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<h2>HL Paper 2</h2><div class="specification">
<p>An ice-skater is skating such that her position vector when viewed from above at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> seconds can be modelled by</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><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>a</mi><mo> </mo><msup><mtext>e</mtext><mrow><mi>b</mi><mi>t</mi></mrow></msup><mtext> </mtext><mi>cos</mi><mo> </mo><mi>t</mi></mtd></mtr><mtr><mtd><mi>a</mi><mo> </mo><msup><mtext>e</mtext><mrow><mi>b</mi><mi>t</mi></mrow></msup><mtext> sin</mtext><mo> </mo><mi>t</mi></mtd></mtr></mtable></mfenced></math></p>
<p>with respect to a rectangular coordinate system from a point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>, where the non-zero constants <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math> can be determined. All distances are in metres.</p>
</div>
<div class="specification">
<p>At time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math>, the displacement of the ice-skater is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>5</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></math> and the velocity of the ice‑skater is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>3</mn><mo>.</mo><mn>5</mn></mtd></mtr><mtr><mtd><mn>5</mn></mtd></mtr></mtable></mfenced></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the velocity vector at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</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>Show that the magnitude of the velocity of the ice-skater 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"><mi>a</mi><mo> </mo><msup><mtext>e</mtext><mrow><mi>b</mi><mi>t</mi></mrow></msup><msqrt><mfenced><mrow><mn>1</mn><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></mfenced></msqrt></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the magnitude of the velocity of the ice-skater when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>At a point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math>, the ice-skater is skating parallel to the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axis for the first time.</p>
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>OP</mtext></math>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A flying drone is programmed to complete a series of movements in a horizontal plane relative to an origin <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math> and a set of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axes.</p>
<p>In each case, the drone moves to a new position represented by the following transformations:</p>
<ul>
<li>a rotation anticlockwise of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi mathvariant="normal">π</mi><mn>6</mn></mfrac></math> radians about <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math></li>
<li>a reflection in the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mi>x</mi><msqrt><mn>3</mn></msqrt></mfrac></math></li>
<li>a rotation clockwise of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi mathvariant="normal">π</mi><mn>3</mn></mfrac></math> radians about <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>.</li>
</ul>
<p>All the movements are performed in the listed order.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down each of the transformations in matrix form, clearly stating which matrix represents each transformation.</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find a single matrix <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">P</mi></math> that defines a transformation that represents the overall change in position.</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>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="bold-italic">P</mi><mn>2</mn></msup></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence state what the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="bold-italic">P</mi><mn>2</mn></msup></math> indicates for the possible movement of the drone.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Three drones are initially positioned at the points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>. After performing the movements listed above, the drones are positioned at points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mo>′</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext><mo>′</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext><mo>′</mo></math> respectively.</p>
<p>Show that the area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABC</mtext></math> is equal to the area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mo>′</mo><mtext>B</mtext><mo>′</mo><mtext>C</mtext><mo>′</mo></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 a single transformation that is equivalent to the three transformations represented by matrix <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">P</mi></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A ball is attached to the end of a string and spun horizontally. Its position relative to a given point, <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> seconds, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>≥</mo><mn>0</mn></math>, is given by the equation</p>
<p style="padding-left: 30px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">r</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>1</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>cos</mi><mo> </mo><mo>(</mo><mn>0</mn><mo>.</mo><mn>1</mn><msup><mi>t</mi><mn>2</mn></msup><mo>)</mo></mtd></mtr><mtr><mtd><mn>1</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>sin</mi><mo> </mo><mo>(</mo><mn>0</mn><mo>.</mo><mn>1</mn><msup><mi>t</mi><mn>2</mn></msup><mo>)</mo></mtd></mtr></mtable></mfenced></math> where all displacements are in metres.</p>
</div>
<div class="specification">
