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<h2>SL Paper 1</h2><div class="question">
<p>A triangular field <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABC</mtext></math> is such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext><mo>=</mo><mn>56</mn><mo> </mo><mtext>m</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BC</mtext><mo>=</mo><mn>82</mn><mo> </mo><mtext>m</mtext></math>, each measured correct to the nearest metre, and the angle at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>105</mn><mo>°</mo></math>, measured correct to the nearest <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>°</mo></math>.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>Calculate the maximum possible area of the field.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>attempt to find any relevant maximum value<em> </em> <em><strong>(M1)</strong></em></p>
<p>largest sides are <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>56</mn><mo>.</mo><mn>5</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>82</mn><mo>.</mo><mn>5</mn></math><em> </em> <em><strong>(A1)</strong></em></p>
<p>smallest possible angle is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>102</mn><mo>.</mo><mn>5</mn></math><em> </em> <em><strong>(A1)</strong></em></p>
<p>attempt to substitute into area of a triangle formula<em> </em> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>56</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>82</mn><mo>.</mo><mn>5</mn><mo>×</mo><mi>sin</mi><mo> </mo><mfenced><mrow><mn>102</mn><mo>.</mo><mn>5</mn><mo>°</mo></mrow></mfenced></math></p>
<p><em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2280</mn><mo> </mo><mfenced><msup><mtext>m</mtext><mn>2</mn></msup></mfenced><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>2275</mn><mo>.</mo><mn>37</mn><mo>…</mo></mrow></mfenced></math> A1</strong></em></p>
<p><em><strong><br>[5 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>Iron in the asteroid <em>16 Psyche</em> is said to be valued at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8973</mn></math> quadrillion euros <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtext>EUR</mtext></mfenced></math>, where one quadrillion <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msup><mn>10</mn><mn>15</mn></msup></math>.</p>
</div>
<div class="specification">
<p>James believes the asteroid is approximately spherical with radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>113</mn><mo> </mo><mtext>km</mtext></math>. He uses this information to estimate its volume.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of the iron in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>×</mo><msup><mn>10</mn><mi>k</mi></msup></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>≤</mo><mi>a</mi><mo><</mo><mn>10</mn><mo> </mo><mo>,</mo><mo> </mo><mi>k</mi><mo>∈</mo><mi mathvariant="normal">ℤ</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate James’s estimate of its volume, in <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>km</mtext><mn>3</mn></msup></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The actual volume of the asteroid is found to be <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>074</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mo> </mo><msup><mtext>km</mtext><mn>3</mn></msup></math>.</p>
<p>Find the percentage error in James’s estimate of the volume.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>97</mn><mo>×</mo><msup><mn>10</mn><mn>18</mn></msup><mo> </mo><mo> </mo><mfenced><mtext>EUR</mtext></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mn>8</mn><mo>.</mo><mn>973</mn><mo>×</mo><msup><mn>10</mn><mn>18</mn></msup></mrow></mfenced></math> <em><strong>(A1)(A1) (C2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>97</mn><mo> </mo><mo>(</mo><mn>8</mn><mo>.</mo><mn>973</mn><mo>)</mo></math>, <em><strong>(A1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>×</mo><msup><mn>10</mn><mn>18</mn></msup></math>. Award <em><strong>(A1)(A0)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>97</mn><mtext>E</mtext><mn>18</mn></math>.<br>Award <em><strong>(A0)(A0)</strong></em> for answers of the type <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8973</mn><mo>×</mo><msup><mn>10</mn><mn>15</mn></msup></math>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><msup><mn>113</mn><mn>3</mn></msup></mrow><mn>3</mn></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in volume of sphere formula.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo> </mo><mn>040</mn><mo> </mo><mn>000</mn><mo> </mo><mfenced><msup><mtext>km</mtext><mn>3</mn></msup></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mn>6</mn><mo>.</mo><mn>04</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mo>,</mo><mo> </mo><mfrac><mrow><mn>5771588</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>,</mo><mo> </mo><mn>6</mn><mo> </mo><mn>043</mn><mo> </mo><mn>992</mn><mo>.</mo><mn>82</mn></mrow></mfenced></math> <em><strong>(A1) (C2) </strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mfrac><mrow><mn>6</mn><mo> </mo><mn>043</mn><mo> </mo><mn>992</mn><mo>.</mo><mn>82</mn><mo>-</mo><mn>6</mn><mo>.</mo><mn>074</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow><mrow><mn>6</mn><mo>.</mo><mn>074</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfrac></mfenced><mo>×</mo><mn>100</mn></math> <em><strong>(M1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution into the percentage error formula (accept a consistent absence of “<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></math>” from all terms).</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>494</mn><mo> </mo><mfenced><mo>%</mo></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>494026</mn><mo>…</mo><mfenced><mo>%</mo></mfenced></mrow></mfenced></math> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2) </strong></em></p>
<p><strong><em><br></em></strong><strong>Note:</strong> Follow through from their answer to part (b). If the final answer is negative, award at most <em><strong>(M1)(A0)</strong></em>.</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Three towns, <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 represented as coordinates on a map, where the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> axes represent the distances east and north of an origin, respectively, measured in kilometres.</p>
<p>Town <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> is located at <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>−</mo><mn>6</mn><mo>,</mo><mo> </mo><mo>−</mo><mn>1</mn><mo>)</mo></math> and town <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> is located at <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>8</mn><mo>,</mo><mo> </mo><mn>6</mn><mo>)</mo></math>. A road runs along the perpendicular bisector of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[AB]</mtext></math>. This information is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the line that the road follows.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Town <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> is due north of town <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and the road passes through town <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>.</p>
<p>Find the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-coordinate of town <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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>midpoint <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>,</mo><mo> </mo><mn>2</mn><mo>.</mo><mn>5</mn><mo>)</mo></math> <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>m</mi><mrow><mi>A</mi><mi>B</mi></mrow></msub><mo>=</mo><mfrac><mrow><mn>6</mn><mo>-</mo><mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mn>8</mn><mo>-</mo><mfenced><mrow><mo>-</mo><mn>6</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math> <em><strong>(M1)A1</strong></em></p>
<p><br><strong>Note:</strong> Accept equivalent gradient statements including using midpoint.</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>m</mi><mo>⊥</mo></msub><mo>=</mo><mo>-</mo><mn>2</mn></math> <em><strong>M1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong> </em>for finding the negative reciprocal of their gradient.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mn>2</mn><mo>.</mo><mn>5</mn><mo>=</mo><mo>-</mo><mn>2</mn><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>2</mn><mi>x</mi><mo>+</mo><mfrac><mn>9</mn><mn>2</mn></mfrac></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>-</mo><mn>9</mn><mo>=</mo><mn>0</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>substituting <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>6</mn></math> into their equation from part (a) <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>2</mn><mfenced><mrow><mo>-</mo><mn>6</mn></mrow></mfenced><mo>+</mo><mfrac><mn>9</mn><mn>2</mn></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>16</mn><mo>.</mo><mn>5</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1A0</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>6</mn><mo>,</mo><mo> </mo><mn>16</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math> as their final answer.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>A large proportion of candidates seemed to be well drilled into finding the gradient of a line and the subsequent gradient of the normal. But without finding the coordinates of the midpoint of AB, no more marks were gained.</p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates worked out the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> correctly (or “correct” following the value they found in part (a)) but then incorrectly gave their answer as a coordinate pair.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram below shows a helicopter hovering at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>H</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>380</mn><mo> </mo><mtext>m</mtext></math> vertically above a lake. Point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> is the point on the surface of the lake, directly below the helicopter.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>Minta is swimming at a constant speed in the direction of point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>. Minta observes the helicopter from point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> as she looks upward at an angle of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>°</mo></math>. After <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math> minutes, Minta is at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">B</mi></math> and she observes the same helicopter at an angle of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo>°</mo></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the size of the angle of depression from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>H</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></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 distance from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> to <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 distance from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</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>Find Minta’s speed, in metres per hour.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>°</mo></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AC</mtext><mo>=</mo><mfrac><mn>380</mn><mrow><mi>tan</mi><mo> </mo><mn>25</mn><mo>°</mo></mrow></mfrac></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AC</mtext><mo>=</mo><msqrt><msup><mfenced><mfrac><mn>380</mn><mrow><mi>sin</mi><mo> </mo><mn>25</mn><mo>°</mo></mrow></mfrac></mfenced><mn>2</mn></msup><mo>-</mo><msup><mn>380</mn><mn>2</mn></msup></msqrt></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>380</mn><mrow><mi>sin</mi><mo> </mo><mn>25</mn><mo>°</mo></mrow></mfrac><mo>=</mo><mfrac><mtext>AC</mtext><mrow><mi>sin</mi><mo> </mo><mn>65</mn><mo>°</mo></mrow></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AC</mtext><mo>=</mo><mn>815</mn><mo> </mo><mtext>m</mtext><mo> </mo><mfenced><mrow><mn>814</mn><mo>.</mo><mn>912</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>attempt to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext><mo>=</mo><mfrac><mn>380</mn><mrow><mi>tan</mi><mo> </mo><mn>40</mn><mo>°</mo></mrow></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>453</mn><mo> </mo><mtext>m</mtext><mo> </mo><mfenced><mrow><mn>452</mn><mo>.</mo><mn>866</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BC</mtext><mo>=</mo><mn>814</mn><mo>.</mo><mn>912</mn><mo>…</mo><mo>-</mo><mn>452</mn><mo>.</mo><mn>866</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>362</mn><mo> </mo><mtext>m</mtext><mo> </mo><mfenced><mrow><mn>362</mn><mo>.</mo><mn>046</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>attempt to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>HB</mtext></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>HB</mtext><mo>=</mo><mfrac><mn>380</mn><mrow><mi>sin</mi><mo> </mo><mn>40</mn><mo>°</mo></mrow></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>591</mn><mo> </mo><mtext>m</mtext><mo> </mo><mfenced><mrow><mo>=</mo><mn>591</mn><mo>.</mo><mn>175</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BC</mtext><mo>=</mo><mfrac><mrow><mn>591</mn><mo>.</mo><mn>175</mn><mo>…</mo><mo>×</mo><mi>sin</mi><mo> </mo><mn>15</mn><mo>°</mo></mrow><mrow><mi>sin</mi><mo> </mo><mn>25</mn><mo>°</mo></mrow></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>362</mn><mo> </mo><mtext>m</mtext><mo> </mo><mfenced><mrow><mn>362</mn><mo>.</mo><mn>046</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>362</mn><mo>.</mo><mn>046</mn><mo>…</mo><mo>×</mo><mn>4</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1450</mn><mo> </mo><msup><mtext>m h</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo> </mo><mo> </mo><mfenced><mrow><mn>1448</mn><mo>.</mo><mn>18</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em> </p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The Voronoi diagram below shows three identical cellular phone towers, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>T</mtext><mn>1</mn><mo>,</mo><mo> </mo><mtext>T</mtext><mn>2</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>T</mtext><mn>3</mn></math>. A fourth identical cellular phone tower, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>T</mtext><mn>4</mn></math> is located in the shaded region. The dashed lines in the diagram below represent the edges in the Voronoi diagram.</p>
<p>Horizontal scale: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> unit represents <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mtext>km</mtext></math>.<br>Vertical scale: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> unit represents <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mtext>km</mtext></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>Tim stands inside the shaded region.</p>
</div>
<div class="specification">
<p>Tower <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>T2</mtext></math> has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mo> </mo><mn>5</mn><mo>)</mo></math> and the edge connecting vertices <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> has equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>3</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why Tim will receive the strongest signal from tower <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>T4</mtext></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>Write down the coordinates of tower <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>T4</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>Tower <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>T1</mtext></math> has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>-</mo><mn>13</mn><mo>,</mo><mo> </mo><mn>3</mn><mo>)</mo></math>.</p>
<p>Find the gradient of the edge of the Voronoi diagram between towers <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>T1</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>T2</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>every point in the shaded region is closer to tower <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>T4</mtext></math> <em><strong>R1</strong></em></p>
<p><br><strong>Note:</strong> Specific reference must be made to the closeness of tower <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>T4</mtext></math>.</p>
<p> <em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>9</mn><mo>,</mo><mo> </mo><mn>1</mn></mrow></mfenced></math> <em><strong>A1A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong></em> for each correct coordinate. Award at most <em><strong>A0A1</strong></em> if parentheses are missing.</p>
<p> <em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct use of gradient formula <em><strong>(M1)</strong></em></p>
<p><em>e.g.</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>m</mi><mo>=</mo></mrow></mfenced><mfrac><mrow><mn>5</mn><mo>-</mo><mn>3</mn></mrow><mrow><mo>-</mo><mn>9</mn><mo>-</mo><mo>-</mo><mn>13</mn></mrow></mfrac><mo> </mo><mfenced><mrow><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced></math></p>
<p>taking negative reciprocal of <strong>their</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> (at any point) <em><strong>(M1)</strong></em></p>
<p>edge gradient <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>-</mo><mn>2</mn></math> <em><strong>A1</strong></em></p>
<p> <em><strong><br>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> have coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>1</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>,</mo><mo> </mo><mn>2</mn></mrow></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>9</mn><mo>,</mo><mo> </mo><mi>m</mi><mo>,</mo><mo> </mo><mo>-</mo><mn>6</mn></mrow></mfenced></math> respectively.</p>
</div>
<div class="specification">
<p>The line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math>, which passes through <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>, has equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">r</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>19</mn></mtd></mtr><mtr><mtd><mn>24</mn></mtd></mtr></mtable></mfenced><mo>+</mo><mi>s</mi><mfenced><mtable><mtr><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Express <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mtext>AB</mtext><mo>→</mo></mover></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Consider a unit vector <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">u</mi></math>, such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">u</mi><mo>=</mo><mi>p</mi><mi mathvariant="bold-italic">i</mi><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mi mathvariant="bold-italic">j</mi><mo>+</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi mathvariant="bold-italic">k</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>></mo><mn>0</mn></math>.</p>
<p>Point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> is such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mtext>BC</mtext><mo>→</mo></mover><mo>=</mo><mn>9</mn><mi mathvariant="bold-italic">u</mi></math>.</p>
<p>Find the coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>.</p>
<div class="marks">[8]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mtext>AB</mtext><mo>→</mo></mover></math> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mtext>OB</mtext><mo>→</mo></mover><mo>-</mo><mover><mtext>OA</mtext><mo>→</mo></mover><mo> </mo><mo> </mo><mo>,</mo><mo> </mo><mo> </mo><mtext>A</mtext><mo>-</mo><mtext>B</mtext></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mtext>AB</mtext><mo>→</mo></mover><mo>=</mo><mfenced><mtable><mtr><mtd><mn>8</mn></mtd></mtr><mtr><mtd><mi>m</mi><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>8</mn></mtd></mtr></mtable></mfenced></math> <em><strong> A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>9</mn></mtd></mtr><mtr><mtd><mi>m</mi></mtd></mtr><mtr><mtd><mo>-</mo><mn>6</mn></mtd></mtr></mtable></mfenced><mo> </mo><mo>,</mo><mo> </mo><mfenced><mtable><mtr><mtd><mn>9</mn></mtd></mtr><mtr><mtd><mi>m</mi></mtd></mtr><mtr><mtd><mo>-</mo><mn>6</mn></mtd></mtr></mtable></mfenced><mo>=</mo><mfenced><mtable><mtr><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>19</mn></mtd></mtr><mtr><mtd><mn>24</mn></mtd></mtr></mtable></mfenced><mo>+</mo><mi>s</mi><mfenced><mtable><mtr><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></p>
<p>one correct equation <em><strong> (A1)</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>+</mo><mn>2</mn><mi>s</mi><mo>=</mo><mn>9</mn><mo>,</mo><mo> </mo><mo>-</mo><mn>6</mn><mo>=</mo><mn>24</mn><mo>-</mo><mn>5</mn><mi>s</mi></math></p>
<p>correct value for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math> <em><strong>A1</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mn>6</mn></math></p>
<p>substituting <strong>their</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math> value into their expression/equation to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>19</mn><mo>+</mo><mn>6</mn><mo>×</mo><mn>4</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>5</mn></math> <em><strong> A1 N3</strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mtext>BC</mtext><mo>→</mo></mover><mo>=</mo><mfenced><mtable><mtr><mtd><mn>9</mn><mi>p</mi></mtd></mtr><mtr><mtd><mo>-</mo><mn>6</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mo> </mo><mi>C</mi><mo>=</mo><mn>9</mn><mi mathvariant="bold-italic">u</mi><mo>+</mo><mi>B</mi><mo> </mo><mo>,</mo><mo> </mo><mover><mtext>BC</mtext><mo>→</mo></mover><mo>=</mo><mfenced><mtable><mtr><mtd><mi>x</mi><mo>-</mo><mn>9</mn></mtd></mtr><mtr><mtd><mi>y</mi><mo>-</mo><mn>5</mn></mtd></mtr><mtr><mtd><mi>z</mi><mo>+</mo><mn>6</mn></mtd></mtr></mtable></mfenced></math></p>
<p>correct working to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> <em><strong> (A1)</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mtext>OC</mtext><mo>→</mo></mover><mo>=</mo><mfenced><mtable><mtr><mtd><mn>9</mn><mi>p</mi><mo>+</mo><mn>9</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mo> </mo><mtext>C</mtext><mo>=</mo><mn>9</mn><mfenced><mtable><mtr><mtd><mi>p</mi></mtd></mtr><mtr><mtd><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mtd></mtr><mtr><mtd><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced><mo>+</mo><mfenced><mtable><mtr><mtd><mn>9</mn></mtd></mtr><mtr><mtd><mn>5</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>6</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mo> </mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>1</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mo>-</mo><mn>3</mn></math></p>
<p>correct approach to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mi mathvariant="bold-italic">u</mi></mfenced></math> (seen anywhere) <em><strong>A1</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>p</mi><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mfrac><mn>1</mn><mn>3</mn></mfrac></mfenced><mn>2</mn></msup><mo> </mo><mo>,</mo><mo> </mo><msqrt><msup><mi>p</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>4</mn><mn>9</mn></mfrac><mo>+</mo><mfrac><mn>1</mn><mn>9</mn></mfrac></msqrt></math></p>
<p>recognizing unit vector has magnitude of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mi mathvariant="bold-italic">u</mi></mfenced><mo>=</mo><mn>1</mn><mo> </mo><mo>,</mo><mo> </mo><msqrt><msup><mi>p</mi><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mfrac><mn>1</mn><mn>3</mn></mfrac></mfenced><mn>2</mn></msup></msqrt><mo>=</mo><mn>1</mn><mo> </mo><mo>,</mo><mo> </mo><msup><mi>p</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>5</mn><mn>9</mn></mfrac><mo>=</mo><mn>1</mn></math></p>
<p>correct working <em><strong> (A1)</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>p</mi><mn>2</mn></msup><mo>=</mo><mfrac><mn>4</mn><mn>9</mn></mfrac><mo> </mo><mo>,</mo><mo> </mo><mi>p</mi><mo>=</mo><mo>±</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math> <em><strong>A1</strong></em></p>
<p>substituting <strong>their</strong> value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>x</mi><mo>-</mo><mn>9</mn></mtd></mtr><mtr><mtd><mi>y</mi><mo>-</mo><mn>5</mn></mtd></mtr><mtr><mtd><mi>z</mi><mo>+</mo><mn>6</mn></mtd></mtr></mtable></mfenced><mo>=</mo><mfenced><mtable><mtr><mtd><mn>6</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>6</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mo> </mo><mtext>C</mtext><mo>=</mo><mfenced><mtable><mtr><mtd><mn>6</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>6</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd></mtr></mtable></mfenced><mo>+</mo><mfenced><mtable><mtr><mtd><mn>9</mn></mtd></mtr><mtr><mtd><mn>5</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>6</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mo> </mo><mtext>C</mtext><mo>=</mo><mn>9</mn><mfenced><mtable><mtr><mtd><mfrac><mn>2</mn><mn>3</mn></mfrac></mtd></mtr><mtr><mtd><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mtd></mtr><mtr><mtd><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced><mo>+</mo><mfenced><mtable><mtr><mtd><mn>9</mn></mtd></mtr><mtr><mtd><mn>5</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>6</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mo> </mo><mi>x</mi><mo>-</mo><mn>9</mn><mo>=</mo><mn>6</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext><mfenced><mrow><mn>15</mn><mo>,</mo><mo> </mo><mo>-</mo><mn>1</mn><mo>,</mo><mo> </mo><mo>-</mo><mn>3</mn></mrow></mfenced></math> (accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>15</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math>) <em><strong> A1 N4</strong></em></p>
<p> </p>
<p><strong>Note:</strong> The marks for finding <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> are independent of the first two marks.<br>For example, it is possible to award marks such as <em><strong>(M0)(A0)A1(M1)(A1)A1 (M0)A0</strong></em> or <em><strong>(M0)(A0)A1(M1)(A0)A0 (M1)A0</strong></em>.</p>
<p> </p>
<p><em><strong>[8 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A piece of candy is made in the shape of a solid hemisphere. The radius of the hemisphere is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo> </mo><mtext>mm</mtext></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMUAAAB3CAYAAACzOoSOAAAMB0lEQVR4Ae2cvc4kxRWGuQ8LWWsIzIrARMaG1FpMaiGZ1AQQmgQCIxOZyEtmjGRCE5jIyEhGMpsYaXOjvQK4gd0raOuZj3e3vmJmvpmeOvXXb0mt7pnpqal66zznnKrunqcWFytgBa4p8NS1V35hBazAYihsBFYgU8BQZIL4pRUwFLYBK5ApYCgyQfzSChgK24AVyBQwFJkgtV/ev39/2bd99923tZvi3/teAUMRZAoPHjxYvvzy38uHH95d3n//j8trr/1mtz399I+WdLtz51ePP9M57G/f/um181588ee7895443e7Oj/55G87mB49ehTUg+1WaygKjD0AYKRvv/37BSPH6GXEAAEYigZrI4C+/9ln/9jVBxzAw28BEMf8DiAalMsG1VCs0E8QYJgYJJs8OMZb2yhpD7AAoKBkz2tDcv4AG4oTNcPwMDIigCAgOqz1/Cf+7OrTgCGFBGgBpzawqzvQ8IuG4oj4OQikRxjbaAVwAVhRxIAcH0FDkemDJ8WjYkBEhFFByLr1+GUKiPoH/C5PFDAU32uBsZBuYCgAsYVUAxiAnj4zUR8xCj4x5XJHm4cCGDAMVnHYM1HeWiE6snLFfIkNh7Dlslkochh47bLsgNg6HJuDAq9ImqTIYBj2uwKiheDYWvTcFBSswCh/Ngz7Ycjf3aJmm4ACT8fkGc+3Na+XG/ma12l0Ze7B65nL1FDkgznzQNboG6tVW3Au00JBRCAysNToVKksMkqpmJvNGDWmhEITaQbPJUYBHA1Rg222i39TQTHzQMWY9uW1MsdgJW8mBzQNFKRLum1hxpB+ufnG1TCb9lNAgZfCW239Smyc2d9cM45I6dToc7jhodC9O7PltTebYZ9nzDAew0KReianS30BMnrkHhIKAcFyq4HoCwi1hlR21JR2OCgEBGHapW8FSGlZ/BhtrjcUFBLZQPQNQ9q6EcdsGChY0dCSayq6j/tXQGCMci1jCCicMvVv+De1UGCMkEp1D4WBuMncxvl8FDC6h4ILQqwyucyhAFe/WZXq+XnwrqFgQg0UXnadAwj1ghSK+SGRo8fSLRRMyhDOQPRoNpe3SX+U0OP4dgkFoZUQ26snudwkXAMK8KdsPabG3UGhpdcRVils2pcpoEUUnn/pqXQHBXMIX5zryURi26IVqZ4m3l1BgcfwxDrWCHusXRPvXm457wYKLdV5HtGj2ca3qaf5RRdQkFvyJwOj3AYQbyLb+4WebKALKEibelyF2J5ptu2xHmttnUY1h6IXIdqag39dCrDI0tpBNoeCiTUXclysAAqQRnHRtuVqVFModFXT5mAFUgVYjWKOCSAtSjMo5BFIn1ysQK4AKVSrDKIZFD3kjvlA+HU/CrScazaBgtUF7m1qvcrQjwm4JfsUwHG2uLuhCRStOrtPeL/XrwKtnGd1KFp1tN+hd8uOKdDCgVaHokUnj4nuz/pWoIUTrQpFiw72PeRu3SkK1HakVaHgdg466GIFzlFAzrTWdYtqUPi6xDlm4HNzBWpet6gGBVcpuaXDxQqsUYDbPrjKXaNUgwIgtvSIKReftKUDyfMiXKlNt/Q+HyJq+hnH+S31pBOqm+OtFKBItYrqdxUo9MhhrZwwSizqxRhltMyPeDgmLbzmwiROgJDPlhpuCSj4fdXNzXP5nzxgOEo3BFXahrS9Ix3Tl1zviPZXgWKUCTbQyuj1jEfqpTEsBoXPZGw9PilIPwCDNsqQ0n7wOdDQFz4ngvfYj9zg0R8HEO1cq0BB2MPYeimIK+NPjUEeVkbPOTN42H260zdgEDS5BwYiPu9p3OgHMEen4eFQYGi1Jkj7Bj99j4FWuoG4GP+sRp/2e80xhgcojJ3SwWgPfUo71a5Tzl17TjgUGB5braLUgd/E8FOj5ziNDLXaNPrvoGkeMRRhcDQ1NaUt0SlUOBQ1UydAQDBgYNDygRzdOHtqPw4Gr81iA2NMBE4dUGRbo1cyQ6HAgyBWRNFEMh0IjnsI8RH97b3OPFoADFEkHZ9SfaDefA5Uqm7qCYWidOMRHs8EaHgL6nfpU4HIsYp0tuFQlF4pAAK2CO/Tp2nN0SqiOqltyXEjZcujUym1QiMF+f1aIbTKENXxUgK6nnUKAMkloJAxMG+MKGFQYMzQfE5hPgAMfI+NY5c5FcA+MGwcJ/tznZ+cZoQ6YVCsmU8QZplAsXfZhgJkElrePafHQBS1iBMGBfR7InzOMPvccxWIWgYOg4LVoWPXCSCdiXjk0tq5Ivv8PhRQFLhpzoD9RGQVYVCQKx4qdJbP2fu6wiGVtv0+DhXHynZovsFE/SZw1qgYAgUdOjTJJqU61tE1nfB35lUAoz80d2CyTbQoXUKgIKRFNLZ0513f2AoompTuRQgU0B0R1kp33vWNrYBuDizdixAo0gsrmjSVbrjr26YCOFvsS+WSC8SqI9+HQEHqRGgTEL4Il8vu12sVIDowJxUYsrW19e37XggUNFr5HisELlagpAJc8GPyrbkrtlayhEBBSPvqq//siC7ZWNdlBaSAgIhYlg2DQo333gpEKhCxqGMoIkfMdYcrMAQU5Hv7rmYzQfLV6ysbWXs7fbiFDfgD+WpUiS4UjxRMep599ifX2sbqE1e4S0+Irv3IQC9YMeGeL8Nx+aC9994flpdf/uXlFSU1FIfi88//udy69ePdTwABBkDkYDMUV8qnmuDpHEETizzzECheeOFnZ37r+OnFobh798/LM8/cevwAiYAwFE8GIoUCXfxA1RNtzj3C3vLM5Nw68vOLQ3Hv3r3lueeu/t80BcLHV9HykA6A4XQqN8+bX3/88V+XV165c/OJZ5xRHAp+m4HnanbuEZ0+XY1MqgsXoUihXNYpMMTqE13jirYe/mCPFwQUQ3E18IKCWxU8n1gHg76luyf0usQ+JFLsez4bog89LFKiI6fW8emnf19ef/23O0g/+ugvp36t6HloYQdxuaRoeOhZi0tqD4EC70djexv4t956cwfDBx/86RLN/N1OFCDiRqSeIVCgGY0ltPVS3n33neX5528v33zzv16a5HZcoIDS8oj0MwwK+gsUPdwl+8UX/9pFCFInl/EVYJVOd8lG9CYUCjW+9fMUpE0vvfSLhWihJdFW84mIQdxSnUSGaGcbCgWD1cODRqRNTK4fPny4sx/NLYggLuMoICD0gFFUy8OhoOECo8WfowEC0SGPDIBC5HAZQwGyDiJENBCoUQUKfggwuF7RYm0eAHIoXn311wsRw6V/BbT0Wmt+Wg0KpCf8sYwGHDWvWZA6saWFOUYOSvq5j/tQABCYVNecl1aFQjKTRpHSsGwbsaSm39H+66//ey2FAgag0BxD53nfjwJEB5wnKVPte8KaQIH0dFRRo4YXYFJNGgWMRA1fr+gHgLQl2AUpNtGhxRyUtjSDQkLoASQA6e0KuNrofbwCZAxkDsDQYt6Z9rA5FGoMXgFBgEM3E+oz7+dVgMigeQNjXztV2qdsN1DQOLyFIgf5JKDUmHPsE8bvxSpAVkBEIJ1l3wMM6nFXUKhR7IEDz6FwWnO1Km2Hj8spIKfH5JlxJUL0BIN62i0UamAaXoke5J09Cqn2ev9DBUiH+aMGogKOrsbCyg9bcfo73UORdgVxtTKBtwEQR5BUoT6OFRHSsSIVHsWZDQVFOuQpIEQQBoD3PAdJVap3jHPC8IkERASc1kggpEoNC0XaCQaEqMFAaEDIVw1JqlLZY0FAWsT8QHM/UqPRHdMUUKTDzYAAA1CkkBBJGDCnW6lapx2jKatFOB4tfgABQBANZtN0Oij2DbMGlEEk1dKED3AYVD4f3bvt6/ea9zBwnAoA7NMLxzLK3GBN//nOJqDIxUk9HxFEeTDej2NgwSgwDoCZrWDU9AuHIO+vqIrTQAPe32pk3SQUh4z8mLEouqTQYDgYl7ZD9dZ6X+2nPRg07WPD49NuRUnBj0Pg81nhX6u7oThDORm/PCwRBWNjk6cFHjYZnj7XXlFIBnvqXoatem76Tc5X3TL62dOeM4by6KmG4qg86z9MvbZgYi+gZLCn7mXYaV2zTXDXq132m4airJ6ubQIFDMUEg+gulFXAUJTV07VNoIChmGAQ3YWyChiKsnq6tgkU+D8U57H7xcMUHQAAAABJRU5ErkJggg=="></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the <strong>total</strong> surface area of one piece of candy.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The total surface of the candy is coated in chocolate. It is known that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> gram of the chocolate covers an area of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>240</mn><mo> </mo><msup><mtext>mm</mtext><mn>2</mn></msup></math>.</p>
<p>Calculate the weight of chocolate required to coat one piece of candy.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>4</mn><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><msup><mn>6</mn><mn>2</mn></msup><mo>+</mo><mi mathvariant="normal">π</mi><mo>×</mo><msup><mn>6</mn><mn>2</mn></msup></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><msup><mn>6</mn><mn>2</mn></msup></math> <em><strong>(M1)(A1)(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong></em> for use of surface area of a sphere formula (or curved surface area of a hemisphere), <em><strong>A1</strong></em> for substituting correct values into hemisphere formula, <em><strong>M1</strong></em> for adding the area of the circle.</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>339</mn><mo> </mo><msup><mtext>mm</mtext><mn>2</mn></msup><mo> </mo><mo> </mo><mfenced><mrow><mn>108</mn><mi mathvariant="normal">π</mi><mo>,</mo><mo> </mo><mn>339</mn><mo>.</mo><mn>292</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>339</mn><mo>.</mo><mn>292</mn><mo>…</mo></mrow><mn>240</mn></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>.</mo><mn>41</mn><mo> </mo><mfenced><mtext>g</mtext></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mfrac><mrow><mn>9</mn><mi mathvariant="normal">π</mi></mrow><mn>20</mn></mfrac><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>45</mn><mi mathvariant="normal">π</mi><mo>,</mo><mo> </mo><mn>1</mn><mo>.</mo><mn>41371</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>In this question, all lengths are in metres and time is in seconds.</strong></p>
<p>Consider two particles, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>1</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>2</mn></msub></math>, which start to move at the same time.</p>
<p>Particle <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>1</mn></msub></math> moves in a straight line such that its displacement from a fixed-point is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mn>10</mn><mo>-</mo><mfrac><mn>7</mn><mn>4</mn></mfrac><msup><mi>t</mi><mn>2</mn></msup></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>≥</mo><mn>0</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the velocity of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>1</mn></msub></math> at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Particle <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>2</mn></msub></math> also moves in a straight line. The position of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>2</mn></msub></math> is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">r</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>6</mn></mtd></mtr></mtable></mfenced><mo>+</mo><mi>t</mi><mfenced><mtable><mtr><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math>.</p>
<p>The speed of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>1</mn></msub></math> is greater than the speed of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>2</mn></msub></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>></mo><mi>q</mi></math>.</p>
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>recognizing velocity is derivative of displacement <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfrac><mrow><mtext>d</mtext><mi>s</mi></mrow><mrow><mtext>d</mtext><mi>t</mi></mrow></mfrac><mo> </mo><mo>,</mo><mo> </mo><mfrac><mtext>d</mtext><mrow><mtext>d</mtext><mi>t</mi></mrow></mfrac><mfenced><mrow><mn>10</mn><mo>-</mo><mfrac><mn>7</mn><mn>4</mn></mfrac><msup><mi>t</mi><mn>2</mn></msup></mrow></mfenced></math></p>
<p>velocity<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>-</mo><mfrac><mn>14</mn><mn>4</mn></mfrac><mi>t</mi><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mo>-</mo><mfrac><mn>7</mn><mn>2</mn></mfrac><mi>t</mi></mrow></mfenced></math> <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach to find speed of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>2</mn></msub></math> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mfenced><mtable><mtr><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mfenced><mo> </mo><mo>,</mo><mo> </mo><msqrt><msup><mn>4</mn><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mo>-</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup></msqrt></math> , velocity<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msqrt><msup><mn>4</mn><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mo>-</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup></msqrt></math></p>
<p>correct speed <em><strong>(A1)</strong></em></p>
<p><em>eg </em><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo> </mo><msup><mtext>m s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p>
<p>recognizing relationship between speed and velocity (may be seen in inequality/equation) <em><strong>R1</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mrow><mo>-</mo><mfrac><mn>7</mn><mn>2</mn></mfrac><mi>t</mi></mrow></mfenced></math> , speed = | velocity | , graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>1</mn></msub></math> speed , <img src="data:image/png;base64,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"> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>1</mn></msub></math> speed <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>7</mn><mn>2</mn></mfrac><mi>t</mi><mo> </mo><mo>,</mo><mo> </mo><msub><mi>P</mi><mn>2</mn></msub></math> velocity <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>-</mo><mn>5</mn></math></p>
<p>correct inequality or equation that compares speed or velocity (accept any variable for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math>) <em><strong>A1</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mrow><mo>-</mo><mfrac><mn>7</mn><mn>2</mn></mfrac><mi>t</mi></mrow></mfenced><mo>></mo><mn>5</mn><mo> </mo><mo>,</mo><mo> </mo><mo>-</mo><mfrac><mn>7</mn><mn>2</mn></mfrac><mi>q</mi><mo><</mo><mo>-</mo><mn>5</mn><mo> </mo><mo>,</mo><mo> </mo><mfrac><mn>7</mn><mn>2</mn></mfrac><mi>q</mi><mo>></mo><mn>5</mn><mo> </mo><mo>,</mo><mo> </mo><mfrac><mn>7</mn><mn>2</mn></mfrac><mi>q</mi><mo>=</mo><mn>5</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mfrac><mn>10</mn><mn>7</mn></mfrac></math> (seconds) (accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>></mo><mfrac><mn>10</mn><mn>7</mn></mfrac></math> , do not accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mn>10</mn><mn>7</mn></mfrac></math>) <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Do not award the last two <em><strong>A1</strong></em> marks without the <em><strong>R1</strong></em>.</p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A farmer owns a triangular field <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABC</mtext></math>. The length of side <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>[</mo><mtext>AB</mtext><mo>]</mo></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>85</mn><mo> </mo><mtext>m</mtext></math> and side <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>[</mo><mtext>AC</mtext><mo>]</mo></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>110</mn><mo> </mo><mtext>m</mtext></math>. The angle between these two sides is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>55</mn><mo>°</mo></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the field.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The farmer would like to divide the field into two equal parts by constructing a straight fence from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> to a point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[BC]</mtext></math>.</p>
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BD</mtext></math>. Fully justify any assumptions you make.</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#999;font-size:90%;font-style:italic;">* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.</p>
<p>Area<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>110</mn><mo>×</mo><mn>85</mn><mo>×</mo><mi>sin</mi><mo> </mo><mn>55</mn><mo>°</mo></math> <strong>(M1)(A1)</strong></p>
<p> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3830</mn><mo> </mo><mfenced><mrow><mn>3829</mn><mo>.</mo><mn>53</mn><mo>…</mo></mrow></mfenced><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup></math> <strong>A1</strong></p>
<p> </p>
<p><strong>Note:</strong> units must be given for the final <strong>A1</strong> to be awarded.</p>
<p> </p>
<p><strong>[3 marks]</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>BC</mtext><mn>2</mn></msup><mo>=</mo><msup><mn>110</mn><mn>2</mn></msup><mo>+</mo><msup><mn>85</mn><mn>2</mn></msup><mo>−</mo><mn>2</mn><mo>×</mo><mn>110</mn><mo>×</mo><mn>85</mn><mo>×</mo><mi>cos</mi><mo> </mo><mn>55</mn><mo>°</mo></math> <strong>(M1)A1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BC</mtext><mo>=</mo><mn>92</mn><mo>.</mo><mn>7</mn><mo> </mo><mo>(</mo><mn>92</mn><mo>.</mo><mn>7314</mn><mo>…</mo><mo>)</mo><mo> </mo><mo>(</mo><mtext>m</mtext><mo>)</mo></math> <strong>A1</strong></p>
<p> </p>
<p><strong>METHOD 1</strong></p>
<p>Because the height and area of each triangle are equal they must have the same length base <strong>R1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math> must be placed half-way along <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BC</mtext></math> <strong>A1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BD</mtext><mo>=</mo><mfrac><mrow><mn>92</mn><mo>.</mo><mn>731</mn><mo>…</mo></mrow><mn>2</mn></mfrac><mo>≈</mo><mn>46</mn><mo>.</mo><mn>4</mn><mo> </mo><mfenced><mtext>m</mtext></mfenced></math> <strong>A1</strong></p>
<p> </p>
<p><strong>Note:</strong> the final two marks are dependent on the <strong>R1</strong> being awarded.</p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext><mover><mtext>B</mtext><mo>^</mo></mover><mtext>A</mtext><mo>=</mo><mi>θ</mi><mo>°</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>sin</mi><mo> </mo><mi>θ</mi></mrow><mn>110</mn></mfrac><mo>=</mo><mfrac><mstyle displaystyle="true"><mi>sin</mi><mo> </mo><mn>55</mn><mo>°</mo></mstyle><mstyle displaystyle="true"><mn>92</mn><mo>.</mo><mn>731</mn><mo>…</mo></mstyle></mfrac></math> <strong>M1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>θ</mi><mo>=</mo><mn>76</mn><mo>.</mo><mn>3</mn><mo>°</mo><mo> </mo><mfenced><mrow><mn>76</mn><mo>.</mo><mn>3354</mn><mo>…</mo></mrow></mfenced></math></p>
<p>Use of area formula</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>85</mn><mo>×</mo><mtext>BD</mtext><mo>×</mo><mi>sin</mi><mfenced><mrow><mn>76</mn><mo>.</mo><mn>33</mn><mo>…</mo><mo>°</mo></mrow></mfenced><mo>=</mo><mfrac><mrow><mn>3829</mn><mo>.</mo><mn>53</mn><mo>…</mo></mrow><mn>2</mn></mfrac></math> <strong>A1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BD</mtext><mo>=</mo><mn>46</mn><mo>.</mo><mn>4</mn><mo> </mo><mo>(</mo><mn>46</mn><mo>.</mo><mn>365</mn><mo>…</mo><mo>)</mo><mo> </mo><mo>(</mo><mtext>m</mtext><mo>)</mo></math> <strong>A1</strong> </p>
<p> </p>
<p><strong>[6 marks]</strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABC</mtext></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AC</mtext><mo>=</mo><mn>15</mn><mo> </mo><mtext>cm</mtext><mo>,</mo><mo> </mo><mtext>BC</mtext><mo>=</mo><mn>10</mn><mo> </mo><mtext>cm</mtext></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>B</mtext><mo>^</mo></mover><mtext>C</mtext><mo>=</mo><mi>θ</mi></math>.</p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo> </mo><mtext>C</mtext><mover><mtext>A</mtext><mo>^</mo></mover><mtext>B</mtext><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>3</mn></mfrac></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>B</mtext><mo>^</mo></mover><mtext>C</mtext></math> is acute, find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo> </mo><mi>θ</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mo> </mo><mfenced><mrow><mn>2</mn><mo>×</mo><mtext>C</mtext><mover><mtext>A</mtext><mo>^</mo></mover><mtext>B</mtext></mrow></mfenced></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><strong>METHOD 1 – (sine rule)</strong></p>
<p>evidence of choosing sine rule <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>sin</mi><mo> </mo><mover><mi>A</mi><mo>^</mo></mover></mrow><mi>a</mi></mfrac><mo>=</mo><mfrac><mrow><mi>sin</mi><mo> </mo><mover><mi>B</mi><mo>^</mo></mover></mrow><mi>b</mi></mfrac></math></p>
<p>correct substitution <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mstyle displaystyle="true"><mfrac bevelled="true"><msqrt><mn>3</mn></msqrt><mn>3</mn></mfrac></mstyle><mn>10</mn></mfrac><mo>=</mo><mfrac><mrow><mi>sin</mi><mstyle displaystyle="true"><mo> </mo></mstyle><mstyle displaystyle="true"><mi>θ</mi></mstyle></mrow><mn>15</mn></mfrac><mo> </mo><mo>,</mo><mo> </mo><mfrac><msqrt><mn>3</mn></msqrt><mn>30</mn></mfrac><mo>=</mo><mfrac><mstyle displaystyle="true"><mi>sin</mi><mo> </mo><mi>θ</mi></mstyle><mn>15</mn></mfrac><mo> </mo><mo>,</mo><mo> </mo><mfrac><mstyle displaystyle="true"><msqrt><mn>3</mn></msqrt></mstyle><mstyle displaystyle="true"><mn>30</mn></mstyle></mfrac><mo>=</mo><mfrac><mstyle displaystyle="true"><mi>sin</mi><mo> </mo><mtext>B</mtext></mstyle><mn>15</mn></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo> </mo><mi>θ</mi><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></math> <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><strong>METHOD 2 – (perpendicular from vertex <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext mathvariant="bold">C</mtext></math>)</strong></p>
<p>valid approach to find perpendicular length (may be seen on diagram) <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <img src="data:image/png;base64,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">, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>h</mi><mn>15</mn></mfrac><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>3</mn></mfrac></math></p>
