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</div><h2>SL Paper 2</h2><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The following diagram shows a pole BT 1.6 m tall on the roof of a vertical building.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The angle of depression from T to a point A on the horizontal ground is \({35^ \circ }\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The angle of elevation of the top of the building from A is \({30^ \circ }\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/building.png" alt></span></p>
</div>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the height of the building.</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the following circle with centre O and radius <em>r</em> .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/Jamie.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The points P, R and Q are on the circumference, \({\rm{P}}\widehat {\rm{O}}{\rm{Q}} = 2\theta \) , for \(0 < \theta < \frac{\pi }{2}\) . </span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Use the cosine rule to show that \({\rm{PQ}} = 2r\sin \theta \) .</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><span style="font-family: times new roman,times; font-size: medium;">Let <em>l</em> be the length of the arc PRQ .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Given that \(1.3{\rm{PQ}} - l = 0\) , find the value of \(\theta \) .</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><span style="font-family: times new roman,times; font-size: medium;">Consider the function \(f(\theta ) = 2.6\sin \theta - 2\theta \) , for \(0 < \theta < \frac{\pi }{2}\) .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Sketch the graph of <em>f</em> .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> (ii) Write down the root of \(f(\theta ) = 0\) .</span></p>
<p> </p>
<div class="marks">[4]</div>
<div class="question_part_label">c(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Use the graph of <em>f</em> to find the values of \(\theta \) for which \(l < 1.3{\rm{PQ}}\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the triangle ABC, where AB =10 , BC = 7 and \({\rm{C}}\widehat {\rm{A}}{\rm{B}}\) = \({30^ \circ }\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the two possible values of \({\rm{A}}\widehat {\rm{C}}{\rm{B}}\) .</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><span style="font-family: times new roman,times; font-size: medium;">Hence, find \({\rm{A}}\widehat {\rm{B}}{\rm{C}}\) , given that it is acute.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = a\cos (b(x - c))\) . The diagram below shows part of the graph of <em>f</em> , </span><span style="font-family: times new roman,times; font-size: medium;">for \(0 \le x \le 10\) .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/N12P2Q5.jpg" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The graph has a local maximum at P(3, 5) , a local minimum at Q(7, − 5) , and crosses the <em>x</em>-axis at R.</span></p>
<p align="LEFT"> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Write down the value of</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) \(a\) ;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) \(c\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the value of <em>b</em> .</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><span style="font-family: times new roman,times; font-size: medium;">Find the <em>x</em>-coordinate of R.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The height, \(h\) metros, of a seat on a Ferris wheel after \(t\) minutes is given by</p>
<p class="p1">\[h(t) = - 15\cos 1.2t + 17,{\text{ for }}t \geqslant 0{\text{.}}\]</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the height of the seat when \(t = 0\).</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 class="p1">The seat first reaches a height of 20 m <span class="s1">after \(k\) minutes. Find \(k\).</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 class="p1">Calculate the time needed for the seat to complete a full rotation, giving your answer correct to one decimal place.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram below shows a circle centre O, with radius <em>r</em>. The length of arc ABC is </span><span style="font-family: times new roman,times; font-size: medium;">\(3\pi {\text{ cm}}\) and \({\rm{A}}\widehat {\rm{O}}{\rm{C}} = \frac{{2\pi }}{9}\). </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/circle.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the value of <em>r</em>.</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><span style="font-family: times new roman,times; font-size: medium;">Find the perimeter of sector OABC.</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><span style="font-family: times new roman,times; font-size: medium;">Find the area of sector OABC.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p>Triangle ABC has <em>a</em> = 8.1 cm, <em>b</em> = 12.3 cm and area 15 cm<sup>2</sup>. Find the largest possible perimeter of triangle ABC.</p>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows three towns A, B and C. Town B is 5 km from Town A, on a bearing of 070°. Town C is 8 km from Town B, on a bearing of 115°<span class="s1">.</span></p>
<p class="p1" style="text-align: center;"><span class="s1"><img src="images/Schermafbeelding_2017-02-01_om_15.15.32.png" alt="M16/5/MATME/SP2/ENG/TZ1/03"></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \({\rm{A\hat BC}}\).</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 class="p1">Find the distance from Town <span class="s1">A </span>to Town <span class="s1">C</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 class="p1">Use the sine rule to find \({\rm{A\hat CB}}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>At Grande Anse Beach the height of the water in metres is modelled by the function \(h(t) = p\cos (q \times t) + r\), where \(t\) is the number of hours after 21:00 hours on 10 December 2017. The following diagram shows the graph of \(h\) , for \(0 \leqslant t \leqslant 72\).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_10.10.26.png" alt="M17/5/MATME/SP2/ENG/TZ1/08"></p>