<p>The string breaks when the magnitude of the ball’s acceleration exceeds <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><msup><mtext>ms</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the ball is moving in a circle with its centre at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math> and state the radius of the circle.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the velocity of the ball 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">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence show that the velocity of the ball is always perpendicular to the position vector of the ball.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the acceleration of the ball at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> at the instant the string breaks.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>How many complete revolutions has the ball completed from <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math> to the instant at which the string breaks?</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A transformation, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>, of a plane is represented by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">r</mi><mo>′</mo><mo>=</mo><mi mathvariant="bold-italic">P</mi><mi mathvariant="bold-italic">r</mi><mo>+</mo><mi mathvariant="bold-italic">q</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">P</mi></math> is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mo>×</mo><mo> </mo><mn>2</mn></math> matrix, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">q</mi></math> is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mo>×</mo><mo> </mo><mn>1</mn></math> vector, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">r</mi></math> is the position vector of a point in the plane and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">r</mi><mo>′</mo></math> the position vector of its image under <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>.</p>
<p>The triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>OAB</mtext></math> 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></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math>. Under T, these points are transformed to <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>,</mo><mo> </mo><mn>1</mn><mo>+</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>4</mn></mfrac></mrow></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><msqrt><mn>3</mn></msqrt><mn>4</mn></mfrac><mo>,</mo><mo> </mo><mfrac><mn>3</mn><mn>4</mn></mfrac></mrow></mfenced></math> respectively.</p>
</div>
<div class="specification">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">P</mi></math> can be written as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">P</mi><mo>=</mo><mi mathvariant="bold-italic">R</mi><mi mathvariant="bold-italic">S</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">S</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">R</mi></math> are matrices.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">S</mi></math> represents an enlargement with scale factor <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>5</mn></math>, centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math>.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">R</mi></math> represents a rotation about <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math>.</p>
</div>
<div class="specification">
<p>The transformation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> can also be described by an enlargement scale factor <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math>, centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi><mo>)</mo></math>, followed by a rotation about the same centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi><mo>)</mo></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By considering the image of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math>, find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">q</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By considering the image of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>)</mo></math>, show that</p>
<p style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">P</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mfrac><msqrt><mn>3</mn></msqrt><mn>4</mn></mfrac><mo> </mo></mtd><mtd><mfrac><mn>1</mn><mn>4</mn></mfrac></mtd></mtr><mtr><mtd><mo>-</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo> </mo></mtd><mtd><mfrac><msqrt><mn>3</mn></msqrt><mn>4</mn></mfrac></mtd></mtr></mtable></mfenced></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the matrix <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">S</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>Use <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">P</mi><mo>=</mo><mi mathvariant="bold-italic">R</mi><mi mathvariant="bold-italic">S</mi></math> to find the matrix <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">R</mi></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the angle and direction of the rotation represented by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">R</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an equation satisfied by <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>a</mi></mtd></mtr><mtr><mtd><mi>b</mi></mtd></mtr></mtable></mfenced></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.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>a</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A sector of a circle, centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math> and radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>m</mtext></math>, is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A square field with side <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo> </mo><mtext>m</mtext></math> has a goat tied to a post in the centre by a rope such that the goat can reach all parts of the field up to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>m</mtext></math> from the post.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p style="text-align: center;"><sup>[Source: mynamepong, n.d. Goat [image online] Available at: <a href="https://thenounproject.com/term/goat/1761571/">https://thenounproject.com/term/goat/1761571/</a></sup><br><sup>This file is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)</sup><br><sup><a href="https://creativecommons.org/licenses/by-sa/3.0/deed.en">https://creativecommons.org/licenses/by-sa/3.0/deed.en</a> [Accessed 22 April 2010] Source adapted.]</sup></p>
</div>
<div class="specification">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> be the volume of grass eaten by the goat, in cubic metres, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> be the length of time, in hours, that the goat has been in the field.</p>