<p>correct perpendicular length <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>15</mn><msqrt><mn>3</mn></msqrt></mrow><mn>3</mn></mfrac><mo> </mo><mo>,</mo><mo> </mo><mn>5</mn><msqrt><mn>3</mn></msqrt></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo> </mo><mi>θ</mi><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></math> <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Do not award the final <em><strong>A</strong></em> mark if candidate goes on to state <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo> </mo><mi>θ</mi><mo>=</mo><mfrac><mi mathvariant="normal">π</mi><mn>3</mn></mfrac></math>, as this demonstrates a lack of understanding.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute into double-angle formula for cosine <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo><mn>2</mn><msup><mfenced><mfrac><msqrt><mn>3</mn></msqrt><mn>3</mn></mfrac></mfenced><mn>2</mn></msup><mo>,</mo><mo> </mo><mo> </mo><mn>2</mn><msup><mfenced><mfrac><msqrt><mn>6</mn></msqrt><mn>3</mn></mfrac></mfenced><mn>2</mn></msup><mo>-</mo><mn>1</mn><mo>,</mo><mo> </mo><mo> </mo><msup><mfenced><mfrac><msqrt><mn>6</mn></msqrt><mn>3</mn></mfrac></mfenced><mn>2</mn></msup><mo>-</mo><msup><mfenced><mfrac><msqrt><mn>3</mn></msqrt><mn>3</mn></mfrac></mfenced><mn>2</mn></msup><mo>,</mo><mo> </mo><mo> </mo><mi>cos</mi><mo> </mo><mfenced><mrow><mn>2</mn><mi>θ</mi></mrow></mfenced><mo>=</mo><mn>1</mn><mo>-</mo><mn>2</mn><msup><mfenced><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></mfenced><mn>2</mn></msup><mo>,</mo><mo> </mo><mo> </mo><mn>1</mn><mo>-</mo><mn>2</mn><mo> </mo><msup><mi>sin</mi><mn>2</mn></msup><mfenced><mfrac><msqrt><mn>3</mn></msqrt><mn>3</mn></mfrac></mfenced></math></p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo><mn>2</mn><mo>×</mo><mfrac><mn>3</mn><mn>9</mn></mfrac><mo>,</mo><mo> </mo><mo> </mo><mn>2</mn><mo>×</mo><mfrac><mn>6</mn><mn>9</mn></mfrac><mo>-</mo><mn>1</mn><mo>,</mo><mo> </mo><mo> </mo><mfrac><mn>6</mn><mn>9</mn></mfrac><mo>-</mo><mfrac><mn>3</mn><mn>9</mn></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mfenced><mrow><mn>2</mn><mo>×</mo><mtext>C</mtext><mover><mtext>A</mtext><mo>^</mo></mover><mtext>B</mtext></mrow></mfenced><mo>=</mo><mfrac><mn>3</mn><mn>9</mn></mfrac><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow></mfenced></math> <em><strong>A1 N2</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>A storage container consists of a box of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo> </mo><mtext>cm</mtext></math>, width <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>42</mn><mo> </mo><mtext>cm</mtext></math> and height <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>34</mn><mo> </mo><mtext>cm</mtext></math>, and a lid in the shape of a half-cylinder, as shown in the diagram. The lid fits the top of the box exactly. The total exterior surface of the storage container is to be painted.</p>
<p>Find the area to be painted.</p>
<p style="text-align:center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAdsAAAESCAYAAAC1nX9IAAAgAElEQVR4Ae2dT8ssx3WH8z2CUHAIjoVClokRDvbCCF9MSDDCljHYxARpEUJMguVs4pW1ir2zFpGXliFZxbEg3nhjgfYWRvubfIHrTzDhmZtzVW/fnun/1fXnKXjfnpnurq56Tk39qk6d7vm9i0kCEpCABCQggUMJ/N6huZu5BCQgAQlIQAIXxdZGIAEJSEACEjiYgGJ7MGCzl4AEJCABCSi2tgEJSEACEpDAwQQU24MBm70EJCABCUhAsbUNSEACEpCABA4moNgeDNjsJSCB+gh89NFvLi+88PvXvydPnlwr8PLLL13fs8/UB4E333zjavN33vnx5gortpsRmoEEJNAaAcV2nUXffvsHF/7uJYQLEashKbY1WMkySkAC1RIYE9tqK5Op4CFM98QWocVj8OjRlzKVattlok7ObLdx9GwJSEACVwKIKwKAEOAuRjCm3MiPHz++vP76154dx/F0zuF2JuM0X/J///1fPDue4+I9++L6IVZ08OG6Ju9XXvns5b33fvrMYrHvrbe+++xc8iBfjovyU8ZbKa5PXiGEnMc51C9Nw/Jw3UgpL84nv2GKa0W52MKHxDZlGayGeaTvh+UZ8uFYrhlco16pfabyGBNb2AZ78iSPOUk38hxKHiMBCTRLAFFJO89UDHgdnXMcEwKRduLpOSFCnBfnxP70PfvHBIjOe+zzyCNEMM0r9rFFdNL3vL4lCPeuk4o0dRrmyXsYkLaI7T3+6eAibYD3yh32+eCDX98t8708gvFQbNNBTMojBkhpGYevFdshEd9LQAJdEUCI6DgRqehkU3G5JbZDSHEOHTRpLN/ovLneUGwRB1KU4frm///xWXTuISYhtiGKcT2OC3GN2WKUKc2T16ngxDmRD/mTuF5cO8SPz+L6cV7U7Z7wRN4h0uQf51HWYB2fYZOxNJbP8Lhh3ck7BiLBOj1njHGUI+oY5wcHzoFDsErzG75WbIdEfC8BCXRFIDrUVCTSjjcEIMQlxA5IiBXnRR6IEq9J8dm9fEPsbokK5/IXnTz5x/WjPOQRZQlRjDJzblqm64HJv7h+KhYxI4zPQthC1OP0GFywJY3VN46NbeSVim3UIxXAlD+vhykVTuoHH+oaLDg+8k0/G+bD+3uMo06Um2sG37FtWv6x6yi2Y1T8TAIS6IZAdKh0upHSzj6EKzrvELuYOXEen7FNhW1OviF2qfhQhvicaww7+rh+lCfEJM7h80jDMsXnsR07h/ypR+QTAlmS2Eb5KRt1TAcjMesc8olzYht1v8c4bDi0wZjYhh0i/+FWsR0S8b0EJNAVgRATOuyYRUUnS6c6Jrbp7I/9/CGYqdjOyTc6/KHYpkKOMSIv8s8ttlFXrh1CRhlCzOKzEHa2t9JYfaOubIN18Mcmc1PMtDmXlObL+9RGlDn2R3nHGEc52EcKUY/31w9n/lNsZ4LyMAlIoE0CdMIhHAjK8C8EII5BaNKZbxwf++nESWP5xjGcw/4x8eHcEI7Im22cG+7KeB8zqsiLzyOFAIYAxeexHTtnOLPl2BCmtDy8TgcJca0oa1wj3cb1Ih/qkop5fB7bEPI0D16nwhjHxjaE8Fa+IeBzGA/F9tZ1I89hOdP3im1Kw9cSkECXBBCYmJkiVqlwjIktkBCC6OARozGRQlxiNsQxqQDcE1v2pQJHJx9lCjHJKbbUl+vGNal3rNVGg2EAEnW9Jz5pvWBGYpt+ji1gdy9Rnrge5eF1sInzyCPsyjFcI7wXcxgPxZZ8hxzSPOO6Y1vFdoyKn0lAAhLYSIBOOcQ4hCM+S2efGy/j6ZUQUGwrMZTFlIAE6iIQM90Q3HR7y61bVw0t7RICiu0SWh4rAQlIYAGBoRsTwR26Xxdk56EVE1BsKzaeRZeABCQggToIKLZ12MlSSkACEpBAxQQU24qNZ9ElIAEJSKAOAoptHXaylI0T+K//+vnlhz/818t3vvMPl9de+8qzKNY0qCZev/TSH1+P4dif/OTdy29/+9vG6Vg9CdRPQLGt34bWoFICv/rVry5f/vKjy6c+9QeXF1984SqgiOeHH354+d///Z+btWIfx/zoRz+8fPvbf3P58z//swsCjPj+8pf/ffM8d0hAAucRUGzPY++VOyTwu9/97vIf//Hvz2avX/jC5y/vvvtvm0kwu0WoX331i8+E1xnvZqxmIIHdCCi2u6E0IwncJsCMk1kormC2CC7Ce0Ri5vv97//LVXRxSTMLNklAAucSUGzP5e/VGyaAyOHaxcXLjJOZ5z338N4oEHOuiZtZ0d2brvlJYBkBxXYZL4+WwF0CuG6ZVSJw/H3rW9+8fPzxx3fPybGT9V1En1l1TsHPUTevIYEaCCi2NVjJMhZNAPEaWy+NWW0p4sZMN9zLiK9JAhLIR0CxzcfaKzVEYBjoxIwxIoHZh9uYP16Xlph9R/lKGQiUxsjySGBvAort3kTNr2kCaaAT66DDQKcQWma1padwLVMHkwQkcCwBxfZYvubeAIG5gU41CW2YhbrFPbrxmVsJSGB/Aort/kzNsQECw0An1jqn7ltlNlvDjHZonhgklOr2HpbX9xKokYBiW6PVLPMhBMYCnXq6R5WBAhHUU4OKQ+CbqQQaJ6DYNm5gq3efALO69IlOaaDT/TPb3EtUNW5lBbdN+1qr8wgotuex98onEpgKdDqxaKdfmsEHgtvTrP506BageQKKbfMmtoJBgNkarlKEhPXJ3E90inLUsEVwebSkkco1WMsy1kBAsa3BSpZxNQHWYdMnOs0JdFp9scZODMHVpdyYYa3OKQQU21Owe9EjCeQIdMINXWPk8VLu4VJWcJeS83gJPCSg2D7k4btKCUSgEwFO8cs68USnvavEtYjaPSr/vcu7NT8FdytBz5fA5aLY2gqqJhAzTAR27IlOR1SOJy9xrZ4SdWaAwUDDJAEJLCeg2C5n5hknEzgz0Amx6TVSF7c5gWUmCUhgOQHFdjkzzziBQCmBTszwelirvWVixLbn+t/i4ucSmCKg2E4Rcv9pBMYCnc5cJ41ZLeXqNQUDbwnqtQVY77UEFNu15DzvEAJ05nTkaaBTKR07Qt/bWu2YkXHjs0ZuhPIYHT+TwDgBxXaci59mJpAGOuGqRGARXlOZBHggiAFTZdrGUpVJQLEt0y5dlCoNdKLj9olOdZkd74Prt3XZzNKeR0CxPY99l1cuJdCpS/g7VzrWb89cR9+5SmYngcMIKLaHoTXjIFBaoFOUy+12Aggtt0Lp8t/O0hzaJqDYtm3f02pXcqDTaVAavTDuZP5MEpDAbQKK7W027llBwECnFdAqP0V3cuUGtPhZCCi2WTC3fRECnfg1HdyJrQU6ISTUyXSfANHjRiffZ+Tevgkotn3bf3XtWYeN5+XSybb603Vxz+9qUB2dyD3ItAmTBCTwPAHF9nkmfnKDALM8bs/hPlhmsdz20XokKnWkzqZpAgzAeNgFW5MEJPCQgGL7kIfvBgR6D3RiUOGTkgaN4s5bPBwGS90B5K5uCSi23Zr+fsUj0Amx6fWJTogs9TfNJxDBUh9++OH8kzxSAh0QUGw7MPLcKrYc6DSXQXqc67UpjfmvWbf1GdLzeXlkHwQU2z7sfLOWaaATs7hWA51uArizg/VaA37uALqzi6C51tfz71TfXRJ4joBi+xyS9j/oMdBpjVVxhRrss4bc5fpDEt4ytY6dZ7VJQLFt067P1epWoBOfmyRwBAHEFle8SQISuFwU28ZbwTDQidtYFNjGjV5I9RBagutMEpCAYttkGxgGOrHuqDu0SVMXXylmt0YmF28mC5iBgDPbDJBzXMJApxyUvcZSAnhSjExeSs3jWySg2FZsVQOdKjZeJ0WnjfpgkE6MbTXvElBs7+Ipc2fc/8mj8XhaD+9dhy3TVpbqcr2djNuoTBLomYBiW4n1DXTKaygGMT6mcR/mLHEwMHRAuA9Pc6mTgGJbsN0i0IkgE/4MdMpnLMTBtB8BBi/+oMN+PM2pPgKKbWE2YxZAp4S4+kSn84yj2O7LHs8MbdokgV4JKLYFWB73WtyTiMD28NN1BWC/WQQGPJ/5zKdv7nfHOgKIrbcBrWPnWfUTUGxPtKGBTifCH7l0eBW+8IXPX9cYuWXF5/uOgFr5Ec/dNlBqJTxPq56AYpvZhAY6ZQY+83KIQER3YyNeMxhiNsYfQmzaRgCGeG5MEuiRgGKbweoGOmWAvPES2CiNlk3XbL21aiPc5HQe36i3IAHiy24IKLYHmTpcksyKYh3WW0kOgn1AtqnYHpB9t1kS/EdkskkCvRFQbHe0eBroRGdtoNOOcFdmxaBnzVqhYrsS+MRp2AO2qRdh4hR3S6AJAortDmY00GkHiDtmEV4FXJbhVTgyCjbW4bmuaZqAruRpRh7RHgHFdqVNo4OlM6fzwD1mZ7sS5g6nhVcBFyUzJ7a51gaxO7Nn2gLXPVLYd0B1ehZ8V4xKPt0MFiAzAcV2AfBhoBMdrAK7AOCBh2IbbtU5M5gJwecpX4guZVF0xw2OrWBkkkBPBBTbCWsjpukTnRiRG+g0Aa3z3YhutBkC5HLNsGvCDhe/RzVZzLJuJaDYjhAMlyTuYQOdRgCd8BGDHuxSW2KmzWzX9JAAXiG5PGTiu7YJKLaJfZmBpGt+Z7okk2J1+zK8ChHo5AyxnaaALbGrSQK9EOhebFlXwzVsoFMZTT68CsNBTxmlsxR7EcDO3gK0F03zqYFAl2LLWhFuLNaN+DPQqYymiluRDpgZT09ehV4j2bGz3ooyvnuW4ngC3Yjt0CVpoNPxjWvpFeh4sVMJCdHPlWiLERvQUwSz67a5WpjXKYFA02IbLkluw4jOzJF0Cc2u/DLkFFto0FZ7u22I7yLfTZMEeiDQpNjyJR6u+dGZmc4hEF4FZjK1pNxiG1xCdFneCHd67GttS13P4twaS+tTPoFmxNZAp7IaGx0p667poKcmr0IJIgA/RLcU1/oRLYz6eb/tEWTNszQCVYvtWKCTX9xzmxiCGmuQMTOr0atQgtiea8k8V2cwxqDCJIHWCVQntuGSpCPndh069p6CSkpukAgtM5UWomsV2zwtjXXqmpYX8lDxKi0SqEJswyX5l3/55esaz1//9V9d/umf/vEaUMKXFbHlz1lti030nDrVIra0+ZrdzHxvDZI6p4171bwEihZbZkrf+tY3rwJL5/dHf/SHF4SWLycz2hgV854/ZlUcx6yX/S3MsPI2h/tXq9EdfL9Gt/fWIra4YCkr7b3GwSYDBX+U4HY7dE87BIoTW0a6dBzxRKd//ufvXX7+8/9c9Fxc8kBoWQ8iH0TYB1esa7ThVYhApxo79DU1r0VsqRuCVfNtQ7DuaSC3pj16Tv0EihFbRujMSBFGOo49XWMRtIPwMgM2IGO64abMag50mq5pO0cgWKnoYsMaEt9JBsgmCbRM4HSx5UsWInu0CMYsDUHn7+jr1dhw8ACEN0A3fI0WfFpm2nZ4dEqvRSz5lF5OyyeBLQROE1uELzp2OvXcCZGPdV5F9xP6sOjFVfxJrdt9VYN7ltk4fyYJtEzgFLGlM2fUjdjt6S5eYyhcbVEWRWYNQc+RwDYCDPCICTBJoGUC2cWWLxYBEWfMZu8ZMta6mG3XMBu4V5exfeFCL437WFn9LB+Bswe71DS8TPlq7ZUkkJ9AVrENQSs1GIKOh9k2a8itzHLHAp3yNzOvWCIBBmBx29CZohuerhIZWSYJ7EUgm9jG7Tw1iBizvxJn33ONDuNYD8dFziDnzM50brk9Lj8B2kW0FVy5Zw2E+b6ZJNAygSxii9DS6dfU4cdom7LX5FbGTU80MR1oDQOblr9cNdWNNh6epzNuxVFsa2otlnUNgcPFNjr/Gjt+OqBwK9ckuGsaguc8JNBr5087x7PD4Ji/XKm2wXguLl6nHQKHii3rhcyyahTa1MQ1ucDTcvt6PYFexTYllvOhGGfMptO6+loCRxM4TGwRWIQ25xf2SFiM9s8cOKSBTrUPXo600155K7Z7kZyXj2I7j5NH1UvgMLElopc1oJZSbpc4ohrBK7jZDHTK15oU23ysuZJim5e3V8tP4BCxRSAQ2xZTDsGNNTMDnc5rQYrtNHuWV/jbI/BRsZ3m7RF1E9hdbMN9vMcXsFS0RwsuM9hW3O+l2nCqXIrtFKGnvzaE2MKK7ZbbhhTbad4eUTeB3cW2RffxmImPFtyxa/pZPgKK7XzWe9w2hFjj0TFJoFUCu4otX5ZW3cdjDSAEd8ksnhmrs9YxmmV9ptgut0eILvEF9ANLZrp4c1qL8VhO0DNaJrCb2PJFY41xyResBbCMyOlYqP+tFIFOdEL8OYK/RaqczxXbbbZgILokap44D8V2G3PPLpvAbmLLF4V1lx4Tj7kb1p3ZroFOPbYG67yGAN8fPT5ryHlOLQR2EdteZ7VhZOrP7JbROYlRfQSN2IEEJbcSuE3AAKnbbNzTBoFdxLbnWW00A2ay8RAPxPeeWznOcSuBXgnwfWEJJuIdFNteW0I/9d5FbHtcqx1rIsxiYREdyNgxfiYBCVyug1HENjxAjx59qbt4D9tBXwQ2iy0u014ikNNAp1uC2vIDPfr6aljbHAQ+/vjjyze+8fXLiy++cPnZz36W45JeQwKnENgstrh/ENxWE6KaBjoxGp+KsmTwYWRlqy3Cem0lwBILfQaBhcxs2X7+83/hzHYrWM8vmsAmsUWIcJu2uD4ZM/Zwcy0JdEKMda0X3e4t3AkE+A4xWOW7wYCU71j0Ha7ZnmAQL5mVwCaxxWXKl6fFRL3SzmBpHWM2HJ3J0vM9XgItEIilFwT23o9pKLYtWNs63COwSWz58iyZ8d0rSIv76EB0J9dpWTwapnUE8HjR7ukfEFkG5VNLL4rtOtaeVQ+B1WIbrtJ6qvpJSSl7jidd0enQaU91NJ+UzFelEFBsl1kCDw7eHNzDCCyeoSUDccV2GW+Pro/AarFl5FqTCzkCnaIzyDXj5Dp0JKa6CCi20/ZCYIeBTmuXXhTbad4eUTeB1WKLaC0ZuZ6BKToDvsh0nktH23uVGXcanZCpHgKK7W1bDQOdmNFujU1QbG/zdk8bBFaJLV8sOqOtX7AjESJulJHbCtaOtvcqHy5rXGsl89qrrq3ko9g+tCRLIay9TgU6PTxr/jvFdj4rj6yTwCqxZWTLl6PkhLDhOi4lwSuX67qUOtdcDsX26Y/D02aXBDqttbliu5ac59VCYJXYMsJVOJaZOIKlShoALKtBX0f3KrYMUvEERWxDrqUXxbav71ePtV0ltnwxzlqvTQOdanPL0nHVFFTW4xci6tyb2CKw6ROdci+9KLbR8ty2SmCV2NIR5RS6GG3zheTadApnif2WhuDsdgu9vOf2ILZHBDqttZJiu5ac59VCYLHYEijBGk6ORGcQo22+jLlH20fUseWnbh3Byzz3JRCBTnyH+WM5qISlDcV2XzubW3kEFottuJtyVIUvILcVlNAZ7FVfZunMmlqq015szOcYArS1eHzo3Cc6HVOS27kqtrfZuKcNAovFlpGwwVHbjO/a7TZ+nj1NIJZecgc6TZds/AjFdpyLn7ZDYLHY8qXYY72U0Xavszvq7ey2nS9RSTUJz1PENtSy9KLYltSKLMsRBBaLLSPltc8VjtE2Xyw6g55nyMxuWb81SWArgbFAp9oGsort1lbg+aUTWCy2iOTS1GKg01IGw+MJVPGpUkMqvp9LYBjoxMCtNoFN66rYpjR83SKBRWIbwT1zQeDCQlCYDbcW6DSXwb3j6GBgZJLAHAKIaRrohHcE0W0hKbYtWNE63COwSGxxH/OlmJvoCFrpDObWeclxCG2u26iWlMtjyyEQSy8MWPEqIbB7xEyUU8OnJVFsS7OI5dmbwKFiu3dhW8wPsV27Bt4ij1LqtGa5ZM+yMxCLe8zZ8h7hbTUptq1a1noFgUViiwuLkXWMtukETNsIECQGU1NZBM4Q2xYCndZaUbFdS87zaiGwSGz//u//7vK5z71ydWfx5Wh9tJ3DiHEbUMuzlhwc975GLrFtLdBprR0U27XkPK8WAovE9qtffe0qtG+88bdVRz6WZpwYuJRWrp7Lc6TYthzotLbNKLZryXleLQQWiS0uz3i2L1HGuD9db9xuajwEBMCYyiGwt9jG0guiQt6tBjqttaBiu5ac59VCYLHYxoMo6Dx4jej6RdlmbljSAdd8n+Q2AuWdvZfYpveY9xDotNaS9iFryXleLQRWi21UMESXqFpmZ8zSTMsJ0BETgGYqg8AWscXbw8zVe8zn21Kxnc/KI+sksFls02ojtIguf4puSmb6ta7kaUY5j1gqtgY6bbOOYruNn2eXT2BXsY3qIhx8eRjZ42pm9mu6T0BX8n0+uffOEdsIdMKjEzEMPsRlnaUU23XcPKseAoeIbVQ/njil6AaR+9tY07t/lHtzELgltgyKYjDJMQY67WMNxXYfjuZSLoFDxTaqzWifTik6JwOBgszDLZ24Dwp5yKSUd2mgE8KArfTY7GcdxXY/luZUJoEsYhtVR2RT0dXlFmSebuFza0b18Ejf5SBgoFMOyk+vodjmY+2VziGQVWyjiswIvG0oaDzcsv7nvcsPmeR8Nxbo5KDweAsotscz9grnEjhFbKPKQ9HFNdd74qEh/qh83lYwFujkgCevDRTbvLy9Wn4Cp4ptWl2E1tuGLtefT/NpUmnLOOb1MNCJtfIWf7ruGHr756rY7s/UHMsiUIzYBhZEF7FBeHnIQ29BKNSXddve6h32P3proNPRhNflr9iu4+ZZ9RAoTmwDXc+3DbluG61gn62BTvtwPDKXe2L75MmTy+uvf+06CGUg+vbbP7hblEePvjR5zN0M3CmBAwgUK7ZR17SjJJK5h9uGWLONZ1AHB7fLCNBO4BhLE7xeEuhkVPgy3luPvie2b7313cvjx4+vl3jvvZ9eRZftWHrnnR9f908J8ti5fiaBIwkUL7ZReTrP9LahlkUXVyedj2kZAdoESw94BuKJTmsDnRTbZey3Hn1PbId5v/LKZy+I6jAhyAjzyy+/5Mx2CMf3pxOoRmyDVMxY6EyXfEHj/Bq21JH6maYJRKATAU4I5F6BTortNPs9j1jyXUZscS0P05tvvnH9XLEdkvF9CQSqE9uARifb8r26iG3Ls/ew49ots//wdNBR7/VEpxBvxXatZdadN0dsP/roN9e12zEXMjPd99//xfXiiu06G3jWsQSqFdvAEp1jrM21cq8unY+3ooSVn25Zc0VgGYjgKsZlvNeAJI0NIG/EljbVSnt6SLK8d1Nii5Bik/gLYaUmiDDu40iKbZBwWxKB6sU2hUnHmIouQlxrYtZukNTlKqZbAp3m2j94p+JNe0IEEPclwVVzr+lxnxCYEts4khks0ca4kiMRqZwmxTal4etSCDQltgGVWUp0knSiNYouHX2vP0qA4O0V6BRtYsuW9lRjG9pS59znzhVbykWkMYJKGs54Y+YbW2a9JgmUQKBJsQ2wqegyO0pnLXFMqVvKjjuzlxTLAXsHOsGPvHXJl92Slogts9vhbDatnTPblIavSyHQtNgGZEQ2gmnY1iK6jM5bT2mgE4MLZvR7zCKH4o3dTeUSmCu23N6DG/mDD359szKK7U007jiRQBdiG3xDdFmDo/Nl9lhyajUiOQ10Yo19z0CnEO80iGoP8b7XTmJtt/T2dK8OZ++7J7aIZ7iFmdFOuYYV27Ot6fXHCHQltgGAzpe1XDrke1/yOP6sbcllW8qEgc6RgU4IeATHYduc3gvaEwOGuD7ia1pGoKW2vqzmHt0LgS7FNoybdpLhwox9JWxZv6y540bwhoFOR62dYssSIoaxVyq6lMs0TUCxnWbkEXUT6FpsU9MNO8l031mv43aUs66/5rqICyzTQKeaBwxrGHAOgwoEBO8JAw7TfQKK7X0+7q2fgGI7sCHCEJ3k2bcN1SS2sVbK2lp4Cfaa1YV417gmSpmPms0Pmm7VbxXbqs1n4WcQUGxvQKKTPFt0Y3Z0o4inf9xaoNPpQDsugGLbsfE7qbpiO2HoEBRmbLlvGwrBnyhi1t2swzLjjnXJpT9dd6+wsE6DqLhOzkCne2Vz37EEFNtj+Zr7+QQU25k2oNNHbEN0cwTjlCK2uINzBDrBl78cbGeaPcth1Ll3V7Nim6WpeZETCSi2C+EjPMy4ctw2hMBznTOSgU75qLMmHZ6CHoPJIK3Y5mtvXukcAortSu5D0T2qk2QmnTNFoBMiv3egU28z1qV2ow3BHOFlQEcb6yUptr1Yut96KrY72P7ImUkOsY21UgSWjh6X8V5rpal44y41TROI5QPs0YvoKrbT7cIj6iag2O5ov3RmgmDtMTM5SmwRUzrycF8eGehE3nuJ947mKj4rRJcBSg/sFNvim6MF3EhAsd0IcOz0PWcme4ot4n9koBMzZMSbGVmPgU5jbcHP5hFQbOdx8qh6CSi2B9ouZiYhPmtmKFvFFoFlxj18otMes+4hOurXe1TtkInv5xFQbOdx8qh6CSi2GWyHCDHTQziXugXXim26VkrQzV5u7Qy4vMQCAngTGEzVnhTb2i1o+acIKLZThHbcj+iyfslMd27nskRsh4FOrMmumU2PVTlm6VzDVA4B7BLr7jWL7tzvQznkLYkElhFQbJfx2uVoXLgI4RzRnRJbxDQCncjv6ECnI9zPu0DtPBM8GQgWbYD2UJudFNvOG3AH1VdsTzQyHSKzkXszkzGx5byjAp0Q72HezmZPbCQLL50G59UUBa7YLjS0h1dHQLEtxGRD0Y2ZSYhtCPPRgU4IP+vKBjoV0jBWFoNBE3bkr4ak2NZgJcu4hYBiu4XeAeemMxPcgYgtHSbuQQOdDgBulkUQUGyLMIOFOJCAYnsg3C1ZI7oxi0V09wp0ihnzlrJ5rgT2JqDY7k3U/EojoNiWZpFBecKNPPh40duIUsZFjICbJBAESlkuUGzDIm5bJaDYFm7ZtWI7Fi5dx7kAAAwMSURBVOjEbNkkgSCAlyOC886+D1uxDau4bZWAYlu4ZZeKbaz5ch6z2FJmLoVj7rp40WbOvG1Ise26CXZRecW2cDMvFVtmtEQ2uzZbuGELLF7ECSC6BOXtFScwp6qK7RxKHlMzAcW2cOstFdvCq2PxKiCAyCK2tL1cgzbFtoKGYRE3EVBsN+E7/uRUbCPQKeeM4/gaegUJXGY/vlRWEqiVgGJbuOUQ2+ETnRTbwo1m8RYTcGa7GJknVEZAsS3QYLjuWHelA0JsDXQq0EgWadc1XcXWBtU6AcW2QAsToELng+CmbuQCi2qROibAs5e5dWiPHz5QbDtuSJ1UXbEt3NCKbeEG6rx4w9uG1i5xKLadN6QOqq/YFm5kxbZwA1m8KwGC9yKCec1tQ4qtDal1AoptJgsz4o9ApyWPTFRsMxnIy+xCgHYeossyyNyk2M4l5XG1ElBsD7RcBDohrojmmkAnxfZAA5n1YQRo+0tcyortYaYw40IIKLYHGCJ1qdGJbHmik2J7gIHMsjgCim1xJrFAOxNQbHcGSnYEjeAyXjKyv1UMxfYWGT9viYBi25I1rcsYAcV2jEpBnym2BRnDouxGgIFo+sMHiu1uaM2oUAKK7ULD0Enk/DkyxXahgTy8GgLpDx/86Z/+ydUjVE3hLagEFhJQbGcAGwt02sNFPOPSPtRiDiSPqZJAPOv7M5/59IU/3psk0CoBxfaOZfkt2LiN4dVXv7gp0OnOZe7ucmZ7F487KyPAIJUnTvHkKdzIPIVKka3MiBZ3FQHF9gY2OgI6hL0CnW5cZvJjxXYSkQcUTgDPUNxjzveKASwDWZMEeiKg2N6wdi438Y3LP/tYsX2GwhcVERhbetlyC1xFVbeoEhgloNiOYinnQ8W2HFtYkmkCsfTCDPaspZfpUnqEBPIT6Eps09E2rqwakmJbg5X6LmMEOpWy9NK3Nax9qQS6ENsYbSNctY22FdtSvzp9lysNdCK2wUCnvtuDtZ8m0KzY0hnQAdQ+2lZspxuxR+QhYKBTHs5epU0CzYots9kWRtuKbZtfvFpqlS690Bb5MY0lv+ZTSz0tpwSOJtCs2B4NLlf+im0u0l4nJRBLLwY6pVR8LYH1BKoU2xhtr692PWcqtvXYqvaSEuhE4GDtSy+128Hyt0mgKrEdjrZLuRf2yKah2B5J17wjtoEgJwOdbA8SOI5A8WLb+20Fiu1xjb/XnBFYn+jUq/Wt91kEihZbRtq4tFoIdFprYMV2LTnPSwnE0gsBTrQpA51SOr6WwPEEihZbfoKr96TY9t4CttU/ll5oR7XdY76t5p4tgbIIFC22ZaE6pzSK7Tnca76qgU41W8+yt0rgFLGN0TY/tWW6T0Cxvc/HvU8JGOhkS5BA2QSyie0w0Amh7SGaeKv5FdutBNs930Cndm1rzdojcKjY0hn4Q9HbGo1iu41fa2cb6NSaRa1PLwQOFVse6+YPRW9rSortNn6tnB1LL7QHA51asar16InAoWLbE8ij6qrYHkW2/HwNdCrfRpZQAnMJbBJbb82Zi3n9cYrtenY1nmmgU41Ws8wSmCawWGy/9723rg+ZiMe7GeQ0DXnLEYrtFnp1nDsW6ORAtg7bWUoJzCWwSGwR2hdffOHy9a+/fsHFZTqegGJ7POMzrjAW6MS6rEkCEmiTwCKxBQFBTzGr5TWdhuk4AortcWzPyDkNdHrtta9cv09+h86whNeUQF4Ci8U2ikenQWfBs4u5vccOI8jsu1Vs9+V5Rm5poBORxPwIgMsvZ1jCa0rgPAKrxTaKzNpSiC4/GGAnEmT22Sq2+3DMnQvfA74P4QXq+cc0crP3ehIokcBmsY1K0blwTy3iwFbRDTLbtortNn45z6bND3+6zkCnnBbwWhIol8BuYhtVDNHFvYzo2tkEmXVbxXYdt1xnRaAT3h1sxU/XGeiUi77XkUA9BHYX26g6nRBruYguHZGiG2SWbRXbZbxyHY2gxm/D0r4NFsxF3utIoE4Ch4lt4EB0ca2xdhWPmYt9bqcJKLbTjHIdwYARbw0DSAOdclH3OhJog8DhYptiGt42lO7z9TgBxXacS65P49eqDHTKRdzrSKBNAlnFNhB621CQmN4qttOM9j7CQKe9iZqfBCRwitgGdtxycduQv28bVB5uFduHPI56tzbQ6aOPfnN59OhL1+CoV1757OX993/xXBHfeefH1/3YktcmCUigPwKnim3gjghmOiNvGwoqT7eK7UMee7/bEuj05MmTCwIbAhqi+sEHv35WzPfe++n1mMePH1/ieD4zSUACfREoQmwD+VB0jWC+XGdEwcftPgT2CnRCXBHbNL3++tcu/EVKxZjPxs6JY91KQALtEihKbAOztw0FCcX2ExLbXh0R6PTmm29cXchpyRDTl19+6foRM1w8E+lMF7fz8LP0fF9LQAJtEihSbAN1iG7Ptw3pRo7WsHx7dKDTW29995mwRunClYzLGHcx9sOFHInP+UxXchBxK4E+CBQttqkJer1tSLFNW8H067WBTtM5P38EwVDYB9ElIaS4kGNmmwpvnB1iyz6TBCTQD4FqxDZMguimEcx0ri0nxXaeddNAJ57slOuJTiGoIbqs0eJeJsXMFoGNxCyXY53ZBhG3EuiDQHViG2bp5bYhxTYs/vx2r0Cn53Ne90msx8btP2NrtmOfrbuaZ0lAAjURqFZsA3L8Viii1OJtQ4ptWPrpdizQibXZsxOzV+63DZdylMdo5CDhVgJ9E6hebMN8rd42pNherj/XOPzpOkS3lIQrOXUfp+WKfYgxLmSO04WcEvK1BPog0IzYhrkigrmVXxvqVWyHgU54LViXLSnFei0z2nsCGsdhS16bJCCB/gg0J7ZhwhDd2m8b6k1szwp0inbjVgISkMARBJoV2xRWzbcN9SC2CKw/XZe2WF9LQAKtEehCbMNoNd421KrYlhroFG3FrQQkIIE9CVQltqyNvf32Dx7Un7UyHiKAKBF8ErddPDho8GZ421DJ9+q2JLbxRCdc+6ypM5stKdBp0Ex8KwEJSGA3AtWIbQSZpGLLfY3x0HeiPePpPenj8e6RoqOnw0fQ2JZwC8mwvLWLbQQ6vfrqF59xLi3Qacjc9xKQgAT2JlCF2CKe8RzaVGyHkZ3xUIHh51PQhrcNlTTbqlVscdnzJCfKn/OJTlO2dr8EJCCBMwhUIbY8/o6ZK+7iVGzHgHHMUrGNfCKCuaTbhmoSWwOdoiW5lYAEJPCQQPFii3DGOuyU2MZzZ5nhbkkhuqwt8hxmZmlnpdLF1kCns1qG15WABGoiULTYIprp4++mxBZhTo/fwxBn3zZUotga6LRHyzIPCUigJwJFi20EP4VB7oltBEixPSLFbUPMdn/0ox9eckUwlyK2Bjod0arMUwIS6IVAsWIbvxWK2Iz9DV3FzGjnRiFvMW7u24bOFlsDnba0Fs+VgAQk8JRAsWI7ZqBbM9tcQpuWKX7eDTE88rahM8TWQKfU0r6WgAQksJ1A9WLLOu1wlrs2GnkNzqNvG8oltgY6rbG+50hAAhKYR6BqseWWIMRo+Ld3kNQclIgua7l73zZ0pNgOA52+//1/8YlOc4ztMRKQgAQWEqhKbBfW7ZTD47ahEN2ttw3tLbZpoFM8MtEnOp3SVLyoBCTQEQHF9kBj73Hb0F5ia6DTgYY2awlIQAITBBTbCUB77EboeDbwmtuGtojtWKBTrluW9uBmHhKQgARaIaDYZrTkmtuGlortMNCJdWTWZk0SkIAEJHAeAcX2BPZLbhuaI7YGOp1gRC8pAQlIYAEBxXYBrL0PRSTTn/gb+7WhW2KLO/gnP3n36p420Glvy5ifBCQggX0JKLb78lyVG6J767ahVGwjktifrluF2ZMkIAEJnEZAsT0N/fMXRkxT0SWwCrE10Ol5Vn4iAQlIoCYCim2h1orbhhDbiGI20KlQY1ksCUhAAhMEFNsJQGfvHlvHPbtMXl8CEpCABJYRUGyX8fJoCUhAAhKQwGICiu1iZJ4gAQlIQAISWEZAsV3Gy6MlIAEJSEACiwkotouReYIEJCABCUhgGQHFdhkvj5aABCQgAQksJqDYLkbmCRKQgAQkIIFlBBTbZbw8WgISkIAEJLCYwP8BlEWvbJWdrqYAAAAASUVORK5CYII="></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>×</mo><mn>90</mn><mo>×</mo><mn>34</mn><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>6120</mn></mrow></mfenced></math> <strong>AND </strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>×</mo><mn>42</mn><mo>×</mo><mn>34</mn><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>2856</mn></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo>×</mo><mn>42</mn><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>3780</mn></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>21</mn></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi><mo>×</mo><msup><mn>21</mn><mn>2</mn></msup><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>441</mn><mi mathvariant="normal">π</mi><mo>,</mo><mo> </mo><mn>1385</mn><mo>.</mo><mn>44</mn><mo>…</mo></mrow></mfenced></math> <em><strong> (M1)</strong></em></p>
<p>use of curved surface area formula <em><strong> (M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>21</mn><mi mathvariant="normal">π</mi><mo>×</mo><mn>90</mn><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>1890</mn><mi mathvariant="normal">π</mi><mo>,</mo><mo> </mo><mn>5937</mn><mo>.</mo><mn>61</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20100</mn><mo> </mo><msup><mtext>cm</mtext><mn>2</mn></msup><mo> </mo><mo> </mo><mo>(</mo><mn>20079</mn><mo>.</mo><mn>0</mn><mo>…</mo><mo>)</mo></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[7 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>Joey is making a party hat in the form of a cone. The hat is made from a sector, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AOB</mtext></math>, of a circular piece of paper with a radius of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo> </mo><mtext>cm</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AÔB</mtext><mo>=</mo><mi>θ</mi></math> as 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>To make the hat, sides <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[OA]</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[OB]</mtext></math> are joined together. The hat has a base radius of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>cm</mtext></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the perimeter of the base of the hat in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the surface area of the outside of the hat.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mi mathvariant="normal">π</mi><mo> </mo><mi>cm</mi></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Answer must be in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math>.<br><br></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>θ</mi><mn>360</mn></mfrac><mo>×</mo><mn>2</mn><mi mathvariant="normal">π</mi><mfenced><mn>18</mn></mfenced><mo>=</mo><mn>13</mn><mi mathvariant="normal">π</mi></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>θ</mi><mn>360</mn></mfrac><mo>×</mo><mn>2</mn><mi mathvariant="normal">π</mi><mfenced><mn>18</mn></mfenced><mo>=</mo><mn>40</mn><mo>.</mo><mn>8407</mn><mo>…</mo></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into length of an arc formula.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>θ</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>130</mn><mo>°</mo></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>θ</mi><mn>360</mn></mfrac><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><msup><mn>18</mn><mn>2</mn></msup><mo>=</mo><mi mathvariant="normal">π</mi><mo>×</mo><mn>6</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>18</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>θ</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>130</mn><mo>°</mo></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>130</mn><mn>360</mn></mfrac><mo>×</mo><mi mathvariant="normal">π</mi><msup><mfenced><mn>18</mn></mfenced><mn>2</mn></msup></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into area of a sector formula.</p>
<p> </p>
<p><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi><mfenced><mrow><mn>6</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mfenced><mn>18</mn></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into curved area of a cone formula.</p>
<p> </p>
<p><strong>THEN</strong></p>
<p>(Area<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math>) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>368</mn><mo> </mo><msup><mtext>cm</mtext><mn>2</mn></msup><mo> </mo><mo> </mo><mfenced><mrow><mn>367</mn><mo>.</mo><mn>566</mn><mo>…</mo><mo>,</mo><mo> </mo><mn>117</mn><mi mathvariant="normal">π</mi></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Allow <em><strong>FT</strong></em> from their part (a)(ii) even if their angle is not obtuse.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Although most candidates understood what to do in part (a), many of them wrote a decimal approximation instead and did not give their answer in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math> as required in this part. Many candidates were able to use the length of arc formula in (a)(ii). Some candidates went wrong with this question by confusing between the two values: <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>6</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>cm</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>18</mn><mo> </mo><mi>cm</mi></math> for the radius. In part (b), although candidates were able to find the surface area of the outside of the hat, several added the surface area of the base to their calculation. A few candidates used the cosine rule to find chord <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>AB</mi></math> which was then used as the circumference of the base of the cone.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Although most candidates understood what to do in part (a), many of them wrote a decimal approximation instead and did not give their answer in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math> as required in this part. Many candidates were able to use the length of arc formula in (a)(ii). Some candidates went wrong with this question by confusing between the two values: <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>6</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>cm</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>18</mn><mo> </mo><mi>cm</mi></math> for the radius. In part (b), although candidates were able to find the surface area of the outside of the hat, several added the surface area of the base to their calculation. A few candidates used the cosine rule to find chord <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>AB</mi></math> which was then used as the circumference of the base of the cone.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Although most candidates understood what to do in part (a), many of them wrote a decimal approximation instead and did not give their answer in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math> as required in this part. Many candidates were able to use the length of arc formula in (a)(ii). Some candidates went wrong with this question by confusing between the two values: <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>6</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>cm</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>18</mn><mo> </mo><mi>cm</mi></math> for the radius. In part (b), although candidates were able to find the surface area of the outside of the hat, several added the surface area of the base to their calculation. A few candidates used the cosine rule to find chord <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>AB</mi></math> which was then used as the circumference of the base of the cone.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>There are four stations used by the fire wardens in a national forest.</p>
<p>On the following Voronoi diagram, the coordinates of the stations are <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mo>(</mo><mn>6</mn><mo>,</mo><mo> </mo><mn>2</mn><mo>)</mo><mo>,</mo><mo> </mo><mtext>B</mtext><mo>(</mo><mn>14</mn><mo>,</mo><mo> </mo><mn>2</mn><mo>)</mo><mo>,</mo><mo> </mo><mtext>C</mtext><mo>(</mo><mn>18</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>10</mn><mo>.</mo><mn>8</mn><mo>,</mo><mo> </mo><mn>11</mn><mo>.</mo><mn>6</mn><mo>)</mo></math> where distances are measured in kilometres.</p>
<p>The dotted lines represent the boundaries of the regions patrolled by the fire warden at each station. The boundaries meet at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mn>10</mn><mo>,</mo><mo> </mo><mn>6</mn><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Q</mtext><mo>(</mo><mn>13</mn><mo>,</mo><mo> </mo><mn>7</mn><mo>)</mo></math>.</p>
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"></p>
<p>To reduce the areas of the regions that the fire wardens patrol, a new station is to be built within the quadrilateral <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABCD</mtext></math>. The new station will be located so that it is as far as possible from the nearest existing station.</p>
</div>
<div class="specification">
<p>The Voronoi diagram is to be updated to include the region around the new station at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math>. The edges defined by the perpendicular bisectors of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[AP]</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[BP]</mtext></math> have been added to the following diagram.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the new station should be built at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</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>Write down the equation of the perpendicular bisector of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[PC]</mtext></math>.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence draw the missing boundaries of the region around <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math> on the following diagram.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(the best placement is either point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math> or point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Q</mtext></math>)<br>attempt at using the distance formula <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AP</mtext><mo>=</mo><msqrt><msup><mfenced><mrow><mn>10</mn><mo>-</mo><mn>6</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mn>6</mn><mo>-</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt></math> <strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BP</mtext><mo>=</mo><msqrt><msup><mfenced><mrow><mn>10</mn><mo>-</mo><mn>14</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mn>6</mn><mo>-</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt></math> <strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DP</mtext><mo>=</mo><msqrt><msup><mfenced><mrow><mn>10</mn><mo>-</mo><mn>10</mn><mo>.</mo><mn>8</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mn>6</mn><mo>-</mo><mn>11</mn><mo>.</mo><mn>6</mn></mrow></mfenced><mn>2</mn></msup></msqrt></math> <strong>OR</strong></p>
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BQ</mtext><mo>=</mo><msqrt><msup><mfenced><mrow><mn>13</mn><mo>-</mo><mn>14</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mn>7</mn><mo>-</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt></math> OR</strong></p>
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CQ</mtext><mo>=</mo><msqrt><msup><mfenced><mrow><mn>13</mn><mo>-</mo><mn>18</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mn>7</mn><mo>-</mo><mn>6</mn></mrow></mfenced><mn>2</mn></msup></msqrt></math> OR</strong></p>
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DQ</mtext><mo>=</mo><msqrt><msup><mfenced><mrow><mn>13</mn><mo>-</mo><mn>10</mn><mo>.</mo><mn>8</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mn>7</mn><mo>-</mo><mn>11</mn><mo>.</mo><mn>6</mn></mrow></mfenced><mn>2</mn></msup></msqrt></math> </strong></p>
<p>(<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AP</mtext></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BP</mtext></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DP</mtext></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math>) <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>32</mn></msqrt><mo>=</mo><mn>5</mn><mo>.</mo><mn>66</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>5</mn><mo>.</mo><mn>65685</mn><mo>…</mo></mrow></mfenced></math> <strong>AND</strong></p>
<p>(<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BQ</mtext></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CQ</mtext></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DQ</mtext></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math>) <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>26</mn></msqrt><mo>=</mo><mn>5</mn><mo>.</mo><mn>10</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>5</mn><mo>.</mo><mn>09901</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>32</mn></msqrt><mo>></mo><msqrt><mn>26</mn></msqrt></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AP</mtext></math> (or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BP</mtext></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DP</mtext></math>) is greater than <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BQ</mtext></math> (or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CQ</mtext></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DQ</mtext></math>) <em><strong>A1</strong></em></p>
<p>point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math> is the furthest away <em><strong>AG</strong></em></p>
<p><br><strong>Note:</strong> Follow through from their values provided their <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AP</mtext></math> (or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BP</mtext></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DP</mtext></math>) is greater than their <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BQ</mtext></math> (or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CQ</mtext></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DQ</mtext></math>).</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>14</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"> <em><strong>A1A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong></em> for each correct straight line. Do not <em><strong>FT</strong></em> from their part (b)(i).<br><br></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>In part (a) many candidates realized that distances were required. Many candidates seemed to have an idea about Voronoi diagrams. However, several candidates did not realize that they had to consider point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">Q</mi></math> as well in their comparison. Hence, several candidates only calculated distances from <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">P</mi></math>. The numerical comparison of the distance from <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">P</mi><mo> </mo><mfenced><mrow><mi>AP</mi><mo>/</mo><mi>BP</mi><mo>/</mo><mi>DP</mi></mrow></mfenced></math> and from <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">Q</mi><mo> </mo><mfenced><mrow><mi>BQ</mi><mo>/</mo><mi>CQ</mi><mo>/</mo><mi>DQ</mi></mrow></mfenced></math> need to be clearly shown. It was a pity to see that some candidates lost marks due to incorrect rounding of the values to three significant figures. The most common error being <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>09</mn></math>. In part (b)(i) not many candidates seemed to understand what was required. A significant number of candidates wrote down the equation of the line through <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>PC</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>6</mn></math>, rather than the required line. In part (b)(ii), it seemed that much time was lost as many candidates attempted to find the equation of the perpendicular bisector of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>DP</mi></math> to draw the boundaries.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (a) many candidates realized that distances were required. Many candidates seemed to have an idea about Voronoi diagrams. However, several candidates did not realize that they had to consider point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">Q</mi></math> as well in their comparison. Hence, several candidates only calculated distances from <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">P</mi></math>. The numerical comparison of the distance from <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">P</mi><mo> </mo><mfenced><mrow><mi>AP</mi><mo>/</mo><mi>BP</mi><mo>/</mo><mi>DP</mi></mrow></mfenced></math> and from <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">Q</mi><mo> </mo><mfenced><mrow><mi>BQ</mi><mo>/</mo><mi>CQ</mi><mo>/</mo><mi>DQ</mi></mrow></mfenced></math> need to be clearly shown. It was a pity to see that some candidates lost marks due to incorrect rounding of the values to three significant figures. The most common error being <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>09</mn></math>. In part (b)(i) not many candidates seemed to understand what was required. A significant number of candidates wrote down the equation of the line through <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>PC</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>6</mn></math>, rather than the required line. In part (b)(ii), it seemed that much time was lost as many candidates attempted to find the equation of the perpendicular bisector of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>DP</mi></math> to draw the boundaries.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (a) many candidates realized that distances were required. Many candidates seemed to have an idea about Voronoi diagrams. However, several candidates did not realize that they had to consider point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">Q</mi></math> as well in their comparison. Hence, several candidates only calculated distances from <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">P</mi></math>. The numerical comparison of the distance from <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">P</mi><mo> </mo><mfenced><mrow><mi>AP</mi><mo>/</mo><mi>BP</mi><mo>/</mo><mi>DP</mi></mrow></mfenced></math> and from <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">Q</mi><mo> </mo><mfenced><mrow><mi>BQ</mi><mo>/</mo><mi>CQ</mi><mo>/</mo><mi>DQ</mi></mrow></mfenced></math> need to be clearly shown. It was a pity to see that some candidates lost marks due to incorrect rounding of the values to three significant figures. The most common error being <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>09</mn></math>. In part (b)(i) not many candidates seemed to understand what was required. A significant number of candidates wrote down the equation of the line through <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>PC</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>6</mn></math>, rather than the required line. In part (b)(ii), it seemed that much time was lost as many candidates attempted to find the equation of the perpendicular bisector of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>DP</mi></math> to draw the boundaries.</p>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="question">
<p>The front view of a doghouse is made up of a square with an isosceles triangle on top.</p>
<p>The doghouse is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>35</mn><mo> </mo><mtext>m</mtext></math> high and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>9</mn><mo> </mo><mtext>m</mtext></math> wide, and sits on a square base.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" 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"></p>
<p>The top of the rectangular surfaces of the roof of the doghouse are to be painted.</p>
<p>Find the area to be painted.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>height of triangle at roof <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>.</mo><mn>35</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>9</mn><mo>=</mo><mn>0</mn><mo>.</mo><mn>45</mn></math> <em><strong>(</strong><strong>A1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>45</mn></math> (height of triangle) seen on the diagram.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>slant height</mtext><mo>=</mo><msqrt><mn>0</mn><mo>.</mo><msup><mn>45</mn><mn>2</mn></msup><mo>+</mo><mn>0</mn><mo>.</mo><msup><mn>45</mn><mn>2</mn></msup></msqrt></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mfenced><mrow><mn>45</mn><mo>°</mo></mrow></mfenced><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>45</mn></mrow><mtext>slant height</mtext></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msqrt><mn>0</mn><mo>.</mo><mn>405</mn></msqrt><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>636396</mn><mo>…</mo><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>45</mn><msqrt><mn>2</mn></msqrt></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> If using <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mfenced><mrow><mn>45</mn><mo>°</mo></mrow></mfenced><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>45</mn></mrow><mtext>slant height</mtext></mfrac></math> then <em><strong>(A1)</strong></em> for angle of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn><mo>°</mo></math>, <em><strong>(M1)</strong></em> for a correct trig statement.</p>
<p><br>area of one rectangle on roof <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msqrt><mn>0</mn><mo>.</mo><mn>405</mn></msqrt><mo>×</mo><mn>0</mn><mo>.</mo><mn>9</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>0</mn><mo>.</mo><mn>572756</mn><mo>…</mo></mrow></mfenced></math> <em><strong>M1</strong></em></p>
<p>area painted <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfenced><mrow><mn>2</mn><mo>×</mo><msqrt><mn>0</mn><mo>.</mo><mn>405</mn></msqrt><mo>×</mo><mn>0</mn><mo>.</mo><mn>9</mn><mo> </mo><mo>=</mo><mn>2</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>572756</mn><mo>…</mo></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>15</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>1</mn><mo>.</mo><mn>14551</mn><mo>…</mo><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>81</mn><msqrt><mn>2</mn></msqrt><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[5 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p>Although the first question on the paper, with appropriate low-level mathematics, the interpretation required seems to have been quite high, and many candidates found this challenging. Many candidates scored only the one mark for the height of the triangle. The most common wrong method seen was calculation of the area of the triangle and adding their result to the calculation 2 × 0.9 × 0.9. Stronger candidates lost the final mark either through premature rounding or incorrect units; both are aspects that can and do occur throughout candidate responses and hence clearly require focus in the classroom.</p>
</div>
<br><hr><br><div class="specification">
<p>The owner of a convenience store installs two security cameras, represented by points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C1</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C2</mtext></math>. Both cameras point towards the centre of the store’s cash register, represented by the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math>.</p>
<p>The following diagram shows this information on a cross-section of the store.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The cameras are positioned at a height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>1</mn><mo> </mo><mtext>m</mtext></math>, and the horizontal distance between the cameras is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>4</mn><mo> </mo><mtext>m</mtext></math>. The cash register is sitting on a counter so that its centre, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math>, is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>0</mn><mo> </mo><mtext>m</mtext></math> above the floor.</p>
<p>The distance from Camera <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> to the centre of the cash register is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>8</mn><mo> </mo><mtext>m</mtext></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the angle of depression from Camera <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> to the centre of the cash register. Give your answer 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>Calculate the distance from Camera <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> to the centre of the cash register.</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>Without further calculation, determine which camera has the largest angle of depression to the centre of the cash register. Justify your response.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo> </mo><mi>θ</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mo>.</mo><mn>1</mn></mrow><mrow><mn>2</mn><mo>.</mo><mn>8</mn></mrow></mfrac></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tan</mi><mo> </mo><mi>θ</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mo>.</mo><mn>1</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>85202</mn><mo>…</mo></mrow></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>θ</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>48</mn><mo>.</mo><mn>6</mn><mo>°</mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>48</mn><mo>.</mo><mn>5903</mn><mo>…</mo><mo>°</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn><mo>.</mo><msup><mn>8</mn><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>.</mo><msup><mn>1</mn><mn>2</mn></msup></msqrt></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>8</mn><mo> </mo><mi>cos</mi><mfenced><mrow><mn>48</mn><mo>.</mo><mn>5903</mn><mo>…</mo></mrow></mfenced></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>.</mo><mn>1</mn></mrow><mrow><mi>tan</mi><mfenced><mrow><mn>48</mn><mo>.</mo><mn>5903</mn><mo>…</mo></mrow></mfenced></mrow></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong> </em>for attempt to use Pythagorean Theorem with <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>1</mn></math> seen or for attempt to use cosine or tangent ratio.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>85</mn><mo> </mo><mfenced><mtext>m</mtext></mfenced><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>1</mn><mo>.</mo><mn>85202</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award the <em><strong>M1A1</strong></em> if <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>85</mn></math> is seen in part (a).</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>6</mn><mo>.</mo><mn>4</mn><mo>-</mo><mn>1</mn><mo>.</mo><mn>85202</mn><mo>…</mo></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>55</mn><mo> </mo><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>4</mn><mo>.</mo><mn>54797</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong> </em>for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>55</mn></math> or equivalent seen, either as a separate calculation or in Pythagorean Theorem.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><msup><mfenced><mrow><mn>4</mn><mo>.</mo><mn>54797</mn><mo>…</mo></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>.</mo><msup><mn>1</mn><mn>2</mn></msup></msqrt></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>01</mn><mo> </mo><mtext>m</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>5</mn><mo>.</mo><mn>00939</mn><mo>…</mo><mo> </mo><mtext>m</mtext></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>attempt to use cosine rule <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msup><mi>c</mi><mn>2</mn></msup><mo>=</mo></mrow></mfenced><mo> </mo><mn>2</mn><mo>.</mo><msup><mn>8</mn><mn>2</mn></msup><mo>+</mo><mn>6</mn><mo>.</mo><msup><mn>4</mn><mn>2</mn></msup><mo>-</mo><mn>2</mn><mfenced><mrow><mn>2</mn><mo>.</mo><mn>8</mn></mrow></mfenced><mfenced><mrow><mn>6</mn><mo>.</mo><mn>4</mn></mrow></mfenced><mo> </mo><mi>cos</mi><mo> </mo><mfenced><mrow><mn>48</mn><mo>.</mo><mn>5903</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(A1)(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong> </em>for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>48</mn><mo>.</mo><mn>5903</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>°</mo></math> substituted into cosine rule formula, <em><strong>A1</strong> </em>for correct substitution.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>c</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>5</mn><mo>.</mo><mn>01</mn><mo> </mo><mtext>m</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>5</mn><mo>.</mo><mn>00939</mn><mo>…</mo><mo> </mo><mtext>m</mtext></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>camera <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> is closer to the cash register (than camera <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> and both cameras are at the same height on the wall) <em><strong>R1</strong></em></p>
