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<h2>SL Paper 2</h2><div class="specification">
<p>A farmer owns a field in the shape of a triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABC</mtext></math> such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext><mo>=</mo><mn>650</mn><mo> </mo><mtext>m</mtext><mo>,</mo><mo> </mo><mtext>AC</mtext><mo>=</mo><mn>1005</mn><mo> </mo><mtext>m</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BC</mtext><mo>=</mo><mn>1225</mn><mo> </mo><mtext>m</mtext></math>.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The local town is planning to build a highway that will intersect the borders of the field at points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DC</mtext><mo>=</mo><mn>210</mn><mo> </mo><mtext>m</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CÊD</mtext><mo>=</mo><mn>100</mn><mo>°</mo></math>, as shown in the diagram below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The town wishes to build a carpark here. They ask the farmer to exchange the part of the field represented by triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DCE</mtext></math>. In return the farmer will get a triangle of equal area <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ADF</mtext></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math> lies on the same line as <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext></math>, as shown in the diagram above.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the size of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AĈB</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DE</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DCE</mtext></math>.</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>Estimate <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DF</mtext></math>. You may assume the highway has a width of zero.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Using geometry software, Pedro draws a quadrilateral <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABCD</mtext></math>. <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext><mo>=</mo><mn>8</mn><mo> </mo><mtext>cm</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CD</mtext><mo>=</mo><mn>9</mn><mo> </mo><mtext>cm</mtext></math>. Angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BAD</mtext><mo>=</mo><mn>51</mn><mo>.</mo><mn>5</mn><mo>°</mo></math> and angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ADB</mtext><mo>=</mo><mn>52</mn><mo>.</mo><mn>5</mn><mo>°</mo></math>. This information is shown in the diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CE</mtext><mo>=</mo><mn>7</mn><mo> </mo><mtext>cm</mtext></math>, where point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext></math> is the midpoint of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BD</mtext></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BD</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>EDC</mtext><mo>=</mo><mn>48</mn><mo>.</mo><mn>0</mn><mo>°</mo></math>, correct to three significant figures.</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>Calculate the area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BDC</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Pedro draws a circle, with centre at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext></math>, passing through point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>. Part of the circle is shown in the diagram.</p>
<p><img style="display: block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>Show that point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> lies outside this circle. Justify your reasoning.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The living accommodation on a university campus is in the shape of a rectangle with sides of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn><mo> </mo><mtext>m</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><mo> </mo><mtext>m</mtext></math>.</p>
<p>There are three offices for the management of the accommodation set at the points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>. These offices are responsible for all the students in the areas closest to the office. These areas are shown on the Voronoi diagram below. On this coordinate system the positions of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> are <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>100</mn><mo>,</mo><mo> </mo><mn>160</mn><mo>)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>100</mn><mo>,</mo><mo> </mo><mn>40</mn><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>250</mn><mo>,</mo><mo> </mo><mn>100</mn><mo>)</mo></math> respectively.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The equation of the perpendicular bisector of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="[" close="]"><mtext>AC</mtext></mfenced></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>615</mn></math>.</p>
</div>
<div class="specification">
<p>The manager of office <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> believes that he has more than one third of the area of the campus to manage.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of campus managed by office <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise find the areas managed by offices <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State a further assumption that must be made in order to use area covered as a measure of whether or not the manager of office <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> is responsible for more students than the managers of offices <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
<p> </p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A new office is to be built within the triangle formed by <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>, at a point as far as possible from the other three offices.</p>
<p>Find the distance of this office from each of the other offices.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a circle with centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math> and radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mtext>cm</mtext></math>. Points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> lie on the circumference of the circle and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>B</mtext><mo>=</mo><mn>2</mn><mi>θ</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo><</mo><mi>θ</mi><mo><</mo><mfrac><mi mathvariant="normal">π</mi><mn>2</mn></mfrac></math>.</p>
<p>The tangents to the circle at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> intersect at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>.</p>
<p style="text-align: center;"><img 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"></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AC</mtext><mo>=</mo><mi>tan</mi><mo> </mo><mi>θ</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> when the area of the shaded region is equal to the area of sector <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>OADB</mtext></math>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram below shows a circular clockface with centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>. The clock’s minute hand has a length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mtext>cm</mtext></math>. The clock’s hour hand has a length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo> </mo><mtext>cm</mtext></math>.</p>
<p>At <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>:</mo><mn>00</mn></math> pm the endpoint of the minute hand is at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and the endpoint of the hour hand is at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p> </p>
</div>
<div class="specification">
<p>Between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>:</mo><mn>00</mn></math> pm and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>:</mo><mn>13</mn></math> pm, the endpoint of the <strong>minute hand</strong> rotates through an angle, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math>, from point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> to point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>. This is illustrated in the diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A <strong>second</strong> clock is illustrated in the diagram below. The clock face has radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mtext>cm</mtext></math> with minute and hour hands both of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mtext>cm</mtext></math>. The time shown is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>:</mo><mn>00</mn></math> am. The bottom of the clock face is located <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo> </mo><mtext>cm</mtext></math> above a horizontal bookshelf.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The height, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> centimetres, of the endpoint of the minute hand above the bookshelf is modelled by the function</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>θ</mi></mfenced><mo>=</mo><mn>10</mn><mo> </mo><mi>cos</mi><mo> </mo><mi>θ</mi><mo>+</mo><mn>13</mn><mo>,</mo><mo> </mo><mi>θ</mi><mo>≥</mo><mn>0</mn><mo>,</mo></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> is the angle rotated by the minute hand from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>:</mo><mn>00</mn></math> am.</p>