<p>The goat eats grass at the rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>V</mi></mrow><mrow><mo>d</mo><mi>t</mi></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn><mo> </mo><mi>t</mi><msup><mtext>e</mtext><mrow><mo>-</mo><mi>t</mi></mrow></msup></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AÔB</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the shaded segment.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the field that can be reached by the goat.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> at which the goat is eating grass at the greatest rate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The goat is tied in the field for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> hours.</p>
<p>Find the total volume of grass eaten by the goat during this time.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the curve <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><msqrt><mi>x</mi></msqrt></math>.</p>
</div>
<div class="specification">
<p>The shape of a piece of metal can be modelled by the region bounded by the functions <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math>, the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis and the line segment <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[AB]</mtext></math>, as shown in the following diagram. The units on 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 measured in metres.</p>
<p style="text-align: center;"><img 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"></p>
<p>The piecewise function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is defined by</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>{</mo><mtable><mtr><mtd><msqrt><mi>x</mi></msqrt><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>16</mn></mtd></mtr><mtr><mtd><mn>1</mn><mo>.</mo><mn>25</mn><mi>x</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>2</mn><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn><mo>.</mo><mn>16</mn><mo><</mo><mi>x</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>5</mn></mtd></mtr></mtable></math></p>
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> is obtained from the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> by:</p>
<ul>
<li>a stretch scale factor of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> direction,</li>
<li>followed by a stretch scale factor <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> direction,</li>
<li>followed by a translation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>2</mn></math> units to the right.</li>
</ul>
<p>Point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> lies on the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>825</mn><mo>)</mo></math>. Point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> is the image of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> under the given transformations and has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>p</mi><mo>,</mo><mo> </mo><mi>q</mi><mo>)</mo></math>.</p>
</div>
<div class="specification">
<p>The piecewise function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> is given by</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>{</mo><mtable><mtr><mtd><mi>h</mi><mfenced><mi>x</mi></mfenced><mo> </mo><mo> </mo></mtd><mtd><mn>0</mn><mo>.</mo><mn>2</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mi>a</mi></mtd></mtr><mtr><mtd><mn>1</mn><mo>.</mo><mn>25</mn><mi>x</mi><mo>+</mo><mi>b</mi><mo> </mo><mo> </mo></mtd><mtd><mi>a</mi><mo><</mo><mi>x</mi><mo>≤</mo><mi>p</mi></mtd></mtr></mtable></math></p>
</div>
<div class="specification">
<p>The area enclosed by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>, the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis and the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>p</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>0627292</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup></math> correct to six significant figures.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>y</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence show that the equation of the tangent to the curve at the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>.</mo><mn>16</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>4</mn></mrow></mfenced></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>25</mn><mi>x</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>2</mn></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 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">[2]</div>
<div class="question_part_label">b.</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"><mo> </mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>.</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>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</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>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area enclosed by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>, the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis and the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the shaded region on the diagram.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The cost adjacency matrix for the complete graph <em>K</em><sub>6</sub> is given below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">It represents the distances in kilometres along dusty tracks connecting villages on an island. Find the minimum spanning tree for this graph; in all 3 cases state the order in which the edges are added.</p>
</div>
<div class="specification">
<p>It is desired to tarmac some of these tracks so that it is possible to walk from any village to any other village walking entirely on tarmac.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Briefly explain the two differences in the application of Prim’s and Kruskal’s algorithms for finding a minimum spanning tree in a weighted connected graph.</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>Using Kruskal’s algorithm.</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>Using Prim’s algorithm starting at vertex A.</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>Using Prim’s algorithm starting at vertex F.</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>State the total minimum length of the tracks that have to be tarmacked.</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>Sketch the tracks that are to be tarmacked.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>At an archery tournament, a particular competition sees a ball launched into the air while an archer attempts to hit it with an arrow.</p>
