<p>Julio is making a wooden pencil case in the shape of a large pencil. The pencil case consists of a cylinder attached to a cone, as shown.</p>
<p>The cylinder has a radius of <em>r</em> cm and a height of 12 cm.</p>
<p>The cone has a base radius of <em>r</em> cm and a height of 10 cm.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the slant height of the cone <strong>in terms of <em>r</em></strong>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The total external surface area of the pencil case rounded to 3 significant figures is 570 cm<sup>2</sup>.</p>
<p>Using your graphic display calculator, calculate the value of <em>r</em>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = 4\,{\text{cos}}\left( {\frac{x}{2}} \right) + 1"> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>4</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mi>x</mi> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>1</mn> </math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant x \leqslant 6\pi "> <mn>0</mn> <mo>⩽</mo> <mi>x</mi> <mo>⩽</mo> <mn>6</mn> <mi>π</mi> </math></span>. 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\left( x \right) > 2\sqrt 2 + 1"> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>></mo> <mn>2</mn> <msqrt> <mn>2</mn> </msqrt> <mo>+</mo> <mn>1</mn> </math></span>.</p>
</div>
<br><hr><br><div class="question">
<p>The following diagram shows triangle PQR.</p>
<p><img src="images/Schermafbeelding_2017-08-11_om_09.36.55.png" alt="M17/5/MATME/SP1/ENG/TZ1/03"></p>
<p>Find PR.</p>
</div>
<br><hr><br>