<p>The point \({\text{A}}(6.25,{\text{ }}0.6)\) represents the first low tide and \({\text{B}}(12.5,{\text{ }}1.5)\) represents the next high tide.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>How much time is there between the first low tide and the next high tide?</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the difference in height between low tide and high tide.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(p\);</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(q\);</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(r\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>There are two high tides on 12 December 2017. At what time does the second high tide occur?</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The diagram shows a circle of radius \(8\) metres. The points ABCD lie on the </span><span style="font-family: times new roman,times; font-size: medium;">circumference of the circle.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img style="display: block; margin-left: auto; margin-right: auto;" src="images/jack.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">BC = \(14\) m, CD = \(11.5\) m, AD = \(8\) m, \(A\hat DC = {104^ \circ }\) , and \(B\hat CD = {73^ \circ }\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find AC.</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Find \(A\hat CD\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Hence, find \(A\hat CB\) .</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><span style="font-family: times new roman,times; font-size: medium;">Find the area of triangle ADC.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(c) Find the area of triangle ADC.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(d) </span><span style="font-family: times new roman,times; font-size: medium;">Hence or otherwise, find the total area of the shaded regions.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">cd.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Hence or otherwise, find the total area of the shaded regions.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The following diagram shows the triangle ABC.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/sunny.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The angle at C is obtuse, \({\text{AC}} = 5{\text{ cm}}\), \({\text{BC}} =13.6{\text{ cm}}\) and the area is \(20{\text{ c}}{\text{m}}^2\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \({\rm{A}}\widehat {\rm{C}}{\rm{B}}\) .</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><span style="font-family: times new roman,times; font-size: medium;">Find AB.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The following diagram shows \(\Delta {\rm{PQR}}\) , where RQ = 9 cm, \({\rm{P\hat RQ}} = {70^ \circ }\) and \({\rm{P\hat QR}} = {45^ \circ }\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/M12P2TZ2Q1atri.png" alt></span></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \({\rm{R\hat PQ}}\) .</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><span style="font-family: times new roman,times; font-size: medium;">Find PR .</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><span style="font-family: times new roman,times; font-size: medium;">Find the area of \(\Delta {\rm{PQR}}\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The following diagram shows triangle ABC.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"> </p>
<p style="font: normal normal normal 12px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><img src="images/maths_1.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find AC.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find \({\rm{B\hat CA}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Two points P and Q have coordinates (3, 2, 5) and (7, 4, 9) respectively.</p>
</div>
<div class="specification">
<p>Let \({\mathop {{\text{PR}}}\limits^ \to }\) = 6<em><strong>i</strong></em> − <em><strong>j</strong></em> + 3<em><strong>k</strong></em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \(\mathop {{\text{PQ}}}\limits^ \to \).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \(\left| {\mathop {{\text{PQ}}}\limits^ \to } \right|\).</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 angle between PQ and PR.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of triangle PQR.</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>Hence or otherwise find the shortest distance from R to the line through P and Q.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The following diagram shows a circular play area for children.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/N12P2Q8.jpg" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The circle has centre O and a radius of 20 m, and the points A, B, C and D lie on </span><span style="font-family: times new roman,times; font-size: medium;">the circle. Angle AOB is 1.5 radians.</span></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the length of the chord [AB].</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><span style="font-family: times new roman,times; font-size: medium;">Find the area of triangle AOB.</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><span style="font-family: times new roman,times; font-size: medium;">Angle BOC is 2.4 radians.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the length of arc ADC.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Angle BOC is 2.4 radians.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the area of the shaded region.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Angle BOC is 2.4 radians.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The shaded region is to be painted red. Red paint is sold in cans which cost \(\$ 32\)</span><span style="font-family: times new roman,times; font-size: medium;"> each. One can covers \(140{\text{ }}{{\text{m}}^2}\). How much does it cost to buy the paint?</span></p>
<p> </p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The graph of \(y = p\cos qx + r\) , for \( - 5 \le x \le 14\) , is shown below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/weather.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">There is a minimum point at (0, −3) and a maximum point at (4, 7) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Find the value of</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) <em>p</em> ;</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) <em>q</em> ;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iii) <em>r</em>.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">a(i), (ii) and (iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The equation \(y = k\) has exactly <strong>two</strong> solutions. Write down the value of <em>k</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows the graph of \(f(x) = a\sin bx + c\), for \(0 \leqslant x \leqslant 12\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-03-03_om_16.53.31.png" alt="N16/5/MATME/SP2/ENG/TZ0/10"></p>
<p class="p1" style="text-align: center;">The graph of \(f\) has a minimum point at \((3,{\text{ }}5)\) and a maximum point at \((9,{\text{ }}17)\).</p>
</div>
<div class="specification">
<p class="p1">The graph of \(g\) is obtained from the graph of \(f\) by a translation of \(\left( {\begin{array}{*{20}{c}} k \\ 0 \end{array}} \right)\). The maximum point on the graph of \(g\) has coordinates \((11.5,{\text{ }}17)\).</p>
</div>
<div class="specification">