<p>The path of the ball is modelled by the equation</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mi>x</mi></mtd></mtr><mtr><mtd><mi>y</mi></mtd></mtr></mtable></mfenced><mo>=</mo><mfenced><mtable><mtr><mtd><mn>5</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd></mtr></mtable></mfenced><mo>+</mo><mi>t</mi><mfenced><mtable><mtr><mtd><msub><mi>u</mi><mi>x</mi></msub></mtd></mtr><mtr><mtd><msub><mi>u</mi><mi>y</mi></msub><mo>-</mo><mn>5</mn><mi>t</mi></mtd></mtr></mtable></mfenced></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> is the horizontal displacement from the archer and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> is the vertical displacement from the ground, both measured in metres, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is the time, in seconds, since the ball was launched.</p>
<ul>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>x</mi></msub></math> is the horizontal component of the initial velocity</li>
<li><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>y</mi></msub></math> is the vertical component of the initial velocity.</li>
</ul>
<p>In this question both the ball and the arrow are modelled as single points. The ball is launched with an initial velocity such that <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>x</mi></msub><mo>=</mo><mn>8</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>y</mi></msub><mo>=</mo><mn>10</mn></math>.</p>
</div>
<div class="specification">
<p>An archer releases an arrow from the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>2</mn><mo>)</mo></math>. The arrow is modelled as travelling in a straight line, in the same plane as the ball, with speed <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo> </mo><msup><mtext>m s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> and an angle of elevation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>°</mo></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the initial speed of the ball.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the angle of elevation of the ball as it is launched.</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 maximum height reached by the ball.</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>Assuming that the ground is horizontal and the ball is not hit by the arrow, find the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> coordinate of the point where the ball lands.</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>For the path of the ball, find an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the two positions where the path of the arrow intersects the path of the ball.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the time when the arrow should be released to hit the ball before the ball reaches its maximum height.</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>The matrices A and B are defined by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \left( {\begin{array}{*{20}{c}} 3&{ - 2} \\ 2&4 \end{array}} \right)">
<mi>A</mi>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>3</mn>
</mtd>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>2</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
<mtd>
<mn>4</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 = \left( {\begin{array}{*{20}{c}} { - 1}&0 \\ 0&1 \end{array}} \right)">
<mi>B</mi>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>Triangle X is mapped onto triangle Y by the transformation represented by AB. The coordinates of triangle Y are (0, 0), (−30, −20) and (−16, 32).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe fully the geometrical transformation represented by B.</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 triangle X.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of triangle X.</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>Hence find the area of triangle Y.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Matrix A represents a combination of transformations: </p>
<p style="padding-left:90px;">A stretch, with scale factor 3 and y-axis invariant;<br>Followed by a stretch, with scale factor 4 and x-axis invariant;<br>Followed by a transformation represented by matrix C.</p>
<p>Find matrix C.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <em>G</em> be 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>Find the total number of Hamiltonian cycles in <em>G</em>, starting at vertex A. Explain your answer.</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 a minimum spanning tree for the subgraph obtained by deleting A from <em>G</em>.</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>Hence, find a lower bound for the travelling salesman problem for <em>G</em>.</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>Give an upper bound for the travelling salesman problem for the graph above.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="indent1" style="margin-top:12.0pt;">Show that the lower bound you have obtained is not the best possible for the solution to the travelling salesman problem for <em>G</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The matrix A is defined by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \left( {\begin{array}{*{20}{c}} 3&0 \\ 0&2 \end{array}} \right)">
<mi>A</mi>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<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>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>Pentagon, P, which has an area of 7 cm<sup>2</sup>, is transformed by A.</p>
</div>
<div class="specification">
<p>The matrix B is defined by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="B = \frac{1}{2}\left( {\begin{array}{*{20}{c}} {3\sqrt 3 }&3 \\ { - 2}&{2\sqrt 3 } \end{array}} \right)">
<mi>B</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mn>3</mn>
<msqrt>
<mn>3</mn>
</msqrt>
</mrow>
</mtd>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>2</mn>
</mrow>
</mtd>
<mtd>
<mrow>
<mn>2</mn>
<msqrt>
<mn>3</mn>
</msqrt>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
