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</div><h2>SL Paper 2</h2><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Give your answers to parts (a) to (e) to the nearest dollar.</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">On Hugh’s 18th birthday his parents gave him options of how he might receive his monthly allowance for the next two years.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> Option A </strong></span><span style="font-family: 'times new roman', times; font-size: medium;">\(\$60\) each month for two years</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> Option B </strong>\(\$10\) in the first month, \(\$15\) in the second month, \(\$20\) in the third month, increasing by \(\$5\) each month for two years</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> Option C </strong>\(\$15\) in the first month and increasing by \(10\%\) each month for two years</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> Option D </strong>Investing \(\$1500\) at a bank at the beginning of the first year, with an interest rate of \(6\%\) per annum, <strong>compounded monthly</strong>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Hugh does not spend any of his allowance during the two year period.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>If Hugh chooses <strong>Option A</strong>, calculate the total value of his allowance at the end of the two year period.</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><span>If Hugh chooses <strong>Option B</strong>, calculate</span></p>
<p><span>(i) the amount of money he will receive in the 17th month;</span></p>
<p><span>(ii) the total value of his allowance at the end of the two year period.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>If Hugh chooses <strong>Option C</strong>, calculate</span></p>
<p><span>(i) the amount of money Hugh would receive in the 13th month;</span></p>
<p><span>(ii) the total value of his allowance at the end of the two year period.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>If Hugh chooses <strong>Option D</strong>, calculate the total value of his allowance at the end of the two year period.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State which of the options, A, B, C or D, Hugh should choose to give him the greatest total value of his allowance at the end of the two year period.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Another bank guarantees Hugh an amount of \(\$1750\) after two years of investment </span></span><span>if he invests $1500 at this bank. The interest is <strong>compounded annually</strong>.</span></p>
<p><span>Calculate the interest rate per annum offered by the bank.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The line \({L_1}\) has equation \(2y - x - 7 = 0\) and is shown on the diagram.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_07.59.34.png" alt="N16/5/MATSD/SP2/ENG/TZ0/03"></p>
<p class="p1" style="text-align: left;">The point <span class="s1">A </span>has coordinates \((1,{\text{ }}4)\).</p>
</div>
<div class="specification">
<p class="p1">The point <span class="s1">C </span>has coordinates \((5,{\text{ }}12)\). <span class="s1">M </span>is the midpoint of <span class="s1">AC</span>.</p>
</div>
<div class="specification">
<p class="p1">The straight line, \({L_2}\), is perpendicular to <span class="s1">AC </span>and passes through <span class="s1">M</span>.</p>
</div>
<div class="specification">
<p class="p1">The point <span class="s1">D </span>is the intersection of \({L_1}\) and \({L_2}\).</p>
</div>
<div class="specification">
<p class="p1">The length of <span class="s1">MD </span>is \(\frac{{\sqrt {45} }}{2}\).</p>
</div>
<div class="specification">
<p class="p1">The point <span class="s1">B </span>is such that <span class="s1">ABCD </span>is a rhombus.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Show that </span><span class="s2">A </span>lies on \({L_1}\).</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 class="p1">Find the coordinates of <span class="s1">M</span><span class="s2">.</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 class="p1">Find the length of <span class="s1">AC</span><span class="s2">.</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 class="p1">Show that the equation of \({L_2}\) <span class="s1">is \(2y + x - 19 = 0\).</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the coordinates of <span class="s1">D</span><span class="s2">.</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 class="p1"><span class="s1">Write down the length of </span><span class="s2">MD </span>correct to five significant figures.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the area of <span class="s1">ABCD</span><span class="s2">.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The natural numbers: 1, 2, 3, 4, 5… form an arithmetic sequence.</span></p>
</div>
<div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A geometric progression \(G_1\) has 1 as its first term and 3 as its common ratio.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State the values of<em> u</em><sub>1</sub> and <em>d</em> for this sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use an appropriate formula to show that the sum of the natural numbers from 1 to <em>n</em> is given by \(\frac{1}{2}n (n +1)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the sum of the natural numbers from 1 to 200.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The sum of the first <em>n</em> terms of <em>G</em><sub>1</sub> is 29 524. Find <em>n</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A second geometric progression <em>G</em><sub>2</sub> has the form \(1,\frac{1}{3},\frac{1}{9},\frac{1}{{27}}...\)</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the sum of the first 10 terms of <em>G</em><sub>2</sub>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Explain why the sum of the first 1000 terms of <em>G</em><sub>2</sub> will give the same answer as the sum of the first 10 terms, when corrected to three significant figures.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">ii.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using your results from parts (a) to (c), or otherwise, calculate the sum of the first 10 terms of the sequence \(2,3\frac{1}{3},9\frac{1}{9},27\frac{1}{{27}}...\) </span></p>
<p><span>Give your answer <strong>correct to one decimal place</strong>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Daniel wants to invest \(\$ 25\,000\) for a total of three years. There are two investment options.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Option One</strong> pays compound interest at a nominal annual rate of interest of 5 %, compounded <strong>annually</strong>.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Option Two</strong> pays compound interest at a nominal annual rate of interest of 4.8 %, compounded <strong>monthly</strong>.</span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">An arithmetic sequence is defined as</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><em>u<sub>n</sub></em> = 135 + 7<em>n</em>, <em>n</em> = 1, 2, 3, …</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the value of his investment at the end of the third year for each investment option, <strong>correct to two decimal places</strong>.</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">A.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Determine Daniel’s best investment option.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate <em>u</em><sub>1</sub>, the first term in the sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the common difference is 7.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><em>S<sub>n</sub></em> is the sum of the first <em>n</em> terms of the sequence.</span></p>
<p><span><span>Find an expression for <em>S<sub>n</sub></em>. Give your answer in the form <em>S<sub>n</sub></em></span><span> = <em>An</em><sup>2</sup> + <em>Bn</em>, where <em>A</em> and<em> B</em> are constants.</span></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">B.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The first term, <em>v</em><sub>1</sub>, of a geometric sequence is 20 and its fourth term <em>v</em><sub>4</sub> is 67.5.</span></p>
<p><span>Show that the common ratio, <em>r</em>, of the geometric sequence is 1.5.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><em>T<sub>n</sub></em> is the sum of the first <em>n</em> terms of the geometric sequence.</span></p>
<p><span>Calculate <em>T</em><sub>7</sub>, the sum of the first seven terms of the geometric sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span><em>T</em><sub><span><em>n</em></span></sub> is the sum of the first <em>n</em> terms of the geometric sequence.</span></span></p>
<p><span>Use your graphic display calculator to find the smallest value of <em>n</em> for which <em>T<sub>n</sub></em> > <em>S<sub>n</sub></em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.f.</div>
</div>
<br><hr><br><div class="specification">
<p><strong><span style="font-family: times new roman,times; font-size: medium;">Give all answers in this question correct to two decimal places.</span></strong></p>
<h1><span style="font-family: times new roman,times; font-size: medium;">Part A</span></h1>
<p><span style="font-family: times new roman,times; font-size: medium;">Estela lives in Brazil and wishes to exchange 4000 BRL (Brazil reals) for GBP (British pounds). The exchange rate is 1.00 BRL = 0.3071 GBP. The bank charges 3 % commission on the amount in BRL.</span></p>
</div>
<div class="specification">
<p><strong><span style="font-family: times new roman,times; font-size: medium;">Give all answers in this question correct to two decimal places.</span></strong></p>
<h1><span style="font-family: times new roman,times; font-size: medium;">Part B<br></span></h1>
<p><span style="font-family: times new roman,times; font-size: medium;">Daniel invests $1000 in an account that offers a nominal annual interest rate of 3.5 % <strong>compounded half yearly</strong>.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find, <strong>in BRL</strong>, the amount of money Estela has after commission.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find, in GBP, the amount of money Estela receives.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>After her trip to the United Kingdom Estela has 400 GBP left. At the airport she changes this money back into BRL. The exchange rate is now 1.00 BRL = 0.3125 GBP.</span></p>
<p><span>Find, in BRL, the amount of money that Estela should receive.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Estela actually receives 1216.80 BRL after commission.</span></p>
<p><span>Find, in BRL, the commission charged to Estela.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The commission rate is <em>t</em> % . Find the value of <em>t</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that after three years Daniel will have $1109.70 in his account, correct to two decimal places.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">B.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the interest Daniel receives after three years.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B.b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">In the diagram below A, B and C represent three villages and the line segments AB, BC and CA represent the roads joining them. The lengths of AC and CB are 10 km and 8 km respectively and the size of the angle between them is 150°.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the length of the road AB.</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><span>Find the size of the angle CAB.</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><span>Village D is halfway between A and B. A new road perpendicular to AB and passing through D is built. Let T be the point where this road cuts AC. This information is shown in the diagram below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Write down the distance from A to D.</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><span>Show that the distance from D to T is 2.06 km correct to three significant figures.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A bus starts and ends its journey at A taking the route AD to DT to TA.</span></p>
<p><span>Find the total distance for this journey.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The average speed of the bus while it is moving on the road is 70 km h<sup>–1</sup>. The bus stops for <strong>5 minutes</strong> at each of D and T .</span></p>
<p><span>Estimate the time taken by the bus to complete its journey. Give your answer correct to the nearest minute.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Mal is shopping for a school trip. He buys \(50\) tins of beans and \(20\) packets of cereal. The total cost is \(260\) Australian dollars (\({\text{AUD}}\)).</span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The triangular faces of a square based pyramid, \({\text{ABCDE}}\), are all inclined at \({70^ \circ }\) to the base. The edges of the base \({\text{ABCD}}\) are all \(10{\text{ cm}}\) and \({\text{M}}\) is the centre. \({\text{G}}\) is the mid-point of \({\text{CD}}\).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down an equation showing this information, taking \(b\) to be the cost of one tin of beans and \(c\) to be the cost of one packet of cereal in \({\text{AUD}}\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Stephen thinks that Mal has not bought enough so he buys \(12\) more tins of beans and \(6\) more packets of cereal. He pays \(66{\text{ AUD}}\).</span></p>