<p class="p1">The graph of \(g\) changes from concave-up to concave-down when \(x = w\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Find the value of \(c\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Show that \(b = \frac{\pi }{6}\).</p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>Find the value of \(a\).</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 class="p1">(i) <span class="Apple-converted-space"> </span>Write down the value of \(k\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find \(g(x)\).</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 class="p1">(i) <span class="Apple-converted-space"> </span>Find \(w\).</p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>Hence or otherwise, find the maximum positive rate of change of \(g\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows part of the graph of \(y = p\sin (qx) + r\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-14_om_09.06.35.png" alt></p>
<p class="p1">The point \({\text{A}}\left( {\frac{\pi }{6},{\text{ }}2} \right)\) is a maximum point and the point \({\text{B}}\left( {\frac{\pi }{6},{\text{ }}1} \right)\) is a minimum point.</p>
<p class="p1">Find the value of</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">\(p\);</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">\(r\);</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 class="p1">\(q\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>Note: In this question, distance is in millimetres.</strong></p>
<p>Let \(f(x) = x + a\sin \left( {x - \frac{\pi }{2}} \right) + a\), for \(x \geqslant 0\).</p>
</div>
<div class="specification">
<p>The graph of \(f\) passes through the origin. Let \({{\text{P}}_k}\) be any point on the graph of \(f\) with \(x\)-coordinate \(2k\pi \), where \(k \in \mathbb{N}\). A straight line \(L\) passes through all the points \({{\text{P}}_k}\).</p>
</div>
<div class="specification">
<p>Diagram 1 shows a saw. The length of the toothed edge is the distance AB.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_15.10.11.png" alt="N17/5/MATME/SP2/ENG/TZ0/10.d_01"></p>
<p>The toothed edge of the saw can be modelled using the graph of \(f\) and the line \(L\). Diagram 2 represents this model.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_15.11.17.png" alt="N17/5/MATME/SP2/ENG/TZ0/10.d_02"></p>
<p>The shaded part on the graph is called a tooth. A tooth is represented by the region enclosed by the graph of \(f\) and the line \(L\), between \({{\text{P}}_k}\) and \({{\text{P}}_{k + 1}}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \(f(2\pi ) = 2\pi \).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of \({{\text{P}}_0}\) and of \({{\text{P}}_1}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of \(L\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the distance between the \(x\)-coordinates of \({{\text{P}}_k}\) and \({{\text{P}}_{k + 1}}\) is \(2\pi \).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A saw has a toothed edge which is 300 mm long. Find the number of complete teeth on this saw.</p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = 3\sin x + 4\cos x\) , for \( - 2\pi \le x \le 2\pi \) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Sketch the graph of <em>f</em> .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Write down</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) the amplitude;</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) the period;</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(iii) the <em>x</em>-intercept that lies between \( - \frac{\pi }{2}\) </span><span style="font-family: times new roman,times; font-size: medium;">and 0.</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><span style="font-family: times new roman,times; font-size: medium;">Hence write \(f(x)\) in the form \(p\sin (qx + r)\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down one value of <em>x</em> such that \(f'(x) = 0\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Write down the two values of <em>k</em> for which the equation \(f(x) = k\) has exactly </span><span style="font-family: times new roman,times; font-size: medium;">two solutions.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let \(g(x) = \ln (x + 1)\) , for \(0 \le x \le \pi \) . There is a value of <em>x</em>, between \(0\) and \(1\), </span><span style="font-family: times new roman,times; font-size: medium;">for which the gradient of <em>f</em> is equal to the gradient of <em>g</em>. Find this value of <em>x</em>.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = 5\cos \frac{\pi }{4}x\) and \(g(x) = - 0.5{x^2} + 5x - 8\) for \(0 \le x \le 9\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">On the same diagram, sketch the graphs of <em>f</em> and <em>g</em> .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Consider the graph of \(f\) . Write down</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) the <em>x</em>-intercept that lies between \(x = 0\) and \(x = 3\) ;</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) the period;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iii) the amplitude.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Consider the graph of <em>g</em> . Write down</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) the two <em>x</em>-intercepts;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) the equation of the axis of symmetry.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Let <em>R</em> be the region enclosed by the graphs of <em>f</em> and <em>g</em> . Find the area of <em>R</em>.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A ship is sailing north from a point A towards point D. Point C is 175 km north of A. Point D is 60 km north of C. There is an island at E. The bearing of E from A is 055°. The bearing of E from C is 134°. This is shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_06.15.07.png" alt="M17/5/MATME/SP2/ENG/TZ2/09"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the bearing of A from E.</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>Finds CE.</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 DE.</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>When the ship reaches D, it changes direction and travels directly to the island at 50 km per hour. At the same time as the ship changes direction, a boat starts travelling to the island from a point B. This point B lies on (AC), between A and C, and is the closest point to the island. The ship and the boat arrive at the island at the same time. Find the speed of the boat.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows the quadrilateral \(ABCD\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-25_om_08.02.56.png" alt></p>
<p class="p1">\[{\text{AD}} = 6{\text{ cm}},{\text{ AB}} = 15{\text{ cm}},{\rm{ A\hat BC}} = 44^\circ ,{\rm{ A\hat CB}} = 83^\circ {\rm{ and D\hat AC}} = \theta \]</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \(AC\).</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 class="p1">Find the area of triangle \(ABC\).</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 class="p1">The area of triangle \(ACD\) is half the area of triangle \(ABC\)<span class="s1">.</span></p>