<p>the larger angle of depression is from camera <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Do not award <em><strong>R0A1</strong></em>. Award <em><strong>R0A0</strong></em> if additional calculations are completed and used in their justification, as per the question. Accept “<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>85</mn><mo><</mo><mn>4</mn><mo>.</mo><mn>55</mn></math>” or “<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>8</mn><mo><</mo><mn>5</mn><mo>.</mo><mn>01</mn></math>” as evidence for the <em><strong>R1</strong></em>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Many candidates calculated the angle from vertical rather than the angle of depression.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates could successfully use their vertical angle from (a) or other correct trigonometry, such as Pythagorean theorem or cosine rule, to find the distance from camera 2 to the cash register. This question is a good example of how premature rounding can affect a final answer, and some had an inaccurate final answer because they had rounded intermediate values.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many provided reasonable justification for their response, even though they often followed correct reasoning with an incorrect conclusion about the larger angle of depression.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>An inclined railway travels along a straight track on a steep hill, as 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>The locations of the stations on the railway can be described by coordinates in reference to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>,</mo><mo> </mo><mi>y</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math>-axes, where the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> axes are in the horizontal plane and the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math>-axis is vertical.</p>
<p>The ground level station <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>140</mn><mo>,</mo><mo> </mo><mn>15</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math> and station <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>, located near the top of the hill, has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>20</mn><mo>,</mo><mo> </mo><mn>5</mn><mo>,</mo><mo> </mo><mn>250</mn><mo>)</mo></math>. All coordinates are given in metres.</p>
</div>
<div class="specification">
<p>Station <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> is to be built halfway between stations <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the distance between stations <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">[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 station <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</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>Write down the height of station <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math>, in metres, above the ground.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>attempt at substitution into 3D distance formula <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext><mo>=</mo><msqrt><msup><mfenced><mrow><mn>140</mn><mo>-</mo><mn>20</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mn>15</mn><mo>-</mo><mn>5</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mn>250</mn><mn>2</mn></msup></msqrt><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><msqrt><mn>77</mn><mo> </mo><mn>000</mn></msqrt></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>277</mn><mo> </mo><mtext>m</mtext><mo> </mo><mo> </mo><mfenced><mrow><mn>10</mn><msqrt><mn>770</mn></msqrt><mo>,</mo><mo> </mo><mn>277</mn><mo>.</mo><mn>488</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt at substitution in the midpoint formula <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mrow><mn>140</mn><mo>+</mo><mn>20</mn></mrow><mn>2</mn></mfrac><mo>,</mo><mo> </mo><mfrac><mrow><mn>15</mn><mo>+</mo><mn>5</mn></mrow><mn>2</mn></mfrac><mo>,</mo><mo> </mo><mfrac><mrow><mn>0</mn><mo>+</mo><mn>250</mn></mrow><mn>2</mn></mfrac></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>80</mn><mo>,</mo><mo> </mo><mn>10</mn><mo>,</mo><mo> </mo><mn>125</mn></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>125</mn><mo> </mo><mtext>m</mtext></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Points A(3, 1), B(3, 5), C(11, 7), D(9, 1) and E(7, 3) represent snow shelters in the Blackburn National Forest. These snow shelters are illustrated in the following coordinate axes.</p>
<p>Horizontal scale: 1 unit represents 1 km.</p>
<p>Vertical scale: 1 unit represents 1 km.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The Park Ranger draws three straight lines to form an incomplete Voronoi diagram.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the gradient of the line segment AE.</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 the line which would complete the Voronoi cell containing site E.</p>
<p>Give your answer in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="ax + by + d = 0">
<mi>a</mi>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
<mi>y</mi>
<mo>+</mo>
<mi>d</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d \in \mathbb{Z}">
<mi>d</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the context of the question, explain the significance of the Voronoi cell containing site E.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{3 - 1}}{{7 - 3}}">
<mfrac>
<mrow>
<mn>3</mn>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>7</mn>
<mo>−</mo>
<mn>3</mn>
</mrow>
</mfrac>
</math></span> <em><strong>(</strong></em><em><strong>M1)</strong></em></p>
<p>= 0.5 <em><strong>A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y - 2 = - 2\left( {x - 5} \right)">
<mi>y</mi>
<mo>−</mo>
<mn>2</mn>
<mo>=</mo>
<mo>−</mo>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>5</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em> <em><strong>(M1)</strong></em></p>
<p><strong>Note</strong>: Award <em><strong>(A1)</strong></em> for their −2 seen, award <em><strong>(M1)</strong></em> for the correct substitution of (5, 2) and their normal gradient in equation of a line.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2x + y - 12 = 0">
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mi>y</mi>
<mo>−</mo>
<mn>12</mn>
<mo>=</mo>
<mn>0</mn>
</math></span> <em><strong>A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>every point in the cell is closer to E than any other snow shelter <em><strong>A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A garden includes a small lawn. The lawn is enclosed by an arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext></math> of 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>6</mn><mo> </mo><mtext>m</mtext></math>, such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AÔB</mtext><mo>=</mo><mn>135</mn><mo>°</mo><mo> </mo></math>. The straight border of the lawn is defined by chord <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[AB]</mtext></math>.</p>
<p>The lawn is shown as the shaded region 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>A footpath is to be laid around the curved side of the lawn. Find the length of the footpath.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the lawn.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>135</mn><mo>°</mo><mo>×</mo><mfrac><mrow><mn>12</mn><mi mathvariant="normal">π</mi></mrow><mrow><mn>360</mn><mo>°</mo></mrow></mfrac></math> <em><strong>(M1)(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>.</mo><mn>1</mn><mo> </mo><mfenced><mtext>m</mtext></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mn>14</mn><mo>.</mo><mn>1371</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of splitting region into two areas <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>135</mn><mo>°</mo><mo>×</mo><mfrac><mrow><mi mathvariant="normal">π</mi><msup><mn>6</mn><mn>2</mn></msup></mrow><mrow><mn>360</mn><mo>°</mo></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>6</mn><mo>×</mo><mn>6</mn><mo>×</mo><mi>sin</mi><mo> </mo><mn>135</mn><mo>°</mo></mrow><mn>2</mn></mfrac></math> <em><strong>(M1)</strong></em><em><strong>(M1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>M1</strong></em> for correctly substituting into area of sector formula, <em><strong>M1</strong></em> for evidence of substituting into area of triangle formula.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>42</mn><mo>.</mo><mn>4115</mn><mo>…</mo><mo>-</mo><mn>12</mn><mo>.</mo><mn>7279</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>29</mn><mo>.</mo><mn>7</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup><mo> </mo><mo> </mo><mfenced><mrow><mn>29</mn><mo>.</mo><mn>6835</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Ollie has installed security lights on the side of his house that are activated by a sensor. The sensor is located at point C directly above point D. The area covered by the sensor is shown by the shaded region enclosed by triangle ABC. The distance from A to B is 4.5 m and the distance from B to C is 6 m. Angle AĈB is 15°.</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 CÂB.</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>Point B on the ground is 5 m from point E at the entrance to Ollie’s house. He is 1.8 m tall and is standing at point D, below the sensor. He walks towards point B.</p>
<p>Find the distance Ollie is <strong>from the entrance to his house</strong> when he first activates the sensor.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{sin}}\,{\text{C}}\mathop {\text{A}}\limits^ \wedge {\text{B}}}}{6} = \frac{{{\text{sin}}\,15^\circ }}{{4.5}}">
<mfrac>
<mrow>
<mrow>
<mtext>sin</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>C</mtext>
</mrow>
<mover>
<mrow>
<mtext>A</mtext>
</mrow>
<mo>∧</mo>
</mover>
<mo></mo>
<mrow>
<mtext>B</mtext>
</mrow>
</mrow>
<mn>6</mn>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mtext>sin</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<msup>
<mn>15</mn>
<mo>∘</mo>
</msup>
</mrow>
<mrow>
<mn>4.5</mn>
</mrow>
</mfrac>
</math></span> <em><strong>(M1)(A1)</strong></em></p>
<p>CÂB = 20.2º (20.187415…) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted sine rule formula and award <em><strong>(A1)</strong></em> for correct substitutions.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{C}}\mathop {\text{B}}\limits^ \wedge {\text{D}} = 20.2 + 15 = 35.2^\circ ">
<mrow>
<mtext>C</mtext>
</mrow>
<mover>
<mrow>
<mtext>B</mtext>
</mrow>
<mo>∧</mo>
</mover>
<mo></mo>
<mrow>
<mtext>D</mtext>
</mrow>
<mo>=</mo>
<mn>20.2</mn>
<mo>+</mo>
<mn>15</mn>
<mo>=</mo>
<msup>
<mn>35.2</mn>
<mo>∘</mo>
</msup>
</math></span> <em><strong>A1</strong></em></p>
<p><em>(let X be the point on BD where Ollie activates the sensor)</em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{tan}}\,35.18741 \ldots ^\circ = \frac{{1.8}}{{{\text{BX}}}}">
<mrow>
<mtext>tan</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>35.18741</mn>
<msup>
<mo>…</mo>
<mo>∘</mo>
</msup>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1.8</mn>
</mrow>
<mrow>
<mrow>
<mtext>BX</mtext>
</mrow>
</mrow>
</mfrac>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <strong><em>A1</em> </strong>for their correct angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{C}}\mathop {\text{B}}\limits^ \wedge {\text{D}}">
<mrow>
<mtext>C</mtext>
</mrow>
<mover>
<mrow>
<mtext>B</mtext>
</mrow>
<mo>∧</mo>
</mover>
<mo></mo>
<mrow>
<mtext>D</mtext>
</mrow>
</math></span>. Award <em><strong>M1</strong> </em>for correctly substituted trigonometric formula.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{BX}} = 2.55285 \ldots ">
<mrow>
<mtext>BX</mtext>
</mrow>
<mo>=</mo>
<mn>2.55285</mn>
<mo>…</mo>
</math></span> <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="5 - 2.55285 \ldots ">
<mn>5</mn>
<mo>−</mo>
<mn>2.55285</mn>
<mo>…</mo>
</math></span> <em><strong>(M1)</strong></em></p>
<p>= 2.45 (m) (2.44714…) <em><strong>A1</strong></em> </p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>The diagram below is part of a Voronoi diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"><strong>Diagram not to scale</strong></p>
<p><em>A</em> and <em>B</em> are sites with <em>B</em> having the co-ordinates of (4, 6). <em>L</em> is an edge; the equation of this perpendicular bisector of the line segment from <em>A</em> to <em>B</em> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - 2x + 9">
<mi>y</mi>
<mo>=</mo>
<mo>−</mo>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>9</mn>
</math></span></p>
<p>Find the co-ordinates of the point <em>A</em>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>Line from <em>A</em> to <em>B</em> will have the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{1}{2}x + c">
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>x</mi>
<mo>+</mo>
<mi>c</mi>
</math></span><em><strong> M1A1</strong></em></p>
<p>Through <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {4{\text{,}}\,\,6} \right) \Rightarrow c = 4">
<mrow>
<mo>(</mo>
<mrow>
<mn>4</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>6</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo stretchy="false">⇒</mo>
<mi>c</mi>
<mo>=</mo>
<mn>4</mn>
</math></span> so line is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{1}{2}x + 4">
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>x</mi>
<mo>+</mo>
<mn>4</mn>
</math></span><em><strong> M1A1</strong></em></p>
<p>Intersection of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - 2x + 9">
<mi>y</mi>
<mo>=</mo>
<mo>−</mo>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>9</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{1}{2}x + 4">
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>x</mi>
<mo>+</mo>
<mn>4</mn>
</math></span> is (2, 5)<em><strong> M1A1</strong></em></p>
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \left( {p{\text{,}}\,\,q} \right)">
<mi>A</mi>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>p</mi>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>q</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> then <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {2{\text{,}}\,\,5} \right) = \left( {\frac{{p + 4}}{2},\frac{{q + 6}}{2}} \right) \Rightarrow p = 0{\text{,}}\,\,q = 4">
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>5</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mi>p</mi>
<mo>+</mo>
<mn>4</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mo>,</mo>
<mfrac>
<mrow>
<mi>q</mi>
<mo>+</mo>
<mn>6</mn>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo stretchy="false">⇒</mo>
<mi>p</mi>
<mo>=</mo>
<mn>0</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>q</mi>
<mo>=</mo>
<mn>4</mn>
</math></span><em><strong> M1A1A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \left( {0,4} \right)">
<mi>A</mi>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>0</mn>
<mo>,</mo>
<mn>4</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> </p>
<p style="text-align: left;"><em><strong>[9 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>The Bermuda Triangle is a region of the Atlantic Ocean with Miami <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtext>M</mtext></mfenced></math>, Bermuda <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtext>B</mtext></mfenced></math>, and San Juan <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtext>S</mtext></mfenced></math> as vertices, as shown on the diagram.</p>
<p style="padding-left: 120px;"><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The distances between <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</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>S</mtext></math> are given in the following table, correct to three significant figures.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math>, the measure of angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>MŜB</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 the area of the Bermuda Triangle.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>attempt at substituting the cosine rule formula <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mo> </mo><mi>θ</mi><mo>=</mo><mfrac><mrow><msup><mn>1660</mn><mn>2</mn></msup><mo>+</mo><msup><mn>1550</mn><mn>2</mn></msup><mo>-</mo><msup><mn>1670</mn><mn>2</mn></msup></mrow><mrow><mn>2</mn><mfenced><mn>1660</mn></mfenced><mfenced><mn>1550</mn></mfenced></mrow></mfrac></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>θ</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>62</mn><mo>.</mo><mn>6</mn><mo>°</mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>62</mn><mo>.</mo><mn>5873</mn><mo>…</mo></mrow></mfenced></math> (accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>09</mn></math> rad <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>1</mn><mo>.</mo><mn>09235</mn><mo>…</mo></mrow></mfenced></math>) <em><strong>A1</strong></em></p>
<p><em><strong><br>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correctly substituted area of triangle formula <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfenced><mn>1660</mn></mfenced><mfenced><mn>1550</mn></mfenced><mi>sin</mi><mfenced><mrow><mn>62</mn><mo>.</mo><mn>5873</mn><mo>…</mo></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>A</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>1140</mn><mo> </mo><mn>000</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>1</mn><mo>.</mo><mn>14</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mo>,</mo><mo> </mo><mn>1142</mn><mo> </mo><mn>043</mn><mo>.</mo><mn>327</mn><mo>…</mo></mrow></mfenced><mo> </mo><msup><mtext>km</mtext><mn>2</mn></msup></math> <em><strong>A1</strong></em></p>
<p><strong><br>Note: </strong>Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1150</mn><mo> </mo><mn>000</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>1</mn><mo>.</mo><mn>15</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mo>,</mo><mo> </mo><mn>1146</mn><mo> </mo><mn>279</mn><mo>.</mo><mn>893</mn><mo>…</mo></mrow></mfenced><mo> </mo><msup><mtext>km</mtext><mn>2</mn></msup></math> from use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>63</mn><mo>°</mo></math>. Other angles and their corresponding sides may be used.</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Most candidates were successful at selecting the cosine rule formula in part (a). In most cases, the cosine rule formula was correctly substituted. Some candidates found it hard to choose the correct side to obtain the required angle. Most of the candidates scored one or two marks out of three in this part. In part (b) some candidates assumed the triangle was right angled and used <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>b</mi><mi>h</mi></math> instead of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>a</mi><mi>b</mi><mo> </mo><mi>sin</mi><mo> </mo><mi>C</mi></math>. In part (b) many candidates who answered part (a) incorrectly were able to recover. Many candidates managed to score full marks in this part despite an incorrect answer in part (a). Some found angle <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>BMS</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>SBM</mi></math> in part (a) but used the correct sides to obtain the correct area. Final answers given in calculator notations (such as <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>1</mn><mo>.</mo><mn>14</mn><mi mathvariant="normal">E</mi><mn>10</mn></math>) scored at most one mark out of two. Calculator notation should generally be avoided; it is considered too informal to earn A marks, and although it can imply a method and earn M marks, we advise that candidates still provide the necessary commentary to support any GDC notation.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most candidates were successful at selecting the cosine rule formula in part (a). In most cases, the cosine rule formula was correctly substituted. Some candidates found it hard to choose the correct side to obtain the required angle. Most of the candidates scored one or two marks out of three in this part. In part (b) some candidates assumed the triangle was right angled and used <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>b</mi><mi>h</mi></math> instead of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>a</mi><mi>b</mi><mo> </mo><mi>sin</mi><mo> </mo><mi>C</mi></math>. In part (b) many candidates who answered part (a) incorrectly were able to recover. Many candidates managed to score full marks in this part despite an incorrect answer in part (a). Some found angle <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>BMS</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>SBM</mi></math> in part (a) but used the correct sides to obtain the correct area. Final answers given in calculator notations (such as <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>1</mn><mo>.</mo><mn>14</mn><mi mathvariant="normal">E</mi><mn>10</mn></math>) scored at most one mark out of two. Calculator notation should generally be avoided; it is considered too informal to earn A marks, and although it can imply a method and earn M marks, we advise that candidates still provide the necessary commentary to support any GDC notation.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{OA}}}\limits^ \to = \left( \begin{gathered} 2 \hfill \\ 1 \hfill \\ 3 \hfill \\ \end{gathered} \right)">
<mover>
<mrow>
<mrow>
<mtext>OA</mtext>
</mrow>
</mrow>
<mo stretchy="false">→<!-- → --></mo>
</mover>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mtable rowspacing="3pt" columnspacing="1em" displaystyle="true">
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{AB}}}\limits^ \to = \left( \begin{gathered} 1 \hfill \\ 3 \hfill \\ 1 \hfill \\ \end{gathered} \right)">
<mover>
<mrow>
<mrow>
<mtext>AB</mtext>
</mrow>
</mrow>
<mo stretchy="false">→<!-- → --></mo>
</mover>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mtable rowspacing="3pt" columnspacing="1em" displaystyle="true">
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
</math></span>, where O is the origin. <em>L</em><sub>1</sub> is the line that passes through A and B.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find a vector equation for <em>L</em><sub>1</sub>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The vector <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( \begin{gathered} 2 \hfill \\ p \hfill \\ 0 \hfill \\ \end{gathered} \right)">
<mrow>
<mo>(</mo>
<mtable rowspacing="3pt" columnspacing="1em" displaystyle="true">
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>p</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
</math></span> is perpendicular to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{AB}}}\limits^ \to ">
<mover>
<mrow>
<mrow>
<mtext>AB</mtext>
</mrow>
</mrow>
<mo stretchy="false">→</mo>
</mover>
</math></span>. Find the value of <em>p</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>any correct equation in the form <em><strong>r</strong> = <strong>a</strong> + t<strong>b</strong></em> (accept any parameter for <em>t</em>)</p>
<p>where <strong><em>a</em></strong> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( \begin{gathered} 2 \hfill \\ 1 \hfill \\ 3 \hfill \\ \end{gathered} \right)">
<mrow>
<mo>(</mo>
<mtable rowspacing="3pt" columnspacing="1em" displaystyle="true">
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
</math></span>, and <strong><em>b</em></strong> is a scalar multiple of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( \begin{gathered} 1 \hfill \\ 3 \hfill \\ 1 \hfill \\ \end{gathered} \right)">
<mrow>
<mo>(</mo>
<mtable rowspacing="3pt" columnspacing="1em" displaystyle="true">
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
</math></span> <em><strong>A2 N2</strong></em></p>
<p>eg <em><strong>r</strong> = </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( \begin{gathered} 2 \hfill \\ 1 \hfill \\ 3 \hfill \\ \end{gathered} \right) = t\left( \begin{gathered} 1 \hfill \\ 3 \hfill \\ 1 \hfill \\ \end{gathered} \right)">
<mrow>
<mo>(</mo>
<mtable rowspacing="3pt" columnspacing="1em" displaystyle="true">
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>t</mi>
<mrow>
<mo>(</mo>
<mtable rowspacing="3pt" columnspacing="1em" displaystyle="true">
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
</math></span>, <em><strong>r</strong> = 2<strong>i</strong> + <strong>j</strong> + 3<strong>k</strong> + s</em>(<em><strong>i</strong> + 3<strong>j</strong> + <strong>k</strong></em>)</p>
<p><strong>Note:</strong> Award<em><strong> A1</strong></em> for the form<em> <strong>a</strong> + t<strong>b</strong>, <strong>A1 </strong></em>for the form<em> L = <strong>a</strong> + t<strong>b</strong></em>, A0 for the form <em><strong>r</strong> = <strong>b</strong> + t<strong>a</strong></em>.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>correct scalar product <em><strong>(A1)</strong></em></p>
<p><em>eg </em> (1 × 2) + (3 × <em>p</em>) + (1 × 0), 2 + 3<em>p</em></p>
<p>evidence of equating <strong>their</strong> scalar product to zero <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <em><strong>a•b</strong></em> = 0, 2 + 3p = 0, 3<em>p</em> = −2</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = - \frac{2}{3}">
<mi>p</mi>
<mo>=</mo>
<mo>−</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</math></span> <em><strong>A1 N3</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>valid attempt to find angle between vectors <em><strong>(M1)</strong></em></p>
<p>correct substitution into numerator and/or angle <em><strong>(A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{cos}}\,\theta = \frac{{\left( {1 \times 2} \right) + \left( {3 \times p} \right) + \left( {1 \times 0} \right)}}{{\left| a \right|\left| b \right|}},\,\,{\text{cos}}\,\theta = 0">
<mrow>
<mtext>cos</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>θ</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>×</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>3</mn>
<mo>×</mo>
<mi>p</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>×</mo>
<mn>0</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mrow>
<mo>|</mo>
<mi>a</mi>
<mo>|</mo>
</mrow>
<mrow>
<mo>|</mo>
<mi>b</mi>
<mo>|</mo>
</mrow>
</mrow>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cos</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>θ</mi>
<mo>=</mo>
<mn>0</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = - \frac{2}{3}">
<mi>p</mi>
<mo>=</mo>
<mo>−</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</math></span> <em><strong>A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The position vectors of points P and Q are <strong><em>i</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + ">
<mo>+</mo>
</math></span> 2 <strong><em>j</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - ">
<mo>−<!-- − --></mo>
</math></span> <strong><em>k </em></strong>and 7<strong><em>i</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + ">
<mo>+</mo>
</math></span> 3<strong><em>j</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - ">
<mo>−<!-- − --></mo>
</math></span> 4<strong><em>k </em></strong>respectively.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find a vector equation of the line that passes through P and Q.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The line through P and Q is perpendicular to the vector 2<strong><em>i </em></strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + ">
<mo>+</mo>
</math></span> <em>n</em><strong><em>k</em></strong>. Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n">
<mi>n</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid attempt to find direction vector <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{PQ}}} ,{\text{ }}\overrightarrow {{\text{QP}}} ">
<mover>
<mrow>
<mtext>PQ</mtext>
</mrow>
<mo>→</mo>
</mover>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mover>
<mrow>
<mtext>QP</mtext>
</mrow>
<mo>→</mo>
</mover>
</math></span></p>
<p>correct direction vector (or multiple of) <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span>6<strong><em>i</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + ">
<mo>+</mo>
</math></span> <strong><em>j</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - ">
<mo>−</mo>
</math></span> 3<strong><em>k</em></strong></p>
<p><strong>any </strong>correct equation in the form <strong><em>r</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = ">
<mo>=</mo>
</math></span> <strong><em>a</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + ">
<mo>+</mo>
</math></span> <em>t</em><strong><em>b </em></strong>(any parameter for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span>) <strong><em>A2 N3</em></strong></p>
<p>where <strong><em>a </em></strong>is <strong><em>i</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + ">
<mo>+</mo>
</math></span> 2<strong><em>j</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - ">
<mo>−</mo>
</math></span> <strong><em>k</em></strong> or 7<strong><em>i</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + ">
<mo>+</mo>
</math></span> 3<strong><em>j</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - ">
<mo>−</mo>
</math></span> 4<strong><em>k </em></strong>, and <strong><em>b </em></strong>is a scalar multiple of 6<strong><em>i</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + ">
<mo>+</mo>
</math></span> <strong><em>j</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - ">
<mo>−</mo>
</math></span> 3<strong><em>k</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><strong><em>r</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = ">
<mo>=</mo>
</math></span> 7<strong><em>i</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + ">
<mo>+</mo>
</math></span> 3<strong><em>j</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - ">
<mo>−</mo>
</math></span> 4<strong><em>k</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + ">
<mo>+</mo>
</math></span> <em>t</em>(6<strong><em>i</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + ">
<mo>+</mo>
</math></span> <strong><em>j</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - ">
<mo>−</mo>
</math></span> 3<strong><em>k</em></strong>), <strong><em>r</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left( {\begin{array}{*{20}{c}} {1 + 6s} \\ {2 + 1s} \\ { - 1 - 3s} \end{array}} \right),{\text{ }}r = \left( {\begin{array}{*{20}{c}} 1 \\ 2 \\ { - 1} \end{array}} \right) + t\left( {\begin{array}{*{20}{c}} { - 6} \\ { - 1} \\ 3 \end{array}} \right)">
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mn>6</mn>
<mi>s</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>2</mn>
<mo>+</mo>
<mn>1</mn>
<mi>s</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−</mo>
<mn>1</mn>
<mo>−</mo>
<mn>3</mn>
<mi>s</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>r</mi>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>t</mi>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>A1 </em></strong>for the form <strong><em>a</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + ">
<mo>+</mo>
</math></span> <em>t</em><strong><em>b</em></strong>, <strong><em>A1 </em></strong>for the form <strong><em>L</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = ">
<mo>=</mo>
</math></span> <strong><em>a</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + ">
<mo>+</mo>
</math></span> <em>t</em><strong><em>b</em></strong>, <strong><em>A0 </em></strong>for the form <strong><em>r</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = ">
<mo>=</mo>
</math></span> <strong><em>b</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + ">
<mo>+</mo>
</math></span> <em>t</em><strong><em>a</em></strong>.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct expression for scalar product <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6 \times 2 + 1 \times 0 + ( - 3) \times n,{\text{ }} - 3n + 12">
<mn>6</mn>
<mo>×</mo>
<mn>2</mn>
<mo>+</mo>
<mn>1</mn>
<mo>×</mo>
<mn>0</mn>
<mo>+</mo>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>3</mn>
<mo stretchy="false">)</mo>
<mo>×</mo>
<mi>n</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<mn>3</mn>
<mi>n</mi>
<mo>+</mo>
<mn>12</mn>
</math></span></p>
<p>setting scalar product equal to zero (seen anywhere) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><strong><em>u</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \bullet ">
<mo>∙</mo>
</math></span> <strong><em>v</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0,{\text{ }} - 3n + 12 = 0">
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<mn>3</mn>
<mi>n</mi>
<mo>+</mo>
<mn>12</mn>
<mo>=</mo>
<mn>0</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n = 4">
<mi>n</mi>
<mo>=</mo>
<mn>4</mn>
</math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Money boxes are coin containers used by children and come in a variety of shapes. The money box shown is in the shape of a cylinder. It has a radius of 4.43 cm and a height of 12.2 cm.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the volume of the money box.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second money box is in the shape of a sphere and has the same volume as the cylindrical money box.</p>
<p style="text-align: center;"><img 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"></p>
<p>Find the diameter of the second money box.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>(<em>V</em> =) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {\left( {4.43} \right)^2} \times 12.2">
<mi>π</mi>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>4.43</mn>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>12.2</mn>
</math></span> <strong><em>(M1)(A1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for substitution into volume of a cylinder formula, <strong><em>(A1)</em></strong> for correct substitution.</p>
<p>752 cm<sup>3</sup> (752.171…cm<sup>3</sup>) <strong><em>(A1)</em></strong><strong><em>(C3)</em></strong></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="752.171 \ldots = \frac{4}{3}\pi {\left( r \right)^3}">
<mn>752.171</mn>
<mo>…</mo>
<mo>=</mo>
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mi>π</mi>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span> <strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for equating their volume to the volume of a sphere formula.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {r = } \right)">
<mrow>
<mo>(</mo>
<mrow>
<mi>r</mi>
<mo>=</mo>
</mrow>
<mo>)</mo>
</mrow>
</math></span> 5.64169…cm <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from part (a).</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {d = } \right)">
<mrow>
<mo>(</mo>
<mrow>
<mi>d</mi>
<mo>=</mo>
</mrow>
<mo>)</mo>
</mrow>
</math></span> 11.3 cm (11.2833…cm) <strong><em>(A1)</em>(ft)<em> </em></strong><strong><em>(C3)</em></strong></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A solid right circular cone has a base radius of 21 cm and a slant height of 35 cm.<br>A smaller right circular cone has a height of 12 cm and a slant height of 15 cm, and is removed from the top of the larger cone, as shown in the diagram.</p>
<p style="text-align: center;"><img 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QEaVIs7D5GQTMm92jh37tw5ZK0rVqwoY8eOlTVr1oQ8L5ofIfvqgPzRXM9rSIAESMCrBGhQLe5ZGDVTci/mYrGrTDhLbLBmFAH5Tcu+TZs2pexr8T3D7EmABNxJgAbVwn6DMYNRM+XdC7kXu8qEk1q3bq1OMy37wpjDqFP2DacXeA4JkEAiEaBBtbC3YcxMy73hGmcrZV/M4VL2tfDGYdYkQAKuJECDamG3mZZ7IzXOkH0XLVpkvIWYw6W3r3GszJAESMDlBGhQLepALfe2atXKSAnRLL2B7IuYwVu3bjVSB50JZV9Ngn9JgARIoIgADWoRC6Of9NylnsuMNfPDhw9HPBerZV8rohtR9o21R3k9CZCA1wgwlq9FPTpu3DiV88iRIy0qoShbBHYItmMNgjAgyAPWkJpMyBfrXbGNm+m8TdaTeZEACZCAXQRoUC0gDbkXRgwjw/bt21tQgjOy7NWrlzzwwAOSnp7ujAqxFiRAAiQQRwKUfC2Ab1rutaCKRrKE7Iu5XSYSIAESIAERjlAtuAvslHstqH7YWVL2DRsVTyQBEkgAAhyhWtDJCOaAJSteT/D2xVIeRHBiIgESIIFEJ0CDavgO0EtUTHn3Gq6e8ewQVpGyr3GszJAESMCFBGhQDXcaHJEQmB5LVhIhIXITNk9H4H4mEiABEkhkAjSohnsfm38ngtyrsWHTdMq+mgb/kgAJJDIBGlSDvQ+5F5GJTMi9WHqj5WODVbRkJEnZ12QPMS8SIAG3EqBBNdhzkHuHDRtmRO7F0huELYRhNZWysrJk4MCBprIrzIeybyEKfiABEkhgAjSoBjsfcm+426uVVSwC64c7F4tISeGkNm3aWBLUXsu+2EydiQRIgAQSlQANqqGe13IvjFasSQfWNz0XixCBVu1lCtkXLwFMJEACJJCoBGhQDfU85N5BgwYZiWtrZaQlq4LaQ/bF+luTErWhrmE2JEACJGALARpUQ5gh9/bt29dIbpHIvZEWaNVeplr21S8DkdaL55MACZCA2wnQoBroQZNyL6qDTcFNy726mVbuZYpg+ZR9NWn+JQESSDQCNKgGetyk3KuNs4mlN8GaZpXsi5cAyr7BqPM4CZCA1wnQoBro4RUrVhiTe+2ItGSV7KtfAij7GripmAUJkIDrCNCgxthl2HFl8eLFYsK7F1WxI9KSln137twZY+uLX45wi1jqQ9m3OBd+IwESSAwC3L4txn6GAfzwww/l9ddfjzGn85cjJi4MUySxgLEO1efzRVQ+XgSSk5MjKiecAtatWyfw+D158qTxvMMpn+eQAAmQQLwIcIQaI/nMzExjci+qgrWikRjTaKuPUaoV5VD2jbZHeB0JkIDbCdCgxtCDpuXeGKrimEthpCH7btmyxTF1YkVIgARIwA4CNKgxUM7OzlaRhzCqjGeKVO61uq7w9oUUzkQCJEACiUSABjWG3obciyUoTMUJQPbFrjtW7JZTvCR+IwESIAHnEKBTUpR9Abm3Tp06sn//fsF8JFNxAuPGjZOqVavK0KFDi//AbyRAAiTgUQIcoUbZsVrupTENDBDLiCj7BmbDoyRAAt4kQIMaZb9S7g0NDgaVsm9oRvyVBEjAWwRoUKPoT+3di4hDJhLWnsY7ma4DHLWw+w4iPzGRAAmQQCIQoEGNopc3bNigvHtNyL06wIJpgxZJsyZPnixTpkyJ5JKwzsXuO5R9w0LFk0iABDxAgAY1ik5cunSpMe9ezMWa2kc1iqaoS6zay5Syb7Q9wutIgATcSIAGNcJew0hy6tSpYkruxVzsbbfdFmEtip+O0IOxJKv2MqXsG0uv8FoSIAG3EaBBjbDHcnJyjMq9CKzfrl27CGth/vT+/ftbEtQesi9242EiARIgAa8ToEGNsIcXLlxoVO7t2bOnI9axtmrVypK9TCH74qUBc8VMJEACJOBlAjSoEfSulntvuOGGCK4KfqqTlt5YFdRey76YK2YiARIgAS8ToEGNoHch97Zt21YaNWoUwVWBTzW99CZwKeEf1UHtrdjLFLIvXh6YSIAESMDLBGhQI+hdyL2YazSRnBhpCUHtR40aJadOnTLRxMI8mjZtStm3kAY/kAAJeJUADWqYPavlXiwxMZGcJPfq9lgl+2K9LuaKKftq0vxLAiTgRQI0qGH2qpZ7scTERBo9erT06NHDRFbG8oDsi2D/7du3N5anzgi78lD21TT4lwRIwIsEuNtMmL06ePBgadGihSN3T8E6VKftiVoSK+aMuTtPSSr8TgIk4CUCHKGG0Zum5d4wivTcKZR9PdelbBAJkEAJAjSoJYAE+rpr1y7l3WtK7g1URiIco+ybCL3MNpJA4hKgQQ2j77GUxJR3bxjFRXyK0+Ve3SCEa0SQB4z4mUiABEjAawRoUMvoUSwhwVISU969ZRTn6Z+17AsHLyYSIAES8BoBGtQyenTz5s2Ue8tgFMnPkH2xnpeJBEiABLxGgF6+ZfTouHHjpGrVqo707i2j6o78WXv7HjlyRBCWkIkESIAEvEKAI9QQPanlXgSOT8SE9pue74Tsi/CNlH0T8Y5im0nA2wRoUEP0L+ReJB1BKMSpZf4Ew4Rt2ty068pTTz0l8+bNK7NtkZ4ABy/KvpFS4/kkQAJOJ0CDGqKH4N07duxYQQShWJMekWGE5pbUpUsXmT17tvHqwsELm7SbHv0arygzJAESIIEICNCgBoGl5V4EjDeRTAbWN1GfcPLAXqYbN26UvLy8cE4P+xys56XsGzYunkgCJOASAjSoQTrKpNwL44wRmVVLbxB60Iqk9zL9+OOPjWdP2dc4UmZIAiQQZwI0qEE6wKTc6+alN1btZUrZN8iNx8MkQAKuJUCDGqTrEMzBlNzr9EhLQRCow5B9Ed3ItDOVln0R1pGJBEiABLxAwJ0G9USeZGfOkwkDusmI7G+C9MM5OZY9UmolJQkkUfVft+mSdy7I6X6Ht27dqr6Z8O7Vc7FWyb1+1bbkI2Rfq/YyheyLlw0mEiABEvACAfcZ1HOfyfTfPC6zMv5Hhs0+ErwPzu2XFXPfkfzCM1Ik/dc3ScMwWrx27Vpj3r16LtbNgfWtCmqPlwwoAXjpYCIBEiABtxMIw7w4rInlmsjAJQtkxlOPSHrQqp2TE1sy5bXLJ8lRn0/tFerzHZRlA5tIOA3GUhGTci+W3rg56aD2Vsm++qXDzYxYdxIgARIIx764kNK3smHBXMl6/jkZOz1TsvOOhd0GyL1YKmJC7kWhmIO8/fbbwy7fiSdi7ez+/fvFijW0vXr1ouzrxE5nnUiABCIm4EmDei7vbXnu+U0ikiXP39dHbm3cV0ZkfiYnwsADuXfYsGFGgjmguPT0dHGz3KuRWWFMkTeUAMq+mjL/kgAJuJmAJw1quUYDZZnPJ2cP5siiacMlDYa1z6MyZdP3ZfYV5F5ECGKyh4BWAij72sObpZAACVhHwJMGVeMql5IqPQc+JysPZsljaZtl4oLNEkr81XIvZFomewggrCPmmOntaw9vlkICJGAdAU8bVI2tXMqt8tcn/iAyZ4XkHAu+bgZy76BBg7itmAZn01/KvjaBZjEkQAKWEkgIgypSTqrUbijNmzeU2lWCNxlyLyIDuS35fD63VblYfSn7FsPBLyRAAi4lENy6uLRBgat9Tk4c+FpSR9wljYK0mHJvYHJ2HNWy75YtW+wojmWQAAmQgCUEgpgXS8qyKdMzkr/pPVm8KV/Oi7tnJH/DP2Ts6lR5MO3yoHWg3BsUjS0/QPa1Yqs4WyrPQkiABEhAoIW6Ln0j2SPayAWN75Ms2STP31pDkkqGFDy6UV5sU0suSEqSWgNeknUnOssTz3SVlBCtXbFihSvl3nh0H/YxNR3dCLIv1v/qsI/xaBfLJAESIIFYCCT53D4BF0vrC65FBKA6derIkSNHjDgkDR8+XP76178ayctA84xn0a5dOxkzZoxaY2sy83HjxknVqlVl6NChJrNlXiRAAiRgC4EQYzZbyndEIdnZ2ca8ezHCGj9+vCPaZVUlrNrLFMuVKPta1WvMlwRIwGoCNKgikpmZaUzutXQu9uR/ZNV762Xv9z9ZfV+EzN+qvUxhUCn7hkTPH0mABBxMIOENKuRe7PdpKphD1EtvfEclb8kE+WO7WpLUsLMMeHK6ZOd9Kz/73zyV6kiD4zOkTZ1u8uQHh/1/sfWz3ss0JyfHaLnYKg7rgPFSwkQCJEACbiOQ8AYVci/2+8TDPNYU/dKb0/LlW09JjzuHycyNVSSt9VVybvMr0jO1pzw4fYMc/lmvM60gdW7qJOknvpQvvjkda3Vjuh6yLxy5TCesA6bsa5oq8yMBErCDQMIbVMi92O/TRIpa7j3zmSz639nynyaPyJu7cyR7wRyZs2SDHM57UboeelUGP7tC8guMatKFF8nFJSqLzdPtTpB9MVds2tuXsq/dPcnySIAETBFIaIOq5V7s92kiRS33Htkrm/5dQdKH/UnublBVzpvHclIhJVV6j5wir3b/XCaNX1loVE3UNdY8tOxrOqg9Zd9Ye4bXkwAJxItAQhtULfea2JoserlXRC6uLJdeWkmurF45wMLgiyXlxvvk8Z5HZearqyX/Jy3/xuuWKSoXsq8VQe0h+1ohJxfVnJ9IgARIwDyBhDaoJuXe7du3R7/05tJWctefrpB3lmyUgwHt5QVSpWlvGXb3zzLvhbdkn/n7IKocW7VqpfYyjeriEBdB9oWjGBQEJhIgARJwC4GENaim5d4qVarIH/7wh+j6PammdHr8VZl08RwZ9fJK+fzE2QD5JMmFKZ3l/kFdpf41zug2RDdCMAzTScu+UBCYSIAESMAtBBI2UhJGp5jzXLRokXP66udjsv/T7fJV1VZyQ73KQep1Vk58ukgWfHeLDOxQQ50DpySvBbzKysqSV155xVn9E6RHeJgESIAEQCBhDergwYPl5ptvFswDuj150aBCQUA4yP3794uJOW639zHrTwIk4HwCztAObeaE4O5Tp04VU969NldfxHdGTv8YfKN02+tjQYEwolgfTNnXArjMkgRIwBICCWlQEeEHD2u3jnx8B5bIxHe/suSGcFKmWB8MaZ6JBEiABNxA4EI3VNJ0HRcuXGgsmIORup3YJm9OWS77w8rMJ6d3r5U96W3DOtvNJ0FBGDBggPL2devLj5v5s+4kQAKREUi4OVTIvcnJyZKbmyuNGjWKjJZVZ/u+lMz7ukmfGZ+FWUID6Z+xSmb1rhPm+e49rVevXurlxwtz3e7tBdacBEggHAIJN0KF3Nu2bVvnGFP0UlId6f7nQXJL+Svl76M6S3IZvfLTrrny4vfhdK/7z9GyLw2q+/uSLSABrxMo49HtveZD7nXewzlJKrXuJ8Ob75Tk2imSUlZo3ktul1/tvcRxnQPPXNPSrJZ9oSyY2MDAcdBYIRIgAc8QSCjJV8u9W7ZsEcSijTXBYaZdu3bGjUis9YrH9abZ+rcBsu8DDzwg6enp/of5mQRIgAQcRSChvHy13GvCmGI01qdPH0d1Zjwro6MbWbGXKWRfKAtMJEACJOBkAgllUE3KvTt37nT10hsrbkqr9jKF7It1wxgFM5EACZCAUwkkjEHFwxgPZezjaSI5bumNiUbFmIdVe5liXhaOZFAYmEiABEjAqQQSxqDu2rVLPZRNyL3aOLs20pJFd6OVsi8cySj7WtRxzJYESMAIgYQxqNi305R3r9sjLRm5c4JkYpXsC2WBsm8Q6DxMAiTgCAIJYVBPnTql9u00Kfd26dLFER2ISiA4vlOSln3z8vKMVgnKAmVfo0iZGQmQgGECCWFQN2/ebFzuNWWcDfdn3LPTsu/HH39svC6UfY0jZYYkQAIGCSSEQYXci7WMJpLJpTcm6uPEPCD7WhHUnrKvE3ubdSIBEtAEPB/YAXJvpUqVBOsj27dvr9sd9d/Jkyera4cOHRp1HqYvdNp+qGCOVLFiRdNNVYE0XnjhBSN9abxyzJAESCChCXjeoK5bt04tlTl58qQlD3gn3D1OM6hWMsELzcMZwIUAACAASURBVLFjx2TkyJFWFsO8SYAESCBiAp43qOPGjVNQvPwATiSDunXrVmnVqpV4+QUp4n/FvIAESMARBDw9h6q9ezt27OgI2KxE7AS0ty8czZhIgARIwEkEPG1Q9UO3devWTmLOusRIAA5mcDRjIgESIAEnEfC05JsIci9upkSSfNHeRJgXd9JDgnUhARIIj4CnDSoMjSnv3vBwxuesRDOopj2349NrLJUESMBrBDwr+cJ5BSkR5F6fz+e1+zJke7AcZ+zYsZR9Q1LijyRAAnYT8KxBxcgUD10r1kLa3UluL890GELwgKPZqFGjRK95dTsj1p8ESMD9BDxrUGfPnq0euia6CKNd7sUZHUlsxN64cWPj/LTyoB3PoqsdryIBEiABcwQ8aVBhADdu3GhE7sUICOsesf0bU+QEsJdpz549je9lqmXfLVu2RF4pXkECJEACFhDwpEGF3Dto0CAjcq8eAekRkQV94PkssTOPFXuZQvaFEsFEAiRAAk4g4EmDiocsArSbSFjvyLnY2EhaFdQeLzlQIrQDWmy15NUkQAIkEBsBzxlULfdiX85YEyMtxUrw/PU6uhF26jGZtOwLRYKJBEiABOJNwHMGVcu92Jcz1kS5N1aCRddbtZcpXpwo+xZx5icSIIH4EfCcQaXcG7+bKVTJVsm+MKiUfUOR528kQAJ2EfCUQTUp96IDFi1aZGzpjZUdikhJTk9Wyb5QIuCARtnX6XcA60cC3ifgKYNqUu7Vxpneveb+EUD2XbFihbkMC3KCAxplX+NYmSEJkECEBDwVyxe7kDzwwAOSnp4eIYbSp7tpI2u3xPJFcAwTc9slewv5JicnC9akYiTMRAIkQALxIOAZg4qIPHXq1JEjR44YeWjDwxf/WWEATHe0Wwyq6Xb75zd48GBp0aKFDB061P8wP5MACZCAbQQ8I/lmZ2eruTRTBhBLMkzlZVtvJnBBkH2tkJMTGCmbTgIkECEBzxjUzMxMY8EcImTI0x1AAN6+ixcvFigVTCRAAiQQDwKeMKh4iOJh2rRp03gwZJkOIAA1Ad6+UCqYSIAESCAeBDxhUPEQRQB2BGJnSlwCkH2hVDCRAAmQQDwIeMKg4iHau3fvePBjmQ4iAIWCsq+DOoRVIYEEI+B6g6rl3s6dOydY17G5JQnoreIo+5Ykw+8kQAJ2EHC9QaXcK+Lz+ey4V4yWgSVJeXl5RvNEZlAqKPsax8oMSYAEwiDgeoNqUu5FgAAmewhg44HGjRsbLwxKBWVf41iZIQmQQBgEXG1QTcu9AwcOlKysrDCw8ZRYCeiQjqb3MqXsG2vP8HoSIIFoCbjaoG7YsMGYd682zib2UY22MxLpOiv3MqXsm0h3EttKAs4hcKFzqhJ5TZYuXWrMuxdzsVjHGM/oSHpO8ZNPPlEwMHr77rvv1Ofc3FxZvnx5xJCaN29ebMecTp06qTzq168vlSpVUuEaYdzikTp27CiPPPKI8XCBkH0HDBggVsUOjgcrlkkCJOB8Aq6N5asDou/fv9/I+lME1sduKHYsv4Hh3Ldvn4rqg4Dua9askR07dhTeLWlpaVK5cmW5/PLLpXr16up4tWrVpGrVqoXnhPvh2LFjcvToUXX66dOnCyMJvfvuu8WyQAxcGNm6detKs2bNbDG0cEyCUbciqL3JjRKKgeIXEiABEghCwLUGFXOdr7zyitqzNEjbwj4MuReB9U0ZZ/+CYfh37dolGGGuXLlS5s2bp35u27at1KxZUxo2bCjaWGJ0XL58ef/LLf986NAh+fHHH+Xrr7+W/Px82bNnj2zatEmV261bN8F/7dq1k2uvvdaS0btVQe2xnduHH34or7/+uuUMWQAJkAAJgIBrDSoexDfffLMaVcbalXj4wlsYG4qbSJBq4cXqb0DvuOMOZTxhRFNSUmw3nJG2C4YWLxgwshhB/uc//5GuXbvKbbfdJpCN4aFrQirGi9Hjjz8umA83mfRLkqndh0zWjXmRAAl4k4ArDaqWe01JhZAHIfVC8o02wYiuWrVKZsyYoeRbyLYwOtdcc41ceeWV0WbrmOvA/KuvvhLM72q5+IknnlAjWHjsRmtcTfelPzCMrMeMGWNkf1z/fPmZBEiABAIRcKVBNTmq0SOZaOReXJuRkSHTpk1TRhSjUMw/1qtXT6pUqRKItyXHfv/738sbb7xhSd6BMj1z5oyaA/7ss89kwYIF6pTRo0crj+toNvg2qTb41xebxG/bto2yrz8UfiYBErCMgCsNqsl5t2jk3nXr1smUKVOUEUtNTZUuXbrYbkT97wi7Dap/2dq4Yt4VI1fIwkOGDFHScLijVjgnhXuuf9llfYZq0KpVK2ObzpdVHn8nARJIbAKuM6imJUKMMr/55hspa2SFhz6W6Tz99NOyfft2tSwDS1KcIOfG06D6//M5ceKEmm/FEqSLL75YLUO69957LXFm8i831GfKvqHo