<p><span>Write down another equation to represent this information.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Stephen thinks that Mal has not bought enough so he buys \(12\) more tins of beans and \(6\) more packets of cereal. He pays \(66{\text{ AUD}}\).</span></span></p>
<p><span>Find the cost of one tin of beans.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Sketch the graphs of the two equations from parts (a) and (b).</span></p>
<p><span>(ii) Write down the coordinates of the point of intersection of the two graphs.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">i.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using the letters on the diagram draw a triangle showing the position of a \({70^ \circ }\) angle.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the height of the pyramid is \(13.7{\text{ cm}}\), to 3 significant figures.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate</span></p>
<p><span>(i) the length of \({\text{EG}}\);</span></p>
<p><span>(ii) the size of angle \({\text{DEC}}\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">ii.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the total surface area of the pyramid.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the volume of the pyramid.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.e.</div>
</div>
<br><hr><br><div class="specification">
<p>Rosa joins a club to prepare to run a marathon. During the first training session Rosa runs a distance of 3000 metres. Each training session she increases the distance she runs by 400 metres.</p>
</div>
<div class="specification">
<p>A marathon is 42.195 kilometres.</p>
<p>In the \(k\)th training session Rosa will run further than a marathon for the first time.</p>
</div>
<div class="specification">
<p>Carlos joins the club to lose weight. He runs 7500 metres during the first month. The distance he runs increases by 20% each <strong>month</strong>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the distance Rosa runs in the third training session;</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>Write down the distance Rosa runs in the \(n\)th training session.</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 \(k\).</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>Calculate the total distance, in <strong>kilometres</strong>, Rosa runs in the first 50 training sessions.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the distance Carlos runs in the fifth month of training.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the total distance Carlos runs in the first year.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Violeta plans to grow flowers in a rectangular plot. She places a fence to mark out the perimeter of the plot and uses 200 metres of fence. The length of the plot is \(x\) metres.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_17.40.47.png" alt="M17/5/MATSD/SP2/ENG/TZ2/05"></p>
</div>
<div class="specification">
<p>Violeta places the fence so that the area of the plot is maximized.</p>
</div>
<div class="specification">
<p>By selling her flowers, Violeta earns 2 Bulgarian Levs (BGN) per square metre of the plot.</p>
</div>
<div class="specification">
<p>Violeta wants to invest her 5000 BGN.</p>
<p>A bank offers a nominal annual interest rate of 4%, compounded <strong>half-yearly</strong>.</p>
</div>
<div class="specification">
<p>Another bank offers an interest rate of \(r\)% compounded <strong>annually</strong>, that would allow her to double her money in 12 years.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the width of the plot, in metres, is given by \(100 - x\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the area of the plot in terms of \(x\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(x\) that maximizes the area of the plot.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that Violeta earns 5000 BGN from selling the flowers grown on the plot.</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 amount of money that Violeta would have after 6 years. Give your answer correct to two decimal places.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find how long it would take for the interest earned to be 2000 BGN.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the lowest possible value for \(r\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">In a game, <em>n</em> small pumpkins are placed 1 metre apart in a straight line. Players start 3 metres before the <span class="s1">first </span>pumpkin.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-04_om_15.01.57.png" alt></p>
<p class="p1">Each player <strong>collects</strong> a single pumpkin by picking it up and bringing it back to the start. The nearest pumpkin is collected <span class="s1">first. </span>The player then collects the next nearest pumpkin and the game continues in this way until the signal is given for the end.</p>
<p class="p1">Sirma runs to get each pumpkin and brings it back to the start.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the distance, \({a_1}\), in metres that she has to run in order to <strong>collect</strong> the <span class="s1">first </span>pumpkin.</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 class="p1">The distances she runs to <strong>collect</strong> each pumpkin form a sequence \({a_1},{\text{ }}{a_2},{\text{ }}{a_3}, \ldots \) .</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Find \({a_2}\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find \({a_3}\).</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 class="p1">Write down the common difference, \(d\), of the sequence.</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 class="p1">The <span class="s1">final </span>pumpkin Sirma <strong>collected</strong> was 24 metres from the start.</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Find the total number of pumpkins that Sirma <strong>collected</strong>.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find the total distance that Sirma ran to <strong>collect</strong> these pumpkins.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Peter also plays the game. When the signal is given for the end of the game he has run 940 metres.</p>
<p class="p1">Calculate the total number of pumpkins that Peter <strong>collected</strong>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Peter also plays the game. When the signal is given for the end of the game he has run 940 metres.</p>
<p class="p1">Calculate Peter’s distance from the start when the signal is given.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><strong><span style="font-size: medium; font-family: times new roman,times;">Part A</span></strong></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The Green Park Amphitheatre was built in the form of a horseshoe and has 20 rows. The number of seats in each row increase by a fixed amount, <em>d</em>, compared to the number of seats in the previous row. The number of seats in the sixth row, <em>u</em><sub>6</sub>, is 100, and the number of seats in the tenth row, <em>u</em><sub>10</sub>, is 124. <em>u</em><sub>1</sub> represents the number of seats in the first row.</span></p>
</div>
<div class="specification">
<p><strong><span style="font-size: medium; font-family: times new roman,times;">Part B</span></strong></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Frank is at the amphitheatre and receives a text message at 12:00. Five minutes later he forwards the text message to three people. Five minutes later, those three people forward the text message to three new people. <strong>Assume this pattern continues and each time the text message is sent to people who have not received it before.</strong> </span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The number of new people who receive the text message forms a geometric sequence</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;">1 , 3 , …</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Write an equation for <em>u</em><sub>6</sub> in terms of <em>d</em> and <em>u</em><sub>1</sub>.<br></span></p>
<p><span>(ii) Write an equation for <em>u</em><sub>10</sub> in terms of <em>d</em> and <em>u</em><sub>1</sub>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of</span></p>
<p><span>(i) <em>d</em> ;</span></p>
<p><span>(ii) <em>u</em><sub>1</sub> .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the <strong>total</strong> number of seats in the amphitheatre.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">A.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A few years later, a <strong>second</strong> level was added to increase the amphitheatre’s capacity by</span> <span>another 1600 seats. Each row has four more seats than the previous row. The first row </span><span>on this level has 70 seats.</span></p>
<p><span>Find the number of rows on the second level of the amphitheatre.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">A.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the next two terms of this geometric sequence.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the common ratio of this geometric sequence.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the number of people who will receive the text message at 12:30.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the <strong>total</strong> number of people who will have received the text message by 12:30.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the exact time at which a total of 29 524 people will have received the text message.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">B.e.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows a perfume bottle made up of a cylinder and a cone.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-22_om_07.37.58.png" alt></p>
<p class="p1">The radius of both the cylinder and the base of the cone is <span class="s1">3 cm</span>.</p>
<p class="p1">The height of the cylinder is <span class="s1">4.5 cm</span>.</p>
<p class="p1">The slant height of the cone is <span class="s1">4 cm</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) Show that the vertical height of the cone is \(2.65\)<span class="s1"> cm </span>correct to three significant figures.</p>
<p class="p1">(ii) Calculate the volume of the perfume bottle.</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">The bottle contains \({\text{125 c}}{{\text{m}}^{\text{3}}}\) </span>of perfume. The bottle is <strong>not </strong>full and all of the perfume is in the cylinder part.</p>
<p class="p1">Find the height of the perfume in the bottle.</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 class="p1">Temi makes some crafts with perfume bottles, like the one above, once they are empty. Temi wants to know the surface area of one perfume bottle.</p>
<p class="p1">Find the <strong>total </strong>surface area of the perfume bottle.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Temi covers the perfume bottles with a paint that costs 3 South African rand (ZAR) per millilitre. One millilitre of this paint covers an area of \({\text{7 c}}{{\text{m}}^{\text{2}}}\).</p>
<p class="p2"><span class="s1">Calculate the cost, in ZAR</span>, of painting the perfume bottle. <strong>Give your answer correct to two decimal places</strong>.</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 class="p1">Temi sells her perfume bottles in a craft fair for <span class="s1">325 ZAR </span>each. Dominique from France buys one and wants to know how much she has spent, in euros <span class="s1">(EUR)</span>. The exchange rate is 1 EUR = 13.03 ZAR<span class="s2">.</span></p>
<p class="p1">Find the price, in <span class="s1">EUR</span>, that Dominique paid for the perfume bottle. <strong>Give your answer </strong><strong>correct to two decimal places</strong>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A geometric sequence has second term 12 and fifth term 324.</span></p>
</div>
<div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the following propositions</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>p</em>: The number is a multiple of five.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>q</em>: The number is even.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>r</em>: The number ends in zero.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the value of the common ratio.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">i, a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the 10<sup>th</sup> term of this sequence.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i, b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The <em>k</em><sup>th</sup> term is the first term which is greater than 2000. Find the value of <em>k</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i, c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write in words \((q \wedge \neg r) \Rightarrow \neg p\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii, a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider the statement “If the number is a multiple of five, and is not even then it will not end in zero”.</span></p>
