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<h2>HL Paper 1</h2><div class="specification">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - {x^3}">
<mi>y</mi>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
</math></span> is transformed onto the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 33 - 0.08{x^3}">
<mi>y</mi>
<mo>=</mo>
<mn>33</mn>
<mo>−<!-- − --></mo>
<mn>0.08</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
</math></span> by a translation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> units vertically and a stretch parallel to the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis of scale factor <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down 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">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <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">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The outer dome of a large cathedral has the shape of a hemisphere of diameter 32 m, supported by vertical walls of height 17 m. It is also supported by an inner dome which can be modelled by rotating the curve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 33 - 0.08{x^3}">
<mi>y</mi>
<mo>=</mo>
<mn>33</mn>
<mo>−</mo>
<mn>0.08</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
</math></span> through 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> = 0 and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> = 33, as indicated in the diagram.</p>
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"></p>
<p>Find the volume of the space between the two domes.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph of <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> is given on the following set of axes. The graph passes through the points <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>−</mo><mn>2</mn><mo>,</mo><mo> </mo><mn>6</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>, and has a horizontal asymptote at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn></math>.</p>
<p><img src="data:image/png;base64,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"></p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>2</mn><mi>f</mi><mo>(</mo><mi>x</mi><mo>−</mo><mn>2</mn><mo>)</mo><mo>+</mo><mn>4</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mn>0</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>On the same set of axes draw the graph of <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>, showing any intercepts and asymptotes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The strength of earthquakes is measured on the Richter magnitude scale, with values typically between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> is the most severe.</p>
<p>The Gutenberg–Richter equation gives the average number of earthquakes per year, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math>, which have a magnitude of at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math>. For a particular region the equation is</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mi>N</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>M</mi></math>, for some <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>.</p>
<p>This region has an average of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math> earthquakes per year with a magnitude of at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math>.</p>
</div>
<div class="specification">
<p>The equation for this region can also be written as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mfrac><mi>b</mi><msup><mn>10</mn><mi>M</mi></msup></mfrac></math>.</p>
</div>
<div class="specification">
<p>Within this region the most severe earthquake recorded had a magnitude of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>2</mn></math>.</p>
</div>
<div class="specification">
<p>The number of earthquakes in a given year with a magnitude of at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>2</mn></math> can be modelled by a Poisson distribution, with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math>. The number of earthquakes in one year is independent of the number of earthquakes in any other year.</p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi></math> be the number of years between the earthquake of magnitude <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>2</mn></math> and the next earthquake of at least this magnitude.</p>
</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">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</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 the average number of earthquakes in a year with a magnitude of at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>2</mn></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>Y</mi><mo>></mo><mn>100</mn><mo>)</mo></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p>The rate, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A">
<mi>A</mi>
</math></span>, of a chemical reaction at a fixed temperature is related to the concentration of two compounds, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="B">
<mi>B</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span>, by the equation</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = k{B^x}{C^y}">
<mi>A</mi>
<mo>=</mo>
<mi>k</mi>
<mrow>
<msup>
<mi>B</mi>
<mi>x</mi>
</msup>
</mrow>
<mrow>
<msup>
<mi>C</mi>
<mi>y</mi>
</msup>
</mrow>
</math></span>, where <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="k \in \mathbb{R}">
<mi>k</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
<p>A scientist measures the three variables three times during the reaction and obtains the following values.</p>
<p><img style="display: block;margin-left:auto;margin-right:auto;" 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"></p>
<p>Find <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> and <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 function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> is defined by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{ax + b}}{{cx + d}}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>a</mi>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</mrow>
<mrow>
<mi>c</mi>
<mi>x</mi>
<mo>+</mo>
<mi>d</mi>
</mrow>
</mfrac>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R},\,\,x \ne - \frac{d}{c}">
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>≠<!-- ≠ --></mo>
<mo>−<!-- − --></mo>
<mfrac>
<mi>d</mi>
<mi>c</mi>
</mfrac>
</math></span>.</p>
</div>
<div class="specification">
<p>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> is defined by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = \frac{{2x - 3}}{{x - 2}},\,\,x \in \mathbb{R},\,\,x \ne 2">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>3</mn>
</mrow>
<mrow>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>2</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>≠<!-- ≠ --></mo>
<mn>2</mn>
</math></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the inverse function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}">