8DcSIAGTBBxtUGE8S64LNSn3hgsSDkswpDCqt99+u/J4tVPSLaueTjGoup4YtcKrGYZ148aNShL/7W9/a8koVJcZ7C9l32BkeJwESMA0AUdHSkpOThbIuzCiMK5ICxcujMl5KBKAkAy7d+8uffr0UZ6tjz32mGC5i5OMaSTtsetcLP3B6P3hhx+WJ598UsaNG6eW3sQjaH2HDh1k6tSphfePXQxYDgmQQOIRcLRBHTZsmHoYYi0kjCu8cPFwxMPaygTj/Ze//EXNv0HSxXwpDKnda0StbKNdeTdq1EhGjRolt956q3oxgQSsI0LZUQdI+eg7rAVmIgESIAErCTjaoMJj1j/NmTNHfcWSlJIjV//zYvkMhyOExPvggw9kwoQJysmGI9JYiIp6EYFRw4sJQiliORGUBrsSXsQQjYqJBEiABKwk4Og5VO2lWRYAjGT/+te/lppvLes6/98xP/qPf/xD/t//+39y//33y/XXX++aEanT5lD9uQb6jDCLkH9vvPFGZWSt8PD1L1ffRydPnozLPK5/XfiZBEjAuwQcPUL9xS9+USZ5jHweeuihmI0plnq8/PLLMnbsWBWBifJumeijPgGS/YMPPihffvml3HDDDYXxhaPOsIwLteyL6FVMJEACJGAVAUcbVHj4wmAGS/gNIx3sgRltwrKZnj17qoc6nGgQHJ7JegLoW0ixiKGMcIZ6XhXz1/qzyVogGhZlX5NEmRcJkEBJAo42qKgsHoSBErZawwMyVmOK6EY//fSTQDYtuUQnULk8Zo4AVAAsp0FwDMyrwpAuWbJEhg8fbq6QgpwwLw7nKEj7TCRAAiRgBQHHG9QmTZqUajeM6UsvvRT1fBgcmrBGcsSIEcqIYqTkZonXzrCDpTrDwAFEV8L+pViehF1tFi9ebFwGRrxhpPBk3zOSv+HvMqBWkiQl1ZJOIzIl78S5AC09J8eyR0qtJJxX8F+36ZIX6NQAV/MQCZCAtwg43qCW9PTFPCe25IrWkQWSIpbeIIg9dlBxuzH1yu0Iowq5HS9LPXr0ML77DO4XzI+XLfuekxNblkqW9JYZB31y9uBCuevQU5L27Go5VhL2uf2yYu47kl94PEXSf32TNHT8v6rCCvMDCZCAQQKO/6ePOTadYEyxEXYsKScnR6677jpZv369YE2km0emsXBw4rUYoSJkoc/nU2EeTdcxLNn33BeSc7S13NsuRfCPo1zKjXLfgDtF5qyQnGP+Q08Y3kx57fJJctTnU3X2+Q7KsoFN1HWm6878SIAEnE/A8QYVIws4DS1btixmY4rugDz66aefqu3aOGfqrBsULzd4yUGQ/eXLlxuPbhSW7FuunqSl1fEzimfk0L4vpPFfekm7qv7/XL6VDQvmStbzz8nY6ZmSnVdq/OosuKwNCZCA5QQcvQ5Vtx4yrQnjB4cULNnAHqVwQmJyJoEPP/xQeW9jW7w777zTaCURBrFq1arhvZydyJPsBTNl1u5O8rcxXSXFz56ey5sutzW+T7IKa5cuwzMmyRO9m4h9G/cVFs4PJEACDiDg94hwQG2CVMGEMUXWGOXu2bNHbbcWpCgedgABBNVAwly56QTZF1v2hU4FzkaXNJZb7/sfmf3RKvlod/ERaLlGA2WZD3OsObJo2nBJkyx5vs+jMmXT96Gz5q8kQAKeJeAKg2qK/muvvaZGp07Ycs1Um7yYD6RfBHx45513LJF9sQMOoicFT+WkaudxctD3oxzMmS3DZab0SRspmV+dKXVJuZRU6TnwOVl5MEseS9ssExdsLu28VOoqHiABEvAigYQxqJB733//fcHuI0zOJwCvXyT0mcmkvX3Xrl0bRrblJSX1Xvmf18ZIev7Hsj63+CjVP4NyKbfKX5/4QwDnJf+z+JkESMDLBBLGoELuRdKOKV7qVC/OB0Pmv/zyy9XyJtN91aZNmzBk36JSyzW8SX6dfnHRgYCfykmV2g2lefOGUrtKwvyzCkiCB0kgUQkkzL98BAvAQ/rSSy9N1L52XbsR5GHFihXGZV8Y1LJlXz9cJw5K7p5Wcn3jqn4HS348JycOfC2pI+6SRgnzr6okA34ngcQmkBD/9CH3zpw5UwJFXUrs7nd266Em4AXI9F6meLFCAIlAsu+5rzLlvlrdZMSsDZKPZafnvpLsv02RQyOHSPpV5QuAnZH8Te/J4k35cn5lKiIr/UPGrk6VB9MudzZU1o4ESMAyAglhUHW4OSyXYHIXgVq1ainvbNO17tu3b0DZt1y1RtK+60F5/g/XS60LkqTWH/8p3/eZJDMGNiu+HOboRnmxTS25IClJag14Sdad6CxPPFN8aY3pOjM/EiABZxNwxTrUWBE+/fTTkpWVpUY7CMbuteS2/VDD5Q9ZFi9DWJdqei9TrG1OTk6WLVu2CLZ3YyIBEiCBWAl4foQKuXf06NFy1VVXyQ8//BArL15vI4HTp0+rIAwIxKFVBlPFh5J9TZXBfEiABBKLgOcNam5urupRzMetXr3ak73r9t1mgnUK9qpt2LChtGrVyjLZF05PTCRAAiRggoDnDeqqVaukX79+csUVVyhehw4dMsGNeVhM4MyZMyqmb82aNZUz2bPPPmt8L1N4+1qxVZzFaJg9CZCAQwl43qBimzZ49yL6TlpamtqyzaF9wWr5Edi3b5/6lpKSIldffbX6bJXsi71xmUiABEggVgKeNqgIL7djx47CBzJixELiw+iHydkENm3apDYdx4sQ/oPKYIU8C2/fzMxMZ8Ng7UiABFxBwNMGVcu9eCAjNW7cWP3dtm2bKzonUSsJWR5buGFnIJ2gMsC5DE5mJlPTpk0p+5oEyrxIIIEJeNqgQu6tV69eYffCsPbo0UOWLFkiJ06cKDzOD84igP654447xH8TA6tk39q1a6v9din7OuseYG1IwI0EPGtQtdzrb1DRQW3btlXrUbGTCZPzCGDt6f79+0vtg6pl3w0bNhivdO/evSn7GqfKDEkg8Qh41qBC7oUTUpUqpbd77t+/v5IU8fBmcg4BSL2TJk2Su+++O2C/QfaF6mA6de7cmbKvaajMjwQSkIBnDSoevHqj6pL9ikX9I0aMUA/vvLy8kj/zexwIIHLRq6++qhyR/OdO/asC2RdOZqH3MvW/IrzPlH3D48SzSIAEQhPwpEENJvf6o8BDe8CAAfLMM88Ijao/Gfs/w5hiZFqnTh3p2LFj0Apo2Rfqg+lE2dc0UeZHAolHwJMGdc2aNUHlXv8uxibWNKr+ROz/7G9MIcVrj+xgNcGcuJWyL+rDRAIkQALREPCkQZ0+fXpQubckJH+jyjnVknSs/Q5lQI9MwzGmqA0MqpWyb05OjrWNZu4kQAKeJeA5g4r4r9u3by+2XKas3oNRffLJJ9XD/e2332bgh7KAGfgdO8hAbu/QoYPam7SskakuEk5mcDazSvZduHChLop/SYAESCAiAp7bvg2j0zlz5qiHdEQkRARepnCMQRo4cKDUrVs30ix4fhkEIKkiMhGWxtxzzz3SqFGjMq4o/TNGqEuXLhXTATrwMoZ53CNHjggc15hIgARIIBICnhuhzp8/P2y5tyQoBBIYNWqUpKamqr8YrTIARElK0X1HuEdI6g899JDK4OGHH47KmOJiyL5QIazw9sU6Zcq+0fUxryKBRCfgqRGqHmFMmTIl4DrGSDr7iy++kLfeeku+++47FV2pRYsWZTrMRJJ/Ip2LudL33ntPscQa02DLYiJhMnXqVOnVq5fAMJtMkydPViPf119/3WS2zIsESCABCHjKoMYi9wbqa4yqICsiFB4SwhbSsAYiFfgYDCli8upA91gSE+5caeAci45C9sXuM1lZWUUHDXzCqBf7r1L2NQCTWZBAghHwlEFNT0+X+vXry80332y0G2lYI8NZ0pDeeOONMSsGJWsAKX7IkCFqLhaBGUymdu3ayZgxYwT3ExMJkAAJhEvAMwZVy70vvfSSZQ4l/oZ1z549hVF9/IO4hwvea+fBwG3ZskVtsabZWGFI/blB9r333nuVA5n/8Vg/U/aNlSCvJ4HEJOAZgwq595VXXpFHHnnE8p6EYcUG2B988IGsXr1a2rRpI+3bt5drr73W+EjM8sbEUACM6Oeffy7r168vxsEuWZyybwydx0tJgASME/CMQe3evbvaSNy03FsWcSwD+fTTT9U8IbxDsUYS+65ed911lo2Uy6qTlb+XNKINGjRQa0nhaGT3SB3s4TWMJThWyL4vvPCCelGykifzJgES8A4BTxhUO+TecLpcG1cYVjjiwNhgCQ6WeVx11VWuNLAwoAcPHhR4PePFAW3TRhRrSOO9VhdG74EHHrBE9j127JiMHDkynK7nOSRAAiQgnjCos2fPFsx7mV5CEcv9oUdykERhXDGvCEOELcgaNmwoNWvWlOTkZEdJxJCy8VKAEV9+fr7s3bu3cE0mNvxGvdEGJwU9QMQl1NMqb9+TJ09KxYoVY7kVeC0JkECCEPCEQUXEnUsuucS4d6/JewCG6ptvvlEjPfzFchKdYKwqV64sKSkpUq1aNalatapaXmKF4YKhx38//vijfP311/L999+ren322WfK6KNOkK0x8oSEW6NGDdulXM0lnL+UfcOhxHNIgATsIOB6g4oHKkZ6Vnr3WtURqPvx48eDGjZdLpyerrjiCv1V/cVoMVjC6PKHH34o/Bmf4TxVMgUy5HbPg5asUzTfEWB/6NChggD7JtO4ceNUdpR9TVJlXiTgXQKuN6iQ+h5//HFHyb0mbhc9kkRehw8fltOnTxfLdvfu3cW++3+Bg06FChX8D6kYtTiAwApWjHyLFWbzF8i+8Lp+//33jZa8bt065XBF2dcoVmZGAp4l4HqD6ga517N3j0MapmVf09GNTp06JZUqVZK1a9fS29chfc1qkICTCbg6OD4epPPmzVNLVJwMmXWzlgBG3FYEtYcz0tixYwUb1jORAAmQQFkEXG1Q9RIOr0mYZXUafy9NoHXr1jJr1qzSP8R4BPGHsQMRRqtMJEACJBCKgKsNKh6g2KCaiQQQSANqBVQLkwmGGgmB+JlIgARIIBQB1xpULfdGs0F1KCD8zZ0EoFJgjSxUC5NJy76IU8xEAiRAAqEIuNagark33pF6QsHlb/YSgFphleyL4CFMJEACJBCKgGsN6ty5cyn3hurZBPwNaoVVsu/GjRsFe6UykQAJkEAwAq40qJB7MWKg3BusWxPzONSKa665xjLZF8tnmEiABEggGAFXGlTIvXhwUu4N1q2Je/ymm24SqBemE6JVUfY1TZX5kYC3CLjSoGKkgAcnEwmUJADVAobPtLcvDCpl35K0+Z0ESMCfgOsMKtYDPvvss5R7/XuRnwsJWCX7wot40KBBKmpSYWH8QAIkQAJ+BFxnULEekHKvXw/yYykCUC+smO/s27cvZd9StHmABEhAE3CdQV22bBnlXt17/BuQAGRfqBimoxtR9g2ImwdJgAQKCLjKoFLu5X0bDgEt+5qObkTZNxz6PIcEEpeAqwyqfkBiI24mEghFoFWrVgI1w3SC7LtixQrT2TI/EiABDxBwlUHFA7Jfv35qT08PsGcTLCTQpEkTy2TfxYsXy4EDByysPbMmARJwIwHXGFQt9+JByUQCZRG4+uqr1Sla1Sjr/HB/17JvdnZ2uJfwPBIggQQh4BqDqh+M+kGZIP3DZkZJoHz58krNsEKeheybmZkZZc14GQmQgFcJuMag4sFIudert6E17YKaMXr0aOPevk2bNhXKvtb0GXMlATcTcIVBhdyLByPlXjffavbXXasZWt0wVYPatWtLz549hbKvKaLMhwS8QcAVBjU3N1fR1g9Ib6BnK6wmYKXs27t3b8q+Vncg8ycBlxFwhUFdtWoV5V6X3VhOqS5UjYyMDOPV6dy5M2Vf41SZIQm4m4ArDOqMGTMo97r7Potb7aFq7Nixw/heppR949alLJgEHEvA8QYVmzrjgUi517H3kKMrpmVfqBymE2Vf00SZHwm4m4DjDSrlXnffYE6ofb169QQqh+mkZV/TW8WZrifzIwESsIeA4w0qHoR4IDKRQLQEcP9YKftiw3smEiABEnC0QdVyLw0qb9RYCFSpUkXS0tLEKtl34cKFsVSP15IACXiEgKMNKh6AeBDigchEArEQuP7662XmzJmxZBHwWsi+U6dOFcq+AfHwIAkkFAFHG1TIvXgQMpFArASgcmzfvt0Sb9+2bdsKZd9Ye4jXk4D7CTjWoFLudf/N5aQWaNl3zZo1xqvVv39/oexrHCszJAHXEXCsQcWDj3Kv6+4nR1cYasf06dON17FDhw6UfY1TZYYk4D4CjjWoePBR7nXfDeXkGmvZ1/Repi1bthTKvk7uedaNBOwh4EiDigce5rvo3WvPTZAopWjZNysry3iTKfsaR8oMScB1BBxpUPHAo9zrunvJFRWG6jF//nzjdaXsaxwpMyQB1xFwpEHFA49yr+vuJVdUGKrH8uXLxSrZd9euXa7gwEqSAAmYJ+A4g4oHHR54lHvNdzZzFLWmOTU1VaySfa3wIma/kQAJuIOA4wwq5V533DhurmWbNm0sk31HjRolp06dcjMe1p0ESCBKAo4zqJB7GzduHGVzeBkJlE3guuuus1T23bx5c9mV4BkkQAKeI+Aog6rlXjzwmEjAKgKXXXaZWuaSnZ1tvIhevXoJZV/jWJkhCbiCgKMMKuRezG/hgcdEAlYSaN26tcybN894ER07dhTKvsaxMkMScAUBRxnUBQsWCOa3mEjAagJQQZYtW2bc2xeGGomyr9U9yPxJwHkEHGNQIffiAUe513k3iRdrpGXfnTt3Gm1exYoVZezYsZR9jVJlZiTgDgKOMaiYz0L4Nsq97rhxvFBLjCZnzZplvCmUfY0jZYYk4AoCjjGoGJ1qucwV5FhJ1xOAGoJ5VNN7mer7mLKv628RNoAEIiLgCIOKBxoebJR7I+o7nhwjAS37mt7LVMu+W7ZsibGGvJwESMBNBBxhUPFAo9zrptvGO3Vt2rSpZbLv7NmzvQOKLSEBEiiTgCMMKuaxtExWZo15AgkYJNCoUSPLZN+NGzfK1q1bDdaWWZEACTiZQNwNKuVeJ98e3q9b3bp1pUGDBmKV7Lt27VrvQ2QLSYAEFIG4G1Q8yPBAo3cv78h4EcDWa3PnzjVePNZUU/Y1jpUZkoBjCcTdoELuxQONiQTiRQCyLwyfaW9fGFTKvvHqVZZLAvYTiKtB1XIvHmhMJBAvApB9r7nmGuOyL1SXQYMGCWXfePUsyyUBewnE1aBquRcPNCYSiCeBm266yRLD17dvX8q+8exYlk0CNhJI8vl8PhvLK1bUgAEDJCkpSbp27VrsOL+QgN0EvvjiCxXU/uTJk4J1pKYSVJjk5GTBmtSWLVuaypb5kAAJOJBA3EaoeNBg3opyrwPvigSskpZ9TUc3ouybgDcTm5ywBOJmUCH3Yt6Kcm/C3nuOazhkX4TANJ0o+5omyvxIwJkE4mZQ4aiBBxgTCTiFAF7unn32WTl16pTRKmlvX+yoxEQCJOBdAnExqHhg4cFFude7N5YbW3b11Veralsl+2JHJSYSIAHvEoiLQcUDi3Kvd28qt7asfPny0q9fP8tk38zMTLeiYb1JgATCIBAXg4p5Ksq9YfQOT7GdQJMmTSyRfRGEf/HixULZ1/YuZYEkYBsB2w0q5V7b+pYFRUHAKtm3du3a0rNnT6HsG0Wn8BIScAkB2w2qnp9KSUlxCSJWM5EIaNl3xYoVxpvdu3dvoexrHCszJAHHELDdoELuxTwVHlxMJOBEApB9MzIyjFetc+fOlH2NU2WGJOAcArYaVC334oHFRAJOJQDZd8eOHcb3MqXs69QeZ71IwAwBWw2qlnv1PJWZJjAXEjBLQMu+q1atMpuxiFD2NY6UGZKAYwjYalAxL0W51zF9z4qEIAAVZcaMGSHOiO4nyr7RceNVJOAGArYZVMi9o0ePFsq9brgtWMdatWpZKvvu3LmTkEmABDxGwDaDmpubq9BR7vXYHeTR5lSpUkXS0tLEKtl34cKFHiXHZpFA4hKwzaDiwUS5N3FvNDe2/Prrr7dM9p06dapgxyUmEiAB7xCwzaBiPopyr3dunERoSb169SyTfdu2bSvYcYmJBEjAOwRsMahbt25VDybKvd65cRKhJVr2XbNmjfHm9u/fXyj7GsfKDEkgrgRsMaiUe+Paxyw8BgKQfadPnx5DDoEv7dChg1D2DcyGR0nArQRsMaiQeyGfMZGA2wjgvt2+fbvxoPYtW7YUyr5uuxtYXxIITcByg6rlXhrU0B3BX51JQMu+WVlZxitI2dc4UmZIAnElYLlBhdyL5Qd4MDGRgBsJQPadP3++8apT9jWOlBmSQFwJWG5QIffigcREAm4lAHVl+fLllH3d2oGsNwnYRMBSg0q516ZeZDGWEoC6kpqaKlbJvlw+Y2n3MXMSsI2ApQYVyw0o99rWlyzIQgJt2rSxTPYdNWqUIDQnEwmQgLsJWGpQsdyAHCyX5AAAHI1JREFUcq+7bxDW/jyB6667zlLZV+/ERN4kQALuJWCZQc3Ly1PLDejd696bgzUvInDZZZepZS7Z2dlFBw196tWrl1gRPMJQ9ZgNCZBAmAQsM6hr166l3BtmJ/A0dxBo3bq1zJs3z3hlO3bsKJR9jWNlhiRgOwHLDCqWGVDutb0/WaCFBCD7Llu2zLi3Lww1EmVfCzuPWZOADQQsMagHDhxQ802Ue23oQRZhGwEt+5rey7RixYoyduxYyr629SQLIgFrCFhiULG8gN691nQYc40vAYwmZ82aZbwSlH2NI2WGJGA7AUsMKuTexo0b294YFkgCVhOA7It5VNN7mVL2tbrnmD8JWE/AuEHVci8ePEwk4DUCWvY1HYyBsq/X7hS2JxEJXGi60ZB7EVUGDx6myAkcOnSo1EX79+8vdSzSAzVr1pSLL7642GXoo/Llyxc7xi9lE2jatKmSfdPT08s+OYIzIPs+8sgjMnLkyAiu4qkkQAJOIZDk8/l8JivTvXt3wUbiN998s8lsXZvXmTNnCuVBbRi///57+eabb1Sbvv76a9m4cWPI9t1xxx0hfw/nx88++0z27NkT9NSGDRsWyvSVK1eWlJQUda42xAi/xw0OzuP74osv1DKXI0eOGH1xRLSkSpUqyZYtWwTbuzGRAAm4i4BRgwq5t06dOvLSSy8ZfdA4HSnm02A4YTBPnz6tllX83//9n5SUBbVh9DdY1apVk6pVqxY28corryz8bPUHXW+U8+OPPwqMO5K/wX/33XeLVQN7eMLIXn755VK9enX1GSNfO+tdrEJx+vLUU0/JK6+8IqZHqePGjVP3w9ChQ+PUMhZLAiQQLQGjBnX27NkyefJkefjhh6Otj6OvgwE6fvy4Mjz5+fnq7+rVqwvrDM9mGEuM9ipUqCA1atRQv3nB2Gjje+zYMTl69Kig/T/88IP4G1zEu73iiitU+/GiAKPrVekfu89A3DHt8Yspk8cff1w2bNhQeF/xAwmQgDsIGDWoXpJ7YUAgy2KkiZG3v+HASFOP0DAiT3Q5VMvahw8fVqNb8PKXmPGiUbduXTWKveqqqzxhZK2SfXHfJScnU/Z1x/OTtSSBYgSMGVT9IHCr3AtnIEi2u3fvLjQGDRo0kCZNmqgRF2TOSy65xBPGoNgdYOGXEydOCOYZISVjRLtp06bCeVy8lNSuXVt+8YtfqPlaNzpHPf3000qRMS37Dh48WFq0aCGUfS28OZk1CVhAwJhB1VKVW+RefwOqR596JIXRlJflSgvuo7Cz1Eb2yy+/lNzcXNGSOdhj7bKbDCxkX9T3mWeeCbv94Zyo/y1R9g2HFs8hAecQMGZQ77nnHjWCc6p3Lx7kn3/+ufpvwYIFqgfc+BB3zq1jrib65Wbbtm2FBhYjWMxFQyVw6jysln1PnjwpWEdqKmm1h96+pogyHxKwh4ARg6ofAE6Te1GvTz/9VHnbQm7Ew7lDhw5qPq9WrVpcBmLPPRZRKZiPhTyMESz6DJ7Sut8aNWqk+i6iDC0+GbLvjBkzpH379kZLouxrFCczIwFbCBgxqJCoHnjgAcHDJd4JowbsxYrt47DuUo9CEbnJqSOdeDNzcvl4Kfrqq69k/fr1avQK44rAIZjbxnrneM+9UvZ18t3DupGAvQSMGFTIvRdddJF07drV3toXlKZHoitWrCg0otg6DrvdMBhBXLrEkkIxet23b59yGoNs74SRK17eMIdqlewLRzk4bzGRAAk4n0DMBlXLvdh+Cs48diU9JwojCmkQI1EaUbvox78cbVzR93Aqg3Ht0qWL2K1EoB4DBw5UiogVsi98Evr37x9/4KwBCZBAmQRiNqh2y72QdOG8okco8XiIlkmVJ9hKAC9Xu3btUkZNv1zdcssttknCb7/9tvJQtsLbF9GYFi1aZCtPFkYCJBAdgZgN6oABAyQpKclSuRejABjRdevWKScVeIBiHg1OKkwk4E8AHsM7duxQEYz0qLVVq1aWSv9Wyb46lCdlX/8e5mcScC6BmAyq1XIvRh4fffSRrQ9H53YVaxYJgZIvYf369ZN27dpZEnPYStm3V69e0rt3b8q+kXQ+zyWBOBG4YPTo0aOjLfvDDz9U3pc9e/aMNouA12GUAUOKedkLL7xQsITgrrvukvr168fdqzNghXnQcQQuuOACQZjDG264QZo1ayaYKvj73/+uNgFAjGWTzmooC/cp4jxjLt9kgrHOzMyU3/zmNyazZV4kQAIWEIhphIqoSAiUbsq7F4Z01apVyskEDybMg1HWtaDXEzRL//sLUwaYOjB1f0H2feutt2T79u1G6VL2NYqTmZGApQSiNqh670YT3r2Qdt955x1lSPGQ69SpkyXSnKUkmblrCGCqAs5L2CnG1P2mZV8rohtR9nXNrcWKJjiBqCVfxBmF5BuL3AtDumbNGiXtYk/Q//7v/5Ybb7zRqByX4P3L5gcggDCBcFi66aab1LpWLQVDIo42hKCWfX/++Wd1DwcoNupDlH2jRscLScBWAlGPUJ988kkVHi4auRcPCHjtLlmyRC699FK5/fbbjUlvttJjYZ4g4C8Fw2u9Y8eOUc3VU/b1xO3ARpBA1ASiMqixyL14eM2fP1++++476dGjh9qmKt7h46Kmxws9RQAG8b333lP35t133y3NmzePqH1QXIYMGWLJXqaQfRHe0/RWcRE1kCeTAAmEJHBhyF+D/Lh582b1S0pKSpAzSh/GqPT9999XARmwhKFz586Udktj4pE4EoCDEuIDQz157rnnlMculqyEGwMansNwpoNjXcuWLY22BPVYuHAhDapRqsyMBMwSiGqECrkXe1liKUs4CUsWpk+fruRduP9feeWV4VzGc0ggbgTguLRs2TLlKAdv9rZt24ZVFwSVwCjXKm9fbNgeroEPq8I8iQRIwBiBiA2qlnthVMtacuA/Kr3//vtVrF3Ku8b6jhnZQAAG8l//+pfUqVNHBVgoy5hZKfsiMMWYMWM4SrWh31kECURDoFykF2m5F9JYqIS5UiypwfKECRMmCIJ805iGIsbfnEgA86gYoSJNmjRJbQ0Yqp5a9oX3uumEIPmQfZlIgAScSSDiESr2PN25c2dIuXfjxo3q4YO50u7du9OQOrPvWasICWCZ2GuvvSZleQJjVLt06VI1FxthESFP37p1qyAuMWXfkJj4IwnEjUBEI1TIvYhUiM2dAyVIvNh5A2/yI0aMUEaXo9JApHjMjQSgskB1web1s2fPFsi7gRL24cUcKqIcmUxwdMJcbk5OjslsmRcJkIAhAhEZ1FByL4wpHjJa4o10yYGh9jAbErCUAPb8HTZsmCpj/PjxAuelkknLvtja0HSi7GuaKPMjAXMEIjKoiI4EGbfkqBMPFby5I+FhQy9ecx3EnJxHAAYThg3xgF966aWA86rY7B7rrU2nDh06yNSpUwMactNlMT8SIIHICERkUGfMmFFK7oUxhcQLL0g8ZPCwYSIBrxPASyWWjbVv316wsTiCQvgnyL7Lly+n7OsPhZ9JwOMEwjaocIiAs4W/dy+MKd7Q8dYMY1py5OpxdmweCaidlrAkrKRRxYslRrBWyb6cR+XNRwLOIxC2QUX0F3+5V49M8YaOeL40ps7rXNbIHgJwVsK67JJGtU2bNpbJvqNGjRI4CTKRAAk4h0DYBhVyL2QsJG1MMTKNJji+c5rPmpCAGQIIcgLPdn+jet1111kq+2onQTMtYC4kQAKxEgjLoGq5FwYVSwX0nCmNaaz4eb2XCMCzHWtUYVQR2ARRlbDMJTs723gzESzfiuARxivKDEkggQiEZVAh9yLoN2RdeC5qB6QE4sSmkkBYBPCSCaP66quvKiWndevWMm/evLCujeQkbDFH2TcSYjyXBKwnEJZBhdyLZQB4I96/f78gwD3nTK3vHJbgTgIwdnjpzMzMVPGuEWTfdJAHGGokyr7uvEdYa28SKNOgarkXDhCzZs2S//qv/+LSGG/eC2yVIQJ42cRLJ14+ETEJsi/WcJtMFStWVGu/KfuapMq8SCA2AmXG8sV86Ztvvilff/212hA83G2sYqsWryYB9xPAtoWQZbFZOYzs3LlzjTZq3bp1asnayZMnBQYWL70YscLIYpQMD3wmEiAB+wiUaVBbtGghFSpUkEqVKsmgQYPsqxlLIgEPEEBA/ffff19gXE0HtYcBxb/LiRMnSn5+viAUok6my9L58i8JkEBwAhcG/0lU9Be9UTICODg/nZJDn6yWRVPmytrvReTaHnL/77pLh3rVJalY5X1y+tBnsuPLvbJp/g9yy9i+0rRi8TOKnc4vJBAlAfgeIL61z+dTQe3T09OjzKnoMixbQ2AHvZXbX/7yl6IfRZTEXNa+rcUu4BcSIAEjBELOocK7t2rVqmo/SOf/A/1Zvtu0VrZIK/nD5DfkjTmT5enW38ubT0yV9z4/WQyW79AHMjlzjWyc/U9Ze6bYT/xCAkYJQOr91a9+JV9++aVMnjw5prwh8Q4ePFiSk5OlW7duKqZvoAzhkc9EAiRgP4GQBhWu/5UrVxbIvo5Pvm/lUKXW0r3ZlVIBlU2qLg263yV9m++Tpev3iX9MmaQrO8qjD9wnvfu2c3yzWEH3E8AONYim9M4778QU1B75bNu2rUwgN9xwQ5nn8AQSIAHzBIIa1N27d6t/vAgA7oolMkk15dprk4tLu0mXSI26l5qnxhxJIEICPXv2VFcsWrQowiuLTq9du7ZailOWL0P9+vWLLuInEiAB2wgENagvvviiknsxB+TuVEVaNKh5ftTq7oaw9i4mgC0NEYrwf//3f2NqBYwq/BlCGdXGjRvHVAYvJgESiI5AUIM6Z84cgXTkitFpsLaf2i/bv/ildGleYuQa7HweJwELCXTq1El27twpe/bsiakULJGBUdUbnftnhpEwfmciARKwn0BAg4rILseOHRM8ANybTsrn2Zvkkn4dpV4FevC6tx+9U3O8oF5yySXy2muvxdwoGM3nn39eXn755WJ5tWtHv4BiQPiFBGwkENCgIiLSVVddpcKn2VgXg0X55PTnH8n6Kp3k1nqVDObLrEggNgLY0g0hCU2loUOHFjOqyJ+JBEggPgQCGtR3331X3PwP0/fddll1oLH06libc6fxua9YahACiDQGyRdOf6YSjOratWtVdldffbWpbJkPCZBAhARKGdQPPvhAyb1udb33fb9T3v/4IrmxgzamPjl9cIOs2XU8QjQ8nQTME/jlL3+pZF8soTGZEGZwy5YtKhi/yXyZFwmQQPgESkVK+uabbwT7OmK3jFDpzJnzERGc47SE6Ec5smjaLFmy63spHja1nQye0CpUcxz7G/afrVKlimPrx4pFTgAvq7t27Yr8wjKuaNmyZRln8GcSIAErCZQaoWJ3Gb01VLCC8/LyZMyYMTEtUg+Wd7THfd/lyJwxk5QxLZVH8xbS+IqLig6f2inzh/5RHn19g8j3b8u4wQ/Kc2sOiq/oDMd8GjJkiCAerH6BcUzFWJGoCeDf1759+6K+nheSAAk4k0Cp4Pj33HOP1KhRQ8UDLVnlQ4cOyZIlS2T16tXqpwkTJgjW1zFZR+D3v/+9yhyL9fG5UaNG1hXGnG0hgH9Hjz76qIrva0uBLIQESMAWAqVGqPPmzZOaNWsWKxyy49tvv60eAtqYFjuBXywnsHfvXnnmmWdU/FY8kJncS0BL+FB6mEiABLxDoNQcKpp28cUXqxZCZkTsUOyJyuQMAnihwX/9+vWTzp07c37VGd0SUS20QY3oIp5MAiTgeAIBDSpqjbdnLJ/B1lNMziOwYMECtYXXnXfeqTYvcI5zmPNYsUYkQAIkYAeBUnOoSUlJctttt8nSpUvtKJ9lGCCQmpqqtvXiyMcATJuywHx4bm4u58Rt4s1iSMAOAgFHqDfeeKNaK4dRUKhEp6RQdMz8pp2SguWGvS979OhB6TcYIB4nARIgAZsIBDSolSpVEmzbhrig/l69NtWJxYRBgF6/YUDiKSRAAiRgI4GABlWXjyUx2CbqlltukTfeeEPgacoUfwIPP/ww503j3w1R14BriqNGxwtJwNEESi2b+d3vfif79+8vVmmsfXz88cfl/vvvL3acX+wlcMcdd8iUKVPUGmE6IdnL3mRp3377rcqOa4pNUmVeJBB/AqVGqPXq1ROEHyyZ8AC/+eabpVWrVoI4pPAAZrKHAJyOfvvb3zKIhj24LS8FWyMivCcTCZCAtwiU8vLF1lLYYxFSb6iE4ALwKqVnaShKsf+G5UscycTO0Uk5IJTkRRddVGzbNSfVj3UhARKIjkApybdZs2YqcEBZ8zyYX6UxjQ56JFfRmEZCyx3nYrlMp06d3FFZ1pIESCBsAqUMqn6A5+fnh50JTyQBEgiPAMJ4ItIVXlyZSIAEvEWglEFF85544gkVKclbTWVrSCD+BD7//HM1f6pfXONfI9aABEjAFIGABrVbt27y73//m1uGmaLMfEiggMD69evlj3/8I3mQAAl4kEBAg4r9GhEgn3s2erDH2aS4EcByGci9ffv2jVsdWDAJkIB1BAIa1IoVK8rAgQO5NMY67sw5AQlgowmEkqxdu3YCtp5NJgHvEwhoUNHsAQMGqJ1muGej928CttB6AnBGmjVrlgwZMsT6wlgCCZBAXAgENaiXXXaZTJw4kaPUuHQLC/UagY8++ki6du0q7du391rT2B4SIIECAkENKn7nKJX3CQnETgBzpxidPvXUU7FnxhxIgAQcSyCkQcUoddq0aTJ37lx6/Dq2C1kxpxNYtmyZDB06lKNTp3cU60cCMRIoFXqwZH6nTp2SX/3qV1KtWjW1pVvJ3/mdBEggOIEdO3bIc889pzacoDNScE78hQS8QCDkCBUNhMfvSy+9JNhs/IsvvvBCm9kGErCFAKRexMbGvx0aU1uQsxASiCuBMg0qaoeoLpB+p0+fLvBWZCIBEghNALGwYUxvvPFGrjsNjYq/koBnCIRlUNFabB+Gh8P8+fM5n+qZ7mdDrCKwZs0aOXLkiLzwwgtWFcF8SYAEHEYgbIMK6XfSpEkCGQsPCyYSIIHABDBvCq/e2bNnCxz7mEiABBKDQKkNxkM1Gw+HhQsXSuPGjdVpWFfHRAIkUEQAgVDghPTuu+9Ky5Yti37gJxIgAc8TiMigggbmU9euXSsdOnQQ7InavHlzz0NiA0kgHAJw2nvmmWfkxRdflNtvvz2cS3gOCZCAhwiELfn6txnRXmBU8SbO0IT+ZPg5UQno4A0wpg8//HCiYmC7SSChCZS5DjUUHcylpqWlyYgRIzhSDQWKv3maAF4q4az3wAMP0Jh6uqfZOBIITSAmg4qs161bp+RfhCnknGpo2PzVewRgTLXMy5Gp9/qXLSKBSAhEPIdaMnMt/2JOFaljx45Svnz5kqfxOwl4joCOgkSZ13NdywaRQFQEYh6h6lLxpn733XdLcnKy9O/fn0ZVg+FfzxFA0AZMd2BpDHwJuIOM57qYDSKBqAhE5ZQUqCR4/7733nty8cUXy9ixY9V61UDn8RgJuJkAIoVhfenmzZtly5YtNKZu7kzWnQQMEzBmUFEvxCt966235N5775WHHnpIIIkxkYBXCGBZzPjx49V9jpdHrjP1Ss+yHSRghoAxybdkdRAAol+/fnLHHXdInz59KAGXBMTvriEAiXf9+vXy2muvqTWmf/rTn9SmEa5pACtKAiRgCwHLDCpqf+DAARk0aJDs3r1bBg4cKHXr1rWlUSyEBEwR0DvGIC7vq6++SonXFFjmQwIeJGCpQQUv7Kf6z3/+U+677z41Yu3cubNUqVLFgyjZJC8R8B+VYvriqaeeYlxeL3Uw20ICFhCw3KDqOsMLGA+mvXv3Su/evRkIQoPhX8cROHTokLz55pty+vRpmTBhgqSnpzuujqwQCZCA8wjYZlDRdIxWlyxZokaqiLDUo0cPFQ/YeVhYo0QkAA/ed955RwW2Hz16tDz44IMclSbijcA2k0CUBIx6+ZZVB2wB17dvX7VPZKtWreTRRx+Vt99+m5uWlwWOv1tKAPLuxo0bZciQIXLu3DnJzc2lxGspcWZOAt4kYOsItSTCrVu3ysiRI2Xp0qWC0IWMslSSEL9bSQCGdNu2bUo1qVy5sloSQ3nXSuLMmwS8TSCuBlWjRTzgp59+Wvbt26e2vWrRogWX2Wg4/GucgL8hhWry5JNPqukHfGYiARIggWgJOMKgovKYX8VIFYYVn+ENDFmYHsHRdi2vK0nA35Du2bOHa0pLAuJ3EiCBmAg4xqDqVsCYfvjhh8q7cvny5UoKTk1NpXOIBsS/EROAs9GuXbsKQ2NiRHrrrbfynoqYJC8gARIIRcBxBtW/spCCERcYI1dEXLrpppsYHMIfED+HJIDlLwh/iSD2v/zlL5Wj0W233cYoRyGp8UcSIIFoCTjaoOpGYQ0rgkNgKUPbtm2VYb322mspB2tA/FtIALIu5uI/+OADWb16tfz+979X3rvcEaYQET+QAAlYRMAVBlW3HWHgFi1aJJMmTZLt27er9axwYGJIQ00ocf/q0ei///1v+c9//iMTJ05UqgZ2QWIiARIgATsIuMqg+gOBHLxs2TJ59tlnpUGDBoINzjnX6k/I+58xN4ot1LCVGtaR6tFo69atKet6v/vZQhJwHAHXGlRNEqPWnJwcNU82b948JQnjgXrdddfR6URD8tBfGNHPP/9c7f4CSbdr167ym9/8RoUHxPaBTCRAAiQQLwKuN6j+4GBcEdoQhhWjV8y3Nm3aVCD7URb2J+Wuz+jXTz/9VEUwohF1V9+xtiSQSAQ8ZVD9O67kyBW/YX/WevXqqf+4vtWflrM+a8cibOi9du1awZrRbt26qf5DJCOORJ3VX6wNCZDAeQKeNaj+HYy1rZhnW7FihWRkZKilFP6j15SUFEZm8gdm82cY0Pz8fPnyyy8LR6GowhNPPKHmxtu0aUP53uY+YXEkQAKRE0gIg1oSCzY+37Bhg6xatUomT56sfoZDU7NmzZQ0XKtWLS7JKQnN4HfMg2LD7pIG9He/+50KuIA58JYtWxoskVmRAAmQgPUEEtKglsSKda6ffPKJMrBr1qxRI9hrrrlGzb02bNhQatasKcnJyTSyJcGF8R2jT8jv+/fvV6NQOBTBIxdp6NChap4bQRcaN25Mz9wwePIUEiAB5xKgQQ3QNxjBYv4O3sMYycLJCcnfyFarVk2qVq3K/Vz9+MFwHj9+XL7++mvZvXu3+quNJ+ZA8R+8r6+++mr1suJ3KT+SAAmQgOsJ0KCG2YUYxR4+fFjN8WHtox7J4nLMx2IUC2eZChUqSJ06dVSuV155ZZi5u+c0GE2MOsHi9OnTynAiqMKmTZsKG4GRZ/369Wk8C4nwAwmQQCIQoEGNoZfh7AQpE6HuMC+IOVkYHD2i1VkjDjGSNrgwujVq1FDHypcv7wiHG9Qf/yFpY4nPGGki4YUCEYh0wvpPyLTYEah69epq/vnyyy93RFt0HfmXBEiABOwkQINqEW1tbE+ePCl79+5VpcDgIn3zzTcyf/78gCWnpaUJNrv2TzBUMFrRJowkIWP7px9++EHFuvU/pj936dJFmjRpor7ecsstcsEFF8gVV1yhXgJoNDUl/iUBEiCB4gRoUIvzsP0bRrQwsDrp0a7+jr9Y8nP06FH/QxF/7tSpU6lr4NWsEw2lJsG/JEACJBAdARrU6LjxKhIgARIgARIoRqBcsW/8QgIkQAIkQAIkEBUBGtSosPEiEiABEiABEihOgAa1OA9+IwESIAESIIGoCPx/zlvmSp4x5QUAAAAASUVORK5CYII="></p>
</div>
<div class="question">
<p>Calculate the radius of the base of the cone which has been removed.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {{{15}^2} - {{12}^2}} ">
<msqrt>
<mrow>
<msup>
<mrow>
<mn>15</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mrow>
<msup>
<mrow>
<mn>12</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</math></span> <em><strong> (M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into Pythagoras theorem.</p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{radius}}}}{{21}} = \frac{{15}}{{35}}">
<mfrac>
<mrow>
<mrow>
<mtext>radius</mtext>
</mrow>
</mrow>
<mrow>
<mn>21</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>15</mn>
</mrow>
<mrow>
<mn>35</mn>
</mrow>
</mfrac>
</math></span> <em><strong> (M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for a correct equation.</p>
<p>= 9 (cm) <em><strong>(A1) (C2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>Emily’s kite ABCD is hanging in a tree. The plane ABCDE is vertical.</p>
<p>Emily stands at point E at some distance from the tree, such that EAD is a straight line and angle BED = 7°. Emily knows BD = 1.2 metres and angle BDA = 53°, as shown in the diagram</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_18.18.28.png" alt="N17/5/MATSD/SP1/ENG/TZ0/10"></p>
</div>
<div class="specification">
<p>T is a point at the base of the tree. ET is a horizontal line. The angle of elevation of A from E is 41°.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of EB.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the angle of elevation of B from E.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the vertical height of B above the ground.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><strong>Units are required in parts (a) and (c).</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{EB}}}}{{\sin 53{\rm{^\circ }}}} = \frac{{1.2}}{{\sin 7{\rm{^\circ }}}}"> <mfrac> <mrow> <mrow> <mtext>EB</mtext> </mrow> </mrow> <mrow> <mi>sin</mi> <mo></mo> <mn>53</mn> <mrow> <mrow> <msup> <mi></mi> <mo>∘</mo> </msup> </mrow> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>1.2</mn> </mrow> <mrow> <mi>sin</mi> <mo></mo> <mn>7</mn> <mrow> <mrow> <msup> <mi></mi> <mo>∘</mo> </msup> </mrow> </mrow> </mrow> </mfrac> </math></span> <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution into sine formula, <strong><em>(A1) </em></strong>for correct substitution.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="({\text{EB}} = ){\text{ }}7.86{\text{ m}}"> <mo stretchy="false">(</mo> <mrow> <mtext>EB</mtext> </mrow> <mo>=</mo> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mn>7.86</mn> <mrow> <mtext> m</mtext> </mrow> </math></span><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><strong>OR</strong><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="786{\text{ cm }}(7.86385 \ldots {\text{ m}}"> <mn>786</mn> <mrow> <mtext> cm </mtext> </mrow> <mo stretchy="false">(</mo> <mn>7.86385</mn> <mo>…</mo> <mrow> <mtext> m</mtext> </mrow> </math></span><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><strong>OR</strong><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="786.385 \ldots {\text{ cm}})"> <mn>786.385</mn> <mo>…</mo> <mrow> <mtext> cm</mtext> </mrow> <mo stretchy="false">)</mo> </math></span> <strong><em>(A1) (C3)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>34° <strong><em>(A1) (C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>Units are required in parts (a) and (c).</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sin 34^\circ = \frac{{{\text{height}}}}{{7.86385 \ldots }}">
<mi>sin</mi>
<mo></mo>
<msup>
<mn>34</mn>
<mo>∘</mo>
</msup>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mtext>height</mtext>
</mrow>
</mrow>
<mrow>
<mn>7.86385</mn>
<mo>…</mo>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into a trigonometric ratio.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="({\text{height}} = ){\text{ }}4.40{\text{ m}}">
<mo stretchy="false">(</mo>
<mrow>
<mtext>height</mtext>
</mrow>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>4.40</mn>
<mrow>
<mtext> m</mtext>
</mrow>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><strong>OR</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="440{\text{ cm }}(4.39741 \ldots {\text{ m}}">
<mn>440</mn>
<mrow>
<mtext> cm </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>4.39741</mn>
<mo>…</mo>
<mrow>
<mtext> m</mtext>
</mrow>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><strong>OR</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="439.741 \ldots {\text{ cm}})">
<mn>439.741</mn>
<mo>…</mo>
<mrow>
<mtext> cm</mtext>
</mrow>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Accept “BT” used for height. Follow through from parts (a) and (b). Use of 7.86 gives an answer of 4.39525….</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A vertical pole stands on horizontal ground. The bottom of the pole is taken as the origin, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>, of a coordinate system in which the top, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math>, of the pole has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>,</mo><mo> </mo><mn>5</mn><mo>.</mo><mn>8</mn><mo>)</mo></math>. All units are in metres.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p><br>The pole is held in place by ropes attached at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math>.</p>
<p>One of the ropes is attached to the ground at a point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> with coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>3</mn><mo>.</mo><mn>2</mn><mo>,</mo><mo> </mo><mn>4</mn><mo>.</mo><mn>5</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math>. The rope forms a straight line from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of the rope connecting <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</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>FÂO</mtext></math>, the angle the rope makes with the ground.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>3</mn><mo>.</mo><msup><mn>2</mn><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup><mo>+</mo><mn>5</mn><mo>.</mo><msup><mn>8</mn><mn>2</mn></msup></msqrt></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>8</mn><mo>.</mo><mn>01</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>8</mn><mo>.</mo><mn>00812</mn><mo>…</mo></mrow></mfenced><mo> </mo><mtext>m</mtext></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>FÂO</mtext><mo>=</mo><msup><mi>sin</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><mn>5</mn><mo>.</mo><mn>8</mn></mrow><mrow><mn>8</mn><mo>.</mo><mn>00812</mn><mo>…</mo></mrow></mfrac></mfenced></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>cos</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><mn>5</mn><mo>.</mo><mn>52177</mn><mo>…</mo></mrow><mrow><mn>8</mn><mo>.</mo><mn>00812</mn><mo>…</mo></mrow></mfrac></mfenced></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><mn>5</mn><mo>.</mo><mn>8</mn></mrow><mrow><mn>5</mn><mo>.</mo><mn>52177</mn><mo>…</mo></mrow></mfrac></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>46</mn><mo>.</mo><mn>4</mn><mo>°</mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>46</mn><mo>.</mo><mn>4077</mn><mo>…</mo><mo>°</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This question was the first of its type to be tested and the problem was reduced (erroneously) to 2D trigonometry. Whilst a minority of candidates did tackle this part correctly, many simply arrived at an incorrect length with <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><msup><mrow><mo>(</mo><mn>5</mn><mo>.</mo><mn>8</mn><mo>)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mo>(</mo><mn>4</mn><mo>.</mo><mn>5</mn><mo>)</mo></mrow><mn>2</mn></msup></msqrt><mo>=</mo><mn>7</mn><mo>.</mo><mn>34</mn></math> metres.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The incorrect interpretation of the diagram as being 2D, meant that there was an assumption that OA was of length 3.2 metres and so <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><mn>5</mn><mo>.</mo><mn>8</mn></mrow><mrow><mn>3</mn><mo>.</mo><mn>2</mn></mrow></mfrac></mfenced><mo>=</mo><mn>61</mn><mo>.</mo><mn>1</mn></math>° was seen on many scripts. If, using their incorrect answer for part (a), the candidate had used <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>sin</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><mn>5</mn><mo>.</mo><mn>8</mn></mrow><mtext>their part (a)</mtext></mfrac></mfenced></math> it was possible to award “follow through” marks.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The straight metal arm of a windscreen wiper on a car rotates in a circular motion from a pivot point, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>, through an angle of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>140</mn><mo>°</mo></math>. The windscreen is cleared by a rubber blade of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>46</mn><mo> </mo><mtext>cm</mtext></math> that is attached to the metal arm 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>. The total length of the metal arm, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>OB</mtext></math>, is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>56</mn><mo> </mo><mtext>cm</mtext></math>.</p>
<p>The part of the windscreen cleared by the rubber blade is shown unshaded 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>Calculate the length of the arc made by <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>, the end of the rubber blade.</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>Determine the area of the windscreen that is cleared by the rubber blade.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute into length of arc formula <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>140</mn><mo>°</mo></mrow><mrow><mn>360</mn><mo>°</mo></mrow></mfrac><mo>×</mo><mn>2</mn><mi mathvariant="normal">π</mi><mo>×</mo><mn>56</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>137</mn><mo> </mo><mtext>cm</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>136</mn><mo>.</mo><mn>833</mn><mo>…</mo><mo>,</mo><mo> </mo><mfrac><mrow><mn>392</mn><mi mathvariant="normal">π</mi></mrow><mn>9</mn></mfrac><mo> </mo><mtext>cm</mtext></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>subtracting two substituted area of sectors formulae <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mrow><mn>140</mn><mo>°</mo></mrow><mrow><mn>360</mn><mo>°</mo></mrow></mfrac><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><msup><mn>56</mn><mn>2</mn></msup></mrow></mfenced><mo>-</mo><mfenced><mrow><mfrac><mrow><mn>140</mn><mo>°</mo></mrow><mrow><mn>360</mn><mo>°</mo></mrow></mfrac><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><msup><mn>10</mn><mn>2</mn></msup></mrow></mfenced></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>140</mn><mo>°</mo></mrow><mrow><mn>360</mn><mo>°</mo></mrow></mfrac><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><mfenced><mrow><msup><mn>56</mn><mn>2</mn></msup><mo>-</mo><msup><mn>10</mn><mn>2</mn></msup></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3710</mn><mo> </mo><msup><mtext>cm</mtext><mn>2</mn></msup><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>3709</mn><mo>.</mo><mn>17</mn><mo>…</mo><mo> </mo><msup><mtext>cm</mtext><mn>2</mn></msup></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>There was some difficulty determining the correct radius to substitute, with several candidates substituting a radius of 46.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>It was common to see candidates subtracting the radii before substituting into the area formula, rather than subtracting the sector areas after calculating each. Using the π key on the calculator rather than an approximated value was prevalent and pleasing to see.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A cylinder with radius <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> and height <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The sum of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> for this cylinder is 12 cm.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an equation for the area, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A">
<mi>A</mi>
</math></span>, of the <strong>curved</strong> surface in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}A}}{{{\text{d}}r}}">
<mfrac>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>A</mi>
</mrow>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>r</mi>
</mrow>
</mfrac>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> when the area of the curved surface is maximized.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p style="text-align: left;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = 2\pi r\left( {12 - r} \right)">
<mi>A</mi>
<mo>=</mo>
<mn>2</mn>
<mi>π</mi>
<mi>r</mi>
<mrow>
<mo>(</mo>
<mrow>
<mn>12</mn>
<mo>−</mo>
<mi>r</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = 24\pi r - 2\pi {r^2}">
<mi>A</mi>
<mo>=</mo>
<mn>24</mn>
<mi>π</mi>
<mi>r</mi>
<mo>−</mo>
<mn>2</mn>
<mi>π</mi>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> <em><strong>(A1)(M1) (C2)</strong></em></p>
<p style="text-align: left;"><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r + h = 12">
<mi>r</mi>
<mo>+</mo>
<mi>h</mi>
<mo>=</mo>
<mn>12</mn>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h = 12 - r">
<mi>h</mi>
<mo>=</mo>
<mn>12</mn>
<mo>−</mo>
<mi>r</mi>
</math></span> seen. Award <em><strong>(M1)</strong></em> for correctly substituting into curved surface area of a cylinder. Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = 2\pi r\left( {12 - r} \right)">
<mi>A</mi>
<mo>=</mo>
<mn>2</mn>
<mi>π</mi>
<mi>r</mi>
<mrow>
<mo>(</mo>
<mrow>
<mn>12</mn>
<mo>−</mo>
<mi>r</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong>OR </strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = 24\pi r - 2\pi {r^2}">
<mi>A</mi>
<mo>=</mo>
<mn>24</mn>
<mi>π</mi>
<mi>r</mi>
<mo>−</mo>
<mn>2</mn>
<mi>π</mi>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span>.</p>
<p style="text-align: left;"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align: left;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="24\pi - 4\pi r">
<mn>24</mn>
<mi>π</mi>
<mo>−</mo>
<mn>4</mn>
<mi>π</mi>
<mi>r</mi>
</math></span> <em><strong>(A1)</strong></em><strong>(ft)<em>(A1)</em>(ft)</strong><em><strong> (C2)</strong></em></p>
<p style="text-align: left;"><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="24\pi">
<mn>24</mn>
<mi>π</mi>
</math></span> and <em><strong>(A1)</strong></em><strong>(ft)</strong> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 4\pi r">
<mo>−</mo>
<mn>4</mn>
<mi>π</mi>
<mi>r</mi>
</math></span> . Follow through from part (a). Award at most <em><strong>(A1)</strong></em><strong>(ft)<em>(A0)</em></strong> if additional terms are seen.</p>
<p style="text-align: left;"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align: left;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="24\pi - 4\pi r = 0">
<mn>24</mn>
<mi>π</mi>
<mo>−</mo>
<mn>4</mn>
<mi>π</mi>
<mi>r</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p style="text-align: left;"><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for setting <em>their</em> part (b) equal to zero.</p>
<p style="text-align: left;">6 (cm) <strong><em>(A1)</em>(ft)</strong><em><strong> (C2)</strong></em></p>
<p style="text-align: left;"><strong>Note:</strong> Follow through from part (b).</p>
<p style="text-align: left;"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A balloon in the shape of a sphere is filled with helium until the radius is 6 cm.</p>
</div>
<div class="specification">
<p>The volume of the balloon is increased by 40%.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the volume of the balloon.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the radius of the balloon following this increase.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><strong>Units are required in parts (a) and (b).</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{4}{3}\pi \times {6^3}">
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mi>π</mi>
<mo>×</mo>
<mrow>
<msup>
<mn>6</mn>
<mn>3</mn>
</msup>
</mrow>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into volume of sphere formula.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 905{\text{ c}}{{\text{m}}^3}{\text{ }}(288\pi {\text{ c}}{{\text{m}}^3},{\text{ }}904.778 \ldots {\text{ c}}{{\text{m}}^3})">
<mo>=</mo>
<mn>905</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>288</mn>
<mi>π</mi>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>904.778</mn>
<mo>…</mo>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1) (C2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Answers derived from the use of approximations of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi ">
<mi>π</mi>
</math></span> (3.14; 22/7) are awarded <strong><em>(A0)</em></strong>.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>Units are required in parts (a) and (b).</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{140}}{{100}} \times 904.778 \ldots = \frac{4}{3}\pi {r^3}">
<mfrac>
<mrow>
<mn>140</mn>
</mrow>
<mrow>
<mn>100</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mn>904.778</mn>
<mo>…</mo>
<mo>=</mo>
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mi>π</mi>
<mrow>
<msup>
<mi>r</mi>
<mn>3</mn>
</msup>
</mrow>
</math></span> <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{140}}{{100}} \times 288\pi = \frac{4}{3}\pi {r^3}">
<mfrac>
<mrow>
<mn>140</mn>
</mrow>
<mrow>
<mn>100</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mn>288</mn>
<mi>π</mi>
<mo>=</mo>
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mi>π</mi>
<mrow>
<msup>
<mi>r</mi>
<mn>3</mn>
</msup>
</mrow>
</math></span> <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1266.69 \ldots = \frac{4}{3}\pi {r^3}">
<mn>1266.69</mn>
<mo>…</mo>
<mo>=</mo>
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mi>π</mi>
<mrow>
<msup>
<mi>r</mi>
<mn>3</mn>
</msup>
</mrow>
</math></span> <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplying their part (a) by 1.4 or equivalent, <strong><em>(M1) </em></strong>for equating to the volume of a sphere formula.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r^3} = \frac{{3 \times 1266.69 \ldots }}{{4\pi }}">
<mrow>
<msup>
<mi>r</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>3</mn>
<mo>×</mo>
<mn>1266.69</mn>
<mo>…</mo>
</mrow>
<mrow>
<mn>4</mn>
<mi>π</mi>
</mrow>
</mfrac>
</math></span> <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \sqrt[3]{{\frac{{3 \times 1266.69 \ldots }}{{4\pi }}}}">
<mi>r</mi>
<mo>=</mo>
<mroot>
<mrow>
<mfrac>
<mrow>
<mn>3</mn>
<mo>×</mo>
<mn>1266.69</mn>
<mo>…</mo>
</mrow>
<mrow>
<mn>4</mn>
<mi>π</mi>
</mrow>
</mfrac>
</mrow>
<mn>3</mn>
</mroot>
</math></span> <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \sqrt[3]{{(1.4) \times {6^3}}}">
<mi>r</mi>
<mo>=</mo>
<mroot>
<mrow>
<mo stretchy="false">(</mo>
<mn>1.4</mn>
<mo stretchy="false">)</mo>
<mo>×</mo>
<mrow>
<msup>
<mn>6</mn>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mn>3</mn>
</mroot>
</math></span> <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r^3} = 302.4">
<mrow>
<msup>
<mi>r</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>302.4</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for isolating <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(r = ){\text{ }}6.71{\text{ cm }}(6.71213 \ldots )">
<mo stretchy="false">(</mo>
<mi>r</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>6.71</mn>
<mrow>
<mtext> cm </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>6.71213</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft) <em>(C4)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (a).</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<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="\theta ">
<mi>θ<!-- θ --></mi>
</math></span> be an <strong>obtuse</strong> angle such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{sin}}\,\theta = \frac{3}{5}">
<mrow>
<mtext>sin</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>θ<!-- θ --></mi>
<mo>=</mo>
<mfrac>
<mn>3</mn>
<mn>5</mn>
</mfrac>
</math></span>.</p>
</div>
<div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {{\text{e}}^x}\,{\text{sin}}\,x - \frac{{3x}}{4}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mi>x</mi>
</msup>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mfrac>
<mrow>
<mn>3</mn>
<mi>x</mi>
</mrow>
<mn>4</mn>