<p class="p2">Find the possible values of \(\theta \).</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 class="p2">Given that \(\theta \) <span class="s2">is obtuse, find \(CD\)</span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The following diagram shows a triangle ABC.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img style="display: block; margin-left: auto; margin-right: auto;" src="images/ross.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The area of triangle ABC is \(80\) cm<sup>2</sup> , AB \( = 18\) cm , AC \( = x\) cm and \({\rm{B}}\hat {\rm{A}}{\rm{C}} = {50^ \circ }\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \(x\) .</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><span style="font-family: times new roman,times; font-size: medium;">Find BC.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The following diagram represents a large Ferris wheel at an amusement park.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The points P, Q and R represent different positions of a seat on the wheel.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/charmed.png" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The wheel has a radius of 50 metres and rotates clockwise at a rate of one revolution </span><span style="font-family: times new roman,times; font-size: medium;">every 30 minutes.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">A seat starts at the lowest point P, when its height is one metre above the ground.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the height of a seat above the ground after 15 minutes.</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><span style="font-family: times new roman,times; font-size: medium;">After six minutes, the seat is at point Q. Find its height above the ground at Q.</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The height of the seat above ground after <em>t</em> minutes can be modelled by the function </span><span style="font-family: times new roman,times; font-size: medium;">\(h(t) = 50\sin (b(t - c)) + 51\).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the value of <em>b</em> and of <em>c</em> .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The height of the seat above ground after <em>t</em> minutes can be modelled by the function </span><span style="font-family: times new roman,times; font-size: medium;">\(h(t) = 50\sin (b(t - c)) + 51\).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Hence find the value of <em>t</em> the first time the seat is \(96{\text{ m}}\) above the ground.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The depth of water in a port is modelled by the function \(d(t) = p\cos qt + 7.5\), for \(0 \leqslant t \leqslant 12\), where \(t\) is the number of hours after high tide.</p>
<p>At high tide, the depth is 9.7 metres.</p>
<p>At low tide, which is 7 hours later, the depth is 5.3 metres.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(p\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(q\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the model to find the depth of the water 10 hours after high tide.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The following diagram shows triangle ABC .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/twins.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">AB = 7 cm, BC = 9 cm and \({\rm{A}}\widehat {\rm{B}}{\rm{C}} = {120^ \circ }\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find AC .</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><span style="font-family: times new roman,times; font-size: medium;">Find \({\rm{B}}\widehat {\rm{A}}{\rm{C}}\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows a quadrilateral <span class="s1">ABCD</span>.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-02-02_om_17.33.03.png" alt="M16/5/MATME/SP2/ENG/TZ2/02"></p>
<p class="p1" style="text-align: center;">\[{\text{AD}} = {\text{7}}\;{\text{cm,}}\;{\text{BC}} = {\text{8}}\;{\text{cm,}}\;{\text{CD}} = {\text{12}}\;{\text{cm,}}\;{\rm{D\hat AB}} = {\text{1.75}}\;{\text{radians,}}\;{\rm{A\hat BD}} = {\text{0.82}}\;{\text{radians.}}\]</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find <span class="s1">BD</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 class="p1">Find \({\rm{D\hat BC}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The following diagram shows a circle with centre \(\rm{O}\) and radius \(5 \rm\,{cm}\).</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; min-height: 25px; text-align: center; margin: 0px;"><img src="images/maths_1_1.png" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The points \(\rm{A}\), \(rm{B}\) and \(rm{C}\) lie on the circumference of the circle, and \({\rm{A\hat OC}} = 0.7\) radians.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the length of the arc \({\text{ABC}}\).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the perimeter of the shaded sector.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the area of the shaded sector.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram below shows a quadrilateral ABCD with obtuse angles \({\rm{A}}\widehat {\rm{B}}{\rm{C}}\) and \({\rm{A}}\widehat {\rm{D}}{\rm{C}}\).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/footie.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">AB = 5 cm, BC = 4 cm, CD = 4 cm, AD = 4 cm , \({\rm{B}}\widehat {\rm{A}}{\rm{C}} = {30^ \circ }\) , \({\rm{A}}\widehat {\rm{B}}{\rm{C}} = {x^ \circ }\) , \({\rm{A}}\widehat {\rm{D}}{\rm{C}} = {y^ \circ }\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Use the cosine rule to show that \({\rm{AC}} = \sqrt {41 - 40\cos x} \) .</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><span style="font-family: times new roman,times; font-size: medium;">Use the sine rule in triangle ABC to find another expression for AC.</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Hence, find <em>x</em>, giving your answer to two decimal places.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Find AC .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Find <em>y</em>.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Hence, or otherwise, find the area of triangle ACD.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">d(i) and (ii).</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram below shows a plan for a window in the shape of a trapezium.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/tpc.png" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Three sides of the window are \(2{\text{ m}}\) long. The angle between the sloping sides of the </span><span style="font-family: times new roman,times; font-size: medium;">window and the base is \(\theta \) , where \(0 < \theta < \frac{\pi }{2}\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that the area of the window is given by \(y = 4\sin \theta + 2\sin 2\theta \) .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Zoe wants a window to have an area of \(5{\text{ }}{{\text{m}}^2}\). Find the two possible values of \(\theta \) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">John wants two windows which have the same area <em>A</em> but different values of \(\theta \) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find all possible values for <em>A</em> .</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The following diagram shows a triangle ABC.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({\rm{BC}} = 6\) , \({\rm{C}}\widehat {\rm{A}}{\rm{B}} = 0.7\) radians , \({\rm{AB}} = 4p\) , \({\rm{AC}} = 5p\) , where \(p > 0\) .</span></p>
