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<h2>HL Paper 1</h2><div class="specification">
<p>A garden has a triangular sunshade suspended from three points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mo>(</mo><mn>2</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>,</mo><mo> </mo><mn>2</mn><mo>)</mo><mo>,</mo><mo> </mo><mtext>B</mtext><mo>(</mo><mn>8</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>,</mo><mo> </mo><mn>2</mn><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext><mo>(</mo><mn>5</mn><mo>,</mo><mo> </mo><mn>4</mn><mo>,</mo><mo> </mo><mn>3</mn><mo>)</mo></math>, relative to an origin in the corner of the garden. All distances are measured in metres.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mtext>CA</mtext><mo>→</mo></mover></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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mtext>CB</mtext><mo>→</mo></mover></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mtext>CA</mtext><mo>→</mo></mover><mo>×</mo><mover><mtext>CB</mtext><mo>→</mo></mover></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>Hence find the area of the triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABC</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The position of a helicopter relative to a communications tower at the top of a mountain at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> (hours) can be described by the vector equation below.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">r</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>20</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>25</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd></mtr></mtable></mfenced><mo>+</mo><mi>t</mi><mfenced><mtable><mtr><mtd><mn>4</mn><mo>.</mo><mn>2</mn></mtd></mtr><mtr><mtd><mn>5</mn><mo>.</mo><mn>8</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></p>
<p>The entries in the column vector give the displacements east and north from the communications tower and above/below the top of the mountain respectively, all measured in kilometres.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the speed of the helicopter.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the distance of the helicopter from the communications tower at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the bearing on which the helicopter is travelling.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>An ant is walking along the edges of a wire frame in the shape of a triangular prism.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The vertices and edges of this frame can be represented by the graph below.</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>Write down the adjacency matrix, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">M</mi></math>, for this graph.</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 number of ways that the ant can start at the vertex <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>, and walk along exactly <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> edges to return to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows the graph <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math>.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Verify that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math> satisfies the handshaking lemma.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math> cannot be redrawn as a planar graph.</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>State, giving a reason, whether <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math> contains an Eulerian circuit.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>An engineer plans to visit six oil rigs <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mtext>A</mtext><mo>–</mo><mtext>F</mtext><mo>)</mo></math> in the Gulf of Mexico, starting and finishing at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>. The travelling time, in minutes, between each of the rigs is shown in the table.</p>
<p style="text-align: center;"><img 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"></p>
<p>The data above can be represented by a graph <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Prim’s algorithm to find the weight of the minimum spanning tree of the subgraph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math> obtained by deleting <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and starting at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>. List the order in which the edges are selected.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find a lower bound for the travelling time needed to visit all the oil rigs.</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>Describe how an improved lower bound might be found.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Points in the plane are subjected to a transformation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> in which the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>x</mi><mo>,</mo><mo> </mo><mi>y</mi><mo>)</mo></math> is transformed to the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>x</mi><mo>'</mo><mo>,</mo><mo> </mo><mi>y</mi><mo>'</mo><mo>)</mo></math> where</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="[" close="]"><mtable><mtr><mtd><mi>x</mi><mo>'</mo></mtd></mtr><mtr><mtd><mi>y</mi><mo>'</mo></mtd></mtr></mtable></mfenced><mo>=</mo><mfenced open="[" close="]"><mtable><mtr><mtd><mn>3</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>2</mn></mtd></mtr></mtable></mfenced><mfenced open="[" close="]"><mtable><mtr><mtd><mi>x</mi></mtd></mtr><mtr><mtd><mi>y</mi></mtd></mtr></mtable></mfenced></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe, in words, the effect of the transformation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mo>(</mo><mn>1</mn><mo>,</mo><mo> </mo><mn>4</mn><mo>)</mo><mo>,</mo><mo> </mo><mtext>B</mtext><mo>(</mo><mn>4</mn><mo>,</mo><mo> </mo><mn>8</mn><mo>)</mo><mo>,</mo><mo> </mo><mtext>C</mtext><mo>(</mo><mn>8</mn><mo>,</mo><mo> </mo><mn>5</mn><mo>)</mo><mo>,</mo><mo> </mo><mtext>D</mtext><mo>(</mo><mn>5</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>)</mo></math> form a square.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the area of this square.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A', B', C', D'</mtext></math>, the points to which <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A, B, C, D</mtext></math> are transformed under <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A' B' C' D'</mtext></math> is a parallelogram.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the area of this parallelogram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.v.</div>
</div>
<br><hr><br><div class="specification">
<p>A geometric transformation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>:</mo><mfenced><mtable><mtr><mtd><mi>x</mi></mtd></mtr><mtr><mtd><mi>y</mi></mtd></mtr></mtable></mfenced><mo>↦</mo><mfenced><mtable><mtr><mtd><mi>x</mi><mo>'</mo></mtd></mtr><mtr><mtd><mi>y</mi><mo>'</mo></mtd></mtr></mtable></mfenced></math> is defined by</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>:</mo><mfenced><mtable><mtr><mtd><mi>x</mi><mo>'</mo></mtd></mtr><mtr><mtd><mi>y</mi><mo>'</mo></mtd></mtr></mtable></mfenced><mo>=</mo><mfenced><mtable><mtr><mtd><mn>7</mn></mtd><mtd><mo> </mo><mo>-</mo><mn>10</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mo> </mo><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mfenced><mtable><mtr><mtd><mi>x</mi></mtd></mtr><mtr><mtd><mi>y</mi></mtd></mtr></mtable></mfenced><mo>+</mo><mfenced><mtable><mtr><mtd><mo>-</mo><mn>5</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd></mtr></mtable></mfenced></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of the image of the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>6</mn><mo>,</mo><mo> </mo><mo>−</mo><mn>2</mn><mo>)</mo></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>:</mo><mfenced><mtable><mtr><mtd><mi>p</mi></mtd></mtr><mtr><mtd><mi>q</mi></mtd></mtr></mtable></mfenced><mo>↦</mo><mn>2</mn><mfenced><mtable><mtr><mtd><mi>p</mi></mtd></mtr><mtr><mtd><mi>q</mi></mtd></mtr></mtable></mfenced></math>, find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> with vertices lying on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mi>y</mi></math> plane is transformed by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>.</p>