</mfrac>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{tan}}\,\theta "> <mrow> <mtext>tan</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span> passes through the origin and has a gradient of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{tan}}\,\theta "> <mrow> <mtext>tan</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> </math></span>. Find the equation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the derivative of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</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>The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> for 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> ≤ 3. Line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="M"> <mi>M</mi> </math></span> is a tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at point P.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAeoAAAGNCAYAAADenDLYAAAgAElEQVR4Ae3dD3BW5b3g8V8otxVEiwGWEhNl0Ca4xUuCgGwTS7Q0irU3mdDUlY7gBXS8GrqrI2CB1rpXKAJTRkHXrUCB9uJYSibZVZFImVCSOwgIYWWqyRWWf4ayQLSYRS9Dk53n6MGXN++bvO97/j3POd8z45Cc95znz+f34o/nnPM8J6urq6tL2BBAAAEEEEBAS4E+WraKRiGAAAIIIICAJUCi5ouAAAIIIICAxgIkao2DQ9MQQAABBBDIMFFflJM1D0tWVpZkZeXI7ct3S4dl2Snnts+XnJxqqfnwAroIIIAAAggg4FAgw0TdV4ZVviRdf3tP1pSJNLx1UNo6VUv6yICbbpcHCj6Sj/+ftcNh8zgdAQQQQACBaAtkmKi/QOuTK6O/VyByqF0++SIv9xmaJzeOuFVG53w12rL0HgEEEEAAARcEnCVq6StXZQ8ROfSBHD19UUQuyIe1v5Hd3y+XogEOi3ahcxSBAAIIIICA6QIOs2lfuWpg9pcGHc3y+73flp9VXC8OC/6yTH5CAAEEEEAgwgIO82kfuXJgtgyTFjl8/APZvvQtuf7RyXKtw1IjHA+6jgACCCCAwGUCDlNqH+n/9WzpL2dk/wsvSUPpA1JxLfemLxPmFwQQQAABBBwIOEzUIn2uypYbRKTvxFky945rueTtIBicigACCCCAQLyA40Qt8hXJ/emvZMkDo2RAfOn8jgACCCCAAAKOBJwl6o7d8tyaPjJn/ndlmLOSHHWCkxFAAAEEEAirQN+0O9axW5b/4DE5ef9jkttyRr7zs4dkJFOx0mbkBAQQQAABBFIRSH8c3Nkhp1v+j+xr+VS+819nyC0k6VScOQYBBBBAAIGMBLK8eh91TU2NvP/++zJ//vyMGsZJCCCAAAIIICDiSaJubW2VgoICy7exsVGKi4uxRgABBBBAAIEMBFxP1J9++qncd999MmTIEFm9erWMGzdOduzYIf369cugeZyCAAIIIIBAtAXSv0fdi9eWLVukrq5O5syZc+nIFStWXPqZHxBAAAEEEEAgdQFXR9QnTpyQvLw8Wb9+vUybNs16X/XmzZtlypQp0tLSIvn5+am3jCMRQAABBBBAwN171A8++KCcPn1aXnnlFetSd1ZWlnR1dUn8ftwRQAABBBBAIDUB10bU9fX1cuedd8r+/fulsLDQqt1O1PEj7dSaxlEIIIAAAggg4Eqibm9vl7vuuksqKioum45lJ2rFvGHDBpk+fbocP35ccnNzkUcAAQQQQACBFARceZjspZdesqp67LHHklZZVVUl5eXlVsJOehAfIIAAAggggMBlAq6MqJuamuTKK6+8dMnbriF2RK32qUvgR48eZV61DcSfCCCAAAII9CLgSqJOVkd8ok52HPsRQAABBBBAILGAK5e+ExfNXgQQQAABBBBwKkCidirI+QgggAACCHgoQKL2EJeiEUAAAQQQcCpAonYqyPkIIIAAAgh4KECi9hCXohFAAAEEEHAqQKJ2Ksj5CCCAAAIIeChAovYQl6IRQAABBBBwKkCidirI+QgggAACCHgoQKL2EJeiEUAAAQQQcCpAonYqyPkIIIAAAgh4KECi9hCXohFAAAEEEHAqQKJ2Ksj5CCCAAAIIeChAovYQl6IRQAABBBBwKkCidirI+QgggAACCHgoQKL2EJeiEUAAAQQQcCpAonYqyPkIIIAAAgh4KECi7gX3xIkTvRzBxwgggAACCHgnQKLuwfbTTz+VvLw8qaiokKamph6O5CMEEEAAAQS8ESBR9+Dar18/OXv2rEyaNElKSkpI2D1Y8RECCCCAgDcCJOpeXLOzs6W6upqE3YsTHyOAAAIIeCNAok7RlYSdIhSHIYAAAgi4KkCiTpOThJ0mGIcjgAACCDgSIFFnyEfCzhCO0xBAAAEE0hIgUafF1f3gZAm7ubm5+8HsQQABBBBAIE0BEnWaYMkOj0/YRUVFMnfuXGltbU12CvsRQAABBBDoVYBE3StRegfEJuzrrrtOCgoKSNjpEXI0AggggECMAIk6BsPNH2MTtiqXhO2mLmUhgAAC0REgUXsca5Wwly5dKi0tLVZNJGyPwSkeAQQQCJkAidqngObn55OwfbKmGgQQQCBMAiRqn6NJwvYZnOoQQAABwwVI1AEFkIQdEDzVIoAAAoYJkKgDDhgJO+AAUD0CCCCguQCJWpMAkbA1CQTNQAABBDQTIFFrFhAStmYBoTkIIIBAwAIk6oADkKx6EnYyGfYjgAAC0RIgUWsebxK25gGieQgggIDHAiRqj4HdKp6E7ZYk5SCAAAJmCZCozYqXkLANCxjNRQABBBwKkKgdAgZ1Ogk7KHnqRQABBPwVIFH76+16bSRs10kpEAEEENBKgEStVTgybwwJO3M7zkQAAQR0FiBR6xydDNpGws4AjVMQQAABjQVI1BoHx0nTSNhO9DgXAQQQ0EeARK1PLDxpCQnbE1YKRQABBHwTIFH7Rh1sRSTsYP2pHQEEEMhUgESdqZyh55GwDQ0czUYAgcgKkKgjGnoSdkQDT7cRQMA4ARK1cSFzt8EkbHc9KQ0BBBBwW4BE7baooeWRsA0NHM1GAIHQC5CoQx/i9DpIwk7Pi6MRQAABrwVI1F4LG1o+CdvQwNFsBBAInQCJOnQhdbdDJGx3PSkNAQQQSFeARJ2uWESPJ2FHNPB0GwEEAhcgUQceArMakCxhnzhxwqyO0FoEEEDAEAEStSGB0q2Z8Qk7Ly9PVq1aJe3t7bo1lfYggAACRguQqI0OX/CNj03Yx44dk0GDBpGwgw8LLUAAgRAJkKhDFMwguxKbsLdt26Znwu58X9bemSNZWVnd/suZvlz+sL1VOoJEpG4EEEAggQCJOgEKuzIXUAm7trZWGhsbRbuE3WekzNjaJn9rWSNlUiVrWj6Vrq4u6frkPVn1jbek6rtT5NG1B0nWmYefMxFAwAMBErUHqBQpUlxcrG/Cjg/QgJFS+cvnZE3ZWdmwcKPsPtcZfwS/I4AAAoEJkKgDo49GxcYk7D6DZXhhjsjJD+TIXy5EIzj0EgEEjBAgURsRJvMbqX3C7jwjR5rbRIbdKMO/8VXzwekBAgiERoBEHZpQmtERfRL2e7Kj8YPP70d3npTdz/1SFtaLlD5eIeOv5q+FGd8mWolANAT4P1I04qxdL4NP2Adlw8yb5Sr1BPhXcuTWZSKPb/5fsvHx8TJAOy0ahAACURYgUUc5+hr0PbiEHfPUt3ryu229PFF5iwzjb4QG3wqagAACsQL8bylWg58DEwguYQfWZSpGAAEEUhIgUafExEF+CZCw/ZKmHgQQMEWARG1KpCLWTu8Sdqec/+SvckHOS/snn0VMle4igICJAiRqE6MWoTa7mrCtJURz5aqxj0uDvC5zxl4jWXeulVbWN4nQN4quImCeQFaXWkPRo02tqexh8R61mmJ1FmhqapJly5ZJXV2drFy5UqZOnSrZ2dk6N5m2IYAAAo4EGFE74uNkvwVcHWH73XjqQwABBDIQIFFngMYpwQuQsIOPAS1AAAF/BEjU/jhTi0cCvSXs9vZ2qampEXXJ/NNPP/WoFRSLAAIIeCfAPWrvbCk5AAGVkJcsWSKvvfaazJs3T5599tlLrfjWt74lf/rTn7infUmEHxBAwAQBErUJUaKNvQqoBL1jxw5ZsGBBj8e+/PLLMmvWrB6P4UMEEEBAJwEufesUDdqStkBzc7NUVFRISUmJXH311bJ//35paWmR8+fPJyzr3XffTbifnQgggICuAiRqXSNDu3oUUPebFy9eLEVFRTJp0iQrMVdXV0thYaHk5+dLv379ZOHChd3KeP7552XFihWi7l2zIYAAAiYIcOnbhCjRxssEVJJV958PHDggv/vd76zEfNkBX/yikvn06dNl06ZN1p4nnnhCXn/9dSupHz16lHnYidDYhwAC2gmQqLULCQ3qSeDEiRNSWVkpo0ePFjU6ViPn3jaV2NVx6j/7fDUSP3XqFAun9IbH5wggELgAl74DDwENSFXATrLpJGlVtlq5zE7oubm51nStX//611bCb2xslG3btsmgQYNk1apVXBJPNRgchwACvgmQqH2jpiInAuoy9tNPP53WSDpZfSpZqwStLotfeeWVUltba/1Owk4mxn4EEAhSgEQdpD51pyzw1FNPWfekU73c3VvBaqGURYsWyUMPPWQthNLbwim9lcfnCCCAgFcCJGqvZCnXNYENGzZYL+JQK4zZl7DdKPyxxx6zilFPgdsbCduW4E8EENBFgIfJdIkE7UgooOZJqwe/tm7dKmVlZQmPcbLTLl/NvVbTuuI33tYVL8LvCCDgtwCJ2m9x6ktZQN2XnjhxorWgyfz581M+L90D586dKx999JGoVcuSbbEJe/369VJVVeXq6D5ZvexHAAEESNR8B7QVUAuaqAe91NKgbl7yju+wepo8Ly/PeqBMXfruabMTdltbmzz55JMyefJkT9vWU1v4DAEEoiFAoo5GnI3rZW+XpN3ukJqapZ76Vv8wSGUjYaeixDEIIOCGAInaDUXKcFXAr0vesY1Wi6KoudRq2lZvo+rY8+rr6y8tVcoIO1aGnxFAwC0BErVbkpTjmoB6yluNcL2+5B3f4HRH1fb56h8WW7ZssV6vqfaRsG0Z/kQAATcESNRuKFKGawLp3C92rdIvCrJH1eoNXOrlHuluJOx0xTgeAQRSESBRp6LEMb4JqCew1bZ06VLf6oytyI36SdixovyMAAJOBUjUTgU53zUB9YCWeq90sjnNrlXUQ0Gtra1SUFAgx48fF7XUqJONhO1Ej3MRQMAWIFHbEvwZuEBFRYX1bmn1XukgN7fbQcIOMprUjYD5AiRq82MYih6op6fvvPNOOXv2rPW2qyA7ZT/J7fbDbCTsIKNK3QiYK0CiNjd2oWm5SmBqBTL1tLR613TQm2pP//79056qlWq7SdipSnEcAggoAV7KwfcgcAE1tUltapUvHTa1CtrKlSulrq7Ok+ao8tU/SNSIXf3jZMmSJdY/VNRLR1QSZ0MAAQRiBRhRx2rws+8Cuo2mbQD7oTI/LsUzwrbV+RMBBBIJMKJOpMI+3wR0G03bHVdv0iovL5eGhgZ7l2d/MsL2jJaCEQiFACPqUITRzE7oOpq2NdUKaepydKrrf9vnOf2TEbZTQc5HIFwCJOpwxdOo3qgkqO7Puv10tVsI9ippbsypzqRNJOxM1DgHgfAJkKjDF1MjeqT7aNpGfPDBB+W2226TadOm2bt8/5OE7Ts5FSKglQD3qLUKR3Qas3PnTquzujzpnUy+qqrKuvyd7HM/9nMP2w9l6kBAXwFG1PrGJtQtU6t/qVGqDvOme4K2X9QR1OXvRG1jhJ1IhX0IhFeARB3e2GrbM3tNbz+mPrmBoP5Rof5BEeTl70T9IGEnUmEfAuETIFGHL6ba98jttbS97rB6+ltdqn/55Ze9riqj8knYGbFxEgLGCJCojQlVOBrq50IibonZT3/rfgWAhO1WxCkHAb0ESNR6xSP0rVHvex44cKDMnz/fqL6OHz9ennnmGSkrK9O+3SRs7UNEAxFIS4BEnRYXBzsRsB/MCvJ905m2f9WqVXLu3Dmj/oFBws402pyHgF4CJGq94hHq1qhkd+DAAW3v9faE39zcLEVFRXL+/HlR06VM2kjYJkWLtiLQXYBE3d2EPR4IqGTh5asjPWjyZUXa7d+/f78UFhZe9pkpv5CwTYkU7UTgcgEWPLncg988ElAv3xg3bpwUFxd7VIO3xapR9Jw5c6x3VHtbk3els3CKd7aUjICXAiRqL3Up+5KAmuKk3r1s8jZhwgTZtm2byV2w2k7CNj6EdCBiAlz6jljAg+iuaQucJDMyZZpWsvYn288l8WQy7EdADwFG1HrEIdStqKurk5UrV0p2drbR/czNzbUu3+/du9fofsQ3nhF2vAi/I6CXACNqveIRutbYo1ATp2QlCsbixYut3abNA0/Ul2T74kfYpswfT9Yf9iNgugAjatMjqHn7a2trpby8XPLz8zVvaWrNmzhxoqg+hXmLH2EvXLhQ1LKv6hYGGwII+C/AiNp/88jUqEZmKrGtWLHC2Ke944NlL9qi09u04tvo9u+xI+ycnBzr6XdTn95324byEPBDgBG1H8oRrcN+5/SYMWNCI6Dus6srBH/+859D06feOhI7wp40aZKUlJQwwu4Njc8RcFGARO0iJkVdLvDiiy9ar4ZU/6MP06aSVdgeKEslPiqO1dXVol5OQsJORYxjEHBHgETtjiOlxAmot2Spp73Vvc2wbWop0bDfp+4pZuqqAgm7JyE+Q8BdARK1u56U9oVAfX29zJo1S9SUprBtN910k+zZs0fUE+1R3kjYUY4+ffdTgETtp3ZE6lIPH82ePVseeOCBUPY4ivepewokCbsnHT5DwLkAidq5ISXECaiHyNS63mF6iCyui6LeTx3F+9TxDrG/k7BjNfgZAfcESNTuWVLSFwJhfYgsNsBjx46N9H3qWIv4n0nY8SL8joAzAeZRO/Pj7DgB9RBZQUGBhH2esb3imnoCWiUmtuQCau75xo0brdshamqbegsZ87CTe/EJAvECjKjjRfjdkUCYHyKLhbEfknvvvfdid/NzAgFG2AlQ2IVAGgIk6jSwOLRnAfUQmXqdZVgfIovvvRoZ7t+/P343vycRIGEngWE3Ar0IkKh7AeLj1AX27dtnHRzmh8hiNdT7qQ8cOBC7i59TECBhp4DEIQjECJCoYzD40ZnAunXrQrkSWTKVUaNGyerVq0VdSWBLX4CEnb4ZZ0RTgEQdzbi73mv1cJVKWmFciSwZVl5envWRenCOLXMBEnbmdpwZDQESdTTi7Hkvt2/fbr2swn7IyvMKNahArX2tVl87ePCgBq0xvwkkbPNjSA+8ESBRe+MauVJXrVoljzzySOT6PXr0aHn//fcj128vO0zC9lKXsk0UIFGbGDXN2tzc3Gytfa0WAYnalp+fz8InHgWdhO0RLMUaJ0CiNi5k+jX4jTfekEWLFkVy4Y/hw4db/0hRi3qweSNAwvbGlVLNESBRmxMrLVuqEtSCBQvk7rvv1rJ9XjdKjajVduzYMa+rinz5JOzIfwUiC0Cijmzo3em4ejGFegFHYWGhOwUaWIpa+OTw4cMGttzMJpOwzYwbrc5cgESduR1nioh6AUd1dXWkLdR86l27dkXaIIjOk7CDUKfOIARI1EGoh6RONXe6rq5O7rjjjpD0KLNu3HDDDdLQ0JDZyZzlWICE7ZiQAjQXIFFrHiCdm1dbW2vNI47S3OlE8bj++ut5oCwRjM/7SNg+g1OdbwIkat+ow1eRegFHVVVV+DqWZo/sf6jwQFmacB4dTsL2CJZiAxMgUQdGb3bFTU1N1ijytttuM7sjLrWeB8pcgnSxGBK2i5gUFagAiTpQfnMr37FjhzV3Wi2jySbCA2X6fgtI2PrGhpalJkCiTs2Jo2IE1Nuiojx3Oobi0o88UHaJQtsfSNjahoaG9SJAou4FiI+7C+zcuTPyc6fjVYYMGcIDZfEomv5OwtY0MDQrqQCJOikNHyQT2LRpU+TnTsfb2CuUnTlzJv4jftdUIFnCbm1t1bTFNCuqAiTqqEY+w37b752O+tzpRHy88jKRiv774hN2QUGBzJ07V0jY+scuKi0kUUcl0i71M4rvnU6Vjldepiql53GxCfu6664TEraecYpiq0jUUYy6gz5H9b3TqZDl5OTI7t27UzmUYzQWsBP28ePHrVaSsDUOVkSaRqKOSKDd6GaU3zudip+aoqWWVGULh4BayGbp0qXS0tJidYiEHY64mtgLErWJUQuozY2NjZF973Qq5Hl5edZh3NtMRcucY9SDgiRsc+IVxpaSqMMYVQ/6pOZOz549WyZOnOhB6eEoUi3+ol75efr06XB0iF5cJkDCvoyDX3wUIFH7iG1yVfv27bOS0JgxY0zuhudtLy0tlUOHDnleDxUEJ0DCDs4+qjWTqKMa+TT7re69Tps2TVgytGc4dZ/64MGDPR/Ep6EQIGGHIoxGdIJEbUSYgm1ke3u7LFu2TEpKSoJtiAG1s5SoAUFyuYkkbJdBKa6bAIm6Gwk74gX27t0r5eXlUlhYGP8Rv8cJ2EuJqnv6bNESIGFHK95+9pZE7ae2oXW9+OKLUllZaWjr/W22+p+12uw5uP7WTm06CJCwdYhCuNpAog5XPF3vjVoyVN2fZsnQ1GnV1QfuU6fuFdYjSdhhjaz//SJR+29uVI21tbWi1rBWiz+wpSag/gfd1taW2sEcFXoBEnboQ+x5B0nUnhObXcGGDRukqqrK7E743PoJEybIsWPHfK6V6nQXIGHrHiF920ei1jc2gbfMXjL0tttuC7wtJjVg6NCh1lPyJrWZtvonQML2zzosNZGowxJJD/rxxhtvWEuGMnc6PVz15Lfa1LQ2NgSSCZCwk8mwP16ARB0vwu+WgJpetGDBApYMzeD7oP4HrLYzZ85kcDanRE2AhB21iKffXxJ1+maROIMlQ52FmSe/nflF8WwSdhSjnlqfSdSpOUXuqHXr1rFkqIOoq//pdnR0OCiBU6MqQMKOauST95tEndwmsp+oe6urV69myVAH3wD15DdzqR0AcqqQsPkS2AIkaluCPy8JNDQ0sGToJY3MflBPfitHNgScCpCwnQqafz6J2vwYut4DNXeaJUOdsbLmtzM/zu4uQMLubhKVPSTqqEQ6xX6yZGiKUL0clpeXZx3Bmt+9QPFx2gIk7LTJjD+BRG18CN3tAEuGuuOp5p6PGzdOTp8+7U6BlIJAnAAJOw4kxL+SqEMc3Ey6xpKhmaglPqe0tFROnTqV+EP2IuCSAAnbJUiNiyFRaxwcv5tmLxk6duxYv6sOZX2jRo2SXbt2hbJvdEo/ARK2fjFxq0UkarckQ1COvWRodnZ2CHoTfBcGDBggH330UfANoQWREiBhhy/cJOrwxTSjHrFkaEZsPZ6kRtRqPjobAkEI6JmwL8rJmoclKyvr8//uXCutnUl0Oo9Kzcybvzx2eo2cTHJo2HeTqMMe4RT7x5KhKUKlcdjgwYOto9WT9GwIBCWgV8LuK8MqX5Kuv/5R5g4TkXc/kBMdiTL1BfmwdplUrz0oMmyGrHnvr9K1vlLUKVHcSNRRjHqCPrNkaAIUh7vsWwjnz593WBKnI+BcIFHCXrx4cSBvebv4b/tksxoen/xAjvzlQrfOdX74mvy8+gVrBD3s/h/LD0de3e2YKO0gUUcp2kn6ypKhSWBc2D1r1iyWEnXBkSLcE4hN2B9//LEMGjRIVq1a5WPC/kwOH3hPbp1WIcPktLR/cvHyznUeldqfr5TPvqc+v0G+d+s3JdppWoREfflXJJK/sWSod2G/5ppreDmHd7yU7EAgNmEfO3bMx4R9Wg7uuEr+oXys9Jfj8u7R2AcuP7/kPVdmyAMlfycnZYxMHPX5+90ddNX4U0nUxofQeQdYMtS5YbISeDlHMhn26yJgJ+zGxkbZtm2b9wn73L/J22f/XopuvUmK5ZA0Hf6/8vmYulM63n9F5v+PG+TV574jnzTuE7lhvIwecYUuVIG1g0QdGL0eFdtLht5zzz16NChkrVBTtHg5R8iCGtLuFBcXi1qZ0OuEre5P/7F0tIwYer3cfIPIoXePirV+X8deeemfauXmxf8ot3QekrffOiTDpoyRb/YNKXga3SJRp4EVxkPtJUPtB5/C2Mcg+zR8+HDZs2dPkE2gbgTSEvA2Yav70x/Id8dcL337/gcZUXyDSNNhabv4sbzz0i/l9e//VB6+ZaB8/rAZ96ftwJGobYmI/smSod4G3p6i1dra6m1FlI6AywLeJGx1f/oKufWmgSJyjVx/c57IoffkwP98SZ54/Tuy/OGxMkBUMt8th7g/fSmiJOpLFNH7oampyRrt3XbbbdHrvE89tq9UMEXLJ3CqcV3A1YT9xf3pUUPV9ewrJGdEgYislZlTGuX7y/9RbhnQR6TziDS+2sj96ZhIkqhjMKL2444dO2TRokWi3vTE5p2AmqJ1+PBh7yqgZAR8EHCesM/J+3/4F3lD3Z+2Mk8fuXJgtgyTUTJj8wvy+C1qlH1BTja8Kr+tPylSPEJyuD9tRZZE7cMXXMcqWDLUv6ioKVptbW3+VUhNCHgokEnCvvjOcrkx6+ty08y1cnDOWPk7a+nQPjIg90YZM+Np+W8V10ufc9tlXs7XJOe7v5AG1f4NUyQn62GpORk3z9rDvuladFZXV1eXV41T67l6WLxXzY5EufX19bJw4ULZvXt3JPobZCdramqst2gtXbo0yGZQNwKeCKhbaMuWLZO6ujpZuXKlTJ06VexbPp5UGMFCGVFHMOiqy5s2bZJp06ZFtPf+dltN0eJhMn/Nqc0/gUxG2P61Lhw1MaIORxzT6oWaO52XlyfHjx+X3NzctM7l4PQFVJIuKCjg6lL6dJxhoAAjbPeDxojafVPtS9y+fbuUl5eTpH2KlD1Fi7do+QRONYEKMMJ2n59E7b6p9iWqe6Zc9vYvTPb9OqZo+WdOTcELkLDdiwGJ2j1LI0pqbm62HvooLS01or1haSRv0QpLJOlHugIk7HTFuh9Pou5uEuo9ah3fOXPm8FSmz1FWU7TYEIiyAAk78+iTqDO3M+5MNXd69uzZ1v1p4xpveINHjRplTdEyvBs0HwHHAiTs9AlJ1OmbGXvGvn37ZNy4cTJmzBhj+2Bqw9UUrY8+in3vrqk9od0IuCNAwk7dkUSdupXxR65bt856iIwlQ/0P5YgRI2T16tX+V0yNCGgukChhq2dp2L4UYB71lxah/qm9vd16IXxLS4uoF8Wz+Stgz6VWT37zDyV/7anNLAE1D1td9ePvyZdxY0T9pUWof3rttdese9Mk6WDCbLurRWbYEEAguYAaYZOkL/chUV/uEdrfmDutR2hPnz6tR0NoBQIIGCNAojYmVJk3lLnTmdu5eaaaFnfq1Ck3i7DMQAEAABfCSURBVKQsBBCIgACJOgJBZu60HkEeOHAgr7vUIxS0AgGjBEjURoUr/cYydzp9M6/OGDlypBw7dsyr4ikXAQRCKkCiDmlg7W4xd9qWCP5PXncZfAxoAQImCpCoTYxaGm1m7nQaWB4fOnz4cGuddY+roXgEEAiZQN+Q9YfuxAio1yqqRTbU3Gm24AX69+9vNULNabffqBV8q2gBAgjoLsCIWvcIOWif/d5pew6vg6I41QWB3Nxcq5QzZ864UBpFIIBAVARI1CGO9KpVq+SRRx4JcQ/N65paa5251ObFjRYjEKQAiTpIfQ/rVsvw7dmzR8aOHethLRSdroB6DzhzqdNV43gEoi1Aog5p/Hfs2CGLFi3iXqhm8WUutWYBoTkIGCBAojYgSOk2UT2stGDBArn77rvTPZXjPRZgLrXHwBSPQAgFSNQhDGpDQ4P13unCwsIQ9s7sLjGX2uz40XoEghAgUQeh7nGdGzZskOrqao9rofhMBJhLnYka5yAQbQESdcjir957XFdXJ/fcc0/Iehau7qilXdkQQACBVARI1KkoGXRMfX29qLc0saCGnkGz57TzXmo940OrENBRgJXJdIxKhm2yX8Ch3pbFprfA+fPn9W4grUMAAW0EGFFrEwrnDdm5c6f1ENmYMWOcF0YJngmoKx6HDx/2rHwKRgCBcAmQqEMUzxdffFGmTZsm/fr1C1Gv6AoCCCAQbQESdUjibz9EVlFREZIehbcbo0aNkl27doW3g/QMAQRcFSBRu8oZXGHqIbJZs2aJ/eKH4FpCzb0JqLnUbAgggECqAlldXV1dqR6c7nFZWVniYfHpNie0x6uHyNQrFNVDZMXFxaHtZ1g61tzcLEVFRfzdCEtA6QcCHgswovYY2I/i9+3bx0NkfkC7VIf9XmqXiqMYBBAIuQCJOgQBXrZsGQ+RGRTHwYMHW609ceKEQa2mqQggEJQAl76DknepXvUQWUFBgagFNLg/7RKqD8Wo20ItLS1iL4DiQ5VUgQAChgowojY0cHazeYjMljDrz3Hjxsnp06fNajStRQCBQARYmSwQdncqZSUydxyDKKW0tFROnToVRNXUiQAChgkwojYsYLHNZSWyWA3zfu7o6DCv0bQYAQR8FyBR+07uXoWsROaepd8lTZgwQQ4ePOh3tdSHAAIGCpCoDQyaarK9EtnUqVMN7QHNRgABBBBIRYBEnYqShsfwOksNg5JGk0aMGCFqWh0bAggg0JsAD5P1JqTh5+3t7TJ79mxrJTINm0eTUhBg0ZMUkDgEAQQsAUbUBn4RGhoarJXIWC7UwOB90WQWPTE3drQcAb8FSNR+i7tQ34YNG+TJJ590oSSKCEogOzvbqvr8+fNBNYF6EUDAEAEStSGBspvZ1NQkdXV1oubhspktwKInZseP1iPglwCJ2i9pl+pRSXrRokVij8hcKpZiAhBg0ZMA0KkSAQMFeJjMoKCplzioJ4XVGtFs4RBg0ZNwxJFeIOClACNqL3VdLru2tlbKy8t5kYPLrkEVN2rUKBY9CQqfehEwSIARtSHBUut6q4fIVqxYYUiLaWZvAgMGDOjtED5HAAEEhBG1IV8Cta632saMGWNIi2lmbwJDhw4VNdWODQEEEOhJgETdk45Gn6l1vaurq6Vfv34atYqmOBEYMmSI7Nmzx0kRnIsAAhEQIFEbEOTm5mZrStY999xjQGtpYroC6rYGGwIIIJBMgESdTEaj/Rs3bmRKlkbxcKsp+fn5VlHHjx93q0jKQQCBEArwMJnmQWVKluYBonkIIICAxwKMqD0Gdlo8U7KcCup9vppux3up9Y4RrUMgaAFG1EFHoIf61b1L3pLVA1AIPrIvf4egK3QBAQQ8EmBE7RGsG8Vu2bKFt2S5AalxGQMHDpS2tjaNW0jTEEAgaAESddAR6KH+JUuW8JasHnzC8NHIkSPl2LFjYegKfUAAAY8ESNQewTotVr0lS82x5S1ZTiU5HwEEEDBbIKurq6vLqy5kZWWJh8V71Wwtyq2oqJBJkyZZi5xo0SAa4YmAmiNfVFTE3xNPdCkUgXAIkKg1jGNra6sUFBTI2bNneZ2lhvFxs0l2rPkHrZuqlIVAuAS49K1hPFevXi1z5swhSWsYG6+a1N7e7lXRlIsAAoYLMKLWLID2CEu9c5qpO5oFx6PmqFtExNsjXIpFIAQCjKg1C2J9fb3MmjWLJK1ZXGgOAgggEJQAiToo+QT1qsufaoGTBx54IMGn7AqrgFqd7MiRI2HtHv1CAAGHAiRqh4Bunq5evqH+p11cXOxmsZSluYC6xdHR0aF5K2keAggEJcASokHJx9XLcqFxIBH7lUQdsYDTXQTSEGBEnQaWl4fay4WOGTPGy2ooW0OBCRMm8GIODeNCkxDQRYBErUEk1GjaXi60X79+GrSIJiCAAAII6CJAotYgEmo0rbbJkydr0Bqa4LfAgAEDRE3LY0MAAQQSCTCPOpGKj/vUaHrixInWyzcqKyt9rJmqdBGw586zOpkuEaEdCOglwIg64Hjs27ePl28EHAOqRwABBHQWIFEHHJ1ly5bJypUrWS404DgEWf3gwYOt6rn8HWQUqBsBfQW49B1gbNSrLEtKSnj5RoAx0KVqlhHVJRK0AwH9BBhRBxgTRtMB4mtY9fnz5zVsFU1CAIGgBUjUAUVAjabr6upk6tSpAbWAanUSUOu7Hz58WKcm0RYEENBEgEQdUCAYTQcEr2m111xzjaYto1kIIBC0AIk6gAgwmg4A3YAq29raDGglTUQAAb8FSNR+i4sIo+kA0DWvUi0jeuzYMc1bSfMQQCAIARK1z+qMpn0GpzoEEEDAcAEStc8BZDTtM7gh1bGMqCGBopkIBCDAPGof0Zk37SO2YVWxjKhhAaO5CPgowIjaJ2y1pjejaZ+wqQYBBBAIkQCJ2qdgqjdkMW/aJ2wDq7GXET1x4oSBrafJCCDgpQCJ2kvdL8q23ze9efNm1vT2wdvEKrKzs61mszqZidGjzQh4K0Ci9tbXKp33TfuATBUIIIBASAVI1B4H1h5NP/nkk9KvXz+Pa6N4kwXKy8vlyJEjJneBtiOAgAcCJGoPUGOLXLNmjfXr5MmTY3fzMwLdBPLz86Wjo6PbfnYggEC0BfpGu/ve9r69vV1mz54tjY2NjKa9paZ0BBBAILQCjKg9DO1LL70k6nJmcXGxh7VQdFgERo0aJbt27QpLd+gHAgi4JMCI2iXI+GLUAhYLFiyQ/fv3x3/E7wgkFFCrk7EhgAAC8QKMqONFXPp99erVMmfOHCksLHSpRIpBAAEEEIiiAEuIehB1e6nQlpYWUQ8IsSGQikBzc7MUFRVJV1dXKodzDAIIRESAEXXKgb4gJ9/5rcy7PUeysnLk9uW7JdHzubFLhZKkU8blQBHp378/DggggEA3ARJ1N5JEOy7IhzWPyy0/aJCC/94sLWtKpOGtg9LW2f1YtbhJW1ubTJ06tfuH7EEAAQQQQCBNAS59pwDW+WGNPDhusQz+3Zvy7B2Dk56hpmPdddddohY3qaysTHocHyCQSEB9fwYNGiTcMkmkwz4EoivAU9+9xv5j2f/KWll78yPSUpo8SatiNm7cKDk5OcLiJr2ickACAXu97wQfsQsBBCIsQKLuMfid0vHOb+SJOfukbM1yubGHGwVqOpZa3ERNx2Kp0B5R+RABBBBAIA2BHlJPGqWE8tAzsn3eeLlq7OPSICelfuZNkr/8HbmYpK/qXdNMx0qCw+6UBVjvO2UqDkQgMgKMqJOGerDc8ewuabu1WnKmtMualg0yI/+KhEfX19eLmjd9/PjxhJ+zE4FUBVjvO1UpjkMgOgKMqHuM9cfy3tt7RcrukpIbEydpNR1r4cKFsn79esnNze2xND5EAAEEEEAgXQESdU9iF4/Kvs3vyLDC4fKNJFIrVqywHiCrqqrqqSQ+QyAlgYEDB1rT+1I6mIMQQCASAlz67iHMnYcPyFuHbpDv3fpNuTrBcbHrefMAWQIgdqUtMHLkSF7MkbYaJyAQboEk48Rwdzq13l2UUwd3S72MkYmjhnQ7RV3ynjt3Lg+QdZNhBwIIIICAmwKMqJNq2venH0l4f9pegWzt2rVJS+ADBNIVUG/QUldq2BBAAAFbgERtS8T/ad2fbpOy+d/uNn/6xIkTMmXKFNm6dauwSEU8HL87ERg+fLjU1dU5KYJzEUAgZAJc+k4S0M/vT5fIvSXDJR7p6aefllmzZklZWVmSs9mNAAIIIICAOwKMqBM6fiYfNP5RLix7Qn4UN3e6pqaGOdMJzdiJAAIIIOCFQPxg0Ys6zCiz86jUzBwrd649IB/uXiOLXs2Xn/24UAbEtN6+5L1582bmTMe48KN7Anl5eVZh3Kd2z5SSEDBdgERtR7DP1+X6m74h9TMLZdwLIo+u+6ncMeyr9qfWn/Ylb96MdRkLv7gowDQ/FzEpCoGQCPCayxQDqS55qwfI1DKhrECWIhqHZSSQlZXFqy4zkuMkBMIpwIg6hbhyyTsFJA5xTYAXc7hGSUEIhEKARN1LGNXCJuqSt3ozFpe8e8HiY1cEeDGHK4wUgkBoBHjqu5dQbtq0SQ4cOCBvvvlmL0fyMQIIIIAAAu4LkKh7MG1ubpbp06dLY2MjC5v04MRH7gt0dHS4XyglIoCAkQJc+k4Stvb2dnnooYdk5cqVUlxcnOQodiPgvsCECRPk4MGD7hdMiQggYKQAiTpJ2JYsWWK9vnLmzJlJjmA3AggggAAC3gtw6TuB8YYNG2TZsmXWVCzmtSYAYhcCCCCAgG8CjKjjqGPvSzNfOg6HX30RGDp0qDQ0NPhSF5UggID+AiTqmBhxXzoGgx8DExgyZIjs2bMnsPqpGAEE9BIgUX8RDzVfet68eTJ69GjhvrReX1JagwACCERZgHvUX0R/zZo1l+ZLc186yn8l6DsCCCCglwBrfYuIvY53S0uLqFWh2BAIUkBd3enfvz/rfQcZBOpGQCOByF/6bmpqsl62sXXrVpK0Rl/MKDeFKzpRjj59R6C7QKQTtXrZxmOPPWYtalJWVtZdhz0IBCSg1pZXo2o2BBBAILKXvtUT3nfddZeUlpbK0qVL+SYggAACCCCgpUAkE7W6B/iTn/zECsjzzz8vXGrU8rtJoxBAAAEERCRyT33bSVq9EWvHjh0kaf4aIIAAAghoLRC5e9QrVqywpmGpJ70ZSWv93aRxCCCAAAIiEqlEvWrVKqmtrbWmY7E8KN9/BBBAAAETBCKTqFWSVi/bUCNpkrQJX03aiAACCCCgBCJxj1ol6dmzZ1sLSJCk+eIjgAACCJgkEPoRtT2S3r9/PwuamPTNpK0IIIAAApZAqEfUdpLmcjffdgQQQAABUwVCmajVFKynnnrKeqcvSdrUrybtRgABBBBQAqFL1LHzpEnSfMkRQAABBEwXCNU9arV293333WfF5M033+TpbtO/nbQfAQQQQCA886ibm5ulsrJShgwZImpZ0OzsbMKLAAIIIICA8QKhGFGrS9xFRUUybdo0efnll1lxzPivJR1AAAEEELAFjL5Hre5HqyVBFyxYII2NjVJcXGz3iz8RQAABBBAIhYCxibq1tVXmzp1rBeH48ePcjw7F15FOIIAAAgjECxh56Vtd6i4oKJDx48fLK6+8QpKOjyq/I4AAAgiERsCoEbV6qvvpp5+23n61detWKSsrC00g6AgCCCCAAAKJBIwYUat70eqFGnl5eXLNNdeImnpFkk4UTvYhgAACCIRNQPsRdVNTkyxbtkza2tp4YCxs3z76gwACCCDQq4C2I2r7YbGSkhJrfvSOHTt4qrvXcHIAAggggICXAu3t7V4Wn7Bs7RK1naDVw2LXXXednD171pof3a9fv4QdYCcCCCCAAAJ+CKgkPWjQIGvGkXpmyq9Nm0StLnE/+OCD1tPcKkG3tLRIdXU1K4z59U2gHgQQQACBHgXUipfqlckNDQ3WM1NqBpIfW1ZXV1eXVxVlZWVJT8Wrf5Fs375d1Oso1aZWFps6dSrJ2auAUC4CCCCAgGMB9YDzmjVrZPbs2VJeXi5Lly6V/Px8x+UmK8D3EbW6tK2e4K6oqLD+RbJz50555plnRN2DZgSdLEzsRwABBBDQRUDdilX5Sl35VZu6VavymkrgXmyej6hVRw4ePCi7du2yLhfs2bNHZs2aJVVVVTJ27FhGz15ElTIRQAABBHwRUMl5y5YtMmXKFGt0/Ytf/EIKCwtdrTtLRDy79O1qSykMAQQQQAABAwTcXta6b0/3kJ169HaP2mn5nI9AWAX4uxPWyNKvMArYs5Xq6upk/fr1ri9r7fs96jAGiT4hgAACCERPQF32Xrx4sXWPesiQIdY9a/VQtNub9iuTud1hykMAAQQQQMCpQHNzszz00EOinrvavHmztTCX0zKTnc+IOpkM+xFAAAEEEIgTUIueqFcsFxUVSWlpqbUoV2VlZdxR6teLcrLmYVG3sbJyqqXmwwsinSdl94rpkpOVJTcuf0cuJjgr0S7Pn/r28h54og6xD4EwCHCPOgxRpA9hE1CXuidOnGh1S00rTunlUB27ZfkPpspb96+Xf/7rNjk4+TGZMfLqtGhI1GlxcTAC/giQqP1xphYE0hGwp2JNnjxZUl/WWo2sqyVnSpPM2PyavFx5vaR7KTvd49PpUy/HXpCT7/xW5t2eI1lZN8v0FU1ysrOXU/gYAQQQQACBgARUclaXuVNP0qqhfWXoqPFSJsXy/f90bdpJWpUQUKLulI53XpCpTxyWOzceka6/vSnTT/9Spv5qt3QEFACqRQABBBBAwDuBvfL2ex9nVHwwibqzVX4//w8y/mePyh3DvirS51q548nHZfyvlsvvWz/LqCOchECYBHi2I0zRpC+RFug8KrXrWqRw2r/Lb7f+bzmXAUYgibrzg3+VV+uvlYLcAV82+eq/lzvv/1BebTwiXAH/koWfEEAAAQRMFTgn769bJ0enzJMF038g0nxE/nLxqNT8fKO0ppHoAkjUn8kHjW9K/bAbZfg3vhqn/+9S/+q/ygdpdCCuAH5FAAEEEEAgYIHPpHXtjyQrq0p+M/BeefCWbLl67CS5/92ZUjrzNcn9px9KfhrZN4AFTzrkRMthkZvvktwBabQ0YHaqRwABBBBAIDWBKyR/xu+la0bM0VffIc+2dcmzMbtS/ZFMmaoUxyGAAAIIIBCAQACJeoDkFowQefcDOdHBNe4AYk6VGgt0nmySFdNv/nw1o9vnS01rJo+eaNxBmoYAAmkLBJCor5AbS+6Ssvimdp6RI80fS9m935YbA2hVfHP4HQHfBToOSG39V+Q//+Zd6fpbm7z9Dx9KdekS2X6Of9D6HgsqREAjgUBSYp8bvy333rxDtu5t/5Kio01a3h0j95YMD2py95dt4ScEfBf4TA7t/VRuvX+CDFN/K/sMk/Ezp8v9Un/53xPf20WFCCAQtEAgiVr65MuPFv9Qdv/zC7L9pFqo/EPZvuRXsvvxJ+RH+VcEbUL9CAQgcIXcUDpBro35G9n5lyPSXPBj+dH47ADaQ5UIIKCLQMz/FvxsUh8ZcMujsvHZwbL+lq9J1ldmyNaCn8vGx8dLzMxqPxtEXQhoJHBOWrevlZ8uOinzNj4qtzA7QqPY0BQE/BfgpRz+m1MjAskFzm2XeSO/K0tPqkPKZO7m5+RnlSP5B2xyMT5BIPQCAY2oQ+9KBxHITOCLuZZ/a3tb1s0VWTqlSv5LzVFW68tMk7MQCIUAiToUYaQTYRPoM2y8TP/lc7Km7KxsefsQL6sJW4DpDwJpCJCo08DiUAR8FegzXEruLfG1SipDAAH9BDxN1LwBSL+A0yKTBNRyu3+VybfewD1qk8JGWxFwWcDTRO1yWykOgfAKdB6Vmplj5fZ5v5V31JRFuSAnt78gz/5lqswpy2NtgfBGnp4h0KsAibpXIg5AwAeBPtfIfyweLS1Lp8nYnK9JVs6D8i8f3yPrfjNdRjI9y4cAUAUC+gp4Oj1L327TMgQQQAABBMwQYERtRpxoJQIIIIBARAVI1BENPN1GAAEEEDBDgERtRpxoJQIIIIBARAVI1BENPN1GAAEEEDBDgERtRpxoJQIIIIBARAVI1BENPN1GAAEEEDBDgERtRpxoJQIIIIBARAX+PyL7IFQiVO59AAAAAElFTkSuQmCC"></p>
<p style="text-align: left;">Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="M"> <mi>M</mi> </math></span> is parallel to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span>, find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-coordinate of P.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>evidence of valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> sketch of triangle with sides 3 and 5, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{co}}{{\text{s}}^2}\,\theta = 1 - {\text{si}}{{\text{n}}^2}\,\theta "> <mrow> <mtext>co</mtext> </mrow> <mrow> <msup> <mrow> <mtext>s</mtext> </mrow> <mn>2</mn> </msup> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mo>=</mo> <mn>1</mn> <mo>−</mo> <mrow> <mtext>si</mtext> </mrow> <mrow> <msup> <mrow> <mtext>n</mtext> </mrow> <mn>2</mn> </msup> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> </math></span></p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg</em> missing side is 4 (may be seen in sketch), <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{cos}}\,\theta = \frac{4}{5}"> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mo>=</mo> <mfrac> <mn>4</mn> <mn>5</mn> </mfrac> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{cos}}\,\theta = - \frac{4}{5}"> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mo>=</mo> <mo>−</mo> <mfrac> <mn>4</mn> <mn>5</mn> </mfrac> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{tan}}\,\theta = - \frac{3}{4}"> <mrow> <mtext>tan</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mo>=</mo> <mo>−</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </math></span> <em><strong>A2 N4</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution of either gradient <strong>or</strong> origin into equation of line <em><strong>(A1)</strong></em></p>
<p>(do not accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = mx + b"> <mi>y</mi> <mo>=</mo> <mi>m</mi> <mi>x</mi> <mo>+</mo> <mi>b</mi> </math></span>)</p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x\,{\text{tan}}\,\theta "> <mi>y</mi> <mo>=</mo> <mi>x</mi> <mspace width="thinmathspace"></mspace> <mrow> <mtext>tan</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y - 0 = m\left( {x - 0} \right)"> <mi>y</mi> <mo>−</mo> <mn>0</mn> <mo>=</mo> <mi>m</mi> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>−</mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = mx"> <mi>y</mi> <mo>=</mo> <mi>m</mi> <mi>x</mi> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - \frac{3}{4}x"> <mi>y</mi> <mo>=</mo> <mo>−</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> <mi>x</mi> </math></span> <em><strong>A2 N4</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>A1A0</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L = - \frac{3}{4}x"> <mi>L</mi> <mo>=</mo> <mo>−</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> <mi>x</mi> </math></span>.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\text{d}}}{{{\text{d}}x}}\left( {\frac{{ - 3x}}{4}} \right) = - \frac{3}{4}"> <mfrac> <mrow> <mtext>d</mtext> </mrow> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mo>−</mo> <mn>3</mn> <mi>x</mi> </mrow> <mn>4</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </math></span> (seen anywhere, including answer) <em><strong>A1</strong></em></p>
<p>choosing product rule <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="uv' + vu'"> <mi>u</mi> <msup> <mi>v</mi> <mo>′</mo> </msup> <mo>+</mo> <mi>v</mi> <msup> <mi>u</mi> <mo>′</mo> </msup> </math></span></p>
<p>correct derivatives (must be seen in a correct product rule) <em><strong>A1A1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{cos}}\,x"> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>x</mi> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{e}}^x}"> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mi>x</mi> </msup> </mrow> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right) = {{\text{e}}^x}\,{\text{cos}}\,x + {{\text{e}}^x}\,{\text{sin}}\,x - \frac{3}{4}"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mi>x</mi> </msup> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>x</mi> <mo>+</mo> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mi>x</mi> </msup> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>sin</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>x</mi> <mo>−</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( { = {{\text{e}}^x}\,\left( {{\text{cos}}\,x + {\text{sin}}\,x} \right) - \frac{3}{4}} \right)"> <mrow> <mo>(</mo> <mrow> <mo>=</mo> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mi>x</mi> </msup> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>x</mi> <mo>+</mo> <mrow> <mtext>sin</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>A1 N5</strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach to equate <strong>their</strong> gradients <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f' = {\text{tan}}\,\theta "> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow> <mtext>tan</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f' = - \frac{3}{4}"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo>=</mo> <mo>−</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{e}}^x}\,{\text{cos}}\,x + {{\text{e}}^x}\,{\text{sin}}\,x - \frac{3}{4} = - \frac{3}{4}"> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mi>x</mi> </msup> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>x</mi> <mo>+</mo> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mi>x</mi> </msup> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>sin</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>x</mi> <mo>−</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> <mo>=</mo> <mo>−</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{e}}^x}\,\left( {{\text{cos}}\,x + {\text{sin}}\,x} \right) - \frac{3}{4} = - \frac{3}{4}"> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mi>x</mi> </msup> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>x</mi> <mo>+</mo> <mrow> <mtext>sin</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> <mo>=</mo> <mo>−</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </math></span></p>
<p>correct equation without <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{e}}^x}"> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mi>x</mi> </msup> </mrow> </math></span> <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{sin}}\,x = - {\text{cos}}\,x"> <mrow> <mtext>sin</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>x</mi> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{cos}}\,x + {\text{sin}}\,x = 0"> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>x</mi> <mo>+</mo> <mrow> <mtext>sin</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>x</mi> <mo>=</mo> <mn>0</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{ - {\text{sin}}\,x}}{{{\text{cos}}\,x}} = 1"> <mfrac> <mrow> <mo>−</mo> <mrow> <mtext>sin</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>x</mi> </mrow> <mrow> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>x</mi> </mrow> </mfrac> <mo>=</mo> <mn>1</mn> </math></span></p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{tan}}\,\theta = - 1"> <mrow> <mtext>tan</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mo>=</mo> <mo>−</mo> <mn>1</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 135^\circ "> <mi>x</mi> <mo>=</mo> <msup> <mn>135</mn> <mo>∘</mo> </msup> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \frac{{3\pi }}{4}"> <mi>x</mi> <mo>=</mo> <mfrac> <mrow> <mn>3</mn> <mi>π</mi> </mrow> <mn>4</mn> </mfrac> </math></span> (do not accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="135^\circ "> <msup> <mn>135</mn> <mo>∘</mo> </msup> </math></span>) <em><strong>A1 N1</strong></em></p>
<p><strong>Note:</strong> Do not award the final <em><strong>A1</strong></em> if additional answers are given.</p>
<p><em><strong>[4 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Two schools are represented by points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mo>(</mo><mn>2</mn><mo>,</mo><mo> </mo><mn>20</mn><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext><mo>(</mo><mn>14</mn><mo>,</mo><mo> </mo><mn>24</mn><mo>)</mo></math> on the graph below. A road, represented by the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> with equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>−</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mn>4</mn></math>, passes near the schools. An architect is asked to determine the location of a new bus stop on the road such that it is the same distance from the two schools.</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 equation of the perpendicular bisector of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[AB]</mtext></math> . Give your equation in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>c</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the coordinates of the point on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> where the bus stop should be located.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>gradient <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext><mo>=</mo><mfrac><mn>4</mn><mn>12</mn></mfrac><mo> </mo><mo> </mo><mfenced><mfrac><mn>1</mn><mn>3</mn></mfrac></mfenced></math> <em><strong>(A1)</strong></em> </p>
<p>midpoint <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext><mo>:</mo><mo> </mo><mfenced><mrow><mn>8</mn><mo>,</mo><mo> </mo><mn>22</mn></mrow></mfenced></math> <em><strong>(A1)</strong></em> </p>
<p>gradient of bisector <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mtext>gradient AB</mtext></mfrac><mo>=</mo><mo>-</mo><mn>3</mn></math> <em><strong>(M1)</strong></em> </p>
<p>perpendicular bisector: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>22</mn><mo>=</mo><mo>-</mo><mn>3</mn><mo>×</mo><mn>8</mn><mo>+</mo><mi>b</mi></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>y</mi><mo>-</mo><mn>22</mn></mrow></mfenced><mo>=</mo><mo>-</mo><mn>3</mn><mfenced><mrow><mi>x</mi><mo>-</mo><mn>8</mn></mrow></mfenced></math> <em><strong>(M1)</strong></em> </p>
<p>perpendicular bisector: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>46</mn></math> <em><strong>A1</strong></em> </p>
<p><em><strong><br>[5 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to solve simultaneous equations <em><strong>(M1)</strong></em> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn><mo>=</mo><mo>-</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>46</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>10</mn><mo>.</mo><mn>5</mn><mo>,</mo><mo> </mo><mn>14</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math> <em><strong>A1</strong></em> </p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A line, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}">
<mrow>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span>, has equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \left( {\begin{array}{*{20}{c}} { - 3} \\ 9 \\ {10} \end{array}} \right) + s\left( {\begin{array}{*{20}{c}} 6 \\ 0 \\ 2 \end{array}} \right)">
<mi>r</mi>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>3</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>9</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>10</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>6</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>. Point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {15{\text{,}}\,\,9{\text{,}}\,\,c} \right)">
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>15</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>9</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>c</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> lies on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}">
<mrow>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c"> <mi>c</mi> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second line, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}"> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> </math></span>, is parallel to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}"> <mrow> <msub> <mi>L</mi> <mn>1</mn> </msub> </mrow> </math></span> and passes through (1, 2, 3).</p>
<p>Write down a vector equation for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}"> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>correct equation <em><strong> (A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 3 + 6s = 15"> <mo>−</mo> <mn>3</mn> <mo>+</mo> <mn>6</mn> <mi>s</mi> <mo>=</mo> <mn>15</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6s = 18"> <mn>6</mn> <mi>s</mi> <mo>=</mo> <mn>18</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s = 3"> <mi>s</mi> <mo>=</mo> <mn>3</mn> </math></span> <em><strong>(A1)</strong></em></p>
<p>substitute their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s"> <mi>s</mi> </math></span> value into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="z"> <mi>z</mi> </math></span> component <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10 + 3\left( 2 \right)"> <mn>10</mn> <mo>+</mo> <mn>3</mn> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10 + 6"> <mn>10</mn> <mo>+</mo> <mn>6</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c = 16"> <mi>c</mi> <mo>=</mo> <mn>16</mn> </math></span> <em><strong>A1 N3</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \left( {\begin{array}{*{20}{c}} 1 \\ 2 \\ 3 \end{array}} \right) + t\left( {\begin{array}{*{20}{c}} 6 \\ 0 \\ 2 \end{array}} \right)"> <mi>r</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>t</mi> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span> (=(<em><strong>i</strong></em> + 2<em><strong>j</strong></em> + 3<em><strong>k</strong></em>) + <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span>(6<em><strong>i</strong></em> + 2<em><strong>k</strong></em>)) <em><strong>A2 N2</strong></em></p>
<p><strong>Note:</strong> Accept any scalar multiple of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 6 \\ 0 \\ 2 \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span> for the direction vector.</p>
<p>Award <strong>A1</strong> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 1 \\ 2 \\ 3 \end{array}} \right) + t\left( {\begin{array}{*{20}{c}} 6 \\ 0 \\ 2 \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>t</mi> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span>, <em><strong>A1</strong> </em>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2} = \left( {\begin{array}{*{20}{c}} 1 \\ 2 \\ 3 \end{array}} \right) + t\left( {\begin{array}{*{20}{c}} 6 \\ 0 \\ 2 \end{array}} \right)"> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>t</mi> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span>, <em><strong>A0</strong> </em>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \left( {\begin{array}{*{20}{c}} 6 \\ 0 \\ 2 \end{array}} \right) + t\left( {\begin{array}{*{20}{c}} 1 \\ 2 \\ 3 \end{array}} \right)"> <mi>r</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>t</mi> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span>.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Point A has coordinates (−4, −12, 1) and point B has coordinates (2, −4, −4).</p>
</div>
<div class="specification">
<p>The line <em>L</em> passes through A and B.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{AB}}}\limits^ \to = \left( \begin{gathered} \,6 \hfill \\ \,8 \hfill \\ - 5 \hfill \\ \end{gathered} \right)"> <mover> <mrow> <mrow> <mtext>AB</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>8</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>5</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </math></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find a vector equation for <em>L</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Point <em>C</em> (<em>k</em> , 12 , −<em>k</em>) is on <em>L</em>. Show that <em>k</em> = 14.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{OB}}}\limits^ \to \, \bullet \mathop {{\text{AB}}}\limits^ \to "> <mover> <mrow> <mrow> <mtext>OB</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> <mspace width="thinmathspace"></mspace> <mo>∙</mo> <mover> <mrow> <mrow> <mtext>AB</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of angle OBA.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Point D is also on <em>L</em> and has coordinates (8, 4, −9).</p>
<p>Find the area of triangle OCD.</p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>correct approach <em><strong>A1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{AO}}}\limits^ \to \,\, + \,\,\mathop {{\text{OB}}}\limits^ \to ,\,\,\,{\text{B}} - {\text{A}}\,{\text{, }}\,\left( \begin{gathered} \,\,2 \hfill \\ - 4 \hfill \\ - 4 \hfill \\ \end{gathered} \right) - \left( \begin{gathered} \, - 4 \hfill \\ - 12 \hfill \\ \,\,\,1 \hfill \\ \end{gathered} \right)"> <mover> <mrow> <mrow> <mtext>AO</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mo>+</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mover> <mrow> <mrow> <mtext>OB</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mtext>B</mtext> </mrow> <mo>−</mo> <mrow> <mtext>A</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>, </mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>4</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> <mo>−</mo> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mo>−</mo> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>12</mn> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>1</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{AB}}}\limits^ \to = \left( \begin{gathered} \,6 \hfill \\ \,8 \hfill \\ - 5 \hfill \\ \end{gathered} \right)"> <mover> <mrow> <mrow> <mtext>AB</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>8</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>5</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </math></span> <em><strong>AG N0</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>any correct equation in the form <em><strong>r</strong></em> = <em><strong>a</strong></em> + <em>t<strong>b</strong></em> (any parameter for <em>t</em>) <em><strong>A2 N2</strong></em></p>
<p>where <strong><em>a</em></strong> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( \begin{gathered} \,\,2 \hfill \\ - 4 \hfill \\ - 4 \hfill \\ \end{gathered} \right)"> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>4</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( \begin{gathered} \, - 4 \hfill \\ - 12 \hfill \\ \,\,\,1 \hfill \\ \end{gathered} \right)"> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mo>−</mo> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>12</mn> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>1</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </math></span> and <em><strong>b</strong></em> is a scalar multiple of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( \begin{gathered} \,6 \hfill \\ \,8 \hfill \\ - 5 \hfill \\ \end{gathered} \right)"> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>8</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>5</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </math></span></p>
<p><em>eg</em> <em><strong>r</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left( \begin{gathered} \, - 4 \hfill \\ - 12 \hfill \\ \,\,\,1 \hfill \\ \end{gathered} \right) + t\left( \begin{gathered} \,6 \hfill \\ \,8 \hfill \\ - 5 \hfill \\ \end{gathered} \right),\,\,\left( {x,\,\,y,\,\,z} \right) = \left( {2,\,\, - 4,\,\, - 4} \right) + t\left( {6,\,\,8,\,\, - 5} \right),"> <mo>=</mo> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mo>−</mo> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>12</mn> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>1</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> <mo>+</mo> <mi>t</mi> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>8</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>5</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mi>y</mi> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mi>z</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mo>−</mo> <mn>4</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mo>−</mo> <mn>4</mn> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>t</mi> <mrow> <mo>(</mo> <mrow> <mn>6</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>8</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mo>−</mo> <mn>5</mn> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </math></span> <em><strong>r </strong></em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left( \begin{gathered} \, - 4 + 6t \hfill \\ - 12 + 8t \hfill \\ \,\,\,1 - 5t \hfill \\ \end{gathered} \right)"> <mo>=</mo> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mo>−</mo> <mn>4</mn> <mo>+</mo> <mn>6</mn> <mi>t</mi> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>12</mn> <mo>+</mo> <mn>8</mn> <mi>t</mi> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>1</mn> <mo>−</mo> <mn>5</mn> <mi>t</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </math></span></p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> for the form <em><strong>a</strong></em> + <em>t<strong>b</strong></em>, <em><strong>A1</strong></em> for the form <em><strong>L</strong></em> = <em><strong>a</strong></em> + <em>t<strong>b</strong></em>, <em><strong>A0</strong></em> for the form <em><strong>r</strong></em> = <em><strong>b</strong></em> + <em>t<strong>a</strong></em>.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong> (solving for <em>t</em>)</p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( \begin{gathered} \,k \hfill \\ 12 \hfill \\ - k \hfill \\ \end{gathered} \right) = \left( \begin{gathered} \,\,2 \hfill \\ - 4 \hfill \\ - 4 \hfill \\ \end{gathered} \right) + t\left( \begin{gathered} \,6 \hfill \\ \,8 \hfill \\ - 5 \hfill \\ \end{gathered} \right),\,\,\left( \begin{gathered} \,k \hfill \\ 12 \hfill \\ - k \hfill \\ \end{gathered} \right) = \left( \begin{gathered} \, - 4 \hfill \\ - 12 \hfill \\ \,\,\,1 \hfill \\ \end{gathered} \right) + t\left( \begin{gathered} \,6 \hfill \\ \,8 \hfill \\ - 5 \hfill \\ \end{gathered} \right)"> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mi>k</mi> </mtd> </mtr> <mtr> <mtd> <mn>12</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mi>k</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>4</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> <mo>+</mo> <mi>t</mi> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>8</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>5</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mi>k</mi> </mtd> </mtr> <mtr> <mtd> <mn>12</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mi>k</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mo>−</mo> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>12</mn> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>1</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> <mo>+</mo> <mi>t</mi> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>8</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>5</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </math></span></p>
<p>one correct equation <em><strong>A1</strong></em></p>
<p>eg −4 + 8<em>t</em> = 12, −12 + 8<em>t</em> = 12</p>
<p>correct value for <em>t <strong>(A1)</strong></em></p>
<p><em>eg t</em> = 2 or 3</p>
<p>correct substitution <em><strong>A1</strong></em></p>
<p><em>eg </em> 2 + 6(2), −4 + 6(3), −[1 + 3(−5)]</p>
<p><em>k</em> = 14 <em><strong>AG N0</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong> (solving simultaneously)</p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( \begin{gathered} \,k \hfill \\ 12 \hfill \\ - k \hfill \\ \end{gathered} \right) = \left( \begin{gathered} \,\,2 \hfill \\ - 4 \hfill \\ - 4 \hfill \\ \end{gathered} \right) + t\left( \begin{gathered} \,6 \hfill \\ \,8 \hfill \\ - 5 \hfill \\ \end{gathered} \right),\,\,\left( \begin{gathered} \,k \hfill \\ 12 \hfill \\ - k \hfill \\ \end{gathered} \right) = \left( \begin{gathered} \, - 4 \hfill \\ - 12 \hfill \\ \,\,\,1 \hfill \\ \end{gathered} \right) + t\left( \begin{gathered} \,6 \hfill \\ \,8 \hfill \\ - 5 \hfill \\ \end{gathered} \right)"> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mi>k</mi> </mtd> </mtr> <mtr> <mtd> <mn>12</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mi>k</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>4</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> <mo>+</mo> <mi>t</mi> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>8</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>5</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mi>k</mi> </mtd> </mtr> <mtr> <mtd> <mn>12</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mi>k</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mo>−</mo> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>12</mn> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>1</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> <mo>+</mo> <mi>t</mi> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>8</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>5</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </math></span></p>
<p>two correct equations in <em><strong>A1</strong></em></p>
<p><em>eg k</em> = −4 + 6<em>t,</em> −<em>k</em> = 1 −5<em>t</em></p>
<p><strong>EITHER</strong> (eliminating <em>k</em>)</p>
<p>correct value for <em>t</em> <em><strong>(A1)</strong></em></p>
<p><em>eg t</em> = 2 or 3</p>
<p>correct substitution <em><strong>A1</strong></em></p>
<p><em>eg </em> 2 + 6(2), −4 + 6(3)</p>
<p><strong>OR</strong> (eliminating <em>t</em>)</p>
<p>correct equation(s) <em><strong>(A1)</strong></em></p>
<p><em>eg </em> 5<em>k</em> + 20 = 30<em>t</em> <strong>and </strong>−6<em>k</em> − 6 = 30<em>t</em>, −<em>k</em> = 1 − 5<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{{k + 4}}{6}} \right)"> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mi>k</mi> <mo>+</mo> <mn>4</mn> </mrow> <mn>6</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>correct working clearly leading to <em>k</em> = 14 <em><strong>A1</strong></em></p>
<p><em>eg </em>−<em>k</em> + 14 = 0, −6<em>k</em> = 6 −5<em>k</em> − 20, 5<em>k</em> = −20 + 6(1 + <em>k</em>)</p>
<p><strong>THEN </strong></p>
<p><em>k</em> = 14 <em><strong>AG N0</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into scalar product <em><strong>A1</strong></em></p>
<p><em>eg </em>(2)(6) − (4)(8) − (4)(−5), 12 − 32 + 20</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{OB}}}\limits^ \to \, \bullet \mathop {{\text{AB}}}\limits^ \to "> <mover> <mrow> <mrow> <mtext>OB</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> <mspace width="thinmathspace"></mspace> <mo>∙</mo> <mover> <mrow> <mrow> <mtext>AB</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </math></span> = 0 <em><strong>A1 N0</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{O}}\mathop {\text{B}}\limits^ \wedge {\text{A}} = \frac{\pi }{2},\,\,90^\circ \,\,\,\,\,\left( {{\text{accept}}\,\frac{{3\pi }}{2},\,\,270^\circ } \right)\,"> <mrow> <mtext>O</mtext> </mrow> <mover> <mrow> <mtext>B</mtext> </mrow> <mo>∧</mo> </mover> <mo></mo> <mrow> <mtext>A</mtext> </mrow> <mo>=</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <msup> <mn>90</mn> <mo>∘</mo> </msup> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mrow> <mtext>accept</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mfrac> <mrow> <mn>3</mn> <mi>π</mi> </mrow> <mn>2</mn> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <msup> <mn>270</mn> <mo>∘</mo> </msup> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace"></mspace> </math></span> <strong><em>A1 N1</em></strong></p>
<p><strong><em>[1 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong> (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math></span> × height × CD)</p>