<p><span>Write this statement in symbolic form.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">ii, b, i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider the statement “If the number is a multiple of five, and is not even then it will not end in zero”.</span></p>
<p><span>Write the contrapositive of this statement in symbolic form.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii, b, ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A greenhouse ABCDPQ is constructed on a rectangular concrete base ABCD and is made of glass. Its shape is a right prism, with cross section, ABQ, an isosceles triangle. The length of BC is 50 m, the length of AB is 10 m and the size of angle QBA is 35°.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the size of angle AQB.</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><span>Calculate the length of AQ.</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><span>Calculate the length of AC.</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><span>Show that the length of CQ is 50.37 m, correct to 4 significant figures.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the size of the angle AQC.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the total area of the glass needed to construct</span></p>
<p><span>(i) the two rectangular faces of the greenhouse;</span></p>
<p><span>(ii) the two triangular faces of the greenhouse.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The cost of one square metre of glass used to construct the greenhouse is 4.80 USD.</span></p>
<p><span>Calculate the cost of glass to make the greenhouse. Give your answer correct to the nearest 100 USD.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Leanne goes fishing at her favourite pond. The pond contains four different types of fish: bream, flathead, whiting and salmon. The fish are either undersized or normal. This information is shown in the table below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the total number of fish in the pond.</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><span>Leanne catches a fish.</span></p>
<p><span>Find the probability that she</span></p>
<p><span>(i) catches an undersized bream;</span></p>
<p><span>(ii) catches either a flathead or an undersized fish or both;</span></p>
<p><span>(iii) does not catch an undersized whiting;</span></p>
<p><span>(iv) catches a whiting given that the fish was normal.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Leanne notices that on windy days, the probability she catches a fish is 0.1 while on non-windy days the probability she catches a fish is 0.65. The probability that it will be windy on a particular day is 0.3.</span></p>
<p><span><strong>Copy and complete</strong> the probability tree diagram below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></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><span><span>Leanne notices that on windy days, the probability she catches a fish is 0.1 while on non-windy days the probability she catches a fish is 0.65. The probability that it will be windy on a particular day is 0.3.</span></span></p>
<p><span>Calculate the probability that it is windy and Leanne catches a fish on a particular day.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Leanne notices that on windy days, the probability she catches a fish is 0.1 while on non-windy days the probability she catches a fish is 0.65. The probability that it will be windy on a particular day is 0.3.</span></span></p>
<p><span>Calculate the probability that Leanne catches a fish on a particular day.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your answer to part (e) to calculate the probability that Leanne catches a fish on two consecutive days.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Leanne notices that on windy days, the probability she catches a fish is 0.1 while on non-windy days the probability she catches a fish is 0.65. The probability that it will be windy on a particular day is 0.3.</span></span></p>
<p><span>Given that Leanne catches a fish on a particular day, calculate the probability that the day was windy.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A closed rectangular box has a height \(y{\text{ cm}}\) and width \(x{\text{ cm}}\). Its length is twice its width. It has a fixed outer surface area of \(300{\text{ c}}{{\text{m}}^2}\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Factorise \(3{x^2} + 13x - 10\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Solve the equation \(3{x^2} + 13x - 10 = 0\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider a function \(f(x) = 3{x^2} + 13x - 10\) .</span></p>
<p><span>Find the equation of the axis of symmetry on the graph of this function.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider a function \(f(x) = 3{x^2} + 13x - 10\) .</span></p>
<p><span>Calculate the minimum value of this function.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that \(4{x^2} + 6xy = 300\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find an expression for \(y\) in terms of \(x\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Hence show that the volume \(V\) of the box is given by \(V = 100x - \frac{4}{3}{x^3}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(\frac{{{\text{d}}V}}{{{\text{d}}x}}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Hence find the value of \(x\) and of \(y\) required to make the volume of the box a maximum.</span></p>
<p><span>(ii) Calculate the maximum volume.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">ii.e.</div>
</div>
<br><hr><br><div class="specification">
<p><strong><span style="font-size: medium; font-family: times new roman,times;">Give all answers in this question to the nearest whole currency unit.</span></strong></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Ying and Ruby each have 5000 USD to invest.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Ying invests his 5000 USD in a bank account that pays a nominal annual interest rate of 4.2 % <strong>compounded yearly</strong>. Ruby invests her 5000 USD in an account that offers a fixed interest of 230 USD each year.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the amount of money that Ruby will have in the bank after 3 years.</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><span>Show that Ying will have 7545 USD in the bank at the end of 10 years.</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><span>Find the number of complete years it will take for Ying’s investment to first exceed 6500 USD.</span></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><span>Find the number of complete years it will take for Ying’s investment to exceed Ruby’s investment.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Ruby moves from the USA to Italy. She transfers 6610 USD into an Italian bank which has an exchange rate of 1 USD = 0.735 Euros. The bank charges 1.8 % commission.</span></p>
<p><span>Calculate the amount of money Ruby will invest in the Italian bank after commission.</span></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><span>Ruby returns to the USA for a short holiday. She converts 800 Euros at a bank in Chicago and receives 1006.20 USD. The bank advertises an exchange rate of 1 Euro = 1.29 USD.</span></p>
<p><span>Calculate the percentage commission Ruby is charged by the bank.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;"><em>Give all answers in this question correct to the <strong>nearest</strong> dollar.</em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Clara wants to buy some land. She can choose between two different payment options. Both options require her to pay for the land in <strong>20</strong> monthly installments.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Option 1: The first installment is \(\$ 2500\). Each installment is \(\$ 200\) more than the one before.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Option 2: The first installment is \(\$ 2000\). Each installment is \(8\% \) more than the one before.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>If Clara chooses option 1,</span></p>
<p><span>(i) write down the values of the second and third installments;</span></p>
<p><span>(ii) calculate the value of the final installment;</span></p>
<p><span>(iii) show that the <strong>total amount</strong> that Clara would pay for the land is \(\$ 88000\).</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>If Clara chooses option 2,</span></p>
<p><span>(i) find the value of the second installment;</span></p>
<p><span>(ii) show that the value of the fifth installment is \(\$ 2721\).</span></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><span>The price of the land is \(\$ 80000\). In option 1 her total repayments are \(\$ 88000\) over the <strong>20</strong> months. Find the annual rate of simple interest which gives this total.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Clara knows that the<strong> total amount</strong> she would pay for the land is not the same for both options. She wants to spend the least amount of money. Find how much she will save by choosing the cheaper option.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A geometric sequence has \(1024\) as its first term and \(128\) as its fourth term.</span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the arithmetic sequence \(1{\text{, }}4{\text{, }}7{\text{, }}10{\text{, }}13{\text{, }} \ldots \)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the common ratio is \(\frac{1}{2}\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of the eleventh term.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the sum of the first eight terms.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">A.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of terms in the sequence for which the <strong>sum</strong> first exceeds \(2047.968\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">A.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of the eleventh term.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The sum of the first \(n\) terms of this sequence is \(\frac{n}{2}(3n - 1)\).</span></p>
<p><span>(i) Find the sum of the first 100 terms in this arithmetic sequence.</span></p>
<p><span>(ii) The sum of the first \(n\) terms is \(477\).</span></p>
<p><span> (a) Show that \(3{n^2} - n - 954 = 0\) .</span></p>
<p><span> (b) Using your graphic display calculator or otherwise, find the number of terms, \(n\) .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">B.b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Jenny has a circular cylinder with a lid. The cylinder has height 39 <strong>cm</strong> and diameter 65 <strong>mm</strong>.</span></p>
</div>
<div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">An old tower (BT) leans at 10° away from the vertical (represented by line TG).</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The base of the tower is at B so that \({\text{M}}\hat {\rm B}{\text{T}} = 100^\circ \).</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Leonardo stands at L on flat ground 120 m away from B in the direction of the lean.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">He measures the angle between the ground and the top of the tower T to be \({\text{B}}\hat {\rm L}{\text{T}} = 26.5^\circ \).</span></p>