</div>
<div class="specification">
<p>The height, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> centimetres, of the endpoint of the <strong>hour hand</strong> above the bookshelf is modelled by the function</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>θ</mi></mfenced><mo>=</mo><mo>-</mo><mn>10</mn><mo> </mo><mi>cos</mi><mfenced><mfrac><mi>θ</mi><mn>12</mn></mfrac></mfenced><mo>+</mo><mn>13</mn><mo>,</mo><mo> </mo><mi>θ</mi><mo>≥</mo><mn>0</mn><mo>,</mo></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> is the angle in degrees rotated by the minute hand from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>:</mo><mn>00</mn></math> am.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the size of angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>B</mtext></math> in degrees.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the distance between points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the size of angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> in degrees.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AC</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the area of the shaded sector, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AOC</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the height of the endpoint of the minute hand above the bookshelf at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>:</mo><mn>00</mn></math> am.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mn>160</mn><mo>°</mo></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the amplitude of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>θ</mi><mo>)</mo></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The endpoints of the minute hand and hour hand meet when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mi>k</mi></math>.</p>
<p>Find the smallest possible value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">i.</div>
</div>
<br><hr><br><div class="specification">
<p>A hollow chocolate box is manufactured in the form of a right prism with a regular hexagonal base. The height of the prism is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo> </mo><mtext>cm</mtext></math>, and the top and base of the prism have sides of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mtext>cm</mtext></math>.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo> </mo><mn>60</mn><mo>°</mo><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></math>, show that the area of the base of the box is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><msqrt><mn>3</mn></msqrt><msup><mi>x</mi><mn>2</mn></msup></mrow><mn>2</mn></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the total external surface area of the box is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1200</mn><mo> </mo><msup><mtext>cm</mtext><mn>2</mn></msup></math>, show that the volume of the box may be expressed as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mn>300</mn><msqrt><mn>3</mn></msqrt><mi>x</mi><mo>-</mo><mfrac><mn>9</mn><mn>4</mn></mfrac><msup><mi>x</mi><mn>3</mn></msup></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mn>300</mn><msqrt><mn>3</mn></msqrt><mi>x</mi><mo>-</mo><mfrac><mn>9</mn><mn>4</mn></mfrac><msup><mi>x</mi><mn>3</mn></msup></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>16</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>V</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> which maximizes the volume of the box.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, or otherwise, find the maximum possible volume of the box.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The box will contain spherical chocolates. The production manager assumes that they can calculate the exact number of chocolates in each box by dividing the volume of the box by the volume of a single chocolate and then rounding down to the nearest integer.</p>
<p>Explain why the production manager is incorrect.</p>
<div class="marks">[1]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>A large water reservoir is built in the form of part of an upside-down right pyramid with a horizontal square base of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math> metres. The point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> is the centre of the square base and point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>V</mtext></math> is the vertex of the pyramid.</p>
<p style="text-align: center;"><img 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"></p>
<p>The bottom of the reservoir is a square of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math> metres that is parallel to the base of the pyramid, such that the depth of the reservoir is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> metres as shown in the diagram.</p>
<p>The second diagram shows a vertical cross section, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>MNOPC</mtext></math>, of the reservoir.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>Every day <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn><mo> </mo><msup><mtext>m</mtext><mn>3</mn></msup></math> of water from the reservoir is used for irrigation.</p>
<p>Joshua states that, if no other water enters or leaves the reservoir, then when it is full there is enough irrigation water for at least one year.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the angle of depression from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>N</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CV</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise, show that the volume of the reservoir is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>29</mn><mo> </mo><mn>600</mn><mo> </mo><msup><mtext>m</mtext><mn>3</mn></msup></math>.</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>By finding an appropriate value, determine whether Joshua is correct.</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>To avoid water leaking into the ground, the five interior sides of the reservoir have been painted with a watertight material.</p>
<p>Find the area that was painted.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The Tower of Pisa is well known worldwide for how it leans.</p>
<p>Giovanni visits the Tower and wants to investigate how much it is leaning. He draws a diagram showing a non-right triangle, ABC.</p>
<p>On Giovanni’s diagram the length of AB is 56 m, the length of BC is 37 m, and angle ACB is 60°. AX is the perpendicular height from A to BC.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>Giovanni’s tourist guidebook says that the actual horizontal displacement of the Tower, BX, is 3.9 metres.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Giovanni’s diagram to show that angle ABC, the angle at which the Tower is leaning relative to the<br>horizontal, is 85° to the nearest degree.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Giovanni's diagram to calculate the length of AX.</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>Use Giovanni's diagram to find the length of BX, the horizontal displacement of the Tower.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the percentage error on Giovanni’s diagram.</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>Giovanni adds a point D to his diagram, such that BD = 45 m, and another triangle is formed.</p>
<p><img 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"></p>