<p>recognizing that OB is altitude of triangle with base CD (seen anywhere) <em><strong> M1</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2} \times \left| {\mathop {{\text{OB}}}\limits^ \to } \right| \times \left| {\mathop {{\text{CD}}}\limits^ \to } \right|,\,\,{\text{OB}} \bot {\text{CD}},"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>×</mo> <mrow> <mo>|</mo> <mrow> <mover> <mrow> <mrow> <mtext>OB</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </mrow> <mo>|</mo> </mrow> <mo>×</mo> <mrow> <mo>|</mo> <mrow> <mover> <mrow> <mrow> <mtext>CD</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </mrow> <mo>|</mo> </mrow> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mtext>OB</mtext> </mrow> <mi mathvariant="normal">⊥</mi> <mrow> <mtext>CD</mtext> </mrow> <mo>,</mo> </math></span> sketch showing right angle at B</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKIAAACBCAYAAABDymGDAAAgAElEQVR4AeydB5xU1fXHv++96TPbd+m9CCJFBcWCig0FaxRjib33xBK7JmqsiT3R2LBjw6hYQAXsFUU6SBepy7J9d8or9/85983Axgb4X5Tovg/DzM68cu995517yu/8Lpe0bauGPTRbOZ6nvO95OXMfUsPoq04es7jJPo6qnnC5astAdcmEcuV55WrCJQMVbS9XE6qd9edxZquHhrVVbS+ZoKpz+wx7SM11ml6rUc19aGSTY7N/6/1y1xmpHprbuP6839POb7d9k9r9nTY1bd+3P2fbx/e1yVG1k29Xe4Bik8757Wv8cn+7br1yvQrVmKpSnueq+rqk8hyl5s5aqTJJpVKplFLKVsmMoxxPbfQ9URvYTH5086hftpAZ9GaXvq1Zv7NDXXXNjx753R+LGTRsGG1nLGRZvdfk53qWzVvc5O+mH03yB+3NcW3n8tHM1TQ9ivrP+MeePdh/1Nz//l4f3pztbtqeDX02ieXlE5bdvtPPDR27ZfzuEUMZJYRCebpB8ViEB+8fyzHHnMcttzxAOKRw3EosM4ntOM3WaHOrflH/ZI31/Jd86G9zgvAhTzz2ASu1JGRY+dlDXHHevazcpGaY5A89nXuGv8n1N77EPH2xWub95w6uv/WLHz5T/hDOu2d3xp13DXd/ttIXuvq5/Odv13AJ53LD77dq8oDkTrOx7U7QYauu2YNS1Nf/fwY2w8ovnuSKM67mTfpy8j2nMzR//aOba9mW/q6U/7gbhofnuHz0UZIb/vkuSyvivDLufeobIgTMVthOmGAw0GzdMYdfcjzpU/sQSJzMcwtS3z1x/hD+OPYWBn90Au0DJqY5iMveK+GEF5/jkrbf3f1HvzE7c9idT3Fl6cvsmR/ANIdww6KBnHfroT9yWIj2h93I20/swapLBxEwTcz83/Ny6elMHn02AxM/cLM3qt0Regw/ncvTV9M70J2Rzy34Hu2aa5pH7aQraW/G6H3qGGAMp/aOYUp79CtC+x0u5dPB1/Li5Dd44LDO3/OA5M61Jb8rxLLIZGzq603+/vf7qK2r46Tf78nD919PKFQvPxMOBUkmZd/m2QyxrZrnVD/1LCnmjTqePeedyZyb9yL/p56m5bhmGQGFwvEcAlaImVNrGTLiHPbYfk9efuFkXKOCYNDAc0uwXQiEwBSp3IjNMIwf3esH1MmPHvMTf8xqlPanMmpubfYcMs2P4oarG7ngiO1bhPAnjmzzHmaQSoW01nMcj7q6FXTpEAcDAlYpjlPC2jWKxYvSVFZunBBuTPuab5Lf4NXERjyXsfc8xd17F3Jq1sBse9yt3DP2QQ4dWLjBM7TssPlHwPM84jGF7Xgk8ixal5QxY8Eq7r33E5YtX8nyVaupbTCY/OUEHrz3akbs369ZGrUFTM3N0o+WkzTTCChckul6opEEdtLkPy8s4aTLb0UZcSwzSDJdTSgQ4orTj+C8c4dQtJH6Y0NTc4sgNtMN/LWcxvE8xGuwTA/tuXkmn326mPffXUxRUZTBO/WmsDhASas4oYhF0Pxx2y83Li2CmBuJlveNGgGFhLBcMIIoZfnHGIpksp5IOKJtRcMIks44hEMBHJXCdRoIBsIYhHBVCMsE1/UPlVBjTY2iXasfF9if0VnZqHFo2WkLHYFQKITEGJVSpDIpzKzkWFiIQ+x6fgw2J4SWBbW1tTz2+HNcfc2NG+zVz+isbLAtLTtsASNgqACoIJjiETtaA+IFsAjjep4O3xhWGsM0SKcasYI2yivBMCFjg2V5LFq0gpdfXsTz41cwbU2S1rGtNtizFkHc4BD9RndQBoahMMRQNJSeqi3TxHM8TIkeuiliYYu0m0c4BK4Nkyd7vPeR4t8vvMeyNV8zop/NpWf3Z7vtttvgILY4Kxscot/YDkqMO0nzBcBwMXTA2v/bsQ2dRaqsrCUStgiFTCqqonw+pYInnx3DlGmLiMdKGDyoGwcOH8ZOgwsoKfVtw6y1+YOD2SKIPzg0v9UfMhjYQCQ7ADJFZ0gnM4TChXw1exlnnnkWW2/dgzPPOJkrb5rGWzMW0SG/kHNP/B2Dti9kxx1jegpPZwwtrHKiDQliy9S8ifL2Q2EIMeL/17amfZFAtmymTMN4pNJpLDNKwJIknkEwmAHVwMS3JjH5y3LenVfA6AnPklRJti5TXPeXwzhgRCftxMgZ5BWWY3QScMNituE9/tdG92du7/+iADYdonUCmHWDPQnZqJCOESo3jTLA8MKkkxGmzcjwwktzCeZ3pHWkGEU9/7jqJPbbbwCtyjxM09PQMPGiAwELJbAPlXWvfzx6I4ZAy7YpIyCC11ST5ASx6Xebcr5fcl/HcbTNl2uD9MV1TBw3iGfUYlk2ETPIvAUmTzw5g9uffJqSSDFlxduwovJrhmzTjyOP3JpozJcygY5ZpoNlihCKfSnitXERwhZBzN2FjXzP3TyBfonwyUu0yv+iIFqWxAD99uf6hZnCsJIEKWXK5GrGvjKfV9+dT0NjFacdeizz5k/mg09fp12ByWWX7EU8Vo0VKMSxAyhHQj+mNgi1ty3qVIG2WjYgaRv4eSPvzm9oN7lhuRuYE0QRyv/VTWtB1yUYDOouVFYGmDW3mEkfpXl8zH8or1rK6Qd14arLz+Sdtxdz16gXKc0rYrc9erDzkG2wzLAWNsO0MS3Rfya27RKwfK8bw8GQTA2xHx2iFkH80eH57o/fp/1EIHNT9HeP2HK/yWlDeZetvLyccRNmcv/j8/l47nIGbrUtfzn/BIbvbRKwDJ5+7nk6te7CmsqVnHT8SUSiYZ3KE5mTh7G+vo5EooBAQDTjpvW7RRA3bbyIxdY/2RsSPs8Vf9PXlq6XJhCUHG4Y5WZtKCMJJDGUnDOezWZsXIM8MQtE0ygJtUjAOaSdA2mTabgo5eApD1O+TwURYXGtDLodZgTlBnWgOulCdXWasa/M4a236/h85ly6luTx0OUHM2y/brRpp0il63nqyfmM/XA+hhXl6ov2ZsCgDjgGWAGB0spmEo8X+NOwbo//HYQ2qkMtgrhRw/TTdjItmZYcXFfiajL1eWQyFYSCUl4lwpfAdRN6SpMrbIoSMbyVYERRFK470NABaAmZRCTgohMiEpUJRur02cV5CIhdKCJrwqpl8K8nk0z44G0+nfUWh+8Uo3/7Ip0t2WNob9q1D5C2q/ji0zRnXXUTBWF48PYTOPzw3XTqr76hkbxYtubppw3RuqNaBHHdUDT/B88zSTaalK+pIhHPIxpRxGL5eNp6t3AdQT37gAEBC2w47Nu0jQmQvLDMqutCIxJrEdSM2GSGzgeLRvZUANMQb1jh2iZzZnu8MX4yE96dTEXNSgYP3IbLzr6IPXftxPEn3c2kL99hypQiunbfj4b6EBdf82+K88o4+uDtGDZsV2zHxjQtYs0khNKrFkFsem+b/bPFP/85ipv/fh8D+g1h2wHbMWJEP/bYoz+RiKVjdK4nkCkHS9egbij/sL6ByvDLPdcLoShGkWbxgjPaGxZhkc3E11qr1tQy6uGPGfXcdNIUcOTQIVx0UT86djL0NL5ysaK6tpb+nbvRuUsB6bTNxRfdwJwVHulkHeeefRR5+Sau62qQg674E7RDM2wtgtgMg/hDp0g2Qk1thNp0gmmLU7w34zUmvvs5p550DMceszOlZZa200xRi+IwbMrcnNtXgAlKpmPRhiJQQQzCCF5Vdkmn6kjWJZg1S/HcuBoef20O7cNpbjqvEwcc1IlozKOx3iMRC2IZitrK5Wy73RB699qFKZ/X8PjYmbQpactFF+9Jhw5RFi74hh7dy3BcGysQ2bQ2/9BAtWjEHxmZZvhJ/JqDDtyNl8a+xbK11Zx9zInU1M7m1jvuorJqEX+56jisoASRPcFPaVn8scuKI6KdETHwDEm5KTzXxTQCGKaF4wqy2iEjISYzQsUaxeTPk7w4diLTZs0jvzDBTecPY/g+PenS0eXrJTU8/ew4jhh5OMGgYuWKKhpTDjsOGkxjvclf/3Y37Vv1ZujgDpxzztF6n27dOpIRIGwwpDV5wPTDPj/W7o367dtUHS1/Nx/dRybjKNdW6vLLnlbEdlZPj16s6qqVuvOOKapt5+Hqk09mKaUcpTxX2Zkfvm6OrcN1XeU4PqWL69Upx6tRnlevbDcjZ9EUIK7KqGQmqSa9O0sdOvLfiu7Xq9POnqYefqReVVV7ylZKpTK1SnkNaszoSSoa66VefWWabufqRZ469MA71VOPr1VHHH6nirX+gxo24klVUS7cIpXKdRuV4yrlKjv7akIvswEamFwffui9ZWreqMf1p+0kiktSXcOG7cN9D97D6vLPMYNxAsEYnpcPqg3ppIUVdLAC4nF8194SDZiL80msLve3H1iP0pAyCEtYCJvqmmq+/NzmiWcqmbboGzqWduU/f9+Vobu3p6g4TmMmg+sYWIgWC6C8IrxQWxYuasTxqihoHaNnj3Y8/NgzzFo4n+7tWnHP34eTly8hmhCSwpNwk1Jic0rISP/7aYPzraNaBPFbA9Kcf+o0IAbb9i+hY6et+eKLco78fRFvvzcJjwBWwEFiv5Kp8ZT7vVNzLlieE8bc3xk7T86AOK4VKxVPP+/xwZQGJkx+jf6tv+bys/bk978fRiYFYQPeHj+LNp2K6N27HUpsSlcEKo3ULruezOmKkBWmc5fe3P70eFoFKrnqkjPp0i1GMCRPVBxlSMxSQlJptLeiH5zvPjw/ZQxbBPGnjNpGHiNRGvFBhB2hpLiYhsYGpk6dymvvv0mfTu3p3LFMx/NSKZtIVMIuP3zinCaUPUQbRqNBGhpTVFbW8cBDX3LDs19jZ+o5Ya/9ufi83mzVy8NxhbEhwJqVissuu4zBu+3CXXddjnaOsDBNRTQS8fPNjkdtQwNPP/+0BH5o26ote+4xRGdMHMcmYDWTLfgDXWwRxB8YmOb42iBJxqkjFCmhY7tujP9wOl9f10iKEEccsj+lZQaOmyEUCuA5Bob1w5KYE0RJMWYyGeZMW8PLryzhvc8raEzZXHVkH/bdpxO9+yQIhyt0UNs0ImC5rFpmUlVXRnmFor4WYnGwDA9FhLRoRBWgriHE2Wc+zvSv17J7v5259cbeFBSnsQKu9sSR6dwLoiRQbqxCZ0x0CKlFIzaHrGzWcygvSsiK4WTATs4joWxmLJzPsIFlHHNCX1JKSK8iWjM5mbTG/QWDaTKOwrTkezS+TzI0rjJQqTCVFQZPvGBx/xMTqWtYzjlH7MAxR2/NVj3b6f3nzlvEPXe/yI03XEQg5BCLuxjKpK6+inQ6TrAAbCOCTQQnEMZWYXbtN4hXn/yUCR9/Rdf8Rm6+sT8Dd9hhnT1qSHpGwkTrbMLW/rj98HOzyePaohE3ecg24QDDI2O7mGaI3YbszJrKDzhl90M58bR9KG0lMT8Hyfy5GUU4JFVySdK2gWUFcV2F4xg6I1K5VjFtRi2vjZvLl7OWUdtQx6mH9mOfvX5Pn62D5BWkcL0Myg2waOEKHnzyaUaOPIg9h26FY9s4UjBvBbAzNslGRSQmWk6m7Vp233YE4ybM4pXXx2BlVnPhn07RxU4y/Ys9Kvbrz7G1COLmHGXTwzClBiTAWWcfwfF/OIJ4IaS9FIbpETRMnRgJBrV7jaMaCIZKyaQhmMUKvPPuIl55bT6PvvoFpXnF/G6/AznzxI706GboFGFtvY1HIwFLPNkQdXUurhsl2ShOiMQVg9iOq8uhTIH9ixbzbMKWSUlxAXOWLqWh8R0WlFdx918v5Kijd8B10xpjGY1GsW3bR9NsznFqCWhv3tEVo1+DHTwTx1GEEzVSDUI4mE/aCfmesyUQewfbSWEFS0nZNp5nUVth8NlnitsfWs07s+YytGuQf9wymN69iglHpMh9DQ31cSa8NYdh+21DXiKqhbqm1vfAJbOiETdemlAshKexWmFwKzFVhIARoFPbjhiGyZwVC+lQkM+wA/IIxlJkMiBC+HNuLRpxM462wLAE8CUmlth7rhfU07Tygj7hqCF4HB8hHQyESGZc5s5WvDVpOi+Pf5+vv1nKnoN35KnrTmSXnQro2BFMS+HYjURCMT6dsZxjz/ozj//rL/zusD2IhHwtaQXzdXhFojIS6XPFRHAFBeQStOQVoKrc5IUxX2C49cSo56LzT6VVu3aa90bCTuIUyfQsD1LOUdqMQ9UCeticg2tmAae2K3AEj2AojuO5BExLs61WVjXQqixOMGSxunwlL4//mj/+YxopB84/9FSuvSTMkF1MIlFYvSpJKinlmcK2IPQeEVKpBNF4N959bwZHHzVUd0V5Ur4QIBAQoZdQj4UZMIlG40Qica05xXka//qX3D1qDGtqvuaf1/6F447fFsvKgBHQNSdiHwrNiGwiwJvbVmzRiJtREj1X4FdBwmGQdLJnikAaOF4DDz90P6+M/YCDDzmNWLQ1Y8bOYvJKOHhgZ847c2sG9EcLneAZk8k0F150N1v36sx554wkv0Aw+Z4O+9TZIiQCkfZrQ4REyfNSBEISxBSVqAiGFf369ESpJKn6OJPemsll1z1JIFzEgzcdwxFHbUM4WodnFKBcpUmURAvmts0thHKdFkHMjfZmeBeNJIk7x1ujBVLwg56XwCLOa68vYPrMRt6bfAeJ/PYc/bujueLyQnbdaUeS6aTOdoQCYqfZ1NVUs6ZSMeGBFzjkkKPpVyzBaJO6upUa8NC+XTsfBaMglZI0nNimAr9JYVoGbVpHGdCvO1MmL8JrMLnv3xOpSyU59ZCdOOm0nTRKx/YUAdM3ITbDUGzwlC2CuMEhao4dDFJ2klAwoREyr437jPqaejJOhuL8Uq669EqOObw7RqKBjz6ZxS47b6NTftmad+25Gp5JVW1NNtMhQfCQ/l5al3MsxBLIy4thGkIHItOqX2UooNuSkhJSqVn8/c6xfDl7GkXx1hx3zAG6c6L9QsGQtg+bo7c/5RzNExb/KVf+DRzjqSQYdRhmKbW1xXz0wVrOPu8Vzr7yXaauKKNLhwG88tw9nHJKRyJFNbwz8R2GjTiRmVNXY3gWtqR0lUztbajK5GMl2hKQTJshmlJ4aGxwagmFMuvSg4lYFC8gxEhlfjmCipKXMNimVzGVNfDEC+9RkFfMA3eewDbbx2m0hcLL8Jm8ZDZfPyP/rHeoRSNuxuE2jSgrlsOsOR6PPjeL0W88S//2rcmzasFdSuviCJ27ZAiGFK6bj+l2JekV8c7bM+nVK59I1EAZQvnhkgh5lEVrUVYVniElnHEMKbjCoKgogmFK/NAhvyBAx+IEZaViF0i9tdRXeey2Sz8KCueQTq5lu20M9h7RE1etJRIRgYVgIIny5Hz6lP77z/h/iyDKYOe0gK790BHf7C2QL/SX6971r0oHXXQMTn73D/cQ7L/E5cQrLS9XTJq0hOdeepdlyxfQtUsbxtx9KfnxAGde9Hfq0rX86aILKS5rp4PbIUthe0nCkVKSmRSBSARXUDJKQBMhIpEItY3oInZL6lJwiIQDBIJRiotLNJJGeS7RqMPhBw2lqEhKXG1cL8DihYqbbhnFV0tns33vNlx//aW6f4asMuUJr6Gr101xXE+jgdb3+eeTxBZBzN6S9UMueVWfkEjfEM3dkhNGcTwkNRYE5ZJxUno9ElOjlCXInAYV443xi7nljheYvCLDAdsP4+pLhzFi//ZIjPj1cV+yqHwlu/bZht332lmA2bjioZoeGZVG8jAlrVrrwicJgpuWlIKaCDchVgGuk4dhSplqhkSeCKtJXiKhS0sFUtapcxsOPXRPgkGXyurVuG4eR532PNX1dfRoX8gjD1xOm/YGtq00LlKm4khQ0niWX+667sFbPyI/x6cWQfyvUc6qRmFMlU0oM3Kb/qjWwaEymRCGKS9FY7IevAQNVVGee8XljkcmsXz1Ui49dn9OPH5runUXircUdY2NzP1qOYYZoFfPPoTlMhJ2cUR7WShPqIGFwCh7W3RhkqFTdQLZyo/HSaWkjRKVlCXIEpoyOBoTZle/3rpjhzx6biXBaEVxfideemEWixa/Q9JOc9Axw2nfwSCVzsjaUlqbYjTNJf9yLkOLIDaZmfUcq4PQegL+b80oDH/KwHYdggEJGAuPdIS6apg912LK1EX85+W3WbN2GcN36sthh17LjgMLEDSNFRDBkEBilAkTPyVq2Oyz9xDtGZvKR2dLIDoga9vpUlBf+iU+mJV/wuEgbcpaEQ5J4tCn0rRCEqy2iMYjKDELJB4XkMxLEs+xmDXb5sbbXiRs1HPAsCFcevGReJ6LabmarSt7ltyj1mQk9FWbfL/5P7YIooyxjLtWhvJBsE4SCPYwNIuC7GBqp0EIhizTH7K0U8PiRUt45pmljPrPDCpsOGPEPlx24ckUlhhEI2ggbCQmwiVI7ABz5y7kw89n0Jh2GLxDL4IhVweflWdiWSFMSRAbFuGQT5KpY8oCrA1AXE6oZDEeCVzLVG4gFsKQvgPIL8xDaqglTCMgC7EVlyyp56TT7+arigYuPPkIrrnyOASBaAUNbXnoKj+Zl7OTwOYXtR+/QosgakHMkpavGysRSKk7luGROyU3TOhCHGprXVZ8U81zzy/juYlLKYkpTv7dVgwb1oUBA7rp8kwRGNupJx6LYWdCOrjcWOfy6adrqTcLOHRoZ1q1SaGUMIoJTYdU50FYyKgNmYpzNqqPlhEkTiRisnjZ16QlpGOALdQigVqG79ebkpJija6RSdYwa2moLeSO2yawqCLDQQO7c8mfR2IEPExlk05LPDNEJuMQzKbw/G5n+6mfynUD8bN9aBFEGWrV4BcTGfFsPM7WVpgihUEE1wlrLTJ7tuL+0WnGvPsxwarxnHPqQI48an+6dO6AEtaFdZtM40UaUygZjpraJMnGMFfeeA8Bq5AzztidWDysPex77nmHkYftRkmZRXGRgBWCWkhkfRKZzsNhKWiH0tI8XSaazihtFyYzDZSUmOy1V1ct6K7diBIV6ZZy+53zeHzca0TtSv7y1/NIJKLZAKEwQ/ghmqDWuk1qqfVkkNOQ8sfPuzUdvZ/3ylvQ1VxkivTpP6RZulBJtFR23kpl4PMvGrjvgVd4/vNK+nfowyUX3MTeeycoLNJ66Ht7Y5kGyZRNQX6UmTOXaK+6T8+eDNh2Ww0kmDRpErffeQ/t28X53aE7EIvJcp8hUqmUDqNIGk82eZPFdXyqEp95KxHJ08z+PXr21IIbDvl1xlO/WMC9Tz5MKBDgzutup3evTt/bti3tyxZBlDuiijANR2tG22kkFMhHGRFqqoJMn7qSx0ZPZtwHUxjQsw+v3L49vXt1pGPHUg1edV1bV8XloonaDTb8aV0YuYJBW2ct3n13OnmxfLp3zqO0NEogYPDV3JUsq3aZOnUGvztsIBGB2QTjOLIGrX4g/BWcxIkuLIz7guibh6QyDZoASYLYoYBLJh2grlpx2dWvair2Q/bswyEjy/AMFzPraPncOk285G/bhzpK8PNrQ+lriyDmNCAmDgGCwRLstMnChYqHnljKnc8+Qd+2Rdxw2YEcekgnSoQSS6BR4shoeg/B6wnFm/7a93Wk5FI1IrR0AStBXT3MmLWaOjfA4O1LCQbjGl1dXp4mFCr08X4kBWyoPXPtYetqvfUghKLCOK4ncUX/QpFgVGMGI5IjdgPUrDG4/paJfDx7AQmzhquuPIe8fCkZTfgNy7VP/5WVQP1d7geZpkVI/XrlbG9+trcWQRSh8mT1JJOKigBffrmKp5+fwOx5KzSr1l0XH8L+w/rQuYugW6Wq18bQGRSpOfELivwp3L+hvmaUG21hWpYOHC9cXM2nU6bhKIe999lWC5DnehSXdNRF74lEKxzPJBoOYAbC2tvWYFpDO8daGGKxiD5OEDICWrU0oAwcO8PatR5nXfAyb0+ZSs92Jfzr9ivp0lUW907hZDJEIt93m3PqMBs7bBoz/dnEb/2Fvq+F63/9jXwSNvypM77hH7e9w5iPFzOwcy9OOf4iDtgvQKcuInBJXUruEsVQYV1bLgLnOGmdfvM8n43BF8Ksx6s9bgvXMxjzwhusrqnlzJGn0atXOzxXHBCT+joPwsVEo0UEzCihkEHb/FLtMIldqCmoswoqF+QW6KHEAgU3KPHuQNDi0Udf4KUpiwmYhfz5vMPZdUgHMnaKYDAPvUrAd5AM2ZNqWZT/clrxl7vhzS+IXrZT8takjxJycFUa5SU1WaRy8/x4qsDl9SEN2FLNFk7ocVFGWmPxZGoxjHpNeSHLLkhyHyW/yWBGdQhED59ersu3reQEAnMXlLJWY8KKlbG1wZ+S9eMsi2CWyaq+Dia/H+TG+xfz9uQPOXy3PlxxxQh69AiSiPthG8ntyvUssb5y98wLEpIAnxQoeZZ+Ny1hQsho8k1dfukp7Aabjz+2CXsZ9tjJRqZU06zHCAqRpjDGWjQ0pNFkC0GDXXr3pa4qpYfOlTGz00QsRSRSIS4Vq2oU3d0owVA1UnKw/OsYEz7IJ5hZTf92YfYeJuSdLoFgRJchBAKN389fnVOIOdn7jrDmfvh53ptfEHWHJOYmPfVvoHRFIv86WW8ZfDVvPvf+ayL1dS7xWB5durRm2H796dW7Pa7r6aIf/44LXZs+GkM5PhJFcr86BZeTch8IKnfO5wf0p0uNWka81gzBgEU46OG5ScJhC+WGWblCMWNWPU8/9w6ffjGNflt1ZMy917Lrzu0pK5Psg7POa/ZTfTkJzN0YuWBWbWU9W8kZCzGmPHTCshC0gowe/QZTl8ymS6ceDNx+ew2REM0pGi8SE45DoQZO6XXvJLOSn5dHOGxgO77JGAqaZNISqikGp4F0OoVlGdouXFsR5Oq/PMyUWbMZPqgr1//1TMpK5Zb6HIZiMgSynneu1Vvq++YTRFEVWpP4XfcLeUzN6VxeXs9jo8eQdOLkx4qoTtZz+12VTJzwCL16d9VC63uf2Zsv0V5Ny+vK0K5fRGS726EAACAASURBVEYmFVngWgu62Dqyvwio0usJy3px0YgARIXNIKlrRWoaavn4gzX869/v8eb0bxjQfR9u/9tJ7Ll7eyIxsReV1tx2xiUUEifEdyBymtU/f+5Svn2ls4LyUbosmRdXYP5B1ko/n3idkNmKovzWTJm6inYdColq38agpKQ1mGHq6mr16SVeKEHtRCJPM8lKPbKhZJYIk5+fr5tSWVmFZYkA5/PoIxN5eeIn9OvRk6cfvxArJOWjfgt9eL8U139b9W2Zopi1VJuxcRq5IsIhLz8boZc4MIRkHI0Czkt0JBzvyrBd+zLuP5dzwB4HUpkuYOrU+bqmVqY3qdWQTQjLFfkoEijDZ6QyLJkP/VnX14KyuEwaQ5MEGdrxkOwBKknGXoNjryHZAG+MX8EFFy7klKum4Vlduffy3zPm4W3Zb/82hONpXNWIaSa1RguH/TphX/tmY4W6b/JZNLWEe7LjZoq9WK2XD5PFs/Wm4N13FvHl4iqwV5MXD3P0OZfw1OixKOHPNoK0b5+vbcK1lRV6tBQ2DakUnmHrNohjIiTtrhuhXbt8nn/kOvYeWqqrAV/+zzxGPfsZlSqPC8/fAxVYTShUhw6ES0Gz3AElpaV+c7b0/5tfI7oSvc9OqWJtZ20PyaMKGNh2FIm8MF3btyMc8ejXvw/FxTPIj5b49RyWJPBlGhbtln1OtG0t9lQKZRTljEoMzcovNpDsJwIg2QrfjpPqNceTteSiLFqguP+xev499i0i9lpuunhHjjm2H/FIAseT+g8hOLd0IXogLP4o1Nc7xGMidNlN+qG9hyZ/y0cRTllxKSBJYH9/ZSTJpKOMfW0uqVAZ/bplOO3k4Yx77yU+/mQuJ51ysJ6a27V36NG+jKqaCjTowXIJxwKEo9InebjkQTS0YxONZTjkwG01G+zs6TZX3Pgaq9cu4c4LD2X3PXphmSLcYQ2wUMjxYVxHyNtzHdiy35tfEH+gv5I/lUxBLGJQWlJMaUkpCxZ+wJtvvsXq1dWsrl5Jhw4dfuDoTf9aFjNctaaab75ZyS23vslLMxUHb7czJxyxAwcdaJK0l+qTSpvkhieTGaJRyWrYelpNxAPZdN/GXdsnTc+GcxQ0NDgsWL6AoBVml10GEY8qzVOtHSiRaeXXmuQn8rCdFfoiYkfn5eWRl/AfQE0PbAR9rWY7BEJRDWR9cNSzfL12BTv1HsARI/dHhFSmb2FlkAde+iSKUGKOOku0cV34RfdqdkHU5pzvYfhTVzY+JYl9yRA4tpjQNoUFLq99EuHYCyag3CTFiVa4YhTp6URsGymZlMdZNE6jtg0NoxhD8sJ6NSNRUPmaNNLz/KlMKHwFh1dZYfPee9O577ElLFy1hu7tevLElZ0ZcVA78vKrtcaOBTrp9ZBE8Wq0c1RuniKcjbnpGU0kVDb5Q/dD7MXcd1LCmTU/lKfz0dJcKeUUM+GTT2pYuGQV3YtKOfDgbQgGw3h2LY2prLAKvrAwRMcO7Zg3bwENSfS1E3lpem/TWTttEqIhYBCMgOdEaagKMGnSPMZOWkqBleHyi/ekVRsxf0IakyHOoGnWaf9eJNYSeuP/kS079zVfa30sp7aysx6vP8HIQoE6RGEZOqc6cOD2xC2LVGM56arZpNKVnHPedcyZW6ttPNEO/iZeqDwvNhmnilRGQJ1CGiloZR+yZQpuzwiSroe331JccMVcjrzseVJ1n3DGETGeGbU9xxzXk7jGUBWDKtBhIDOHxNZTatYpWXddkTgJB8mN9m0u3R6/O1mHScI18qBYGmktK76bZpj6hhgPPjKJVRULOfPEbdm6Tzfy8iOai7Ax6ZL20lqeCwrLKGvVXhfUNyYzGoldVOIQT8j5ggTNKK5XB6oaLx3jpZfg0LNvoqZmAX+7fHf23rcXjY21SE67IVmPGZDzCmInltXmKd9Mar7bu9nO1OwaUasMfePkRjY5vYQ0bE+HHgKmQf9+22LY5ey4dV8uvuBiyivinH3ZmYx6+CluvOlkffPFbvO9Et/QCVlBlCYSkvBEUrPg25kA5asM3nhrEW9M+JQVqytpWxbk+X+cwR67taekWNweR68x4gus7wDlAKhSY6KvobXet8dZBD0nhPKek8LcflkDTMnNF4YtIWaHjz6cy1ufvMM2Xbox4oA9iEQj5OdbtCppw5rKRpLJpC6KF8+2desyGpNJqmtSFBXHiMTCeHo9OxCiVgl0i5A+/8xUrrjhKTrmt+W044Zwwgl749hp8vIKNEpHABO2ncnGTqWp0i8Z/9wDnWvzlvneRFKaqYG63zltsn4g5Gttu8iyXKZBu7YlWKqSYftsxf779eeqv7yNFcrH88QzltRWTgCywmhYZGxHG+DCnCBlFsl0FR9+WMH1t0zm/cVr2aZ1B/564akcdmjED4d4gquRm+l3U5xJ8dy1FssioWWtEH851yb9l+ZrZyl7H317Y/1Nld/1lhVEcSksh3RjStcuP/LoBCQHfPghB9CzRwHKkD5Drx69mb+0kpqaGm0Lymk6d8jTscdUUvLSAWLxmM6WiBkjbXUJMW3GPG6+43Fd5HTgkP344/n7YJjV2hGTEgPZpJTAnzlyeW9ByUqRldjA6xrsN3sL/L/5BVF3UjRJNqDV5ImURIdwRYuQCW1GIq8d495YyPSZ/+TlT+fSKr8tR4wcput1DUGw6GNtP02lUgQDEtaButowH32wmseeX8KkKdMZ3KMNL982gG36tqdrt6AOAJuBaJbDRYLLwk+dIZBtk4SB/JvkOw0GYjeaKDOqWVHX3afcQ5V7z91PbVhK0lf/oJWO45QTDIT55JMq3p5SrsGtnTuVsGLVWtq2LSIvz2DPPXdl/D9fZfUqh06d5NppenQLUVBQCEa+z3FIVBMtCdusVNhN+XIZp5z1FMsbgpx/+L6ce+7OJPLrdemn5wW1SRAI1pEREk6ht9PPUINmdlVeNpSUbea6fm2BHzaDIMrdEg9AsipZQ79Jx6WWwgyaRGOVHHHoLjz81EQ+mf4R+RHFlVdewo47d9R+geOlZYLCEySLOCV2jMaqKDNmKu566FNe+ORNhvdRPHbzYAYP3oni0iIcR26AIhSOZwO54vxAUGcXfPi9NMWPKPli7jexwG+hbnpO2rKN/i/Aq8ie5J4lzegQ1JrWJzi3zHY0VsOll9yJnargLxfsjZOuZuFXJu3a1mptt+PANsjcveKbJXjbdach6dG+jUFB3MHOZPAI0VA5l9rydlg9tqa+Bm649h2qauDA7QxuumMo6XQa5RZiBqT90lvZElk+xVzbY37gKxs6y/Zki37bDIL4/f3Vi9GII5xNORUXF3PmmWey/fYHU15RSccOBey9T1/fyNaBbz8ALmeT4V2waBUP3fca4yd9Ra3RicuPvYSDhgfYbjvxdGVlTikcCiIAhIZk8y1W+H29kXXttEMvF5VpW7wwz2Hp0mrmf71QKo4ZusdQXnzxDcrKuuC5RZqOLi+Rp4Gv33yzVB+Wnxck0wBdu3ShuEhMEoMhQ4ZgJ1exenUlM6ZV8Mm0yazJGJx77mVk0gKYDWbNi+9r2f/ud80viGLbrfM8c2aVeNE+5ZmEZ6T8VwKtPXsW0r17AmVmNF+LcP8JWkUgUgEzpCvmFs2vY9wbX/H82IXYTikpNY9ScwqHjDiAQTu21vW+Em8TAIAVlAIkj4Sg4XPKodnvTe7EHsqTQLh4zeJZB3jzzRkEggmG9utM/75t+et1M+jSuT+m2VlP1a3bZuhWmMdbk8o58SSXvJCFEVa0bRPSGkwwjL17xkg3dOSVFz/lr7e8qJfBfeCakxg0uC2GGdbOXtqxCWXt3mbv3i90wmYP3/j9yNZCyD0Tn8OTtFtYw5/kpgVDNmZAsvoZAiET5QV0jldijZIrdTMmyxYZjHkuwCHHPs6f/3YbPdrO4+XH9+Slxy+kJpnkwYc/Z225z2oqawZLnlUsAmEryGa4NtOQinMj5JtCfCnXlCxSUAOC3v1wPmtsk+0HlFJRqUg2ZPh6qeAa/aKoNm1K6du9NV/OnE8qaeK5aUKBNPn59QSDHpbXSEDBOxPXcOqlD1BdX8OB+2zHqafvSDia1BV4tY0yHUvm5Ne1Nb9G1NpQNOB6SJZISDAgt88vFpc1g2UTwRPSckmxSZlmdaWQllcz9pX3+XL6YlaUL2XkAUM55uiL6NwRQgGHDh3zueCs07jk+tvo37eI8/84VHO+SJBc+KKFBDMtWYisidrct0ueLbH9JYdrmWKDmqQbLV5/9Ss+mvYFBZEYRx21P/GYgaMsVq5eo9OawtZgWlHatSmi7uMa0ikpppcxMdm6V3dMU+KBCT56v5Ib/36/JkYauHVHrrnmZE28LnTGogQjER+Q29z9+qXP1/yC6N8m3yOQO5al7MhoNIsInIRhxIuVmKIEuQXgaTJ9+hIefexD7hz9FoRKGdKrD0+PupXttjVJSgkljUR1bS+cevJefPTJNB5+8lkOOngrOnRso7VFKimoF0PzuGQjus0/vjqUY+gHR4dXbEF2O/zp0uuwvQTXXXAFW/UqY9WqJFYgjONKFV89eYkI4XCA/n078MBTVdTUpukkS184sOuuO+oc+deL1nLm+XezeM1ajh5xJHfcvB95xWLS2Br2JUMrz7D5LQeq+Tv585+x2admETAJEitXwihBzTggiXuJi8mAul6KUEjoNeQLFyuQ5K1xHn+9tYE7X5hO1KumlTubTO2rJBKrdBRIPMp/3vUsM6ZW4roNRGI2p592MtOXKUY/vYRMyiGdXkk0UqOvsfnsQ1+La39b4neqHuU28tJLC1iRDhINhamtmaEdGSkXDQSi1De4NNTbBIP+6qNt2yXwpI6lTtZYgVTa16oCWhj3ajnlNWm6tyrjrNMHkVfSgEcaT1BHloAqhIWp8btxz59fbpr9is0uiDknUmJgIQHiSDG4IwvWpPUUahohnIynV1qaOsXh9DOe5rwrr2bN6he4/U+HM/65fzJ0t2HMnFfBny++hzWrBdENs2Z/xb77H87rr72N65n06xNj+E47c+1tN3LzrfcTCpSQccK6LDRj5xyKZh8v7RylUg26X65r8M03Ho+PfobWsQSOk+Se++/gg/cmU5hvEg4GsYWBIRDTQW3JaRcURIjF27BmTTWZjEc86qOS3pm0hHtGvYqTWct115zKNn0TOmcs15D5IPe//ykXSG/+/v1SZ2z2qVmnzAyxffxNwhwCRnBdgeiHqalxmTO7ildfncB9z0yjIVDKLWcfx+mnb60FToRuhwEXMOyQej6bvohnnh7Huecfxu3/uIljplSy806FrFheyR8vuIw5c0N0at2Z2+55mCOPPpSte3fNAmVFy8it2xybgDck2A6ppMOnn3zFnCVfU1ZQwpDtBzN+4pMsW7YGOwOxRJSF36yhodHLhntc2rQppDGTpKJCCDaFfjjJ/Hkr+d0f/kyocEfuuOEa9t67uwbp1tRV6gxMDg4nCB/ZvpMJ2hzd/JnP2ewaUZ5gP/GQROlak0YymXqSjRHeGv8V5//pKQ498S6efL2Cw/cdyPtPHsgZp/fWXDGmlcYwUwQTHmedOpzGZDX3Pzie2TNmEIwsYate83nyyVfY/5C/8/70PKxIa4buuj1PPXIXW23VCdGEtmDsdWJv84yk7SYJ6pJORxcrjX9rJo4Vom/PMIcdOpQ6Tx42HzHTtUtnlqxaw5q1yzVmUhbeEVJOgnmUr16l7WM3E+bWW8cTjXdir21LOOz3rYgkMtQnG0nkFeuSAcFnaldPvG/JluQyOpuni7/IWZtfI2rP2NXJf9NKsHaNYsUqGP38Qm557EFKYwZXnHUIe+/djd69uxAMiRe4BijT9cRWJEggWM5hI3sxZ/bh3P/0R/zx/MfYcfCu3PTA/RAspFUszAG79+Cyy8+ka7cyQhGBgfnLRtiykI54tOt0cvOOqyzOI5vED6dON3l/8kwKIwlOOH5PEgkBLXSgujqtMyDbbTeA1aPeoKLiK5TqSTodIxRqgPqFmIbUqRjcfuc0Jn7+FRnH5cordyURM0k7go1MaCGUGUJgG4YnQXs/U6S71uwqpHnHaVPP1uyCaNsuobCpgZrffFPF6Kc+4t0P5jBu2jfs1GtHbrz8D2w7wKCo1J++ZZUjcWQk3BiJSGYkC0NUKf584bG8/WE5c+ZP5P0pkynO74hrJdhjpx24585TSBT4XqQmuszOxDkbdXMtIadDToaL1Nd/8cUXrK5eQ5+Ofek/oD/19SWkvDSVlZVEImHKykrBSVFfX6+deEkqCcn6iD1G0Kp1a54e/SJ3P/q6zrbceumN9OkTw1Z1BKy4T4Eidydn42zqnf0f2z+gdD5SxMBnpNLt1+SN6x85w84yDGg0iKM9ORkfz5VwTARTVJAUnZvCBx1g9swV/OfFRYydtIhpS2eyY9dtGPXX3Tno4F4UFGY0EgUjopFY4tBglOlwj5RBGsLv5+YRiFganXXKyYM478optG7bm6J4ESMPNjjn/IPJK7FxVdCPDkmZgKbiqEM4YAzlp/w2+l40tSd1/NPXejpfrsNP2TMJENYtFhXFgjnz+NtdL1EWSXDhmQPp1qOMufNdvEwVlQ0C+gDxkONBh4ULJfySJBq1CYUjjHrwKKZPbeSos16ASAdG7tGaY48P6MKrAEX6YhpjrYVQBkigOE0lsunnje7lFr2jTp37mD893/j/faufRsAg46YRyJRphDFU3Pf4YiauUw9uGKHvrVgaZMJHihvufI5ZC95hr4E9mfjoKQwc1JVYVMABLrYjCGufBkND5rQmkwvKBx8BLTB/qUu2LIejjtydz7/4gtEvTqVPt+059g9HU1goiJwGTEPoOmR8BZVjoxBIlS5w+X8MehY5JGf4LwGVJsqqTyY11YqJE5brIvd+vXtz5HH7YgQc8vM9upTFqa1ZQzrt0KoswE59O1BcJNkYQfZE8dwGwsFSbr7zbp1/pvodrrxsDPF4fB2E4f/R+P/ZQ3W+w4+L/XAfXE006a+wLmv/SnVcJAgNNWCnFVOnrebD96Yy4b3PmLG0nD13GsC1l93GbkM6UlKiEK0rZaBCJhkMSFG84ORky2Vf5LMvhPJJFKw4PAFRdMrj+uv+xPJv/sE7X77NsSd8wpgxN1FcZmmiSpFff1b2Nbp8bio/+jIb/O9bT15TLSjH5h4WBem0p8naH3lqAoXRCK5bR0V5FWVt8yjID7D7roNZtbpe11PnxQP07duBr75apB8YeWgaaoOcfd59zJwzi769OnLf7S9R1ipGfX2aeF4WtrXB9v76dlg//+pYVS5e5Y+9jL++B6boGZNUykTqfcVgN1SaaDDCeefew7l/uou/P/QCtXUR/nXzVTx6/1kcfFAPSsrEEUkRMBW2I6hqIR+SWJ9fhK5rPvRUmBME/4q6TMBQpNOybKzS5JfXXHk6hUGTmQtX8vSzEwiHhSVVIGJyU+R4/xz6odrU+5TrqD6X/CfDIsDSdVKeHQiDUMDk8cdeZMHaJAXxMIMH9WfmzDko19Nk7XsO3ZWKqlpdjCUaf8TwXUinXOrqBCUOTzz1AWPfn0HHNu1568Wr6dItQSweJJHwyZ02tem/lv21IDa9D/5nXfmg+bGEI0sKmZRTScAoJxxK46XzWDqngIN/N5q3v0yytHwJrWJJbv7bQRx2uIQfbDBTOp3nuiGqa4RtIYwQlAqXpM/f4q+WqVXFutICf1iFQT+Tzmh7z7YlwZ9kq95xDhnei4ZwB54bu4DqtYqQJVOyqM8QyhC2fVcHjmUi3LRNhFijM/zDRKXqlzyJuZoVwaZZzJmV5r4HxmpNeNQR3ejcLZ9Fi6U2RGw8k44diimviZJKirZXFBUYlK9eSNXaciorFKNfXEBpIp/h+7ZHKlCTqTSOJwQATWeHTWv9r2Fv32vWykQACNlVKLXhJQgTod6Q9RekcC5OwIMvP63mkYdf5P3P59LQkGTfHftw2mln06V7Ka1a+5AoKWTSMC7bQQrVw2GpuXXW1XWYphQ7CYRdYhO+JstpNFE9QssmRr1C8tEhgoIzDMBFF5/EslWvMnHyJzz08OecccY2RBOOBk34wUu5hqTSmij6jb5LuXasP0CWuXVdqQMRB0hKTuHZZ96nugF6tC7ksMP24MOP5rB0mc/UgKsoKAhTnUqTSlejKGSHQQO5+uorMCjjjHPvZt6S+YwY0p1zzj6exoYkRYVhHMfVgI0czHV9C347n/SKHdJd0SHCOCWzkZ2WpbsExGqRbhQmLMWa1RY33fgKBx1xBWPf/YquHfpx7203c9+/Tma7waUUt0pihuxsNZtoFFOvQbLOYNNB2QyWZkiQp9/QGER/GpSrrxcEyxJqEhFSKX6XNU1kWk/RqWuC2286ji6tO/Hnf9zFhx/O1RVsInZyBkF1+0/Npt7ArAZd91D4xwvINiRkSQY0JmHJ1yu587EXqPWC7D90Jzp1E6phQQwtoq62Vmv67t3a06V1N5LJKh80Cwzcrh//vPcFPpu1msH9t+aWm06nTWvh1g5rjZvVA5va6F/V/llwli8Ers7RZnOjroH8vXJFPWNGv83Dz3xKXSpNWautOe2Y/hx+ZH9atavCUzaOSmAF83A8g5DOpqR1bEymMi0i+vSi4SJZDShfyFQoAisCJ2TqOUBtVii0wyCOkaxBAsFQTAeJO3aHU/4wmKtvW8ztd73Hjjv01vXBZlBqYYKilLT22jSdKNeUlx/G8j/LgykPgDB1GURDFk888Q4F+Z1J2imSqTV4Xj2J/AJe/ehT5s7bhR0GDdLLWWzbo4BYLKBBunU1aZ57di7/GTdFF3Fd+qehdOjg4UjKMxjzWc5MD09MUv82/KoEbGM740/NWiCEIUDsIP9+CIR93Pg5/OOOf7NgjUEgPZeTjt+Xiy49hnAsQSScTyotAiI1IehSRsEUyjKwsvmzowT3JCYnI5wb5dxNl6+yQqd/yzoGud30WUSqPAzT0oBXnwV/LUce1Y/PPpvO6x/M5Y47JnLZZQcRsXwmCXFW1mUgNnYU5Jq5pugB8MVYNKK8LDPE10sU/3l1Ml5tFe0KiliyREoSDCLxOJ5dz4wZi9hh4A5EI3G6dhKNX4qTDnHttWN4ZOyXGJkKnn/0fHbfoyfKEPNB7FtJf8YwZPkzJ0nIWl9Xs7FN/7Xs913F4cHaCpt773+RK66+ksXfLKZTqw48++QzXPe3i4lGY0QjUerrBc4l07ega2xtXyqJu2ymTWKLmlJDVjuOx7nmyvP1NR9/6gmWLV+tryp1vbIJtV1zbPJgZqSoyYPps+aztraKHp26s33f7amtrcXOCLxLUoqKhob67ApRsgJAmbZrp0ydy6OjH6cyWc3eO+/B0D18tlh57sT2lgdGZ5JMAQ7/dkM3cq+yNqKvpSrKaxg/7iNOOeUKbrp9FIFIN845+U+8/MKJ7LBrkVZgZrgQWxmE4xae4ei6oSBBIlZUo6MNK4UhhJVaw4iGlfyd2HkCmV6ndtYRFvmsWtkpcZ2GlKaJUIvWEHtVguANWJZ4p0XaDm3drpZz/zCcKifKnXe/jmP7mtD1HF1u8NMEUbTy+odJYpihUISaujS33/Fvar0w55yyC8ce3ZeK6iQNjRbt25cSVNUs/bocV2L2Cg46aFtqauDPV74BhbuwW/cyrrlyuO6+JUvbKgvXDWK7cUKhCvBS2M6vD9q1SffAc5TyMkpNnbxKbdPnWFXWej+VVzBYHXHY+eqTD6Yp5Srled4W8HJVJl2vXJVWSbtB2Uqp2XNXqlDp0aqs/Ylq0QxPuel65Xm28pS02VW6b9I/eel+ZJTnpZTnOf7f8p28bKVsR6m0l1Suu1opr1G/Gu1aJds7r81XhQXDVLeOf1CzZi9Un38+QxV2OlPNnZNWyTql9tzjKLVNn+PViqWe8lJKrV3hqsMPfU4VtjlGDRlyspo0YYlybaXSKUdl7KTyVFp5nrRFxlXamnttCeO8edqgB/JH/jMllTZ1+mJOOvU0WreNc9D+Q3nykfu4995b2WFwfx3P2yTJ3ow7y6I6sryXeLFCwN6pYyv+ef0VZOxGLr7iX8z7qlbnr4WUab1N2rRBovGaaOWmP2kNLFpJFlf087vi/DQ2wDPPjtPF/yP2H0LnTm3p0qU9vTq2JZlcrkNMw/c/lPmL57B8+TdUVjVyyRUP8u7k8ew2sC+jHrqVobt3Jp2R5W7FNvRnHx0tEOXb9PVf7flt/SGmF1v17MSoh++hXdtOFOQbhMLCauWPUUjXDK+frn654TEIhcJ4RgZLge0JgMDiiMO34aWXd+DVDyYSvaGGu/91EcUlQiknjk62teuanxOC3A/Z37Py6VN2CCOt/7tpGMyYvYxPJ09lRc1Kdti+F/F4CMvy6Nq5DNOqIhrtzBEjf88Nt9zNnNkLeenFZ3jt3VXkhUxuuv4MevQo1suWRSRSI0EAW0hGReBzQadfbkS3pCubZsAjnu+y7cAOFBbbhOPZCkldDJ97XLeAJq9rihj1ipCucHf1Aowj9h9AxqlnwseLmf9VCk/Xw2Ttvf+SPZEE0Xa537KxnnXyKMXycoB/sVRSFuVxWdugKC3oyPQZU/Sx4kl3aNNAfa3kzA3ad0wx7YvXqawq4YZHpmute9N1v6dP/2LtwMg6Po4njpSkRyWnLq9vPQxbwBD/kk0wxeNLp5KaWUpAqrKSiF53ROg+lEPGliDxL7+JIywxQiH81JV/ApPQYZ0Mhx22K/vttBv1tsMDDz1HTZVQguRutAhV1oteJ8zSn9wf8i6iKSIlmSH5Q5wtm9UrKrnu1tuQFW7j0TDlFUkcWfkgFOXww/ejVavWuhw2Y5vMn7eaUU+PoSS/LZefcwQjR+6uM1OGaePo7IwwhglR0ncDFb/86P7yLTAlhCBso44rHNQS85P1g31mf2Gv14Tmv3w7tYCIIEoeWjJAwtovKUCpX27V2uLakDqi6gAADQFJREFUv1xCp7KujHltAm++8fG6Mlbd9HWesJaybG+aCKL+2o9A+iakPw4T3vqUZRV1DOy3AyMPO4SGjEkm5ZfEDhrUm+5dW5FJe7w69k2OPP485q5YxS2X3MwZp++EFRZtm9ILi0tgXEJcksrTGnGdzdBkYHPPTZOvfksfTcEXKsKEw7L+XCC7hIToCx3l0jd7SxgQWSneCriaIUuWlw1aEUzEFhSaJpttB1pcc8lROqA86tEvWLNGkNGeDkg7TkYH3P+rH5LJ0WALQytPqTqUeVTWgcmkDRrqgrz+2iyipsuhhwxit6FdSaWlVNZfZV7HTE0Y9/oCzr36PTKx/pz6u7045g8ZAuFqDWuT9KQ4J4ImknVdAoFwdsUE0boiqK4f8JeQjiai/68W/qb+0HFEXxdYWZxg0BdIXfUR8JeT2CKGRPCG/tRpyjrHYmfJdO1GNM1dOJzUdS79e3TinS8/49VXppKImliGpCwtDdH3J2HpTDZuKdOzMvSULxAMz1aaFkUwk3O/Mnl/ynzIVDF0r86075IkEa8mmmjE8GoIBgNM+czjzvs+oNaGzokaLvzT7kRjCkNnSISnUOKn4vxkbcKcEpbr6rSmZGBybfltq8T/eYNFIGXCGNGYbtT82TvusCNFsXwmvP3BusdHCvRl+6Fbrb+X2LsrU6cpxF68/PLLGpo1YOt+FJcU06NHT44+6mh9nvqGelaurOJf9z3AZ/O/pDRWwM1/u5Hu3cqw7XSWkHTd5Vs+bMQI6EqIdQ+qBqn6T6hGJGpK3h+6fRtx9mbcRbfHkKnO1yIaqSYuhxKPNKh5Y2Jxjz8cswNFEYfPpi7jzYlLNRhVE6mLdK3rynrdKF+K/+B4wjrha8j3PqjgX6OeJW65XHD+SPILlV5u9oADt8VzYlhWEffe8wZvTF7LgI4deOXxozng4Jieuk2jCM/1WW/9C667aJPRyGlB6YBodmEwzab9m+z1W/ooc5y2V/T6JCoD+uXDtNY5llvIiGjxEdoNvSJx00aFNB1cOp2kZ88Czj3jIBZXN/DIo89SUeF7qhJy0bFFOUw7LyIg64VEHDUr6JHJpHngoecJmga92sY44KB+NCSFKCpBIGhSu9bgpTGrePjlhdiVn3L5hYPZbmB3UDEiESlfSGcph32/vGkr/c/+ePsB7fWhHG2jfnfn38w3ZlYOs16mn1GQ+hFZOssPaTTVHr/cuIjImFoNShwxC6jVC0GKFvOp4oKhCGYwyOG/35eBHVrz2psf8O9/vkpjvehTidDLAyZa1MTLvQTdo/0Wcc5MPp+8nNcmvE0sXER5lWL1qmXIKmpSPlq+MsWFlz7GOdf8jfxAHbfdcgkHHrwbyAKWkneX7HhGVspSKCljWPck5+ac7FhKaEmHl6RXOUWwZYzzL3WHNbe5rxvEXA9kX0JAmS3ZkA9bwCbGrI9uFK5BEcT1Ck0o7/w/LQzLoHX7CPsN2Z68eDv+8dDzfPbRTMyAgWMLoad0RlJtuZc4rw6m1DAYFi+8NJ1AIK4XjqzOmLikNaWeLEf2yANvMH7yN1S5EQ4eMYjjjh+C7dVrbKF4wOIhB4NRrXFlyYl1OjHX1tx7riZGWp377n/eWv//CcmvtvuHjezP6sZKShIlTJq4EDuVJBiWKIDvqAo7q7y0drQERxnEaYyycHEFZfkBRh6yF316bEX5yhqUG2DhgjU8M6GayjUzKLDnctwfdtVKTaiEg0Ephcil7eQCv23t9lNE8lcriP237ch9f7maZLqWsW9NYfasSj0zy5rKvlYUVeR3XyZTsSFnzljNlFmLqK5dwsGH7sLxx+1EIt6FaZ8v5dRTr2XaN1M4fN9BTBr3JFtv3ZZMplEXTKUE0aCnWhHA3EvO37Jt7AgYAkXa2J3/l/Yz3Ebchjijnviac2+6lb36mDzz7F8pKJIi9xjKTPp6y4hSn04TM8Nc+sf7+ddr87no2G5cdeXZWnU6NQYHHfln0pkEpZ178tITf9CYBQmjBwJ+wNwHS4hQZ4VQDG/xhlu2dSPgo47W/fmdD79ajShLxNqBFEce3Ybh2w/ivelr+fC95aTFA7YUppIFFqM6HJQXCTNz1jKefPltWgVdhg/fing8w4oVK/nd8ffz5dd1FHfoxu1/3xfMJGm7GqWSeJ542SKMOe0nXk82z60dku+Md8sXPzACv1pBNMwIgVCS/OIMRxzWFdfK47HHP8dulCUHMnoRRoHA6fIDF14dO5NaYgzePsyQgfuQrgnx12um89GcT9lpQB4vjjmeDm3yCQQiRCIFBAIxDENSo5F1S3b4BWDiDQl5fYup+AMy971f/2oFUSI9Ao4QYGXffr1on9+aOfPmsGyFLLLokYiJEGb3UfDJ558SCgQpKijWmbnXX3+L8R9PRDCJZ5x2CnX1GfRi5N87jC1f/n9H4FcriI6oJCMP2w3Rp2+Ykw7fmeWVVdx99+fUVZs4XgOBQFJ7zQvn1PPN17U0uC577bkXxx15L2dcOJqgFeWWK45l72HdiUT88JHGK8pU/H02oEzHGv2aBYLnZuz/7136DRz/qxVEWVlXyGMFwGAFQpx6yq4M6Nqe0a8/w6S35pFJJ3X5rGRb3nhzCotXLWffrbfnuadn8NpHn2mkzAkHFnPeWXsRMwNENK2JHxDXcqFTjRLIzpUliNQJwEGIw6VMb32c8zcgR//vLv5qBdF1bb/cQfMmRmjdIZ+jj9ifmOlwx71P0VAvCwNZrFhZwWOjn6UgkmDGV9OYMmMynUqL+OOpR3DRpSfiZhoJCPTLg7QmVhcBEwPQ1kyuuWxNzmH2I9Tyu2Aa5b1l25gR+NUKonivUiosM2UmJVoKjjxyZ4rjYeYsXs748e8CQRbMn8PnX80kaAYpjhZopPo/77yZP/95b1q1CWMFTV2eGtLVsP55ROMJnbAvaE2FTbRitgxh3e8bcxta9vnVCmLEVJgSSfFAsm4E0oSKklx21eFk0ms57+LRfPmhR/kCg0R+F2pch3nVKzlwxDb03yGFijgoQxbxjuCaAUQZhnWOUWKFwgYkxJp52ao/kb//a+9qXqKK4uh5782MOh+m2UItVCQSpUAMIkRCJMiSIKSN/4GuzJ0RRAglRUEFtdN1JS2KKJAI0t0woVILqVAsSLJQdErHmfcR5/eeH61mRnTzvAMzbwbuuzBnztx7f1/nt5HMQB8iWUuZuf2dUZPP38u3RGQXeNoU8vQ8Kez8dLbtNM63tiBk6BgYvIc3ryfxN5NGUHdw7lQD+q50IRoLi7iTGy0hnJYo0kpNSz7oqrE5I+BjIhrCI/Er08il99DMoLwigt6eLuiWg9kvc3gfn0JVWQ2WV5fQ092J+oYK6QZPPW+xOCQvwe3PrM58OfMq74G+JSLFOzczW4SImmRyswXb8cYqXL7YjGRyFrWV5WhuqsDzoX60t9cgtf5TbttsfC6GCWnMSXguVI+9QMC3sWbuyZLsS4FQ2O55zwlI0mpmPQPLdPAhMYG6YydQUspifbbxJdHCon8diRTC0SgQzwIt1yHI5FmpldmLX8Lnc2aLNe8rIpqWgYChuXYFHTDs8SIGCOPGlhRnBYLFQgn2YtYDioi79f/IRkQfm3VyKvRwZHE7hTOlYlTKIawMa44ZYSnEyjJ7oERgMDnWzblxu6lKdMazdGR7Z+Iw51WP3UbAt2dEWzdhshOqVghTKxLXcsa0xSfo2BkUBIsRQhRvX31Dy5k+XO1/guVFtvOlXDGr/tYAaSREa4XZ15ST22341XwbCPh2a7YZDZFvyTWMmjf8YMOQXEEbCz9SGHn2Dg8ejaC6phJ/kinomonhoWs4UqUhFi2G49BXyAJ81p8wfbZAPIgb4Klr7ghk25p9uyLS9SJdC7wsbM8Uhmkz9KdhbDyBwTv3UV/XhOHHt3H31nV8/b6E0dExxKIx0f3Z8iMScDqscwdejcwPAd+eEXVTHIDQNAe2TkEprpBc3XQkUzbmF39j/tccwiVpVB9lwK4MthZGIrEgxVUimET6MYKnGXBESk7tzfnRK/fRviWiK+nBUBytDFYl8uogqBvQLAdWmtkQIZQUH5JS0Xh8BhnHxFpqBczuNvSgkFAWQb4oDubOqh2M9C8RGWiWvZQUJBF1UF+bAu0HwgYOl1fjYGklPn76jO7ep4gnprCeTqHpZCN0FGB1zZZm5v8JzEq+oWLkDniW9RbfGituOI5KClsYSBteWd10LC2m8eLlOG4OPsTMUggFwRAutbZh4EYnamojCFJ+RBQltiZgooObaLg1p3qXGwLZjBUfE5HbqWddkEt8S1UHja3e6MahUhcwMTWH6elJsNtVR8cFRCI6ksllFIXDMCRMuI2IliY9UXKDXo3ajoAiItHYRkR2NKV6mGVSho/Cn25avwzRgNT6GgqpMSKGiidt4iHqKCJ6SOR/yUpEdhzIf1p1h0JgdxH4B+ywZubungLMAAAAAElFTkSuQmCC"></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{CD}}}\limits^ \to = \left( \begin{gathered} - 6 \hfill \\ - 8 \hfill \\ \,5 \hfill \\ \end{gathered} \right)"> <mover> <mrow> <mrow> <mtext>CD</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mo>−</mo> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>8</mn> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>5</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{DC}}}\limits^ \to = \left( \begin{gathered} \,6 \hfill \\ \,8 \hfill \\ - 5 \hfill \\ \end{gathered} \right)"> <mover> <mrow> <mrow> <mtext>DC</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>8</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>5</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </math></span> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p>correct magnitudes (seen anywhere) <em><strong>(A1)(A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\mathop {{\text{OB}}}\limits^ \to } \right| = \sqrt {{{\left( 2 \right)}^2} + {{\left( { - 4} \right)}^2} + {{\left( { - 4} \right)}^2}} = \left( {\sqrt {36} } \right)"> <mrow> <mo>|</mo> <mrow> <mover> <mrow> <mrow> <mtext>OB</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>4</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>4</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <msqrt> <mn>36</mn> </msqrt> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\mathop {{\text{CD}}}\limits^ \to } \right| = \sqrt {{{\left( { - 6} \right)}^2} + {{\left( { - 8} \right)}^2} + {{\left( 5 \right)}^2}} = \left( {\sqrt {125} } \right)"> <mrow> <mo>|</mo> <mrow> <mover> <mrow> <mrow> <mtext>CD</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>6</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>8</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <msqrt> <mn>125</mn> </msqrt> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>correct substitution into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}bh"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mi>b</mi> <mi>h</mi> </math></span> <em><strong>A1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2} \times 6 \times \sqrt {125} "> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>×</mo> <mn>6</mn> <mo>×</mo> <msqrt> <mn>125</mn> </msqrt> </math></span> </p>
<p>area <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 3\sqrt {125} ,\,\,15\sqrt 5 "> <mo>=</mo> <mn>3</mn> <msqrt> <mn>125</mn> </msqrt> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>15</mn> <msqrt> <mn>5</mn> </msqrt> </math></span> <em><strong>A1 N3</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong> (subtracting triangles)</p>
<p>recognizing that OB is altitude of either ΔOBD or ΔOBC(seen anywhere) <em><strong>M1</strong></em></p>
<p>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2} \times \left| {\mathop {{\text{OB}}}\limits^ \to } \right| \times \left| {\mathop {{\text{BD}}}\limits^ \to } \right|,\,\,{\text{OB}} \bot {\text{BC}},"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>×</mo> <mrow> <mo>|</mo> <mrow> <mover> <mrow> <mrow> <mtext>OB</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </mrow> <mo>|</mo> </mrow> <mo>×</mo> <mrow> <mo>|</mo> <mrow> <mover> <mrow> <mrow> <mtext>BD</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </mrow> <mo>|</mo> </mrow> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mtext>OB</mtext> </mrow> <mi mathvariant="normal">⊥</mi> <mrow> <mtext>BC</mtext> </mrow> <mo>,</mo> </math></span> sketch of triangle showing right angle at B</p>
<p><img src="data:image/png;base64,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"></p>
<p>one correct vector <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{BD}}}\limits^ \to "> <mover> <mrow> <mrow> <mtext>BD</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{DB}}}\limits^ \to "> <mover> <mrow> <mrow> <mtext>DB</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{BC}}}\limits^ \to "> <mover> <mrow> <mrow> <mtext>BC</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{CB}}}\limits^ \to "> <mover> <mrow> <mrow> <mtext>CB</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </math></span> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{BD}}}\limits^ \to = \left( \begin{gathered} \,6 \hfill \\ \,8 \hfill \\ - 5 \hfill \\ \end{gathered} \right)"> <mover> <mrow> <mrow> <mtext>BD</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>8</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>5</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{CB}}}\limits^ \to = \left( \begin{gathered} - 12 \hfill \\ - 16 \hfill \\ \,10 \hfill \\ \end{gathered} \right)"> <mover> <mrow> <mrow> <mtext>CB</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"> <mtr> <mtd> <mo>−</mo> <mn>12</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>16</mn> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mn>10</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\mathop {{\text{OB}}}\limits^ \to } \right| = \sqrt {{{\left( 2 \right)}^2} + {{\left( { - 4} \right)}^2} + {{\left( { - 4} \right)}^2}} = \left( {\sqrt {36} } \right)"> <mrow> <mo>|</mo> <mrow> <mover> <mrow> <mrow> <mtext>OB</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>4</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>4</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <msqrt> <mn>36</mn> </msqrt> </mrow> <mo>)</mo> </mrow> </math></span> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p>one correct magnitude of a base (seen anywhere)<em><strong> (A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\mathop {{\text{BD}}}\limits^ \to } \right| = \sqrt {{{\left( 6 \right)}^2} + {{\left( 8 \right)}^2} + {{\left( 5 \right)}^2}} = \left( {\sqrt {125} } \right),\,\,\left| {\mathop {{\text{BC}}}\limits^ \to } \right| = \sqrt {144 + 256 + 100} = \left( {\sqrt {500} } \right)"> <mrow> <mo>|</mo> <mrow> <mover> <mrow> <mrow> <mtext>BD</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <msqrt> <mn>125</mn> </msqrt> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>|</mo> <mrow> <mover> <mrow> <mrow> <mtext>BC</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <msqrt> <mn>144</mn> <mo>+</mo> <mn>256</mn> <mo>+</mo> <mn>100</mn> </msqrt> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <msqrt> <mn>500</mn> </msqrt> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>correct working <strong><em>A1</em></strong></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2} \times 6 \times \sqrt {500} - \frac{1}{2} \times 6 \times 5\sqrt 5 ,\,\,\frac{1}{2} \times 6 \times \sqrt {500} \times {\text{sin}}90 - \frac{1}{2} \times 6 \times 5\sqrt 5 \times {\text{sin}}90"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>×</mo> <mn>6</mn> <mo>×</mo> <msqrt> <mn>500</mn> </msqrt> <mo>−</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>×</mo> <mn>6</mn> <mo>×</mo> <mn>5</mn> <msqrt> <mn>5</mn> </msqrt> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>×</mo> <mn>6</mn> <mo>×</mo> <msqrt> <mn>500</mn> </msqrt> <mo>×</mo> <mrow> <mtext>sin</mtext> </mrow> <mn>90</mn> <mo>−</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>×</mo> <mn>6</mn> <mo>×</mo> <mn>5</mn> <msqrt> <mn>5</mn> </msqrt> <mo>×</mo> <mrow> <mtext>sin</mtext> </mrow> <mn>90</mn> </math></span></p>
<p>area <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 3\sqrt {125} ,\,\,15\sqrt 5 "> <mo>=</mo> <mn>3</mn> <msqrt> <mn>125</mn> </msqrt> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>15</mn> <msqrt> <mn>5</mn> </msqrt> </math></span> <em><strong>A1 N3</strong></em></p>
<p> </p>
<p><strong>METHOD 3</strong> (using <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math></span><em>ab</em> sin <em>C</em> with ΔOCD)</p>
<p>two correct side lengths (seen anywhere) <em><strong>(A1)(A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\mathop {{\text{OD}}}\limits^ \to } \right| = \sqrt {{{\left( 8 \right)}^2} + {{\left( 4 \right)}^2} + {{\left( { - 9} \right)}^2}} = \left( {\sqrt {161} } \right),\,\,\left| {\mathop {{\text{CD}}}\limits^ \to } \right| = \sqrt {{{\left( { - 6} \right)}^2} + {{\left( { - 8} \right)}^2} + {{\left( 5 \right)}^2}} = \left( {\sqrt {125} } \right),\,"> <mrow> <mo>|</mo> <mrow> <mover> <mrow> <mrow> <mtext>OD</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>9</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <msqrt> <mn>161</mn> </msqrt> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>|</mo> <mrow> <mover> <mrow> <mrow> <mtext>CD</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>6</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>8</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <msqrt> <mn>125</mn> </msqrt> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mspace width="thinmathspace"></mspace> </math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\mathop {{\text{OC}}}\limits^ \to } \right| = \sqrt {{{\left( {14} \right)}^2} + {{\left( {12} \right)}^2} + {{\left( { - 14} \right)}^2}} = \left( {\sqrt {536} } \right)"> <mrow> <mo>|</mo> <mrow> <mover> <mrow> <mrow> <mtext>OC</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> </mover> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mn>14</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mn>12</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>14</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <msqrt> <mn>536</mn> </msqrt> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>attempt to find cosine ratio (seen anywhere) <em><strong>M1</strong></em><br><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{536 - 286}}{{ - 2\sqrt {161} \sqrt {125} }},\,\,\frac{{{\text{OD}} \bullet {\text{DC}}}}{{\left| {OD} \right|\left| {DC} \right|}}"> <mfrac> <mrow> <mn>536</mn> <mo>−</mo> <mn>286</mn> </mrow> <mrow> <mo>−</mo> <mn>2</mn> <msqrt> <mn>161</mn> </msqrt> <msqrt> <mn>125</mn> </msqrt> </mrow> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mfrac> <mrow> <mrow> <mtext>OD</mtext> </mrow> <mo>∙</mo> <mrow> <mtext>DC</mtext> </mrow> </mrow> <mrow> <mrow> <mo>|</mo> <mrow> <mi>O</mi> <mi>D</mi> </mrow> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <mrow> <mi>D</mi> <mi>C</mi> </mrow> <mo>|</mo> </mrow> </mrow> </mfrac> </math></span></p>
<p>correct working for sine ratio <em><strong>A1</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{{\left( {125} \right)}^2}}}{{161 \times 125}} + {\text{si}}{{\text{n}}^2}\,D = 1"> <mfrac> <mrow> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mn>125</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </mrow> <mrow> <mn>161</mn> <mo>×</mo> <mn>125</mn> </mrow> </mfrac> <mo>+</mo> <mrow> <mtext>si</mtext> </mrow> <mrow> <msup> <mrow> <mtext>n</mtext> </mrow> <mn>2</mn> </msup> </mrow> <mspace width="thinmathspace"></mspace> <mi>D</mi> <mo>=</mo> <mn>1</mn> </math></span></p>
<p>correct substitution into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}ab\,\,{\text{sin}}\,C"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mi>a</mi> <mi>b</mi> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mtext>sin</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>C</mi> </math></span> <em><strong>A1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.5 \times \sqrt {161} \times \sqrt {125} \times \frac{6}{{\sqrt {161} }}"> <mn>0.5</mn> <mo>×</mo> <msqrt> <mn>161</mn> </msqrt> <mo>×</mo> <msqrt> <mn>125</mn> </msqrt> <mo>×</mo> <mfrac> <mn>6</mn> <mrow> <msqrt> <mn>161</mn> </msqrt> </mrow> </mfrac> </math></span></p>
<p>area <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 3\sqrt {125} ,\,\,15\sqrt 5 "> <mo>=</mo> <mn>3</mn> <msqrt> <mn>125</mn> </msqrt> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>15</mn> <msqrt> <mn>5</mn> </msqrt> </math></span> <em><strong>A1 N3</strong></em></p>
<p><em><strong>[6 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A solid glass paperweight consists of a hemisphere of diameter 6 cm on top of a cuboid with a square base of length 6 cm, as shown in the diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAesAAAEKCAYAAAAy632GAAAgAElEQVR4Ae19C5QcVbX2nog8kxAjKANoMMSAGhSNhKvCZQgQ4EcMBB9XfkgQ8LHkoSAEiLLkXkGBjOSCgCiGG4KieJkQhasSCQSBq4ZEUeEniZEVIGRkhYch4RWT6X99NfPN7Dlzqrq6p3u6p+ertSr79e19Tn3VqT3Vfbq6qVAoFEybGBADYkAMiAExULcMDKvbmWliYkAMiAExIAbEQMKAmrVeCGJADIgBMSAG6pwBNes6P0GanhgQAzViYMtyax3XZE1Nh1rr8k1mtsXaF3zBmpqarGnGAmuv0bQG97AdtmnVEru99QKbk3CacTSbVtm9t7faF+Ysty0ZsPoMVf61omZdn2dasxIDYkAMNB4DW/5oN/yfQ+0T5y+1rZlHt8mW3/B5O+wT59s92cDMKo0U3KaRDkbHIgbEgBioHgPbWPO0G6xQuKF6Q6iyGEhhQHfWKcTILQbEwFBi4CVb9es5NmN3vO3dZLvPmGO/XvVCQEDaW5u9czvzW23B8nbr6K6At3/vttYZ+3W+jX7oBXbz8lW2tPXQxB7X2vVWb/sCm4G32cf9uy24+9/tUOhNn7SbVr1mZkENxHafYa0Lllt710BblrfauCT/crv3//nxZtmCVS+ZbVplv26dYbsndY+0C25e2p3bPdVu5WlbMGOcNTWNsxm3/86WL2h1/FxnS9s3dyMTpetta3LY1HSkXXDTvbZqU9fkcGxv/KCd/zegl9j5HxxhTeNabXmf97gx7v72wfOXJGX/dv4H7Y3dH0XA9ZKtuve2Hi6bdrdDL7jJ7sXxZW2Y300XdHEKXlPyOtp7HWtT0342o/XunuNIxshzzmOTwTm812664MjO10HaHGKp+OqWNjEgBsTA0GXg9cLatjMKzWb4GmtkbynMXraxUCj8s7Cu7fOd8elthXUJYRm5zWcU2ta+nqC2rm0rnNoc1G4+rjD9xAlJvb1nLyv8E8h1bYXp4RyaLyos3rC1EK2RYCcUTm1bU9iKGS6bXdg7zKfdckZh5vTO8XqOc2Jh5uL1Kaf+qULb9L0jfHQdx5S5hZUYFNvGvxTm9qndhWu5qrBs49b4se09u7AsOfCuOomIjctzsKHw+NxTU87VMYXZy170hZz+YmHZ7GPix8L5Jeh0XPOpbYW1yfHmOeex10oh/Rw2n1qY+/gGN9++qvV1ySMGxIAYGEIMbFhcmJk00uZCy0WLCutwQd66rvD7q6Z3NQU2isgFeOvjhblTmgtmPY2ip6ky79XCyrmf6GwULZcUFq9DA3+9sG7xJYWWrkbat1k3F1pm/76APxG2btxYeLnAGj3+wtY1hbZTezf7nmY9oTB97l8KGwtbCxuXXdU9TvP0eYXH0Tg3/r4wuwXztkL32H1OuWuaLRcV2laimfhG9flC2zp0Ws7NCuaaztZ1iwoXJWO4Of9zWWH23mji5KbPoF2OjYVls1v6zG/ryrmFKV1/oHQeHwhaW1h80ZQufrv+MAjLdo/r/jjp5qC5MGXu48kfOz31pxQuWry209d9HF25uc555LVSWF9YPHNiwYznBpPs+eOjeebiQla71tvgsbcb5BMDYmDIMNDx9zX2SLK0+2N21lmHWjOuisOabdJpM+zk5iI0DNvXTr17nRW23miHrr3XFiy40S466Uy7Kam30dZveM2sY409eNuDZtZsU07+lLU0b2tm21rz5DPs4pkTUwY4yE7+2HttOKYyfLjtaNvb+FN/aoXCGrv10Ods0YLb7aaLPmcn3PRokv/K+g32iq/UfKzN+Pi7bbgNs+Hv+1c7Zm8EJ9rJM46xfYcPMxv+bjv0mH18RoaOeU+348aPTOa9x4cm2xEe7Y/v0vPtlH2BA4WH2YUXn2LN1m5LbviNrezzdrcvkkd/zVY/+CtbBOiUc+yrp0xI+LFhe9jkCy+wmThXS35u963sxURn4WG72NhDJpjZcrvysENtRuuttmDRWntn63LbWlhnd5+6rw2zLfbso0s760//vJ01eQ/rfCkcYd+8b50VCsvsism7mOU557HD2fKk/aFtuZk9avNP289GJB9F7GzvOu2m5JsF7bfcY8te6vngJCyhBWYhI7LFgBgYUgx0bHzBko9Rm0fbqJ3c/cuOO9uuOxaj4iVbcdM5NrnrgtsbPcJ23Xl7s46X7YW/oXtPtP332iVpAJ247W3nXUf0TqHVPM722g1NnVuHbVpxi50x+RSbH/nO2I677my9prrjaNt5R3csSZmu+bBkbrmj7TZqp5557zrG9kPzT0jDR+k8vhY74n179uBsmO248+jOef1ttT25fotN3DX3oBHgFtv4wvrEv/cR77Ox/vC6z9XT9pcnXzSbiD9z3DZsjB136Vybt8vFdsqVi2z++f/X5jPccpG1fe9CmzZ+mK17YiW9GTLHOY9lr3/S/kLOYvH2F+wfL3eYjfQH1gOMe3vi0sSAGBADDc3AsBGjLbnxbF9ta/7uFk29ssHWR27SPBkdq263LyWNeorNnPvftnDZOtv6z2U2OynYhRy2k43eG7d96+yRNc+5RWev2Yb1G325Hj1sth2r7Kdfusjmtzdby8zvW9vCZbZu60ZbNrulJ6dWWvfxrbRf/2mtO74Oe2XDC513/HuPszG79vfecBsbMbqz2//t13+yJ/xNaPe5epvtN+ZNUSaGNU+yGVfcbYXCBlu5eKG1tf3IZk+fYLbkW3bCWbfbqo7tbfexXe82/P0fttHXdxVznXOH71Z3GmW7Je/UtNjsZRvxEXSw32DTmtM5UrPuZlKKGBADQ5GBYeM+bJ+agqvog3bLvAc6V0d3tNvSuTfbLZG72B6OOmzT2tX2Fzia32kHHvkxmzrxzfbsb+6y//F3UMP2soM+dZCZtduiW26zJckq6s3Wfu919o0r8bZojm3TOlv5F0zmzTb2wCl23NSJ9tZnf2tt/5PnTjBH/f5A/PF9bbbNW9G5KrujfbFd/o151m7N1vKFf7V90vtQztG3t3EHHWVTgF40xy6b96jhUTXW8Yzde/kVdiXoafmYHbpPr/cYktodzyyw05KV/kfarHs32rjJU23atI/bp6ceYkn/TFDb2FsnTOqqf5vNW/JM5x8emx61m5JV/LvbkTf9P9uQ55wn9YJ/Rr7XjjwZH3sssauuabMVWCWPuc/qXBm++wX3WuZ69vBzeNliQAyIgaHFgF80FazYThYzcTFU30VDPYvJfN7EQksLVlH3LGaK4rJWg4erpN1isp6V3M2FD7d8OFkEx8VJ3QvMfH734ioeB85ufAFX7/POBWZ7F6a3PdUT6q7HBWYo17NgrWd+wWpwVOhenNUV8/PsGaH3orVe5yB9tbZf5NerVGJk5fWspi8UMnBdiwOj59LCc973tVLAYr/H5xWmh98KwPG5hXl9597p0Z118MePTDEgBoYaA9vaHtO+aUsWXWXTu26zmqdfZYseW9T77ewILcP2+Khdeud8m9nSldgy0+Ytu8N+eNbhyWKmW+7+c3K3NGyP4+zqJb/qfNsVN+Kov+RaO/v9u0SqRlz8zHVmcl+JFVY2c95Cu/2HX0kWexVbnBSpWFnX8El23p1LbPF/z+7mMJnj3MW28s4v2UQsasM2bKwd/Y2v9mDe9gaz12LvN29v447+kl2Ft6mTbafkca9mo2ziebfaysU/6eYSC/daZs61xStvtfMmjurCh4J5c3vOFSAtM23u4ja7etqYrs/aR9nEc2+0ZW3+OCbY9NlttuzWi2xy87aW95yHMzAs9tv3ZLtuyWKb230e+VqYY6d2Lczrm9fpaULPTgvKLwbEgBgQA/1lYJMtbz228yEfzWdY28NX2bQ9tjXbtNRajz3Ozl+yo01vu89unva2/g6k/AZmQM26gU+uDk0MiIF6YKDDNi2/2o794LnW+UyuYE6+gQchmWKADOhtcDIhKQbEgBioCgPDbPjEM+zWZW3urVsM1PX27ZJvdt5pV2VsFW0UBnRn3ShnUschBsSAGBADDcuA7qwb9tTqwMSAGBADYqBRGOj3N98ahYiheBxHHXVU8qV8/EoQ9mHDhnXb0L2fcfp23XVXu+6664YibTpmMSAGxMCAM6C3wQec8oEb8KSTTrKnn346GRBNFlusCYeNmA055mc+ankc9De84Q3dvquvvtp23nnnZEz9IwbEgBgQA/1jQM26f/zVTXZra6u1tbUl80lrsmy0vsnSRxmL0QcMNtqQYV4YJwa4733ve0m+/hEDYkAMiIHSGFCzLo2vukIfcMAByXzYEL30um+oaTrwPifNzvJjMmEN+phHG3fh1157bTJ//SMGxIAYEAPZDKhZZ/NTV9GpU6faU0891ashhs3X22ycMR9jbKKhHeak4eDHFsPD7/NC28dGjx5tX//615Na+kcMiAExIAZ6M6Bm3ZuPurNOOOEEW716dTIvNsRiEk0QGOLYFNN8xHscdS/DephU6CMeMeox6ePUWQ9Ne+TIzt/EhU+bGBADYmCoM6BmXaevgPe85z3RO+iw4cZsNEc20VD6WJbOBuvzQVXopx1Kj82KeRx1Sox9xRVXwNQmBsSAGBjSDKhZ19HpP/74423lys6fvEOj8o0SDS/Nx1hM0sdasOmLScZ9zPuy/IhhCzH0sY63Yzp9lMi75JJLbLvttoNLmxgQA2JgyDGgZl0Hp/xd73qXdXR09GrObK5epulsgogTw4bp7ZjPx9N01me+t/PooNjjvE2dEjjqoURs1KhRdt555yUY/SMGxIAYGCoMqFnX8Ezvs88+3U2ajRKSOxuct0MdGO+jnSUZQx50v9NHyVho0w/60mLAYCM2tH0sptPnJfXtt9/eZs2aBVObGBADYqDhGVCzrsEpHj9+vG3durW7yfFhImh6bHyUjKHRMc6Y91GPSfrCPPohQz3Lx1haDuOgljpkls0YpcfTB4nNx0aMGGHnnntuV0RCDIgBMdCYDKhZD+B5PeaYY+zxxx/v1Rh9A2YzpWSjpk0sG6C382CQ53N8Hcboi9l5Y8Bh8/iYz2OoU3o8fZDYwhh8eFra2Wef3QnQv2JADIiBBmNAzXqATug73vGO7uYVNlbfQBnLatTE+Dw0sCw7jMXw8GX5fZx6KEFn6IMd+r0d0+nLkj4GHcd40UUXQdUmBsSAGGgoBtSsq3w6x44dm3wujYaFZkLpm2daYw7xzKWMxRmj9Bj6IL1OjPcRQ0kMJf2Q2Lwd6rG498V0+rKkj3kdc5w5cyZc2sSAGBADDcGAmnWVTiPe8n7ssceS6mhebHKQ3OmP2Wkx74/p9FH6ceEL/d7HGH2UrEG7FAkCQnzo8zb1PNJjQh02Vtkfe+yxULWJATEgBgY1A2rWVTh9eMu7UCgkldmo2PDYmL0EJo/tcTE95uO4YQx2mo9+L4kvRYKAEB/6vB3T6YtJ7wt12jj+c845B6Y2MSAGxMCgZUDNuoKnzt9NoywbFRumb8jUgaEewzFOGWLop4zFwxjtmITP+9Ns+mPSH3sYD2Pepk6JXOox6X2hHtpq2GBEmxgQA4OVATXrCp05fjbty4WNkzY+o6YOyR3NiTrjMR8xjFEyJy1OHCXxsLnTR0l/JSS48XW8XUxnHBIb6niZGF3/MOZ90LfZZhs788wzQ7dsMSAGxEDdM6BmXYFT5N/2Zjk0jLBp0qb0GDZHxorZzKUM87yfOiR11qftYzGdvnIlePG5WTZjlMijnihd/9BPX2in5Zx11llMkRQDYkAMDAoG1Kz7cZrCt71ZCk2DzdA3Ua8TQ18pNrGQfiW5H5MY+tJs+Bnzkn5KX4e+PBKcxHCh39vUvUzTUZub17N8iOkOmwxJigExMBgYULMu8yxNmDDBNm3a1CebjYnNDTJsqPBxB546ZejzNnXIsK6P+Vr0w0cd0uuMhX7aXoZYH6MOYqiHMox5m7qXXketmJ04u/4hxvti+vDhw23GjBmxkHxiQAyIgbpiQM26jNMR+3yaZdjIIGM7Gknohy9svLE6zKX0deij9PmhD3bMxxzGifF2f3XwFNagrxTpsdC5obbfQtvHoOOYP//5z4du2WJADIiBumJAzbrE0xH7fJol0BjYQKH7Bux1j6FO6WvAV8z2GI+N6fDRT8l8xuj3dpovxBSzwVOIoS9NAs8tj+7rMK+YBAef+9znisEUFwNiQAzUjAE16xKo32uvvVLRbEK48KftwOSNhdjQZh36KeH3Om36YtL7oHP3ufSlYX08poM476dNiVio045J74POjXXSbPpDibzPfvazoVu2GBADYqAuGFCzznkasho1SoTNk3bsjppNkJhQonF4X8z2dX3c6xyHPsqYHzHGqVN6PH0x6XHgJIbxfq8Dy416mmReiKcdxr0/S8d4p59+ehZEMTEgBsRATRhQs85Be7FGjYs8GhWbFRopbfogfYONxeljvRiesRALOxajj5I42pChHrPTfMwvJkGzx3ibOiVw3KiHMozTpiSedl6JvNNOOy0vXDgxIAbEwIAwoGZdhOa8jRoXeTbQLElcrBGzkfp84r0vDw55zKX0eWE8r52Goz+UoDfN52PUs6SPQceG2rEtzR/Dhj7knnrqqaFbthgQA2KgZgyoWWdQX6xRI5VNFBd46GzCkL45EudlmONjWbnMIz5m00fp68FHfzE9FqePkrVpQ2LzdujzcepZEjFsrNNl9rGL+RkvJjHOZz7zmWIwxcWAGBADA8KAmnUKzXkaNS7ovmGyQdPHJka/x3sMcaGPNvP4hwD9zGOcftqUxIWScchQj9lpPuZ7CVq9Td37qVMCQz1RcjRn5hBPmeZnPI9EjVNOOSUPVBgxIAbEQFUZULOO0Jv19SzCcSHHzgZZqszKLSUWYmlThg2aNuOQWXoYi+Hpg8TmbereT53S59EHyY1x2F6P2bEc+sqVatjlMqc8MSAGKsWAmnXAZJ5GjRQ2PTZp3vXmuYtmDiUaEPU0GcOEPtqUqEXdS68T433Q89jEpUnw5GPeDnXakNiQxy1ND3ExfBqG2Jjkz5v6mJ505tmQLgbEwEAzoGbtGM96MpmD9WpkaHZs0L7RosHQD5046h7r9aw4a4YY2pSsRzsmvS9LD2MxG9zAn7b7eKjT9jKv7nEYO7al+WPY0OebNn6x68QTTwwhssWAGBADA8KAmnUXzfvtt59t3LgxF+m+GbIh01dMonkAgzzqeXM8Drm+RliLdkx6n9dRHzZ3b3ud8TQJEn0szSbZwBIT+tL8zAnjsXz60rDw+8bs8d6/ww472Mc//nEfli4GxIAYGBAGthmQUep8kGOPPTZ3o/ZNqJQGxjzk+LzQJs5LYsI8YOgLMd7va4U5jBHv46FOG6eTeWkyhuHLADmMe+l1YugLbfi5MUYZ+mlnyTAXWDRq73/ttdeySigmBsSAGKgaA7qzNrM8K79xBnDhxu4bI3V/l+t1xEObOV6iLnDeBz1tPB8LMbTzSI/Jq4MLjo8c7J4f+ryf8SwZxpjv/V5nnNLHoGPzsS5XLuHvqJHgbb0dnotCgcSAGKggA0O+WeddUAbOceEPmylsNlnEvR7GaKfVidX2vjAvtIGlL4+MYbwv1GEX28kTcbSzJGPIoV6K9NhQhx3bOBZivhHHsB7Du+1/+7d/S4PKLwbEgBioOANDulnnXVAG1tl8fPOEzuYc+rNs1GIedNaJ+dPqMI853mZO6IMd8wEfxjyOsbzS80W9mERtbtQ5XrFc5nmc92X5Q1xa4w792223nR133HFhumwxIAbEQFUYGLKfWeNz6o6OjtyksnFQ+oZIX17pmyNyaFOyTp4xmBNK1ghliKOdNQ/W8FgQBxsb45T0FZPF8IizhtcTZ+QtbmKYQxylj9PnJe+aQx9s5PqGvXnzZg+TLgbEgBioKgND9s467+fUYB8XajYqSN4VQx+IHeNzTM7Fj0sfJWLUs2SxGOLcWZM2JfhBjDzBTz1N+lyPL6b7el73efBzo5+2l4z5Buzj0MMYbUrU0OrwkDXZYkAMVIOBIdmsS/mcGqSzUUFiZ+OkXUwCjws7caEd86dhgPW1mEtfJSRqcOd4tNMkeEKM0uv0UbKGt72elUtcTHofdGys1WXmFmzITPA2dUjwM23aNMIkxYAYEANVYWDIvQ2Ot795sc3DKBsLZZ7mlYUJY7C5p40R5gAX5jCXkjmlSuZzDG+n6eCRMeqhDONpNvw+l3roT7OT5K5/iPG+vDpz+VrxNnT46ctbUzgxIAbEQLkMDLk761Le/gapvtnlvaP2d8XMwYWdOmt6G75iO2qEGO+jniY5bppEHndiaGdJ8IQ4pdfJIWOUsXqMhdLX8zpw2OjrMvvYMQyxMckGzViWzdjxxx9PuKQYEANioOIMDKlmXcrqbzDNhsIGmdZc4QcWOGJgU2d+f6Ufgzolasd0+vJIYDyOdpb0PFGn9HkxH+OMUcLvdW8ngaBBF4vHcujzko03zcc4JXDUt99+ezvqqKN8qnQxIAbEQMUYGFJvg5ey+hsMs5kUk8SyYQLv9az8EOdtr7NmzMf6YYx+5mZJYrNqEEPJ44adphPrpceGuWk2c7Kkj0Hnxpq00yRxbMDAeZ/XEQMOPsjXX389raz8YkAMiIF+MzBk7qxLXVSGizB2NC/saXfJ/bmrZk2O422vcw5eMge+YjrjWRIxH6dNiXGw0U7TY3H6vPT59Ic+2nmkx0Dnhtrlbr5po0bMpg8SY2FNhDYxIAbEQKUZGBJ31kceeWSfC20eItlEsiTqIM6mGeqxXI9l3Pu8znhY12O87vGhTlwoiaOfNiX8PE76vO31WNzX9VivMw+Sfkrvo85YAnZ3wFl+YvNINl9g2ZAxNnXW4HzgD2PESIoBMSAG+svAkLizLnVRGUhFgwl33u2GftiM4eJNPQ1XDBPmeTx0xovpsXjog00f9WIS/BDjdfqyZBaeMUrWoe2l14HzdpaeAIv8EzZd2pRIhx7a9H/0ox8tMoLCYkAMiIHSGGj4Zj1u3DjbsmVLSazg4s+G6GWxJuyxaXpWjbQc7/dzK0WPYeHjjjGoZ0kQybjX6StHsg4la9AOJeKhz9uhnoDL/CetIaMcY2HjxqNIDzvssDJHVJoYEANioC8DDf82eKmNGhSxWXiZ1cwYS8tlHeCKYYgtVXIOaXlh3M8jjKXV8Dlej+FZsxgOuTEMfaH0+DAGGxsxXWYvkRZj4+0F7qrFGHKhp0nitNgsZFG2GBAD/WWgs3v0t0qd5uOuutQNF2J/QadNiXrUvUzzewx0NrHQT7tYnLisWr6G132u18mR94W6Pz6vhziMlzYmY2Gc/rAWbGI9hrqPxXKZH+K9n3keQ93HQp0YyLAefPfddx9plRQDYkAM9JuBhr6zLueumozyAsyLNCQ2b1Onnxdu+r1EjDjv93pWvseVq2fVT4slk3bHzWMIjyctP22urOPjoS/Nph8SG2rEpPclgMg/zA1DvIOGnzrvnEMsangMdP3QR8iSbDEgBvrDQMM26/Hjx5fFi28eXkcx2KU2JV8jTy7H6e9YftyYHs7Fj0t86PO218NazM8rfS2v+3z6IbExRt3LLB2xYhsbL3ChTp+X0DEfYiGxb9iwwXbeeWeEtYkBMSAG+sVAw74NXs6dDRtAHgnWYziejTCWhieuvw2PdSh9PerF5sDc2DGk5bI2c0OJeDGMzyGe0seo+xhre0kdeK8zv5j0OdBpx6SP+7rwP/zww6RSUgyIATHQLwYa8s566tSpZZHCiy2SoVPST1/MzxgkL+o+L4/u65ZbI884wPixmJM4gz9CYj7is+YYxvx4iHmb9bxknBKxLJ2xBNT1D3PoC236KXE3zA3YmM0ajEFiJ55+1PE660qKATEgBsphoCG/ulXq08pAHC622NFIsPMrVpT0e5kWi/ljPtZiLBzf28SGPm97HXhvQ6cd0+mj9JzQ5yXrex/1MIZaMR/xMRmO723qXnod9bh5PcsXNlZvU6dEnVCHTR91SIw/efJkDi0pBsSAGCiLgYa8s+ZFs1RG0poG66TFK+0PGxvrYx7US5Fp84/5Y75Sxkqbu6+BMWI4+EOct6ETkygO7/3EeR/xadLnAONfQ9S9BJ42x4FNH+O008aVXwyIATGQh4GG+8wav6xVzoaLq99Rw9sxPQ1TCX9aDT+PPBji2RzDHO8PY7CxsQYlc2hTpvkZpywFB2wMTz9jMUmfH9fnhTpxkIxRz5JpefT/5je/6WJSQgyIATFQHgMNd2dd6i9rgTZcVP3Gi2woiQn9eWyOEzaQWC6xPhbz+Xi5euyYvI/zLTY+caXMAznF6jJOyfrepg6JDZhwi/limPBOGHnwMZ9xSPqp+3rMQ6yc16SvJV0MiAEx0FDN