<mrow>
<msup>
<mi>f</mi>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span>, stating its domain.</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>Express <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A + \frac{B}{{x - 2}}">
<mi>A</mi>
<mo>+</mo>
<mfrac>
<mi>B</mi>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
</mfrac>
</math></span> where A, B are constants.</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>Sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = g\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>. State the equations of any asymptotes and the coordinates of any intercepts with the axes.</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>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> is defined by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h\left( x \right) = \sqrt x ">
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msqrt>
<mi>x</mi>
</msqrt>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≥ 0.</p>
<p>State the domain and range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h \circ g">
<mi>h</mi>
<mo>∘</mo>
<mi>g</mi>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the time, in days, from December <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mtext>st</mtext></math> and the percentage of Christmas trees in stock at a shop on the beginning of that day.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAqcAAABcCAYAAABTLxz3AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAADOXSURBVHhe7Z0LWFTXuff/Z45PTB3CIdQqxYhEJUbMBanSNFqvHwMlypmobWJURCXWWzEYT6xBiSUq1RrGoCZ8BMMIenJpxF1iqIEQ0U+NAR2pCeNlIpKpQUwMUgRjLBm+tfbeMwzDDAzXMMP7e555GNbs21pr77X/613vetd/NDBAEARBEARBED0AhfyXIAiCIAiCIH50SJwSBEEQBEEQPQYSpwRBEARBEESPweJz6ud3n5hAEARBEARBEN2F0XhF/ibRZEIUF6i2GxAE0bPprc8t5bv3QHXdu6B89x4c5ZmG9QmCIAiCIIgeA4lTgiAIgiAIosdA4pQgCIIgCILoMZA4JQiCIAiCIHoMJE4JgiAIgiCIHgOJU4IgCIIgCKLHQOKUIAiCIAiC6DGQOCUIgiAIgiB6DCROCYIgCIIgiB5D+8VppYAYv/vE6P5NP9MRry2EodYkb+gK/BNCzCPs2sOg0dXKaT8m9ax4V9iUq/wJj4e20ICecJVtoV6XjCB+/TECKuU09+I2DNo5rI7mQGu4Lac5gekCtJEj4BephcGVHhmCIAiC6CK6wHJ6BlkJczF11k7oXEqgugj6PUiImoZZmmKXE6g/DjUwFL4PQdiN+PAQxAj/lNOd5Q4qcg+hpF7+1xE1J6HdcgQICsW4YXfLic0xVerwfnYyYmbIYlQxBONmjAFK0qE9el3ayC0wodZwFII2HuF+KyBUtlaA7sAdVBanImak3JEcuQiaAtfrSLYfqc6zNYswUuxMu3u9s7alIKWxvsPjkaWrZKXg4tQaUNhCe2mqPIGUmBApz34jEB6/D7rKO/Kvrooz7RV7Fwgr5Xtb/ri8UYG/HwVo46fbNxyZKqHL4mVizvN0xGcVo7Ib8txxceq9CkLZFXFtVKPRCH1BBuJUvkxE7cKLb5x2kYZ5MNTpZ9n1f4i4YA85rWfgHZeDMrFs+UePgowXoFLWQa/ZjDd01fJWhH2uozB+Kbbs3YnY2JeQpW+DRVPGVJGLxER9Ky+c2zBkv4GsOiWCZvwKwxw9VTWFWD85EsufS8apXz+C+8Xt7sawcaEIQjmykg+6j/W05iiSIp9BbMIe6OUk94a93HRa7PjkEWwsZc9qeREyf/s1NAs24L22WNJdFvaSEzZg1tRnkXb9cWwVTqHcuBNqnz7y7+4GFyrrEblCj/GCXmyb85/+FpvVS/GqS7fLrM1MWoAoR+1lbTFeXZcPvzUfsTyXoWh/HO7LXgN1dKprG6Ocaa9q/4F3UiuxWPhcfh+zT040ArrAxNc9mNgraRsio1YgIeuMnGYNu8dzkjAn/ix+kVIAPdd3+b/Dtc1zsTjzQpd3wjq5WBXwCAjFyjXL2MuWCai093GqRs5CMwXOemWafGn43zy06Tce8YXW1iPzUOkIRGp5Ydj0VJ3qtfEeUT40lp4e+zTr4doO6zcOqwdpCnDOck575+PHL5R6HpZr0qLQUCP/zuB5F5Kb9LDbNzTviYCpi7FmzUT2vRhp+0tYicg4cw7eIxZ7ho634ZY9wWL5sM2LlbtBzG4UWpdLQgHrTVlbjvi+gh33jtuo0O1jvXJe3/dhZEwqipuUJzuGTrCqL1s3kVroNGEs/RHEaN+HVtzO9r4x0x+TNu1Deno6UlTecprzmCoLsGHhGuS2pi1MX+J49in2ZQxmjBvi+KHyfAzRYt3544nRfjC/thXDfoUZQUqgJB/HL7mJkPGchE3nvkBBIs9vb4C1fcGLsSn2cfjwG0Dhi0nLFkGFL2H4yjW66O1HFmqxh3BfYjbe27QI04N9Ovvl0rMwXUbem4fQd/FizB3hyRI8MSIqDmuC9NBsYO2ebbPnMvA28xjKCzayd7gt7A186jT+c9lKqAN4nu+Cz9ho6X2k/wBHLt6SNnNFWm2v2D3+0V7s8Z+Np4K85DRXR8GynYhz5QVI5O+fZrB38eXzqFOORuiUAHjwNm7EJEwb1xcGw9UuNzx2SfthednWXUL5NS48mMjMfB7qeOteSQXyNAsQmXQUNYr7oVoYDiXKkZ3/uZXgsn7pD0YtV/kLtiKvTvqZnQD6rFZ6bWKPaAE0eRVyAkO/B/FO9nCrNPMRZjmndL45O05YrtFUkYPVkXOteh58m3WIityGQlGYV0P36lKoY5Mbr1scmp+D1YLRSiA7i9nSxs70WTmuiQdw4hwmI4TVcxBl3TMUt1mAJLOw473i6NmI1XzIcsEx52U9hAqbDkDeS4iyLhftMkSzhjp65sYmZfX8e4amecxbDbV6DeuVy2fI24iZlvrj1qdURKtXWNWX5CYSuToHFU0OVIW8hKVIELdTor+n46H0Fqm9AMHSseAfPqRzh+l4Aeujl0HLr7MqGeqh7DdH/rJfn8OxEradchj8B94lJ8qwTkNxChf7TKz/JRMH+f2snILQYCuxrPgp/B/+GfvyGY6VfiOluQV9cI/XvfL33gZ7kZ/X4VTEaiyf0F9Oc0/E0YW1+4GIF5EYNYq9xHoB5mfeGrOLjqEMXzl6H7kIinu8MED+3ggXM0sQG2wtzuRnXPlLjB7eT05zVVpor2pOYBe7x6tyV2Dq4mRku+C8D4co+sFrQF/5H2tY5+P+B6GsO4S3P74i64hbqP76Z5gR+hDrjnUtXdO5tWT2Om7crAfq9Ti4/Qi7gWci5WSZOBxwMmUmkxRmgXUXfKc8iRlcz2Z/DJ1sbTVd+gTZrAFQRvwWqmEmfHHmUyZ5lAhKLEA5N6nrDyAukO2kfxf7T1WJ+9hS/4UOH/A2JGgjCsq5Kf5zCHFjWYKN5dERymlIzOfDNlbX/IEOX4guKddxdNc25HJdokpCvt4IY/kJpET4so3eQXK2AfUVhUhLKwYClyCziOedm8aToFJWIDdVQEk7GjFLw2Gswk22u6nVc9QzjZ6OtblMyDXLj3k4WeoZpjHlGhi9B0ViWemRnzhNvDlT3/mHzcM4GtGZRawezOXJxGjetwixSSs5dg5fi9ubGY154hDBFZQX7UG0WH+7sIGLWNMVfJS2l4ln87F5HX+IRJUv6nL34J0Sm86EOb/6LMx+oD0NI+s0vZeI2OzRyPyc1Z3+MDLiHsR/8h5igBp/2vx7iBLS7LqSroaPuF9T6ivKwLtQCBiKQR5WjxTvECyLxMzXPZB08h94d+wVpPH7ecYUBHtaP3oeGBQwhP2twqnL36A3eGe6N3yEZydWPQds3xoJX7c2Id7Gpby/sjbQF+OGfY6EUVInr/mIiJvRzwsDWdP1/fUaNLMX1lWh+pZri1Pnqcb54hI7bZqbIVpW+TsrB1vHf4u0qMkYG5OFCy7eCWkZpsvUL0NIDMbJg0dgqL2NyqN/RfaAaESNaftIZFvpnrupTzDiStjLvXgFvIpyIWj/hIWx+5l0YcgCC54PIXSGP3uwP0a+jgtN1ugdz0cJ/DHj6fGsgWe9mnu5BYIJnoRIRMTvhvDRVxi++QgTMcewaZJ964TiHm/48S8l6zA1Ih5aoRDG4etF8XVu06RW1b9yxtOYIQ7bsIp6bDLGSckSpm9R/hm3dLFrnPsbjODCROEHdWoRE3YXkBMdgFsXdTjCM6pPRVTIUNZw+yEwdK1kXdR/irNXO9qAm1Db6jlqca38kljeTfKjfhXnLH4zNbhYfJptw62g8xHiz18ygQhNOCilHS7FVevnMGgm5k3w5X1pDB/9sCjaG9O88MjEX0vCzha2TXTkCNG6ovAZh3lPj2Hf6qRhgtoyFB/hltAz0EaFwJ9bMgPDZOuoHofPXmtihfUOi8B4n7uYthsAH2tR2FaY+N6rPYnKfgGYGrcC09vkJ1eP60zoi12jAV64x3IZ3F/nFdYhACKSnkekr9miqkRAwM9trEuNPfaqUiPr8hAuS70OmqBATOWjClVvIuqXcc1HHdwJ8+hWYCgmTo1B2jnuh7gO445vxMzF/+s+PtS2yO+ruqxXsEW4IHbcuUvU348Z2CPuDa9+bizUrDBVHMPbH/wCScsf73JLWk9A4ROM6dEv4738JPEeX+ky82raiycCwqOw8KcHsXLscEzeOwR/2T5H0jpdTNecQTT9fs++9Me997AXvXloM3AyomJXOHA69kZw6BTRkicO7ZtnP1uGQO9GQNQr2L86jG3Dh4xfQiw71nL1GPiHb0Shg166IuAZpLHGUsXVEx/G5udfHsnE13QkFFY0ETv26NvfEw5tcqY63DCKks/BsLIJt6qr2NU6QrYstxHTzWrJGunnzcSQM+e4jZs3JMnjOD/fofpaC3ZkcyfCjEWIKdDP0wvioEATceaAJts0irK6a9W4dasa1xxmpA7GG3VW9aWE373KDt7Ad2NY+EJEB/4Ledt+h5CIBAjWvsIdQR4GqlOG4+kp97HrvCN3EFrxSyVcG7kjzi0sKXGsrarbj7W7Gt2A3A65DVT+IhT/LfqZcj/Ep7Fs8Vj38qFuRn9MWrsbKfOArNipCPSbjvVv/Q25rCPt9lZEMyYjchIFjHjzT1BbOt+9Ae57+VusWTOGSYr/h4tuPNQlzruIfhU/PPV/kXv4XSzFDoQG/rdT2qmjdMkTZKo8h5MGpjJkHzzTpUN4eduH7EUdhrjt6RCKylAmrJIsa6LA4l8U8AyeIg/t5+Ojj/KRXadE4OLpGGN+0BU+GBu7G+f4LEEhHSkp2+TIAKlYauUH2hTeWC5BumyS35WyE9v5S4Nb55am4qh5wlZ7UChxrx9XvXW4XmOvEWbCzcubnYuh2okibqVs8mlPdIA7qCw9A9Y/h/JhfwxUOHMOJghFq7ODYSiRn8BrIO/7ekOV8onNMdinZBWCO2Pi7dfVViK3Hjerb4jflAO90E8eKgPUSCkqb3YNJXHBTM6a6ct0br8O38AKn6lIfO8gMvg9oX8TsVPnQ9Ph2bYm1Og+Zvcvy5f5ReVkqCmxHOTvhOvCLSzqlS9gTRDrSvOOl5zeO/CA7/2D2N/2db5dBo8RUG96X26f/oY1o/viS4zF4plBvcCKWIMLmRk4+/RmrGzig9pbuAsD/YdJ71235TqO7ngJ2rt+g2lBXqxNexyx2zOQqLoGbXIeLnWxOu10cWqqLMa+XbuRaxGWJnxdegol/Mchj2KiSoXgAddxTDgsDYVaYxna34PnntsjWpmenvawNARqmdEfghitAR7B4VCrwzFxFG8EZcub+M0a82x/7gOVBYNHEKarI6Ga+Ci4h1+HfYMsE1nKkb3377L/STV0mielc8YfhWnQUATwbfN24zWxt8Fntsqx0tocI43PZP8rdqUeYmVjbgRZL67VczQ+SHXZbyP7ApfxfPJRijRzf2QCCmv6Wfwe81L3SJZo7jO5hM+GN0dL6ARKXsOWzFJ5GOw4st7m3pr+koO1x88REMCvMh+prx0RY6mZKgQsEWf/tzG4fVvw4MP5b6BY9NMtxp4jZW3w++yD/n5DpY6WRXjfkv2jvTFu7DBWR6w+Pj4gdraC7IaaahTpLVrqCddCbB/uQyBro9x2klAfP4x+wr/JXAELbjFJxhlYW3phH1YtfQdD4l7Es24v1th7qDAdmZiFVZO4G1dvhI+EGTFk/q/xQGcYbXoiFrdFK1iHLHxaSPOR1C6g4/eVeSYzFzns4x/yJOL5zPXA5dj87C9Yo9wHA0aNkcJS6LdCHegHP/8QRGnl2e1NMtkfE6JjGkNYWFuZFAGYtWE5Avks/4QwBIrnewhqTTH70R/z5o63M1nlbgTMek6cNFWXtxah/NzcH1O9VXQrUM6bhSkdisPHrnf5akQwPdV4fPM1SeLRK0CNDeLkILMf5VA8Jvrb+iJi4RTHMTFlqjSRGCqXrR/bN0Sc6c6K16oRVLR6DgU8J8QgSZyodRAJoYFW5WDuRPSzlJXFd9Wf9ZTESVThWKi6v5Maocb68w+ZL82GD/wdZnIHa0sdN/q9+j+2QppwJk6Ka+eMfIubyfdMP96yEtn1qHx/pxwonYv8BzFqiD8eu79/07x+X42aWiOOHr1sV6D3GR6MJ7imtszSNftHcxpQaziBvOIylquf4eHB36PkqO1Mz1p8ZfiS/W0aYsr1MYvuG6h2ZwuaXfgLPBV/Pj0Zf5z9qPuKU3MbiHfw522HpQ5l5RG8lloC1ZqnGke93BUxPN96zArdASzNgHblWLeoa8l1zLa95PD7eid2lIdhbXRjZAY+/JuoOeri7iuO2ituFDoE4X2dHHyex/TdjD+8HSxrHBfH/H5sMqrJsCwQY21Q4s/2UQR2gyjvgpZjNOYl7kXBeysQLDvNNvH75GJo3hYIJ3Ol2FpVp3H2cqNFzBKGim3X1MrExEPwEmiFndJQvpnA+UjMzMBaBxOi4DEWK7VvSf5fcpL5GnPWTujw8IvCNxLbcvYicd5oOYVduWoVUoTX5eEOLwSvfB1Cyio5/wzu3pCxD9vUfm2vADG/B/EeE6OND4UT5+ATtbbtQ2bifCb+ZPg2KW81Nqh2ykqpegEZOS93nk+RahsEYQvmcRHMUKrWYb92iXyv2KtjX6jiMpCzrT2znuX4tf5TkSCGfeGT6aYy8W61Ash/BSFi5Dd4k8dLZR2q0oit2BAplVmfoGfwBvdxrnsTS1cfwcBgB76iZouvJXTa3Rim+i3rtFTh+EEBn7ISHyfGBWS97dJa+I7nMeOssPRQhyBgkMs3dRLixKDhmJpwhP1zBAlThyNIo2uDRdrVaBwxkT4z2Qucvby0L2ASn7Tnxkht4Bb8omiZ1KEM2Y4f5miw0Z3DSon3N6vnwGn4s2Eolgs5SDPHuHVppDjS/lPXocTcXgYlQyc+uFyYbkV0VDKyLAYi6eMf8hK+Hx3ouu4MrbVXNaeQKs5V4fmdA231FOyw0jiuirisuPn9yCeN+1sv4S7N8xE2heKKxaDEn+3d3dIJ+48GhvxdvMm4/8yPieSAy+NLjkFiwW5EB7TTWkYQ3QZ3H1nEGrbPoEr5AOnqwXK6k1QKiAlZgTwe7kxo+4ojPeG5/TGgfPceqK57F5Tv3oOjPPcc2c9f0OwizUO9ynnPYgYJU8IlYD3MGc9iHreUFl9q49CWFKz9OHdNWTXNhZfCIwiCIIjOoee8Ci0ztaVh/31/6B1x0wg3QV6atC77AD5uS1xLkwHZye+gLigG0W6+khBBEARBOEOPG9YnCKJt0BBY74KG/noPlO/eBT3bjdAgIkEQBEEQBNFjIHFKEARBEARB9BhInBIEQRAEQRA9BhKnBEEQBEEQRI+BxClBEARBEATRYyBxShAEQRAEQfQYLKGk+HR+giAIgiAIguhObMNJUZxTgnBxKCZg76I35pvqundB+e49OMozDesTBEEQBEEQPQYSpwRBEARBEESPgcQpQRAEQRAE0WMgcUoQBEEQBEH0GEicEgRBEARBED0GEqcEQRAEQRBEj4HEKUEQBEEQBNFjIHFKEARBEARB9BhInBIEQRAEQRA9hvaL00oBMX73idH9m35GIDx+H3SVd+QNXQkTag2F0CZmQVcvJ7kM/NoFxIePkOthDrSG2/JvdjBVQickI2akdb3txvu6SnYkM/+EEPMI+y0MGl2tnNYW2rt/DQyFWiRqS+By1UAQBEEQRIfoAstpHfRZa6COToWutlHmuASVOXhu6lwkZH8jJ7gSX+GjLQnI0tfJ/7dAbSm0iyOhjk1GnmVzXm8vYbk6EssEo5VA7W7qWb/nRUyNWofsGy52/xAEQRAE0WE6Lk69V0EouyKujWo0GqEv2Il5gUpA/y72n6qSNyK6nPpvcFks71GIE86zutiH6IC7pd+aUA3dG+uQkFcBpWod9heVSXWnL0DKvNHs9wrkrk3H0ZrOEIaDoU4/y47/IeKCPeQ0giAIgiAIx3Sy5VQBj4D/g5lh/ux7Da5Vfycl2w4hh8dDW2iAZaC3XgdNEP9tCbQFu6XtRiagUBRI8lB7/HRpX3H4WYtCQ420L6e141sPLxfqUKBZhJHisaYjPqsYlfw03E0hZAXy+OZVyVAPvQ9BGp00rMyPnxWPcHEf/glBjCYfBmvLcJNt2HGFUhiEFdL2MQIqLZvpIFjObycvdrmDSp0ATUyIfH4b1wl+7UMjoRH7AqXQqB9scs4m1JRgf1oxoJyJpMSFGOtzl5TuMQLqNc8jOmIVtr8+D2M8bW6NH67a5O+CpXzrdckIEvO5GwXaJWLeRsYXsjvAzrB+rcGq/OVjmetAtJo+h5BYQdy0ShOJoeK+1SzdXJa7UViQItc1K4eEArYvK5/i1Ma0eKGFuuEf2/qrgcFyTPMxXNU1hSAIgiBcm04Wp1xIfoT9H5az754Y6PUT9rcauleXNh1C1u9BQtQcrG42fHwQCQtekrbr6wXPfgqYKnKwOnIuErLOSJuIw8/rEBW5TRavbTk+E25RkVig+ZAdhXMGWfFx2HH0uviffW7DkPk81PF7oJdTuHUxT7MAkUlHmazhyNdg2YYdN3Y2/pBaIv5nobYYr0bPRqzl/Oa8rIdQ4UgIsTLVpSJavQKavAo5TXadmPw/LexnDxNqdB8jm5983GQ85isLUzOek5CYugozJgWgqZ3zKj5cv8Amf4uQVGhTbnkvYUHCQTFvfft7op+UasV1FCYtsCp/Dq+DuYh+tdiqM9EC7BxRC7bKdc3KQbsM0YsXI3rmxsY0VjbPv2eQ6761+mNlUrgNkZZjcuTydUXXFIIgCIJwcTouTmUro2Rx8kPg1BWS32Pg7zBzjDcTl4VI45a6wCXIFIeQjdDnJ0GlrEBuqoCSJi9/JQKj96ConG1zaC4e6HMdR3dtQy47nFKVhHy9EcbyE0iJ8GX64R0kZxtQ36bj2zkOyvHBGSPqfdRIL9oJFd9IdlUoiQtGn3o9Dm4/IloaU07y45fhZMpMdqXsEj4rxzV+eLM1Er5QJX4IvfEKyos0CIG17+odVHy0F2lMIUl55G4QeuQnToOy7hBS3/mHfXFmMuC9DbuYsGLHXv2utJ95CL5uP9buOoEafu1lOYjz5jvIw/rpaviIB7DGhFvVVaIw9B7lh/5SohNU4cv7fm+/3KQNZEYjOrMI5cbzODT7AfSRUy3UG3HmA95xmYjEgi+kuhJeQCAXg2nv41SNAj7q7ShKUYube8floKyZS4D5HJ9DiBvL/mf75n2LEJu0kmPn8DXfvNX6u4UvznzK9lAiKLGAHYOX7wHEkWsKQRAEQfwodLLllMNEVNxOCNol4Jqi9qIOR7ga0qciKmSoJGBD10pWKv2nOHvV2vLnjzD1L+GjUMDDZwA8TN+i/DMu8PwxY+5vMMKDXa7CD+rUIiYyLiAnOgC32nj8xuP44rHwEDm9BfoEI66ECZbiFfAqymX5+hMWxu4XBR6MVbjJxKnpWjk+4wneT2PZ3FGi1VHhMxHLloTyrWRqcLH4NNuPW/vmI8Sfi/lAhIqWRpZ2uBRX7RjpTJc+QXYJOzg/9rLHWdmwRD4E/4dFopCuy/4Yuk7xD20JJ8vNezLU4325cwd8fOz4mCqUuNePy8IjSJj6W8RrBXxkfACbeafiXCIm2boS2CNoJuZN4OfwxPDRD4siszHNC49M/DVEjW6m1frrg3vu5TKdCdqESETE74bw0VcYvvkIE6rHsGmS8xKeIAiCIIiO44QaaIUmE6L4pwjpcWoEi76MjZY6+1zHjZvWtrf+uPceK3ubqQ43jHxvJfp72pvc09bjOzpOC5gqUZyyCCMDJyMqdgViE6yHhyVMN6tg5F/GDIWv5fL7oL/fUCuh9B2qr7XgWyoLXVvsH5vR3w+j+MHrqlB9y1lxqkA/L29R0FWVGlnpOIuT5ebnjXtauqMUIxCVloHVKm55PYOshFjExsZAHfKw7DsqbdYiA7zkc7C8eHqhb5M0O7Raf3cjIOoV7F8dxnLJh/NfYte0AsvVY+AfvhGF5HdKEARBEN1Kx8VpizSKIah2osgiYM0f2yHbe+FlLU4tlrY6XK+xF7OzrcdvO6ZLh/Dytg9RpwxD3PZ0CEVlKBNWSaJTFmOKe7zhx/8/VYYKixaux3VjGRoHhX8Cr4Ge7K83VCmf2Fwn+5SsQnCzcXBHx2ZcN6KUH1zpDa9+zlajAp4PBmMc/3r8ME7a+qvWFkMTk2AzmawNtCQSZRQ+jyM2vQjG8lMQdu1EyvZVUCm5NfmlVnx/24cz9ccuCmNjd+Mcq68iIR0pKdsQxwW0PhVLd5yQ/YoJgiAIgugOulycegwaigD+NW83XiusgIn7XgorpdnakVoYWrKWKX4K/4d/xr6UI3vv33FB9B+thk7zpOjjOjL+KEwdOb4tZmtkVRmM17kSrMfXpacgTmsa8igmqlQIHnAdx4TDVqKTXeZAfzwsmiPfxmt7S0VhZ6o8gtdS88XfJTwwKGAI+1uFvNQ9kkXOZISwhM/AH4FI7QV27c1R/HwUJnP/R37s105I1sXaCxB27BYjCyhnTEGwM8PhZnwmYRn3y+T+qglvothsGeTHTEqEJu9NJERtwHstBfBvJyaDFpG8XkYugdbQD8HT1VCrfo1RQ3jhmaM7NFqc22bdtYcT9We6AG0kX7ggBDFaAzyCw6FWh2PiqEHiz3XXqnFL/EYQBEEQRHfQxeKUnSBAjQ3iJJUz0EaFwJ8Jj8dEnz9fRCycgmEtXkF/TFi+GhFMu9TlrUVooB8TEQ9BreGTj8Zi8cwgeHXo+I4QEBvijyDNWXiPGoMgnqTfCjU/v38IorRy5ADzULznY4heM5F9qUBeQhgCmQDzD9mKivt4SC0zdyNg1nPyRBvZP9b/ccTmVjCFGY6FqvvtV4bHo5j9x3kI5Mfe9jvJVzVwKmJ59AIeDmr54+D2WOfxQvCzG5Go8mVluhEzRT9dq2Nyn+HEFzHLbozUjmG5F+oOIiE0UD7vk9DwCXRKNeZOkQShhbwVCGn36lScPhjQWv2xrs2sDcul8pXrrvEe88e8uePtTCxzd/gKXYIUvs1BSDJT5QmkmEObhccjq8nKYhzb8F7uEZrLVCFgiSXkGP/YrsTWetm5Ftb1yD/Wod/M2IRis3s/uBhmdyBzPTvKU60BhcJuxIezzq3wTznRxWklT6bKYmRZQju6SX2zq681HIWg5SEHV0CotB6mtIGXT7Y5dOUjLl7vbWivTBUoTGDbBSV3ywqaXS5ORTG08nUIKXz4Vk7iQ6wZ+7BN7dfqBSh8I7EtZy8SxQDxEkrVKqQIr2NlsBf7r2PHb0KfhzD7jXXycZRMlPyAOwHPIG1/Y1rgvC0QTuYiMYglVJ3G2cv8xST5LQqb5jORwzcLw+r96UicJtp0G/EYi5Xat5ASx/0bJZSqF5CR8zLUtmGdLNwFn0kvQCvslIaaReTrOPyXFvZrAY9RiE7LaVpmDKlcc5AWLU3q6nzs1JWYl43IzFltmRDVJ+gZvCH6gHJ4QKr2PwmKVuvvDjyCl9iULyNwPhIzM7C2102IkkNrRa2wCt9mgxgSbQlyfZNQVF6Goj/+BPvmJCHH4iYihz+b+QF8Xy9Ceflh/PE/38acDbmocOk3WDVK3nkL5YsPiBE5JJcc68UunCg7l4LXYxrWCT5YU8wjdZzC/tUDkN0k9BsfqVqPyBV6jBf0rDz0yH/6W2xWL8WrumpxC9eDhwZMguD3AopZHZcXvYvV9+UjvlmepNB4UbEvIUvf+SNNPw6t5MlkRA7rzMefHo2UAuv6fh6ZXTDa1m3UHEVS5DN255Q0wgWsgPhZ0xCV9i3Gb81h7d9ZpKsHy7+7Gm1pr9hznrMFS82Gne6gwYrBgwfJ34g28e/TDcmPDmLl90BDWHJRw02e9sNXDYfXTxPL9NHk0w3/FjckiM6nS57bH843ZEx/oGHwogMNV+Ukie8aLmY80zD4wfUNh//1g5Qkb/vgi4cb/mXvf550MaNh+uBxDS8e/kZO6Tjd3V798NWBht8/Gttw4Kvv5RQHOCy7zqH78v1Nw+Hk9IbTN+V65pjz9ugrDad5oyb/36SNM28zPaPhotWuHaFb6/pfRxqSX5XbcRnp/rXflku/Pdyw6IBRTuk8uvseN+MwT/K7zvrZbrh6oGGRiz/bEnLbNnh5w4Grzd/Y4vP/IMv7osyG89bPRCfyo+TbifZKavumNIRNtXr2OwlHee4Gy2kvoI8fRj/Bh/DroNc8KQ0NW4aPx2L+xKHNY34SRE9G0Q9eA8RYCE0xfYnj2aeAccF40OzrrBiCcTPGWMKaSeHP+mLc2GEWlxPFsF9hRtA3yM7/HK45wUyOuVy1H7FTl0KTfbTpKmTWOCo7l6M/JsUtQjAPIWdGzpvyiWAM543a1+dwjIe6s0a+H2Aow1euuIiF5wTExY5tMnqkuMcLA+CPJ0b7NWvLpd/cC4d5UvTH/Y/5smf9AD6WR0pMN6vxtXIKQoPFaaYuTB/c43Wv/N0GbjFO3Ixc8JUVn5LCKroLrbVXtaXITBAw4k0Nlvh3X7tG4rRTYI342gxkJsrD+jJN3Q8Iwg2ovQqDoc5mEQe5Ua+7hPJrt1H7VRkM+DlG+Vk19HIDaFm4wuVgz/imY1KUia2P43ras5g6dhm0F3pZLIeaSyg+7okZoQ9JHY9+XhioBL6/XtN84mCbwtz1ZEyoOa/DcbcQYB2ExxnfloHEcedxMM+AWlMFjmblY8Cap5ovee1GmC59jDdzK6Ac9zMYEsZLvrYjFyGl2NV9bVujGro3/oJj4/8HzwY7EO5dBInTzsIjAJOiN+GQxRftCs6lr4I62IcKmXAfblXjmsPAwjyu8J2WYw87iOfrMih8EDx9ETa9l81e0DokrNT2oiVu76Di4wP4YOJqLJ8gd008H0LoDH/UZb2CLcIFOVKJDn8/ZmC987aEuevBmK7g47c/xcSkGExwYwHmNOxdF/77mfhpdizG+quxd+iL2N5l8xR6Ardx6Xg+SjAaMyaGYV5akeSHPO4zbJvp4r62LcJ9zvfitRvzsDGq++uXnjSCIDoJm0U07NHaQg2ugscoRK1ZhiD9BzhysXcEGzNV5CLxzWF4c1skfC11yEeNdiNlHpAVOxWBftOx/q2/ITevou1h7nokfCJICt4csbHtE2zdkjuoLNyK6PW38dT/foDD+xcCW8IQ6NYLltTj5o3rrLM1GqH//QtxlUaFz2NYuGwuAnEK2ce/dEvrqanyMLa+Bix7YbK0MmU3Q88aQRDOM2AkxgcpbYZxb6PiMreUDYP/wH5y+C6bhTPqv8HlU1VQPuyPgW7S6ljiG/cGuN/ZrjI8ncaXpbapQL6c8qb35RGjv2HN6L74Ug7117Ywdz0NE2ov/BW7zv4GaSub+qD2WmpOYMfSLNz1dBiCPO6Gz9jF2C4kQfVlFpIPXXbzIW5rFPDw9cN9rJ0z3qhzw3zX4+uTB6DN+7MUglEMG/YrxOZVAVXJUA/t+hBaJE4JgnAem8lPIqavcPZwucVSZm/yk+nyWRyu8m/0VXQDTNfK8dmQJzDxAR7uzI3h8Q2T3wOiYjBJXJbaEVzM7cOqpe9gSNyLeNbFfe255Sg5k2V71Y9jOeqJiPd8E58dJtJGTMK0cX3dVKRx+mH46F9CWfcx8nXWy+9w7E+Sc336wEe90+KiKH0+QYrKW16yvutDaHXgkeMxvwqhTczqloCs7eefEGIeYaq/rcHca2AQEhBuDjQsrjblTJ7rUSmsEPcJ0ug6EKGzDfCgwNpkaNsdrL4F6nXQBPEyaEcwfPPqS86u1NXW7Ymuw3QL1V9/D3xdbeMjejeGqX6LCBzC3uxzqOXPSc4+vG0Ib1wQQnE/VAvDgey3kc0nDNVeQI52PwwRVr6KLgb3o3xfOCQvJMDbAQHr//B3TN4c1dyS6LDsXBAuTDe+gfKn4hA9wtyt4EO7KdAUWq3fJrZB6zErdAewNANaF7c0mioLsHFHJZ5aO7txZjYvi8SdKDR3ymTE2er4nlX3LbcRZ47yJHU8gZItGmSKkwH5vbAHqXnD3CAqTT1uVt9gf2+g+qb1m1sBzwkxSIq4g6w/p8qrO7J74bXdOK76PaLGuPgkuZ7aXskhpUTaFGNLjG02qNNjXnU+xoYDix5meVM1JJ+2jlzXCub8mT88Zt8VZ/L8b7brcnGf7olv2s78OYslhmtbj/9Dw78Or294cPADDdMzzrP/nMEcZ65zY+a5O216bp3g36dfaXjUfN+LH9u6/6Hh5sUDDS+GPSD9Hra+4cBFS9RDmX81XDywviFM3P+BhrAXDzRc7OTYgJ2d75b44epHDevN+RXzk9FwuFmenSm7jtNt+baK1dzsY45zax3j+cX0hpzTV5181tsGP2d30bSum36axPdsuNlwOlnVdJtuigHZdbSepx+uFjVkvmh1X4S92JDZyfXOj9utWO7jxk+z9/fN8w0HLPnm9/vehtNXW4l53Ea6O99ta69krdFN9ziJUwdYKs06fz0yzz1UnJoD+w5+piHj4ndyYuuYg113ZgBvd6e7G7SeAuW790B13bugfPceHOW5fcP6lQJiQlYgj38XnWOlIezbumQE8SHwmN0o0C4R1yUeGV8o+Z2ZKqETzOvRsk94PLSFBnkJPJlWt7FZw7kDa3bzYTpBY147mR9Hi0IDv1JpWH6oOhmid4nZ+Tc5yW6emw/b2xvWt3ItKNShwHJee+tUW8OHD/OhMa9hzj9N1jHmx31CclJGKTTqB5use9s0j7b7muFr62oRHz5CPge7Jm2h4wDjfPaqsFI6ZgszNKVA7HVAUCjGDXN+nX5p2EgJlOTj+CV3DdFBEARBEIQjusbNO+8lLEg4KMY67NvfE/3EtYqXQh2bjDyzM7V+DxKi5mC1YJTFUmvbyOvALtja+DtfkSlrDdTRqW2LNSiuDT4bsZoP5XiM/DjrEBW5HoJlffCugAnIqEgssJz3DLLi47DjqJXvljXier8LoMmrkBMYrEyar/Fsh2Z5ZIj7RmKZpczldbGj1iFLb96KXVPCXEQmHZU6FU1gYlmXioWx+1GnnIbEV2MdTJCox9elp1DCvjXOzr4Ng3aOLIBHIFJ7QbqG2gsQ4qfDb2SC5Mul+Cn8H/4Z++EzHCv9hm9BEARBEEQvon3i1EeN9KKdUPHv4sytKyiJC7Zyhh6N6MwilBvP49DsB6CoKERaWjEQuASZRWUwGo3Q5ydBpaxAbqqAEiYsTa1uU4svznzKhJYSQYkF7NhXYNQfQFygkomud7H/lO0sOkcwQfbRXqTp2ami96ConM9C0yM/cRqUdYeQ+k4pPNQ7USasgujmbJ6ZtmptK3l2DqUqCfl6I4zlJ5AS4ctSyvHBGaMdCyyTeF/o8AHXjEEbUSBe5+cQ4sayhGKk7S9h4nEw1OkfSDPoMApxwnkYS1YhuA8Tgu9th4YJTqVqHfaL5alHQcpCBIKV59p0HOVCsOYEdq1lQhO+UCV+CD0r0/KTOxHBirQu6w1k2wQXri/Pxuo5W6HHWMTt+7PVBAlb5NBCrK4CAn4uT4y4GwHR++Tj16Fkyz52DVXQvfFHxGbxZV7NeGBQwBD2twqnLn9jt1wIgiAIgnBfusZy6j0Z6vG+7OAe8PHph9qLOhzhIkufiqiQofDz80Ng6FrJAqr/FGev3nZiGxPuuZfP9GXCJiESEfG7IXz0FYZvPsKE6jFsmuTsLOAaXCw+zY5SB712PkL8uSUvEKGipZelHS4FO1UX4Y8Zc38jzf5U+OKx8BA53T6Ke7zhx7+UrMPUiHhohUIYh68XBfW5TZMch+Qxr3/OBOviZXMxVrRueiJA/SyWcCErh8SwhAVRhmPujJGiiFT4qpF6jgvhfYgOsB6OL8WO59Yhl22vjJiPp4JaChNzA8bSq+xvXwzw6tfkJlP4jsfTM/zZNRyC9oU0lEbsYedi5zuXiEliwO7G9Y2rSo1wYFMmCIIgCMJN6Rpx2mQVGFPLyxk6s+ShuE0fBES9gv2rw6DkIjLrJcTGrsBy9Rj4t2l1iu9Qfa35gLWFLl1eUYn+nm3wvwx4Bmn710HFA31zFweW39jlkUxQT0dCYYU8NG8HUx1uGHlpBuB+X+vz3Qu/UT9nf2twrfo7mG5WwciT+3rBsw3LDNbl7sE7Ja24FTjEG8GhU1hJVKBkhAqzHVpfCYIgCILojXSNOB3gZSVOFejn5c3ECEO1E0WWgK7mz4eIC/Z0YhsPdigfjI3djXPGMhQJ6UhJ2YY4la9obV2644QdH0l7/AReA7kg8oYq5ROb87CPOCwubfnjcxd8xi5B+rkrKC/Kwa6Undgex8X5GWiXpkpD8/ZQKHGvHy9NAy5XWA/Nmy2anhjo9ZNGy+z31ai51boiV0ak4MOMhez8xUhLK0RFu0S8Ap4PBmMc+1Z1+Cwut3AM5UAvuHl4c4IgCIIgbGi/OO3vh1Hc1bGqDMbrLXkGKuAxaCgC+Ne83XhNtPhZzfgWA647sU29HKDdLwQxWgM8gsOhVodj4qhBfC/UXau2Wk6xJRp9GvNS98gBdY0QlvAZ8VYTdezhdJ47g8YJRCNjsmDwCMJ0dSRUEx8Fv3rUVaFaFJRma+hVlBp5AGGGYiAemRzIvpQi7bW9KBatynxRgTeQymf2K6cgNNi7cfnFOnNAdUZtMTTizP3xiLcOss1dBBarMHLyHKwJUqIudxt2OZrIZbmm5kGcTZUnsOvdb/H4bH8HM/LNgZDNk+kIgiAIguhNdILlVEBsiL+DsEoSigA1NogTec5AGxUCf7+heIzP+IYvIhZOwTB2Fa1u0ycAszYsFyf05CWEIVCc9f0Q1Jpito8/5s0dDx9+sla5GwGznpMnUsn+rf6PIza3gom2cCxU3e9EobSe547TeJ11eWsRKq5v64dANZ+QxC513ixM8bE28TKxHfsrOZSUF4Jmr0C0uO9GzBR9eAMxNfZNti8rz6QYTOD+nZ6PY3nSTHGI3VKmgU+KE6kQ+DvMtLfyhcJcD+XISj7oYCUnebk3VnsGw1XUWgTvffCPPoVfLZyPWb/hQ/un8PbBz1BrqkRJiTnEVS2+MnzJ/rrrsnAEQRAEQbRE+8Vpn4cw+w3ZH5LJDB/8AMdRKb0QvPJ1CCmr5O0ZyjDEZezDNrWffBGtbaOAR/ASaIWd0lC+mcD5SMzMwFqnJ0QxPMZipfYtpIhD5BJK1QvIyHkZal97oZFk2pTnTsDOdfJICPMS9yJn7QR5QpQHE6IvYbW5TLhgvW2CwmcqNtjuy8pqk5CD1yxlfhd81S8jJ3Mj5nGxLuILVdxOCNolzZdlFGH1EKTGEh5poCQdWrvW00ZLeN1n5bgmC1gljxwgHrcPPMc8hTWq/4Jek4ikff+EzyM+0jWZvkX5ZzyE1BAEDHLlBRAJgiAIgmgP/8Ej8cvfRcsW97skiA7D18lXRyKhJBQpRduhbmLlbQHzAg88fJYQjYD2d596Db31uaV89x6ornsXlO/eg6M806uf6BoUAZix6ikoUYLi887O7Deh5rwOx7mbxqppJEwJgiAIohdCr3+ii1DAcwKfPPUNst8+5tzMfpMB2cnvoC4oBtET2uCmQRAEQRCE20DilOg6FCMQnXMB51LV8HXmTpO3N+bQcD5BEARB9FZIAhAEQRAEQRA9BhKnBEEQBEEQRI+BxClBEARBEATRYyBxShAEQRAEQfQYSJwSBEEQBEEQPQYSpwRBEARBEESPwbJCFI/STxAEQRAEQRDdie0qUU2WLyUIgiAIgiCIHxMa1icIgiAIgiB6CMD/B7v4c+mj9BqUAAAAAElFTkSuQmCC"></p>
<p>The following table shows the natural logarithm of both <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> on these days to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> decimal places.</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>Use the data in the second table to find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math> for the regression line, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mo> </mo><mi>x</mi><mo>=</mo><mi>m</mi><mo>(</mo><mi>ln</mi><mo> </mo><mi>d</mi><mo>)</mo><mo>+</mo><mi>b</mi></math>.</p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Assuming that the model found in part (a) remains valid, estimate the percentage of trees in stock when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>25</mn></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> is defined by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 2{x^3} + 5,{\text{ }} - 2 \leqslant x \leqslant 2">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>2</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>5</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>x</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>2</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}(x)">
<mrow>
<msup>
<mi>f</mi>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</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>Write down the domain and range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}">
<mrow>
<msup>
<mi>f</mi>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = \frac{1}{{{x^2} + 3x + 2}},{\text{ }}x \in \mathbb{R},{\text{ }}x \ne - 2,{\text{ }}x \ne - 1">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>x</mi>
<mo>≠<!-- ≠ --></mo>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>x</mi>
<mo>≠<!-- ≠ --></mo>
<mo>−<!-- − --></mo>
<mn>1</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Express <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^2} + 3x + 2">