<p>Explain why both <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> and its image will have exactly the same area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A ship <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>S</mtext></math> is travelling with a constant velocity, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>, measured in kilometres per hour, where</p>
<p style="padding-left: 210px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mo>-</mo><mn>12</mn></mtd></mtr><mtr><mtd><mn>15</mn></mtd></mtr></mtable></mfenced></math>.</p>
<p>At time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math> the ship is at a point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mo>(</mo><mn>300</mn><mo>,</mo><mo> </mo><mn>100</mn><mo>)</mo></math> relative to an origin <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>, where distances are measured in kilometres.</p>
</div>
<div class="specification">
<p>A lighthouse is located at a point <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>129</mn><mo>,</mo><mo> </mo><mn>283</mn><mo>)</mo></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the position vector <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mtext>OS</mtext><mo>→</mo></mover></math> of the ship at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> hours.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> when the ship will be closest to the lighthouse.</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An alarm will sound if the ship travels within <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math> kilometres of the lighthouse.</p>
<p>State whether the alarm will sound. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram below shows a network of roads in a small village with the weights indicating the distance of each road, in metres, and junctions indicated with letters.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZcAAAEcCAYAAAALEfkWAAAgAElEQVR4Ae2d3c9uN3nm+38M2R9JShJIFChkNmmAJCRAB0jJTorER1Rlh4YgpVECUQmddtIjMlJm+JCm06FDKmWPygGpFGk6VNOTog5hOJ8K5YSjFP4AOOH0Gf2enXu/fv3a69P2sr0uS4/WWl5eXvZl+75837eXn986KAgBISAEhIAQSIzAbyXOT9kJASEgBISAEDiIXNQJhIAQEAJCIDkCIpfkkCpDISAEhIAQELmoDwgBISAEhEByBEQuySFVhkJACAgBISByUR8QAkJACAiB5AiIXJJDqgyFgBAQAkJA5KI+IASEgBAQAskRELkkh1QZCgEhIASEgMhFfUAICAEhIASSIyBySQ6pMhQCQkAICIFs5PKP//i/D9/85n8+fOYzj17/vfjifzi88sr3Dr/4xb8KeSEgBISAEOgYgaTk8utf//pIKO96162HBx984PDcs88evv3tbx3+x9Wrx9+f/9mfHb7w+c8fbrjh3xz+4A8eOfz0pz/tGFpVTQgIASGwXwSSkQtEAak8/OlPH4mE69jvR//0TweIhvRoMwpCQAgIASHQFwJJyOUHP/jBkSjQUmKEEor/hx/+8KjhfOxjHz2g9SgIgT0g8Ktf/eqovaPB+7/bb3/X4a/+6r/uAQbVsXMEVpMLvhU0kL977bUjsaCVfPGJJ84MGncQ3X77u0+lx4T2xBNXOoda1RMCpxF46aVvHMcJZGPhy19+6hj3wgtfsygdhUCTCKwiF7QNiMXVWCCW8+dvGNRgIJqbbrp4QHNBo4GQIJjvfe+/NwmiCi0EliCAhsJYcMmFfD73uc8e0GAUhEDLCKwil6985bmjg941eTFYPvrRB48+Ffwqod9TX/rScVB97U/+5DoJ4fS/7bZbZB5ruTep7LMQGCKXEOnMyrzzxJ/4xL87oPm54fvf/9sjKYPdPffcffjhD/+Xe1vnIwiAHxMb8OPH+b/8y/87g/NINtdvLyYXtBYKYNoHBINpDI3kxz/+8XXScInHzv/vT35yeOFrXzt86cknT6VjJRnLlxWEwB4QCJGLxcksFu8BhpFLLghBhCEBTdC0v7feeiueke5cR8BMtG6/AzvD8XrCGSeLyeW1135wRmtB+3jggY8cfvLGG6dIw0jFPX7n298+Qy7f/e5/O2o9M8qvpEKgWQRMSNpM0Y7MuhXCCCDwEICYDV1yAUs3QDbg6ce7aXR+DQE0liGs0BJ90+0U7BaTy7PPPnt46RvfOEUikMvnPvvZow/FJZLQ+d/8zStnyIV0VFIrx6Y0ndK0joCRiztwiUNwQjCadZ9tYRY8gJdPLmdTHo5pRC4hZE7H0deGfHyQz5K+uJhcHnnkkTPfs0AuDz30qcP/+ed/PkU6IXIhLU58/94jj1w+xp2uvq6EQH8IhMiFWlq8a6Lor/bzawQu5kcZIxeEIRNVNBiFOAKGE9pJ6rCYXB59NEwurB5jxRhmr9jvP7388nGVWYhc+AgTwlEQAr0jYCTiai7U2cwUIpeTHgBJuHiMkQvYuulPctKZiwBkDQmjEaYOycnlllt++1hYCjz2E7mkbk7l1xIC5kR1yYXBjplCs+7TLWnOeosdIhfwJL2Lqz2n42kEzDfl43s61bKrxeTC3mCYtlyzFtcMCpYi//Vff/eonfgEwzLk//jSS8d0IXLhWWkuyxpTT7WBAELPHxfuNQPdzD9t1ChvKW127WLknvumLzSWJT6CvLWoN3eIml/qsJhc2BOMb1hC5AKxEP+V5547NYgwmf3oRz863oNEfHLhY0o6jYIQEAJCYAiBmOYiYhlCLXzPNGhMiaEAufsEHkrnxy0mF7Z9uXTpriC5QCI+sdhMA1J57AtfOJLI/fffd+p5vvS/ckXbwPiNpGshIAROIxAiF4SjLwRjAvN0brpCW0ZGQ86uORH8lmK4mFxoDkjENY3xQeVUn8vFi+ePjn9X84Gs+H5GQQgIASEwhIBPLrYnm01i7Sin/gmKfOKBvI196gGJmL8P/FhBxuKSpWEVubAXmG/a4it9vryncBxDP+79+z/901NaC9/MXLp0aWk99JwQEAJCQAgEEODPGR944P6jTH73u287Hj/+8Y9m/9PGVeRCPdgu39/GBXaEQFytxD3370FIaEGkURACe0KAgf/YY9f+QI9xwYz8L/7ixT1BoLpmRAAthS256Fv+7+abb4xqMSmKtJpcGBwQg+/cd8lk6NyIRTsip2hO5dESAoyd0MC/cOHc4cqVx1uqispaKQL0I59U3Ovnn/9qtpKvJhdK9rOf/exo0mLjSVZ8DZGJe4+9xCAmbVaZrX2VccUIXL78cHTg45OU/7HixitYNCYhrtycc37rre+M9jFI5oMf/N1sNUlCLpQO9YuVXqbFuLsl+2BAKg8//OkjIbHqTEEI7BEBdwYZOn/wwY8sFir+mJtz/cor3zt861vf3PTH33l85jOPbv4LtUvpOGTqUizGyvqBD+TzcycjFxMOdGJIhkrh7EebwWT23LPPHgkFoFgVhhkstmrB8tKxLgT8FTn+sk9KyzJGWzeP/0DhLAL0e8bJ2MBn1rlUqKx5DsG+NblAcHMIMVfa1mXUffd9eLCfPfTQJ8920EQxycnFLRcNjmrPIKKzco2Kp9AeAhDJ2P5DpIFQ9IX5SfvaGMBJj8BncsV44BzfyhDByO9ygqPOliHw+uuvR/sZ/Y/+mStkJRcrNANIoW0EIJaQpmK1YrsNiGWMgCx9b0ezizOJ+uIXnziw1JN+j9mBa+IxAbuTK5ypMXLB55Jz4PeGv+oTR4B+Rn9y+xrXV6++Gn8owR2RSwIQe88CUrGOCYFg9vL3vuKDqxzbdteILUIfs41pI2BjdnHi0NanEAMmF0zEvgbDde6BXyOuKlM+BFh09cwzTx9Jhj7qTnJyvVXkkgvZDvOFUCAWSIQveS0Y+aC1cA9hi2ms9c0DGZBoG6aNoIVQN7QS00YgkbUDFSLhI7c777zj8J733DmJmAx7HYXAVAToq5hjSwWRSymkO3qP7VL7xhs/PtaKbSMQurZVhPleWtFkzMGONmKrlFxtBHJBG4FscgYGf87VOznLrrzrR0DkUn8bqYSHa38ha6YxtBl/ZZgRTm3aCwQBUUAYzOJMG+HcVkkxCLdaJQSpKQiBHAiIXHKgqjyTI4BWYuQCkfjkYtrN0CKA5IVyMjRtBBKBNFwHO0RCPCav3NqIU6RJp5QTIaAgBFIjIHJJjajyy4KASyaYx5hxm5mMF2Iic9NkKcTbmTJo0EbMwe4u9yXOvpnYShuZU3eIkPIqCIHUCHRBLgxiHJ6PPPLI4dFHHzlcuvRvj0fO+QdLfZWfutvkzQ+iMA2EjyRx1pt/xd5MHNoM9/lxjkaTMixZ7pvy/SXyMr9PiXfpHftCoAtyYbZ42223HNjmhf97cX9ffuqp47LNfTVr27W1L+7RToY+kOQeafitJRYGAoLWtBHyXLLctzXkqTemMQUhkBqBLsgFmzbEQmVCPwSFghAAgVLLfVtCW+OjpdZqp6zdkAvaCoOEH5Wyczu20yQqaQoEzMFuZh8mIPQF00ZKLfdNUZfcebCCjTGjIARSImCLW1LmOZRXlu9cEBzu3x/72gtCRaFfBGpf7ls78vgrWaCgIARSIgC58CsVspKLaSmhY6kKhpbJlnp37+8xbcRmRK0s9629XcATX5OCEEiJQJfksqVZjG1KIDd/dVPKRttDXrRhL8t9a28vsEb7VxACKRHoilx8c5hdlzKL8SEfS2IhmL3u1ju3c+5hue9cTEqnRyMsNUZK103v2w4BkUtC7CEUNJYXXvja8YM+vr9QOEEAst/jct8TBOo9w6lf2+4B9aKlkk1BQOQyBaUJaSAS27nXviBf++3FhNdWmUTLfatslsFCYRaTU38QIt2ciYDIZSZgseQQCR//WYBoMJH1HMzBruW+7bcygkBO/fbbsaYaiFwStQZkYluWkCVkgx27tl16l1ZXy32XItfGc2yRJKd+G23VSimZrEAwpUK2pchbfqFvO/JCJv6vNdOYaSN0ipZ29y3VgXt9Dwsr+MBUQQikQoDJCn7WUiELuTz33LPHgfF3r712ZvuXLz35ZPaVMObI90Fk7yvzw/j3arim4bXct4aWqKMMkMvaf7msoyYqRQ0IdEEuDIiPf/xjZ7QGtAgGTE5HJavDYlu9c48yuL6YLRpdy323QL29dyIMtIN4e+1Wa4m7IBcfXAR6iWB+FTOFuUuPfVOZ79xH4OMIx/wE+WGOShG03DcFivvMo7QDdp8o76fWIpcN2vrq1VfPaFk33XTx8Prrr08uDeTELBOBwN5Q9ve5bInCNfEQDekUhMAUBJjkIBAUhEAKBEQuKVCckQeEcOHCuTPkYtqPTwbmYNdy3xkgK+kiBFgRKKf+Iuj0UAABkUsAlJxRly7dFSUWCOZTn/rEUeugYUwb4ZyVW6aNpDKh5ayn8m4TAfqg+lebbVdbqUUuhVvENJTY8eabbzySCBqOtuMo3Dh63dEsVnL5qCDvFwGRS+G2jZGKxX/wg79buER6nRA4QaD0h28nb9ZZbwiU3q8uy3cufqMgqGsNDz30yUGz2PPPf7XWoqtcO0AApz4LQhSEwFoESsvh3ZMLpi7TUvzjxYvnZe9e26P1/CoE6J/MOGOB5fd8HBz6doul+Nyzft3a7hSxOit+GQIil2W4rXoKm/Ztt916fRDeeOOFw5133nG49dZ3ys+yClk9nAIBhELIqW8fBXM/RC4Qi/2PEfvs8XGxCCZFi7SZR4xc/ElIqC9RY+LZ4YRvBqeE3WsuBhIOe/wrEI057lluzKwxNLDtOR2FQG4E+FZqyKkPafgCwf5mwt2oFWKJ7V6Ruw7Kf3sEYuTC/11ZP7EJC0c3kIbn+RUll1/+8peHn//859Hf+9//O9F79txvfvMbty7Fz2OOU9sssniB9EIh8DYC9EEmOrEQIheIBEHg7lJhhMNRYX8IxMjFRwLtJKThov0WJReI5blnn139e/nll/06Fr0emh1yjwGuIAS2QMA+2I29O0QuNgN1iWSucIi9T/FtIjCHXNxJidV2bv9ZbBbDdMS6aey6T/7RHw3+2MdrLA33yY+VMaXNULxvCHjuYx4bmj1aA+goBFIjgEmMCU4shMgF4UA849MEhZk2EBIK+0NgSMaBBv2C/uKbxAyp4uQCIaT8bUEu+Fuow1CATNmKg7QKQqA0AkOCIUQulA/bOCYOnkVo8Kv5LydKY7q39w31IX9j35BfpRi59NQwtpXLWJ0gFgjGHP5j6XVfCKRCYMhsGyMX/90Qi+/499Pouk8EkFlDS9qt1vhasDSFJiEiF0NpxhHQh1bjuFlpBZmLhs5LIYBGHzPLTiEXliT7fzNRqux6z/YIIN/GrDNWSiYg9Ck/iFx8REau2fV4SF0MPa4VZCFUFJcTATZJZUVjKCAI8KeEAuYNzGEQi/leQukU1zcCc8gF7YU+4weRi4/IyPXS/8zQCrIRYHU7KQIh4WCDnckRP1czsXsQT2hZadLCKbPqEQj1n1Ch+d6FfuSuMrR0tpQ95vC3dHZcvFrMMmj9OPYNQax+WkEWQ0bxORAYW9GY453Ksx8EhsiFCYhNUNBYmJj4gQmKpeE4xXe3e3LB37LUQa8VZH4X1HVOBNb01ZzlUt71IzBELrlKv2tywd+y9p/+tIIsV9dUvj4COPUx4yoIgbkIiFzmIrYyfartzLWCbGVD6PFJCAw59SdloES7RUDkUrjpl/pbQsXUCrIQKopLicCUj31Tvk959YOAyKVwW6b+IFIryAo34M5et2TZ/M4gUnUjCGyh9e7W52LO+EhbLIrWCrJFsOmhGQgwIYJkFITAHAQgF34lw27JBT8JDtLUwUhLe5ClRlb5gQBfWatvqS/MRUDkMhexFemHttNYke3xUa0gW4ugno8hsIWQiJVF8e0gsEW/2a3mktu8oBVk7Qy8lkoqp35LrVVPWUUuhdoC09WUHULXFmfNCjLb3yf0JSx7RPElrX0xq+091rZUO8+b2bWdEqukNSAgcinUCmgVCP4SYckKMvsXwdg2CxALu9wS2KpB+0eVaMl63kG/kFO/nvZooSQil0KtVPJL5zUryCANX3OxzePYYM4CmgtpFfaBAE59vltQEAJTERC5TEVqZbrc/ha/eGbKmLt1R4hcbAM5d/t0I5zQTqZ+WXTdPgJsvY+wUBACUxFI+cH41HfuzqHPjK+Ev8VvgCUryELkYiYzl0hse/XQX5P65dB1+wik2raofSRUg6kIbKHt7o5cmPGV8rf4DY+vB60JU9mUECIXNBbi8buY9sIfRWGHD22VPeU9StMWAqUWpLSFiko7hIDIZQidRPcAea55KtGrj9nYCrIpBBMiFzJBQ+E/riEUSIZf6D+vU5ZbedWFAG0/pQ/VVWqVZisERC4FkK9hUE5dQRYjFx8miMV3/PtpdN0XAlsIi74Q3FdttugvuzKL4W9BsG8dbAXZmFN2CrmwJNn9e9ut66b3l0EADXis/5Qpid7SAgIil8ytxGBkpU0NYcoKMsgFf0ooYBrDHAaxmO8llE5xfSJQ8lutPhHcV61ELpnbG4Br2vQvtoLMVn9hwuPnaiZ2D+LRl/mZO0zF2deihVcMkYrmICByccDIcVqDv8Wv19wVZP7zut4vAvRnBSEwBQGRyxSUFqZBS6jB3xIq/pwVZKHnFbdPBOjP+lJ/n20/t9alPxynfLtx6ONrqcXfEuoYU1eQhZ5V3D4RYFKC5jsUWPBh5tXQ0faoG8pD99pHYAstdzfkgvCuyd/id9epK8j853S9XwSmfhBs2wP5OziwEKTVJeyUmyX4fp2sNxipDqWxtHs4ilwytTKCG3Br/+hsygqyTBAp2wYRwCSGLX0s2CKQmCAee762+7YjBWM6VCfus5KSALGy+MXd6LW2+pQoj8glE8poLFMGYabXz8o2toJsViZKvAsEbNI0VtneyIX6xupk8e7ee2gxezf/iVzGRsnC+63tIqsVZAsbeoePsQkrGu9QMIHrzvKZybdqEqOuoToRH/r7iVDcEF493hO5ZGrVFlfVaAVZps7QWbZT/pvIBDECxv21PJu3OrmESdNiEvP32SMN9d6zaUzkkmHgTzUdZHj16iy1gmw1hN1nMGXXiZAgRtDGdn9oAbRQnSg3hOl+dEyckQvP7DWIXDK0fEv+Fr/6ECNmD+0h5SOja0NgilM/JogtjxaPsTpBmD652H8gSXMp29LdL0VufYM/rSArOyBae9svfvGvR5PPULljgphncHwjfFsLsTqF/CuhuNbqu6a8W20V1D25MPNv/StmrSALDy1zSqPyD23eiSDCXEK6lv0MYRQOxz+gG3Lqx75zARf8Ey3O6GPkYvHuajGWJffY7rH+4MbTL5hgIweRI35g3DAuhn5DY8vPz73umlymzOpcMGo+1wqys62DYLRBERsAzFqNVFoUomdrfTaGZfYhwUFKI1XDyT/a9yBnc607xggzpHVRZ6sX/pa9fudy5crjh4sXz18fIxcunDtiEZqIYE6kb/jjiPil46Zrcuntv8a1guyswDPy8AcFKc3WTpqeAz65PfnlrM2NKENLqiEX7u/1C30+v4BMDCP3GPqrdTAkTWgcLR07XZMLwnhs76WlwG31HLNU6qVwDQETNP6g4Hro/3B6we/q1VcPt976zutC5NKlu6JaTC91Vj3GEbjxxgvX+4RLLJyjzfh/9S5yGcf0VIopH5ideqCBC1aQsUR5TzPVoWaJkYvFM2ggGQZVb3Z3Zqfnz99wRogwY4V0FOpGAPMU/uC5P4jBtNXQkcnnELkwFvwJqk8uTM6IWxO61Vzwt6D+9RjolNTNn330WNexOhmJ+JoLZhFMIjh4CZZu7YAZK0+p++ZP9Geldn3TTRdLFSXLe3IJ3pAwJg6ixiqw5GeYzz0y+V3yPj6cjdWD+K9//YVTvpZQuWLk4qZdOxnrllx687f4I5jZDgQTcs75aYeuTei6ncrOEdDcrzlY+X1y4VsHf3AY4dRcn6llw9xr7RQ6YvogjTsr5npIKMXuIYiWCEE07FDZpsTlEryxOhLvYjXnHGtCbYHJRQxntF1/YirNZUYLMiB687f41aeDhJxzfrqxa1aD0BFdImHGb05RjrWGGLlQZr/cDCBMZK0GBB6rwhCEUwQ3aVxSYEwMCdfYPZ+k5gjeVrFuvdyYRWMO/bvv/sCZ6vnkcibBgohuNZcUs/oFeBZ/BIGBEFkze2LW75OLVcSWKNZqToqRC/E+kVAXn3CsnrUcXQIxjYG+TPvYbB4Tzh//8dNBf4vNVhEsa7XaWjBROZYh8J3vfPvYb2w5MseYrBC5TMTYfBITkzefjNkpgmhpGCIX8kRI+4J66btSP2fk4q/Fp074XMw0hiZGHdyP61KXZWp+UwnETDUhkmAyYULDCMU9PvDA/VOLo3SdIoBMYBKC5gmp4KeLBZtE+uMoln5KfJeaC2Di9NpLWLuCbIxcmO0juMw5XguuEIcrUP0dchko+F5IA9GEPrjLVZcUBDJUNgTH+9733iDB7EVrH8Jn7/dswQdH+iIT0FCwse+Oo1RWii7JZco25CGgW44zbc131E2pk3UwtIBQMCHuC+9Q2j3FgTkDFw3DVhuFTFhDGshcvJhIICjMvIHw4N1c8/vLv/wvq0ykc8uj9HUiwOTDrBlD5JKz9F2SCwN8SAXMCeiWedOJlsxax8ilVs2lBNYhAsH3wUzP9YGkJJBYvUxDZfLEuYIQCCFA33BloMglhNKCOIQBg36vYckKsjFywVeBWanXUBOBxDCmjAgMm43G0ileCDDRcfvJVjKxO80Ff4sL7B67GvU3s8mU+g+Rizn6YiazKfnXkKYFAonhZLtiLzF5xvJUfJ8ImNZCf3cDmnbp0B257NHfEuo0c1aQjX3nYiuuQu+pKa5lAonhaJqoiCWGkOJdBNBaQs57kYuL0sJz19a4MIsuHjP7PJ1tKNhSXne1iJ3jaym5wmqonHavRwKxuvlHHPVLfGh+PrreBwKmteBj8YPIxUdk5jWg7tnf4sOFIEY4tTbr3ROB+G3GNULCTJt7XJgSwkRx4wjEtBaeFLmM4zeYwndkDSbeyc2lK8hyw7N3AonhaxrnHJ9ZLC/F7wsBJpIhrQUURC4r+wK2xtZm6SurPOlxs9sjuJgJc80PAZ8ziEDmoQtekMreF6TMQ02pQYDxHPK1GDoiF0Ni4REAEaAKZxFAYLGk2N3MjvPLlx9ehZkI5CzWS2LAkZnnmI9sSd56pn8EcAfEtBZqL3JZ0QcAllmfQhiBZ555+nDu3DuOnYyO5v7GcBOBhDFNFcusk/bgqCAE5iJAvxnzNYtc5qLqpGfGx+oahbMIYAob2uQQDebv//5/ntnKhA5Lp+SIyg2+4AyRQzgK6xHgu6whW/n6NyiH3hFgfI5NTEQuK3oBwo+PzRTOIgAZ0LmGfgg4EchZ7HLGYKoEdxF1TpT7znuK1gICIpcV/QDw5G8JAziFXGTrD2OXI5Z+CpFrRVgOdPeV5xStBURELgv7BRrLmN9gYdZdPIZZbEhr0R9LlWtmiIW+qs0ny2He65uYNEIuU4LIZQpKgTT4AuRvCQDjRH360w9FCUbE7ACV8dRWhGmpcUaQd5Q12u+Yr8Xg2MKy08XeYghH+VusG5090gGx7f/hHz52yrGPxgJ2MieexSx1jG0+iQNfQQisRWCO1sK7ICKeKRk2JRf+JdD/1zP+7dD998CxP6hCMG7ByiUbac270Ohcp7F9RImQkyN5DbLTnzVynzrLnJ6zUu4VAchijp90V+RiGya65MLW7/xviG3vbmmG/vecGSHAKZxFQKuRzmJSOsYn99Lv1/v6QwANhAnjHIvDbsiFLd75nxC+GHfJBTLx/5SKnXn5xQKDdw6Dx/LpLR5ikclr21a1NpCGuG079Pb2uVoL9d8NufD/IGgpPrkQj0nMDRAO6WIBAVralhgrSy3xJtTmzGxqKXsP5QB3+qXIvYfWrKsOtihk7tjeBblAFuZH8cnFtBm3Oc00Bhn5AYC3WGLnl6OWa/BgiauE2nYtwuAHfwheQQikRoB+tcRS0z254KyHQCz45ALpQBaWBkLBJBbTXORvMSSv/QeIZssneGxxZrNKLYvfAv3+38linLm+FkOle3LxfSc+uQCEaSpGMvhgYn+zu5TFDfBejmaGAY+56nIvGGxdD60I27oF+n8/45vfktA1uZhWAmmEfmg1fiCOtGZG8+/zdere/S0usfj46LoMAtp8sgzOe36L7bLBcUnomlxCgIQ0F0uHSQznvpnILN6OBrZd7/EIBrLvb9vyzCTd74i2LY3e3isCa7QWMBG5vN0zMI0NmcNIhhkC5/Veg9n3l6rJe8UtVb21eCIVkspnDAGbSC/VWsh/9+Ri/hY0lu9//28HMUeo7nUrDSOWJatGBkHVzUkImClSm09OgkuJViLAApG1k8jdkcsazPG3IGT3FoxYtJXINi1v+K8d7NuUXm9tDQEmMphd12gt1BlyKb3/4qZ7iy1taIAG8L0FE2wilm1a3rbd2KvGvA3q+34r1okUExnyKW3paJJc9uhvoc6snBOxbCNshP82uO/5raa1pFgRK3KZ2JP25m9BsKGpiVgmdpDEybT5ZGJAvezskwP3EwX8r3sPEALmrBRB5DIRxT0t/TRi2aN/aWJ3yJqMiQzLvYV/VpiPmQ/txpH/7XW9IaXWQs1ELhPa1/wOE5I2n0TEsl0T2oowiIVzhfwIsBNHbKun/G+v6w0ptRZqJnKZ0L44U/fwfYtMMRM6Q6YkTGDs41QRSyaQA9mKXE5ASb37iMjlBNvoGcTSu+8BU8yeTH/Rxt7ghmnG2nyyPPgil2uYI99S+VqsFUUuhsTAEaG7ds33QPab3zIbv2bM5ZvCzJC9T17KIzvtjSKXazihtaT+JkXkMtIHmVUCfHHBPQMAAB7aSURBVK9BxLJdyxqxpB7U29WovTeLXK5ta5VDxolcRsYD/hYEcG8BLQVzn5zH27SszJDb4O6/VeRyOE6ec2jOIhe/t3nXPfpbIBZIRcTiNXaBS5F6AZBnvAJy8f/zacbjzSeFVHJoLQAjchnpHiX8LS+99I3r/zdDRw/9vTIfeHGPtGuCEQszZ84VyiFg2OM4Neztn0/tYz6EnRtCH/uRlo1WFZYhYJvVvvHGj49jas8fT0IsObQWWkbkMtA/2QIhF6vba+nY9sdkCBK2/ff/T4bdmk34rCEXE249mvkMz1qP5rvzsaetrf2tnd32p73pF27g/p4FoovFknPw5NsWxpSL9ZK8Wn4mt3wTuQz0DsDxhcFA8iS36Oz+7NUyHvqjM0sTO7Lazb6jiKVRfB4EYptPvvXWW2dIwvcB+MRCCZmAhOLzlF659ooAGnQurQXMWKiSennzWFs0s3FlbvBDQGH6Ql0PhaXkYt9RlCbKUB32FsfgZYY8dRCjkQx9MU7fgFwUhMAaBGzCsyaPsWd5h8glghJCwWzjkSTJorG9M2sdUtOXkIsRC1qYQlkEwHzuh6lDmiul575MYuvbkVn1Y499/qjNP/PM011/xxZCC6GfWyaIXELIHw4HgMGMVCJALOZT4Rjzq8wlFyOWqbPmEnXdyzvQEvHX0QZzAloJ5rJYkEkshsz0+CtXHj9cvHj+1Jjj+urVV6dn0nBK01pyT5xFLpFOAquX3o4Dxy5mMQgmJGDmkIuIJdKwmaNt0cSSZd5oJENaiUxi6xuPMX3hwrlTxGITOwgGgdh7KKG1gKHIJdKTaIAtvpyGYOjsIYftVHKZa+ePQKDomQi4iybmzgohjpjGasWQScyQWH7ETGlkEjqi1fQcbNI5t38uwUTkEkGNjleiAfzX2zJJP57rKeQCsTCAZAoLIZgvzgbtkkUTtPkYsVBymcTWt1+IUNy4Uqbw9TVZlgP9M7evxUomcjEknCMay1adDLNYzDQCuQw5/I1Y5tr5narrdAEChvsSQsf86bcpcXzz4gY0Wn046SKy7NwlktD55csPL8u4gafQrJl4lpo0i1wCnQK7bCl/i/lY6OgID1+oUDxmtu5ACAkZE3AilkCDZowy3JeYUE1LddvWzn2fm0xiaRrx93//U6fGkuHNEV9Mz059tJYlmvVS5EUuAeTQWpYIi0BWRaIgwrlLXosUrPOXMFCFezuNzMTr3ns/dDh//oYgwVy6dFc7lZlZUrQWCJRjqSBy8ZBGZaQRSqmO3utnX0rAzYZs9QP0DdtRuuRgXV3wHWfAZJGJAP4GSOaBB+4/RTBPPfVkdWMeH5tpVpy7Ac3WrB4cfU3XTct5aa2Fd4pcvFagE5b+qtQrwuRLOsySJa+TX6CEZxCAWMCcPtLKBORMJXYWAaFALCFrRK3jfWxZOqZxWwRC2pCp3Jp5C62Fd4tcrAXePmJiKrWawnv1rEsRyyy4kiRmxsuHkWCvUD8CroYZ80UieCGe2sIQWUAmLO5xA5pNbCEQ8myLPitycVvocDjOSgGl1uAOGM2cy7USwsnMKuXeqjctRYD2QsPEfDk2Tmozg0MSZg4zDcU1e2EG4+cGto7y47hP3em3W5hveTf1KBmq3bhyCzDmAE/5GDAyhc1BbX1aVoQxSJYsNV7/duUwFwHXvzLlWUycNU4oIRlMX2gp7k7paCn+8nXS+X4Z6r6V1mK4i1zeRqJW+yvFM2JBveVcoQwCZq+PmVXKlEJvmYqAtVfIvxLLgzHFc7UGIxgrX+hjaj8NaZETaC1bEqfI5e1Wq7WTucRiHUzH/AjQH5ZsPpm/ZHqDjwBjxFbwzZ0IvPLK9zbxSfh1iF2zNRBC2v6hFg0FMnEDmoyvuUCYWy9OErm83UoIki1Z3u0sdo6tFDMYgk6hDAIIKgalzI9l8F77ljn+ldC7GPNbC+FQuSzOdk03cgn5XPy4GrQWyi9yORyODq/SQFjniR0ZNKi1IpYYQunjXTJngCrUjcBc/0qoNrRzbWPfLSeai+usD60Ww1TmrhZDG6uBMEvjWqVDH2ctanUtwYilZltwLVilKodhLjJPhWjefJb4V2IlYhJH+9cQIAnTUtgiiBVj7moxyogJzMgEE5m/dLkWK4zI5e0vWGH7GoIJOa1OKtcaNgMW5uUwX/omNA0mgin9Yczy5ywCWFr2Kc+hpSCU+bFKzCcW8iAOQiEN6d009OEatBbKOZVcQgTpYmV/RWKk695zz6vUXFJ2VLeyc89FLHMRW5+ewcjMVcSyHsvcOTA+8IUhPFOaLdGCerESIMtq6ctTyMUWLPjal/UlCAVNjbyaI5davtKlQwBgLR3DGrfnIyawmkwiPWO9tm443mmrHDuWM+ZqMosvxYp6QC61hCnkguaFhhYjF1bC8WuSXGroWJRBs+dyQ4JZL8TCLHiLr5fL1bSPN2Gyzjk+0IhqEspLW60mrYU6jJEL5jA0lxi5YA7Dt8SvSXJByGzpbzFioYMr5EcAYoFUtNQ4P9Zr32CTAIRm7vExJgjX1iX387VpLdR3CFNIxb7XCZELJjDiCc2Sy5ZmERFL7iF3On+boWpF2GlcaryyZeGp/SuxujLZqO07t1hZQ/GUH3lSUxgiF3d5dYhcMIXZQoUmyQVhA7lsEfQnX2VRt7buxXFbFr2yb8vpX4nVBJ9LbcI5VlY/HrxqNOvFCBviYJm1BZ9c+EdeCMVCk+SCOWwLR54cydZtyhwRGsyiWhUeZVCq4y25/SuxWjLpyLFYIPa+lPFodzX2bcrla4OYuxiLsR9EYsusQ2nMVBbCr6qlyFvMVsyRnHIpZQhoxV1DAKGBdup3cuFTFwIl/SuhmtM/EIatBcpN/65RnoTIJYSvr7n4aZrUXGiUkquFRCx+t8l7Dd4lnMF5a9F/7qX9KyFEKcNWJvJQeabGIcBrNfXullzMuTu1EdekY1aBlqQVSmtQnP4seNOxhfd0zLZKaTPvGkxSmGFKTjbXYm7Y1ai1ULfdkgu2XWa2uQMNj5CToMuN9LX8DW/IvNZBVwaJ+t+ylX8lhsxUYRh7vnQ85a1VawGL0nhW43Mp4W8xQQeJSdDlH3q2IqzEpCF/bfp9A2OhRpMl2lPNwtrtEWbGq1mu7JZccvtbXGJxO4XO8yCgzSfz4Jo61xr8K7E6lbJmxN4/Jx5yrp0Id0ku2Cpzrgu3AaQZ9JzhsjwtyzCZLNS4HHN5rfp70nwEtY4Lyof5uvaAfME/VLPWAoa7JBcYP1cHl2mm7NDUx6hl8V76NrQCBGLNEwCENWWsPSC7csmvlHXfJblQ6Ryd3IildnU1ZQfaKi8EAQOMmSYzOYV6EaCd0CwZH7WH2peum9bSQp/fJbnkUCmNWHKQVu0DsnT5zJ+lFXilkZ/3vhbbCYFYyx+HhdBuRWuh7Lsjlxx2VRFLaBjkiQNrSKUFs0AeBNrI1cZEa+2E1aFWy0NLWgu9dHfkQsdJ+cEWmkrttuQ2xNF4KU1gpWy/8bcqxVwEWh4TlB2hWGNAdrVE1pQVX1upsPl3LinVXjqiVimV6TotC6wyCNXxFgRKK/6VEGJMYHKuJA29c0ocJkZwbcHXYvUprQVuTi6p/C1GLHRGhbwI2JfcmDQVpiHAlubu7rLuFubkYJsBMh7cn/2B07S3nKRq0b9yUvrTZ+BRW0BQ8+F3S2FX5IKjLsU69tLEwv8b3H77u45C4J577j7w959+cIWFL0j8tC1dtz4T3gpr/ozJ/mzJ/oOcfmSBnWjZ/twN9C3+IXBuMHNlSyaboToiI2qayJjWUlOZhvCze7siF2z1a+31PF9S7WcGav/ahjDgHKIxwUFDIjQQDMSRhnNXkFhjt3RkQGHC1Iqw+a1G27t/xkQO9Am3H/nEQnrSzA09mivREEr6CsYwR0jX6gcaKvuuyAVBtWaZ4RazaF8LQQigtrvxCAX3mvMlgmKoo5S8ZyYWbT6ZDnU0FSOXUK70GTScOWGL8TCnfEvTIhTXTkKXvtt/rlWthXrshlxoJIQyxyWBgVTLLBrNxcgEMwb1cs0ZRkBu3JI6b/GMb2KxulBH+xFHQGBaHEeuFcII+BMQPxX3p/YXI/9axoNfl7XXmJ9q0RTQoGopy1xcd0MuaCxLG6kmYsH0hSA1AYsJhGvXTIbJg7haTWMQyH33ffg6Mdx008XjTJFBjckxZJLAOc3PD/ifqGvID+Wn3es1fSWEneHB/amark/+lkdPR1Zk0Q9rCKxca83XYrjthlxQc6nsnMAMDdNMTTM033zBNcLVtaEbuZh2M6fOudMinCiv/zt//obDxYvno9vyoJWENBMEI3kZ2eYuf4v5g9sQPn6fitWxR/9KrK70qa2X/YL30glxrF4l43dDLhDEnBlAjao/pIHd3CUS01zcONNuatRcLl266wyxGNFcuHAu2kYil2ViAeIY0+qmmMTMvzJnDC0rcR1PIdS3ritaCwTTatgFuUAUCLCpwYiFAcV5LQGHq2v+olwhn0soroY6MBNEOzEyCR2feebpYFFFLkFYBiMhlrEJxphJzMYCk7OtZ/KDlU18c4mlI2URIJUaP+acU8ddkMscf4sNJoilphAiFiuf76xFqEy1oVseuY6YwZgB4kcBU7STEKlY3OXLDweLArlYmtBxyOwTzLDzSLQV+oEbiPOd9nw0GftwkrZDwNU2yXLrlOvc+muu/MfybV1roX67IBcGBxUdC8zMmKHVRiwICV94uoLDyATTGJoNxDI2Yx3DYs59IxAwZsaHSYHBAQngGOXa2iBEDG5cbAmoNJfpLUJ/cDG189CEgzifcHgTM+fY4orpJdkmJX1/7KNjK5mNHTByxxgTImTBFqEHrQXcdkEuCLox+ykCksFUG7HEZuz+NwmuQOE8dQA/NEA6DBi5BAK+XJspgbTgGQpXrjweFHwMbkxmMdOLyCWEZp442pGxMDZm8rx9Xa4QhH3PYz5K/6Nj3sA9VtBBrrHxQp/cIjCWWva1GGbUoeSWNcX3FkNYjXUSI5Yp2o0B19sRc2CIQBAy4Mcsjk5vs5EhAhnChvfcffcHDqwOI1/7cX3XXe+L+rhELkOoprlH29DGLftXfKKAbOhjfrwtbXcXwvgoMmmKTZL8tKmuGVe8t4dAXehPpUJxchljTyOWHmYKY41oBEJdIQlmFTS+CXiXQLA50zlimsTYu8buU4bHHvv8UZAxUx4zSZow8PPFj0D5x1ZE+c/p+jQCjAOEGlop/aSn4H50TL3wMYW0Gb/OjI01O3r4+U255p29yKLuyYXBEvooj4bukVgQ0jQqdYZA6KwugXAOqXCPTkzaWoQJ5YDgXNOkzTyNADmabdw3GXKtMB8B+kGr/pWx2tqyfOszpMcUhumMH/2J69DkxLT0sXekus9YpB1qGY9r69U9ucRUWwYUHavFWQKk6BMIQpn60DkhEAR0jQQy1mEZWL0KurG6b3G/Zf/KFLwwh7n+SVumb3Hme0GT8U1kc1aZTinLWBrGLWO2l9A1uTCLR1D5wWZqNROLEQidDQFAx4MoQwTCIKAhewk9apS1tQ0kTp9q2b8yhilk4X90bGZUV5MxwvFXWNIPS/k/GL89aS20TdfkAnn4qxWMWOg4WwfAT7ECa+t65Hg/7QOR9kSaOXBakqcJzR79Ky4eoW/DjEjc5deQEH3Nd/qTF/ElzFRmqnbL3/p51+Ti+1tKEwudMkQgzFDotK4DHQ2FtDWQXi2dunR71VLvnOUwTGN+yJzvLpl3iFjs/b6D3/wyLuFYWsZo7gmOWVhKkJjVq8SxS3KhUvxuueW3rwtrsy2nFt5GIAxaCGLLFVglOkzpdyAEezMXlMbQ3mdjILewtPdtdUQDcc1elMPVSjiHYCwNC0Hs2xi/zP4E1b+f4tr8oynyqimPrsgFExPbt99444WjZoB2gGDiwz2OS4ml5RVYNXW2pWVh8DGD7G1mtxSPuc+BW+/+FcPEX0GIDOBnDnxLB8HYPZ7xnfmWznyedp36iGyhHBx7C92QC8RhncU/njv3jsObb7452HY8DxjuEl4EGnlBTAxOs4uipZBWwm4Q0qQ3jWCSZrqDzOjXOKXpu+qv8xs8t4CkX/PrMeTGzscs20eUDz30ySi5QBBoL0YgNhvZ0wosvyFau0YwQva9DsQc7WH+Ffq7wjIETLNY9vTwU5Z3j1oLNe+GXDCH+RqLf80MDkLB9syAo/L8FNpAIAXBTNnU0DWZuLb6NlC6Vkr6Nxo3pmKFdQiAYw4C6FlrAfFuyMUnEv/6ttuuDTSZBtYNtK2fZpAz2JmVzw04cM1xa99A+NuAQD58sc0KItJw7n//MPe9JdPTvzGBoeWhqSusR4AJaepJKO2EjMpBWutrnCYHM8mmyW08l83MYvfe+6Gj1kKDosEwa0BAaQCON1ptKWizJQTjayGQDf3BjYdM3GvOiWshgAukIv9K2tYyS0fKXNEs92DiZXyVCtnIhZnF0L8cujME0uK4ZxAipPhxbqayUmDoPcsRwNxDu62dHLjfPIQ+sDMCCn0Dsbz06Z80POjDCmkRMFmRKle0FvquK5NS5V1bPl2QC6BevfrqcSmy/dshR3wxY3ZnGhkthpmErRAz3wzPypRWW5e9Vh5zWC8lGPt4zr53wPzFYCDegn29XbNpTP4Va608RyajyIVUgfZCvuwhNEEutk02heXH2nSEgGvCoLEgAgiBBlxKDG4edALeJ1NanUOBdqZtlkwA6Dvu9w9c09buNw9GLn4/qwEN6iz/SpmWoF+kCLQZWktqH06KsuXIIxVuU8o22yzG4Lb/8nC3xTbnLCRTIsiUVgLlZe8wjXMOwdCv/E0NTXNxycW0m9o0F/lXlvWVpU8xgVmqIbvv3JPWQr2rJhf7K1J3wLuN5c483fjc5zKl5UZ4Xv7M4OeYGkJ7T4V8LqG4eSVLnxqNnNkvgkqhDAL0rSUrFN3S7U1roe7Vkottj12jScLtNJzTccwcJ1Oaj07+a/DHLj5lBU6IWKyEta8Wg1AgFvqaQjkEwH0tmUNOcyZA5WqX703VkgtCgMLVvlIn1jQypcWQyRMPwWC+GBICTFTMgW+lcCcvnEMwaMqYxDivwSRG3eRfsRYrf4TM1xIDfXMvvhZroWrJBZMYhfOFAQOfePfnp7HK1XSUKS1/a2AXZ2YfMmEs2dTQJZ78pQ+/Qf6VMC4lY2kDyGFpoD+mXHG2tByln6uWXHC4UjjXke+Cg7DgO4VWg0xpeVrOCKYH0xF1gCz5kE9hWwSQRYzZJQFiCk14luTV0jPVkguzRgoXc9rb8uSWwB4rq0xpYwhNu89ARihDNK0G86/sUSjV2GZoHkvMWrTfGq2nRiymlqlacsH8hc2bAob8Lj2Si99oY6Y07iuEEWiVYJgdszABgdQyOYZbpd1Y2oSv9eeGvWot4FQtuVA4fCmYvtxtOoiHeDCbtWwWm9tJST9kSqPjSxidRhVzEjPOpeaM07nlv2KyQHlxHrdS5vyo1PEGNMm55sk9ay20GtaDUhPg2R9RUkCIxLQUmNB++FxqWMmzddd3TWnMkmhQhBODYYkav3V9Ur9/yUeWqcswJT/aSv6VKUhtk4b2mbtijPR7NmtS/1IyaBG5bNOV2n2rmdJs1g4ZMxvmGgdxqZlETQjSyVnKW2tA64RY9iyIam0bKxea5BwzD0J1r74Ww0zkYkh0emRQ0NHRZGhsBgid3mzIezClgQEES51rCpSLMtEee2iHmrBfUpY5Zh7G2hIfzZJy1fqMyKXWlslYLgQZHZ/Z/F5MaQhyhEMtA17+lYwdPFPWU4Ulkzn6Gn1uz2EqXikwklksBYoZ8tiLKQ1SrcH8ZMJnroM4Q9MryxkI0F5YAMYCQnVKurF8Wr8vcmm9BTOUnxlXr6Y0CAbTIPXbIsi/sgXqad6JT2zMd2cTh71rLSAucknT77rPpSdTGkICDYY6lQoIG/lXSqGd5z0QB767oQD5SGu5hpDIZainNHiPZdvMzPn5/1niVseWeJNuyfdCrZvSjGBKrJ6Tf8XteW2fM15igXaWr+UEHZHLCRbNn7Flju3Fxgeo7HAQ2j7HPk6FfCz92sq3aEpDk2AmmtOEYWYS+VfW9rA6nmcBTMykSn+S1nLSTiKXEyy6O4NY/H/rZCt5NBU/PkflWzClGcHkqD/+FWa6+n4lB7rb5InZK9SeaC20dQlNeJuaz3+ryGU+Zs08gWbi78tmfxu9RSUYeAxMZvFoDAxGjlxv9YEnWgtlgGRSBfOvlPbrpCq/8okjgGYS0k7oPyn7ULwE7dwRubTTVpNLij8FzcQ3iWEOQ6Bzz/4vBwJCm9ki1GJKS0kwllduc9sW7aV3Ho6TIISmG6S1uGicnItcTrDo4gxigUDsh4Pfgv2Nge3JZr4XiKaWsJUpDQGx9hsYyk4emsHW0pvSl8Pa2M1ZWouLxrVzcLrvvg8fXnzxz4uYCvUR5dk2yBaDox6tBJIxzcQ2AHVfaoRjadx7NZyXNKWZ4AjZ1Mew4BmwXvLsWN66XxcCtDMaKoEjEwr6qcI1PC5ffvhw4cK56xPcixfPH5555ums8IhcssJ7NnMIhoGAhkKASPxlx36as7nUFcNgZrUOdm/UbuqXcq808iZPiGZqYOYq/8pUtNpP55p76IfSVE/a1HypjCH3B9nkJBiRy0kbFDkzs5e9DOc+De46+TGR+YRj6Vs5QgQp90pD+5hCFvKvtNJD0pWThSd33nnH4Y473n348Ic/eLj55hsPb775ZroXNJwT49DVWFxysfNcGp7IpXDHwSyGtuIG4vCx4Jvhx7mfxk3f4nkKUxozUgjm9ddfP9qOGRxcP/XUk0dTiJnQNGttsYcsK/OVK48fzp+/4dSM/Ny5dxwuXbrruplsWc7tPMXYQrsP/VimbSQSO/JcjiByyYGqk6f5WGhYSMMc906S46mbrjdi8evK9VJT2oc+dM8B4eEPFGzIxMm/EkK7zziE4tCs/Pnnv7pJxZnkhAQ9cWjzTJJCPyZFmPdCP8zMfp+3ayZYoWeIw4Fv6WJHkcsm3UQvLYnAmCmN+0YioYFy770fKllcvWtjBB577PODgvOmmy4eSxgT9MSHhLzFMeuPCW0EeqgPEgcRxJ6DQCx//wjxxMpK318SeG6IgBlPMostQVbPNI1AyJQWG9AWP7fCscG8RTy+A1/gbHnNh7QxIblFfMwxbW0fO/JcrLzUMYYxWnCsH+QSyHP775T0Mdzk0J+CntLsAoEHH/xIdLYYEyxj8UOCJyaQcsbHBN1W8THhulW829FZXjvWvm76vZ5jgg4tRcZflTPI55ITXeWdFIGvf/0FCZOkiLadGZrFkJkUs5nCCQKYyMCMXwnNS+Rygr3OKkdgzOeCFqKwLwSYfYd8CiVXi7HC012QE9uAlg+m2RU91a7nqVva30kErXDNJxEil9QtpPyyIsAADQkTvm0oMRvLWjllvgiBq1dfPbz//b9z1GrdpemLMlvwEPsFGmGwGhSh7O8hyLWZ8CztglcVeYQxRlntQ++lLxW5LEVOz22GAI7v3/u9jx9YDfTe977nwJJT7Mo9Bn9WzMD3g310i0CoeWbsl7uHa7Zo8j8dQHMJzfgR1rRR7eRCfSgnfW9NELmsQU/PCoHMCDDjtT3mbFbsfiuFoEIQmICz67WzzszV6jp72kLkcjiIXLru5qpcbwigmRiRUDc0GV+Qce2m6Q2D2uvDhCDkd5HmUnvLqXxCYMcIQC6uuQIS8U0tkMseNBfqSd3tZ4TKThgWx7E0FrSRaZtuVxW5uGjoXAhUiACzQld4cO4K3AqLvLpICCZWJLkmMcsUYWqEAja12/St3CmOaAnU3W9/4sDLj0/xzqE8IDgjOT+dyMVHRNdCoEIEbDfp2ECusMiLi2R+FCNUnzwQoDZbDzn8F7+4gQdDZkH6xBY40CeH3ityaaBDqYhCwAbqHsjFWpu6QiKYXdyANoNQM42O2fxegk8uXG/RJ+iPQ8RCe1if9ScHtbUV+MWsAdyjHlOCHPpTUFKa6hCwgbqFINkSDF+YIqgwAVkwLWcvuLh4QKpb1Bv/ik/oxPkmTNO2/Xhru1qOYAq5uP8xRdkoN5ObqUHkMhUppasKgb2SC8ITX4IFtBVfkyGO3x6CkQuYuLiUqjv9EHI3k6V7dJ36tJt7j3LXFjCvumUMnfskOlQHkcsQOrpXLQJ7JBeEFTNHd0ZpQstm7KSBbOy62gZMVDAjF5ttU3f6hsL2CIhctm8DlWABAnshF3dWzMw8JDiNYJhpkn4vxEK3MXLhHGwgF3DYEwYLhk+RR0QuRWDWS1IjsBdySY1bb/m55ELdMO1AwhDMXkyDtbapyKXWllG5BhEQuQzCs5ub+ADQ1vzvWUyDgWj8e7sBZ+OKilw2bgC9fhkCtvJG5o9l+PXwlGsydE1h5n8hzn4hc2IPGNRcB5FLza2jsgURwNxhQsOOmp0GoVKkENgMAZHLZtDrxUJACAiBfhEQufTbtqqZEBACQmAzBEQum0GvFwsBISAE+kVA5NJv26pmQkAICIHNEBC5bAa9XiwEhIAQ6BeB/w+NJEl1swQduAAAAABJRU5ErkJggg=="></p>
<p>Musab is required to deliver leaflets to every house on each road. He wishes to minimize his total distance.</p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Musab starts and finishes from the village bus-stop at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>. Determine the total distance Musab will need to walk.</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>Instead of having to catch the bus to the village, Musab’s sister offers to drop him off at any junction and pick him up at any other junction of his choice.</p>
<p>Explain which junctions Musab should choose as his starting and finishing points.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Two lines <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub></math> are given by the following equations, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>.</p>