<p> </p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAboAAACGCAIAAAAkWtiwAAAVuklEQVR4nO2dz2sjaX7G5z+R2CKHNjRsyGVOLQw59DrBNHsQhiYQ6O7QcnIYNrAByfRe9iIfunebYEEguFl5ITRMSuwSAlMziIZQDG3M1maXYIrehmHLmKEpBiOowQfx5vDIb79+q1QqlaT6+XzQQZZKVa+lqqee932/7/f7iSCEEJKAT/JuACGbZWSaRqO53WrtdzpGo7nXbuOJ0Wjm3TRSMiiXpOL0ul3HcYQQrusajebINIUQQRDstdt5N42UDMolqTi2beOJKpf4M79GkVJCuSR1QZNLQpaFcknqAuWSrAjlktQFyiVZEcolqQuUS7IilEtSFyiXZEUol6QuUC7JilAuSS3wPO9kODQazf1OhyFEJB2US1ILPM9zFfJuDikllEtCCEkE5ZLUCN/3824CKTGUS1ILHMc56PWQWSMIgrybQ0oJ5ZJUGd/3R6a5124bjeZf/OAHkMvtVgtJNwhZCsolqSaO4xz2+9DHXrc7Ho/xHDncjEbzsN+nzSRLQbkklcL3/ZPhcLvVgos8GQ4xXomgS9kZR1ARbSZZCsolqQi2bfe6XWknZd42gCTBalZg13VhM3vdLqeASBIol6TczLOTGof9PrZRk6irNtOyrAxbTfJm4o4/f/7kh8/GV9PkH6JckrISbyc19jsdubH2lud5KEdBm1kbPox794xG07hDuSSVJqGd1MBq8ZgSPbKkD23mOpn++c2b9/MEaXrx9Zs/fZ9pez7yvXv8kHJJKstSdlIF8zwLt6fNXDfTydm/do7P5wjSd2fPe69cyiUh6yOdnVSxbdtoND3PS7IxbebamLx9cf8vH0TL5XRy9nKn8ZBySch6SG0nNTCfk3x71WYmFNlKc+WOX7949PSV+61rPttpNI07T1+dX318f+KOj3s7jabRaN599PIr90oIaOXWTTTCvYPxB2WH0MpZoMJHzYrcT5jJ+ai3azQ+ffLcPH3ztTPTu+nE/eLFo0+NRtO48/jl28sbFby+PPv1wawluwfm+WT2ekguJ+5Xzx/fbTSNxqdPnn/hTiJklHJJCsfqdlKj1+32ut1lPyXHOuudInN6NX52t9E0Gj/qPP+P08vr2TzJ7rE7k6lvRk9/9OT4jxNxI2RSTKfnr3bnuUsxdY8fqO4yZj+3+N49ftoxv5kKIcT1xW9ev7mazvT3/s/Hl9dCXF+Yn9292fPUPX5w57PRxbUQV+fHT+9+POJtuZy8fdn7t9PLayGEmPzx1aNP7/bG4WNTLkmBWJed1DAazcHRIMUHfd9He/Y7nRrbTChmpNBMr8bP7t7yaG9f3N+aac0Schm7n1sfO3+1e+/Jc/MM0jbjw7j3Y2lgp5f2y0d//+Lsu9lRbnZ7+4ih/0K6Xc3zKlAuSf6s3U5qOzcaTQxExsyMx2BZFtpWV5sZI5e3naYQs1fw7hJyGbufW8A8No07j198/mbWZb4aH9zR+vu3j3V59tvPnz+50zTm/hd/Pa+dKpRLkicbspMqjuMYjSZSAqeTS1F3m7lILm+J2gpyOW8/OteXZ//1qrdrNJoGOtpX44M7WzvP305Cm4rp5ekvH//Vo+f/+Zuzi/N57jIs1tFQLkkObNROamAIEtk0UsslqKvNXNQZb/wYPV8hBKQnZWd83n7mNevSfolBxun5q92t2zM53znj31+hqTc6uKgzvrXT+/VNH386+d3/nLEzTvIlAzupcdjv77XbeL6iXIrbNrM2RSxi5HI2MWLcfzZyr4SYTs6HT36IqRXI5dbd3vhq8vvfjv+sac/UPX7QuHcw/nbyuy/GF9dx+7nFhzfm1zMNnX4zenrvwfH5VJtqbzSNmfJ+GPfuGfdfnk2mYnp59qveTuPewZdnb968n4amepR5/KbRkF71+sL87C72QLkk2ZClndTYa7cP+308X10ugbSZJ8Nh1bPAfe8eP1Tigf5vtnywoYwDfgzB2drpHY8/BgBdX45/vtPY2nn25WXYYU4vxs92jcbuz8YXszfn7kfFd8b//ZX57wf3t4zG7sGvZMSQEjB0v/dq7MJmTi+//Nn9rVls0MWXB3e2dnqmO/k2/F9ML98O0cG/FUhEuSQZkr2dVAmCQO07r0suhRC+7yOf5l67XRubWXcol2Qj5GgnVbD8USa1XKNcAsdxamMzCeWSrJt87aSGZVlGo7lRpQ6CgDazJlAuyXooiJ3UGBwN1msn50GbWQcol2RVCmUnNZDmMptj0WZWHsolSUkx7aQG7F6WR5Q2k6XTqgflkixNke2kiud5SdJcrh2WTqsqlEuSlFLYSRWkuVT7xWufGY9Blk6jzawMlEuymLLYSQ0sf1RfyVIuBW1m5aBckrmodnKv3S6+ndTodbv7nY76SsZyCWgzKwPlkugEQWDbNtKJ4yIvqTPabrXk8keQi1wK2syqQLkkH/E8b3A0kHZyZJrlspMqSHOppQ7KSy6BtJksnVZSKJekOnZSBcsftfjHfOVSCBEEAUunlRfKZa2pkp3UUNNcSnKXS8AKvSWFcllHKmknNQ77/e1WS3uxIHIJaDNLB+WyXlTYTmpkufwxNbSZ5YJyWQvqYCc1SlQigjazLFAuK0597KSKluay+Kg2s36l00oD5bKa1NBOqiDNZel0Z2SatSydVhool1WjnnZSAzHhebciDfWu0Ft0KJcVoeZ2UqPX7UbO8xRqZjyGulboLTqUy9JDOxnGaDQHR4PI10shl4I2s5BQLssK7eQ8sPwxcpa5RHIJaDMLBeWyfNBOxuM4Tnj5IyidXIrbNpM1LfKFclkaaCcTEk5zKSmjXAJpM1k6LUcolyWAdnIpet3uXrsd+VZ55VKwdFoBoFwWF9rJdOy121qaS0mp5RKwQm+OUC6LCO1kaoIgqPzECG1mXlAuCwTt5OqUbvljamgzs4dyWQhoJ9cF5nlq8u3RZmYM5TJPaCfXDu46ebciU6TNZOm0TUO5zAfayQ1RijSXa4el07KBcpkptJObBmN5Me+WfWY8Blbo3TSUy4ygncwAz/OMRtO27XkbVFsuBW3mhqFcbhbaySyxbTs+zWXl5RLQZm4IyuWm0OykZVm0k5tmYZrLmsiloM3cDJTLNRMEgWVZuLcjjRgjPDKj1+3udzoxG9RHLoG0mSydthYol2vDdd3B0QAXJOwk+0EZs91qRaa5lNRNLoUQQRCwdNq6oFyuCu1kQUCay/jljzWUS8AKvWuBcpke2slCgeWPvFfFQJu5IpTLpaGdLCbQAt6x4qHNXAXK5RLQThaZw35/XppLokGbmQ7K5WJoJ0vBXrtdw+WPqVFtJkunJYRyGQftZJb4vu+GSN5hrHyay00wMk2WTksO5TIC2skMCILAcZyRaaJWBL7qeQ8kSB+Z5rwfoj5pLtcOK/Qmh3J5C9rJTYNbEa5PTQotywq7y5FpapK63Wod9vvawnDLsuKXP4LaBhIthBV6k0C5FIJ2MhNc10UuW0jkyXDoOM5SdyPf923blktLEZSO3vrC5Y+AchmDtJn/8PgJbWYkdZdL2skMcF0X1yEEbi2XouM4UnwHR4N//slPkszzxHf51/VY/b/LBfkz4UGbGaamckk7mQ2e50mhHJnm2m9Fvu/Lu90vf/GLhdtTLiPR7md/evdOjmbyulCpnVzSTmaDmhFnE0Kp8v79e6PRTBJCuGk5K51c+r4Pkx7+meRoJkunSeoil7STWeJ5nsy3mMHSEcdxjGTLHymXKgsFkaXTNKovl7STGYNJ6izTLGKNSpItKZdA6mCS4CFW6JVUVi5pJ3MBd6b9TifL9cgIM8rscDGUQi6l948paqRBmwkqKJe0k3mBr31wNMj4C0ckZpZHnEfx5dLzvO1WK533p82sjlzSTuYL3Ed8dt5NEARBcaJeCi6XqGW03WqljuWquc2sglzSTuaO9JXZH7pQaS6LLJfQyrWMk0ibWbfSaSWWS9rJgpCjVoqbeZ6CpG4srFyiD77Xbq9L3epZOq2Uckk7WRzgWfLSSiEE1kQm3LieM+O+72O8cu1LG+tWobdMckk7WTTgWfY7nRwvlf1OJ3may3rKJfJabmgZeK1sZjnkknaymOx3OpvwLEux1DxPDeUSWrbprOk1sZmFlkvVTmI1K+1kccCgYb7VCzDPoyVzi6FuconvJ5soK9VmJv9FykVB5VLNN7Pf6di2XeFbVhnBcFjuxR4wcprc3tZNLvfa7e1WK8trR9rMSpZOK5Zc+r4/Mk3VTjLvXjHB2Ejuv07CNJeSWskl7H+M0fN9HymZI9/1PM+yrHkfV1M44xX0BeFsqlo6rShySTtZInzfX2o23LbtcFSz4ziYpdHmB06Gw/1OR83NEQQB1Pmw39cEutft7nc6yVs+T85wiP1OZ2SaqieKbCTu6HvtdlhKiiOXQRBgFm7eBlA0OR+gfRbfxrz8zejj44EeRhAESPmMD4qKVujNWS5pJ8sIxCvhNWDbNm6EqlxiSt11XVzVcvEyTgaU8ZEfGZkmNsA9Vd05zpkV/x3ZGCHEYb8ve6+RjfR9H5EAvu+HwxiLI5dQw3nOMQgCJNeQtyIp/Xir1+3G+JVet2vbtlp7zrZt+SOqpSUrZjNzk0vayZKCRYdLiVR44Y2aFEPGmXuep05zw2MK5fKDbMmdwOSufh1iOjG8z8hGWpYldeGw39escXHkMn5kGd82nms/6MlwGD/ciV8zbMPlHvbabfWtKtnMrOWSdrLsID/bUiEKmlxCkqToyNltzRDhbiqEsG271+26rou+ntxt8jSX8fS6XVVZ5IUd2Uj0Oh3HwQiDtquCyCVmwJYKGMAdAncsVI6bF64nXY4WwoWBEXTJw5+qhs3MTi5pJ6sBhu2W+ogml9KeaH9i3kZuJg1dEARQTC3dNzZY/SzS1gVBLuc1UtxEAUfe6Qsil5CthBtjLhtfI+6F+KqxKjzyboQac9hAM5Ix/lHazPJW6N24XNJOVgm4j2UNQkK5RH0YKX/xo29CiMN+fy1pLuFSMY8EX3bY78fIZQxFkEvNF8cjBzHxJ8Yx5Vvxoy4Y202eNBNIIS5IEqml2KBc0k5WD7iPZUegEsql5hZx6cacM3vt9roCP+FeD/t9nLEIrympXCYsuQ4GRwOtQ622H6u24j+e4ieQFXpLZzPXL5e0kxUmXd5yTS5hW6QrkUOQ2qhor9uNuVbTpblcKGcyrltrJFznwnHSIshlctONIQU8x7+MO5a8YHELSbiHZZGVgkpkM9cpl7STlWfZOXEQnhk/7PdlSODgaIDLW52V1gKM5u1z2ZwO8XKGC1iKRWQjV9l/NiT8jRAgiWAgy7KQBxOLteTH5XwR5tlwOY9MEz8lBj1Xmewunc1cg1zSTtaEdAOX4sY/qhO1GPZCEgDVzmBgy3EcBKvH3G7TDQvMkzOEH2rpQuY1MsX+MwO/0cI5ccyqqQ95Y3AcZ6/dxu1B6qZ0nbiN4Urfa7fXcqWXyGauJJe0k7UiXeCO67oYl5SuBHied9jvh9OmYM5HC+sLo05KJCdSzizLGhwNIlewzGvkUvvPkmUX0c8jPMet7hOh+yseQkXazILXtPhECCFjAsLqLm8m6hlDO1lPktenzQAtWDIhm5az3OWyUL/RskTWPXddF0q63WotvIlumpm7lEGk2k0DXR75A7x79+5ffvpTvPJ3Dx++fv36D//7B5fUg8HR0T/t7+fdihky3GfZT8Egb4hN738h/7i/v/s3f5tjA1YEQwFaJ8ZNFpaQAR/lEq3U2oSJQimXUj354IMPPjb3UIWoiHKJtaJq6AaC0dRQrCAIcr77EEJqgNrpdgsolzJOWE6rIc5Ai1wlhJAsKahcYmIH8WWu6+IJ5ZJUBt/3YV7kn/m2hyShoHIpbuIz0A2HzaRcktzxfV/WtkP+iO1WK5wtOIYgCLAkCRGdSJ1bhCuQLKS4comVFWpGE8olKQiYjcRzz/PwZxLFRCIJda0Lsvwumx6C5EKkXDqOk338oi6X4sZgysUblMsCMi9IOPJ1LAfecIuyQDsVEZKdRPJw+9e+BIzLr7+VeRM5wlDqEyMsl8g6mn1LPkFrcD5hBa7rujLLgIxgPxkOOdAjkWuZwqvNkJrBaDR73e7p6SkS/BmNpiyPp4bgpgBZadEDUFdMY6w5vP+T4XCv3UbC19QHLQiaXCas3It1gZGqutFT2vd9eZ4g5gT54dVsabi41OWGq4BzQ3Nh8iiDo4H6/45ME0UmCn5iyK8R+eHxwFBM9o35RAjheZ6cv8erMtf/vKl9gp8wbE9kwD/+hHrKzRzHwZWTTjExF2dZFtZWy/3I18XtZBDwX7jzYVFEqv+1KEAuLctCBQh8sQu/SQQLq6KAZWnykUGb8Vzmx5UXmpYReRXcm5RO6n+ESQis8jSU1BtYz4rUyylyVmaJnJ2LiTTKjKJUgiwdMrBfPddlaEG4mIH8E1dIulu6WuZUVQE1NaR7UyZBCKHehBfWYCk+kB5onLxdLRzAwg1M68pBL2RFs023Wf6J42qpK9bYBiNUEEL+4lBqPNdODGMdSenrAOUyJSPTlJn65Yu2bSNh6kK51DKPuUoeCu0xrwGukhUtLNAyj47cQ4oaO0Ujcuxy4fgjJCncd0vy2dWJlEu18mX8j6IZ4YUnRswMMnokIjQUmDCVJxGUy9Qgvw4uBtkvQD6VsFzidRQXjbx0U8ilWlpLu/LxJy4DObSnus6SEp51xMhg/KcwdhlZ5DYzuXQcx3EcCBYyS+LdLOXysN+X9YeNUKL4UlccywzKZUoglzjV0LfCOJGIqiyIAXhE/GH71fs+aqqrSLnULsUKXBWR7lImaowBgxXaXSpLuYTA4XkvVIZ7c51xCaZz1fpl7pxaICQGymVKZPZGKCDi+PBKfGccl642uI7LJvIReXStxEqkXMJEyF5/qTvjcrRRk57kWbjxtcN0w8sbqTLDL0u8xC+US/cmy1HCEyNS+BB2I78orZ+BJi2bl76eUC5TIuVSjqCpgf0xcin7hqkPjRFS9ZX9Tkdegdg/MgOqF8/opg5t6uPmyLzcLkvtROvYZhPkHB5AUOvNRsrlKgMmYblEiL4WGFCZEyNjKJcpORkO5Q0ZU+TyjNxrt9UeoiaXK/oaVStRMkHcSDbOeITK4rkq3AvLVJFNoMklnJ28WYblEsFGqQ8XjgFQtRK2Gq2SR0mXaLmeUC7T4Ps+Yr8xGKTOusjeE8wLhAxjlzL8RR3sXwrsTX1I6YTBhFZKHZfVZpCnmsEiGYO1A3IAARHjMnpJVlw47PexAYK9Uo8vy4LpOLugldoJg3ODJ0Y6KJdpkB063LcxsiZC3b3T01NtNlMNnFzluOEeZRAECF/X+pie5+G47G1lTOSktqtUuZk35Z3ul1IPh9MysgFye54YKaBcEkJIIiiXhBCSCMolIYQkgnJJCCGJoFwSQkgiKJeEEJIIyiUhhCSCckkIIYn4fxAexs+0SMkVAAAAAElFTkSuQmCC" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the volume of the cylinder<strong> in cm<sup>3</sup></strong>. Give your answer correct to <strong>two</strong> decimal places.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The cylinder is used for storing tennis balls. Each ball has a <strong>radius</strong> of 3.25 cm.</span></p>
<p><span>Calculate how many balls Jenny can fit in the cylinder if it is filled to the top.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Jenny fills the cylinder with the number of balls found in part (b) and puts the lid on. Calculate the volume of air inside the cylinder in the spaces between the tennis balls.</span></p>
<p><span>(ii) Convert your answer to (c) (i) into cubic metres.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Find the value of angle \({\text{B}}\hat {\rm T}{\text{L}}\).</span></p>
<p><span>(ii) Use triangle BTL to calculate the sloping distance BT from the base,</span> <span>B to the top, T of the tower.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the vertical height TG of the top of the tower.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Leonardo now walks to point M, a distance 200 m from B on the opposite side of the tower. Calculate the distance from M to the top of the tower at T.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the sequence \({u_1},{\text{ }}{u_2},{\text{ }}{u_3},{\text{ }} \ldots ,{\text{ }}{{\text{u}}_n},{\text{ }} \ldots \) where</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\[{u_1} = 600,{\text{ }}{u_2} = 617,{\text{ }}{u_3} = 634,{\text{ }}{u_4} = 651.\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The sequence continues in the same manner.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of \({u_{20}}\).</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><span>Find the sum of the first 10 terms of the sequence.</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><span>Now consider the sequence \({v_1},{\text{ }}{v_2},{\text{ }}{v_3},{\text{ }} \ldots ,{\text{ }}{v_n},{\text{ }} \ldots \) where</span></p>
<p><span>\[{v_1} = 3,{\text{ }}{v_2} = 6,{\text{ }}{v_3} = 12,{\text{ }}{v_4} = 24\]</span></p>
<p><span>This sequence continues in the same manner.</span></p>
<p><span>Find the exact value of \({v_{10}}\).</span></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><span>Now consider the sequence \({v_1},{\text{ }}{v_2},{\text{ }}{v_3},{\text{ }} \ldots ,{\text{ }}{v_n},{\text{ }} \ldots \) where</span></p>
<p><span>\[{v_1} = 3,{\text{ }}{v_2} = 6,{\text{ }}{v_3} = 12,{\text{ }}{v_4} = 24\]</span></p>
<p><span>This sequence continues in the same manner.</span></p>
<p><span>Find the sum of the first 8 terms of this sequence.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>\(k\) is the smallest value of \(n\) for which \({v_n}\) is greater than \({u_n}\).</span></p>
<p><span>Calculate the value of \(k\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A farmer has a triangular field, ABC, as shown in the diagram.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">AB = 35 m, BC = 80 m and BÂC = 105°, and D is the midpoint of BC.</span></p>
<p> </p>
<p> </p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the size of BĈA.</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><span>Calculate the length of AD.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The farmer wants to build a fence around ABD.</span></p>
<p><span>Calculate the total length of the fence.</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><span>The farmer wants to build a fence around ABD.</span></p>
<p><span>The farmer pays 802.50 USD for the fence. Find the cost per metre.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Calculate the area of the triangle ABD.</span></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A layer of earth 3 cm thick is removed from ABD. Find the volume removed in cubic metres.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The following graph shows the temperature in degrees Celsius of Robert’s cup of coffee, \(t\) minutes after pouring it out. The equation of the cooling graph is \(f (t) = 16 + 74 \times 2.8^{−0.2t}\) where \(f (t)\) is the temperature and \(t\) is the time in minutes after pouring the coffee out.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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" alt></span></p>
</div>
<div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Robert, who lives in the UK, travels to Belgium. The exchange rate is 1.37 euros to one British Pound (GBP) with a commission of 3 GBP, which is subtracted before the exchange takes place. Robert gives the bank 120 GBP.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the initial temperature of the coffee.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the equation of the horizontal asymptote.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the room temperature.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the temperature of the coffee after 10 minutes.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the temperature of Robert’s coffee after being heated in the microwave for 30 <strong>seconds</strong> after it has reached the temperature in part (d).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the length of time it would take a similar cup of coffee, initially at 20°C, to be heated in the microwave to reach 100°C.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">i.f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate <strong>correct to 2 decimal places</strong> the amount of euros he receives.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>He buys 1 kilogram of Belgian chocolates at 1.35 euros per 100 g.</span></p>