+vjjjy/7jOLiGttZMBajLw+GWErkUK+mjI2TNt+Yn75ymnHsuMI6sfn5vDAes+mDxIZ8LxMj5z/MBRyNFht81FmGPvi9HuKIlxQDYkAM9IeBhnob/JFHHimLC1xs/Y4isCl9jDoHoh2Taflp/lgN+GL4mC8tnzViOUnxrn+y8hnj3bCvFTZgYkMZ4lADvnD3eYzRF9rww0fpdeZ4yfyY9DjWoy+tLv3Es67Pg+/BBx/0VEsXA2JADJTEQEPdWVfiroYX2VCSVfixhXH6PS4NA7+/yMdw9MXGyuMrNg/UD+swJ/RzLj4n7/yRUwrWj+HHpc65URJPGxIb/ZRd7l4x+vi68Vjvo048cKX6QjxrSYoBMSAG8jDQMM263J8lxIU3tnvyYnH6iKMdk1mYtFiaP1a/mA+1iPE6fH4jxvu9L6ajEXNLi8f83sca3hfqGAM+Sq/TF5PeBz22sRZjaKz0UfeSOGBCP33wY9cmBsSAGKgEAz1X2kpUq2GNxx57rKzRcXHlhdlL+kPpBwlj3gYONqWP0Z8VC/FZOWGdZFDXoJnLmoyHeYyXIlmj1LtnjIGcPI3azyc2Dn2h5Bg+P4/OOsyHTR9lsTrM8fj//d//9dRLFwNiQG4wzKMAACAASURBVAzkZqBh7qz7exeTdfElm3kwwKbhitXJiqfVTfNzDj7udR+Hnxv9oSwWD/GwfaPy8dCP2qEPeGw+z9sxnT5IbKwR6p3R+L98HSGXOpGsBz93j/M6cyBxbMR7v3QxIAbEQF4GGqZZ5z1gj8PF1e+Iwfabj4c6caHf26zpfTE9DZc2Ril+X5t5lOFc0vwhrlw71pSL1eL8KT2ePj/vNB8xWRK12aShY6Pt84hjjDYwXvc50sWAGBAD5TLQEM263AeheNJwgcWOjTolfTE8MV56PPy0QwzreT/1YjHivAzH8bbXw5yssTzW62FOaJfTlH19r8fmTl+W9DHo2FA3trHpEuNt+iBjfvhCfzgGxsX3rR9//HF717veFYZliwExIAYyGWiIZl3uQyfChgCm/MWcupc+h7pnmL5QEgM/x0nDFIuHeb5mmOtt6OHmazFWzOfjpehZDRwxbMXqEUMJPPVEceeQsdBP20tgfcNlLnyxmMeiDjHwhzGOg2PcuHEjTUkxIAbEQG4GGqJZ5z7aDCAutuEOuPcxHT6/eQz1YnHifC3v8zpreR/1tJj3QyfeS2Ji8ZjP5xbTWZu4tEbt/cgp1rT9vKhTYixuXmecsTSJnLRGG4vFfLHawOEPyrz4WA35xIAYGNoMDPpm/eKLL5Z1BnHhjO2+GOLcYlj6PAY6/WmS+CxsMQzjfgzWo0SMeqIE/4S5xNIf2qzn/V73jZc1QpmGh79Yo2Yt1qDkvCjpj0n4sjbfrKGjpveFNmqFPtr+HR8cm6+TNQfFxIAYEAMhA4O+WU+cODE8ppJtXFy5QY/tjIcyhqUPWOjcqDPuJTGUPub1tDj8wIXS51JnDUr6Y5L1YrFiPt+8OZb3MR+xsFETFxvf+6hToiZ1LxNnjn+Y7xs1fGGjjfnC8jgG5PGumvG//vWv9s53vpOmpBgQA2KgKAODvlmHF9GiR9wFwMWWO3Ngcwt1YmMSOR7va8TwxFIyP4ZlLco0DGulSebHxmKMtUPb1yTGy1hNH4/pvhn7Rk0/c9Jq008Z4uHHBr/fQpuxtNcR8IhRhjj6WSe04ccx+Yb90ksvES4pBsSAGMjFwJBt1p4dXGDDHXH6QixtxImjZA4lsaFkPJTl4FADm69F28sEFPzjc8I6zCXG2yzDGHM9xseg+0bM/KxGzfxYzTQf/TEJX9rm5++bM/CIeR/0sGmn1aXfN+xSc1lDUgyIgaHLwKBv1uWcOn9h9rqv5f3QYzvwxIWSsVgefX486ozFJDFhbW8Tg3z6KbNq+liI97bXfU65Ouv5Rh7WIib002Y8Jr0Pep4NdX1zDnMYD5s2/P4OOsxjww79ssWAGBADxRgY1M16zpw5xY4vNR5e6GlTMhF22sYYc0Lp84ilL8R6m5hQegx1YKBzS/Mz7iWxlIjFdPjCmLcZz+Nj/VJlWNvn+xh1SGzh3LrcqSK860V+VuMOC6EhhzU8Rg3bsyFdDIiBvAwM6mb9ne98J+9xpuJ4MackEDZ91EPpsdS9DPHe9rhQ97hQj2HhIy5NRzxtY4wyrEGbkmMR7+00X4jxdtZdNXEcm1jaYZx+L0MddrENdWNNN/TTBjbrrtqPh5zNmzfbtttu693SxYAYEAOpDAzqH/KIXUxTj9QFcLHk7tzdKmLcvE4fpa9B3UviYtLjYnosB74Q631hDrB+S8v1NTzG+6mzXhqOfuJpQ3LzPq/HcpiHJs1G7XNCnRhKxEMddrizTogN84mLSZ8bi3sfnmSmTQyIATGQl4FBc2f91FNP2auvvmrr1q2z559/3tavX5/3GDNx/gJKHQmhTh+LIc6NOqX3s04oiUmTId7bPgd+v9Gm9DGvsx58XqftJXXiKL3f67E4fZDc6KPNZudrQaefeEqPY900SSxkbEMe//jzuseG/tD22JjO+jge6jGcfGJADIiBkIG6adavv/66Pfvss30a8urVqy3tqy7VuuDhIsyNOqTfEadNrJfMI87H6GN+KENsaHt8WIs2JbG+BnzcvM4cSuZS+hzvow4Zy435fA511kcz45bWqGNj+XGosw7xoe1fQ8DQpk7JvHIka+JY8FY57XJqKUcMiIGhycCANms2ZDx17IUXXrCnn37aXn75ZfvDH/4wYOzj4hvbOQHE8mweF6vnfWE9nxvGYPvcmB7LoY+1Kb2ftbwPOv3MoV0KjjlhDfrDceiPSWKzGjXziA1t+r0MdW+zgaIONtqJ0cWR9wHnbeK8ZNw3adb3OOliQAyIgWIMVLxZ10NDLnbQsXh4saftJfNKveD6Glk66xeTrAFcqBfLjeWgBjdfj9gsyRhr+HzqlFljEFOq9OMj19vUE2cXV9RDiVw2V8ZiPsbyyKwmHY6Vp54wYkAMDF0GKt6sP/e5z9nIkSPttddeq3tW/cWdk6WPtpeIMU49lMAT43Pz6GEtb8fy/ThpeiyPPp8Dn7eh06b0eYxTZuUzRmwos+qGWG8jDw0xrE87JhNwyj+ojS1spPB7X2inlEvcrBli0vwhTrYYEANiAAxUvFk/8MADtt1229mkSZOq+tWUrVu3Vv0M+guq17MGJg4ybc/KT4vFagFLP/Ngez/jXhIb4rxNjM+jzhjxXlIHNtRpJwE397Bumk1/KFmXfm9T55h5JWr5Bp03L8Shjt9YM/R7jHQxIAbEQMhAxZs1BsBb4WjaI0aMsEMOOSRZNBYO3F971apVZZXgBZ0XSy+9nlWcOGCoU3pfWg1gi+1puVl+zoEyDevH9pgwL82m30vofkfdrHixWFiL9byfNYrdXTM3dqxsnj7mdYzhMaHtsV5nDucY2h4rXQyIATFQjIGqNGsOunHjRrvrrrts9OjRSdNOW9VNfCkSX+Hq78YLKSXqUYf0O2M+nmd84okNbfpD6ceO6SE+rx2OH7M5HmrmiXsM9VCGtRD3GNppkg2ZdZgLP3WfS1xMwseNubDZUBkrR7KGr4s63iamnPrKEQNiYGgy0PMdmSoeP1Z+33HHHfboo48mn2dXcaiqlfYXW+qQsR2ToD/UKznBcAyOlWcM5PrN16KfGMZoh/HQjuGZyxhyvJ5l+1zftH2jpu6x0L2f46VJYilDHPx+nj6eBNwxMeb9XkdcmxgQA2IgLwMD0qw5GXyPGk0bDzTZaaed6K6JrObF0tcOddh59mKkhHWB975Yfhj38yA+hmEsNkZYgzZzvO1rhzpt4mlzTPq9zTGymijz2IAhYztxXjIn9MXm4DHUPY4+SsQGwyJMciwpBsRAbRkY0GbNQ/3zn/9sP//5z5PnI2+//fZ0V13yQgmJjTYHpp+xmJ++akvOLU1mjV8sxx8n64S+mE0fJHfmQzJOn7eJp0zDeL/HUo9Jjs1Y2GRDmzgviaH0MeocBxhujIWSWPpp+7wnnniCpqQYEANiIJOBqn5mnTmyWbIIjSvHd95556osRCs2B8TDCyrsND9jjHsZ6rCruYXzxlh+frGxGaf0GPpCGcPQR6y34fN+rwPHuPd7H/3eF+b5WEwHnk2V9VgDMtzwOXKIi322TJ/H+lph3NvQked9Ple6GBADYiCNgZ5bhDRElf1cOX7//ffbDjvskHs0XvByJ1QQiAsuL9Zehjpx3l/BaZRcivNgYmjDn+YL/d6Gzp21WYs4ylg8zM1rExeTYaMOMYhjp9/r9JUieVw+hxz4GH3A4dGj9913X/LtCWIkxYAYEAMxBmrerDkprhxfunSp7bjjjnSnSlzs+rMxn7I/tfLkchzItD1PnWpgODdfmz5KxLxOO+bzdYijDPH0U/o4dNrUQxt52Hw81NmIQwkcfaGeVrNztJ7xQht1uFGH9LuP33rrrfatb33L/vSnP9EtKQbEgBjow0DdNGvODE37zjvvrMnKcV5cMZc0nfOshvQX9Cyd8/NzLGU+rM06lGG90OYYaX7GWS/N9uMT42uG8WKxtDjrQPqmzPkxz+O8HuKybNYiBhIb63WZ3T4o/PrhM888Y9dee61dcskltnLlSg+VLgbEgBhIGKi7Zs3zUmzl+GGHHUbogMrYRTnmw6S8v5qT5DiUecfKi/c46pQcCzZ9lDEOwpjPC/HFYuHYabXpZz3aHI/+0E7DEU/p5+F1n+/9HOe2226jO5Fo2q2trfbd737X8JOw2sSAGBADZKCmC8w4iSyJlePY999/f9tjjz16fd0FF8NafnadNe9YLHbxjuGq4Stl7Bi2HB9zKP1xFfP5OPTQRi3vpx6TIdbPoxw9fM1hTPqgY6PN+qE/jBMHiV+hw37wwQfb1KlTDYsvtYkBMTC0GajbO+vwtDzyyCN2zz33JF/34kK0ww8/PIQNCZsX/kodbKxeXl/aHPLmE0eJelm6jxEb+kI/4sRQx9visbfGfS5zvI86pN9Y1/ug+xq04fv2t78dQvvYeGTveeedZ7fffrsWofVhRw4xMLQYGDTNGqcltnIcd9t5N15QeQH1MqbnrVtLnJ835gE7tnOOxNMOZbF4iIddTo6v4/O9XgzjsdD9zlz6OE/Yvkl7nRjm0kZOuLEuZSxOX5hf6sNQ7r77bps1a5ZWjpNQSTEwBBkYVM2a58evHH//+9+fXHwZq6T0F+JQr+Q49VArbChZc/JY6pRhHv2UiHs9xHs7hqOPMlYPMe6sRztNsmnH8PRxLNRI23wspuPrWtdcc01aeqofz9XHynE0ba0cT6VJATHQsAzU/WfWWcyjaf/iF7+wt771rfbGN75Ri3KyyHIx30ScO6pWCxsbzI+Vpod5HhfGYCMe20MsPkP2tfxnyvAzTj99YZ3Q9jg06iuvvDKElGSjaWPlON5R+vSnP2377LNPSfkCiwExMDgZGNTNmpRj5Ti2N73pTfbiiy/SXVXJC3soqzpolYvzWPIMUy1snrGJ8XOgTkmMl2kx72cz9nnQgUmLhfEY9umnn7b58+eHZcu2uXL8Ax/4gB1zzDH29re/vexaShQDYqD+GWiIZk2aN2zYkLwljotq1oWV+EpLf9GvdO1Gqec58nq1j49jUWI86KW+TsrJufTSS6t2eFw5jqZ94oknauV41ZhWYTFQWwYaqlmTSlxQ8cxxLEgr9WLMGpLVZwDnxjfP6o/Ye4RqvzawkOyKK67oPWiVLDbtI4880o444gg17SrxrLJioFYMNGSzBpmbN29OGsEb3vAG27JlS9X45QUfknrVBqtyYcw/b/MsBeunXW6er0Hd16JOSQwl/NzCY0SMOzGhZD5lWhx+YPA0slpseNb4ihUrrKWlxQ466KBaTEFjigExUAUGGrZZkyss6sFKX+zQK7WlXbQrVb+adTD3sGGljVcJbCk1OA+f43XGKbNiwCDODcfsbfopEYvF6aME3us+/+KLL6ZZNbntttvaqFGjkjUau+22W/Lb8Fhg6f8oxes93F599VX75S9/adOmTQtDssWAGKhzBhq+WZN/Nmr8fvY///lPuotKXpQhvZ632RUdoE4AOLa8x+SxXo8dSiwe8yE39Id2DBPzIY+bPyb+4ebjxHkfdNqUxEGGPthf/epXPaTfep6G7Afxjdr7vT537lw766yz7Pnnn7fRo0f7kHQxIAbqnIEh06x5Hl555ZVE3XPPPe2FF15IdFxseQEOdX+xZ416lJg35srjCOfI4yAujNMuFiculMXysuI+5nU/hvdD5xYeF2P0A0cfdDRsH/Nx4DzW6xyPPtTB87uvv/56hkqWw4cPT35hDq/FESNGJDvuiLdu3RqtlachRxPNbO3atUmjRvzyyy/v91fI0saRXwyIgeowMOSaNWnExQvbe9/7XsPbg+vXr2eo7iUaBhuO18udeKxGXh/GzIvNwvmY1/0xxfzeF+rMBVeMQVLn3ImDnz7iQokmPXPmTKYUlaU0ZIyV1qiLDlQE4B/EMnv2bDv99NNt/PjxRbIUFgNioF4YGLLNmicAPxKCleOTJk2ykSNH2qpVqwwPnmi0DY2ADb7YscWw5fiYQ+nHLcXHPN906YNELWw8Ptoe43XWoc/jodOmjgb9la98hfA+Et/vx2fG48aNM7x9jR/eQG6s8ab5+xStoOOhhx4yNGi/4Q+OhQsXepd0MSAG6piBId+scW74zHE07UMOOaTXRXb16tXdTSA8j/6izhh9sL0es5lTK4n5scFlzcHjqFP6PPooEfN6aDNGGdaiHc4R+NiGpoq3kcNmDGzMxxq+HnTUefLJJ23OnDmEJIu58jbk/rxd3T1ghRS8axQ2apT+2c9+ZgsWLNBiswrxrDJioNoMNBX8laoCo40dO7YCVWpbAp8fomnjQhdueHIULvxoCtjx1TAvs/QwBjtt92PEMD5O3Uvo4Y46HuNtrxNDX5ZdDMNcL2O6r4O4x2TFcH48lrmQjNFHOwm4f9igv/nNb3bfIeMPN/y6G2KxO2SXXpfqW97yFvvwhz+cNOQTTjghOscDDjjA7r///uQ4owA5xYAYqBsG1KwzTgWeOY4LXtbb4ni8KZsFmgp2NvBQZ7wS0o9J3Uvo4Y5x6eMcQjvEIO6xjKf5iPfS68z3vrx6iINdbMfpBcZL6Lj7xa9ZoSHjThp7I21s1uExgYsK/30eDiFbDIiBKjCgt8EzSMUzx++4447kh0IOPPBAe/nll/ug8XlluOGBLNxwYfQ7/bWQmAcbVynjc/4+1/ugYwvrh3aIYR4bCOv7PI9hfjJYjn+YC4k7yLAhh99NzlFSEDEgBsRATRhQs85BO5r2z3/+82Tl+F577RVt2r4MFhn5Dc0Cb6WyKflYpXSMwfpserHaHkedONjYsaXViOV4LGvQx3o+jz6Pge79Xsd8aHOulKyBRgz9gQceYEhSDIgBMdAwDKhZl3AqsXJ85cqV3SvH8eznUja89RpbfLTTTjsZHtYSa0jwxXY2N8TYsMK5hPWIi+WEPtje523o2Hw8tInxY8Z8Pu511IPNHF//4YcfhqlNDIgBMTBkGFCzLvFU+5Xj+LpXeBddYrkEjrfXY2+x+1q4o2fzQgPD7psbY5TIZZx1fE6aL8TksT0GemhzHvRTYg4hHn8APfHEE5yepBgQA2JADJiZmnWZLwM27ayV42WWjqatWbMm6i/mfPe73518f5w4NEds/PwWi+Ho800UGNqhZC3UwIIxxPk2NG1+dMDvIOd9ShdrS4oBMSAGxEAPA1oN3sNFvzQ8axlf98paOd6vAeo4mQ05z0NB6vgwGmpqWg3eUKdTByMGdGddqdcAnjPOlePFvu5VqTEHsk4pDTn2ufxAzlVjiQExIAYajQG9DV7hM8qve+GZ43lWjld4+H6Vw90Yn9LFh4Lg7W2+Ze6LqyF7NqSLATEgBqrLgJp1lfjFynHsBx98cPKZcakrx6s0LVNDrhazqisGxIAYqB4DatbV4zapjO/98odCKrFyvNh0McaoUaOSZ1nvtttuhq+FZT38Q3fIxRhVXAyIATFQewbUrAfgHFR65bga8gCcNA0hBsSAGKgjBtSsB/BkbNy40e666y7DyvGPfOQj9sorr6SOHvsdZHzNKu1OOM2fOoACYkAMiAExMGgYULOuwanCyvE777wzeeY4vu41ZswYw/e1seN7yrFfecJ3mdWQa3CyNKQYEANioA4YGFYHcxiyU8DKcfxucnNzs+FOGg051qiHLEE6cDEgBsSAGEgYULPWC0EMiAExIAbEQJ0zoGZd5ydI0xMDYkAMiAExoGat14AYEANiQAyIgTpnQM26zk+QpicGxIAYEANiQM1arwExIAbEgBgQA3XOgJp1nZ8gTU8MiAExIAbEgJq1XgNiQAyIATEgBuqcATXrOj9Bmp4YEANiQAyIATVrvQbEgBgQA2JADNQ5A2rWdX6CND0xIAbEgBgQA2rWeg2IATEgBsSAGKhzBtSs6/wEaXpiQAyIATEgBtSs9RoQA2JADIgBMVDnDKhZ1/kJ0vTEgBgQA2JADKhZ6zUgBsSAGBADYqDOGVCzrvMTpOmJATEgBsSAGFCz1mtADIgBMSAGxECdM6BmXecnSNMTA2JADIgBMaBmrdeAGBADYkAMiIE6Z0DNus5PkKYnBsSAGBADYkDNWq8BMSAGxIAYEAN1zoCadZ2fIE1PDIgBMSAGxICatV4DYkAMiAExIAbqnAE16zo/QZqeGBADYkAMiAE1a70GxIAYEANiQAzUOQNq1nV+gjQ9MSAGxIAYEANq1noNiIGhzkD7ApvR1GRN2A+dY8s3dVhH+0M2Z8Z+1tR0qLUu3zTUGdLxi4GaM7BNzWegCYgBMVBbBpqn2c2F1+2bC861A074kf100Vj7ze9fsqOv+5Odc7P+nq/tydHoYqCTAf1P1CtBDIgBM9vW9jh8mp3cvNyuPPPXNubsT9m+w3V50EtDDNQLA/rfWC9nQvMQA7VmYOR77ciTJ5rt9wGb0LxtrWej8cWAGHAMqFk7MqSKgSHNQMfL9o/nXjdb9Ct7cPVrQ5oKHbwYqDcG1Kzr7YxoPmKgJgxstmcWXm//s8sh1mJP2Mq1WlRWk9OgQcVACgNq1inEyC0GhhIDHc/cZd9YdKD9x2Vn2slT1tktd//Rnll+g81a8KR1DCUidKxioE4ZULOu0xOjaYmBgWBgy/JWG9e0ux12jdm5rcfZHtvsZu874gPWfmWrXfNki82aNsZ0kRiIM6ExxEA2A/rqVjY/ioqBhmZgm4nn2erCee4YR9nE8+6yXi4XlSoGxEBtGNAfzbXhXaOKATEgBsSAGMjNgJp1bqoEFANiQAyIATFQGwbUrGvDu0YVA2JADIgBMZCbATXr3FQJKAbEgBgQA2KgNgyoWdeGd40qBsSAGBADYiA3A2rWuakSUAyIATEgBsRAbRhQs64N7xpVDIgBMSAGxEBuBtSsc1MloBgQA2JADIiB2jCgZl0b3jWqGBADYkAMiIHcDFS0Wb/66qu5BxZQDIgBMSAGxIAYyMdARZv12rVr840qlBgQA2JADIgBMZCbgYo269yjCigGxIAYEANiQAzkZkDNOjdVAooBMSAGxIAYqA0Data14V2jigExIAbEgBjIzYCadW6qBBQDYkAMiAExUBsG1Kxrw7tGFQNiQAyIATGQmwE169xUCSgGxIAYEANioDYMqFnXhneNKgbEgBgQA2IgNwNq1rmpElAMiAExIAbEQG0YULOuDe8aVQyIATEgBsRAbgbUrHNTJaAYEANiQAyIgdowoGZdG941qhgQA2JADIiB3AyoWeemSkAxIAbEgBgQA7VhQM26NrxrVDEgBsSAGBADuRmoaLN+85vfbJMmTco9uIBiQAyIATEgBsRAcQYq2qxHjx5tP/nJT+z73/++jRkzpvjoQogBMSAGxIAYEANFGahos+Zohx9+uP3iF7+wOXPmqGmTFEkxIAbEgBgQA2UyUJVmjbnssMMONnXqVGtra7OZM2eWOT2liQExIAbEgBgQA1Vr1qQWb41/4QtfsGXLltmnP/1puiXFgBgQA2JADIiBnAxskxOXC7Z27Vp75ZVXemHXrFljmzZtSnxf+cpX7JRTTrF58+bZj3/84144GWJADIgBMSAGxECcgYo26yeffNIOOuig6Einn366TZs2zXCnfdlll9knP/lJ+9a3vmVLly6N4uUUA2KgfAZGjRpVfrIyxYAYqDsGKvo2+Ec+8hE7//zzowcZ+t/3vvclK8d/9KMfDelFaHvuuWeULznFQH8YeOMb39ifdOWKATFQZwxUtFnj2C688MI+h3jcccfZ+PHj+/jh+NCHPjSkV46PHTs2youcYkAMiAExIAbIQMWbNd7mxgpwv+22226Ghv3QQw95d7fOleP4updWjnfTIkUMiAExIAbEQMJAxZs1qh599NHJ17agf+c737Hvfve7dskll9js2bOTpr1q1aoo/WjaXDkOqU0MiAExIAbEgBgwayoUCoVqEIGGvM8++9jzzz+fLCrjGLi7Puecc6ylpcWw6Czt7XHg//rXvzb8ynF8lt/c3Ex6JMVARRh4z3veY+985zv71GpqarIq/ZfvM5YcYkAMVI6BqtxZY3pown/84x97NWr4sQjt/vvvt3/5l3+xk046ya699lp74YUXokeEiw1Wjt9xxx165niUITnFgBgQA2JgKDBQtWYN8vbff/8oh3i7G1/jQtPGhh8AmT9/vr366qtRvF85rh8KiVIkpxgQA2JADDQwAxX9nnWpPKFpn3nmmXbiiSfaDTfcYIccckiymhyfeSMWblg5jj8AFi1aZP/5n/9p+F63NjEgBtIZWLBggf3ud7/rBfCLOPHtDSwK1SYGxEB9M1C1z6zLOWx8zv2DH/zAIPFZLt4yT9twF44L0cUXX5wGGRR+fWY9KE7ToJskP7PGR0x45yq24SOmWbNmxULyiQExUGcM1FWzJjdo1vzr/8orr8xchIaL0U9/+lMDbjBuataD8azV/5zZrDFTfMQ0Y8aMPpMOF3/2AcghBsRA3TBQ1c+syz1KLE5buHBhcneNpo0dDTy28YdC7r77bv1QSIwg+YY8A5/4xCfsgAMO6MUDnoWgt797USJDDNQ1A3XZrMkY3gbHD36UsnIcTVuL0MigpBjo/LnaSy+9tJsKNG6sC9EmBsTA4GGgrps1aPQrx0eOHJl8/oave6WtHMfXvX7yk58Ynjmupj14XoiaaXUZmDJlSveDiubMmRNdwFndGai6GBAD/WGg7ps1Dw5Ne/r06clDVuDDynEsMEtr2lg5/l//9V+GC9OYMWNYRlIMDFkGsK6j2MLNIUuODlwM1DkDdbnALA9nXDm+ZMmSpCEP1pXjWmCW52wLk8UAfmHrTW96k0HipzF33HHH5PPo2NcfsSBTn1VnsamYGKhPBgZtsyadfuU4nj+e9iAW4Otx5biaNc+kZBYDbMg77bRT0ozxkRB8arxZrCkmBhqHgUHfrHkq8Mxx/FAIVpIXe+b4M888Y9dff32yeI35tZJq1rVivv7GLbUhP/LII8nz92N30PV3dJqRGBAD/WGgYZo1/GA6CgAACk9JREFUSMDn17/85S/t8ssvT37dC7/clXXngR8KwZPQkFOrTc26VszXZlzcGWPH29VoznhgCeSIESNKnhAWWp511lnJL9thAVnWj+KUXFwJYkAM1BUDDdWsySyb9gknnJBcyE477bTM1a+//e1v7eqrr7alS5eyxIBJNesBo3rABqpkQ86aNBZY4jXOberUqfbFL37RDj744MzXO/GSYkAMDB4GGrJZk358Rn3rrbcmT3DCM5DTnjlO/M9+9rMBf+a4mjXZH1ySC7p23XXX5M6YnyGXc4dc7pHjbfD3v//90XT84l3W+o1okpxiQAzULQMN3azJ+tq1a+2aa64xrBzHwyHwlmHahrty/FAIfnN7IDY164FgubwxYg0Znw8P9GfEeP2+8sor9uijj9qmTZsSiYWV+OMytuHpZPhVO21iQAw0DgMN16w72pfbnQ/dZwvOPt/m20W2eMWlNnlk59fJcYHDIrT169cX/b7pQK0cV7Ou7X+mt7zlLcmdMb/yxGY80A0Zr01ssYaMt7fxefSECRNs+PDhicTXs/bcc09ramrqJhBPJvv+97+vO+puRqSIgcZhoIGa9WZrX3qjXXjcDWbnfs1mfOxomzx+ZPRM1dPKcTXr6CmqqDPWkPG29TbbDOwvxKIh4w75iSeesHXr1tlTTz2VvNvz8MMPJ08XS2vIWWTgKX3IxzcgrrjiiswFlVl1FBMDYqC+GWiQZt1hm5Zfbcce+4h9bOHl9qVJzZbn0WxYoIOV4y0tLcnvaBdbOT5v3ryKf91Lzbr//0HCrzzhrhN3xgPdkPERytNPP53akNFQ8dY6nnWPO+S99tor+c407pDL3fAjN29/+9ut2CLKcusrTwyIgfpgoDGa9aal1nrsF+3xs9rsxmljcjVq0h+uHD/xxBMz704qvXJczZpnIluGDZkLurL+wMquWF6UDRkfpTz77LO2YsUK+8c//pF8vIKKsYa8yy67ZL6myptJZxY+z+5Ps+/P2MoVA2Jg4BhogGb9mq26abrtc8s7bO4Zu9r9+Ky6fYJNn91qX/3CETZ+eJ577M6nm5Wycvyee+6xyy67zJ588sl+nS016x76+JUnSNwd12tDxjnDZ9z77ruvvfWtbzWsCK9mQ+5hSJoYEANDlYHB36w7VthNR3/Ubtn/69b65U/ZxOZtbNOKW+yMyRfZU+cutDvPm2TDSzi7WFiGt8ZLWTmOB6uU27SHWrNmQ67EQ0FKOK19oDjPzz33nK1ZsyZZYf273/3OXnzxRfvBD36QYGMN+W1ve9uArwTvM3E5xIAYGJIMDP5m/dK9dsG+M81++Cu7YvIuXSex6277NLO5K+fbqeO3L/nkYjEQLtyQuHBn/VBIf1aON2Kz5lee6rkhY+U01irg897dd9+9+w5ZDbnk/ypKEANiYAAYGPTNumPVTXb0Ptfb/ot9szZL85fKKVeO461ONNasRzqiaX/7298uaRHaYG3WbMj+oSD82lOpHPcHH/sOMu+Qw4Y8duzY5O31rHPYn7koVwyIATFQLQYG9rsrVTiKYbvtZfs3r7NH1jxnHbZLsLhsrO2zZylvgvedIO6oseNBKSeddFJyN3b22WdHF/VgsRM+xz7llFOsGivH+86uup56bsh4xwMPBeF3kHmHjAWC+Lz7xhtvrC45qi4GxIAYGEAGBv2dtdlzdu8FR9lJz82yh2+cZnsk68k67KV7v2b7XjHOlvzyVBufb41ZUdq5chyfaU+fPt0qsXK81nfW9fwd5LAhxx4KUvSkCSAGxIAYaAAGGqBZm3U8s8A+e8DXbculP7brTp1gO7Y/ZFdfeL1tPfs6O2/iqIqfJrzdjZXj+MUjPNqx2DPHs1aOD0SzrueGjIV8fKgH7uTVkCv+clVBMSAGGoCBhmjWZh22adWv7YbLzrPz5z9q1jLT5rV+2U6emO/hKOWeRzRtrhzHD4VkPY8Zd+V4Kz1cOV6JZp32HeRaPRSE30EOn9JV2e8gb7b25ffYQ/fdZmefP99s5mJbccVkiz+zrtwzrDwxIAbEQH0w0CDNurZklrJyHE375ptvtiuvvDKZdN5mndaQh+RDQTrabenVF9pxs83OveYz9rGj/jX39+lr+0rR6GJADIiB8hhQsy6Pt2gWfrLwkksuSR6SgSYcrjpGU8fd9Zlnnmm4K8dXw/CTis3NzUm92HeQERjohoy54TvIvEMOn9KFYwsfCjJwX3n6hy1vPcmO/cvRtvDyz9qk5m2j50JOMSAGxEAjMaBmXYWzia974Sc28T1ev3Icz3HGr36tXLmyu5G3t7cnz4kOfwcZd+DV/OUnNuTB9VAQPgP+b3bWw1fZtD3UqKvw8lVJMSAG6pABNesqnZRw5fiBBx5o+IUkbPi60cKFC1NHZrNfunRpKiZPgN9BjjXktO8gD9wdcp4jCDDdT6u7wM7Y9cHks+r25uk2++av2heOGF/Sk+qCyjLFgBgQA3XNgJp1lU8PmvbcuXOTleN+KKwiDxekhdhCoeBTojobcux3kNMacvj2fLRwHTo7H3Rzm+0/7xv25ZMnWfOwl2zFTefY5NOetXOX/bAqK//rkAZNSQyIgSHIgJr1AJx03CkfdNBBvUZCI/3Vr37V/Xk03pa+4IILup9NDTDfLs9qyHwoiP/KE3IHa0PuRVIvo+u78yeZ/XDFpTZ5ZNeX55O77cl2ml1qKyv4nfpeQ8sQA2JADNSYgUH/BLMa81d0eNwt43PqcMN3i2+44QabNWtW8vxxPB0NPr/hzvuxxx7rfkoXGzK+AoWndGW9le7rNIa+2f6+ZrW127jehzNsLzvoUweZfW21rd3UYePZxHujZIkBMSAGBjUDatZVPn0PPPBAr8di+uHwO8h4+3q//fbz7m79S1/6kn32s5/ttoe2sq3tttc4a25fbWv+vtlsZPDjLPuNsz1z/hzq0OZRRy8GxMBgZEDNuspnbcqUKVbss+fnn38++UnO+fPnJ42dU3r99depStowG/nBw+3k5jvtoUeftVPGj+l6DvwmW7vyGZvyqQ/buAo9VlZkiwExIAbqjQFd3urgjOB71HjLG29r//GPf0x+DATTeuqpp+pgdnU0hZEH2dnXHmK/PPM/bN6Kl8xss7Uvvc1ufuTj9s1Pjg9+xKWO5q2piAExIAb6yYAWmPWTwGqlY8EZmvX+++9frSEGad2XbNWv59plM861+e3N1jLzCmv98qdsoh6OMkjPp6YtBsRAHgbUrPOwJIwYEANiQAyIgRoyoLfBa0i+hhYDYkAMiAExkIcBNes8LAkjBsSAGBADYqCGDKhZ15B8DS0GxIAYEANiIA8DatZ5WBJGDIgBMSAGxEANGVCzriH5GloMiAExIAbEQB4G1KzzsCSMGBADYkAMiIEaMqBmXUPyNbQYEANiQAyIgTwMqFnnYUkYMSAGxIAYEAM1ZEDNuobka2gxIAbEgBgQA3kYULPOw5IwYkAMiAExIAZqyICadQ3J19BiQAyIATEgBvIwoGadhyVhxIAYEANiQAzUkIH/DwjMDO2eUr2WAAAAAElFTkSuQmCC"></p>
<p style="text-align: left;">The height of the cuboid, <em>x </em>cm, is equal to the height of the hemisphere.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>x</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the volume of the paperweight.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>1 cm<sup>3</sup> of glass has a mass of 2.56 grams.</p>
<p>Calculate the mass, in grams, of the paperweight.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>3 (cm) <em><strong>(A1) (C1)</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>units are required in part (a)(ii)</strong></p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2} \times \frac{{4\pi \times {{\left( 3 \right)}^3}}}{3} + 3 \times {\left( 6 \right)^2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>4</mn>
<mi>π</mi>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mn>3</mn>
</mfrac>
<mo>+</mo>
<mn>3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span> <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for <strong>their</strong> correct substitution in volume of sphere formula divided by 2, <em><strong>(M1)</strong></em> for adding <strong>their</strong> correctly substituted volume of the cuboid.</p>
<p> </p>
<p>= 165 cm<sup>3 </sup>(164.548…) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></p>
<p><strong>Note:</strong> The answer is 165 cm<sup>3</sup>; the units are required. Follow through from part (a)(i).</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>their 164.548… × 2.56 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for multiplying their part (a)(ii) by 2.56.</p>
<p> </p>
<p>= 421 (g) (421.244…(g)) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a)(ii).</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>Six equilateral triangles, each with side length 3 cm, are arranged to form a hexagon.<br>This is shown in the following diagram.</p>
<p><img src="data:image/png;base64,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"></p>
<p>The vectors <em><strong>p</strong></em> , <em><strong>q</strong></em> and <em><strong>r</strong></em> are shown on the diagram.</p>
<p>Find <em><strong>p</strong></em>•(<em><strong>p</strong></em> + <em><strong>q</strong></em> + <em><strong>r</strong></em>).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><strong>METHOD 1 </strong>(using |<em><strong>p</strong></em>| |2<em><strong>q</strong></em>| cos<em>θ</em>)</p>
<p>finding <em><strong>p</strong></em> + <em><strong>q</strong></em> + <em><strong>r (A1)</strong></em></p>
<p><em>eg </em> 2<em><strong>q</strong></em>, <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKsAAACNCAYAAADIHYoyAAAgAElEQVR4Ae1dB1wURxf/31EsgCV8KvaOvUWwYUFFRVSaGhJFARt2wIKisdeoYIsgWGNULLGhooIFa8QGSuwo2GNDBZF++/1m8QjoAXt3u3u7B+MPb3fmzWvzdm5u5817EoqiKBSXYg2IQANSEfBYzGKxBmgNFBsrh4aQmpqKY6Gh+Oeff3D06FEOKRUN1MXGyuE4rw8IgISS4OKFi1i+bDmHlIoG6mJj5XCcjxw5Cus+vREfHw/ThqYcUioaqIuNlaNx/uOPrdDR1cHnpGRs3/En+tjYcESp6KAtNlaOxrpcOWMkfPiA4yeO4c2bN2jUqBFHlIoOWt2iIyq/ktrZ9YOpaT34rVyJ9PQMGBtX4JcBLaRWPLNyOKilS5fG3j170KxZM5QqVZJDSkUDdfHMyuE4kxn14MGDyMzMRHp6Oojx8llkMhlSUlJgYGDAJ1nOaEmKd7A4063GERNjHerigvlz56BO3Xoa50ddBoqXAepqUMD9pVIpIv/+G82at0APKysEBwcLmNvCWdO6mdV3mS9u340BZBQyJYA+KGRJpIAsExJKBzIdgJIBOhIKkOoiU5YBHUoKSgKAAiQSQEcqRTpFQScrC5SuLpCVRSqhmwVkSCnoZMpA6emCypKBkkqgSxEaEkhkWYBUBzJKBl2ZBFlkKpBKIM2QgdKVQIeSIJOMiUxGE5JIJJBlZkGqT2jIaB50dfToV16ABBQlA4HJdt+QQCqVgMyW8jqJRErDEKMk9aSPHIbUgaIQvGsXEhMTcyzB2XkIrKy6w9nZGTo6Ojn1YrjQijUr2dY8e/YsFi5YiC8pyTCt3xCz58wCBQrEXihigbn8dYjnDrFNYpnEEOhr+l5usBLIcuolNB4JyD8KtEkQBNJsnPQlRWhkD3c2VDZO2kOI1JNOBJ4UGUXDkjsCS9OhcZFGCpnkQSBPk9qFYAeOHT9OG6u+vj5sbW3x4MEDGBoYwKSKCXr16KU2FT4RiN5YExLew83VDSGHD9N6CwwKwqNHD/H+3Tt07NSJT10KkhaZhQcMGIjZs+chNvYe/YNr0KBBmDljpuiMVdRr1vDwcPq1kNxQibVkpKVi1q+zcSS02HEkKysL8+bNxd695PVZI9y4fgPEUEkpX64c7t65LcgHLD+mRG2sHTp0oGdUa2vrHPnSMzNhaGiI0qUMcefO3Zz6onhB1q0uLq606IcOhcDEpFKOGvr07QMPTy98/Pgxp07oF6I2VvL+sPWPrdHHpg927wpG06ZNQNavpLi6DsXo0e5ITU0T+hhwxh9ZApBCHtqFixbi519+yaHVqHFjjB03DiEhh3LqhH4hamOVK/fps6f4yelnbN6yFXWq16Sra9SogRo1qmPDhk1ysCL7uXTJQgwZ7AxjY+M8OrDpbYNHjx7nqRPyjaiNNT0jHdN9fGBpaUnr2NzMDE6Ds9dkpMLX1w9hYccQHR0t5DHglLewsBMwMamOkSNHfkdHX1+PNmCyyyaKQnawxFqCNmygLDp1pDIyMvIVIT09jZo3b26+7dreMH78eCr5S3K+YiYlJVHt2rWjHj58mC+MUBpEO7MmJiXiz23bsXnzFuiSF/f5FD09ffrdJdmbL2rl1atXqFGzJkqXyt8ngfwYdXDsDz9fP8GrR7TGemD/AUyf7g3TeoXveXft2gWurq5IScn+8SX4UWGBwWfPnmPChPGwt7UtFNskL0/o6Ovi0qVLhcJqEkCUxko2ox48uA8bht73Xbt2Q+3atTF39mxN6ppX2kOcB8OsdRvUNy38OA35ZlrttwqbNwv7x6gojXVXcDCqVa2m1OB7TPDA6dOn8Snxk1L9xAgcFR2NSpWrYor3ZMbsS3WkKFu2PJKTBbxcEsrimSkfly5dpOzsbKkXL14w7ZIDd+rUKeq3pUtz7rX14rely6hHj2KVFu+fmH8o58FDqI8fPyrdl48OoppZMzIyMMlrMmb9OgdVqlRhPGvIAbt164asjAytXrs+fBiLV69fok6dunKxGX82adoEzVs0h9swtzyOP4wRcA3IxxPBFo01a9ZQ+/b9pRa6q1evUuMnjKdSU1PVwiPEzgkJCdSA/o5UfHy8yuwlJ3+mJk3yosLCwlTGwVVH0cys5GjI+4T3cHTsr9bza2Zmhsz0DFyOvKwWHiF2Pno0FC5uw1CzZvYunio8li5tQG+mnDoZrkp3TvuIxlhDjx5FrZq1WFHGjJkzEHEmghVcQkJy//491uITlClTDk+exAtJPNo3WVAMKWJmz57d8A/wh4O9g6JmpeuqV69Buz7HPRbPvnhhQu7cvROVTCrRpwgKg2XSbmvXDyNGDMfbt2+ZgPMDw9X6gi28Ce8TKHMzM+r+/XtsoaTxxMbGUpaWllRWloxVvJpAFh8XR5mbm1OvX//LKvntf26jbG37sYpTHWSCXwacPn0Ko9xHwdS0AatPb506dVCrdh2sXbOWVbyaQDZ16lSMGjUSFSv+56/KBh8Df3KCjp4u7ty+wwY6tXEI2liJb+rVa9dyHIjVljYXAuLr+dvSJTgcchC3bt3K1SKuy+PHjqFe/fqc6Iic2/Jd7os/tv0hCKUI2ljX+a9Ds+bNoaenx4myKlasiGPhYThwYD8n+PlAejT0KBYsWMiZjsg2dfUa1XFHAEdgBGusnz9/RvDOHbC3teN0zPV0dOnTBGKMVv/2zVvUrFUbOjrcDmOzJs2xMWgDp+PABDm3UjLhIB+YAwcPYPac+TAw5D70Tbfu3THc1Y0O8ZMPO4KrfvT4EcaNHwfbvn05582iUwekZ2bhypVIzmkVRECwxnrv7j3Y9uN+IIhySLSScsbl4efnW5CuBNVGjp+TSCumDdj94alISF0dXaxc5YutW7YqauatTnDGSpykiR+mhUUH3pRACM2ePRuPH8fjypUrvNJVhdiRI0fQv39/zPDxUaW7Sn30dPXRvEWLAnMj/LVvH7y9p8J5yBDcvMn+j1bejPX58+eIiYnBg4cPEBeX/8v4det+R/KXNNjY9FFJqap2KleuPJYsXggSsVro5dzZCHh4eHC+Vv1WD05OTpg3bz7evXv3bRN9/+j2XUTdiEIFY2OUNiilEEadSt6M9cKFC3D6+Rds2boFQ4YOVcgzCc+4e/dueE9l7oepEJGKlcb/q4DKJpWRlJSsIgbuu0VFRUFHX597QgoolC9fHo4ODvAYPfprbK28QBGXLoAc8V65ahXq16uft5GFO96MlbxY7u/oCM+JHkhKTFLIeoB/AGbO+BUNGzZU2M5HZXcrK8z6dUZO/AE+aDKlERcXh9mzZmHcmLFMu7AO5+nlCcMKxoiIyOtb8fjxY1y4eAldu2afNGadMAkXxgXSb3GS11Dr1/ujZauWWLpoCYhf6bclPS0NHxI/oZ9tv2+beL1v3749UtNSsXatsHa2sjIzMWGCB0aOcke1asqdkmBTgSVLlkRgQCDCw8LyoL1/PxYjRwxHl85d8tSzecOLsR4MCcHbd+9hXL48ws+chIury3cynDhxAqb1lHcY/g4RCxU+06dj9+5d+PDhAwvY2EFBov9lpKfBVsMPs1ya0oYGSHj/Xn6L3r170vkTfvgmkEYOABsX6jgWMO1rbW1NVa1albp46RL1MPb74xbBwcFUv362gjpOEXIohCLO3kIpPjNmqOVUzbYcN27coJ1cVDlepCovJD4pp+XZ02ckTCnl4OCgkM7rN68pc/M21PPnzxW2a7LSx8dHk+RzaEdF36T8/Pxy7oVysX37dsrOzo43djhfBnz4+AHTpnmjW3dLpKSmfPdlcO7cebi5uaFq1arftWm6omXLVti6WfOvslYs/w2dOnbUtDq+o29vb4+UtBQ8fvzouzZOKnh7LBQQSktLo6ZOmUKlp6UraNV81afET1S3bpZUTEyMxpg5cjSUIkuAzMxMjfFQEOFHsY+o6dOnFwTCWhvnM2tBT1iAvz+at2wBPX1uvKoKos2krYxRGRw4cBAhISFMwDmBOX4sFPPnzRNs/P86devAuGJFPH7E/eyqMWONj4vHnr27YW9nz8kgs4W0TJmy+PIl5WsSCrawMsMTGxuLevXqFxjLixkmbqF+bNECxJ2T66IRY01OTsaUqVMxY+ZsOko110Kqi79jRwsMHuyMjAw614q66Bj1j419CB8fH1j3Fn6SChJyNCnpMwID1mdnEGEkofJAGjFWkgvAqltX9LHprTzHGuhBwsBXq14V8xfM44W6TJYFF9ehILtpDVg+zsOFACQcfGBgILb8sRVXrl7lggSNk3djJVFVTp06hZHu7pwJxQVib29vkKULF95E3/J77NhxDOjvhNEi0hE5JhS0IQgnw099Kw5r97wb6/wF8+nof2JLGPY/4/9hzerVCAokX3XclpOnTsHLy5NbIhxgb96sOSQ60jxJ4tgkw6uxpqek4lT4SbT68Uc2ZeANV/kffgDZTiQpe7gqxI2yZAnNeFWxIVNbc3NM9Z7CyQ9SXo11nb8/Zs2aBZNK7B4ZZkPJTHGQmLBTJk8B+ZHIdrlz5w5mzpyJ8eMnsI2aN3wdO3aEro4+Is6cYZ0mb8ZKYlUlfk5Eb4YBgFmXlCWExCvr48cEen3GEkoaDZmtp8+YjpEjRgpyN4+prOT4NnGgDws/ybQLYzjejHXnzmA0aNCIMWNCBpw1ew727A7O12NeFd5v374NCSXRuIukKrwr6lOmjCHevHmjqEnlOl6MddeuXdi5czv69rVRmVEhdSTRXCZN8sauXeylRN++fQc2bND8cWe29Gxl1YOO8/qGxVhZnBvry5cvERAQgN9/94ehoRFbutA4noEDB+Dly1es8EFyqlauYgISdENbirm5OQbYO8JjLHunGjg31vPnL8B5iDPqCcSxmk1jaNKsCfYf2Kc2yt9+E6ZXlbqCDXT6iV4KPH/+Ql1UdH9OjfXLl2RER0dh6BDFBwRZkUCDSGysbRDoH4j9+1ULP5SenobJkyfBtGFDtGolztd5Banf0MgIa/zXISgwsCAwxm2cGqufnx9at26NEiVKMGZITIDktOfBkENYvmI5/v1X+SXB5cuRePLkpaC9qtQdjyZNmuKHH37Ak6dP1UXF3YHBHTt3IPZRHPr21ewBQLU1VAiCUqVKwc93OXbu2FkI5PfN58+dx5YtG/A1efX3AFpSY9PHBj7TpuP1a/XeDnAys7598wa+vqvo2KclS2rnrJrbjtq374iHsQ9BEh8zLadOnqTjeBkZac+PzvxkNzU1RdPmjelvkPxgmNRzYqx/X74MZ+efYWTEfVA1JkLyAUO+QVb6Mct/KpPJMHP2bJANhqJSPD0n4dr1q4iJUT2sEOvGmp6egbDwcHh5ehWVcaDl7Nq1K27fuYuoqMLTxR8OOYRhrq5o07ZtkdERSXa8efNmHDlyVGWZWTfWFcuXwaZ3b0gkrKNWWUg+OpYuXRqLFy3C1q1bCiV3/sIljBo1CpJCIbULgPzYInFwk5IUR+QpTFpWLerJkyc4HnaiSH295VYwiZRSrnx5kJhd+ZWLFy/CoDT7Qcvyoye0eosOFnSUSJBs0UoW1oyVROcY6uIKn+k+IK90imqx6t4d8xbMVxgr6/79B1i2fDlGjR5dVNWDdu3bQQIJVnxd37948RLkj1Fh65zspk2bqRMnjrOFTtR4HG3tqPWB6/PIkJGRQfXo2ZM6feZMnvqiejNw4ADKz28lZWRkRP8x0QNrM2vsw4fo2VP4h9sYPcFqApHAxDu2ByMhISEHE8n+V6KEPrpachdlL4eYCC5qVK9F796R9SvTNSwrxrp50wbUqVtbBCrih8UWrX+Eh8d4BAf/55W17Y8/Ebg+iB8GBEwlNDSU9hPxW+mr9GkCtY319et/ERi0CT///IuAVcQ/a/37DwCJ9k3K3bv3UKlSJVSpUpl/RgRG0bp3b0zymoyqVaoozZmErBWU7pWrw/59++gnpP+AAblqiy+JBvYfOACpRIJ9f+3FdJ8ZaNKkSbFivmrg/ft3cHYejOPHs+O8MjFDtY11+IgRaNSgIShk27ycKDmaS67z+yQ8K2oj9bpSHToRsNhH9nPSZyxYvABNmzXDqJGjQMmyIFMgGXnfSoda/BrdmcCQrzz5LEI+CQz5y91ffp8bVlEd6S+HkeOi9f8VH2mT4yX95XS/haH76khRSq80ZJIsSCgpKPknZPS7dWIHtK8DBVASChKZFJB8pSqlAJmEvtfV0QPxOtuzdy89zCeOHy90uHULhSgEwKJDB7Rq1Yr+KwS0yDVHRl7G7bv/0EeTnZx+KtKv9PIb/IQP//0IzQ9GXk8eKrVKv379MM17GuLj4tTCo42djx07hj93bMf8BQsY7Wxpow4KkunmzZuIjs7+KwhO3qa2sVaoUAHePt44FHJYjrP4E8CePXtQsaIJ9HT1YGZmhvj4J/jy5UuxbnJpYMuWLdgQtIH+y1Wd76XaxkowW3WzwnOmuxD5sqJdDUuXLsmz7dyjZ0/8vvZ37RJSDWkyM9ORlZmF0qVL0X9MULFirIRQW/PWWLfOX2F+JCaMaAsMiY8wZuxYuI8ejZYtW+SIZdmlC27ejCowQ18OsJZfpKamYuJED4WJUAoUnck2FxOYlJRUqnat2tShQ4eYgGstzOnTJykvL0+F8j2Nj6fatTKjkj5/VtheVCqneU+jPD09lBaXtZmVnAjYsHEDgtYHgkQKLKrl1s0YjBkzTqH41WvWhL3TABw5XHTX98+eP6OzTHp4KO/vzJqxktHp3r07HAf0x7796h9PVjjaAq/85/ZtvEt4j/r16+XLKcm5Sk78pqWl5QujzQ37/9pHhzytVaum0mKyaqyE+rBhw3DksOre4EpLIJAOmZkZmDZtKlyGfp+QLjeLJEMfOXYdvPM/v4Hc7dp8TZLgffz0CU2bNlVJTNaNlXDRuXNHRESwH0VOJQl56hQVfRMk/0C9evnPqnJWunbthqCgAFZjZclxC/nz15kz0bCR6vHOODFW2362dGbk+/fuC1l3rPL219698PNbxQhnxYoV4D56LP76q+gsl7Zt20bnQevXry8jHSkC4sRYTSpXxrixYzFmzEhFNLWu7uqVq6hRowYqmzCPO+vi4oKnT59onS4UCfTy5QsEbdyINWt/Bzk4qGrhxFgJMz169ICD40Ds2L5DVd5E0e/+vbtYsGgRHB0dlebXysoK48eP5yQwsdLMcNhh/779WOXrB0MD9Y7mc2as5HTrhAkTcOsWOZqc24+HQ63wjPrTp0/o3bMXpk6ehMqVlfdVJce3yU7O4sWLeeacP3Ivnr9A7INYmJmbqU2UM2OVc1a3Xj1ERl6R32rV5/Ub12HeoT06de6sklzERfK3ZSsQFnYCH5TwPlKJmIY6bdmyGZ0sVdPPtyxzbqwkUsm8hQtx7tzZb2mL/v7c2XPYsrnwOAEFCVq2TBksX7YC2/78syAwUbaRGApxj+Nga2fHCv+cG2uVKlUwwmUYSB4psiesLYXkdP2fsTFIcAt1i2VXS9y5c1urlkvkKM/atb9j1Zo10NNV222aVjHnxkqoOA5wgIVFZ5AAD9pQ0tPSsHTxYnRU8etfkQ5IFpiA9dzn2FJEm4u6iIjT8PKaBCMjQ9bQ82KshNs5c2bhbESE6L2yiFeVu7s77VnVssV/XlXqjohV9x50Op6jR8W/+0e2kt+8fkufsVJXL7n782asZcqUQZmyZXH4kObSoecWXNVrsjNXuUoVuLq5qopCYT8DAwMsWbIEixcuwmcVY0EpRMxzJTl3Rxx5OnfuxDpl3oyVcO7k5ITVa1YjPZ15HFPWJVYT4c3om5jo4aEmFsXd69SpSzsChRwRr1fWk6dPEBp6COZt2igWUo1aXo21evXqINttYv2qu337Du2IwWWGRLLEIG6GGenidLMMOXAQYWGnYGjI3lpVbt+8Gish6jVpMvbu3SOnL5pPsg7z9p4KV9eCvarUFYgMcvPmzbH36xFldfHx2T8x8RPef/xE888FXd6NlQjRtl073LhReNBdLgRWFSdJOleiREnUrVu4V5WqNOT9unTpTDuyv37zWl4lis8ZPjPRuGFDznjViLE6/eSEOXNn4/69e5wJxibiyMhIHDwYgo0bN7KJNl9cVatWxYgRI+Hm5obERNUC7+aLnKMGcv4OUgns7NnZAFDIptIHYVjqEBJymLLp1ZuiZDKWMHKHZsH8BdSrf//ljkA+mLdt+4MKDg7Op1U41fHx8VTPXj2ohIQETpnSyMxKnpq+ffugVx8bbNsm7G1GEgDYwMhQI2nnf/llEKKvXxf8zh+J6eW7wo/ziDMaM1bixDFxwnhE34xSOOMLoTLx0yfa1dGey6+2AgTV1dVFy9atsWbNmgKgNNv06tUrxMfFq3xURRnuNWasciZJjqSoqOvyW0F93oiKQhfLTqhdS3OxZ21tbbF3718g55eEWMh7857du/HCmsaNtW+ffpgzdz6uXb/Gi8DMiVAgGQAD/DW7X08cZebMmYPdu3cxZ50nyG3b/sC7t+/Qw9qaF4oaN9Zq1ath7JixcB81usAsJ7xoIxcRkhzXxMSEk5fbucgwuiTr+1u3YkBO0AqlXL9+HRvXr8f69QHQ19fnhS2NGyuR0tq6FzpaWOCKQJy0U9PSsD4wCOZtzHkZBCZErLpbYfOWzUxAeYG5EhmJEe5joaurxws9QkQQxkoYmTN3Dk6fOa10nHm2NUW8qka7u2PSJC+0bNmSbfQq47PqYYXTJ8/gxPFwlXGw1ZH4drx+8wZDXIawhZIRHsEYK0nzTc5tnT2r2XgD58+fo0NVOjvzOxCFjRbxWps161csXDxP48uliR4TYGFhwXuGRMEYKxmswYMHYcVyX6SkaC6O6fXrN+DhMbEw29FIe5OmTWFl1ROhoUc0Qp8QPXnyFE6Fn0T7du1450FQxlq/fn30su6FKVO9NeJGeCvmFj5+/IiqVZXPJMLXyE2dMgWRl68hKyuLL5I5dF6+eolVq1Yi9NhxGGog9bygjJVoZcKEiUhK/MS7GyFJsObp6YGx4xRHAMwZMQ1fkFdZP7ZuhT17dvPOyf79B/DrrJkgk4omiuCMlSghIGA9om+qnpdeWUWSxMDTpk/HTwOdUEWF8//K0lMXnuRx2LxpC3bt4u/d69s3b/H4USzatW2vLvsq9xeksZIjHrVr1cQxBulmVJY8V8dDhw7CoFRpjBZJAmCinw2bNmLd72tBtjv5KGPGjik0QiLXfAjSWInQbdq0wcoVy7mWn8b/8GEs/eqMF2IsEalVsyZ+GTQYFy9xf2L41asX+PffV2jUuDFL3KuGRrDG2rBhQ/Tu24/zr7pbt26hXLmynHsMqTY8BfciCfOuX7nOeaysXbv20Eszvnaq8pNasMYqlUrh5emJa1e5Cz309OlTdOrUEQ4O/fPTj6DrS+jro8WPLbDOfx1nfJL8ZnFx8WjWrBlnNJgiFqyxygWoXacebt8m0UrYL+sD12PQoMEgUWPEWqx79cKRkCMgDx4XJSgoCD179eACtfI4OXXtZgH58+fPKete1tStWzEsYPsPxbVr1yg3t+FUenrGf5UivQoLO0H17duX+vDhA6sSBAVuoNzc3KjMzExW8aqKjOzFC77s2LGDMmvdmsrIYM+wxo0bR6WmfBG87EwZXLp0GbVp02am4IXCXb9xg2rbrh2VlpZWKCxfAIJfBpDvikGDBqF9RwtcuHBe+a8OBT2Is4pUR4oSJUspaBVnFUm+EfsoljXm/754AdO8vXlz/2PCuCiMlQgyw8cHFy9cYiJTgTAkR9foMaMxzG1YgXBibKxZoybOnVP/VVZy8me8T/gIBwcHQalBNMZqUsmEng2PhYaqpcDw8HDUq1tfUO5/agmUq/PAgQMw3WcKiLGpWmRZWXBxHYZu3SxVRcFZP9EYK9GAg4M9/AMD1HLiuHP3DuvR7TgbHSUREzfLzp0sEXFW9eXSmTNncPHCWTpXl5LkOQcXlbE2aNAQlp26gngeqeJ1FHUjCklJn1GtWjXOFaspAjNm+OBsxBnIZMp7ZZGt29WrViMi4izIlq7QiqiMlRzfnjxlEuKfPsWJE8eV0uXnz58xZdpkDB+ufWvV3IogTtqNmzTG4cPK+7weOHAA06ZOA5kUhFhEZaxyBW4ICsKVK8xPwyYlJcLD0xMuQ1xRo3oNORqt/bS3s8fGjZuwS4mUm2RT4emzZ7Do0lGwehGlsRobG8OksgkuXbrMSLGHDh1CWSMDDB06lBG82IHKlSuHNatXwdd3Bd5/eMdInAkenvj5p58YwWoKSJTGSpTVpVMnLFo0n5He4uKeYOaceYxgtQWodp06GDHKHWdPnytUpONhYcjKTAM5NiPkIlpjJQlrO3exxLDhwwo8AhN9kyQANoJxuXJCHgdOeCNRCCOvRBaYLv7169dYvXIlfH1XQk+Pv2PVqggsWmMlP7bIDouejg7OnVc8e8THx4E4evTvL06vKlUGNHcffX09NG7SBIGBgbmr81yvXbsWc+fNRQNT0zz1QrwRrbHKlbls+Qpcu3pVfpvnMyAgAA4D7LX6VVUegRXc2NvZYeeOnXjzVnFg4sSkZLRt01ZBT+FVid5Yy5YtC0gkuHHjRh7tEgMm71T9ljNLq56nsxbdEP14T/OGx0SvPMHdZDIZAvwDBblTla/6+fKY4ZJOTEwM1bJFCyoz6z9XNjc3FyorK4tLsqLC7bdyFRUUFJTD8+XLl6m2bdvk3IvhQvQzK3kKmzZtCjMzM1y9mv3uNSUlFQYGRiCnDYpLtgbGjRuH5y9e5Kjj6rWrmOo9LedeDBdaM5qLlyxBeFg4UlPTMGLEcLiPdheD/nnjUV9Plz5mfvXaFRAXyXfv3qG/oyNv9NkgxE4GWDY4URNHhQoVoKMjRadOFnBw7A/T+g3o8OYUKEgoglxCJ/KlKHqJC1JFaiSQgMCQkv1/doOU+lpPARQBlGOQAPp6JehZOwc+u1nQ/5NZicwUOYwAAACISURBVPzY+mXQIJQxKo8pUz0Fza8i5iRkraKoQYx1Dx88gFXPHmjUqBEdB0BGyYipQvLVQmnzI9J+NT4iIzFkYozZppxtoMSASR+6ngJkuY2VhF6USGkjF5OOiAhkWRQVHQ1DA0P8Hfk3SpYsKSYRyJhoj7GKSvPFzCqtAa1ZsyoteXEH0Wng/65KasgnZrAhAAAAAElFTkSuQmCC"></p>
<p>| <em><strong>p</strong></em> + <em><strong>q</strong></em> + <em><strong>r </strong></em>| = 2 × 3 (= 6) (seen anywhere) <em><strong>A1</strong></em></p>
<p>correct angle between <em><strong>p</strong></em> and <em><strong>q</strong></em> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\pi }{3}"> <mfrac> <mi>π</mi> <mn>3</mn> </mfrac> </math></span> (accept 60°)</p>
<p>substitution of <strong>their</strong> values <em><strong>(M1)</strong></em></p>
<p><em>eg</em> 3 × 6 × cos<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{\pi }{3}} \right)"> <mrow> <mo>(</mo> <mrow> <mfrac> <mi>π</mi> <mn>3</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>correct value for cos<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{\pi }{3}} \right)"> <mrow> <mo>(</mo> <mrow> <mfrac> <mi>π</mi> <mn>3</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2},\,\,\,3 \times 6 \times \frac{1}{2}"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>3</mn> <mo>×</mo> <mn>6</mn> <mo>×</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math></span></p>
<p><em><strong>p</strong></em>•(<em><strong>p</strong></em> + <em><strong>q</strong></em> + <em><strong>r</strong></em>) = 9 <em><strong> A1 N3</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong> (scalar product using distributive law)</p>
<p>correct expression for scalar distribution <em><strong>(A1)</strong></em></p>
<p>eg <em><strong>p</strong></em>• <em><strong>p</strong></em> + <em><strong>p</strong></em>•<em><strong>q</strong></em> + <em><strong>p</strong></em>•<em><strong>r</strong></em></p>
<p>three correct angles between the vector pairs (seen anywhere) <em><strong>(A2)</strong></em></p>
<p><em>eg </em> 0° between <em><strong>p</strong></em> and <em><strong>p</strong></em>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\pi }{3}"> <mfrac> <mi>π</mi> <mn>3</mn> </mfrac> </math></span> between <em><strong>p</strong></em> and <em><strong>q</strong></em>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2\pi }}{3}"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mn>3</mn> </mfrac> </math></span> between <em><strong>p</strong></em> and <em><strong>r</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>A1</strong> </em>for only two correct angles.</p>
<p>substitution of <strong>their</strong> values <em><strong>(M1)</strong></em></p>
<p><em>eg </em> 3.3.cos0 +3.3.cos<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\pi }{3}"> <mfrac> <mi>π</mi> <mn>3</mn> </mfrac> </math></span> + 3.3.cos120</p>
<p>one correct value for cos0, cos<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{\pi }{3}} \right)"> <mrow> <mo>(</mo> <mrow> <mfrac> <mi>π</mi> <mn>3</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> or cos<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{2\pi }{3}} \right)"> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mn>3</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> (seen anywhere) <em><strong>A1</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2},\,\,\,3 \times 6 \times \frac{1}{2}"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>3</mn> <mo>×</mo> <mn>6</mn> <mo>×</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math></span></p>
<p><em><strong>p</strong></em>•(<em><strong>p</strong></em> + <em><strong>q</strong></em> + <em><strong>r</strong></em>) = 9 <em><strong> A1 N3</strong></em></p>
<p> </p>
<p><strong>METHOD 3</strong> (scalar product using relative position vectors)</p>
<p>valid attempt to find one component of <em><strong>p</strong></em> or <em><strong>r</strong></em> <em><strong>(M1)</strong></em></p>
<p><em>eg </em> sin 60 = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{x}{3}"> <mfrac> <mi>x</mi> <mn>3</mn> </mfrac> </math></span>, cos 60 = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{x}{3}"> <mfrac> <mi>x</mi> <mn>3</mn> </mfrac> </math></span>, one correct value <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{2},\,\,\frac{{3\sqrt 3 }}{2},\,\,\frac{{ - 3\sqrt 3 }}{2}"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mfrac> <mrow> <mn>3</mn> <msqrt> <mn>3</mn> </msqrt> </mrow> <mn>2</mn> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mfrac> <mrow> <mo>−</mo> <mn>3</mn> <msqrt> <mn>3</mn> </msqrt> </mrow> <mn>2</mn> </mfrac> </math></span></p>
<p>one correct vector (two or three dimensions) (seen anywhere) <em><strong>A1</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = \left( \begin{gathered} \,\,\,\frac{3}{2} \hfill \\ \frac{{3\sqrt 3 }}{2} \hfill \\ \end{gathered} \right),\,\,q = \left( \begin{gathered} 3 \hfill \\ 0 \hfill \\ \end{gathered} \right),\,\,r = \left( \begin{gathered} \,\,\,\,\frac{3}{2} \hfill \\ - \frac{{3\sqrt 3 }}{2} \hfill \\ \,\,\,\,0 \hfill \\ \end{gathered} \right)"> <mi>p</mi> <mo>=</mo> <mrow> <mo>(</mo> <mtable rowspacing="3pt" columnspacing="1em" displaystyle="true"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <mn>3</mn> <msqrt> <mn>3</mn> </msqrt> </mrow> <mn>2</mn> </mfrac> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mi>q</mi> <mo>=</mo> <mrow> <mo>(</mo> <mtable rowspacing="3pt" columnspacing="1em" displaystyle="true"> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mi>r</mi> <mo>=</mo> <mrow> <mo>(</mo> <mtable rowspacing="3pt" columnspacing="1em" displaystyle="true"> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mfrac> <mrow> <mn>3</mn> <msqrt> <mn>3</mn> </msqrt> </mrow> <mn>2</mn> </mfrac> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </math></span></p>
<p>three correct vectors <em><strong>p</strong></em> + <em><strong>q</strong></em> + <em><strong>r </strong></em>= 2<em><strong>q</strong></em> <em><strong>(A1)</strong></em></p>
<p><em><strong>p</strong></em> + <em><strong>q</strong></em> + <em><strong>r </strong></em>= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( \begin{gathered} 6 \hfill \\ 0 \hfill \\ \end{gathered} \right)"> <mrow> <mo>(</mo> <mtable rowspacing="3pt" columnspacing="1em" displaystyle="true"> <mtr> <mtd> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( \begin{gathered} 6 \hfill \\ 0 \hfill \\ 0 \hfill \\ \end{gathered} \right)"> <mrow> <mo>(</mo> <mtable rowspacing="3pt" columnspacing="1em" displaystyle="true"> <mtr> <mtd> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </math></span> (seen anywhere, including scalar product) <em><strong>(A1)</strong></em></p>
<p>correct working <em><strong>(A1)</strong></em><br><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{3}{2} \times 6} \right) + \left( {\frac{{3\sqrt 3 }}{2} \times 0} \right),\,\,9 + 0 + 0"> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mo>×</mo> <mn>6</mn> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>3</mn> <msqrt> <mn>3</mn> </msqrt> </mrow> <mn>2</mn> </mfrac> <mo>×</mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>9</mn> <mo>+</mo> <mn>0</mn> <mo>+</mo> <mn>0</mn> </math></span></p>
<p><em><strong>p</strong></em>•(<em><strong>p</strong></em> + <em><strong>q</strong></em> + <em><strong>r</strong></em>) = 9 <em><strong> A1 N3</strong></em></p>
<p><strong><em>[6 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>A line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> passes through points <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}( - 3,{\text{ }}4,{\text{ }}2)">
<mrow>
<mtext>A</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mo>−<!-- − --></mo>
<mn>3</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>4</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>2</mn>
<mo stretchy="false">)</mo>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}( - 1,{\text{ }}3,{\text{ }}3)">
<mrow>
<mtext>B</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mo>−<!-- − --></mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>3</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>3</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<div class="specification">
<p>The line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> also passes through the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{C}}(3,{\text{ }}1,{\text{ }}p)">
<mrow>
<mtext>C</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>p</mi>
<mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{AB}}} = \left( {\begin{array}{*{20}{c}} 2 \\ { - 1} \\ 1 \end{array}} \right)"> <mover> <mrow> <mtext>AB</mtext> </mrow> <mo>→</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find a vector equation for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The point D has coordinates <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="({q^2},{\text{ }}0,{\text{ }}q)"> <mo stretchy="false">(</mo> <mrow> <msup> <mi>q</mi> <mn>2</mn> </msup> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>q</mi> <mo stretchy="false">)</mo> </math></span>. Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{DC}}} "> <mover> <mrow> <mtext>DC</mtext> </mrow> <mo>→</mo> </mover> </math></span> is perpendicular to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span>, find the possible values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q"> <mi>q</mi> </math></span>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>correct approach <strong><em>A1</em></strong></p>
<p> </p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 1} \\ 3 \\ 3 \end{array}} \right) - \left( {\begin{array}{*{20}{c}} { - 3} \\ 4 \\ 2 \end{array}} \right),{\text{ }}\left( {\begin{array}{*{20}{c}} 3 \\ { - 4} \\ { - 2} \end{array}} \right) + \left( {\begin{array}{*{20}{c}} { - 1} \\ 3 \\ 3 \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{AB}}} = \left( {\begin{array}{*{20}{c}} 2 \\ { - 1} \\ 1 \end{array}} \right)"> <mover> <mrow> <mtext>AB</mtext> </mrow> <mo>→</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span> <strong><em>AG N0</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>any correct equation in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = a + tb"> <mi>r</mi> <mo>=</mo> <mi>a</mi> <mo>+</mo> <mi>t</mi> <mi>b</mi> </math></span> (any parameter for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span>)</p>
<p> </p>
<p>where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 3} \\ 4 \\ 2 \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 1} \\ 3 \\ 3 \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b"> <mi>b</mi> </math></span> is a scalar multiple of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 2 \\ { - 1} \\ 1 \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span> <strong><em>A2 N2</em></strong></p>
<p> </p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \left( {\begin{array}{*{20}{c}} { - 3} \\ 4 \\ 2 \end{array}} \right) + t\left( {\begin{array}{*{20}{c}} 2 \\ { - 1} \\ 1 \end{array}} \right),{\text{ }}(x,{\text{ }}y,{\text{ }}z) = ( - 1,{\text{ }}3,{\text{ }}3) + s( - 2,{\text{ }}1,{\text{ }} - 1),{\text{ }}r = \left( {\begin{array}{*{20}{c}} { - 3 + 2t} \\ {4 - t} \\ {2 + t} \end{array}} \right)"> <mi>r</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>t</mi> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>y</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>3</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>3</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mi>s</mi> <mo stretchy="false">(</mo> <mo>−</mo> <mn>2</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>1</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>r</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mo>−</mo> <mn>3</mn> <mo>+</mo> <mn>2</mn> <mi>t</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>4</mn> <mo>−</mo> <mi>t</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mo>+</mo> <mi>t</mi> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1 </em></strong>for the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a + tb"> <mi>a</mi> <mo>+</mo> <mi>t</mi> <mi>b</mi> </math></span>, <strong>A1</strong> for the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L = a + tb"> <mi>L</mi> <mo>=</mo> <mi>a</mi> <mo>+</mo> <mi>t</mi> <mi>b</mi> </math></span>, <strong>A0</strong> for the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = b + ta"> <mi>r</mi> <mo>=</mo> <mi>b</mi> <mo>+</mo> <mi>t</mi> <mi>a</mi> </math></span>.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1 – finding value of parameter</strong></p>
<p>valid approach <strong><em>(M1)</em></strong></p>
<p> </p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 3} \\ 4 \\ 2 \end{array}} \right) + t\left( {\begin{array}{*{20}{c}} 2 \\ { - 1} \\ 1 \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 3 \\ 1 \\ p \end{array}} \right),{\text{ }}( - 1,{\text{ }}3,{\text{ }}3) + s( - 2,{\text{ }}1,{\text{ }} - 1) = (3,{\text{ }}1,{\text{ }}p)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>t</mi> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>p</mi> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>3</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>3</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mi>s</mi> <mo stretchy="false">(</mo> <mo>−</mo> <mn>2</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>1</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mn>3</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>1</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>p</mi> <mo stretchy="false">)</mo> </math></span></p>
<p> </p>
<p>one correct equation (not involving <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>) <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 3 + 2t = 3,{\text{ }} - 1 - 2s = 3,{\text{ }}4 - t = 1,{\text{ }}3 + s = 1"> <mo>−</mo> <mn>3</mn> <mo>+</mo> <mn>2</mn> <mi>t</mi> <mo>=</mo> <mn>3</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo>−</mo> <mn>1</mn> <mo>−</mo> <mn>2</mn> <mi>s</mi> <mo>=</mo> <mn>3</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>4</mn> <mo>−</mo> <mi>t</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>3</mn> <mo>+</mo> <mi>s</mi> <mo>=</mo> <mn>1</mn> </math></span></p>
<p>correct parameter from their equation (may be seen in substitution) <strong><em>A1</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 3,{\text{ }}s = - 2"> <mi>t</mi> <mo>=</mo> <mn>3</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>s</mi> <mo>=</mo> <mo>−</mo> <mn>2</mn> </math></span></p>
<p>correct substitution <strong><em>(A1)</em></strong></p>
<p> </p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 3} \\ 4 \\ 2 \end{array}} \right) + 3\left( {\begin{array}{*{20}{c}} 2 \\ { - 1} \\ 1 \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 3 \\ 1 \\ p \end{array}} \right),{\text{ }}3 - ( - 2)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>3</mn> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>p</mi> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>3</mn> <mo>−</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> </math></span></p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 5\,\,\,\,\,\left( {{\text{accept }}\left( {\begin{array}{*{20}{c}} 3 \\ 1 \\ 5 \end{array}} \right)} \right)"> <mi>p</mi> <mo>=</mo> <mn>5</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mrow> <mtext>accept </mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>5</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> <strong><em>A1 N2</em></strong></p>
<p> </p>
<p><strong>METHOD 2 – eliminating parameter</strong></p>
<p>valid approach <strong><em>(M1)</em></strong></p>
<p> </p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 3} \\ 4 \\ 2 \end{array}} \right) + t\left( {\begin{array}{*{20}{c}} 2 \\ { - 1} \\ 1 \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 3 \\ 1 \\ p \end{array}} \right),{\text{ }}( - 1,{\text{ }}3,{\text{ }}3) + s( - 2,{\text{ }}1,{\text{ }} - 1) = (3,{\text{ }}1,{\text{ }}p)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>t</mi> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>p</mi> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>3</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>3</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mi>s</mi> <mo stretchy="false">(</mo> <mo>−</mo> <mn>2</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>1</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mn>3</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>1</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>p</mi> <mo stretchy="false">)</mo> </math></span></p>
<p> </p>