<p> </p>
</div>
<div class="specification">
<p style="text-align: justify;" align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Consider the circle with centre B that passes through the point C. The circle cuts the </span><span style="font-family: times new roman,times; font-size: medium;">line CA at D, and \({\rm{A}}\widehat {\rm{D}}{\rm{B}}\) is obtuse. Part of the circle is shown in the following diagram.</span></p>
<p style="text-align: justify;" align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><img style="display: block; margin-left: auto; margin-right: auto;" src="images/minion.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Show that \({p^2}(41 - 40\cos 0.7) = 36\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Find <em>p</em> .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the length of BD.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \({\rm{A}}\widehat {\rm{D}}{\rm{B}}\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Show that \({\rm{C}}\widehat {\rm{B}}{\rm{D}} = 1.29\) radians, correct to 2 decimal places.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Hence, find the area of the shaded region.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">d(i) and (ii).</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the following circle with centre O and radius 6.8 cm.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/gaston.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The length of the arc PQR is 8.5 cm.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the value of \(\theta \) .</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><span style="font-family: times new roman,times; font-size: medium;">Find the area of the shaded region.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram shows a parallelogram ABCD.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/tired.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The coordinates of A, B and D are A(1, 2, 3) , B(6, 4,4 ) and D(2, 5, 5) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Show that \(\overrightarrow {{\rm{AB}}} = \left( {\begin{array}{*{20}{c}}<br>5\\<br>2\\<br>1<br>\end{array}} \right)\) .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) Find \(\overrightarrow {{\rm{AD}}} \) .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(iii) <strong>Hence</strong> show that \(\overrightarrow {{\rm{AC}}} = \left( {\begin{array}{*{20}{c}}<br>6\\<br>5\\<br>3<br>\end{array}} \right)\) .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a(i), (ii) and (iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the coordinates of point C.</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Find \(\overrightarrow {{\rm{AB}}} \bullet \overrightarrow {{\rm{AD}}} \).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) <strong>Hence</strong> find angle <em>A</em>.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">c(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Hence, or otherwise, find the area of the parallelogram.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram below shows triangle PQR. The length of [PQ] is 7 cm , the length of [PR] is 10 cm , and \({\rm{P}}\widehat {\rm{Q}}{\rm{R}}\) is \(75^\circ \) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/park.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \({\rm{P}}\widehat {\rm{R}}{\rm{Q}}\) .</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><span style="font-family: times new roman,times; font-size: medium;">Find the area of triangle PQR.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">A ship leaves port A on a bearing of \(030^\circ \) . It sails a distance of \(25{\text{ km}}\) to point B. At B, the ship changes direction to a bearing of \(100^\circ \) . It sails a distance of \(40{\text{ km}}\) to </span><span style="font-family: times new roman,times; font-size: medium;">reach point C. This information is shown in the diagram below.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/barking.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">A second ship leaves port A and sails directly to C.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the distance the second ship will travel.</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><span style="font-family: times new roman,times; font-size: medium;">Find the bearing of the course taken by the second ship.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows a circle, centre <span class="s1">O </span>and radius \(r\) <span class="s1">mm</span>. The circle is divided into five equal sectors.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-03-03_om_15.31.24.png" alt="N16/5/MATME/SP2/ENG/TZ0/03"></p>
<p class="p1">One sector is <span class="s1">OAB</span>, and \({\rm{A\hat OB}} = \theta \).</p>
</div>
<div class="specification">
<p class="p1">The area of sector <span class="s1">AOB </span>is \(20\pi {\text{ m}}{{\text{m}}^2}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Write down the </span><strong>exact </strong>value of \(\theta \) in radians.</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 class="p1">Find the value of \(r\).</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 AB.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows triangle \(ABC\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-14_om_10.08.48.png" alt></p>
<p class="p1">\[{\text{BC}} = 10{\text{ cm}},{\rm{ A\hat BC}} = 80^\circ \;{\text{and}}\;{\rm{B\hat AC}} = 35^\circ .\]</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \(AC\).</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 class="p1">Find the area of triangle \(ABC\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(f(x) = p\cos \left( {q(x + r)} \right) + 10\), for \(0 \leqslant x \leqslant 20\). The following diagram shows the graph of \(f\).</span></p>