<p>B represents the combined effect of the transformation represented by a matrix X, followed by the transformation represented by A.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe fully the geometrical transformation represented by A.</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>Find the area of the image of P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the matrix X.</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>Describe fully the geometrical transformation represented by X.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>In triangle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{PQR, PR}} = 12{\text{ cm, QR}} = p{\text{ cm, PQ}} = r{\text{ cm}}">
<mrow>
<mtext>PQR, PR</mtext>
</mrow>
<mo>=</mo>
<mn>12</mn>
<mrow>
<mtext> cm, QR</mtext>
</mrow>
<mo>=</mo>
<mi>p</mi>
<mrow>
<mtext> cm, PQ</mtext>
</mrow>
<mo>=</mo>
<mi>r</mi>
<mrow>
<mtext> cm</mtext>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{Q\hat PR}} = 30^\circ ">
<mrow>
<mrow>
<mi mathvariant="normal">Q</mi>
<mrow>
<mover>
<mi mathvariant="normal">P</mi>
<mo stretchy="false">^<!-- ^ --></mo>
</mover>
</mrow>
<mi mathvariant="normal">R</mi>
</mrow>
</mrow>
<mo>=</mo>
<msup>
<mn>30</mn>
<mo>∘<!-- ∘ --></mo>
</msup>
</math></span>.</p>
</div>
<div class="specification">
<p>Consider the possible triangles with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{QR}} = 8{\text{ cm}}">
<mrow>
<mtext>QR</mtext>
</mrow>
<mo>=</mo>
<mn>8</mn>
<mrow>
<mtext> cm</mtext>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>Consider the case where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>, the length of QR is not fixed at 8 cm.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the cosine rule to show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r^2} - 12\sqrt 3 r + 144 - {p^2} = 0">
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>12</mn>
<msqrt>
<mn>3</mn>
</msqrt>
<mi>r</mi>
<mo>+</mo>
<mn>144</mn>
<mo>−</mo>
<mrow>
<msup>
<mi>p</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>0</mn>
</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>Calculate the two corresponding values of PQ.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the area of the smaller triangle.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the range of values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> for which it is possible to form two triangles.</p>
<div class="marks">[7]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the set of values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> that satisfy the inequality <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{k^2} - k - 12 < 0">
<mrow>
<msup>
<mi>k</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mi>k</mi>
<mo>−</mo>
<mn>12</mn>
<mo><</mo>
<mn>0</mn>
</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 triangle ABC is shown in the following diagram. Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\cos B < \frac{1}{4}">
<mi>cos</mi>
<mo></mo>
<mi>B</mi>
<mo><</mo>
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
</math></span>, find the range of possible values for AB.</p>
<p><img src="images/Schermafbeelding_2017-08-09_om_18.13.24.png" alt="M17/5/MATHL/HP2/ENG/TZ2/04.b"></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A water trough which is 10 metres long has a uniform cross-section in the shape of a semicircle with radius 0.5 metres. It is partly filled with water as shown in the following diagram of the cross-section. The centre of the circle is O and the angle KOL is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta ">
<mi>θ<!-- θ --></mi>
</math></span> radians.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-09_om_11.09.30.png" alt="M17/5/MATHL/HP2/ENG/TZ1/08"></p>
</div>
<div class="specification">
<p>The volume of water is increasing at a constant rate of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.0008{\text{ }}{{\text{m}}^3}{{\text{s}}^{ - 1}}">
<mn>0.0008</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>s</mtext>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the volume of water <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V{\text{ }}({{\text{m}}^3})">
<mi>V</mi>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</math></span> in the trough in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta ">
<mi>θ</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}\theta }}{{{\text{d}}t}}">
<mfrac>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>θ</mi>
</mrow>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
</mfrac>
</math></span> when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta = \frac{\pi }{3}">
<mi>θ</mi>
<mo>=</mo>
<mfrac>
<mi>π</mi>
<mn>3</mn>
</mfrac>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>An aircraft’s position is given by the coordinates (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="z">
<mi>z</mi>
</math></span>), where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> are the aircraft’s displacement east and north of an airport, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="z">
<mi>z</mi>
</math></span> is the height of the aircraft above the ground. All displacements are given in kilometres.</p>
<p>The velocity of the aircraft is given as <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 150} \\ { - 50} \\ { - 20} \end{array}} \right)\,{\text{km}}\,{{\text{h}}^{ - 1}}">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>150</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>50</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>20</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>km</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mrow>
<mtext>h</mtext>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span>.</p>
<p>At 13:00 it is detected at a position 30 km east and 10 km north of the airport, and at a height of 5 km. Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> be the length of time in hours from 13:00.</p>
</div>
<div class="specification">
<p>If the aircraft continued to fly with the velocity given</p>
</div>
<div class="specification">