<p>Find the angle of elevation of A from D.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A sector of a circle, centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math> and radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>m</mtext></math>, is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A square field with side <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo> </mo><mtext>m</mtext></math> has a goat tied to a post in the centre by a rope such that the goat can reach all parts of the field up to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>m</mtext></math> from the post.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAcwAAAEJCAYAAAAZ/heBAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAByVSURBVHhe7d0NeBTVof/xX/OnCoQioEIEjIEKkSAKAZE3RZS3IvJE4LZaJYBSKoJAEEWNIjcqFKUEI1IuLyWCKNWCexGoBCmBvyICBlCJ0ChiijFQjDQQRYzbO2d2AkkIyYDJspv9fp5nn8ycednZ2WR+OWfOzPzsPxYBAIByhTk/AQBAOQhMAABcIDABAHCBwAQQvHI9GhHZVJGRY+TJLbQK/inPiGus8T5Kzjjmmwfl8OpYVrpSk5Yow+y+M8pXVnqqklJ3qtzZAkqh9esxxvpdaKq2yRmVst0EJgCEqtyVGn/L3Zq84l9OQVlM8DymW+If14pvvE5ZaCIwAVQjlytuwYfKzl6rhNg6ThlQOQhMAEHihHIzliqxb7TdzNZqRIrW7/namVakrCbZksudXDYr35lu8eYqY0mi+trTb1OiZ7eynOa8yBEe5VqzFGbMVFt7fKHWp96nVmY9iemy11JiefPqqBHJ65R1zNTITjUNmmXT16doRCszT7T6Tl6vXK+1fdvmnipL9DjLlaV4M+N6fVJ8XYlLlZF7wpnPMJ/bo+QRHX3vXXoe05zdcYzSzHDeTMU1L6vp0rzfeHUc67HH8pIHqHnxfWs+t2emsw3mZe27Jdusz+SbXLZ8ZZ3c7jNtu+VYltJTi+3TvolKTc/SqYZ2F99rGby5GfIk32t/f773TlV6BcsUITABBAGvjmXM1bC4SVqSWWCXFKQ9q+HxT/oO+OXwZr2ikcWWM+xlB8xQer45sh9RxvOjFJf4kjLtqTu0ZOydemDuTnvsNGlPavjkVTJru/CSuqqt48pa/GCx5Y0cpSUP14Bpm3yBWsRaNn74s0qzN6VAman3a9jIkRo26OlTZUsm6cG/ZlmfuHx5yUPVp/i6rOXuemGz835F+2uMktNy7JKieeJ6PCRPTqlwOifOfhs709kGw9p3iberx/0e5ZT5AbzKT5+hASe323C2a9hcZRT9o+DNlmfiXYqfXGyfZr6kyfHDNS39sD1a8fdahmPb9PywOzU2ea31roZ578cVP+AJV/uEwAQQBPK0fflr9sEzvPc0rcvMVvb+rVo8rJ1v8hkd085Vr2qnGqtfymbtzz6g/Vtmq1+4NangM+0/aB0k83dq+bxtVkFj9U5aq0wzz9ZkddSZzuu107DFW6117dFbd7ZUjcJMrZq10dqwQUrZsk/Z2fu0JWWQ7Lf4aL8Oljh2Fy37sTwJ11nj1gE77Wt1LFW2851PdMievxzh/ZW0LrPk+63O0KemiujN0l+nvGjtL+szTXxNW/cfUHbmeqUMsfZXwXI9+qIVrBFxWrB1tnqbdTWYIM++A9qZEKsaZvykGoqIm6WtKXH2WIOEldrnNHd7szyakmztt/A+mrh8u7X92cpcP1tDYsJVsGaGXtzkC7aSvtWnO963PmG42iatt7+P7Mw3lGAto8zXtHx7njWPFaqbFujRNVbQn/YZ92vJzFXK8rr4Xk9zQjlvv6x51i9RzLCXfPskO1PrkvorvOAtzf3LrmK117IRmAACX2G2dqzebw201sj7b1d0HevQFdZYN91/r++Af0Z1FJuw1jowvq0H6+3SSs9CPXHPJK2xqxeH9c3RQnkP7tdHZrzBHbr/7tbWEtaqI7rr/vt6mZlO16CH4ro1tg6edRQRYc1dI1YJO62D77Yxqrd1jTyp/617xi731WCy83S0eGC2HaQhN5pl6+rKdm3skDtVVk/XdL9BDewZKxY+8A4NjK5rDV2gxp16qKuv2Ob97D2t2GltgflM93dRhDnS14lW3AO+/VWw4u/KOFMtzJXj+uzddVZgWW8xcrTuvy7C2n5rj7Torwfs/bZfK9Z9XLJ2bauhX9S/xPpp/VMweYD6JS6U5+0vdeXUjVbovaNnbjLTTujg/s/s/VfiM8Y9r09MwK4cphZhFX+vp8vXP7Z9YK3X+icldag6Rpkm2Rj1slsLrLINu/VVBbuEwAQQRFqoWeOazrDlkki1Ljdhis4PxuiW+FEaO/bJEk14hvdonrLNQIfmanyyelXDWnXzssMrsoF+UfzI6c3VtpR71Sqmh+LHjtHY4s2IpTWs5ywbptp16+nCEmVnx9ccXLayP5OlaH8V5OnItz8lMAt19BtTg2ygDs0uLVYrPbXfCg4eseqTpdVUi/g/avnEPtY/C6Y59EnrOxmj0XEdFNX3aaXb5zGL1l3eZ6z4ez3ddzpysJxzlaX/uSkDgQkg8IWFq36kqY9l6fOc474y43C2dptWvDPxfq63nkpWWkFj9U6YoRc927V/30ol2El4ier/oobCftFAkWZ0+z7lnKyYFFqr3qcyV10q4LyfvaWnZqxVQXgfJcxaIM/WfdrnmeAL29Lh6idlfyZL0f4Kb6B6tX/KhhXVFPO0/fN/FesodGq/hTeqV3bYhUXourELrdriPm31LFBKygwl9G4sZc7VKPscbNG6pe8P55cRuhYX3+vpaqleI1NbbaDeKe9ZtVPTJFvstXOCYstarBgCE0DgC7tYUW0utQZ2a96cN7TXdA7x5ih9zsLyO/0c+kTvmKZJNVHr7n11W2wDHXpnjdYWS8KwRlFqY7I4b5nmvLzbPo/lzd2oOXPX2dPLV6hDu7fbTZO64lp1791bsQ0P6x3PhrLD1k/CLmutHua8oPlMczb7eq0e2yvPC779FT7wZsXWtQ7/RTXOvH3KPlxWM6ZxqtaYtztbvrrfBbrsmusVY8rmvag523LlNR2NslbpBXu/RWlgr6tl4qkE716lDjC9WjtqRGqW6sT2VVxcX3Vv3cSe7KuVXqBGUb/0nZNdsUwr9ppaoenElOLrMdtqstKzPq7wez1dHTVpcYX1M09pc1/y1WZN56L7TC/iaA1I3Wu9S/kITABB4BLdOHqi3amjIO1R9YqJVGRUR8Wn7nCmn0HDVurW1hx6tyk57mrrwNhcHePnOk2mzrmuup00bFJ3azxHaZP7KMY6KEd1fFY5TaPsucpXQw1bd1BbM5j5rOJKb5eLZr4qUeda3fnIECvQrM8049e+83Uxt2jsEmu7wgdp2ugupcLMo7Edoyq+I07aGHW0Lyv5VnXaDtYjptNVwVrNGNRBUZGRirlljN00Gt5vokbf6KsllhDWQoOnjPZtl7OvIyOvVpzpPGSF7JC7u8mcDa174whN62fVOgtWaXKvGGsea91xz1rfW7hiRt6mDi2urvh7PU1NtRg83ulgNFfxHZtb31UXjbU7F/XVPb2bVRiIBCaAoBDWuJ+mLJ1u98I0wns/rEWL/7v8Tj9h0Yqft0gTTZOfETNUz3j+v9YlmYDcrw0ffmnVKnzn1TzPDLVrTL5enwuU1L+FGatQWIvfat7yx9Xb3izrgD5kujxb1ijJHNDzPtCHnxdrQvabCxRx08NK9cz2NXfanG3b8JziGl/gK6pxte6cf2rbI/SjytraGm1/q/n2eUfDNLRagWQ6XU2ZL0/KBGd5o52GPPOGNsyJU+My0yXMqlXeV2q7LNb3krR4kR61O/1YwiIVN2OpFic534lhmrxTXlXquOtUx9X3WoY612lc6qtKSSj6LNZqze/RyqdO7ZNy8DxMAKGtMEPJHQYoOc8KlISX9dcE64Bsmnun/N6uKZpLKbafdrkFQhGBCSDEHVZ6Ypzil5jLVkq7TgmeRUqIreeMI5TRJAsgxF2imx5dVLL5zxLee4JSPH/SOMISDmqYAAC4QA0TAAAXCEwAAFwgMAEAcIHADGHe3G1aknibip4lZ543tyTD3LEDAFAagRmqvNlaOWW0Ej9op5T15vE5mVp3x9eaGvegFmedjwutASCwEZihyntYn2/JUXj7m3VzC3OTrLqK7ttXXfWFsr6s6KlwABB6CMxQFXaJmnVqrIIVb+jvzpPGvUeP6FD4zeoVa9/yHwBQDIEZqux7NS5SUtc9WpWWpWPeHG1ask4NJ/1GHcxTDAAAJXDjgpBmHsKaquSn/qKVO4+qa9IizRrme+I8AKAkqhIhywrL9Gc17Inj+s0rq7Vh+T3S9D6KOfnUcwBAcQRmqMrfrBdGLdEFd/RR2zo1FXHdSM3yTFPvL5Zo5lufc2kJAJRCYIYo78H9+sg8sPykMNWJvkn9u16o7G8KCEwAKIXADFFhv+ysgW2lndOTtXhvvlVimmhf0ty0X2po9+Y8+w8ASqHTTwgzd/pZ+kKSEpfs8BWYp5ZPfUB3xUbwnxQAlEJgAgDgAhUJAABcIDABAHChUptkzRMvAPhXdvYBZwhAVar0wOSPF/Af/uYA/6FJFgAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcCMrAzMvL0+bNm7Vo0SKNGzdOmzZtcqYAAFA1guo6zKysLM2c+Udt2bJFTZv6bpKQm/uVunTppueff94eB0IJ12EC/hM0Ncy5c+dq0KCB+u6779SzZ08VFhbqq6++0uDBv9aQIUOcuQAAqBpBUcOcMWOGVq9+U7fc0tMOyTffXGnVNGfp1ltvVa1atZy5gNBDDRPwn4CvYZrzk6+//podlv/+97/tsHzzzdVWzXIwYQkA8JuAD8xp06aqc+fOqlGjht599x39z//M17XXXutMBQDAPwI6ML/88kt99VWOIiIilJ+fr4suqqdf/epXzlQAAPwnoAPz22+/1WWXNbaHDx8+rJtu6mEPAwDgbwHfJGt6wxonTpxQw4YN7WEAAPwtIHvJmhsTbN26VR7PG3av2IsuukjfWbXNC2vW1KWXXOrM5dOmTRvdc++9zhgQWuglC/hPwASmub7S9Ih97bXXlJm5W7169rI799SyQvJMcnJytDszU8mzZjklQGghMAH/Oa+BaUJyx44dWrdunRYunK//Gvxfim0Xq6uuukoXXnihM9eZLUpdpGuubauhQ4c6JUBoITAB/zkvgblr1y6t/N//1fwF89TvV/10Q7cbXIekYa7HXJuWpvV/X6+3317P9ZgIWQQm4D9+C0xziciKFcv16quvKuqKKN3co4datWpln59064XZL+hvb/3NHn7wwYkaMiReDRo0sMeBUERgAv7jt8C8Z/hwRbdsqW7dupUZkt9//70SH09U0yZNNX78eKe0JBOYEx96WC1atHBKgNBGYAL+45fLSsxTRn4o/MG+9+uZapTHjx/XF9lfKH1jut3kWpbmzZrro48+csYAAPAfv12HeVHdus5Q2UyQzvxjsl54YfYZQ9U80mv16tXOGAAA/uO3wFz55kr169/v5Kssl1uBaF5nYjoGZWZ+bF+nCQCAP/ktMAfcNkBrVq05+ToXphftnXf8VlOnPuOUAADgHwF/a7zSunbpopwvczR79mynBACAqueXXrLmBgVjxoxRyyuvVK3atZ3SkmrXqqVOnTo5Y+U7dOiQHns8Uf3799eHH36kLVs2W7XOP+juu+925gBCA71kAf/x22UlJjRXrXpTa99aq7D/F6aaxW559+mnn6pzp8768cdCDR402Cktn+lJ+/tR9yk//1SPWvNgaZ6ViVBCYAL+4/c7/YwbN04XXPBzXXzxxfZ4bm6u9TqoZcuW6amkJF0WEeG6plm681Dnzl10ReQVat+hvVPiXuEPhdr83nv6/vvjdhjXr19f4eHhzlSpcePG6t27D4GMgEJgAv5zXs9hmkd37dq18+S9YFtGt9S3Vk3UrdGjRjtDPm2ubqPrr79eB60APtvX119/bd9Y4Zo216jVVa20IyNDe/Z8oho1aqhRo0Z2M/CkSQ+rgxXGf/nLMucdAQCh4rzVMGvXrq1NmzaqdeurNXv2i/Y0E0QmvMxt89za+49/6Ju8PHm9Xj099WlNe2ZapdUCzT1vn095Xm3btVP79u3185//XEeOHFFaWppatozWvffeS40T5xU1TMB/zksN891337HPZ9511xA999wMp/TcmFqhacLt0qWLHZaPJj5qB11lMGH4pzl/0tH8o9b2rtIPP/ygevXq6fbbb7em/kcPPDDGPmCZV0JC2bfzAwBUD36vYZqbsH/77bdl3g/2XGqYpZmwNKFZmTVNw9zH1jQX9yhj2/bt2yezF595hutD4V/UMAH/8XsNs0mTJlV683QTkpVd0zRG/m6k9u7ZowMHSh6cTK3TPPja3CcXAFB9Bd2NC9yoitA0dxkaN3ac1q9/2+4AZF6mZrl06VLFxd1uNwkDAKqvahmYRlWEplnnhRfW1Mcf77bC8vOTzbATJkxw5gAAVFfVNjCNqgjNTtd30sCBAzVv3jw7LG+44UZnCgCgOqvWgWlUdmhGXn65MjN3O2MAgFBR7QPTqMzQNHf8yf93vjMGAAgVARWY5vxgVamK5lkAQOgIqMBs1qxZlTZ3EpoAgHMVUIHZsmVLrfnbGn3//fdOSeUjNAEA5yKgArNWrVp68MGJenfzZqekahCaAICzFXCdfoYMideMPz5n3xigKhGaAICzEXCB2aBBA82fv1CPJT5WpU2zBqEJAHAr4ALT6NOnj5o0barnZjxHaAIAAkJABqYRGRlpP3+S0AQABIKADUyj9dVX60evV6+8+opTUnUITQBAeQI6MI2ePXtqQ3q6srOznZJTTM3TlFfWq379+ho/drwdmmlpaVXe8QgAEDz8/gBptxISxqtRo0Zq2LChvvjiC/t2dPfec48z1feg6NlzZlvzRKhZVDOntHJ8+NEuZWVl2cNdOnfRQxMfsh/vZZhgTd+4Uc8+95w9DpxPPEAa8J+gCEzzkOYF8+dr0Z8XOVOl3/3+d2rbNlYzZ860r9+sTOZzxMcP1eLFL9njo0eNPvmAaAITgYTABPwn4JtkDdP55+Chg86Y7KZSU7OsirAs0rx5czs0jfe3vm//BACErqAIzNKOHz9uN8NWVVgWMaF5220DtP2D7XQEAoAQF5SB6U+XX365OrTvQO9ZAAhxBKYLl1566clLTvbs2eOUAgBCCYHpUtF1mrNSZumr3K+cUgBAqCAwz4IJTXOd5saN6dpcxU9UAQAEFgLzLF111VXq3v0m3XHHrwlNAAghARuYrVrFnLfzhY0bN9GRI0fs4e+++87+WdxlEZdp2bLXKjc0vTlKn3ybItvOVEahU3Ym3mx57utoX4Pne0VrQOpeeZ3JAIDKF7CBOXLkSF15ZQtNmfKk/fKn5ctXWIH4qv2+ixb92SktqUuXLpUYmieUs3K6RqXucMbL49WxnR7N3X+3PJnmln4HrNderRwWTXMBAFShgD7GPv74404gHFDPnr1PXtaRk5NjPzezqjRp0kRbt2633/e9997Xl9b7FT0xZcv776tVTIw9XFmh6c1Zo6QpH+uKluFOSTm8B/T2vNWKui9ObesQkQDgL0FzxH3xxRe1fsMG9evfT+9v3aqJDz3kTKlaJjwfeeRR3T7odvu9TVAPHz7cmVoJoXlstxZP9ij6z8m6L8p3v9oz8yp/0wI9uma31owdrJHJrys9K9+ZBgCoSgF7L9lgY8LShKYJTxOi7hxRRvJ4zan/kGYNq6u3R9yqsduHybN9gmJrOLOU6YRyM97WW8v/pMlLDqp30iJr+daq40xF6OBesoD/0KZXSc6+punVsYyXNeebIXo6/mzD7gJFxPbTsGeWal1SrN6d/LjmZ/g6KQEAqgaBWYnOJjS9uRv07Bzp/od7KOKcv4W6io5P0KS2mXpp4z5V1LkWAHDuCMxK5i40C3VoyxtKTfuD4mIinUtDOmtsWp6UN1Nxza/RCM8/nXkrEHaxotpc6owAAKoKgVkFKg7NGoqIm32yB7Dv9Z5SejeQGkyQZ9+HWhB3uTNvBbxfa/9HTTS0e3NrrQCAqkJgVpGzP6fpgjdXGW969GZGru8mBcf2yvPEI1rWY6J+F1vPngUAUDUIzCr000Pzn/KMuEaRkWPkyTVnKL3K37ZQo+M6KMo04w5erCO9ntVfE66jhywAVDEuK/EDE5YmNE14mhAFKgt/c4D/UMP0gyppngUA+BWB6SeEJgAENwLTjwhNAAheBKafEZoAEJwIzPOA0ASA4ENgnieEJgAEFwLzPCI0ASB4EJjnGaEJAMGBwAwAhCYABD4CM0AQmgAQ2AjMAEJoAkDgIjADDKEJAIGJwAxAhCYABB4CM0ARmgAQWAjMAEZoAkDgIDADHKEJAIGBwAwChCYAnH8EZpAgNAHg/CIwgwihCQDnD4EZZAhNADg/CMwgRGgCgP8RmEGK0AQA/yIwgxihCQD+Q2AGOUITAPyDwKwGCE0AqHoEZjVBaAJA1SIwqxFCEwCqDoFZzRCaAFA1CMxqiNAEgMpHYFZThCYAVC4CsxojNAGg8hCY1RyhCQCVg8AMAYQmAPx0BGaIIDQB4KdxEZgnlJuxVIl9oxUZ2dR6Ratv4lJl5J5wpiNYEJoAcO4qDExvzhpNuStJH7SfrvWZ2crOXKE7Dj6vuJGvKMvrzISgQWgCwLmpODBz92lLwaVq36ubWtSxZq9j1TD7d5Sy9unLYyRmMCI0AeDsVRiYYRHN1Sl8v1Yse0c5dj4W6uiRbxQ+8GbF1nXRoouAVDw0O3Robze3v/zyy85UAEBpFQdm4wGa4ZmmrlveUlpWvlXjfFdLVtTXpPhY1XXmQXAyodmwYSMdOnTQHn/ssUe0a9cuexgAUJKLKmKY6rTopd/fU0crxnVTVI/X1fy5qRoWTVxWB0VhWaSgoMAZAgAUV3FgenOUPmWUnvjxN3plTZqWj/pB03tdp76T1yuXU5hBb+rUPzhDUrNmzdWuXTtnDABQ3M/+Y3GGy+BVfvoUXR//mSatX6hhLWpaZfnam/qw4iYfLVbmY86DZWcfcMYQLEwz7L/+dUhdu3ZTrVq1nFIEA/7mAP+poIZ5Qgf3f6aSjXR1Fd23r7rqsL45WuiUIZhde+216tmzF2EJAOWoIDBr6pdde6mtNmr69Ne111xGYppo5yxUWsyt6t6ytjMfAADVW8W9ZFv8VvM80zXwwNPqFROpyKge+sOPd8iTep9izXWZAACEgArOYZ4dzqcA/sXfHOA/VBEBAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAFwhMAABcIDABAHCBwAQAwAUCEwAAF372H4sz/JNFRjZ1hgD4S3b2AWcIQFWq1MAEAKC6okkWAAAXCEwAAFwgMAEAcIHABADABQITAIAKSf8HHGDHW6lhIZoAAAAASUVORK5CYII="></p>