<p style="margin: 0px; font-style: normal; font-variant: normal; font-weight: normal; font-size: 21px; line-height: normal; font-family: 'Times New Roman'; text-align: center;"><span style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; background-color: #f7f7f7;"><img src="images/maths_6.png" alt> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The graph has a maximum at \((4, 18)\) and a minimum at \((16, 2)\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Write down the value of \(r\).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find \(p\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find \(q\).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Solve \(f(x) = 7\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The following diagram shows a circle with centre O and radius 4 cm.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/yes.png" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The points A, B and C lie on the circle. The point D is outside the circle, on (OC).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Angle ADC = 0.3 radians and angle AOC = 0.8 radians.</span></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find AD.</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><span style="font-family: times new roman,times; font-size: medium;">Find OD.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the area of sector OABC.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the area of region ABCD.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">A circle centre O and radius \(r\) is shown below. The chord [AB] divides the area of the </span><span style="font-family: times new roman,times; font-size: medium;">circle into two parts. Angle AOB is \(\theta \) .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/crop.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find an expression for the area of the shaded region.</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The chord [AB] divides the area of the circle in the ratio 1:7. Find the </span><span style="font-family: times new roman,times; font-size: medium;">value of \(\theta \) .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The population of deer in an enclosed game reserve is modelled by the function \(P(t) = 210\sin (0.5t - 2.6) + 990\), where \(t\) is in months, and \(t = 1\) corresponds to 1 January 2014.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the number of deer in the reserve on 1 May 2014.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the rate of change of the deer population on 1 May 2014.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Interpret the answer to part (i) with reference to the deer population size on 1 May 2014.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b(ii).</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The following graph shows the depth of water, <em>y</em> metres , at a point P, during one day. The time <em>t</em> is given in hours, from midnight to noon. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/ffs.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Use the graph to write down an estimate of the value of <em>t</em> when </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(i) the depth of water is minimum; </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) the depth of water is maximum; </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> (iii) the depth of the water is increasing most rapidly.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a(i), (ii) and (iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The depth of water can be modelled by the function \(y = \cos A(B(t - 1)) + C\) . </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(i) Show that \(A = 8\) . </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Write down the value of <em>C</em>. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> (iii) Find the value of <em>B</em>.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">b(i), (ii) and (iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A sailor knows that he cannot sail past P when the depth of the water is less than 12 m . Calculate the values of <em>t</em> between which he cannot sail past P.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The diagram below shows a triangle ABD with AB =13 cm and AD = 6.5 cm.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Let C be a point on the line BD such that BC = AC = 7 cm.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/blaine.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the size of angle ACB.</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><span style="font-family: times new roman,times; font-size: medium;">Find the size of angle CAD.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a triangle ABC.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_10.20.56.png" alt="N17/5/MATME/SP2/ENG/TZ0/01"></p>
<p style="text-align: center;">\({\text{AB}} = 5{\rm{ cm, C\hat AB}} = \) 50° and \({\rm{A\hat CB}} = \) 112°</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find 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 triangle ABC.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram below shows a circle with centre O and radius 8 cm.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/lone.png" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The points A, B, C, D, E and F are on the circle, and [AF] is a diameter. The length </span><span style="font-family: times new roman,times; font-size: medium;">of arc ABC is 6 cm.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the size of angle AOC .</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><span style="font-family: times new roman,times; font-size: medium;">Hence find the area of the shaded region.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The area of sector OCDE is \(45{\text{ c}}{{\text{m}}^2}\).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the size of angle COE .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find EF .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = \frac{{3x}}{2} + 1\) , \(g(x) = 4\cos \left( {\frac{x}{3}} \right) - 1\) . Let \(h(x) = (g \circ f)(x)\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find an expression for \(h(x)\) .</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><span style="font-family: times new roman,times; font-size: medium;">Write down the period of \(h\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the range of \(h\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The circle shown has centre O and radius 3.9 cm.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/1234.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Points A and B lie on the circle and angle AOB is 1.8 radians.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find AB.</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><span style="font-family: times new roman,times; font-size: medium;">Find the area of the shaded region.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The following diagram shows a circle with centre O and radius \(r\) cm.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img style="display: block; margin-left: auto; margin-right: auto;" src="images/scooby.png" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Points A and B are on the circumference of the circle and \({\rm{A}}\hat {\rm{O}}{\rm{B}} = 1.4\) radians .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The point C is on [OA] such that \({\rm{B}}\hat {\rm{C}}{\rm{O}} = \frac{\pi }{2}\) radians</span><span style="font-family: times new roman,times; font-size: medium;"> .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that \({\rm{OC}} = r\cos 1.4\) .</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><span style="font-family: times new roman,times; font-size: medium;">The area of the shaded region is \(25\) cm<sup>2</sup> . Find the value of \(r\) .</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows a circle with centre \(O\) and radius \(3\) cm.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-22_om_15.51.50.png" alt></p>