<p>When the aircraft is 4 km above the ground it continues to fly on the same bearing but adjusts the angle of its descent so that it will land at the point (0, 0, 0).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a vector equation for the displacement, <strong><em>r</em></strong> of the aircraft 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>verify that it would pass directly over the airport.</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>state the height of the aircraft at this point.</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 time at which it would fly directly over the airport.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the time at which the aircraft is 4 km above the ground.</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>Find the direct distance of the aircraft from the airport at this point.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the velocity of the aircraft, after the adjustment of the angle of descent, is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 150} \\ { - 50} \\ a \end{array}} \right){\text{km}}\,{{\text{h}}^{ - 1}}"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mo>−</mo> <mn>150</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>50</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>a</mi> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mrow> <mtext>km</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <msup> <mrow> <mtext>h</mtext> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></span>, 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">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Two submarines A and B have their routes planned so that their positions at time <em>t</em> hours, 0 ≤ <em>t</em> < 20 , would be defined by the position vectors <em><strong>r</strong><sub>A</sub></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left( \begin{gathered} \,2 \hfill \\ \,4 \hfill \\ - 1 \hfill \\ \end{gathered} \right) + t\left( \begin{gathered} - 1 \hfill \\ \,1 \hfill \\ - 0.15 \hfill \\ \end{gathered} \right)">
<mo>=</mo>
<mrow>
<mo>(</mo>
<mtable rowspacing="3pt" columnspacing="1em" displaystyle="true">
<mtr>
<mtd>
<mspace width="thinmathspace"></mspace>
<mn>2</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mspace width="thinmathspace"></mspace>
<mn>4</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>t</mi>
<mrow>
<mo>(</mo>
<mtable rowspacing="3pt" columnspacing="1em" displaystyle="true">
<mtr>
<mtd>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mspace width="thinmathspace"></mspace>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>−<!-- − --></mo>
<mn>0.15</mn>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
</math></span> and <em><strong>r</strong><sub>B</sub></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left( \begin{gathered} \,0 \hfill \\ \,3.2 \hfill \\ - 2 \hfill \\ \end{gathered} \right) + t\left( \begin{gathered} - 0.5 \hfill \\ \,1.2 \hfill \\ \,0.1 \hfill \\ \end{gathered} \right)">
<mo>=</mo>
<mrow>
<mo>(</mo>
<mtable rowspacing="3pt" columnspacing="1em" displaystyle="true">
<mtr>
<mtd>
<mspace width="thinmathspace"></mspace>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mspace width="thinmathspace"></mspace>
<mn>3.2</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>−<!-- − --></mo>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>t</mi>
<mrow>
<mo>(</mo>
<mtable rowspacing="3pt" columnspacing="1em" displaystyle="true">
<mtr>
<mtd>
<mo>−<!-- − --></mo>
<mn>0.5</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mspace width="thinmathspace"></mspace>
<mn>1.2</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mspace width="thinmathspace"></mspace>
<mn>0.1</mn>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
</math></span> relative to a fixed point on the surface of the ocean (all lengths are in kilometres).</p>
</div>
<div class="specification">
<p>To avoid the collision submarine B adjusts its velocity so that its position vector is now given by</p>
<p style="padding-left: 120px;"><em><strong>r</strong><sub>B</sub></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left( \begin{gathered} \,0 \hfill \\ \,3.2 \hfill \\ - 2 \hfill \\ \end{gathered} \right) + t\left( \begin{gathered} - 0.45 \hfill \\ \,1.08 \hfill \\ \,0.09 \hfill \\ \end{gathered} \right)">
<mo>=</mo>
<mrow>
<mo>(</mo>
<mtable rowspacing="3pt" columnspacing="1em" displaystyle="true">
<mtr>
<mtd>
<mspace width="thinmathspace"></mspace>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mspace width="thinmathspace"></mspace>
<mn>3.2</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>−<!-- − --></mo>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>t</mi>
<mrow>
<mo>(</mo>
<mtable rowspacing="3pt" columnspacing="1em" displaystyle="true">
<mtr>
<mtd>
<mo>−<!-- − --></mo>
<mn>0.45</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mspace width="thinmathspace"></mspace>
<mn>1.08</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mspace width="thinmathspace"></mspace>
<mn>0.09</mn>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the two submarines would collide at a point P and write down the coordinates of P.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>t</em> when submarine B passes through P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>t</em> when the two submarines are closest together.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the distance between the two submarines at this time.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A canal system divides a city into six land masses connected by fifteen bridges, as shown in the diagram below.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>State with reasons whether or not this graph has</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a graph to represent this map.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the adjacency matrix of the graph.</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>List the degrees of each of the vertices.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>an Eulerian circuit.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>an Eulerian trail.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of walks of length 4 from E to F.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the costs in US dollars (US$) of direct flights between six cities. Blank cells indicate no direct flights. The rows represent the departure cities. The columns represent the destination cities.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The following table shows the least cost to travel between the cities.