<p><span>Calculate the cost of his chocolates in GBP <strong>correct to 2 decimal places</strong>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Nadia designs a wastepaper bin made in the shape of an <strong>open</strong> cylinder with a volume of \(8000{\text{ c}}{{\text{m}}^3}\).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Nadia decides to make the radius, \(r\) , of the bin \(5{\text{ cm}}\).</span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Merryn also designs a cylindrical wastepaper bin with a volume of \(8000{\text{ c}}{{\text{m}}^3}\). She decides to fix the radius of its base so that the <strong>total external surface area</strong> of the bin is minimized.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAcUAAAD9CAIAAABC/funAAAXeUlEQVR4nO3d/28b933H8f4nJEovqAQIWdb+IOwHsyq6QlUzwTU2QkO6Na3tzRSapOhSrCAFGcsCrGQ6GTY2HlAslRAqQOshOSaDWyCnjjOQHVJ7RK5AGmifIS2SnMIlxtXQiJ7nODT3w5s8H79I1pcPefzyfIA/ONHx7kO+wdd9Pp/79qkGAECHT0XdAAAYE+QpAOhBngIjo16t/OtLa+dOr6t6o1F7a+PMbGLq26WdO1G3a2y1feEHMLl56vu+2pfrulG3EQjZLa9MxROx+Ey2vNsY2zytV+1/Wrd3e/zlTvV6cePazcE1pfmFT59a3z5YnI5LngbhaNt2yTRLprlZLGYzmeCViMU7XnPJZHiB7tdyOt39rqVUKlggn8vJtkqmSQSj/26r9ccSsZMr5QFmykDVa8pcmX+kV37tKnN1IfbYhro90Aap9VOH+cJHLE8ltiTCJNTmkslwOBoFQ/5qWVa4s6mrAZ7nBet0HCfI044IXk6ng8bYtq2U8jxPVxswWerVG5fOzsSmF/I/vLg4nZhaLe/WG/Vq5dWXNrKn70dPc7HZ9PPG96bizcUa9Zoqb2QXE7F4Ira4Ym7Xmiu9U6387OW1s5/Nbu1sF89NtSKj90pk4fN/sr5dr22XsotBG25cOjsTO32xcqur0aG31KuVF7ILsdm0+e79lKyp8np2IRZPxGbPXbKr9UZD1iwdl+Z2mx+spsyV+Wn5U7NvHv5cU2cvX6929x/rVfvymdlELD5zZu3ll66U37nd6Hzj+Y3t3baFp5740fNPz9zfym21/lh7Y3ZV+crF5mqL27XOzQ5vnkpyBT1NyU3Jqc1isWSajuMMbU5J4FqWVTLNfC4Xbr/0aiVko24mhl793dJ5GdTf3i2vtn7qN8vZk4lY/H5fVRabf7Zc3ZE/SSLUd8z0VCs4WtMFicV/vrG1OiNv37q2sTjdHNL2XkldtpuInVzZul46P9vc7tab5VWJv+7hcOgtZVVZO91MycXmLGS9unVhfnrmTHG7dne3vDrT+hR1tX7qfpaFdXTM71TLzy7EZs+tv1WTr6It8oR8RY9tqNv16taFxWeaOwZ54yW7enenvLoY+pamF1a3qrfkKwq+1e2Nxen77altl7KnQ4v16CwPUZ66rmvbdjg9g+gc2tw8rGBGIp/LLaVS4YRVSvm+H3UDMVTu7Jjfnmn27CSkWuFV394I+qpti0mOSCJIDLUSSvK0GWryp8XvrZlO9Y2Li0+Xdmp7rKTRzKaps8/ln7l83d5YnE5MnX0uv/pM+Z3tveYfms07+1x+9YL59k5by98tnZ9thVG4hfLvXpOVsrZWfjV3EvJBmn/qboN8BMnc+u6bb75Tb+Xm2vVaM7tPX6zcCu2x7jS/olY6tw326zvl1cXE/OVKrd7M/fPmTlevOMo89X1fhswyvzmXTEqyOI4zHul5ENKN3SwWZa5gKZUyCoZlWUzFov3nLXHT6hPtllemggNT1y/OB9l6v1/WaIvFVp8xvNj8E5fL7zczYc+VtDLri0sXXn23Lk364tLKC2/V2jK9V8vlLW1rq4d62Y3WhiRD2zfavbbmnqA963f36irWa5XLMp/Qmmfouf7mYnvvcprNrlUuL8SmT62/vSuTD/PPlqs9DgMOOk8lQ4P4kB7oRAXo/iRepfcqOxiydVK1R0/bT70eGibvt1gtmBuVuIw1e2fNxeYvV5ozgPuspBHqjrUWO2/u1PcZnrct1r5X6JWG4b7hYveZSe0d87a1tW+ok4zuWwv3Xn/3Lqd9BNAW4vFELJ6Yz26Y11TXzKkYUJ66rlsyTcnQ5XRahreD2fTo8jzPtm2jYMwlk3PJpFEwbNtmTmBihPtuMqJvHzK39VvDi4UyrqZ+fum5C3/TPG5z0axU78dxeGS9z0rkT3LQSZok/+5eSUfLe3VI20buzQ+1sHa91tlv7V5b2xxra7AvUwfdB8Ruq1dfC/UxT66Ub7a9MRBuT3Nt4Q21Z+sBzi7ob546jmMUDOlqGQXDcRzi4Ghc17UsK+jUW5ZFj37cBRn39m7zkPTJla1fVq6p3WbHcGtHvVGp7nYtNn3q+a0b11Stdv3i/CML2edLr1aqPTpl4XTo3lZrJeFBfdsAv7mSH5Xta6o9A3v07Jotr93f9O9q28VzchSoLfjeUdferHZH3tRqeWf7WqVav9/N3N1ePz8TW7xQ7u6b3ixnH18xt2sS2eH+aWtnUFPXSq9WqneDoPxQlddX5qdbn+jDVnt2qpVypXmArjV1UFNl82eVgY33lVLSq1pKpTaLRYarGvm+b9t2PpeTnj491jEmB15mzlz+efPn3Ty1qHlAZn61pHaDxRLzqyX1TvMgTPMMpLc2zszeP3u6tXzHUZfwtrpXEh7Utw/wb1XWTrefg9VaVY/FWk0KncaUmM9ulFXrvc1AX8ianUPpZt8w2NCd6nXj3FQ8EZteyK6XVa8T/+vvVipvVV7ILoQ/9f03xmfOrL3c3HSrj5w11c7WylRw9pU0Oz5zxrhRvdN+ztbiynp5EON9z/NKprmUShGjAxAO1nwu5zhO1C3CMKlXK+blldUfl8tXSy+tnZtqO2MJfaInT5VS8sOWQb2WdeKAwruxkmnSXUVr1jI0ot/nWDz0OW6e2rbNL3lIOI4T7NWYXZ1scn5PeJS9dWH+kebBffTN0fM0SFLbtjU2CMfkeZ5RMEjVibfbOsASbz+4jz46Sp46jkOSDrlwqjJuAAbjcHnqeZ5cDEqSjgTP8/K53FwyaVlW1G0Bxt8h8rRkmolYnHnSkaOUWkqlltNpzrgA+upAeep53nI6zQ9ypMnukI4q0D8PzlOl1FwyuVksDqA16CvXdeV+K4wwgH54QJ7ats1s6TjxfV/ue02kAtrtl6cSpozxx49RMIhUQLs985QwHW9EKqBd7zx1XTcRixOm4y2fy+VzuahbAYyPHnnq+z7n6k8C3/eX02mO+AO69MhTebrR4JuCwXNddy6ZZNQPaNGZp77vJ2JxrvueHEbB4GQ4QIvOPLUsyygYkTQFkfA8by6ZjLoVwDjozNPldJobmE4aig5o0ZmniVg8knYgQiXTLJlm1K0ARl5bniqlltPpqJqCqDiOk81kom4FMPI685Tf1QSi7oAW9E9B/xTQozNPmT+dQCXTJE+B4+uRpxzqnTTL6TR5Chxfjzzl/NOJ4nleIhYnT4Hj6zF/OpdMcn3U5DAKRjaTIU+B4+txfJ/ZtMkhD1/geBSgRY88lftLcduhsRcUmvOlAC16n3/K/U8nQXD/U/IU0GLP8/m5P/94C9+fnzwFtNjv+igidVx1POyEPAW0eMD1prZtJ2Jx7tU/NuSe/B1PjiJPAS0efP2+HALeLBa5i/uok1IaBaOjlOQpoMWB7ofieZ48tJ2x/+gqmeZcMtnztA3yFNDiEPeXkh8kHdWRo5RaSqWymcxel2mQp4AWh7tfn3RU55JJZlRHgud5+Vxur25pgDwFtDjK/U+lv8MzpYeZ53lGwUjE4gcZT5CngBZHv5+0bduk6hAKktQoGAe8DwN5Cmhx3Pvz27Ytt1ApmSZ3UYmWXIYvR/APVQvyFNBCz/NOlFLSJ8rnctw+dcA8zyuZpowVLMs6wtFC8hTQQufzozzPsyxrKZWS0wA4uaqvfN+3bTubycjQ/ji7MfIU0KIvz+NzXXezWJQe02axqJQ6/johPM+zbTufy8lowLbt45++Rp4CWvT3+aZKKQlWmdTT8uOfTK7rlkxzOZ3WGKMB8hTQYkDPi3Zd17IsGZwup9ObxaLjOGTr/uRLkxNIl1IpGdT340sjTwEtBpSnAd/3HcfZLBalqyXZats25wYIpVTJNCVD55LJfC5nWVa/Z6LJU0CLQedpmO/7Eh9yls9cMilPW3EcZ3LiVSllWZbcQE92MDIxMsijeeQpoEWUedrB8zzHcYJ4lYduGgWjZJpKqTE4W0D2H7Zty2dcSqWCAJWHjkTVMPIU0GKI8rSDpI9lWZvFYpA+cl+PzWJRurFKqeHsySqlpPEyeJeJY9lD5HM5afzw7CGGqu7A6BrePO3JdV2ZIghySnJWoipIK3mpEF2HcaQB4bgsmaYkfndjJPdt29bYgH4Y/roDI2HE8nQfknEyYyAvCTV5yQRCx0tmbPd6dS8vw/NgAZmLKJmmjNaHtrP8QCNdd2B4jE+eHoFMKfQ0PIPxAZi0ugN9MtF5CkHdAS3IU1B3QA/yFNQd0IM8BXUH9CBPQd0BPchTUHdAD/IU1B3QgzwFdQf0IE9B3QE9yFNQd0AP8hTUHdCDPAV1B/QgT0HdAT3IU1B3QA/yFNQd0IM8BXUH9CBPQd0BPchTUHdAD/IU1B3QgzwFdQf0IE9B3QE9yFNQd0AP8hTUHdCDPAV1B/QgT0HdAT3IU1B3QA/yFNQd0IM8BXUH9CBPQd0BPchTUHdAD/IU1B3QgzwFdQf0IE9B3QE9yFNQd0AP8hTUHdCDPAV1B/QgT0HdAT3IU1B3QA/yFNQd0IM8BXUH9CBPQd0BPchTUHdAD/IU1B3QgzwFdQf0IE9B3QE9yFNQd0AP8hTUHdCDPAV1B/QgT0HdAT3IU1B3QA/yFNQd0IM8BXUH9CBPQd0BPchTUHdAD/IU1B3QgzwFdQf0IE9B3QE9yFNQd0AP8hTUHdCDPAV1B/QgT0HdAT3IU1B3QA/yFNQd0IM8BXUH9CBPQd0BPchT7FH3uzdV5fXXXvnJxguvV+9F0Sxg1JCn2DtP//PlZ77wezPZ8m4UrQJGDnmKveu+W16Z+sPvvvbhwFsEjCTyFHvV/d7vXv+7hz/9ZOmDuxG0CRhB5Cn2qvv/Vtb+OJF68Tf3Gvdqv/6Pq69Vqv8XQeOA0UGeYo+6f/KrH/7Rw6fWf7X7q+JTf/rVhd9PPPStqx9F0TxgVJCn6F33ulo/Ffvqmll8Nv/zDz7+9b/8xcMcmAL2R56iZ93vvHfl/EOfnv3itzb/6/a9ex9dferE7FNXdzhvCtgHeYpedb/3XukvP5s48VcvvuM3Gnc/uvr0Z048/dOPODAF7Ic8Ra+6//a17554eGn97Y8bjUbjZjl78jNPXP2I3imwL/IU3XWv75ZXZ4IzpXbLK1OzTxZf/vEr6uOIWgiMBPIU3XW/9Yvvf/mhr195716j0Wh88st/PBmbnnviJ+o2HVRgP+QpHlT3e7X3t90aWQo8CHkK6g7oQZ6CugN6kKeg7oAe5CmoO6AHeQrqDuhBnoK6A3qQp6DugB7kKag7oAd5CuoO6EGegroDepCnoO6AHuQpqDugB3kK6g7oQZ6CugN6kKeg7oAe5CmoO6AHeQrqDuhBnoK6A3qQp6DugB7kKag7oAd5CuoO6EGegroDepCnoO6AHuQpqDugB3kK6g7oQZ6CugN6kKeg7oAe5CmoO6AHeQrqDuhBnoK6A3qQp6DugB7kKag7oAd5CuoO6EGegroDepCnoO6AHuQpqDugB3kK6g7oQZ6CugN6kKeg7oAe5CmoO6AHeQrqDuhBnoK6A3qQp6DugB7kKag7oAd5CuoO6EGegroDeoxhnvq+r1osyyqZZvDKZjJHfhkFI7wqx3FkE67rRv2Jj2s86g5EbiTzVBLTcZxwSi6n04lYPBGLzyWTQQhuFovhEFTHYNt2eFX5XG6v7UryWpY1Kmk7KnUHhtyw56lEp3Qzw+ElyRXuKkaeXEG/WFprFIxsJrOUSgVRKznrOE7kTe0whHUHRtHQ5ank0WaxmM1k5pJJic4giZRS0TbvaDzPC+8VJGSX0+l8Liefy/O8CJs3DHUHxkD0eeq6rm3bRsGQvmeQMkqpaFOm32QOIdhzSB9WPrjv+wNuCXkKHF80eaqUkp7aXDK5lEoFATqATQ8tz/OCeJX9ilEwbNsewE6FPAW0GFyeep5nWVY+l5MMHVhYjKhglyPZulksOo7Tv22Rp8Dx9T1PlVKbxeJSKjWXTOZzOTL0COQ7lPkQ+Q71TgiQp4AW/cpTpZRRMKQr2te+1UQJ+vjSabUsS0uwkqeAFprz1PM86Y1KjA7biUFjw/d927YlWKXHepy1kaeAFtry1LZtOb5kFIwJP7I0SL7vW5a1nE7PJZObxeLR5lLIU0CL4+ap7/sl05QOqfZ5PRyc67pGwZDu6mH3Z+QpoMXR81SSVM6apEM6JI5WFPIU0OIoeRr8aI2CwQzpEJLZ1aVU6oCpSp4CWhw6T23bpk86EoLdXj6X239elTwFtDhEnrquK9eek6QjxPf9zWJxLpksmeZey5CngBYHzVPLshKx+D6/SQwzpdRyOr2cTvfsqJKngBYPzlPf9/O53FIqxVTpqJOOave1FeQpoMUD8tR1XbnhEydCjQfHcbrH/uQpoMV+eeq6rpwlPvBWoY9c15X70QT/hzwFtNgzTyVMj3khI4aT7/tyP0D5T/IU0KJ3nsrvjaNPY8z3/WB/SZ4CWvTO03wuFx4PYizJEMR1XfIU0KJHnjqOs5RKcQBqEsi9VMhTQIseecoZ+xNlOZ2+cuUKeQocX2eefvPxb/DTmiiO4yx+5VGKDhxfZ57Of+lLHNOfNItfefSpJ5+MuhXAyOvM00QszszppPmHH/zgz7/2tahbAYy8tjy9cePG5x75g6iagqhcuXJl8dFHo24FMPLa8tSyrC98/vNRNSVyJdOczOcGTnjdAV36/rzoERI8uOXID2IaURNed0CXtjz1fT8Ri0fVlCERPOl6OZ3u7xOx7t5Ulde3fvH+x41Par9+w6p8cLdfW3qAkmlylwbg+D7V8d/cl0/II0OymUwiFjcKhvZ5gHu33rbWswuxRx6/8vbOv/39o5+OJ86YVb3bOLDjP3EaQKM7T42CwWX7YZ7n9WkeoK7WT8VSa5vGsy+84ZgXL7/+P/d0rfow5EL+iZrfAPqkM0/lmm5Omeqmex7gzntXzj904ktfX/v3jyLJ0ZaSaeZzuShbAIyLzjxtNBrZTIYu6l60zQPc2/npE7OJz/1t+befaG3g4UjnlMuLAS165KnneYlYnFnU/R13HuC3r333xMN/9uJ/1/vTvAPiRmKARj3ytNG67RCj/oM40jxAfbe8OnPiqdIHH/e9fXuzbZsbiQEa9c7TRqNhFAwi9eAOOQ9w6xff/3Ii9eJvops5tW1bbn4aWQuAsbNnnjYajWwmQ6QeVv/OB9DItu1ELM60KaDXfnnq+z691CMb3HUBh2RZFseggH7YL0+FhAI/v6Pp93UBh22MVJNhPtAPD87TRmuujZOojiPyeQDXdZfT6WwmMzw9ZWDMHChPG61fozxrqK8NGnuDnwfwfb9kmolYnD0i0FcHzVMhU29GwRjOwywjZGDzAHJSVDaToWRAvx0uTxuNhud50r0qmSYjx+PzPM+yrH7MAwRPV+ReJ8BgHDpPheu62UyGVNXIdV1d8wCSpEx5AwN2xDwVSql8LicjVoaTuti2HXyrh50HkNH9UirFfg4YvGPlqQhmALKZDENLXQ41D+B53maxGPRtB9ZIAGEa8lTIAZbldFoOWHGGoy77zAPwnQNDRVueBlzXlb6SdKz4kesSzANcvnTplVdekX/LrfUZ2gPDQH+eBhzHMQqGjFgjvzRoDMgMwF9/5zuJWPybj3/DsizmrIGh0sc8DUiPdTmdTsTi2UzGsiw6rQfk+36wW5pLJumNAsNsEHka8DzPtu1wOliWxQVXHTzPcxwnvAcqmSbfEjD8BpqnYeFsldTYLBZt257Arqvv+0opeY5T8G2QocDIiSxPw3oGijxpVSk1frOESinbtkumKdcvTfjuBBgbQ5GnHSReLcvaLBblOh9JnHwuVzJN27ZHKGSVUrKrkM8i6bmcTstncRyHAAXGxjDmaTdJWOnTGQUjCFm5iEBGxyXTlNlYpdTAQkoappRyHEfaIM2TqU+JzqB5g2wYgMEbjTzdi+d5QQcwyLJwnCVicbm7UvglCx/8Faw2eAUrDwI9WK10n5n6BCbQaOfpQQSZGzhsngYRGYj6MwEYRuOfpwAwGOQpAOhBngKAHuQpAOjx/9TEGO/GcZufAAAAAElFTkSuQmCC" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Let the radius of the base of Merryn’s wastepaper bin be \(r\) , and let its height be \(h\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate</span><br><span>(i) the area of the base of the wastepaper bin;</span><br><span>(ii) the height, \(h\) , of Nadia’s wastepaper bin;</span><br><span>(iii) the total <strong>external</strong> surface area of the wastepaper bin.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State whether Nadia’s design is practical. Give a reason.</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><span>Write down an equation in \(h\) and \(r\) , using the given volume of the bin.</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><span>Show that the total external surface area, \(A\) , of the bin is \(A = \pi {r^2} + \frac{{16000}}{r}\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down \(\frac{{{\text{d}}A}}{{{\text{d}}r}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Find the value of \(r\) that minimizes the total external surface area of the wastepaper bin.</span><br><span>(ii) Calculate the value of \(h\) corresponding to this value of \(r\) .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Determine whether Merryn’s design is an improvement upon Nadia’s. Give a reason.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The lengths (\(l\)) in centimetres of \(100\) copper pipes at a local building supplier were measured. The results are listed in the table below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the mode.</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><span>Using your graphic display calculator, write down the value of</span><br><span>(i) the mean;</span><br><span>(ii) the standard deviation;</span><br><span>(iii) the median.</span></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><span>Find the interquartile range.</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><span>Draw a box and whisker diagram for this data, on graph paper, using a scale of \(1{\text{ cm}}\) to represent \(5{\text{ cm}}\).</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><span>Sam estimated the value of the mean of the measured lengths to be \(43{\text{ cm}}\).</span></p>
<p><span>Find the percentage error of Sam’s estimated mean.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The sum of the first \(n\) terms of an arithmetic sequence is given by \({S_n} = 6n + {n^2}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the value of</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>\({S_1}\);</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\({S_2}\).</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 class="p1">The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\).</p>
<p class="p1">Show that \({u_2} = 9\).</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 class="p1">The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\).</p>
<p class="p1">Find the common difference of the sequence.</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="p1">The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\).</p>
<p class="p1">Find \({u_{10}}\).</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 class="p1">The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\).</p>
<p class="p1">Find the lowest value of \(n\) for which \({u_n}\) <span class="s1">is greater than \(1000\)</span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The \({n^{{\text{th}}}}\) term of the arithmetic sequence is given by \({u_n}\).</p>
<p>There is a value of \(n\) for which</p>
<p>\[{u_1} + {u_2} + \ldots + {u_n} = 1512.\]</p>
<p>Find the value of \(n\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>Abdallah owns a plot of land, near the river Nile, in the form of a quadrilateral ABCD.</p>
<p>The lengths of the sides are \({\text{AB}} = {\text{40 m, BC}} = {\text{115 m, CD}} = {\text{60 m, AD}} = {\text{84 m}}\) and angle \({\rm{B\hat AD}} = 90^\circ \).</p>
<p>This information is shown on the diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.24.18.png" alt="N17/5/MATSD/SP2/ENG/TZ0/03"></p>
</div>
<div class="specification">
<p>The formula that the ancient Egyptians used to estimate the area of a quadrilateral ABCD is</p>
<p style="text-align: center;">\({\text{area}} = \frac{{({\text{AB}} + {\text{CD}})({\text{AD}} + {\text{BC}})}}{4}\).</p>
<p>Abdallah uses this formula to estimate the area of his plot of land.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \({\text{BD}} = 93{\text{ m}}\) correct to the nearest metre.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate angle \({\rm{B\hat CD}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of ABCD.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate Abdallah’s estimate for the area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the percentage error in Abdallah’s estimate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;"><strong>Give all your numerical answers correct to two decimal places.</strong></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">On 1 January 2005, Daniel invested \(30000{\text{ AUD}}\) at an annual <strong>simple</strong> interest rate in a <em>Regular Saver</em> account. On 1 January 2007, Daniel had \(31650{\text{ AUD}}\) in the account.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>On 1 January 2005, Rebecca invested \(30000{\text{ AUD}}\) in a <em>Supersaver</em> account at a nominal annual rate of \(2.5\% \) <strong>compounded annually</strong>. Calculate the amount in the <em>Supersaver</em> account after two years.</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><span><span>On 1 January 2005, Rebecca invested \(30000{\text{ AUD}}\) in a <em>Supersaver</em> account at a nominal annual rate of \(2.5\% \) <strong>compounded annually</strong>. <br></span></span></p>
<p><span>Find the number of complete years since 1 January 2005 it would take for the amount in Rebecca’s account to exceed the amount in Daniel’s account.</span></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><span>On 1 January 2007, Daniel reinvested \(80\% \) of the money from the <em>Regular Saver</em> account in an <em>Extra Saver</em> account at a nominal annual rate of \(3\% \) <strong>compounded quarterly</strong>.</span></p>
<p><span>(i) Calculate the amount of money reinvested by Daniel on the 1 January 2007.</span></p>