<p class="p1">Points A, B, and C lie on the circle, and \({\rm{A\hat OC}} = 1.3{\text{ radians}}\)<span class="s1">.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the length of arc \(ABC\)<span class="s1">.</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 class="p1">Find the area of the shaded region.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a circle with centre O and radius 40 cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_17.31.00.png" alt="M17/5/MATME/SP2/ENG/TZ2/01"></p>
<p>The points A, B and C are on the circumference of the circle and \({\rm{A\hat OC}} = 1.9{\text{ radians}}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of arc ABC.</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 perimeter of sector OABC.</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 area of sector OABC.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The following diagram shows a waterwheel with a bucket. The wheel rotates at a </span><span style="font-family: times new roman,times; font-size: medium;">constant rate in an anticlockwise (counter-clockwise) direction.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/bucket.png" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The diameter of the wheel is 8 metres. The centre of the wheel, A, is 2 metres </span><span style="font-family: times new roman,times; font-size: medium;">above the water level. After <em>t</em> seconds, the height of the bucket above the water level </span><span style="font-family: times new roman,times; font-size: medium;">is given by \(h = a\sin bt + 2\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that \(a = 4\) .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The wheel turns at a rate of one rotation every 30 seconds.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Show that \(b = \frac{\pi }{{15}}\)</span><span style="font-family: times new roman,times; font-size: medium;"> .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">In the first rotation, there are two values of <em>t</em> when the bucket is <strong>descending</strong> at a rate </span><span style="font-family: times new roman,times; font-size: medium;">of \(0.5{\text{ m}}{{\text{s}}^{ - 1}}\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find these values of <em>t</em> .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">In the first rotation, there are two values of <em>t</em> when the bucket is <strong>descending</strong> at a rate </span><span style="font-family: times new roman,times; font-size: medium;">of \(0.5{\text{ m}}{{\text{s}}^{ - 1}}\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Determine whether the bucket is underwater at the second value of <em>t</em> .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">In triangle \(\rm{ABC}\), \(\rm{AB} = 6\,\rm{cm}\) and \(\rm{AC} = 8\,\rm{cm}\). The area of the triangle is \(16\,\rm{cm}^2\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the two possible values for \(\hat A\).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Given that \(\hat A\) is obtuse, find \({\text{BC}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(f(x) = \cos \left( {\frac{\pi }{4}x} \right) + \sin \left( {\frac{\pi }{4}x} \right),{\text{ for }} - 4 \leqslant x \leqslant 4.\)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of \(f\).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the values of \(x\) where the function is decreasing.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The function \(f\) can also be written in the form \(f(x) = a\sin \left( {\frac{\pi }{4}(x + c)} \right)\), where \(a \in \mathbb{R}\), and \(0 \leqslant c \leqslant 2\). Find the value of \(a\);</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The function \(f\) can also be written in the form \(f(x) = a\sin \left( {\frac{\pi }{4}(x + c)} \right)\), where \(a \in \mathbb{R}\), and \(0 \leqslant c \leqslant 2\). Find the value of \(c\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c(ii).</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows a circle with centre \(O\) and radius \(8\) cm.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-14_om_08.25.41.png" alt></p>
<p class="p1">The points \(A\), \(B\) and \(C\) are on the circumference of the circle, and \({\rm{A\hat OB}}\) radians.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the length of arc \(ACB\).</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 class="p1">Find \(AB\).</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 class="p1">Hence, find the perimeter of the shaded segment \(ABC\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">There is a vertical tower TA of height 36 m at the base A of a hill. A straight </span><span style="font-family: times new roman,times; font-size: medium;">path goes up the hill from A to a point U. This information is represented by the </span><span style="font-family: times new roman,times; font-size: medium;">following diagram.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/squeak.png" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The path makes a \({4^ \circ }\) angle with the horizontal.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The point U on the path is \(25{\text{ m}}\) away from the base of the tower.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The top of the tower is fixed to U by a wire of length \(x{\text{ m}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Complete the diagram, showing clearly all the information above.</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><span style="font-family: times new roman,times; font-size: medium;">Find <em>x</em> .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows a square \(ABCD\), and a sector \(OAB\) of a circle centre \(O\), radius \(r\). Part of the square is shaded and labelled \(R\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-14_om_15.28.33.png" alt></p>
<p>\[{\rm{A\hat OB}} = \theta {\text{, where }}0.5 \ \le \ \theta < \pi .\]</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that the area of the square \(ABCD\) is \(2{r^2}(1 - \cos \theta )\).</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>When \(\theta = \alpha \), the area of the square \(ABCD\) is equal to the area of the sector \(OAB\).</p>
<p>(i) Write down the area of the sector when \(\theta = \alpha \).</p>
<p>(ii) Hence find \(\alpha \).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>When \(\theta = \beta \), the area of \(R\) is more than twice the area of the sector.</p>
<p>Find all possible values of \(\beta \).</p>
<div class="marks">[8]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Consider a circle with centre \(\rm{O}\) and radius \(7\) cm. Triangle \(\rm{ABC}\) is drawn such that its vertices are on the circumference of the circle.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><img src="images/maths_8.png" alt></p>