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</math></span> in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{(x + h)^2} + k">
<mrow>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>+</mo>
<mi>h</mi>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>k</mi>
</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>Factorize <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^2} + 3x + 2">
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</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>Sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>, indicating on it the equations of the asymptotes, the coordinates of the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept and the local maximum.</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>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{x + 1}} - \frac{1}{{x + 2}} = \frac{1}{{{x^2} + 3x + 2}}">
<mfrac>
<mn>1</mn>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</mfrac>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</mfrac>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> if <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^1 {f(x){\text{d}}x = \ln (p)} ">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mn>1</mn>
</msubsup>
<mrow>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
<mo>=</mo>
<mi>ln</mi>
<mo></mo>
<mo stretchy="false">(</mo>
<mi>p</mi>
<mo stretchy="false">)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( {\left| x \right|} \right)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mo>|</mo>
<mi>x</mi>
<mo>|</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</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>Determine the area of the region enclosed between the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( {\left| x \right|} \right)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mo>|</mo>
<mi>x</mi>
<mo>|</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis and the lines with equations <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 1">
<mi>x</mi>
<mo>=</mo>
<mo>−</mo>
<mn>1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 1">
<mi>x</mi>
<mo>=</mo>
<mn>1</mn>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f'\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>, 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ 5 is shown in the following diagram. The curve intercepts the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis at (1, 0) and (4, 0) and has a local minimum at (3, −1).</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The shaded area enclosed by the curve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f'\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis and the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis is 0.5. Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( 0 \right) = 3">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>3</mn>
</math></span>,</p>
</div>
<div class="specification">
<p>The area enclosed by the curve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f'\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> and the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 1">
<mi>x</mi>
<mo>=</mo>
<mn>1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 4">
<mi>x</mi>
<mo>=</mo>
<mn>4</mn>
</math></span> is 2.5 .</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-coordinate of the point of inflexion on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( 1 \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( 4 \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the curve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>, 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ 5 indicating clearly the coordinates of the maximum and minimum points and any intercepts with the coordinate axes.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Roger buys a new laptop for himself at a cost of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>£</mo><mn>495</mn></math>. At the same time, he buys his daughter Chloe a higher specification laptop at a cost of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>£</mo><mn>2200</mn></math>.</p>
<p>It is anticipated that Roger’s laptop will depreciate at a rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>%</mo></math> per year, whereas Chloe’s laptop will depreciate at a rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>%</mo></math> per year.</p>
</div>
<div class="specification">
<p>Roger and Chloe’s laptops will have the same value <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> years after they were purchased.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the value of Roger’s laptop after <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> years.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</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>Comment on the validity of your answer to part (b).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = 4\,{\text{cos}}\,x + 1">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>4</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cos</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>+</mo>
<mn>1</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a \leqslant x \leqslant \frac{\pi }{2}">
<mi>a</mi>
<mo>⩽<!-- ⩽ --></mo>
<mi>x</mi>
<mo>⩽<!-- ⩽ --></mo>
<mfrac>
<mi>π<!-- π --></mi>
<mn>2</mn>
</mfrac>
</math></span> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a < \frac{\pi }{2}">
<mi>a</mi>
<mo><</mo>
<mfrac>
<mi>π<!-- π --></mi>
<mn>2</mn>
</mfrac>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = - \frac{\pi }{2}"> <mi>a</mi> <mo>=</mo> <mo>−</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </math></span>, sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = g\left( x \right)"> <mi>y</mi> <mo>=</mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>. Indicate clearly the maximum and minimum values of the function.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the least value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span> such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g"> <mi>g</mi> </math></span> has an inverse.</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>For the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span> found in part (b), write down the domain of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{g^{ - 1}}"> <mrow> <msup> <mi>g</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span> found in part (b), find an expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{g^{ - 1}}\left( x \right)"> <mrow> <msup> <mi>g</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>ln</mi><mfenced><mfrac><mn>1</mn><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfrac></mfenced></math> is defined for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>2</mn><mo>,</mo><mo> </mo><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>.</p>