<p>one correct equation (not involving <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>) <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 3 + 2t = 3,{\text{ }} - 1 - 2s = 3,{\text{ }}4 - t = 1,{\text{ }}3 + s = 1"> <mo>−</mo> <mn>3</mn> <mo>+</mo> <mn>2</mn> <mi>t</mi> <mo>=</mo> <mn>3</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo>−</mo> <mn>1</mn> <mo>−</mo> <mn>2</mn> <mi>s</mi> <mo>=</mo> <mn>3</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>4</mn> <mo>−</mo> <mi>t</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>3</mn> <mo>+</mo> <mi>s</mi> <mo>=</mo> <mn>1</mn> </math></span></p>
<p>correct equation (with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>) <strong><em>A1</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2 + t = p,{\text{ }}3 - s = p"> <mn>2</mn> <mo>+</mo> <mi>t</mi> <mo>=</mo> <mi>p</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>3</mn> <mo>−</mo> <mi>s</mi> <mo>=</mo> <mi>p</mi> </math></span></p>
<p>correct working to solve for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span> <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7 = 2p - 3,{\text{ }}6 = 1 + p"> <mn>7</mn> <mo>=</mo> <mn>2</mn> <mi>p</mi> <mo>−</mo> <mn>3</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>6</mn> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mi>p</mi> </math></span></p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 5\,\,\,\,\,\left( {{\text{accept }}\left( {\begin{array}{*{20}{c}} 3 \\ 1 \\ 5 \end{array}} \right)} \right)"> <mi>p</mi> <mo>=</mo> <mn>5</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mrow> <mtext>accept </mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>5</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> <strong><em>A1 N2</em></strong></p>
<p> </p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{DC}}} "> <mover> <mrow> <mtext>DC</mtext> </mrow> <mo>→</mo> </mover> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{CD}}} "> <mover> <mrow> <mtext>CD</mtext> </mrow> <mo>→</mo> </mover> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 3 \\ 1 \\ 5 \end{array}} \right) - \left( {\begin{array}{*{20}{c}} {{q^2}} \\ 0 \\ q \end{array}} \right),{\text{ }}\left( {\begin{array}{*{20}{c}} {{q^2}} \\ 0 \\ q \end{array}} \right) - \left( {\begin{array}{*{20}{c}} 3 \\ 1 \\ 5 \end{array}} \right),{\text{ }}\left( {\begin{array}{*{20}{c}} {{q^2}} \\ 0 \\ q \end{array}} \right) - \left( {\begin{array}{*{20}{c}} 3 \\ 1 \\ p \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>5</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mrow> <msup> <mi>q</mi> <mn>2</mn> </msup> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>q</mi> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mrow> <msup> <mi>q</mi> <mn>2</mn> </msup> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>q</mi> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>5</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mrow> <msup> <mi>q</mi> <mn>2</mn> </msup> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>q</mi> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>p</mi> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p> </p>
<p>correct vector for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{DC}}} "> <mover> <mrow> <mtext>DC</mtext> </mrow> <mo>→</mo> </mover> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{CD}}} "> <mover> <mrow> <mtext>CD</mtext> </mrow> <mo>→</mo> </mover> </math></span> (may be seen in scalar product) <strong><em>A1</em></strong></p>
<p> </p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} {3 - {q^2}} \\ 1 \\ {5 - q} \end{array}} \right),{\text{ }}\left( {\begin{array}{*{20}{c}} {{q^2} - 3} \\ { - 1} \\ {q - 5} \end{array}} \right),{\text{ }}\left( {\begin{array}{*{20}{c}} {3 - {q^2}} \\ 1 \\ {p - q} \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mn>3</mn> <mo>−</mo> <mrow> <msup> <mi>q</mi> <mn>2</mn> </msup> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>5</mn> <mo>−</mo> <mi>q</mi> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mrow> <msup> <mi>q</mi> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mn>3</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>q</mi> <mo>−</mo> <mn>5</mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mn>3</mn> <mo>−</mo> <mrow> <msup> <mi>q</mi> <mn>2</mn> </msup> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>p</mi> <mo>−</mo> <mi>q</mi> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p> </p>
<p>recognizing scalar product of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{DC}}} "> <mover> <mrow> <mtext>DC</mtext> </mrow> <mo>→</mo> </mover> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{CD}}} "> <mover> <mrow> <mtext>CD</mtext> </mrow> <mo>→</mo> </mover> </math></span> with direction vector of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span> is zero (seen anywhere) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} {3 - {q^2}} \\ 1 \\ {p - q} \end{array}} \right) \bullet \left( {\begin{array}{*{20}{c}} 2 \\ { - 1} \\ 1 \end{array}} \right) = 0,{\text{ }}\overrightarrow {{\text{DC}}} \bullet \overrightarrow {{\text{AC}}} = 0,{\text{ }}\left( {\begin{array}{*{20}{c}} {3 - {q^2}} \\ 1 \\ {5 - q} \end{array}} \right) \bullet \left( {\begin{array}{*{20}{c}} 2 \\ { - 1} \\ 1 \end{array}} \right) = 0"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mn>3</mn> <mo>−</mo> <mrow> <msup> <mi>q</mi> <mn>2</mn> </msup> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>p</mi> <mo>−</mo> <mi>q</mi> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>∙</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mover> <mrow> <mtext>DC</mtext> </mrow> <mo>→</mo> </mover> <mo>∙</mo> <mover> <mrow> <mtext>AC</mtext> </mrow> <mo>→</mo> </mover> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mn>3</mn> <mo>−</mo> <mrow> <msup> <mi>q</mi> <mn>2</mn> </msup> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>5</mn> <mo>−</mo> <mi>q</mi> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>∙</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </math></span></p>
<p> </p>
<p>correct scalar product in terms of only <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q"> <mi>q</mi> </math></span> <strong><em>A1</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6 - 2{q^2} - 1 + 5 - q,{\text{ }}2{q^2} + q - 10 = 0,{\text{ }}2(3 - {q^2}) - 1 + 5 - q"> <mn>6</mn> <mo>−</mo> <mn>2</mn> <mrow> <msup> <mi>q</mi> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mn>1</mn> <mo>+</mo> <mn>5</mn> <mo>−</mo> <mi>q</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>2</mn> <mrow> <msup> <mi>q</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mi>q</mi> <mo>−</mo> <mn>10</mn> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>2</mn> <mo stretchy="false">(</mo> <mn>3</mn> <mo>−</mo> <mrow> <msup> <mi>q</mi> <mn>2</mn> </msup> </mrow> <mo stretchy="false">)</mo> <mo>−</mo> <mn>1</mn> <mo>+</mo> <mn>5</mn> <mo>−</mo> <mi>q</mi> </math></span></p>
<p>correct working to solve quadratic <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(2q + 5)(q - 2),{\text{ }}\frac{{ - 1 \pm \sqrt {1 - 4(2)( - 10)} }}{{2(2)}}"> <mo stretchy="false">(</mo> <mn>2</mn> <mi>q</mi> <mo>+</mo> <mn>5</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>q</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mrow> <mo>−</mo> <mn>1</mn> <mo>±</mo> <msqrt> <mn>1</mn> <mo>−</mo> <mn>4</mn> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mn>10</mn> <mo stretchy="false">)</mo> </msqrt> </mrow> <mrow> <mn>2</mn> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </mfrac> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = - \frac{5}{2},{\text{ }}2"> <mi>q</mi> <mo>=</mo> <mo>−</mo> <mfrac> <mn>5</mn> <mn>2</mn> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>2</mn> </math></span> <strong><em>A1A1 N3</em></strong></p>
<p> </p>
<p><strong><em>[7 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the vectors <em><strong>a</strong></em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 0 \\ 3 \\ p \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>p</mi>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span> and <em><strong>b</strong></em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 0 \\ 6 \\ {18} \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>6</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>18</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> for which <em><strong>a</strong></em> and <em><strong>b</strong></em> are</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>parallel.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>perpendicular.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg <strong>b</strong></em> = 2<em><strong>a</strong></em>, a = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span><em><strong>b</strong></em>, cos <em>θ </em>= 1, <em><strong>a</strong></em>•<em><strong>b</strong></em> = −|<em><strong>a</strong></em>||<em><strong>b</strong></em>|, 2<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span> = 18</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span> = 9 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of scalar product<em> <strong>(M1)</strong></em></p>
<p><em>eg </em><em><strong>a</strong></em>•<em><strong>b</strong></em>, (0)(0) + (3)(6) + <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>(18)</p>
<p>recognizing <em><strong>a</strong></em>•<em><strong>b</strong></em> = 0 (seen anywhere) <em><strong>(M1)</strong></em></p>
<p>correct working<strong> (A1)</strong></p>
<p><em>eg</em> 18 + 18<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span> = 0, 18<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span> = −18 <em><strong>(A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span> = −1 <em><strong>A1 N3</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Yao drains the oil from his motorbike into two identical cuboids with rectangular bases of width <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10">
<mn>10</mn>
</math></span> cm and length <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="40">
<mn>40</mn>
</math></span> cm. The height of each cuboid is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="5">
<mn>5</mn>
</math></span> cm.</p>
<p>The oil from the motorbike fills the first cuboid completely and the second cuboid to a height of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2">
<mn>2</mn>
</math></span> cm. The information is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAhgAAACcCAYAAAA9OtL3AAAgAElEQVR4Ae2df6xcZbnvx7i1iqT4IxszKNS4BbSS1rSFCFa744aKEA/QuCOltmAvpp6aA3J7ijRys0UivcCBpkoLcmzo8dzQdEvjvbmXeyynTf8QTnfoNQazaTEx0djuxmByKd3NFc4+k+fmu/Y8M++sWT/etdY7M+vHd5LJWrN+vO+7vut9nvez3vddz9SEHypABagAFaACVIAKOFag5jg9JkcFqAAVoAJUgApQASFgsBJQASpABagAFaACzhUgYDiXlAlSASpABagAFaACBAzWASpABagAFaACVMC5AgQM55IyQSpABagAFaACVICAwTpABagAFaACVIAKOFeAgOFcUiZIBagAFcipAjMTsqFWk1ptk0zMzInIW3J6/zKp1Wqy4OFj8lZOi52vYp2WE89vli/t/D8xetkel6erc1sfCBh5urcsCxWgAlSglwoQMDKqa9sA2x6XsTjOT3dbbgKG8xvEBKkAFaACOVWgCzByWs7cFsu2AbY9Lm8X6rbcBIy83V+WhwpQASrgRIFzMvNv98jWlUPeEMjQ+sfkfzy/yWqIpHHqWdlzd907D8MntfoGGf9fr8nrrXKZaddl+J7n5Pjx+31pvy7Htg9LrTYii588IP946/ukVlsuowf/IiLm+RiyqQnKt/PVM80cfi3PrVvQPPd/yy8fWCx1b2hntYy9cEoajWk5+lB72+i+E0bZWoX0pTUq47+c6khrdPdRmW4YxzemZeqfx2VDfb5MtdpqaR/Tbnw9TbzyjMr41KyRAFZjjovMw5dU6+dpee1/rjXKBc33yuTJt1tHeCtnj8jBH43KqFe2mtRG75XNz5vaxOneLrs5ZNY4OSmTrXuAvP9Rdk3rveosgvmLgGGqwXUqQAWoQCkUmJPZqbXthkYbnNYyYg5G45DsGZuHknZDigZX4SA47aGVK+UaL31NWwFDG2ss5xvkxonNsrpVFmN/fZvsOoMWXwHD2Nc6flTWrAG4mPvGZfOJv4bcuai09Jpw6kk59sOP+tKdz2No4wF5pTHXmq/SzjspYMTlEXQJc/LmC2NNwDKvGQDxuEzONgmp8bIc2ACI8x3Tum8i8boHAMbss/JIE1I70q5/Wyb8gOMrPgHDJwh/UgEqQAWKr8Dv5fCWhc2egb1y6GxDpPGKHNqivRIKAd0NytzUuIygR8FrVEWk1XDVpf70CWmIbdoGYIx+X3adelvkzddk+uz/bfZsXCFLJv8omGraODkhG71eAwUFAwr0XLOh69o2Iosn/xRy29ppDa1XLdqNsT6ptxrf+gZZ+9JpmZM5mT0+0ewBUhDp1is40+Dj7PLwp6g6zusPvaSlhZbLgJD6Rtns9QSdk1P7r5wHk9V75EjjrIXuneX+d9E06jL89webvT2n5cTuJVKv1WV4+1REz5EwVLj/VvI3FaACVKDwCsxNyqMjeJL1PWF3zcHobFDab5HMyez0U/IP/3C/PG0MlaAxnmv1cMSlrQ1j2Bsqp+X4gQdlz55NrWGcdnkVCoxGtQU25jbNwwYwtDHG3e287n+XN+V3T414QKbAMV8H2scNbT0swA67t27a57XTs83DX/va59XQqN/zpExMTMiDL854cDZ/dPuY+XL60zB/R+neWe65lub+XpHmbw9czLQ719mD0akHf1EBKkAFiq9ACzC0p6J5SV3bOxsUAEbj1DPymDdfortR8QCjK42wtLXxN4EAx56TmRfvMOYTmPkotChgmOCg6cVt898+TUvTxv7O656ToLTn09EendqGAzKdCTBs8/CXHzfFnHNi6KU9Oa3yh8Ec0rTR3a+LamfkaQ7BjDwqk16XSkCZhT0YwapwKxWgAlSgyApY9zJ0Nijmk/zQ+kfk/t0vyXSra30eFBrWaYc0qK3zr5DFD/yT9yTeaEGLf4gkDiZC8ui4d9pIhgOGed3tHgck0tZncD0Y5sWck5lfPSJPPLFV/msTAufL9f9aPTChPRhWurev14PJVg+GeR/M8kSvswcjWh/upQJUgAoUUAHbeRL+BkUb4/b4euPUTrnPm+TXBIxWo4M3P3ROQ9D8jpDGvzVMc6OMT70x/2R98IbmhNTBAMZb8h/tSbGRczBEOns0wqtG93HG5NiYPDpSNcHgyd825zwYk0W9npVGeyJoaw6Gmd82+e/T32u+5ROle2d9MMGrpr0lvjk5ER0YnIPRcSP5gwpQASpQEgXaEyeDurd16CSiQTG7wpvr+nTfmqzYOqYuw2v+pgkJmnYIYLQazKByaS+Dgo755ByUXtA2/w3UtDRt7O+8bm/uScck2M6ytSa8igEY3rWbaXbm2wIM8zjLPHwpteGnpbeWz5hX0mr4dZ8u52HxrJXuAbq0JpRqes0l3yLpvE38RQWoABWojgKdMQ+s42B0jPfPx4E49WrztdLWpD4z7Stk8UO/kpmT/jDk4Y1/xzyP0XvlrqO/l+PeJEvtJVEo6CNgoGLYxKjo0Ed7AwJqVdhxNnl0JXdOZl6aaA2LeK+LdsW4EBF/HAzEL/nnqVasjzjd/yMIvLy3fMw4GP6YJV2FbW3gEElLCq5QASpABahAvAIKDmYchnMyo8McMRP/4tPnEWVRgIBRljvJ66ACVIAK9EUBI+ZCV5d9e+5GX4rCTHKtAAEj17eHhaMCVIAK5FGB+X8K1TDkXpe9rzs+j6VmmfqrAAGjv3ozNypABagAFaAClVCAgFGJ28yLpAJUgApQASrQXwUIGP3Vm7lRASpABagAFaiEAgSMStxmXiQVoAJUgApQgf4qQMDor97MjQpQASpABahAJRQgYFTiNvMiqQAVoAJUgAr0VwECRn/1Zm5UgApQASpABSqhAAGjEreZF0kFqAAVoAJUoL8KEDD6qzdzowJUgApQASpQCQUIGJW4zbxIKkAFqAAVoAL9VYCAEaL3n//8Zzn//PPFC4HbFW/f97e13G+l0wUXXBCiNjdTAbcKrFmzxqpO0r7tfdlvfvMbtzeJqZVeAQJGwC0GXKxYsUI+9rGPyVNPPcVvRg22b98uF198sbz3ve8NUJubqIBbBe6++2657rrrPMD4xS9+Ifym12D//v0yNjbmaXnkyBG3N4qplV4BAkbALV61apXcdNNN8tnPfpZw4QgubrjhBs9JBcjNTVTAmQIKF2gY0TtBuMgOF9dee60sWbJECBjOqmllEiJg+G711772NVm5cqX8+Mc/JmBkhAtoeM0118gXvvAFufPOOwkYvrrGn24VAFSMjIzIz372Mw8sCBjp4QJgdvPNN8vnP/95z3YJGG7ralVSI2AYd9qECwyNDKIHA43yAw880PpieMHlMA3S/973viebNm2SO+64Q1avXu19b731Vm/b1q1b5bHHHsucp8IFAANwQcAwKhpXnSugcPHTn/601WtBwEgPGN/85jflyiuv9HwEbJeA4bzKViJBAkbzNu/YscObJ2A2rkGAoQ0ylmik0VijMU0LATgXjTqGZDDnA07RzONzn/uct23p0qWesacFDpQTeWj6KDu+CjN33XWX91uPQb4oV9prw/nLly9vwQUBoxL+ZCAXia571GsTLvAETsBIBxh+uCBgDKRalyJTAoaIKFz4G+8gwNAGWXsBFADQA4B9tqABkME5gAoARVzPAdJGjwOOt238kQfAAXCCL9ZtgEGhB/kgP5QT12vCV9R14vgrrrhCbr/9dgJGKdxEfi8CbzagjsJ2/fMtCBjJAQM6Llq0SNavX99hu+zByK8N5LlklQcMnQzmhws0oEGAEdSwouFFbwAcnfY0oEEGFGAfvgomOM6EEttG28xXezzgQJEWeh20RwJLAIvmgX043jw/yTp00TRxbcgT3zCYCoML9mDk2Q0Us2xRcMEejHRwAR+2du3aDrhgD0Yx7SMPpa40YBw+fFguuuii0AbYFjDMBlt7NnSYQ3sP9Dd6IbIMPZh5YR0NveapkKFw4z+217/RQwI9b7vtti4HRcDIg7mXpwxvvPGG9/ok6py/50J/swfDHjIef/xx78EhCC4IGOWxm35fSWUBIw4u0BinAYxeN+J5TR/Q9JGPfES++tWvBsIFAaPfpl3e/BQuMFdAYSJoScCwAwzMXfn4xz8uCE4GOw36coikvPbUyyurJGBoIC30JkQ12AQMuyBj999/v/f0EwUXBIxemnG10kZDuG7duki4AHAQMOIBwwYuYLsEjGrZmKurrRxgKFxgrkAUXGBfGQADEzZ1/kfc9abZjzkaiNKJQFpBTz7mNjh8fqhAFgXMQFpBvRbmNgJGNGBg/tlVV13lDTWZdhq0TsDIUmure27lPD6CaGHiY1hjajbIy5YtCz0u7Pyo7WjoMU8CcKNzMrDEb2wPmzgZlaZ/H+ZfID1zQqbmBYeLLyaAovcmaGKrP72o30ngAk6LgFFdR+PiypPABXsw4uECIcARpTMIKPzbCBguanD10qgUYPgDaQU1nmg0tUH+wAc+4DWK+G37iqc/TaSHBh+zs7VhR1raq4AlfqPBx34ch+OTNP6AIgCKTihFemHn41iFEOSFa0sz6RTpIL+rr77aykERMKrnXFxesQbS0iidZk9F2Dp7MMIhA3ChUTr9MBH0m4DhsjZXJ63KAIYNXPjhAEMkaEjRAKMhhsNC448G2n+s+ds8B4044MH2dVQch+MVSLRnwzwf6QNMUC6UB+VC+ZL2gGg59ZVWpIG8kSe+5jWZ6zgPETrNKJ1BTsm/jT0Y1XEsLq9U4cIfSCsMLHQ7ASMYMIICaflt1f+bgOGyRlcnrUoAxsTEhFxyySXWjbw2pv45GNr46/ADGmR80Rijoce6NtZYpu310PwBMmjwkS6AAw5Tv9iGoR7kYcKHnpt0qdCicBEFGGngAg6LgFEdx+LqSgELqDdJ4ULPU9jgch420sAFbJeA4apGVyud0gNGWJROmwbYDxjmOdogo9cAjTF6E7CetBfBTLMI6wCpoCid/ieeoN8EjGo5l6xXGxdIKw4aUN/ijqnSfn3QwkNLkH1GbSNgZK3N1Ty/1ICxe/du7+knbD5CXIMeBRhx55Zxfxa4gPMiYFTTyaS56qxwAXAgYLSHSOAD0QsaFkgrCi6wj4CRphbznNIChk0grTgIIGC042BgKKZer3f9v0icYzL3EzDocGwUQCAt/FEe6lyWHgYCxjxgIEpnFrggYNjUWh4TpEApAcMFXAA+sgAGnhh0yARLDKnEAU2S/UgfDtic/4EeBvzGdpdDNRj+iYvSaYJE2DoBI8gEuc1UwDZKpw14EDB+4c1diYvSGWav5nb2YJi1lOu2CpQOMBBI65Of/KRs3LgxtEHXt0IwURKNMhrkoGGUJICB8zG2qZM8MREU6esXzg5PEfrnY2mAA5M5ARD6OqofKHBdChw4BvmhTFkmgSJKpwu4gLMiYNiaZXWP++IXv2gVpZOA0R7+CNPCNkqnCRJh6wSM6tpklisvFWDYRulEg6u9C4ALNNRojAEHaKS18bcBDIUVbcyjeg6Qr3k88g0CG39PBtLEsWigsYzKwzwXaZvXlrRnA+fbRukMc0zmdgJGFlMt/7lJA2mFNay6HfVN16u21Cid119/feIJnabN6joBo/z214srLBVgIPImGlSzkU2y7m/8P/3pT3uNuUIAlmjccZw23OgpwO8k+eBYwAZ6F7SnAT0d+I0eCO2FwDaAC47J0hMBYNIyaw8LnC/SDyu3a7iAoyJg9MKEy5Gma7hAfXvPe97Titeir1ZXYYngd7A186ugoEtzn7mu+7FctWqVN7kTcDE8PCz79u0rR2XjVfRNgdIARppAWmGNKxp/PO3j6R2NMBp4GCGW+I1hDkCAgkdYOrbbFVwULrDU3gaUxTYdV8cBSHCtcDCmw8m6Dg35oQJ+BX7yk5/IJz7xCcFTt4uehu9+97ty4YUXyqWXXuoFxUM8map88SBx3nnnef+OmtVe8cbJ+Pi4XH755R5gHDlyxH/r+JsKRCpQCo/vEi7MRtpmiMQ8vgzrgAt9ysvqoPznEzAibbGSO9NG6QwDEYWLH/zgB5kmaRfVlvH2Df7i4Otf/7qThwP4AgAGYt8QMCppopkuuvCAocFjdN6ES8dQRcDoFVwANggYmWy1dCcDEkZGRlJF6QwCjCeeeMKrYxrKv2r26xouYLO33HKLNzzLORilM7++XFChASNLlE4bEMmTg8JQCeZ/9AKkVAvMK0kbpdPfWxH0m4DRF5suRCYuAmmZkAG4+PCHPyzf/va3W0OK/bRf2CaGNc1hTqxjyMLVUGrYXwdgnhZeRX3Xu97lrOfCb78EjEKYVe4KWVjAQJROzJEIM16d12D7xoU2suYyyEGhoYfTgPPAXAzMyTDnZWBf1nkTOB/OCunCeaBhxhK/sY4v5kgACJCfWea0672GCzgsAkbu7H8gBXINF3v27OmCC9iB335N+4E9ZXllHOnDt8BuUK8xeRrrfsBAHrBV5If9Yf4qzG7hC5AmzkceWEe+po/BEDHg4sYbb3QyLOKHC/wmYAzEVAqfaSEBwyaQFt66gEPRtyZg5NiWxMBNB4WGHGmpY4Kh44kCxo4v1rENDkWdQdLGH+ngfDgsOCOkaToS0wnhOgAhWqYsb5mg3FmjdAY5Jf82Akbh/UXmC9AonZgrYfZApF1/9tln5TOf+YzXuJr2gXXTfv37YD+wT9PebHwDehBNXwDbCbNRM0+kDRtV3wDbDcsP6dmWbf369T2HCwJG5mpf2QQKBxg2cGEatq77DRwGHDfcgNde1SkAVnCOphe19DshhQW/Q4EjAVTASSkoYD2uXP68kS7ygPMCSMFpIh18kb7/ePM3rslVIC0/UPh/EzAq62e8C3cZpRNAEgUXqONRgGHaAOwQdg7b8duP2hH2aw8IbNXWF5j56DrOhY0iL9gEvuY67Bh5AUKi4OW+++6Td7/73d51+m0tzW+8NYLXUQEt/vPZg1Ft20179YUCDI3SCaNXY02zVAOHYcNZwJjhQJAuDB+/YeTnn3++13DHNdJRZUDjj3SRJvJSh6JORfNGb0VUOrb7kB+uTx1jVNlxXL/gAg4L18xPdRVAlE78XXja3gr/ebCdKIiI2hdmT377UTvCEraUFP7D8vFvj7JT/7H4rXCBmBd+GEjzG1ABuPjKV74SmB4Bo7p2m+XKC+PxbaN0Bhlj1DYYNr54WoATQaOL33hySOOgovLK0z44UpdROm2cGgEji6kW+1zXgbRuvvlmb17Azp07Q8G8rPaLPy9DzwUCAdrYXdwxeLjCq6h4gyzsWAJGse1vUKUvBGAALrJG6UzTuJfVQQ0CLuC4CBiDMvPB5usaLtatWxcLF7D3Mtov4AJBxPDWSBgMJNluAxdIj4AxWBsqau6FAIxeBdKKg44yOih08V5yySXOo3TaODUCRlHdRPpyP/LIIz2J0olAWmW1X/Sg6qRxHaJBD+u2bducwgVsdsWKFR48xNkvASO9DVT5zNwDxqDgQp+AdAhFh03inFqS/Wjska46EUzUNCdowsm4HPNFWr0MpBXnpAgY1XI1vYzSGWRnpi3BpvB2SVb7wfkYNoVt+udQoT7jq/Oo0DMYVC6bbbB12D7S03lh6hewRP6I87Fw4UJvvlicrdnsx7wLAAZ6MeKOJ2BUy3ZdXW2uAeM73/mOLFq0KNRJwLDx1UY560RJdSZID5M8TWNHPuY2GGVahwJHqM5EnROcCJ5SzCcX7FMHBidn46jCjhk0XMCB4Vr4qYYCzzzzjNMonY8++qhXf6Js3AQM2CeGElDnYGtR5wXZDOZg6ZtZaPBhm0jffyzsCtuRn76FgmOx3X+s/7f6G/O8sLdGehGlMw4qzP0EjGrYreurzK3Ht4nSCcPGF40vDByOABAAx5Ck8YdR43yci0Yd6UVN8oSzUuejx8c5lCBnEncOHJKep9eGciL/MEfkd2L6G+VdvHix3H777bFPK6ZjcblOwHBtvvlMz3UgraAonVqvo5YY4oSdAN61EYf9BIEC0oHPgO0r/MNmktoZbFPPh2/QXghsR9r6O8nDA47FP8O6+n+RNDZNwMinreW9VLkEDBu4CHMscAgKC2iUYdAKInqO/sY+NfQgZxI3B8Ns/LWnAemoE8ESzgbl0CcpOBktR9IlHCCuDWXW3hSkG+YwNX2UqZchwG0dFgEj7+4ge/nyAheo+377RSMP+1F7RH00v4AQ2Cts1Ab+1b6Cljgf+akvQLr46m/ss8njtttu60sgrTgbJmBkt40qppA7wEgbSCvIyNWhoEE2nQrWsQ0Nb5Qz8TuooDx0G5wFGnp0j6oTwRLpxwGAptGLJcqAv8IeZM+FOi8CRrldDAJpAXz7EaXTxlaS2K9Nev0+xjVc4K/XV61alaoHk4BRbtvt1dXlCjBcwoULZ1B0BwW46WcgLQWJsCUBo1dmPPh0+x2l08a+i2y/rgNpaZTOsEBaYTar2wkYg7exIpYgN4CBWBcXXXSR1wNg4zz6cUyRHVTe4AKOioBRRBcRX2bXcIGInStXruwa4khq80W137zBBWyXgBFvBzyiW4FcAEavonQmdUj+44vqoDBXo99ROvVJJ2pJwOg2wDJs0UBa/lDeaX/bROn022rQ76T2i/lbGM40hzh1Hdtt5kwElcPchjwwjGrOzYJd4IvhJYRTxz+jIrBglC3Z7sOck7gonTZpETDKYKn9v4aBA0Ze4QJOIamDMh3JoNbzChdwYgSM/ht4r3NUuEDMi7RAYZ4XBxdo6LVBxhJzqdCIot77bc7GfgENaPAxL0vfIkN6ChZY4jfyQX44Lmrelr8M+hvzwZAG8tC5X/65WQ8++KB86EMf8o6xafTjjnEFF8iHgNFrSypn+gMHDA2kpYaYp6WNg8pTeeEsEaXzuuuuc/L0E+fAku4nYJTLiSBK51VXXSWu4AKTQxG74uGHH+6ChSA704nVaEjRcPsb/yj7BZCgoVeoAAAE5WFuQ36ACxMUot4G0d4QfUU2Kj6G6xDgsM0vf/nLXiCtpHYadDwBo1y226+rGShgKFzAcE1Dzst6lIPKSxm1HNBwkFE6g5ySfxsBo19m3ft8+h2lU+t51FIbf+3ZGBkZ6eiJQG8EhibQ4GtPQtI4F5o/AMXs2dDeDUAO1vU3IMYGXhBI6/3vf38uHwxgxwSM3ttUGXMYGGAgSicqbV7hAo6kKIBRBLiAk4LT5af4CriGCx32sPl/EW3go5awB6R52WWXdQEGICRoOCUqPdt9SNc/7GFz7qCjdPofBIJ+EzCKb7eDuAKnHh+zyW0+OE4pn8vOYD9p9UCUziDHkJdteE2OgGFjHfk/Jm0dDTvvHe94R6X9wTvf+c6BRumM8xE6BHXkyJH8V06WMFcKOAMMQAO6Hm0hA84mrmJz/51WGl177bWCb171Uge1ZcuWXFV+FiadAq5sN2tshrzW9yTlQvAr9A4kOSfs2FtuuUWgadj+tNs/9alPyZo1a9JVFp5VaQWcAQYiRcLxTExMWAnqykmlNZoynZdnwABcwEF94xvfsKoXPCj/CriyXTSsaSNLlsV+XQEG0sF9cQ0YmNeFV2ZtHxzzX3tZwn4q4AQw0HWGyq3fP/zhD7HX4MpJlcXRZLmOPAMGn35iTaFwB7iyXfxdeJZ6X4ZzXQBGr3qCCBeFM83cFdgJYOApROECS8zUjvu4clJlcDJZryGvgEEHFWcFxdxP27UburSx66yA0Su4wCuueGXY5mGxmLWYpe6HApkB45lnnumACwWNuAlBdFLunFQeAYNw0Q/zHUweWWw37X9h2DTWRTwmC2Bg+BFROl0PM+EeAS7wz7j8UIEsCmQCDIzLLVq0KBAwMOEz6pPFSRXRkfSyzHkDDH364bhtlAUUd19a2wV0okHspS0ULe0sgOEiBLhfL0wUTQMXiMaKeXjs8SiuXfei5JkBAz0V+oXj0XUsoxqYtE7KbxD8faf3BgkgIw9apH36gYPasWNHL+o403SsQBrbRb0YHh4Wzrvo7LnMAhiutdThlr1791rVGIWKCy64oPWQaXUiD6qMApkAw68SHI/tJ42TykMDmscy5KUHI+nTj99B4X8t+Mm/AkltV+HC9RsOebTFpGXKAhhJ84o6PglcoKfChArUB3wxVMMPFTAVsCcC86yQdVQy209SJxVlHFXflwfAsHVQ6ELFJGB1SuYS83n4yb8CSWwXDSiOJ1x09lyoz8oDYGicGkRStflgbkYQYNiGKLDJg8eUQwF7IrC4XjgS208SJ6XGyGWwkxo0YNjChdYNjZmCOmB+OalMFcr3MontovFCzxZtN9h2kwBGLyAtbZwaPChcfPHFHfaLHkl+qICpgD0RmGeFrMPx2H6SOCk6p2DnpLoMEjCSPv1o/cBwiAkXSeqOpsHlYBSg7Ubbo9qlzdIWMHSYyfW8i7RB8NDbuHDhQu//XtSOOcFzMPaY51zticDiKpI0EnRS7pzUoAAj7dMPqhJ6McwnII7fWhhYTg6Js13UC3xtGtiqH2MDGOgBguauezDSvkquQyToscBEftguhkz4oQJ+BQgYd7pr6AflLAcFGGmffjBWi9eb4Zw0jgrHb/2mmd/fUYABsMDrk6iTg7KHIuUbBxg6/IgeDJfXlRUu/POlODySX3sdZMkIGASMVI4rrYOCY8LTjjnfAut4rZmfYigQBRiAixUrVqSqUy4b0KKkFQUYvYKLtHFq8EAA2+Xr5MWw0zyUkoBBwEjcGLiEizwYAcuQTIEwwEC9AGBweMS+VzQMMKAhevnyEqUTcIHgiRja5IcK2CpAwCBgJAIMdH0j0h8cTpKPOW6b5Dwemz8FggCDcGEPFWbvShRgoKfBPDbretI4NVrzCBeqBJdJFSBgEDCsnRjGgdOEEVa48I/bJq2sPD4fCgQBBuqG6zccsjaoRTg/DDBcl12HW2yjdJo1DXFr4v76wTye61RAFYgGjMbLcmDD+4zXCetSf/qEzOnZviUcj+0nyEm5NqqqpB5tmkUAAA9HSURBVNePSZ5p4YLjtrYWUZzjaLvpeiuC/FE/ACMLXGBIBHCRtMeyOLWZJe2lAhFEMCezU2tlePgRmZxtWJWBgOHO8QQ5o7BtvQYMdVBJeyDYtWplNoU7iIDhzs57DRiYy4H/gLGN0mlWRsSq0be9zO1cpwK2CoQDRuNlee7WYVky+cfQHgt/JgQMd44nDCaCtvcSMBQuknatEi781lGe37Bz1As0PhwWyWbzChiYb7FkyRLr4cogP+DfBrhI+yp50Nte5anBvJJ+KRACGHPy5gtjUvdCOV8hix/4b7Jr+kxsmQgY2ZyN30HY/u4VYGR5+tGu1dhKwwMKpwDsHE/FrmMz2Nb3Mh0HwBgZGfH0BLS5ujbCReHMqpQFDgEMvdZzMvOr7fL03XWp1a6QxU/+Vl7XXQFLAkZ5ACOLg1K44LhtgJHkeJNtqGcFDDxxhz1145iwb1AjGnYstpfteICZaofXes8777yeROlcvnx54rkTmJANzRk4K8eGWqCixQCGXslpObF7idRrN8r4VPjriaiYtp8wxxHkTLgtGlxc92BkgQszSqdtXeBxg1cAcIEgSjZQCNvFk7d+aZ/R9unXB8NKqt3111/vDWP4j8nyO22cGr7tNXg7LFsJ7ImgcUj2jA3JgoePyVshKhAwkjmaLE7EPNc1YMBB4ekn6YfjtkkVy8/xCOgE+7UJpMSHA3d2DtAI6wUybdx2Hb4gTZwaBcykE7nzU4NZkjwqYA8Y8ns5vGUhASOHcTNcAkbapx/CRR7N265MCNMOaNAvnmSjPgSMfAJGllfJGaUzqsZzX1oF7AGjcUierl/DIZISAwZA5dJLL7XqJjcrHMdtTTWKt463QRQusIz7Z1sCRv4Ag3BRPLurQomDAaMxLS/9aEIefHFm/hXVs4fk53/3URnePsVJniUFjLQOiuO2xXYT+OMqEy50PWqSHwEjX4Chr5JH3bOwWooonXFAGXYut1OBOAVCAOMVObQFb440u01H75XNz5+IhAtkhONtP3RS7pxU1iGStHCh47b8d0XbWp+v4zChExM7W3au9l6rRQZYou26s92sczAULpLGqUFN5Nte+bLHMpbGnggsrp6A4c7x2E7qwnFZAEMdVNKnHwbSsjCIAR3SOPWMPHarhvivy/A9e2Xy5NtdpcE9xPwL/cJ+dR3LsDdKCBju7DwLYGicmp07d3bd27gNiNLJEOBxKnF/VgUIGDkc8kgCF1kAQ+Ei6dMP4SKr2fXw/Nln5YHF98jEcQTGOyczL94hG+o1qY0+Hhvy3/YBgYAxeMDI8ip53ITsxqmdct/KgDcGG9Ny9KHFzQCMq2V091GZtvsXiR5WeCadZwUIGBUFjCxPP9H/rnhOZg7eIKO1URmfmu2o+x1P1qP3yl1Hm3N8Oo7ij/QKzMmb/3KHrO2IVfOm/O6pEakF3A9/PgQMd+Bg+5CQpgejl3Ahxh9cdoYkOCnHfvhRqY1+X3adelsAIfcuXZjoryT89Y2/y68AAaOCgJHFQcWN2zZOTshGPDH7G7TZZ+XhqxfI8N8flOnG2x6ErBz6W5kI6Lovv9n18wrfktP7l0mtvk12nYl+3CRgFAMw0sap0be9MPwV/Dknp/ZfKQuuvlquqdU6QhI0TmyW1bXlMnrwL81Tm+BqUa+C8+LWKihAwKgYYGSBi9hx28bL8vPbPihLly70AUaAM2oGbhvaelhOV8HSBnaN8/FrbHQmYOQfMNLGqYl/22tOZl+9S26qPyIvHb9fNnQAhvaCbZKJmblWTe6GjtYurlABTwECRsUAY8WKFT2K0olw8suk/tCv5DU8MZs9GE2YqG04INMtwwuAjtY+rrhSAD1Kdyz4llVPEQEj34CRJU4N3haKjNI5+6w8VF8vm189IzIz4QOMeUitjTwqk22+aB5Xl/rTJ6z/cdtVvWY6xVCAgFEhwEj79BM3KUxkTman1kr9pj1y6Ozb813yJmCc2SX31ju7XEWaXfe1cdl84q/FsJailbLxskyuvjwyOJ55SQSM/AJG2lfJ7SZkn5SX/8uVMvbCqXlQ6AKMX8tz6xZIMGD47dqsUVyvugIEjIoABoLpZInSGT5uKyLemwvbvMlfbXAwJnl2OSyYnQKGcVzVrdHp9Z+W4zu/JF862Gw0LNImYOQTMHoLF+dk5pd/I4sfONqOc9Rlr1GAwR4MC9Oq7CEEjAoARloHFT9uKyKNV+Rf/9OVxlNyADh0OSzYmx7HHgz33uecnP7luIz+6JV2o2GRCQEjf4CBV8lxX5LGqcHtxkNFfJTOJjwYQdaQX/uLeRez828i+SZ0zk2Ny0jHxE+LSsZDKqUAAaPkgJEWLjRKZ+S4LUylCQ9th2Q6p5pg3sWfAid0vi7Htg9bvd1QKYvMfLHBcIHXCr/0n/81ckIt7qHNB8fZvobJ46KhJeo11bRxanAP4972irzPAQ8E3RM6OYcqUkPu9BSw8yiWYtk6KCRHJxXteJI45rBInmmffuzGbcMqhfZMmEMfAc4oEDrC0uR2OwU0BokP8rwnUvMVw+DUbO2XtuvOdsMAY/369TI8PCxponRmggtUjQDA0PgYQ+v3yqGzczJ7fEK2MA5GsCFxa0uBTICBhsgMLQzHY/7G/rAPnZQ7JxUEGGmffrLBBe52EGCIePExhi6TxU/+Vt6Q0/LavjFhHIww6+jPdvRSTUxMtL6wSfN3mP3Sdt3ZbhBgZHmVPH5CtkXdCgIMnIY/vbxb/6NqtYzui/9/KovceEiJFcgMGGn+LAl60km5c1J+wNCnn6QhwHFfsv+7YjBgeG+aHJ+QrSuH5sd3R7c1w1mX2LoKcGkYo4ct+r9RY/e0XXe26weMgcNFAeosi1gcBTIBBi4TTzx+54TfcWP3dFLunJQJGFkcVOau1eLUe5a0qQB6HIPsF70bYR/arjvb9QMG4tTgm/Sj9xETs/mhAnlRIDNg4EIWLVrU4aSinn70wumk3DkpBYwscBEbpVNvHJelUwBgaUIGHhqiPrRdd7ZrAkbaODVWb3tF3VDuowI9UsAJYCg9q5OyoWg6KXdOSgEDTz5jY2OJq4qTcdvEufKEvCigbwzBJjHkGTb3QstL23VnuwoYeChbtmxZrPZ6D3RJuFAluMyjAk4AAxemY7l4GrL50Em5c1IADMw4T+OgCBc2tbX8x+hQZ9zQJpSg7bqzXQAGbPfCCy+UuAcz7DeP0QnZ6H3khwrkUQFngKFPQXFPPyoCnBS/7jSwgQt/sB7tecKSn2orALvFBF+bD+3Wnd2qliY4hN2DHTt2eD4TEKhwYftAF5Ymt1OBXirgDDBQyKiJYb28CKZtp/3SpUu9niY4Jzi02D9AorBUgAr0XAHbhzIAoALJ5Zdfbg2EPb8AZkAFQhRwChgheXBzThRQ53TZZZfJwoULY9/0yUmxWQwqQAUCJtN/61vfoi5UINcKEDByfXvcFU6HQxQyPvjBD3aM57rLiSlRASrgWgH0cqjtmksOkbhWmum5VICA4VLNHKel47emc8IQic3Yb44vi0WjApVQwP+AoHaMYU/acCWqQCEvkoBRyNuWvNDm+K06JyxtJ/Ylz5FnUAEq4EoBfctHbRYTPTnnzZW6TKdXChAweqVsztI1g6EBKnQmes6KyeJQASoQoAAAgzYbIAw35VoBAkaub4+7whEq3GnJlKgAFaACVCBegdwABiYxIWCMTZjx+Msq5xF4igEosGu0nPeXV0UFqAAVKJMCuQAMdP3pv7ISMMKrlzkOi3Xb9+fDU+QeKpBdAQAvwJcB28K1xBAl9QnXh3vKqcBAAQMGh1nQ5qRDAkZ4RTMBA5rBaQHO+KECg1AAgGvWSTag4XdBfRx7IMM14p7yKTAwwMBwiBodl9lCDxPKymeYeb8igK05cRg2TMAIv2t+H8ceyHCtuKc8CgwMMHTOhd/w2FiGVy7zaVF1g16ckxGuGfe4VQB1DXVO6x+X6R8OMCxMKHNbP5lavhQYGGCoDAgSYzosAoYq0700AYNjut36cEt/FEDQNp0zZQIGG8tw/U2ddB29uJxHFa4Z9xRfgYEDhkqIf/pEo0nAUEW6lwAMOHY4eH6owCAVCOqBJGCE3xGFCizh4xh9M1wr7imPArkBDJXU/5fiup1L8bpT+cTDmpAnBcwhEwJG+J0BWOABiv4tXCPuKZ8CuQOM8knMK6IC5VcADSfnAoXfZ/Y6hmvDPeVVgICBe3v2iDy/Z5NsWf4+WTz5p4C7fU5mXrxDNtQxoasuw/fslcmTbwccx01UgApQASpABagAFCBgyO/l8JaFzVnxIwGAMSezU2tltLZaxl44JY3GK3JoS12GNh6QVxqsRFSACgxOgTmZnX5K9v1oVEZrm2RiZq67KI1pOfrQYqnX8HCwWkZ3H5Vp2m23TtxCBXqgAAGjKWrjxGZZXQsAjMYh2TM2JENbD8vpjmOXy+jBv/TgljBJKkAFrBQ4s0vu9XoVAQ9BgHFSjv3wo1Ib/b7sOvW2NE7tlHuXLpQlk3+UABSxypIHUQEqYK8AAUO1mpmQDQGAEQgeAdChyXBJBahAPxV4U3731EggYMzbrvkg0Dy2vk12nWE3Rj/vEvOqpgIEDL3vgYAxJ2++MCb12qiMT83qkSLya3lu3QKprd4jR+inDF24SgX6rcBbcnr/sgDACAaPbujod3mZHxWojgIEDL3XgYChzisEMEYelUn2taqCXFKBASigNuofImnOrfLbqGfndak/fYLDJAO4W8yyWgoQMPR+pwEM9mCoelxSgQEpEAYYzV7GQMCoyYKHj8lbAyoxs6UCVVGAgKF3OhAwRAK7VOcm5dGRWsfET02GSypABfqpQBrAYA9GP+8Q86quAgQMvfchgCEBEzoDoUPT4ZIKUIE+KhAGGMETOuemxmWkZk787GNRmRUVqJgCBIzmDZ+HhqAnm3Nyav+VMjS0UTa/ekbk7CH5+d2Mg1ExO+Hl5laBMMAI6n0Mho7cXhoLRgUKrgABQ16XY9uHO/9+2j9uK6fltX1jMuoF60Ekz+fkyFm+PlLwus/il0IBfVtkXDaf+GvnFTVelgMb3idD6/fKobNzMnt8QrYwDkanRvxFBXqoAAGjh+IyaSpABXqoQHMulPlPpV2TN5s9jvPHrJbRfSfk9R4WiUlTASrQVoCA0daCa1SAClABKkAFqIAjBQgYjoRkMlSAClABKkAFqEBbAQJGWwuuUQEqQAWoABWgAo4U+P/csLvOtN/UrwAAAABJRU5ErkJggg=="></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the volume of oil drained from Yao’s motorbike.</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>Yao then pours all the oil from the cuboids into an empty cylindrical container. The height of the oil in the container is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="30"> <mn>30</mn> </math></span> cm.</p>
<p><img style="display: block;margin-left:auto;margin-right:auto;" 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"></p>
<p>Find the internal radius, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span>, of the container.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>units are required in both parts</strong></p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {V = } \right)\,\,5 \times 10 \times 40 + 2 \times 10 \times 40"> <mrow> <mo>(</mo> <mrow> <mi>V</mi> <mo>=</mo> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>5</mn> <mo>×</mo> <mn>10</mn> <mo>×</mo> <mn>40</mn> <mo>+</mo> <mn>2</mn> <mo>×</mo> <mn>10</mn> <mo>×</mo> <mn>40</mn> </math></span> <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitutions in volume formula for both cuboids. Award <em><strong>(M1)</strong></em> for adding the volumes of both cuboids.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2800"> <mn>2800</mn> </math></span> cm<sup>3</sup> <em><strong>(A1)</strong></em><em><strong> (C3)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>units are required in both parts</strong></p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2800 = \pi \times {r^2} \times 30"> <mn>2800</mn> <mo>=</mo> <mi>π</mi> <mo>×</mo> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>×</mo> <mn>30</mn> </math></span> <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in volume of cylinder formula. Award <em><strong>(M1)</strong></em> for equating <em>their</em> expression (must include <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi "> <mi>π</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span>) to <em>their</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2800"> <mn>2800</mn> </math></span>.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {r = } \right)"> <mrow> <mo>(</mo> <mrow> <mi>r</mi> <mo>=</mo> </mrow> <mo>)</mo> </mrow> </math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="5.45"> <mn>5.45</mn> </math></span> cm (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="5.45058"> <mn>5.45058</mn> </math></span>… cm) <em><strong>(A1)</strong></em><strong>(</strong><em><strong>ft)</strong></em><em><strong> (C3)</strong></em></p>
<p><strong>Note:</strong> Follow through from <em>their</em> part (a).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows triangle ABC, with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AB}} = 3{\text{ cm}}">
<mrow>
<mtext>AB</mtext>
</mrow>
<mo>=</mo>
<mn>3</mn>
<mrow>
<mtext> cm</mtext>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{BC}} = 8{\text{ cm}}">
<mrow>
<mtext>BC</mtext>
</mrow>
<mo>=</mo>
<mn>8</mn>
<mrow>
<mtext> cm</mtext>
</mrow>
</math></span>, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{A\hat BC = }}\frac{\pi }{3}">
<mrow>
<mrow>
<mi mathvariant="normal">A</mi>
<mrow>
<mover>
<mi mathvariant="normal">B</mi>
<mo stretchy="false">^<!-- ^ --></mo>
</mover>
</mrow>
<mi mathvariant="normal">C</mi>
<mo>=</mo>
</mrow>
</mrow>
<mfrac>
<mi>π<!-- π --></mi>
<mn>3</mn>
</mfrac>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-11_om_09.17.57.png" alt="N17/5/MATME/SP1/ENG/TZ0/04"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AC}} = 7{\text{ cm}}"> <mrow> <mtext>AC</mtext> </mrow> <mo>=</mo> <mn>7</mn> <mrow> <mtext> cm</mtext> </mrow> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The shape in the following diagram is formed by adding a semicircle with diameter [AC] to the triangle.</p>
<p><img src="images/Schermafbeelding_2018-02-11_om_10.50.00.png" alt="N17/5/MATME/SP1/ENG/TZ0/04.b"></p>
<p>Find the exact perimeter of this shape.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>evidence of choosing the cosine rule <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{c^2} = {a^2} + {b^2} - ab\cos C"> <mrow> <msup> <mi>c</mi> <mn>2</mn> </msup> </mrow> <mo>=</mo> <mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mi>b</mi> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mi>a</mi> <mi>b</mi> <mi>cos</mi> <mo></mo> <mi>C</mi> </math></span></p>
<p>correct substitution into RHS of cosine rule <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{3^2} + {8^2} - 2 \times 3 \times 8 \times \cos \frac{\pi }{3}"> <mrow> <msup> <mn>3</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mn>8</mn> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mn>2</mn> <mo>×</mo> <mn>3</mn> <mo>×</mo> <mn>8</mn> <mo>×</mo> <mi>cos</mi> <mo></mo> <mfrac> <mi>π</mi> <mn>3</mn> </mfrac> </math></span></p>
<p>evidence of correct value for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\cos \frac{\pi }{3}"> <mi>cos</mi> <mo></mo> <mfrac> <mi>π</mi> <mn>3</mn> </mfrac> </math></span> (may be seen anywhere, including in cosine rule) <strong><em>A1</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\cos \frac{\pi }{3} = \frac{1}{2},{\text{ A}}{{\text{C}}^2} = 9 + 64 - \left( {48 \times \frac{1}{2}} \right),{\text{ }}9 + 64 - 24"> <mi>cos</mi> <mo></mo> <mfrac> <mi>π</mi> <mn>3</mn> </mfrac> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>,</mo> <mrow> <mtext> A</mtext> </mrow> <mrow> <msup> <mrow> <mtext>C</mtext> </mrow> <mn>2</mn> </msup> </mrow> <mo>=</mo> <mn>9</mn> <mo>+</mo> <mn>64</mn> <mo>−</mo> <mrow> <mo>(</mo> <mrow> <mn>48</mn> <mo>×</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>9</mn> <mo>+</mo> <mn>64</mn> <mo>−</mo> <mn>24</mn> </math></span></p>
<p>correct working clearly leading to answer <strong><em>A1</em></strong></p>
<p>e<em>g</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}{{\text{C}}^2} = 49,{\text{ }}b = \sqrt {49} "> <mrow> <mtext>A</mtext> </mrow> <mrow> <msup> <mrow> <mtext>C</mtext> </mrow> <mn>2</mn> </msup> </mrow> <mo>=</mo> <mn>49</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>b</mi> <mo>=</mo> <msqrt> <mn>49</mn> </msqrt> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AC}} = 7{\text{ (cm)}}"> <mrow> <mtext>AC</mtext> </mrow> <mo>=</mo> <mn>7</mn> <mrow> <mtext> (cm)</mtext> </mrow> </math></span> <strong><em>AG N0</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award no marks if the only working seen is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}{{\text{C}}^2} = 49"> <mrow> <mtext>A</mtext> </mrow> <mrow> <msup> <mrow> <mtext>C</mtext> </mrow> <mn>2</mn> </msup> </mrow> <mo>=</mo> <mn>49</mn> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AC}} = \sqrt {49} "> <mrow> <mtext>AC</mtext> </mrow> <mo>=</mo> <msqrt> <mn>49</mn> </msqrt> </math></span> (or similar).</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution for semicircle <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{semicircle}} = \frac{1}{2}(2\pi \times 3.5),{\text{ }}\frac{1}{2} \times \pi \times 7,{\text{ }}3.5\pi "> <mrow> <mtext>semicircle</mtext> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo stretchy="false">(</mo> <mn>2</mn> <mi>π</mi> <mo>×</mo> <mn>3.5</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>×</mo> <mi>π</mi> <mo>×</mo> <mn>7</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>3.5</mn> <mi>π</mi> </math></span></p>
<p>valid approach (seen anywhere) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{perimeter}} = {\text{AB}} + {\text{BC}} + {\text{semicircle, }}3 + 8 + \left( {\frac{1}{2} \times 2 \times \pi \times \frac{7}{2}} \right),{\text{ }}8 + 3 + 3.5\pi "> <mrow> <mtext>perimeter</mtext> </mrow> <mo>=</mo> <mrow> <mtext>AB</mtext> </mrow> <mo>+</mo> <mrow> <mtext>BC</mtext> </mrow> <mo>+</mo> <mrow> <mtext>semicircle, </mtext> </mrow> <mn>3</mn> <mo>+</mo> <mn>8</mn> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>×</mo> <mn>2</mn> <mo>×</mo> <mi>π</mi> <mo>×</mo> <mfrac> <mn>7</mn> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>8</mn> <mo>+</mo> <mn>3</mn> <mo>+</mo> <mn>3.5</mn> <mi>π</mi> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="11 + \frac{7}{2}\pi {\text{ }}( = 3.5\pi + 11){\text{ (cm)}}"> <mn>11</mn> <mo>+</mo> <mfrac> <mn>7</mn> <mn>2</mn> </mfrac> <mi>π</mi> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mo>=</mo> <mn>3.5</mn> <mi>π</mi> <mo>+</mo> <mn>11</mn> <mo stretchy="false">)</mo> <mrow> <mtext> (cm)</mtext> </mrow> </math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A buoy is floating in the sea and can be seen from the top of a vertical cliff. A boat is travelling from the base of the cliff directly towards the buoy.</p>
<p>The top of the cliff is 142 m above sea level. Currently the boat is 100 metres from the buoy and the angle of depression from the top of the cliff to the boat is 64°.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="question">
<p>Draw and label the angle of depression on the diagram.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><img 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"> <strong><em>(A1)</em><em> </em></strong><strong><em>(C1)</em></strong></p>
<p><strong>Note:</strong> The horizontal line must be shown and the angle of depression must be labelled. Accept a numerical or descriptive label.</p>
<p><em><strong>[1 mark]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>Helen is building a cabin using cylindrical logs of length 2.4 m and radius 8.4 cm. A wedge is cut from one log and the cross-section of this log is illustrated in the following diagram.</p>
<p style="text-align: center;"><img 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"></p>
<p>Find the volume of this log.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>volume <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 240\left( {\pi \times {{8.4}^2} - \frac{1}{2} \times {{8.4}^2} \times 0.872664 \ldots } \right)"> <mo>=</mo> <mn>240</mn> <mrow> <mo>(</mo> <mrow> <mi>π</mi> <mo>×</mo> <mrow> <msup> <mrow> <mn>8.4</mn> </mrow> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>×</mo> <mrow> <msup> <mrow> <mn>8.4</mn> </mrow> <mn>2</mn> </msup> </mrow> <mo>×</mo> <mn>0.872664</mn> <mo>…</mo> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>M1M1M1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong> </em>240 × area, award <em><strong>M1</strong> </em>for correctly substituting area sector formula, award <em><strong>M1</strong></em> for subtraction of their area of the sector from area of circle.</p>
<p>= 45800 (= 45811.96071) <em><strong>A1</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>The magnitudes of two vectors, <em><strong>u</strong></em> and <em><strong>v</strong></em>, are 4 and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt 3 "> <msqrt> <mn>3</mn> </msqrt> </math></span> respectively. The angle between <em><strong>u</strong></em> and <em><strong>v</strong></em> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\pi }{6}"> <mfrac> <mi>π</mi> <mn>6</mn> </mfrac> </math></span>.</p>
<p>Let <em><strong>w</strong></em> = <em><strong>u</strong></em> − <em><strong>v</strong></em>. Find the magnitude of <em><strong>w</strong></em>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><strong>METHOD 1 (cosine rule)</strong></p>
<p>diagram including <em><strong>u</strong></em>, <em><strong>v</strong></em> and included angle of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\pi }{6}"> <mfrac> <mi>π</mi> <mn>6</mn> </mfrac> </math></span> <em><strong>(M1)</strong></em></p>
<p><em>eg </em> <img src="data:image/png;base64,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"></p>
<p>sketch of triangle with <em><strong>w</strong> </em>(does not need to be to scale) <em><strong> (A1)</strong></em></p>
<p><em>eg</em> <img src="data:image/png;base64,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"></p>
<p>choosing cosine rule <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{a^2} + {b^2} - 2ab\,{\text{cos}}\,C"> <mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mi>b</mi> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mn>2</mn> <mi>a</mi> <mi>b</mi> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>C</mi> </math></span></p>
<p>correct substitution <em><strong>A1</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{4^2} + {\left( {\sqrt 3 } \right)^2} - 2\left( 4 \right)\left( {\sqrt 3 } \right){\text{cos}}\frac{\pi }{6}"> <mrow> <msup> <mn>4</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <msqrt> <mn>3</mn> </msqrt> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mn>2</mn> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <msqrt> <mn>3</mn> </msqrt> </mrow> <mo>)</mo> </mrow> <mrow> <mtext>cos</mtext> </mrow> <mfrac> <mi>π</mi> <mn>6</mn> </mfrac> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{cos}}\frac{\pi }{6} = \frac{{\sqrt 3 }}{2}"> <mrow> <mtext>cos</mtext> </mrow> <mfrac> <mi>π</mi> <mn>6</mn> </mfrac> <mo>=</mo> <mfrac> <mrow> <msqrt> <mn>3</mn> </msqrt> </mrow> <mn>2</mn> </mfrac> </math></span> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg </em> 16 + 3 − 12</p>
<p>| <em><strong>w </strong></em>| = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt 7 "> <msqrt> <mn>7</mn> </msqrt> </math></span> <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><strong>METHOD 2 (scalar product)</strong></p>
<p>valid approach, in terms of u and v (seen anywhere) <em><strong>(M1)</strong></em></p>
<p><em>eg </em> | <em><strong>w </strong></em>|<sup>2</sup> = (<em><strong>u</strong></em> − <em><strong>v</strong></em>)•(<em><strong>u</strong></em> − <em><strong>v</strong></em>), | <em><strong>w </strong></em>|<sup>2</sup> = <em><strong>u</strong></em>•<em><strong>u </strong></em>− 2<em><strong>u</strong></em>•<strong><em>v </em></strong>+ <strong><em>v</em></strong>•<em><strong>v</strong></em>, | <em><strong>w </strong></em>|<sup>2 </sup>= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\left( {{u_1} - {v_1}} \right)^2} + {\left( {{u_2}\; - \;{v_2}} \right)^2}"> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> </mrow> <mo>−</mo> <mrow> <msub> <mi>v</mi> <mn>1</mn> </msub> </mrow> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> </mrow> <mspace width="thickmathspace"></mspace> <mo>−</mo> <mspace width="thickmathspace"></mspace> <mrow> <msub> <mi>v</mi> <mn>2</mn> </msub> </mrow> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </math></span>,</p>
<p>| <em><strong>w </strong></em>| = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {{{\left( {{u_1} - {v_1}} \right)}^2} + {{\left( {{u_2}\; - \;{v_2}} \right)}^2} + {{\left( {{u_3}\; - \;{v_3}} \right)}^2}} "> <msqrt> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> </mrow> <mo>−</mo> <mrow> <msub> <mi>v</mi> <mn>1</mn> </msub> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> </mrow> <mspace width="thickmathspace"></mspace> <mo>−</mo> <mspace width="thickmathspace"></mspace> <mrow> <msub> <mi>v</mi> <mn>2</mn> </msub> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mrow> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> <mspace width="thickmathspace"></mspace> <mo>−</mo> <mspace width="thickmathspace"></mspace> <mrow> <msub> <mi>v</mi> <mn>3</mn> </msub> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </math></span></p>
<p>correct value for <em><strong>u</strong></em>•<em><strong>u</strong></em> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg</em> | <em><strong>u</strong><strong> </strong></em>|<sup>2</sup> = 16, <em><strong>u</strong></em>•<em><strong>u</strong></em> = 16, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_1}^2 + {u_2}^2 = 16"> <msup> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> </mrow> <mn>2</mn> </msup> <mo>=</mo> <mn>16</mn> </math></span></p>
<p>correct value for <strong><em>v</em></strong>•<em><strong>v</strong></em> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg</em> | <em><strong>v</strong><strong> </strong></em>|<sup>2</sup> = 16, <strong><em>v</em></strong>•<em><strong>v</strong></em> = 3, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_1}^2 + {v_2}^2 + {v_3}^2 = 3"> <msup> <mrow> <msub> <mi>v</mi> <mn>1</mn> </msub> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <msub> <mi>v</mi> <mn>2</mn> </msub> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <msub> <mi>v</mi> <mn>3</mn> </msub> </mrow> <mn>2</mn> </msup> <mo>=</mo> <mn>3</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{cos}}\left( {\frac{\pi }{6}} \right) = \frac{{\sqrt 3 }}{2}"> <mrow> <mtext>cos</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mi>π</mi> <mn>6</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msqrt> <mn>3</mn> </msqrt> </mrow> <mn>2</mn> </mfrac> </math></span> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em><strong>u</strong></em>•<strong><em>v</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 4 \times \sqrt 3 \times \frac{{\sqrt 3 }}{2}"> <mo>=</mo> <mn>4</mn> <mo>×</mo> <msqrt> <mn>3</mn> </msqrt> <mo>×</mo> <mfrac> <mrow> <msqrt> <mn>3</mn> </msqrt> </mrow> <mn>2</mn> </mfrac> </math></span> (= 6) (seen anywhere) <em><strong>A1</strong></em></p>
<p>correct substitution into <em><strong>u</strong></em>•<em><strong>u </strong></em>− 2<em><strong>u</strong></em>•<strong><em>v </em></strong>+ <strong><em>v</em></strong>•<em><strong>v</strong></em> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{u_1}^2 + {u_2}^2 + {v_1}^2 + {v_2}^2 - 2\left( {{u_1}{v_1} + {u_2}{v_2}} \right)"> <msup> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <msub> <mi>v</mi> <mn>1</mn> </msub> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <msub> <mi>v</mi> <mn>2</mn> </msub> </mrow> <mn>2</mn> </msup> <mo>−</mo> <mn>2</mn> <mrow> <mo>(</mo> <mrow> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> </mrow> <mrow> <msub> <mi>v</mi> <mn>1</mn> </msub> </mrow> <mo>+</mo> <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> </mrow> <mrow> <msub> <mi>v</mi> <mn>2</mn> </msub> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> (2 or 3 dimensions) <em><strong>(A1)</strong></em></p>
<p><em>eg </em>16 − 2(6) + 3 (= 7)</p>
<p>| <em><strong>w </strong></em>| = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt 7 "> <msqrt> <mn>7</mn> </msqrt> </math></span> <em><strong>A1 N2</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>Two fixed points, A and B, are 40 m apart on horizontal ground. Two straight ropes, AP and BP, are attached to the same point, P, on the base of a hot air balloon which is vertically above the line AB. The length of BP is 30 m and angle BAP is 48°.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="question">
<p>On the diagram, draw and label with an <em>x</em> the angle of depression of B from P.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><img 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"><em><strong>(A1) (C1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br>