<p style="text-align: center;"><sup>[Source: mynamepong, n.d. Goat [image online] Available at: <a href="https://thenounproject.com/term/goat/1761571/">https://thenounproject.com/term/goat/1761571/</a></sup><br><sup>This file is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)</sup><br><sup><a href="https://creativecommons.org/licenses/by-sa/3.0/deed.en">https://creativecommons.org/licenses/by-sa/3.0/deed.en</a> [Accessed 22 April 2010] Source adapted.]</sup></p>
</div>
<div class="specification">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> be the volume of grass eaten by the goat, in cubic metres, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> be the length of time, in hours, that the goat has been in the field.</p>
<p>The goat eats grass at the rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>V</mi></mrow><mrow><mo>d</mo><mi>t</mi></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn><mo> </mo><mi>t</mi><msup><mtext>e</mtext><mrow><mo>-</mo><mi>t</mi></mrow></msup></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AÔB</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the shaded segment.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of a circle with radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>m</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the field that can be reached by the goat.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> at which the goat is eating grass at the greatest rate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A king rules a small mountain kingdom which is in the form of a square of length 4 kilometres. The square is described by the co-ordinate system <span class="mjpage"><math alttext="0 \leqslant x \leqslant 4{\text{,}}\,\,0 \leqslant y \leqslant 4" xmlns="http://www.w3.org/1998/Math/MathML"> <mn>0</mn> <mo>⩽<!-- ⩽ --></mo> <mi>x</mi> <mo>⩽<!-- ⩽ --></mo> <mn>4</mn> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>0</mn> <mo>⩽<!-- ⩽ --></mo> <mi>y</mi> <mo>⩽<!-- ⩽ --></mo> <mn>4</mn> </math></span>.</p>
<p>The king has four adult children, each of which has a luxury palace located at the points <span class="mjpage"><math alttext="\left( {1{\text{,}}\,\,1} \right){\text{,}}\,\left( {3{\text{,}}\,\,1} \right){\text{,}}\,\left( {1{\text{,}}\,\,3} \right){\text{,}}\,\left( {3{\text{,}}\,\,3} \right)" xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mn>3</mn> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>3</mn> </mrow> <mo>)</mo> </mrow> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mn>3</mn> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>3</mn> </mrow> <mo>)</mo> </mrow> </math></span>. Each child owns all the land that is nearer their palace than any other palace.</p>
</div>
<div class="specification">
<p>The king has a fifth (youngest) child who is now just growing up. He installs her in a new palace situated at point (2, 2). The rule about ownership of land is then reapplied.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch a Voronoi diagram to represent this information.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch a new Voronoi diagram to represent this new situation.</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>State what the shape of the land, owned by the youngest child, is.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the youngest child’s land.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find how much land an older child has lost.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State, with a reason, if all five children now own an equal amount of land.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>The Voronoi diagram below shows four supermarkets represented by points with coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext><mo>(</mo><mn>6</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>6</mn><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext><mo>(</mo><mn>2</mn><mo>,</mo><mo> </mo><mn>2</mn><mo>)</mo></math>. The vertices <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>X</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Y</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Z</mtext></math> are also shown. All distances are measured in kilometres.</p>
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"></p>
</div>
<div class="specification">
<p>The equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>(XY)</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>2</mn><mo>−</mo><mi>x</mi></math> and the equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>(YZ)</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>3</mn><mo>.</mo><mn>5</mn></math>.</p>
</div>
<div class="specification">
<p>The coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Y</mtext></math> are <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mo> </mo><mn>3</mn><mo>)</mo></math> and the coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Z</mtext></math> are <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>7</mn><mo>,</mo><mo> </mo><mn>7</mn><mo>)</mo></math>.</p>
</div>
<div class="specification">
<p>A town planner believes that the larger the area of the Voronoi cell <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>XYZ</mtext></math>, the more people will shop at supermarket <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the midpoint of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[BD]</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>(XZ)</mtext></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>X</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the exact length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[YZ]</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the exact length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[XY]</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>32</mn></msqrt></math>, find the size of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>XŶZ</mtext></math> in degrees.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>XYZ</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State one criticism of this interpretation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>A pan, in which to cook a pizza, is in the shape of a cylinder. The pan has a diameter of 35 cm and a height of 0.5 cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_11.14.51.png" alt="M17/5/MATSD/SP2/ENG/TZ1/04"></p>
</div>
<div class="specification">
<p>A chef had enough pizza dough to exactly fill the pan. The dough was in the shape of a sphere.</p>
</div>
<div class="specification">
<p>The pizza was cooked in a hot oven. Once taken out of the oven, the pizza was placed in a dining room.</p>
<p>The temperature, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P">
<mi>P</mi>
</math></span>, of the pizza, in degrees Celsius, °C, can be modelled by</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="P(t) = a{(2.06)^{ - t}} + 19,{\text{ }}t \geqslant 0">
<mi>P</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>a</mi>
<mrow>
<mo stretchy="false">(</mo>
<mn>2.06</mn>
<msup>
<mo stretchy="false">)</mo>
<mrow>
<mo>−<!-- − --></mo>
<mi>t</mi>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mn>19</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>t</mi>
<mo>⩾<!-- ⩾ --></mo>
<mn>0</mn>
</math></span></p>
<p>where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> is a constant and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> is the time, in minutes, since the pizza was taken out of the oven.</p>
<p>When the pizza was taken out of the oven its temperature was 230 °C.</p>
</div>
<div class="specification">
<p>The pizza can be eaten once its temperature drops to 45 °C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the volume of this pan.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the radius of the sphere in cm, correct to one decimal place.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the temperature that the pizza will be 5 minutes after it is taken out of the oven.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, to the nearest second, the time since the pizza was taken out of the oven until it can be eaten.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the context of this model, state what the value of 19 represents.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>Abdallah owns a plot of land, near the river Nile, in the form of a quadrilateral ABCD.</p>