<p style="padding-left: 210px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub><mo>:</mo><mi>r</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mi>p</mi><mo>+</mo><mn>9</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mo>+</mo><mi>λ</mi><mfenced><mtable><mtr><mtd><mi>p</mi></mtd></mtr><mtr><mtd><mn>2</mn><mi>p</mi></mtd></mtr><mtr><mtd><mn>4</mn></mtd></mtr></mtable></mfenced></math></p>
<p style="padding-left: 210px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub><mo>:</mo><mi>r</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>14</mn></mtd></mtr><mtr><mtd><mn>7</mn></mtd></mtr><mtr><mtd><mi>p</mi><mo>+</mo><mn>12</mn></mtd></mtr></mtable></mfenced><mo>+</mo><mi>μ</mi><mfenced><mtable><mtr><mtd><mi>p</mi><mo>+</mo><mn>4</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>7</mn></mtd></mtr></mtable></mfenced></math></p>
<p>It is known that <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub></math> are perpendicular.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the possible value(s) for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</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>In the case that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo><</mo><mn>0</mn></math>, determine whether the lines intersect.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>The following diagram shows a corner of a field bounded by two walls defined by lines <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub></math>. The walls meet at a point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>, making an angle of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo>°</mo></math>.</p>
<p>Farmer Nate has <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo> </mo><mtext>m</mtext></math> of fencing to make a triangular enclosure for his sheep. One end of the fence is positioned at a point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mtext>m</mtext></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>. The other end of the fence will be positioned at some point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math>, as shown on 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>He wants the enclosure to take up as little of the current field as possible.</p>
<p>Find the minimum possible area of the triangular enclosure <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABC</mtext></math>.</p>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a frame that is made from wire. The total length of wire is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mtext>cm</mtext></math>. The frame is made up of two identical sectors of a circle that are parallel to each other. The sectors have angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> radians and radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo> </mo><mtext>cm</mtext></math>. They are connected by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mtext>cm</mtext></math> lengths of wire perpendicular to the sectors. This is shown in the diagram below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The faces of the frame are covered by paper to enclose a volume, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mfrac><mn>6</mn><mrow><mn>2</mn><mo>+</mo><mi>θ</mi></mrow></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> in terms 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">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the expression <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>V</mi></mrow><mrow><mo>d</mo><mi>θ</mi></mrow></mfrac></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Solve algebraically <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>V</mi></mrow><mrow><mo>d</mo><mi>θ</mi></mrow></mfrac><mo>=</mo><mn>0</mn></math> to find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> that will maximize the volume, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>At <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>:</mo><mn>00</mn><mo> </mo><mtext>pm</mtext></math> a ship is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mtext>km</mtext></math> east and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mtext>km</mtext></math> north of a harbour. A coordinate system is defined with the harbour at the origin. The position vector of the ship at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>:</mo><mn>00</mn><mo> </mo><mtext>pm</mtext></math> is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd></mtr></mtable></mfenced></math>.</p>
<p>The ship has a constant velocity of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn><mo>.</mo><mn>2</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>0</mn><mo>.</mo><mn>6</mn></mtd></mtr></mtable></mfenced></math> kilometres per hour (<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>km h</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression for the position vector <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">r</mi></math> of the ship, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> hours after <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>:</mo><mn>00</mn><mo> </mo><mtext>pm</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 time at which the bearing of the ship from the harbour is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>045</mn><mo>˚</mo></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the following directed network.</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>Write down the adjacency matrix for this network.</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 number of different walks of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> that start and end at the same vertex.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A vertical pole stands on a sloped platform. The bottom of the pole is used 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;" 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"></p>
<p>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 these ropes is attached to the platform at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><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><mo>−</mo><mn>0</mn><mo>.</mo><mn>3</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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mtext>AF</mtext><mo>→</mo></mover></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 length of the rope.</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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>FÂO</mtext></math>, the angle the rope makes with the platform.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The position vector of a particle, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math>, relative to a fixed origin <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math> at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is given by</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mtext>OP</mtext><mo>→</mo></mover><mo>=</mo><mfenced><mtable><mtr><mtd><mi>sin</mi><mo> </mo><mfenced><msup><mi>t</mi><mn>2</mn></msup></mfenced></mtd></mtr><mtr><mtd><mi>cos</mi><mo> </mo><mfenced><msup><mi>t</mi><mn>2</mn></msup></mfenced></mtd></mtr></mtable></mfenced></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the velocity vector of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</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>Show that the acceleration vector of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math> is never parallel to the position vector of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A submarine is located in a sea at coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>.</mo><mn>8</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>.</mo><mn>3</mn><mo>,</mo><mo> </mo><mo>−</mo><mn>0</mn><mo>.</mo><mn>3</mn></mrow></mfenced></math> relative to a ship positioned at the origin <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>. The <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> direction is due east, the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> direction is due north and the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math> direction is vertically upwards.</p>
<p>All distances are measured in kilometres.</p>
<p>The submarine travels with direction vector <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math>.</p>
</div>