<p><span>(ii) Find the number of complete years it will take for the amount in Daniel’s <em>Extra Saver</em> account to exceed \(30000{\text{ AUD}}\).</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Prachi is on vacation in the United States. She is visiting the Grand Canyon.</p>
<p><br>When she reaches the top, she drops a coin down a cliff. The coin falls down a distance of \(5\) metres during the first second, \(15\) metres during the next second, \(25\) metres during the third second and continues in this way. The distances that the coin falls during each second forms an arithmetic sequence.</p>
<p> </p>
<p>(i) Write down the common difference, \(d\) , of this arithmetic sequence.</p>
<p>(ii) Write down the distance the coin falls during the fourth second.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the distance the coin falls during the \(15{\text{th}}\) second.</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>Calculate the <strong>total</strong> distance the coin falls in the first \(15\) seconds. Give your answer in kilometres.</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>Prachi drops the coin from a height of \(1800\) metres above the ground.</p>
<p>Calculate the time, to the nearest second, the coin will take to reach the ground.</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>Prachi visits a tourist centre nearby. It opened at the start of \(2015\) and in the first year there were \(17\,000\) visitors. The number of people who visit the tourist centre is expected to increase by \(10\,\% \) each year.</p>
<p>Calculate the number of people expected to visit the tourist centre in \(2016\).</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>Calculate the total number of people expected to visit the tourist centre during the first \(10\) years since it opened.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A lobster trap is made in the shape of half a cylinder. It is constructed from a steel frame with netting pulled tightly around it. The steel frame consists of a rectangular base, two semicircular ends and two further support rods, as shown in the following diagram.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; min-height: 25px; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-20_om_14.54.16.png" alt><br></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The semicircular ends each have radius \(r\) and the support rods each have length \(l\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(T\) be the total length of steel used in the frame of the lobster trap.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down an expression for \(T\) in terms of \(r\), \(l\) and \(\pi \).</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><span>The volume of the lobster trap is \(0.75{\text{ }}{{\text{m}}^{\text{3}}}\).</span></p>
<p><span>Write down an equation for the volume of the lobster trap in terms of \(r\), \(l\) and \(\pi \).</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><span>The volume of the lobster trap is \(0.75{\text{ }}{{\text{m}}^{\text{3}}}\).</span></p>
<p><span>Show that \(T = (2\pi + 4)r + \frac{6}{{\pi {r^2}}}\).</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><span>The volume of the lobster trap is \(0.75{\text{ }}{{\text{m}}^{\text{3}}}\).</span></p>
<p><span>Find \(\frac{{{\text{d}}T}}{{{\text{d}}r}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The lobster trap is designed so that the length of steel used in its frame is a minimum.</span></p>
<p><span>Show that the value of \(r\) for which \(T\) is a minimum is \(0.719 {\text{ m}}\), correct to three significant figures.</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><span>The lobster trap is designed so that the length of steel used in its frame is a minimum.</span></p>
<p><span>Calculate the value of \(l\) for which \(T\) is a minimum.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The lobster trap is designed so that the length of steel used in its frame is a minimum.</span></p>
<p><span>Calculate the minimum value of \(T\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A water container is made in the shape of a cylinder with internal height \(h\) cm and internal base radius \(r\) cm.</p>
<p class="p2" style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_08.31.01.png" alt="N16/5/MATSD/SP2/ENG/TZ0/06"></p>
<p class="p1">The water container has no top. The inner surfaces of the container are to be coated with a water-resistant material.</p>
</div>
<div class="specification">
<p class="p1">The volume of the water container is \(0.5{\text{ }}{{\text{m}}^3}\).</p>
</div>
<div class="specification">
<p class="p1">The water container is designed so that the area to be coated is minimized.</p>
</div>
<div class="specification">
<p class="p1">One can of water-resistant material coats a surface area of \(2000{\text{ c}}{{\text{m}}^2}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down a formula for \(A\), <span class="s1">the surface area to be coated.</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 class="p1">Express this volume in \({\text{c}}{{\text{m}}^3}\).</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 class="p1"><span class="s1">Write down, in terms of \(r\) </span>and \(h\), an equation for the volume of this water container.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \(A = \pi {r^2}\frac{{1\,000\,000}}{r}\).</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 class="p1">Show that \(A = \pi {r^2} + \frac{{1\,000\,000}}{r}\).</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 \(\frac{{{\text{d}}A}}{{{\text{d}}r}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Using your answer to part (e), find the value of \(r\) <span class="s1">which minimizes \(A\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of this minimum area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the least number of cans of water-resistant material that will coat the area in <span class="s1">part (g).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">On Monday Paco goes to a running track to train. He runs the first lap of the track</span> <span style="font-size: medium; font-family: times new roman,times;">in 120 seconds. Each lap Paco runs takes him 10 seconds longer than his previous lap.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the time, in seconds, Paco takes to run his fifth lap.</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><span>Paco runs his last lap in 260 seconds.</span></p>
<p><span>Find how many laps he has run on Monday.</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><span>Find the <strong>total</strong> time, in <strong>minutes,</strong> run by Paco on Monday.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>On Wednesday Paco takes Lola to train. They both run the first lap of the track in 120 seconds. Each lap Lola runs takes 1.06 times as long as her previous lap.</span></p>
<p><span>Find the time, in seconds, Lola takes to run her third lap.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the <strong>total</strong> time, in seconds, Lola takes to run her first four laps.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Each lap Paco runs again takes him 10 seconds longer than his previous lap. After a certain number of laps Paco takes less time per lap than Lola.</span></p>
<p><span>Find the number of the lap when this happens.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the function \(f(x) = {x^3} + \frac{{48}}{x}{\text{, }}x \ne 0\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate \(f(2)\) .</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><span>Sketch the graph of the function \(y = f(x)\) for \( - 5 \leqslant x \leqslant 5\) and \( - 200 \leqslant y \leqslant 200\) .</span></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><span>Find \(f'(x)\) .</span></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><span>Find \(f'(2)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the coordinates of the local maximum point on the graph of \(f\) .</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;">
<address><span>Find the range of \(f\) .</span></address>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the gradient of the tangent to the graph of \(f\) at \(x = 1\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>There is a second point on the graph of \(f\) at which the tangent is parallel to the tangent at \(x = 1\). </span></p>
<p><span>Find the \(x\)-coordinate of this point.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The Brahma chicken produces eggs with weights in grams that are normally distributed about a mean of \(55{\text{ g}}\) with a standard deviation of \(7{\text{ g}}\). The eggs are classified as small, medium, large or extra large according to their weight, as shown in the table below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sketch a diagram of the distribution of the weight of Brahma chicken eggs. On your diagram, show clearly the boundaries for the classification of the eggs.</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><span>An egg is chosen at random. Find the probability that the egg is</span><br><span>(i) medium;</span><br><span>(ii) extra large.</span></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><span>There is a probability of \(0.3\) that a randomly chosen egg weighs more than \(w\) grams.</span></p>
<p><span>Find \(w\) .</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><span>The probability that a Brahma chicken produces a large size egg is \(0.121\). Frank’s Brahma chickens produce \(2000\) eggs each month.</span></p>
<p><span>Calculate an estimate of the number of large size eggs produced by Frank’s chickens each month.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The selling price, in US dollars (USD), of each size is shown in the table below.</span><br><span><img src="data:image/png;base64,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" alt></span><br><span>The probability that a Brahma chicken produces a small size egg is \(0.388\).</span></p>
<p><span>Estimate the monthly income, in USD, earned by selling the \(2000\) eggs. Give your answer correct to two decimal places.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A manufacturer has a contract to make \(2600\) solid blocks of wood. Each block is in the shape of a right triangular prism, \({\text{ABCDEF}}\), as shown in the diagram.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{AB}} = 30{\text{ cm}},{\text{ BC}} = 24{\text{ cm}},{\text{ CD}} = 25{\text{ cm}}\) and angle \({\rm{A\hat BC}} = 35^\circ {\text{ }}\).</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/Schermafbeelding_2014-09-03_om_12.17.46.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the length of \({\text{AC}}\).</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><span>Calculate the area of triangle \({\text{ABC}}\).</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><span>Assuming that no wood is wasted, show that the volume of wood required to make all \(2600\) blocks is \({\text{13}}\,{\text{400}}\,{\text{000 c}}{{\text{m}}^3}\), correct to three significant figures.</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><span>Write \({\text{13}}\,{\text{400}}\,{\text{000}}\) in the form \(a \times {10^k}\) where \(1 \leqslant a < 10\) and \(k \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the total surface area of one block is \({\text{2190 c}}{{\text{m}}^2}\), correct to three significant figures.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The blocks are to be painted. One litre of paint will cover \(22{\text{ }}{{\text{m}}^2}\).</span></p>
<p><span>Calculate the number of litres required to paint all \(2600\) blocks.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the function \(f(x) = \frac{{96}}{{{x^2}}} + kx\), where \(k\) is a constant and \(x \ne 0\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down \(f'(x)\).</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 class="p1">The graph of \(y = f(x)\) has a local minimum point at \(x = 4\).</p>
<p class="p1">Show that \(k = 3\).</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 class="p1">The graph of \(y = f(x)\) has a local minimum point at \(x = 4\).</p>
<p class="p1">Find \(f(2)\).</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="p1">The graph of \(y = f(x)\) has a local minimum point at \(x = 4\).</p>
<p class="p1">Find \(f'(2)\)</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 class="p1">The graph of \(y = f(x)\) has a local minimum point at \(x = 4\).</p>
<p class="p1">Find the equation of the normal to the graph of \(y = f(x)\) at the point where \(x = 2\).</p>
<p class="p1">Give your answer in the form \(ax + by + d = 0\) where \(a,{\text{ }}b,{\text{ }}d \in \mathbb{Z}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The graph of \(y = f(x)\) has a local minimum point at \(x = 4\).</p>
<p class="p1"><span class="s1">Sketch the graph of \(y = f(x)\)</span>, for \( - 5 \leqslant x \leqslant 10\) and \( - 10 \leqslant y \leqslant 100\)<span class="s1">.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The graph of \(y = f(x)\) has a local minimum point at \(x = 4\).</p>
<p class="p1">Write down the coordinates of the point where the graph of \(y = f(x)\) intersects the \(x\)-axis.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The graph of \(y = f(x)\) has a local minimum point at \(x = 4\).</p>