<p>The lengths of the sides are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AB}} = {\text{40 m, BC}} = {\text{115 m, CD}} = {\text{60 m, AD}} = {\text{84 m}}">
<mrow>
<mtext>AB</mtext>
</mrow>
<mo>=</mo>
<mrow>
<mtext>40 m, BC</mtext>
</mrow>
<mo>=</mo>
<mrow>
<mtext>115 m, CD</mtext>
</mrow>
<mo>=</mo>
<mrow>
<mtext>60 m, AD</mtext>
</mrow>
<mo>=</mo>
<mrow>
<mtext>84 m</mtext>
</mrow>
</math></span> and angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{B\hat AD}} = 90^\circ ">
<mrow>
<mrow>
<mi mathvariant="normal">B</mi>
<mrow>
<mover>
<mi mathvariant="normal">A</mi>
<mo stretchy="false">^<!-- ^ --></mo>
</mover>
</mrow>
<mi mathvariant="normal">D</mi>
</mrow>
</mrow>
<mo>=</mo>
<msup>
<mn>90</mn>
<mo>∘<!-- ∘ --></mo>
</msup>
</math></span>.</p>
<p>This information is shown on the diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.24.18.png" alt="N17/5/MATSD/SP2/ENG/TZ0/03"></p>
</div>
<div class="specification">
<p>The formula that the ancient Egyptians used to estimate the area of a quadrilateral ABCD is</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{area}} = \frac{{({\text{AB}} + {\text{CD}})({\text{AD}} + {\text{BC}})}}{4}">
<mrow>
<mtext>area</mtext>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<mtext>AB</mtext>
</mrow>
<mo>+</mo>
<mrow>
<mtext>CD</mtext>
</mrow>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mrow>
<mtext>AD</mtext>
</mrow>
<mo>+</mo>
<mrow>
<mtext>BC</mtext>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
<mn>4</mn>
</mfrac>
</math></span>.</p>
<p>Abdallah uses this formula to estimate the area of his plot of land.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{BD}} = 93{\text{ m}}">
<mrow>
<mtext>BD</mtext>
</mrow>
<mo>=</mo>
<mn>93</mn>
<mrow>
<mtext> m</mtext>
</mrow>
</math></span> correct to the nearest metre.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{B\hat CD}}">
<mrow>
<mrow>
<mi mathvariant="normal">B</mi>
<mrow>
<mover>
<mi mathvariant="normal">C</mi>
<mo stretchy="false">^</mo>
</mover>
</mrow>
<mi mathvariant="normal">D</mi>
</mrow>
</mrow>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of ABCD.</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>Calculate Abdallah’s estimate for the area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the percentage error in Abdallah’s estimate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A water container is made in the shape of a cylinder with internal height <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> cm and internal base radius <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_08.31.01.png" alt="N16/5/MATSD/SP2/ENG/TZ0/06"></p>
<p>The water container has no top. The inner surfaces of the container are to be coated with a water-resistant material.</p>
</div>
<div class="specification">
<p>The volume of the water container is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.5{\text{ }}{{\text{m}}^3}">
<mn>0.5</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>The water container is designed so that the area to be coated is minimized.</p>
</div>
<div class="specification">
<p>One can of water-resistant material coats a surface area of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2000{\text{ c}}{{\text{m}}^2}">
<mn>2000</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a formula for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>, the surface area to be coated.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Express this volume in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{c}}{{\text{m}}^3}"> <mrow> <mtext>c</mtext> </mrow> <mrow> <msup> <mrow> <mtext>m</mtext> </mrow> <mn>3</mn> </msup> </mrow> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span>, an equation for the volume of this water container.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + \frac{{1\,000\,000}}{r}"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}A}}{{{\text{d}}r}}"> <mfrac> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>A</mi> </mrow> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>r</mi> </mrow> </mfrac> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your answer to part (e), find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> which minimizes <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of this minimum area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the least number of cans of water-resistant material that will coat the area in part (g).</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>A factory packages coconut water in cone-shaped containers with a base radius of 5.2 cm and a height of 13 cm.</p>
</div>
<div class="specification">
<p>The factory designers are currently investigating whether a cone-shaped container can be replaced with a cylinder-shaped container with the same radius and the same total surface area.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the slant height of the cone-shaped container.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the slant height of the cone-shaped container.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the total surface area of the cone-shaped container is 314 cm<sup>2</sup>, correct to three significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the height, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span>, of this cylinder-shaped container.</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>The factory director wants to increase the volume of coconut water sold per container.</p>
<p>State whether or not they should replace the cone-shaped containers with cylinder‑shaped containers. Justify your conclusion.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>An archaeological site is to be made accessible for viewing by the public. To do this, archaeologists built two straight paths from point A to point B and from point B to point C as shown in the following diagram. The length of path AB is 185 m, the length of path BC is 250 m, and angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}\mathop {\text{B}}\limits^ \wedge {\text{C}}">
<mrow>
<mtext>A</mtext>
</mrow>
<mover>
<mrow>
<mtext>B</mtext>
</mrow>
<mo>∧<!-- ∧ --></mo>
</mover>
<mo><!-- --></mo>
<mrow>
<mtext>C</mtext>
</mrow>
</math></span> is 125°.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The archaeologists plan to build two more straight paths, AD and DC. For the paths to go around the site, angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}\mathop {\text{A}}\limits^ \wedge {\text{D}}">
<mrow>
<mtext>B</mtext>
</mrow>
<mover>
<mrow>
<mtext>A</mtext>
</mrow>
<mo>∧<!-- ∧ --></mo>
</mover>
<mo><!-- --></mo>
<mrow>
<mtext>D</mtext>
</mrow>
</math></span> is to be made equal to 85° and angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}\mathop {\text{C}}\limits^ \wedge {\text{D}}">
<mrow>
<mtext>B</mtext>
</mrow>
<mover>
<mrow>
<mtext>C</mtext>
</mrow>
<mo>∧<!-- ∧ --></mo>
</mover>
<mo><!-- --></mo>
<mrow>
<mtext>D</mtext>
</mrow>
</math></span> is to be made equal to 70° as shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the size of angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{C}}\mathop {\text{A}}\limits^ \wedge {\text{D}}">
<mrow>
<mtext>C</mtext>
</mrow>
<mover>
<mrow>
<mtext>A</mtext>
</mrow>
<mo>∧</mo>
</mover>
<mo></mo>
<mrow>
<mtext>D</mtext>
</mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the size of angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}\mathop {\text{C}}\limits^ \wedge {\text{D}}">
<mrow>
<mtext>A</mtext>
</mrow>
<mover>
<mrow>
<mtext>C</mtext>
</mrow>
<mo>∧</mo>
</mover>
<mo></mo>
<mrow>
<mtext>D</mtext>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows the straight line <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math>. Points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mfenced><mrow><mo>-</mo><mn>9</mn><mo>,</mo><mo> </mo><mo>-</mo><mn>1</mn></mrow></mfenced></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext><mfenced><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mo> </mo><mn>2</mn></mrow></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> are points on <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math>.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> is the midpoint of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AC</mtext></math>.</p>
</div>
<div class="specification">
<p>Line <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub></math> is perpendicular to <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math> and passes through point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math>.</p>
</div>
<div class="specification">