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A travelling salesman has to visit each of the cities, starting and finishing at city A.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show the direct flights between the cities as a graph.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the adjacency matrix for this graph.</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>Using your answer to part (b), find the number of different ways to travel from and return to city A in exactly 6 flights.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether or not it is possible to travel from and return to city A in exactly 6 flights, having visited each of the other 5 cities exactly once. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b"> <mi>b</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the nearest neighbour algorithm to find an upper bound for the cost of the trip.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By deleting vertex A, use the deleted vertex algorithm to find a lower bound for the cost of the trip.</p>
<div class="marks">[4]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>The adjacency matrix of the graph <em>G</em>, with vertices P, Q, R, S, T is given by:</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\begin{array}{*{20}{c}} {} \\ {\text{P}} \\ {\text{Q}} \\ {\text{R}} \\ {\text{S}} \\ {\text{T}} \end{array}\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\text{P}}&{\text{Q}}&{\text{R}}&{\text{S}}&{\text{T}} \end{array}} \\ {\left( {\begin{array}{*{20}{c}} 0&2&1&1&0 \\ 2&1&1&1&0 \\ 1&1&1&0&2 \\ 1&1&0&0&0 \\ 0&0&2&0&0 \end{array}} \right)} \end{array}">
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mtext>P</mtext>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mtext>Q</mtext>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mtext>R</mtext>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mtext>S</mtext>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mtext>T</mtext>
</mrow>
</mtd>
</mtr>
</mtable>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mtext>P</mtext>
</mrow>
</mtd>
<mtd>
<mrow>
<mtext>Q</mtext>
</mrow>
</mtd>
<mtd>
<mrow>
<mtext>R</mtext>
</mrow>
</mtd>
<mtd>
<mrow>
<mtext>S</mtext>
</mrow>
</mtd>
<mtd>
<mrow>
<mtext>T</mtext>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>2</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>2</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</math></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the graph of <em>G</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Define an Eulerian circuit.</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>Write down an Eulerian circuit in <em>G</em> starting at P.</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>Define a Hamiltonian cycle.</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>Explain why it is not possible to have a Hamiltonian cycle in <em>G.</em></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of walks of length 5 from P to Q.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Which pairs of distinct vertices have more than 15 walks of length 3 between them?</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>The sides of the equilateral triangle ABC have lengths 1 m. The midpoint of [AB] is denoted by P. The circular arc AB has centre, M, the midpoint of [CP].</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find AM.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the shaded region.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows two circles with centres at the points A and B and radii <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2r">
<mn>2</mn>
<mi>r</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>, respectively. The point B lies on the circle with centre A. The circles intersect at the points C and D.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-02-28_om_17.29.37.png" alt="N16/5/MATHL/HP2/ENG/TZ0/09"></p>
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\alpha ">
<mi>α<!-- α --></mi>
</math></span> be the measure of the angle CAD and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta ">
<mi>θ<!-- θ --></mi>
</math></span> be the measure of the angle CBD in radians.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the shaded area in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\alpha "> <mi>α</mi> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta "> <mi>θ</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">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="\alpha = 4\arcsin \frac{1}{4}"> <mi>α</mi> <mo>=</mo> <mn>4</mn> <mi>arcsin</mi> <mo></mo> <mfrac> <mn>1</mn> <mn>4</mn> </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>Hence find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> given that the shaded area is equal to 4.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p>In triangle ABC, AB = 5, BC = 14 and AC = 11.</p>
<p>Find all the interior angles of the triangle. Give your answers in degrees to one decimal place.</p>
</div>
<br><hr><br><div class="specification">
<p>In a triangle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ABC, AB}} = 4{\text{ cm, BC}} = 3{\text{ cm}}">
<mrow>
<mtext>ABC, AB</mtext>
</mrow>
<mo>=</mo>
<mn>4</mn>
<mrow>
<mtext> cm, BC</mtext>
</mrow>
<mo>=</mo>
<mn>3</mn>
<mrow>
<mtext> cm</mtext>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{B\hat AC}} = \frac{\pi }{9}">
<mrow>
<mrow>
<mi mathvariant="normal">B</mi>
<mrow>
<mover>
<mi mathvariant="normal">A</mi>
<mo stretchy="false">^<!-- ^ --></mo>
</mover>
</mrow>
<mi mathvariant="normal">C</mi>
</mrow>
</mrow>
<mo>=</mo>
<mfrac>
<mi>π<!-- π --></mi>
<mn>9</mn>
</mfrac>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the cosine rule to find the two possible values for AC.</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>Find the difference between the areas of the two possible triangles ABC.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>Boat A is situated 10km away from boat B, and each boat has a marine radio transmitter on board. The range of the transmitter on boat A is 7km, and the range of the transmitter on boat B is 5km. The region in which both transmitters can be detected is represented by the shaded region in the following diagram. Find the area of this region.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
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