<div class="specification">
<p>The submarine reaches the surface of the sea at the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Assuming the submarine travels in a straight line, write down an equation for the line along which it travels.</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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>OP</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The cost adjacency matrix below represents the distance in kilometres, along routes between bus stations.</p>
<p><img src="data:image/png;base64,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"></p>
<p>All the values in the matrix are positive, distinct integers.</p>
<p>It is decided to electrify some of the routes, so that it will be possible to travel from any station to any other station solely on electrified routes. In order to achieve this with a minimal total length of electrified routes, Prim’s algorithm for a minimal spanning tree is used, starting at vertex A.</p>
<p>The algorithm adds the edges in the following order:</p>
<p>AB AC CD DE.</p>
<p>There is only one minimal spanning tree.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find with a reason, the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>If the total length of the minimal spanning tree is 14, find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s">
<mi>s</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>Hence, state, with a reason, what can be deduced about the values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span>, <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">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle P moves with velocity <em><strong>v</strong></em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 15} \\ 2 \\ 4 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>15</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>4</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span> in a magnetic field, <em><strong>B</strong></em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 0 \\ d \\ 1 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>d</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d \in \mathbb{R}">
<mi>d</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <em><strong>v</strong></em> is perpendicular to <em><strong>B</strong></em>, find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
<mi>d</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>The force, <em><strong>F</strong></em>, produced by P moving in the magnetic field is given by the vector equation <em><strong>F</strong></em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span><em><strong>v</strong></em> × <em><strong>B</strong></em>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a \in {\mathbb{R}^ + }">
<mi>a</mi>
<mo>∈</mo>
<mrow>
<msup>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
<mo>+</mo>
</msup>
</mrow>
</math></span>.</p>
<p>Given that |<em><strong> </strong></em><em><strong>F </strong></em>| = 14, find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The equation of the line <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> can be expressed in vector form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">r</mi><mo>=</mo><mi mathvariant="bold-italic">a</mi><mo>+</mo><mi>λ</mi><mi mathvariant="bold-italic">b</mi></math>.</p>
</div>
<div class="specification">
<p>The matrix <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">M</mi></math> is defined by <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>6</mn><mo> </mo><mo> </mo></mtd><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mn>4</mn><mo> </mo><mo> </mo></mtd><mtd><mn>2</mn></mtd></mtr></mtable></mfenced></math>.</p>
</div>
<div class="specification">
<p>The line <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> (where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>≠</mo><mo>−</mo><mn>2</mn></math>) is transformed into a new line using the transformation described by matrix <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">M</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the vectors <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">a</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">b</mi></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> and/or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>det </mtext><mi mathvariant="bold-italic">M</mi></math>.</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>Show that the equation of the resulting line does not depend on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows a sector, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>OAB</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"><mi>r</mi></math>, such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AÔB</mtext><mo>=</mo><mi>θ</mi></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>Sam measured the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> to be <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mtext>cm</mtext></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> to be <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo>°</mo></math>.</p>
</div>
<div class="specification">
<p>It is found that Sam’s measurements are accurate to only one significant figure.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Sam’s measurements to calculate the area of the sector. Give your answer to four significant figures.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the upper bound and lower bound of the area of the sector.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find, with justification, the largest possible percentage error if the answer to part (a) is recorded as the area of the sector.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><img 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"></p>
<p>The above diagram shows the weighted graph <em>G</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="indent1a" style="margin-top:12.0pt;">Write down the adjacency matrix for <em>G</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 class="indent1a" style="margin-top:12.0pt;">Find the number of distinct walks of length 4 beginning and ending at A.</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 class="indent1" style="margin-top:12.0pt;">Starting at A, use Prim’s algorithm to find and draw the minimum spanning tree for <em>G</em>.</p>
<p class="indent1" style="margin-top:12.0pt;">Your solution should indicate clearly the way in which the tree is constructed.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Sameer is trying to design a road system to connect six towns, A, B, C, D, E and F.</p>
<p>The possible roads and the costs of building them are shown in the graph below. Each vertex represents a town, each edge represents a road and the weight of each edge is the cost of building that road. He needs to design the lowest cost road system that will connect the six towns.</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>Name an algorithm that will allow Sameer to find the lowest cost road system.</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 lowest cost road system and state the cost of building it. Show clearly the steps of the algorithm.</p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p class="indent1" style="margin-top:12.0pt;">The diagram below shows a weighted graph.</p>
<p class="indent1" style="margin-top:12pt;text-align: center;"><img src="data:image/png;base64,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"></p>
<p class="indent1" style="margin-top:12.0pt;">Use Prim’s algorithms to find a minimal spanning tree, starting at J. Draw the tree, and find its total weight.</p>
</div>
<br><hr><br><div class="specification">
<p>Let <em>G</em> be a weighted graph with 6 vertices L, M, N, P, Q, and R. The weight of the edges joining the vertices is given in the table below:</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>For example the weight of the edge joining the vertices L and N is 3.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="indent1" style="margin-top:12.0pt;">Use Prim’s algorithm to draw a minimum spanning tree starting at M.</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 class="indent1" style="margin-top:12.0pt;">What is the total weight of the tree?</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>In the following diagram, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{OA}}} ">