<p>The point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>N</mtext><mfenced><mrow><mi>k</mi><mo>,</mo><mo> </mo><mn>4</mn></mrow></mfenced></math> is on <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the gradient of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub></math>. Give your answer in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi><mi>y</mi><mo>+</mo><mi>d</mi><mo>=</mo><mn>0</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi><mo>,</mo><mo> </mo><mi>d</mi><mo>∈</mo><mi mathvariant="normal">ℤ</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the distance between points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>N</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AM</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>45</mn></msqrt></math>, find the area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ANC</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>Farmer Brown has built a new barn, on horizontal ground, on his farm. The barn has a cuboid base and a triangular prism roof, as shown in the diagram.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">The cuboid has a width of 10 m, a length of 16 m and a height of 5 m.<br>The roof has two sloping faces and two vertical and identical sides, ADE and GLF.<br>The face DEFL slopes at an angle of 15° to the horizontal and ED = 7 m .</p>
</div>
<div class="specification">
<p>The roof was built using metal supports. Each support is made from <strong>five</strong> lengths of metal AE, ED, AD, EM and MN, and the design is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">ED = 7 m , AD = 10 m and angle ADE = 15° .<br>M is the midpoint of AD.<br>N is the point on ED such that MN is at right angles to ED.</p>
</div>
<div class="specification">
<p>Farmer Brown believes that N is the midpoint of ED.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the area of triangle EAD.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the <strong>total</strong> volume of the barn.</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>Calculate the length of MN.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of AE.</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>Show that Farmer Brown is incorrect.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the <strong>total</strong> length of metal required for one support.</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>A manufacturer makes trash cans in the form of a cylinder with a hemispherical top. The trash can has a height of 70 cm. The base radius of both the cylinder and the hemispherical top is 20 cm.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>A designer is asked to produce a new trash can.</p>
<p>The new trash can will also be in the form of a cylinder with a hemispherical top.</p>
<p>This trash can will have a height of <em>H</em> cm and a base radius of <em>r</em> cm.</p>
<p style="text-align: center;"><img 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"></p>
<p>There is a design constraint such that <em>H</em> + 2<em>r</em> = 110 cm.</p>
<p>The designer has to maximize the volume of the trash can.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the height of the cylinder.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total volume of the trash can.</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 height of the <strong>cylinder</strong>, <em>h</em> , of the new trash can, in terms of <em>r</em>.</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>Show that the volume, <em>V</em> cm<sup>3</sup> , of the new trash can is given by</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V = 110\pi {r^3}"> <mi>V</mi> <mo>=</mo> <mn>110</mn> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>3</mn> </msup> </mrow> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your graphic display calculator, find the value of <em>r</em> which maximizes the value of <em>V</em>.</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>The designer claims that the new trash can has a capacity that is at least 40% greater than the capacity of the original trash can.</p>
<p>State whether the designer’s claim is correct. Justify your answer.</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>A restaurant serves desserts in glasses in the shape of a cone and in the shape of a hemisphere. The diameter of a cone shaped glass is 7.2 cm and the height of the cone is 11.8 cm as shown.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.40.46.png" alt="N17/5/MATSD/SP2/ENG/TZ0/06"></p>
</div>
<div class="specification">
<p>The volume of a hemisphere shaped glass is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="225{\text{ c}}{{\text{m}}^3}">
<mn>225</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>The restaurant offers two types of dessert.</p>
<p>The <strong>regular dessert </strong>is a hemisphere shaped glass completely filled with chocolate mousse. The cost, to the restaurant, of the chocolate mousse for one regular dessert is $1.89.</p>
</div>
<div class="specification">
<p>The <strong>special dessert </strong>is a cone shaped glass filled with two ingredients. It is first filled with orange paste to half of its height and then with chocolate mousse for the remaining volume.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.44.32.png" alt="N17/5/MATSD/SP2/ENG/TZ0/06.d.e.f"></p>
</div>
<div class="specification">
<p>The cost, to the restaurant, of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="100{\text{ c}}{{\text{m}}^3}">
<mn>100</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span> of orange paste is $7.42.</p>
</div>
<div class="specification">
<p>A chef at the restaurant prepares 50 desserts; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> regular desserts and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> special desserts. The cost of the ingredients for the 50 desserts is $111.44.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the volume of a cone shaped glass is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="160{\text{ c}}{{\text{m}}^3}">
<mn>160</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span>, correct to 3 significant figures.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the radius, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>, of a hemisphere shaped glass.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the cost of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="100{\text{ c}}{{\text{m}}^3}">
<mn>100</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span> of chocolate mousse.</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>Show that there is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="20{\text{ c}}{{\text{m}}^3}">
<mn>20</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span> of orange paste in each special dessert.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total cost of the ingredients of one special dessert.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{16}}{x}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>16</mn>
</mrow>
<mi>x</mi>
</mfrac>
</math></span>. The line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> is tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 8">
<mi>x</mi>
<mo>=</mo>
<mn>8</mn>
</math></span>.</p>
</div>
<div class="specification">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> can be expressed in the form <em><strong>r</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left( {\begin{array}{*{20}{c}} 8 \\ 2 \end{array}} \right) + t">
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>8</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>t</mi>
</math></span><em><strong>u</strong></em>.</p>
</div>
<div class="specification">
<p>The direction vector of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x">
<mi>y</mi>
<mo>=</mo>
<mi>x</mi>
</math></span> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 1 \\ 1 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the gradient of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <em><strong>u</strong></em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the acute angle between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x"> <mi>y</mi> <mo>=</mo> <mi>x</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {f \circ f} \right)\left( x \right)"> <mrow> <mo>(</mo> <mrow> <mi>f</mi> <mo>∘</mo> <mi>f</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}\left( x \right)"> <mrow> <msup> <mi>f</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise, find the obtuse angle formed by the tangent line to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 8"> <mi>x</mi> <mo>=</mo> <mn>8</mn> </math></span> and the tangent line to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2"> <mi>x</mi> <mo>=</mo> <mn>2</mn> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A farmer owns a plot of land in the shape of a quadrilateral ABCD.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AB}} = 105{\text{ m, BC}} = 95{\text{ m, CD}} = 40{\text{ m, DA}} = 70{\text{ m}}">