</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"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo></math>. You are not required to state a domain.</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>Solve <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>It is believed that the power <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math> of a signal at a point <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> km from an antenna is inversely proportional to <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>d</mi><mi>n</mi></msup></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>∈</mo><msup><mi mathvariant="normal">ℤ</mi><mo>+</mo></msup></math>.</p>
<p>The value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math> is recorded at distances of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">m</mi></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo> </mo><mi mathvariant="normal">m</mi></math> and the values of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mi>d</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mi>P</mi></math> are plotted on the graph below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The values of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mi>d</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mi>P</mi></math> are shown in the table 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>Explain why this graph indicates that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math> is inversely proportional to <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>d</mi><mi>n</mi></msup></math>.</p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the least squares regression line of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mi>P</mi></math> against <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>10</mn></msub><mo> </mo><mi>d</mi></math>.</p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your answer to part (b) to write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> to the nearest integer.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</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>P</mi></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p\left( x \right)"> <mi>p</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> is defined by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p\left( x \right) = {x^3} + 3{x^2} + 8x - 24"><mi>p</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>−</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mi>x</mi><mo>−</mo><mn>24</mn></math></span> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}"> <mi>x</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 the remainder when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p\left( x \right)">
<mi>p</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> is divided by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {x - 2} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the remainder when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p\left( x \right)">
<mi>p</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> is divided by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {x - 3} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>3</mn>
</mrow>
<mo>)</mo>
</mrow>
</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>Prove that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p\left( x \right)">
<mi>p</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> has only one real zero.</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>Write down the transformation that will transform the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = p\left( x \right)"> <mi>y</mi> <mo>=</mo> <mi>p</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> onto the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 8{x^3} + 12{x^2} + 16x - 24"><mi>y</mi><mo>=</mo><mn>8</mn><msup><mi>x</mi><mn>3</mn></msup><mo>−</mo><mn>12</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn><mi>x</mi><mo>−</mo><mn>24</mn></math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span> follows a Poisson distribution with a mean of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
<mi>λ</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6{\text{P}}\left( {X = 3} \right) = 3{\text{P}}\left( {X = 2} \right) - 2{\text{P}}\left( {X = 1} \right) + 3{\text{P}}\left( {X = 0} \right)">
<mn>6</mn>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo>=</mo>
<mn>3</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>3</mn>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo>=</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mn>2</mn>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>X</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
<mi>λ</mi>
</math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>It is believed that two variables, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> are related. Experimental values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> are obtained. A graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,m">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>m</mi>
</math></span> against <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> shows a straight line passing through (2.1, 7.3) and (5.6, 2.4).</p>
</div>
<div class="specification">
<p>Hence, find</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the straight line, giving your answer in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,m = ap + b">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>m</mi>
<mo>=</mo>
<mi>a</mi>
<mi>p</mi>
<mo>+</mo>
<mi>b</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a{\text{,}}\,\,b \in \mathbb{R}">
<mi>a</mi>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>b</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</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>a formula for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>.</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>the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 0">
<mi>p</mi>
<mo>=</mo>
<mn>0</mn>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A function is defined by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>2</mn><mo>-</mo><mfrac><mn>12</mn><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>7</mn><mo>,</mo><mo> </mo><mi>x</mi><mo>≠</mo><mo>-</mo><mn>5</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the range of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the inverse function<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><msup><mi>f</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo></math>. The domain is not required.</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>Write down the range of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><msup><mi>f</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the functions <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> defined by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {\text{ln}}\left| x \right|">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mrow>
<mo>|</mo>
<mi>x</mi>