<p class="p1">State the values of \(x\) for which \(f(x)\) is decreasing.</p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Cedric wants to buy an €8000 car. The car salesman offers him a loan repayment option of a 25 % deposit followed by 12 equal monthly payments of €600 .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the amount of the deposit.</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><span>Calculate the total cost of the loan under this repayment scheme.</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><span>Cedric’s mother decides to help him by giving him an interest free loan of €8000 to buy the car. She arranges for him to repay the loan by paying her €<em>x</em> in the first month and €<em>y</em> in every following month until the €8000 is repaid.</span></p>
<p><span>The total amount that Cedric’s mother receives after <strong>12</strong> months is €3500. This can be written using the equation <em>x</em> +11<em>y</em> = 3500. The total amount that Cedric’s mother receives after <strong>24</strong> months is €7100.</span></p>
<p><span>Write down a second equation involving <em>x</em> and <em>y</em>.</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><span>Cedric’s mother decides to help him by giving him an interest free loan of €8000 to buy the car. She arranges for him to repay the loan by paying her €<em>x</em> in the first month and €<em>y</em> in every following month until the €8000 is repaid.</span></p>
<p><span>The total amount that Cedric’s mother receives after <strong>12</strong> months is €3500. This can be written using the equation <em>x</em> +11<em>y</em> = 3500. The total amount that Cedric’s mother receives after <strong>24</strong> months is €7100.</span></p>
<p><span>Write down the value of <em>x</em> and the value of <em>y</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Cedric’s mother decides to help him by giving him an interest free loan of €8000 to buy the car. She arranges for him to repay the loan by paying her €<em>x</em> in the first month and €<em>y</em> in every following month until the €8000 is repaid.</span></p>
<p><span>The total amount that Cedric’s mother receives after <strong>12</strong> months is €3500. This can be written using the equation <em>x</em> +11<em>y</em> = 3500. The total amount that Cedric’s mother receives after <strong>24</strong> months is €7100.</span></p>
<p><span>Calculate the number of months it will take Cedric’s mother to receive the €8000.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Cedric decides to buy a cheaper car for €6000 and invests the remaining €2000 at his bank. The bank offers two investment options over three years.</span></p>
<p><span>Option A: Compound interest at an annual rate of 8 %.</span></p>
<p><span>Option B: Compound interest at a nominal annual rate of 7.5 % , <strong>compounded monthly</strong>.</span></p>
<p><em><strong><span>Express each answer in part (f) to the nearest euro.</span></strong></em></p>
<p><span>Calculate the value of his investment at the end of three years if he chooses</span></p>
<p><span>(i) Option A;</span></p>
<p><span>(ii) Option B.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the average body weight, \(x\), and the average weight of the brain, \(y\), of seven species of mammal. Both measured in kilograms (kg).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_10.57.27.png" alt="M17/5/MATSD/SP2/ENG/TZ1/01"></p>
</div>
<div class="specification">
<p>The average body weight of grey wolves is 36 kg.</p>
</div>
<div class="specification">
<p>In fact, the average weight of the brain of grey wolves is 0.120 kg.</p>
</div>
<div class="specification">
<p>The average body weight of mice is 0.023 kg.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the range of the average body weights for these seven species of mammal.</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>For the data from these seven species calculate \(r\), the Pearson’s product–moment correlation coefficient;</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>For the data from these seven species describe the correlation between the average body weight and the average weight of the brain.</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>Write down the equation of the regression line \(y\) on \(x\), in the form \(y = mx + c\).</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>Use your regression line to estimate the average weight of the brain of grey wolves.</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 percentage error in your estimate in part (d).</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>State whether it is valid to use the regression line to estimate the average weight of the brain of mice. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">In a college 450 students were surveyed with the following results</span></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">150 have a television</span></em></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">205 have a computer</span></em></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">220 have an iPhone</span></em></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">75 have an iPhone and a computer</span></em></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">60 have a television and a computer</span></em></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">70 have a television and an iPhone</span></em></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">40 have all three.</span></em></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a Venn diagram to show this information. Use <em>T</em> to represent the set of students who have a television,<em> C</em> the set of students who have a computer and <em>I</em> the set of students who have an iPhone.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of students that</span></p>
<p><span>(i) have a computer only;</span></p>
<p><span>(ii) have an iPhone and a computer but no television.</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><span>Write down \(n[T \cap (C \cup I)']\).</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><span>Calculate the number of students who have none of the three.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Two students are chosen at random from the 450 students. Calculate the probability that</span></p>
<p><span>(i) neither student has an iPhone;</span></p>
<p><span>(ii) only one of the students has an iPhone.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The students are asked to collect money for charity. In the first month, the students collect <em>x</em> dollars and the students collect <em>y</em> dollars in each subsequent month. In the first 6 months, they collect 7650 dollars. This can be represented by the equation <em>x</em> + 5<em>y</em> = 7650.</span></p>
<p><span>In the first 10 months they collect 13 050 dollars.</span></p>
<p><span>(i) Write down a second equation in <em>x</em> and <em>y</em> to represent this information.</span></p>
<p><span>(ii) Write down the value of <em>x</em> and of <em>y </em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The students are asked to collect money for charity. In the first month, the students collect <em>x</em> dollars and the students collect <em>y</em> dollars in each subsequent month. In the first 6 months, they collect 7650 dollars. This can be represented by the equation <em>x</em> + 5<em>y</em> = 7650.</span></p>
<p><span>In the first 10 months they collect 13 050 dollars.</span></p>
<p><span>Calculate the number of months that it will take the students to collect 49 500 dollars.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the function <em>f </em>(<em>x</em>) = <em>x</em><sup>3 </sup><em>–</em> 3x– 24<em>x</em> + 30.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down <em>f</em> (0).</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><span>Find \(f'(x)\).</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><span>Find the gradient of the graph of <em>f</em> (<em>x</em>) at the point where <em>x</em> = 1.</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><span>(i) Use </span><em>f '</em><span>(</span><em>x</em><span>) to find the </span><em>x</em><span>-coordinate of M and of N.</span></p>
<p><span>(ii) Hence or otherwise write down the coordinates of M and of N.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sketch the graph of <em>f</em> (<em>x</em>) for \( - 5 \leqslant x \leqslant 7\) and \( - 60 \leqslant y \leqslant 60\). Mark clearly M and N on your graph.</span></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><span>Lines <em>L</em><sub>1</sub> and <em>L</em><sub>2</sub> are parallel, and they are tangents to the graph of <em>f</em> (<em>x</em>) at points A and B respectively. <em>L<sub>1</sub></em> has equation <em>y</em> = 21<em>x</em> + 111.</span></p>
<p><span>(i) Find the <em>x</em>-coordinate of A and of B.</span></p>
<p><span>(ii) Find the <em>y</em>-coordinate of B.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<h1><span style="font-family: times new roman,times; font-size: medium;">Part A</span></h1>
<p><span style="font-family: times new roman,times; font-size: medium;">100 students are asked what they had for breakfast on a particular morning.</span> <span style="font-family: times new roman,times; font-size: medium;">There were three choices: cereal (<em>X</em>) , bread (<em>Y</em>) and fruit (<em>Z</em>). It is found that</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">10 students had all three</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">17 students had bread and fruit only</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">15 students had cereal and fruit only</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">12 students had cereal and bread only</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">13 students had only bread</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">8 students had only cereal</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">9 students had only fruit</span></p>
</div>
<div class="specification">
<h1><span style="font-family: times new roman,times; font-size: medium;">Part B</span></h1>
<p><span style="font-family: times new roman,times; font-size: medium;">The same 100 students are also asked how many meals on average they have per day. The data collected is organized in the following table.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">A \({\chi ^2}\) test is carried out at the 5 % level of significance.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Represent this information on a Venn diagram.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">A.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of students who had none of the three choices for breakfast.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the percentage of students who had fruit for breakfast.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Describe in words what the students in the set \(X \cap Y'\) had for breakfast.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that a student had <strong>at least</strong> two of the three choices for breakfast.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Two students are chosen at random. Find the probability that both students had all three choices for breakfast.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">A.f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the null hypothesis, H<sub>0</sub>, for this test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of degrees of freedom for this test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the critical value for this test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the expected number of females that have more than 5 meals per day is 13, correct to the nearest integer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find the \(\chi _{calc}^2\) for this data.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Decide whether H<sub>0</sub> must be accepted. Justify your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.f.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows two triangles, OBC and OBA, on a set of axes. Point C lies on the \(y\)-axis, and O is the origin.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-04_om_16.03.31.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The equation of the line BC is \(y = 4\).</p>
<p class="p1">Write down the coordinates of point C.</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 class="p1">The \(x\)-coordinate of point B is \(a\).</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Write down the coordinates of point B;</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Write down the gradient of the line OB.</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 class="p1">Point A lies on the \(x\)-axis and the line AB is perpendicular to line OB.</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Write down the gradient of line AB.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Show that the equation of the line AB is \(4y + ax - {a^2} - 16 = 0\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The area of triangle AOB is <strong>three times</strong> the area of triangle OBC.</p>