<mrow>
<mtext>AB</mtext>
</mrow>
<mo>=</mo>
<mn>105</mn>
<mrow>
<mtext> m, BC</mtext>
</mrow>
<mo>=</mo>
<mn>95</mn>
<mrow>
<mtext> m, CD</mtext>
</mrow>
<mo>=</mo>
<mn>40</mn>
<mrow>
<mtext> m, DA</mtext>
</mrow>
<mo>=</mo>
<mn>70</mn>
<mrow>
<mtext> m</mtext>
</mrow>
</math></span> and angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{DCB}} = 90^\circ ">
<mrow>
<mtext>DCB</mtext>
</mrow>
<mo>=</mo>
<msup>
<mn>90</mn>
<mo>∘<!-- ∘ --></mo>
</msup>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_08.23.38.png" alt="N16/5/MATSD/SP2/ENG/TZ0/05"></p>
<p>The farmer wants to divide the land into two equal areas. He builds a fence in a straight line from point B to point P on AD, so that the area of PAB is equal to the area of PBCD.</p>
<p>Calculate</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the length of BD;</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the size of angle DAB;</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the area of triangle ABD;</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>the area of quadrilateral ABCD;</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the length of AP;</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the length of the fence, BP.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>The base of an electric iron can be modelled as a pentagon ABCDE, where:</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\begin{array}{*{20}{l}} {{\text{BCDE is a rectangle with sides of length }}(x + 3){\text{ cm and }}(x + 5){\text{ cm;}}} \\ {{\text{ABE is an isosceles triangle, with AB}} = {\text{AE and a height of }}x{\text{ cm;}}} \\ {{\text{the area of ABCDE is 222 c}}{{\text{m}}^{\text{2}}}{\text{.}}} \end{array}">
<mtable columnalign="left" rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>BCDE is a rectangle with sides of length </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<mn>3</mn>
<mo stretchy="false">)</mo>
<mrow>
<mtext> cm and </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<mn>5</mn>
<mo stretchy="false">)</mo>
<mrow>
<mtext> cm;</mtext>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>ABE is an isosceles triangle, with AB</mtext>
</mrow>
<mo>=</mo>
<mrow>
<mtext>AE and a height of </mtext>
</mrow>
<mi>x</mi>
<mrow>
<mtext> cm;</mtext>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>the area of ABCDE is 222 c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mrow>
<mtext>2</mtext>
</mrow>
</msup>
</mrow>
<mrow>
<mtext>.</mtext>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</math></span></p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_11.05.55.png" alt="M17/5/MATSD/SP2/ENG/TZ1/02"></p>
</div>
<div class="specification">
<p>Insulation tape is wrapped around the perimeter of the base of the iron, ABCDE.</p>
</div>
<div class="specification">
<p>F is the point on AB such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{BF}} = {\text{8 cm}}">
<mrow>
<mtext>BF</mtext>
</mrow>
<mo>=</mo>
<mrow>
<mtext>8 cm</mtext>
</mrow>
</math></span>. A heating element in the iron runs in a straight line, from C to F.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an <strong>equation </strong>for the area of ABCDE using the above information.</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>Show that the equation in part (a)(i) simplifies to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3{x^2} + 19x - 414 = 0">
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>19</mn>
<mi>x</mi>
<mo>−</mo>
<mn>414</mn>
<mo>=</mo>
<mn>0</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of CD.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{B\hat AE}} = 67.4^\circ ">
<mrow>
<mrow>
<mi mathvariant="normal">B</mi>
<mrow>
<mover>
<mi mathvariant="normal">A</mi>
<mo stretchy="false">^</mo>
</mover>
</mrow>
<mi mathvariant="normal">E</mi>
</mrow>
</mrow>
<mo>=</mo>
<msup>
<mn>67.4</mn>
<mo>∘</mo>
</msup>
</math></span>, correct to one decimal place.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of the perimeter of ABCDE.</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>Calculate the length of CF.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The Maxwell Ohm Company is designing a portable Bluetooth speaker. The speaker is in the shape of a cylinder with a hemisphere at each end of the cylinder.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>The dimensions of the speaker, in centimetres, are illustrated in the following diagram where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> is the radius of the hemisphere, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math> is the length of the cylinder, with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>></mo><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>≥</mo><mn>0</mn></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The Maxwell Ohm Company has decided that the speaker will have a surface area of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><mo> </mo><msup><mtext>cm</mtext><mn>2</mn></msup></math>.</p>
</div>
<div class="specification">
<p>The quality of sound from the speaker will improve as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> increases.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math>, the volume (cm<sup>3</sup>) of the speaker, in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an equation for the surface area of the speaker in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given the design constraint that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mfrac><mrow><mn>150</mn><mo>-</mo><mn>2</mn><mi mathvariant="normal">π</mi><msup><mi>r</mi><mn>2</mn></msup></mrow><mrow><mi mathvariant="normal">π</mi><mi>r</mi></mrow></mfrac></math>, show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mn>150</mn><mi>r</mi><mo>-</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi><msup><mi>r</mi><mn>3</mn></msup></mrow><mn>3</mn></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>d</mtext><mi>V</mi></mrow><mrow><mtext>d</mtext><mi>r</mi></mrow></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your answer to part (d), show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> is a maximum when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mn>75</mn><mi mathvariant="normal">π</mi></mfrac></msqrt><mo> </mo><mtext>cm</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of the <strong>cylinder</strong> for which <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> is a maximum.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the maximum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your answer to part (f) to identify the shape of the speaker with the best quality of sound.</p>
<div class="marks">[1]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>Haraya owns two triangular plots of land, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABC</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ACD</mtext></math>. The length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo> </mo><mtext>m</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BC</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo> </mo><mtext>m</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AC</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn><mo> </mo><mtext>m</mtext></math>. The size of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext><mover><mtext>A</mtext><mo>^</mo></mover><mtext>C</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>55</mn><mo>°</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>D</mtext><mo>^</mo></mover><mtext>C</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>°</mo></math>.</p>
<p>The following diagram shows this information.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>Haraya attaches a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mtext>m</mtext></math> long rope to a vertical pole at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AD</mtext></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the size of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>B</mtext><mo>^</mo></mover><mtext>C</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the area of the triangular plot of land <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABC</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine whether the rope can extend into the triangular plot of land, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ACD</mtext></math>. Justify your answer.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the points A(−3, 4, 2) and B(8, −1, 5).</p>
</div>
<div class="specification">