<p style="font-stretch: normal; margin: 0px; text-align: center;"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'Times New Roman';"><span style="line-height: normal;">\(\rm{AB}=12.2\) cm, \(\rm{BC}=10.4\) cm and \(\rm{A}\hat{\rm{C}}\rm{B}=1.058\) radians.</span></span></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find \({\rm{B\hat AC}}\).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find \({\text{AC}}\).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Hence or otherwise, find the length of arc \({\text{ABC}}\).</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p>The following diagram shows the chord [AB] in a circle of radius 8 cm, where \({\text{AB}} = 12{\text{ cm}}\).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_13.20.17.png" alt="M17/5/MATME/SP2/ENG/TZ1/05"></p>
<p>Find the area of the shaded segment.</p>
</div>
<br><hr><br><div class="specification">
<p>At an amusement park, a Ferris wheel with diameter 111 metres rotates at a constant speed. The bottom of the wheel is <em>k</em> metres above the ground. A seat starts at the bottom of the wheel.</p>
<p style="text-align: center;"><img 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"></p>
<p>The wheel completes one revolution in 16 minutes.</p>
</div>
<div class="specification">
<p>After <em>t</em> minutes, the height of the seat above ground is given by \(h\left( t \right) = 61.5 + a\,{\text{cos}}\left( {\frac{\pi }{8}t} \right)\), for 0 ≤ <em>t</em> ≤ 32.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>After 8 minutes, the seat is 117 m above the ground. Find <em>k</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>a</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find when the seat is 30 m above the ground for the third time.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows quadrilateral ABCD.</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;">\({\text{AB}} = 11\,{\text{cm,}}\,\,{\text{BC}} = 6\,{\text{cm,}}\,\,{\text{B}}\mathop {\text{A}}\limits^ \wedge {\text{D = 100}}^\circ {\text{, and C}}\mathop {\text{B}}\limits^ \wedge {\text{D = 82}}^\circ \)</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find DB.</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 DC.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A Ferris wheel with diameter \(122\) metres rotates clockwise at a constant speed. </span><span style="font-family: times new roman,times; font-size: medium;">The wheel completes \(2.4\) rotations every hour. The bottom of the wheel is \(13\) metres </span><span style="font-family: times new roman,times; font-size: medium;">above the ground.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img style="display: block; margin-left: auto; margin-right: auto;" src="images/open.png" alt></span></p>
<p> <span style="font-family: times new roman,times; font-size: medium;">A seat starts at the bottom of the wheel.</span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">After <em><strong>t</strong> </em>minutes, the height \(h\) metres above the ground of the seat is given by\[h = 74 + a\cos bt {\rm{ .}}\]<br></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the maximum height above the ground of the seat.</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 style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">(i) Show that the period of \(h\) is \(25\) minutes.</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">(ii) Write down the <strong>exact</strong> value of \(b\) .</span></p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(b) (i) Show that the period of \(h\) is \(25\) minutes.</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (ii) Write down the <strong>exact</strong> value of \(b\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(c) </span><span style="font-family: times new roman,times; font-size: medium;">Find the value of \(a\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(d) </span><span style="font-family: times new roman,times; font-size: medium;">Sketch the graph of \(h\) , for \(0 \le t \le 50\) .</span></p>
<div class="marks">[9]</div>
<div class="question_part_label">bcd.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the value of \(a\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Sketch the graph of \(h\) , for \(0 \le t \le 50\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">In one rotation of the wheel, find the probability that a randomly selected seat is </span><span style="font-family: times new roman,times; font-size: medium;">at least \(105\) metres above the ground.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows a circle, centre O, with radius 4 cm. Points A and B lie on the circumference of the circle and AÔB = <em>θ</em> , where 0 ≤ <em>θ</em> ≤ \(\pi \).</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the shaded region, in terms of <em>θ</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The area of the shaded region is 12 cm<sup>2</sup>. Find the value of<em> θ</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let \(f\left( x \right) = 12\,\,{\text{cos}}\,x - 5\,\,{\text{sin}}\,x,\,\, - \pi \leqslant x \leqslant 2\pi \), be a periodic function with \(f\left( x \right) = f\left( {x + 2\pi } \right)\)</p>
<p>The following diagram shows the graph of \(f\).</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">There is a maximum point at A. The minimum value of \(f\) is −13 .</p>
</div>
<div class="specification">
<p>A ball on a spring is attached to a fixed point O. The ball is then pulled down and released, so that it moves back and forth vertically.</p>
<p style="text-align: center;"><img 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"></p>
<p>The distance, <em>d</em> centimetres, of the centre of the ball from O at time <em>t</em> seconds, is given by</p>
<p style="padding-left: 90px;">\(d\left( t \right) = f\left( t \right) + 17,\,\,0 \leqslant t \leqslant 5.\)</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the graph of \(f\), write down the amplitude.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the graph of \(f\), write down the period.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
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<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, write \(f\left( x \right)\) in the form \(p\,\,{\text{cos}}\,\left( {x + r} \right)\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
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<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the maximum speed of the ball.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
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<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the first time when the ball’s speed is changing at a rate of 2 cm s<sup>−2</sup>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">e.</div>
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