<mo>|</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span> \ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left\{ 0 \right\}">
<mrow>
<mo>{</mo>
<mn>0</mn>
<mo>}</mo>
</mrow>
</math></span>, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = {\text{ln}}\left| {x + k} \right|">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mrow>
<mo>|</mo>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mi>k</mi>
</mrow>
<mo>|</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span> \ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left\{ { - k} \right\}">
<mrow>
<mo>{</mo>
<mrow>
<mo>−<!-- − --></mo>
<mi>k</mi>
</mrow>
<mo>}</mo>
</mrow>
</math></span>, where <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>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k > 2">
<mi>k</mi>
<mo>></mo>
<mn>2</mn>
</math></span>.</p>
</div>
<div class="specification">
<p>The graphs of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> intersect at the point P .</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the transformation by which <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right)"> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> is transformed to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right)"> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g"> <mi>g</mi> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graphs of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)"> <mi>y</mi> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = g\left( x \right)"> <mi>y</mi> <mo>=</mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> on the same axes, clearly stating the points of intersection with any axes.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The tangent to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)"> <mi>y</mi> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> at P passes through the origin (0, 0).</p>
<p>Determine 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">[7]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question">
<p>The graph of the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>ln</mi><mo> </mo><mi>x</mi></math> is translated 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> so that it then passes through the points <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><msup><mtext>e</mtext><mn>3</mn></msup><mo>,</mo><mo> </mo><mn>1</mn><mo>+</mo><mi>ln</mi><mo> </mo><mn>2</mn><mo>)</mo></math> .</p>
<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>
<br><hr><br><div class="specification">
<p>Adesh wants to model the cooling of a metal rod. He heats the rod and records its temperature as it cools.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>He believes the temperature can be modeled by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T\left( t \right) = a{{\text{e}}^{bt}} + 25">
<mi>T</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>a</mi>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mi>b</mi>
<mi>t</mi>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mn>25</mn>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a{\text{,}}\,\,b \in \mathbb{R}">
<mi>a</mi>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>b</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>Hence</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{ln}}\left( {T - 25} \right) = bt + {\text{ln}}\,a">
<mrow>
<mtext>ln</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>T</mi>
<mo>−</mo>
<mn>25</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>b</mi>
<mi>t</mi>
<mo>+</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>a</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the regression line of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\left( {T - 25} \right)">
<mrow>
<mtext>ln</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>T</mi>
<mo>−</mo>
<mn>25</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>predict the temperature of the metal rod after 3 minutes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="question">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^4} - 6{x^2} - 2x + 4">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>6</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>4</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
<mi>x</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> is translated two units to the left to form the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>.</p>
<p>Express <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a{x^4} + b{x^3} + c{x^2} + dx + e">
<mi>a</mi>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>b</mi>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>c</mi>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>d</mi>
<mi>x</mi>
<mo>+</mo>
<mi>e</mi>
</math></span> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
<mi>c</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
<mi>d</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="e \in \mathbb{Z}">
<mi>e</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
</math></span>.</p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{{1 - 3x}}{{x - 2}}">
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mn>3</mn>
<mi>x</mi>
</mrow>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
</mfrac>
</math></span>, showing clearly any asymptotes and stating the coordinates of any points of intersection with the axes.</p>
<p><img src="images/Schermafbeelding_2018-02-07_om_17.42.06.png" alt="N17/5/MATHL/HP1/ENG/TZ0/06.a"></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>Hence or otherwise, solve the inequality <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {\frac{{1 - 3x}}{{x - 2}}} \right| < 2">
<mrow>
<mo>|</mo>
<mrow>
<mfrac>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mn>3</mn>
<mi>x</mi>
</mrow>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
</mfrac>
</mrow>
<mo>|</mo>
</mrow>
<mo><</mo>
<mn>2</mn>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the graphs of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \left| x \right|">
<mi>y</mi>
<mo>=</mo>
<mrow>
<mo>|</mo>
<mi>x</mi>
<mo>|</mo>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - \left| x \right| + b">
<mi>y</mi>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mrow>
<mo>|</mo>
<mi>x</mi>
<mo>|</mo>
</mrow>
<mo>+</mo>
<mi>b</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b \in {\mathbb{Z}^ + }">
<mi>b</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<msup>
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
<mo>+</mo>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graphs on the same set of axes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the graphs enclose a region of area 18 square units, find the value of <em>b</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{2 - 3{x^5}}}{{2{x^3}}},\,\,x \in \mathbb{R},\,\,x \ne 0">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mo>−<!-- − --></mo>
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>5</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>2</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>≠<!-- ≠ --></mo>