<mover>
<mrow>
<mtext>OA</mtext>
</mrow>
<mo>→<!-- → --></mo>
</mover>
</math></span> = <strong><em>a</em></strong>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{OB}}} ">
<mover>
<mrow>
<mtext>OB</mtext>
</mrow>
<mo>→<!-- → --></mo>
</mover>
</math></span> = <strong><em>b</em></strong>. C is the midpoint of [OA] and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{OF}}} = \frac{1}{6}\overrightarrow {{\text{FB}}} ">
<mover>
<mrow>
<mtext>OF</mtext>
</mrow>
<mo>→<!-- → --></mo>
</mover>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
<mover>
<mrow>
<mtext>FB</mtext>
</mrow>
<mo>→<!-- → --></mo>
</mover>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-07_om_14.26.10.png" alt="N17/5/MATHL/HP1/ENG/TZ0/09"></p>
</div>
<div class="specification">
<p>It is given also that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{AD}}} = \lambda \overrightarrow {{\text{AF}}} ">
<mover>
<mrow>
<mtext>AD</mtext>
</mrow>
<mo>→<!-- → --></mo>
</mover>
<mo>=</mo>
<mi>λ<!-- λ --></mi>
<mover>
<mrow>
<mtext>AF</mtext>
</mrow>
<mo>→<!-- → --></mo>
</mover>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{CD}}} = \mu \overrightarrow {{\text{CB}}} ">
<mover>
<mrow>
<mtext>CD</mtext>
</mrow>
<mo>→<!-- → --></mo>
</mover>
<mo>=</mo>
<mi>μ<!-- μ --></mi>
<mover>
<mrow>
<mtext>CB</mtext>
</mrow>
<mo>→<!-- → --></mo>
</mover>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ,{\text{ }}\mu \in \mathbb{R}">
<mi>λ<!-- λ --></mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>μ<!-- μ --></mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find, in terms of <strong><em>a </em></strong>and <strong><em>b </em></strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{OF}}} ">
<mover>
<mrow>
<mtext>OF</mtext>
</mrow>
<mo>→</mo>
</mover>
</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, in terms of <strong><em>a </em></strong>and <strong><em>b </em></strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{AF}}} ">
<mover>
<mrow>
<mtext>AF</mtext>
</mrow>
<mo>→</mo>
</mover>
</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 an expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{OD}}} ">
<mover>
<mrow>
<mtext>OD</mtext>
</mrow>
<mo>→</mo>
</mover>
</math></span> in terms of <strong><em>a</em></strong>, <strong><em>b </em></strong>and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
<mi>λ</mi>
</math></span>;</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{OD}}} ">
<mover>
<mrow>
<mtext>OD</mtext>
</mrow>
<mo>→</mo>
</mover>
</math></span> in terms of <strong><em>a</em></strong>, <strong><em>b </em></strong>and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
<mi>μ</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu = \frac{1}{{13}}">
<mi>μ</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>13</mn>
</mrow>
</mfrac>
</math></span>, and find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
<mi>λ</mi>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce an expression for <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> in terms of <strong><em>a </em></strong>and <strong><em>b </em></strong>only.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that area <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\Delta {\text{OAB}} = k({\text{area }}\Delta {\text{CAD}})">
<mi mathvariant="normal">Δ</mi>
<mrow>
<mtext>OAB</mtext>
</mrow>
<mo>=</mo>
<mi>k</mi>
<mo stretchy="false">(</mo>
<mrow>
<mtext>area </mtext>
</mrow>
<mi mathvariant="normal">Δ</mi>
<mrow>
<mtext>CAD</mtext>
</mrow>
<mo stretchy="false">)</mo>
</math></span>, find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the lines <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{l_1}">
<mrow>
<msub>
<mi>l</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{l_2}">
<mrow>
<msub>
<mi>l</mi>
<mn>2</mn>
</msub>
</mrow>
</math></span> defined by</p>
<p><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>
<mo>:</mo>
</math></span> <em><strong>r</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left( {\begin{array}{*{20}{c}} { - 3} \\ { - 2} \\ a \end{array}} \right) + \beta \left( {\begin{array}{*{20}{c}} 1 \\ 4 \\ 2 \end{array}} \right)">
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>3</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>2</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>a</mi>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>β<!-- β --></mi>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>4</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{l_2}:\frac{{6 - x}}{3} = \frac{{y - 2}}{4} = 1 - z">
<mrow>
<msub>
<mi>l</mi>
<mn>2</mn>
</msub>
</mrow>
<mo>:</mo>
<mfrac>
<mrow>
<mn>6</mn>
<mo>−<!-- − --></mo>
<mi>x</mi>
</mrow>
<mn>3</mn>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mi>y</mi>
<mo>−<!-- − --></mo>
<mn>2</mn>
</mrow>
<mn>4</mn>
</mfrac>
<mo>=</mo>
<mn>1</mn>
<mo>−<!-- − --></mo>
<mi>z</mi>
</math></span> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> is a constant.</p>
<p>Given that the lines <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{l_1}">
<mrow>
<msub>
<mi>l</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{l_2}">
<mrow>
<msub>
<mi>l</mi>
<mn>2</mn>
</msub>
</mrow>
</math></span> intersect at a point P,</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</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>determine the coordinates of the point of intersection P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>Nymphenburg Palace in Munich has extensive grounds with <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math> points of interest (stations) within them.</p>
<p>These nine points, along with the palace, are shown as the vertices in the graph below. The weights on the edges are the walking times in minutes between each of the stations and the total of all the weights is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>105</mn></math> minutes.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>Anders decides he would like to walk along all the paths shown beginning and ending at the Palace (vertex A).</p>
<p>Use the Chinese Postman algorithm, clearly showing all the stages, to find the shortest time to walk along all the paths.</p>
</div>
<br><hr><br><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="\sin \frac{\pi }{4} + \sin \frac{{3\pi }}{4} + \sin \frac{{5\pi }}{4} + \sin \frac{{7\pi }}{4} + \sin \frac{{9\pi }}{4}">
<mi>sin</mi>
<mo></mo>
<mfrac>
<mi>π</mi>
<mn>4</mn>
</mfrac>
<mo>+</mo>
<mi>sin</mi>
<mo></mo>
<mfrac>
<mrow>
<mn>3</mn>
<mi>π</mi>
</mrow>
<mn>4</mn>
</mfrac>
<mo>+</mo>
<mi>sin</mi>
<mo></mo>
<mfrac>
<mrow>
<mn>5</mn>
<mi>π</mi>
</mrow>
<mn>4</mn>
</mfrac>
<mo>+</mo>
<mi>sin</mi>
<mo></mo>
<mfrac>
<mrow>
<mn>7</mn>
<mi>π</mi>
</mrow>
<mn>4</mn>
</mfrac>
<mo>+</mo>
<mi>sin</mi>
<mo></mo>
<mfrac>
<mrow>
<mn>9</mn>
<mi>π</mi>
</mrow>
<mn>4</mn>
</mfrac>
</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>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1 - \cos 2x}}{{2\sin x}} \equiv \sin x,{\text{ }}x \ne k\pi ">
<mfrac>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mi>cos</mi>
<mo></mo>
<mn>2</mn>
<mi>x</mi>
</mrow>
<mrow>
<mn>2</mn>
<mi>sin</mi>
<mo></mo>
<mi>x</mi>
</mrow>
</mfrac>
<mo>≡</mo>
<mi>sin</mi>
<mo></mo>
<mi>x</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>x</mi>
<mo>≠</mo>
<mi>k</mi>
<mi>π</mi>
</math></span> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k \in \mathbb{Z}">
<mi>k</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the principle of mathematical induction to prove that</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sin x + \sin 3x + \ldots + \sin (2n - 1)x = \frac{{1 - \cos 2nx}}{{2\sin x}},{\text{ }}n \in {\mathbb{Z}^ + },{\text{ }}x \ne k\pi ">
<mi>sin</mi>
<mo></mo>
<mi>x</mi>
<mo>+</mo>
<mi>sin</mi>
<mo></mo>
<mn>3</mn>
<mi>x</mi>
<mo>+</mo>
<mo>…</mo>
<mo>+</mo>
<mi>sin</mi>
<mo></mo>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mi>n</mi>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mi>x</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mi>cos</mi>
<mo></mo>