<p>A line <em>L</em> has vector equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \left( {\begin{array}{*{20}{c}} 2 \\ 0 \\ { - 5} \end{array}} \right) + t\left( {\begin{array}{*{20}{c}} 1 \\ { - 2} \\ 2 \end{array}} \right)">
<mi>r</mi>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>5</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>t</mi>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>2</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>. The point C (5, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>, 1) lies on line <em>L</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\overrightarrow {{\text{AB}}} } \right|"> <mrow> <mo>|</mo> <mrow> <mover> <mrow> <mtext>AB</mtext> </mrow> <mo>→</mo> </mover> </mrow> <mo>|</mo> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y"> <mi>y</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{AC}}} = \left( {\begin{array}{*{20}{c}} 8 \\ { - 10} \\ { - 1} \end{array}} \right)"> <mover> <mrow> <mtext>AC</mtext> </mrow> <mo>→</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>8</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>10</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the angle between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{AB}}} "> <mover> <mrow> <mtext>AB</mtext> </mrow> <mo>→</mo> </mover> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{AC}}} "> <mover> <mrow> <mtext>AC</mtext> </mrow> <mo>→</mo> </mover> </math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of triangle ABC.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p>The vector equation of line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> is given by <em><strong>r</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left( {\begin{array}{*{20}{c}} { - 1} \\ 3 \\ 8 \end{array}} \right) + t\left( {\begin{array}{*{20}{c}} 4 \\ 5 \\ { - 1} \end{array}} \right)">
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>8</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>t</mi>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>4</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>5</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
<p>Point P is the point on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> that is closest to the origin. Find the coordinates of P.</p>
</div>
<br><hr><br><div class="specification">
<p>A communication tower, T, produces a signal that can reach cellular phones within a radius of 32 km. A straight road passes through the area covered by the tower’s signal.</p>
<p>The following diagram shows a line representing the road and a circle representing the area covered by the tower’s signal. Point R is on the circumference of the circle and points S and R are on the road. Point S is 38 km from the tower and RŜT = 43˚.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question">
<p>Let SR = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>. Use the cosine rule to show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^2} - \left( {76\,{\text{cos}}\,43^\circ } \right)x + 420 = 0"> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mrow> <mo>(</mo> <mrow> <mn>76</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <msup> <mn>43</mn> <mo>∘</mo> </msup> </mrow> <mo>)</mo> </mrow> <mi>x</mi> <mo>+</mo> <mn>420</mn> <mo>=</mo> <mn>0</mn> </math></span>.</p>
</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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\mathop {{\text{PR}}}\limits^ \to }">
<mrow>
<mover>
<mrow>
<mrow>
<mtext>PR</mtext>
</mrow>
</mrow>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</math></span> = 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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{PQ}}}\limits^ \to "> <mover> <mrow> <mrow> <mtext>PQ</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\mathop {{\text{PQ}}}\limits^ \to } \right|"> <mrow> <mo>|</mo> <mrow> <mover> <mrow> <mrow> <mtext>PQ</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </mrow> <mo>|</mo> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>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>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;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\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 ">
<mrow>
<mtext>AB</mtext>
</mrow>
<mo>=</mo>
<mn>11</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cm,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>BC</mtext>
</mrow>
<mo>=</mo>
<mn>6</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cm,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>B</mtext>
</mrow>
<mover>
<mrow>
<mtext>A</mtext>
</mrow>
<mo>∧<!-- ∧ --></mo>
</mover>
<mo><!-- --></mo>
<msup>
<mrow>
<mtext>D = 100</mtext>
</mrow>
<mo>∘<!-- ∘ --></mo>
</msup>
<mrow>
<mtext>, and C</mtext>
</mrow>
<mover>
<mrow>
<mtext>B</mtext>
</mrow>
<mo>∧<!-- ∧ --></mo>
</mover>
<mo><!-- --></mo>
<msup>
<mrow>
<mtext>D = 82</mtext>
</mrow>
<mo>∘<!-- ∘ --></mo>
</msup>
</math></span></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>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{AB}}} = \left( {\begin{array}{*{20}{c}} 4 \\ 1 \\ 2 \end{array}} \right)">
<mover>
<mrow>
<mtext>AB</mtext>
</mrow>
<mo>→<!-- → --></mo>
</mover>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>4</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\overrightarrow {{\text{AB}}} } \right|"> <mrow> <mo>|</mo> <mrow> <mover> <mrow> <mtext>AB</mtext> </mrow> <mo>→</mo> </mover> </mrow> <mo>|</mo> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{AC}}} = \left( {\begin{array}{*{20}{c}} 3 \\ 0 \\ 0 \end{array}} \right)"> <mover> <mrow> <mtext>AC</mtext> </mrow> <mo>→</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span>. Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{B\hat AC}}"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mrow> <mover> <mi mathvariant="normal">A</mi> <mo stretchy="false">^</mo> </mover> </mrow> <mi mathvariant="normal">C</mi> </mrow> </mrow> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a circle, centre O and radius <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> mm. The circle is divided into five equal sectors.</p>
<p 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>One sector is OAB, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{A\hat OB}} = \theta ">
<mrow>
<mrow>
<mi mathvariant="normal">A</mi>
<mrow>
<mover>
<mi mathvariant="normal">O</mi>
<mo stretchy="false">^<!-- ^ --></mo>
</mover>
</mrow>
<mi mathvariant="normal">B</mi>
</mrow>
</mrow>
<mo>=</mo>
<mi>θ<!-- θ --></mi>
</math></span>.</p>
</div>
<div class="specification">
<p>The area of sector AOB is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="20\pi {\text{ m}}{{\text{m}}^2}">
<mn>20</mn>
<mi>π<!-- π --></mi>
<mrow>
<mtext> m</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <strong>exact </strong>value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta "> <mi>θ</mi> </math></span> 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>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span>.</p>
<div class="marks">[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>OAB is a sector of the circle with centre O and radius <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>, as shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>The angle AOB is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta ">
<mi>θ<!-- θ --></mi>
</math></span> radians, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 < \theta < \frac{\pi }{2}">
<mn>0</mn>
<mo><</mo>
<mi>θ<!-- θ --></mi>
<mo><</mo>
<mfrac>
<mi>π<!-- π --></mi>
<mn>2</mn>
</mfrac>
</math></span>.</p>
<p>The point C lies on OA and OA is perpendicular to BC.</p>
</div>
<div class="question">
<p>Find the area of triangle OBC in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> and <em>θ</em>.</p>
</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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{A\hat OC}} = 1.9{\text{ radians}}">
<mrow>
<mrow>
<mi mathvariant="normal">A</mi>
<mrow>
<mover>
<mi mathvariant="normal">O</mi>
<mo stretchy="false">^<!-- ^ --></mo>
</mover>
</mrow>
<mi mathvariant="normal">C</mi>
</mrow>
</mrow>
<mo>=</mo>
<mn>1.9</mn>
<mrow>
<mtext> radians</mtext>
</mrow>
</math></span>.</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="question">
<p>The following diagram shows the chord [AB] in a circle of radius 8 cm, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AB}} = 12{\text{ cm}}"> <mrow> <mtext>AB</mtext> </mrow> <mo>=</mo> <mn>12</mn> <mrow> <mtext> cm</mtext> </mrow> </math></span>.</p>
<p><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>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">
<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>
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