<mn>0</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> has a local maximum at A. Find the coordinates of 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>Show that there is exactly one point of inflexion, B, on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The coordinates of B can be expressed in the form B<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {{2^a},\,b \times {2^{ - 3a}}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mn>2</mn>
<mi>a</mi>
</msup>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mi>b</mi>
<mo>×</mo>
<mrow>
<msup>
<mn>2</mn>
<mrow>
<mo>−</mo>
<mn>3</mn>
<mi>a</mi>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> where <em>a</em>, <em>b</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \in \mathbb{Q}">
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">Q</mi>
</mrow>
</math></span>. Find the value of <em>a</em> and the value of <em>b</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>Sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> showing clearly the position of the points A and B.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A rational function is defined by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = a + \frac{b}{{x - c}}">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>a</mi>
<mo>+</mo>
<mfrac>
<mi>b</mi>
<mrow>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mi>c</mi>
</mrow>
</mfrac>
</math></span> where the parameters <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a,{\text{ }}b,{\text{ }}c \in \mathbb{Z}">
<mi>a</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>b</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>c</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}\backslash \{ c\} ">
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
<mi mathvariant="normal">∖<!-- ∖ --></mi>
<mo fence="false" stretchy="false">{</mo>
<mi>c</mi>
<mo fence="false" stretchy="false">}</mo>
</math></span>. The following diagram represents the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-02-28_om_09.42.27.png" alt="N16/5/MATHL/HP1/ENG/TZ0/03"></p>
<p>Using the information on the graph,</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>state the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> and the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
<mi>c</mi>
</math></span>;</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>find the value of <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">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graphs of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{x}{2} + 1">
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mi>x</mi>
<mn>2</mn>
</mfrac>
<mo>+</mo>
<mn>1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \left| {x - 2} \right|">
<mi>y</mi>
<mo>=</mo>
<mrow>
<mo>|</mo>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>|</mo>
</mrow>
</math></span> on the following axes.</p>
<p><img 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"></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>Solve the equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{x}{2} + 1 = \left| {x - 2} \right|">
<mfrac>
<mi>x</mi>
<mn>2</mn>
</mfrac>
<mo>+</mo>
<mn>1</mn>
<mo>=</mo>
<mrow>
<mo>|</mo>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>|</mo>
</mrow>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>A function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mi>p</mi><msup><mtext>e</mtext><mrow><mi>q</mi><mo> </mo><mi>cos</mi><mfenced><mrow><mi>r</mi><mi>t</mi></mrow></mfenced></mrow></msup><mo>,</mo><mo> </mo><mi>p</mi><mo>,</mo><mo> </mo><mi>q</mi><mo>,</mo><mo> </mo><mi>r</mi><mo>∈</mo><msup><mi mathvariant="normal">ℝ</mi><mo>+</mo></msup></math>. Part of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is shown.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>The points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> have coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>6</mn><mo>.</mo><mn>5</mn><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext><mo>(</mo><mn>5</mn><mo>.</mo><mn>2</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>2</mn><mo>)</mo></math>, and lie on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>.</p>
<p>The point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> is a local maximum and the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> is a local minimum.</p>
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>, of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math> and of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>.</p>
</div>
<br><hr><br><div class="question">
<p>It is believed that two variables, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
<mi>v</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span> are related by the equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = k{w^n}">
<mi>v</mi>
<mo>=</mo>
<mi>k</mi>
<mrow>
<msup>
<mi>w</mi>
<mi>n</mi>
</msup>
</mrow>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k{\text{,}}\,\,n \in \mathbb{R}">
<mi>k</mi>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>n</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>. Experimental values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
<mi>v</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span> are obtained. A graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,v">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>v</mi>
</math></span> against <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{ln}}\,w">
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>w</mi>
</math></span> shows a straight line passing through (−1.7, 4.3) and (7.1, 17.5).</p>
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n">
<mi>n</mi>
</math></span>. </p>
</div>
<br><hr><br><div class="specification">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>a</mi><mo> </mo><mi>cos</mi><mo> </mo><mfenced><mrow><mi>b</mi><mfenced><mrow><mi>x</mi><mo>-</mo><mi>c</mi></mrow></mfenced></mrow></mfenced><mo>,</mo><mo> </mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>∈</mo><msup><mi mathvariant="normal">ℝ</mi><mo>+</mo></msup></math>.</p>
<p>Part of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math> is shown below. Point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> is a local maximum and has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>1</mn><mo>,</mo><mo> </mo><mn>3</mn></mrow></mfenced></math> and point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> is a local minimum with coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>,</mo><mo> </mo><mo>-</mo><mn>3</mn></mrow></mfenced></math>.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question">
<p>Write down a sequence of transformations that will transform the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>cos</mi><mo> </mo><mi>x</mi></math> onto the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math>.</p>
</div>
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