<mn>2</mn>
<mi>n</mi>
<mi>x</mi>
</mrow>
<mrow>
<mn>2</mn>
<mi>sin</mi>
<mo></mo>
<mi>x</mi>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>n</mi>
<mo>∈</mo>
<mrow>
<msup>
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
<mo>+</mo>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>x</mi>
<mo>≠</mo>
<mi>k</mi>
<mi>π</mi>
</math></span> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k \in \mathbb{Z}">
<mi>k</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
</math></span>.</p>
<div class="marks">[9]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise solve the equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sin x + \sin 3x = \cos x">
<mi>sin</mi>
<mo></mo>
<mi>x</mi>
<mo>+</mo>
<mi>sin</mi>
<mo></mo>
<mn>3</mn>
<mi>x</mi>
<mo>=</mo>
<mi>cos</mi>
<mo></mo>
<mi>x</mi>
</math></span> in the interval <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 < x < \pi ">
<mn>0</mn>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mi>π</mi>
</math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p class="indent1" style="margin-top:12pt;text-align: left;">The weights of the edges in a simple graph G are given in the following table.</p>
<p class="indent1" style="margin-top:12pt;text-align: left;"><img style="display: block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p class="indent1" style="margin-top:12.0pt;">Use Prim’s Algorithm, starting with vertex F, to find and draw the minimum spanning tree for <em>G</em>. Your solution should indicate the order in which the edges are introduced.</p>
</div>
<br><hr><br><div class="question">
<p class="indent1" style="margin-top:12.0pt;">Apply Prim’s algorithm to the weighted graph given below to obtain the minimal spanning tree starting with the vertex A.</p>
<p class="indent1" style="margin-top:12.0pt;"><img style="display: block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p class="questionChar">Find the weight of the minimal spanning tree.</p>
</div>
<br><hr><br><div class="question">
<p class="indent1" style="margin-top:12.0pt;"><em>In this part, marks will only be awarded if you show the correct application of the required algorithms, and show all your working.</em></p>
<p class="indent1" style="margin-top:12.0pt;">In an offshore drilling site for a large oil company, the distances between the planned wells are given below in metres.</p>
<p class="indent1" style="margin-top:12pt;text-align: center;"><img 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"></p>
<p class="indent1" style="margin-top:12pt;text-align: left;">It is intended to construct a network of paths to connect the different wells in a way that minimises the sum of the distances between them.</p>
<p class="indent1" style="margin-top:12pt;text-align: left;">Use Prim’s algorithm, starting at vertex 3, to find a network of paths of minimum total length that can span the whole site.</p>
</div>
<br><hr><br><div class="question">
<p>Let <em><strong>a</strong></em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 2 \\ k \\ { - 1} \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>k</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span> and <em><strong>b</strong></em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 3} \\ {k + 2} \\ k \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>k</mi>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k \in \mathbb{R}">
<mi>k</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
<p>Given that <em><strong>a</strong></em> and <em><strong>b</strong></em> are perpendicular, find the possible values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>.</p>
</div>
<br><hr><br><div class="specification">
<p>The lengths of two of the sides in a triangle are 4 cm and 5 cm. Let <em>θ</em> be the angle between the two given sides. The triangle has an area of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{5\sqrt {15} }}{2}">
<mfrac>
<mrow>
<mn>5</mn>
<msqrt>
<mn>15</mn>
</msqrt>
</mrow>
<mn>2</mn>
</mfrac>
</math></span> cm<sup>2</sup>.</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{sin}}\,\theta = \frac{{\sqrt {15} }}{4}">
<mrow>
<mtext>sin</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>θ</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msqrt>
<mn>15</mn>
</msqrt>
</mrow>
<mn>4</mn>
</mfrac>
</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 the two possible values for the length of the third side.</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>Solve the equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\sec ^2}x + 2\tan x = 0,{\text{ }}0 \leqslant x \leqslant 2\pi ">
<mrow>
<msup>
<mi>sec</mi>
<mn>2</mn>
</msup>
</mrow>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
<mi>tan</mi>
<mo></mo>
<mi>x</mi>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo>⩽</mo>
<mi>x</mi>
<mo>⩽</mo>
<mn>2</mn>
<mi>π</mi>
</math></span>.</p>
</div>
<br><hr><br><div class="specification">
<p>Three points in three-dimensional space have coordinates A(0, 0, 2), B(0, 2, 0) and C(3, 1, 0).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the vector <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{AB}}} "> <mover> <mrow> <mtext>AB</mtext> </mrow> <mo>→</mo> </mover> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the vector <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{AC}}} "> <mover> <mrow> <mtext>AC</mtext> </mrow> <mo>→</mo> </mover> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise, find the area of the triangle ABC.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p class="indent1" style="margin-top:12.0pt;">The weights of the edges of a complete graph G are shown in the following table.</p>
<p class="indent1" style="margin-top:12pt;text-align: center;"><img src="data:image/png;base64,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"></p>
<p class="indent1" style="margin-top:12.0pt;">Starting at <em>B</em>, use Prim’s algorithm to find and draw a minimum spanning tree for <em>G</em>. Your solution should indicate the order in which the vertices are added. State the total weight of your tree.</p>
</div>
<br><hr><br><div class="question">
<p>A sector of a circle with radius <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> cm , where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> > 0, is shown on the following diagram.<br>The sector has an angle of 1 radian at the centre.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>Let the area of the sector be <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span> cm<sup>2</sup> and the perimeter be <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P"> <mi>P</mi> </math></span> cm. Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = P"> <mi>A</mi> <mo>=</mo> <mi>P</mi> </math></span>, find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span>.</p>
</div>
<br><hr><br><div class="specification">
<p>The vectors <strong><em>a</em></strong> and <em><strong>b</strong></em> are defined by <strong><em>a </em></strong>= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 1 \\ 1 \\ t \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>t</mi>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <strong><em>b</em><em> </em></strong>= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 0 \\ { - t} \\ {4t} \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mi>t</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>4</mn>
<mi>t</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t \in \mathbb{R}">
<mi>t</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find and simplify an expression for <em><strong>a</strong></em> • <em><strong>b</strong></em> in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</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>Hence or otherwise, find the values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> for which the angle between<em><strong> a</strong></em> and <em><strong>b</strong></em> is obtuse .</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<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>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find 50° in radians.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the volume of this log.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br>