<p class="p1">Find an expression, <strong>in terms of <em>a</em></strong>, for</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>the area of triangle OBC;</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>the <em>x</em>-coordinate of point A.</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 class="p1">Calculate the value of \(a\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A pan, in which to cook a pizza, is in the shape of a cylinder. The pan has a diameter of 35 cm and a height of 0.5 cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_11.14.51.png" alt="M17/5/MATSD/SP2/ENG/TZ1/04"></p>
</div>
<div class="specification">
<p>A chef had enough pizza dough to exactly fill the pan. The dough was in the shape of a sphere.</p>
</div>
<div class="specification">
<p>The pizza was cooked in a hot oven. Once taken out of the oven, the pizza was placed in a dining room.</p>
<p>The temperature, \(P\), of the pizza, in degrees Celsius, °C, can be modelled by</p>
<p>\[P(t) = a{(2.06)^{ - t}} + 19,{\text{ }}t \geqslant 0\]</p>
<p>where \(a\) is a constant and \(t\) is the time, in minutes, since the pizza was taken out of the oven.</p>
<p>When the pizza was taken out of the oven its temperature was 230 °C.</p>
</div>
<div class="specification">
<p>The pizza can be eaten once its temperature drops to 45 °C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the volume of this pan.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the radius of the sphere in cm, correct to one decimal place.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(a\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the temperature that the pizza will be 5 minutes after it is taken out of the oven.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, to the nearest second, the time since the pizza was taken out of the oven until it can be eaten.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the context of this model, state what the value of 19 represents.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Antonio and Barbara start work at the same company on the same day. They each earn an annual salary of \(8000\) euros during the first year of employment. The company gives them a salary increase following the completion of each year of employment. Antonio is paid using plan A and Barbara is paid using plan B.</p>
<p>Plan A: The annual salary increases by \(450\) euros each year.</p>
<p>Plan B: The annual salary increases by \(5\,\% \) each year.</p>
<p>Calculate</p>
<p>i) Antonio’s annual salary during his second year of employment;</p>
<p>ii) Barbara’s annual salary during her second year of employment.</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 an expression for</p>
<p>i) Antonio’s annual salary during his \(n\) th year of employment;</p>
<p>ii) Barbara’s annual salary during her \(n\) th year of employment.</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>Determine the number of years for which Antonio’s annual salary is greater than or equal to Barbara’s annual salary.</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>Both Antonio and Barbara plan to work at the company for a total of \(15\) years.</p>
<p>i) Calculate the <strong>total amount</strong> that <strong>Barbara</strong> will be paid during these \(15\) years.</p>
<p>ii) Determine whether Antonio earns more than Barbara during these \(15\) years.</p>
<div class="marks">[7]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A cross-country running course consists of a beach section and a forest section. Competitors run from \({\text{A}}\) to \({\text{B}}\), then from \({\text{B}}\) to \({\text{C}}\) and from \({\text{C}}\) back to \({\text{A}}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The running course from \({\text{A}}\) to \({\text{B}}\) is along the beach, while the course from \({\text{B}}\), through \({\text{C}}\) and back to \({\text{A}}\), is through the forest.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The course is shown on the following diagram.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-02_om_11.39.47.png" alt><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Angle \({\text{ABC}}\) is \(110^\circ\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">It takes Sarah \(5\) minutes and \(20\) seconds to run from \({\text{A}}\) to \({\text{B}}\) at a speed of \(3.8{\text{ m}}{{\text{s}}^{ - 1}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using ‘<em>distance </em>= <em>speed </em>\( \times \) <em>time</em>’, show that the distance from \({\text{A}}\) to \({\text{B}}\) is \(1220\) metres correct to 3 significant figures.</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><span>The distance from \({\text{B}}\) to \({\text{C}}\) is \(850\) metres. Running this part of the course takes Sarah \(5\) minutes and \(3\) seconds.</span></p>
<p><span>Calculate the speed, in \({\text{m}}{{\text{s}}^{ - 1}}\), that Sarah runs from \({\text{B}}\) to \({\text{C}}\).</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><span>The distance from \({\text{B}}\) to \({\text{C}}\) is \(850\) metres. Running this part of the course takes Sarah \(5\) minutes and \(3\) seconds.</span></p>
<p><span><span><span>Calculate the distance, in metres, from </span></span><span><span>\({\mathbf{C}}\)</span></span><span><span> </span></span><strong><span><span>to </span></span></strong><span><span>\({\mathbf{A}}\).</span></span></span></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><span>The distance from \({\text{B}}\) to \({\text{C}}\) is \(850\) metres. Running this part of the course takes Sarah \(5\) minutes and \(3\) seconds.</span></p>
<p><span>Calculate the total distance, in metres, of the cross-country running course.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The distance from \({\text{B}}\) to \({\text{C}}\)</span><span> is \(850\) metres. Running this part of the course takes Sarah \(5\) minutes and \(3\) seconds.</span></p>
<p><span>Find the size of angle \({\text{BCA}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The distance from \({\text{B}}\) to \({\text{C}}\)</span><span> is \(850\) metres. Running this part of the course takes Sarah \(5\) minutes and \(3\) seconds.</span></p>
<p><span>Calculate the area of the cross-country course bounded by the lines \({\text{AB}}\), \({\text{BC}}\) and \({\text{CA}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The cumulative frequency graph shows the speed, \(s\)<span class="s1">, in \({\text{km}}\,{{\text{h}}^{ - 1}}\), of \(120\) </span>vehicles passing a hospital gate.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-21_om_07.03.09.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Estimate the minimum possible speed of one of these vehicles passing the hospital gate.</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 class="p1">Find the median speed of the vehicles.</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 class="p1">Write down the <span class="s1">\({75^{{\text{th}}}}\) </span>percentile.</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 class="p1">Calculate the interquartile range.</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 class="p1">The speed limit past the hospital gate is \(50{\text{ km}}\,{{\text{h}}^{ - 1}}\).</p>
<p class="p1">Find the number of these vehicles that exceed the speed limit.</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 class="p1">The table shows the speeds of these vehicles travelling past the hospital gate.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-21_om_07.07.41.png" alt></p>
<p class="p1">Find the value of \(p\) and of \(q\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The table shows the speeds of these vehicles travelling past the hospital gate.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-21_om_07.07.41.png" alt></p>
<p class="p1">(i) Write down the modal class.</p>
<p class="p1">(ii) Write down the mid-interval value for this class.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The table shows the speeds of these vehicles travelling past the hospital gate.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-21_om_07.07.41.png" alt></p>
<p class="p1">Use your graphic display calculator to calculate an estimate of</p>
<p class="p1">(i) the mean speed of these vehicles;</p>
<p class="p1">(ii) the standard deviation.</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">It is proposed that the speed limit past the hospital gate is reduced to \(40{\text{ km}}\,{{\text{h}}^{ - 1}}\) from the current \(50{\text{ km}}\,{{\text{h}}^{ - 1}}\)<span class="s1">.</span></p>
<p class="p2">Find the percentage of these vehicles passing the hospital gate that <strong>do not </strong>exceed the current speed limit but <strong>would </strong>exceed the new speed limit.</p>
<div class="marks">[2]</div>
<div class="question_part_label">i.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For an ecological study, Ernesto measured the average concentration \((y)\) of the fine dust, \({\text{PM}}10\), in the air at different distances \((x)\) from a power plant. His data are represented on the following scatter diagram. The concentration of \({\text{PM}}10\) is measured in micrograms per cubic metre and the distance is measured in kilometres.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAp4AAALiCAYAAABwltYpAAAgAElEQVR4AezdCXxU1dnH8T8RLGBEQRAEFDAJVhapKCrQIiJq0RYRWyviAlU2N7S4gyLaRVxQxKUEFKhbXUF8xVcLgr4sKjWKLCoBWQREWYUIkWXu+7mBhEkmyTkzc2bIzfzm84Hcuffc+zzne+/k82SWZ6p4nueJGwIIIIAAAggggAACCRZIS/DxOTwCCCCAAAIIIIAAAgUCFJ5cCAgggAACCCCAAAJJEaDwTAozQRBAAAEEEEAAAQQoPLkGEEAAAQQQQAABBJIiQOGZFGaCIIAAAggggAACCKRY4blH66fcqMymzZTZtKUueHS+8gqugZC2zRquk1rcrDfX7eKqQAABBBBAAAEEEEiAQIoVnlXVoMfjWvbN/+ruNtLXsxbru5Cvmqb0X3ZSzyZbtfWnghUJoOaQCCCAAAIIIIBAagukWOG5/2SnNVLrzk2k1Vu0fX+dmXZ0YzVreqpaH3Noal8RzB4BBBBAAAEEEEiQQGoWnqqqw2vXkbas0Lcb90japXVTn1POeb/Xr9KLk+zcuVPXXXttgvg5LAIIIIAAAgggkDoCxauslJl3VR1+ZJ0Ds81boNc/O123dz9OJUEmTZykd6e9ozenTDkwniUEEEAAAQQQQACBqAVK1llRHyCYO6Sp5pG1VVPLtOLb5Zo16n0dN+A8NSyhkZubq4dHjiyY4ujHHpP/7Cc3BBBAAAEEEEAAgdgESpRasR0keHulqWatI3WotuiLseP1f52u0O8bRr63c9LEibq092UF06tfv778Zz+5IYAAAggggAACCMQmkKKFp5R2eG0dK6nqr/vo5s4NI15inzdvnv79wosatP/9nTfedFPBs59r166NTZq9EEAAAQQQQACBFBdI2cJTqqpjrvqr7ruypdJLXAT+S+qPP/aYbrn9djVq1Khga/v27Que/Xz6qadKjOYuAggggAACCCCAgI1AahaeefP15KQ0Db71LDUoReC9d9/V999/r6v6XFXM8Ko+fQqeBV2wYEGx9dxBAAEEEEAAAQQQMAuUUnaZdwrkiLz5eqzbObpz4hsa88Dn6njHpTqhROskf16bN2+W/0GiwTfdpBo1ahSbalZWVsGzoA/8/e980KiYDHcQQAABBBBAAAGzQOoUnqGftGnVOn2xLF8dr79KbUspOn2uZ8aPl/9Bogt79ChV75I/XVLwbKj/rCg3BBBAAAEEEEAAAXuBKp7nefbDK/9I/2X0mjVryn92s/Dmf7f7spUrCu+qtDFFG1lAAAEEEEAAAQQQKFWAwrNUluIrSxaexbdyDwEEEEAAAQQQQMBGIHVearfRYAwCCCCAAAIIIIBAwgQoPBNGy4ERQAABBBBAAAEEwgUoPMM1WEYAAQQQQAABBBBImACFZ8JoOTACCCCAAAIIIIBAuACFZ7gGywgggAACCCCAAAIJE6DwTBgtB0YAAQQQQAABBBAIF6DwDNdgGQEEEEAAAQQQQCBhAhSeCaPlwAgggAACCCCAAALhAhSe4RosI4AAAggggAACCCRMgMIzYbQcGAEEEEAAAQQQQCBcgMIzXINlBBBAAAEEEEAAgYQJUHgmjJYDI4AAAggggAACCIQLVA2/k8rLvXr1Lnf6pu3l7sxGBBBAAAEEEEDgIAu89NILBzkDSR43o0BGk6bGMTPe/6DcMabt/s6mMStXrvb8f+XdLr30svI2F2xzEcd0DD+Qacx//jPd8/+VdzMdwyaOjZtNHJOtqzimXGzimHK1cbMZY8rV5hj+GFO+ruKYjvPZ5194W7f+6KdU5s2Uq7+jizimY9jEcZGrTRwXufpxTPnanB8XudjEMeWaTDfTnF3kamNiysPGxEWuNnFc5GpzzZri+L9vfNvybqZj2MzXJtfycnC5jZfaD37tTwYIIIAAAggggEBKCFB4psRpZpIIIIAAAggggMDBF6DwPPjngAwQQAABBBBAAIGUEKDwTInTzCQRQAABBBBAAIGDL0DhefDPARkggAACCCCAAAIpIUDhmRKnmUkigAACCCCAAAIHX4DC8+CfAzJAAAEEEEAAAQRSQqCK35spJWYaxyQzmzZT9oRJcRwhebuOyx6rfv0HJC9gHJEWL1pUsHfLVq3iOErydg2SbZBy9c9gkPIl18Q95rBNjC2uiXEN4u8uGsi77EiawGPRQD4S10VDWxrIR7r6a0y2NJCPzc3G1qZJtosG1zZxTNeBzXxc5GoTx0WufhxTvslys4ljyjWZbiZ/F7namJjysDFxkatNHBe52lyzpjg0kE/cHwUcGQEEEEAAAQQQQCDFBXiPZ4pfAEwfAQQQQAABBBBIlgCFZ7KkiYMAAggggAACCKS4AIVnil8ATB8BBBBAAAEEEEiWAIVnsqSJgwACCCCAAAIIpLgAhWeKXwBMHwEEEEAAAQQQSJYAhWeypImDAAIIIIAAAgikuAAN5C0uABrIWyDFMIQG8jGgWe4SpIbR/pSClC+5Wl6EMQzDNgY0i11wtUCKcUjQbGkg73dfDcCNBvKRJ8nUFNffwzSGBvKRrjZuNJCPzc3G1qZJtosG1zZxTI8fm/m4yNUmjotc/TimfJPlZhPHlGsy3Uz+LnK1MTHlYWPiIlebOC5ytblmTXFoIB9jxc9uCCCAAAIIIIAAAgiYBHiPp0mI7QgggAACCCCAAAJOBCg8nTByEAQQQAABBBBAAAGTAIWnSYjtCCCAAAIIIIAAAk4EKDydMHIQBBBAAAEEEEAAAZMAhadJiO0IIIAAAggggAACTgTo42nBSB9PC6QYhtDHMwY0y12C1FvOn1KQ8iVXy4swhmHYxoBmsQuuFkgxDgmaLX08/SZYAbjRxzPyJJl6k/l7mMbQxzPS1caNPp6xudnY2vQqdNFn0CaO6fFjMx8XudrEcZGrH8eUb7LcbOKYck2mm8nfRa42JqY8bExc5GoTx0WuNtesKQ59PGOs+NkNAQQQQAABBBBAAAGTAO/xNAmxHQEEEEAAAQQQQMCJAIWnE0YOggACCCCAAAIIIGASoPA0CbEdAQQQQAABBBBAwIkAhacTRg6CAAIIIIAAAgggYBKg8DQJsR0BBBBAAAEEEEDAiQCFpxNGDoIAAggggAACCCBgEqCBvElIEg3kLZBiGEID+RjQLHcJUlNjf0pBypdcLS/CGIZhGwOaxS64WiDFOCRotjSQ97uvBuBGA/nIk2RqiuvvYRpDA/lIVxs3GsjH5mZja9Mk20WDa5s4psePzXxc5GoTx0WufhxTvslys4ljyjWZbiZ/F7namJjysDFxkatNHBe52lyzpjg0kI+x4mc3BBBAAAEEEEAAAQRMAhXwPZ7blDvrLU1+tJ9OHTZL2wwzCK2bomtbXK5JufklRu7S+pwXdXe3lsps2l79H5+n9aESQ7iLAAIIIIAAAgggkDSBClZ45it34u36x/Mvavjo6dplYgit1lv3j9R7O0oODCkvZ6yuHrpCZ0/4TMu+eV2XbXpYV4+er7ySQ7mPAAIIIIAAAgggkBSBClZ4VldWn6f1bPa9GtKmpgFgq3JGP6qPjvqlIkaGcvX6iKlqe/sAdW5wqJTWUJ2H3KC240br9YhnRg1h2IwAAggggAACCCDgRKCCFZ62c/Kf0XxB/9SluqHrcRE7hZbP05QF9ZXZKP3AtlqtdHbP7zVlzirxivsBFpYQQAABBBBAAIFkCQSz8Mz7VOOfkgb2O0VhpeV+s3wtnzNdC2tmqEn9Q0s47tLCyfO0nMqzhAt3EUAAAQQQQACBxAsEsPDcqpxxr0jX9lbb9NLSz9PaZd9KWc3UqNTtiUclAgIIIIAAAggggECkQMVsIB/6WpMu6qlHWj+p2X/trFpFefsvsT+jh1efp3t6HKc0hbRt1gj9us9yDfnPeF2VVV3SRs0adrGuWdhX70zuo6yi2rSs9fsO3qtX76IoJRfmz5urdu07lFzNfQQQQAABBBBAIDACNJD3u6+Wdtv7lTexewuv9dCZ3o/h27d/4j1+z1Rv7d7ClXu9H2fe47Vu0tubuHTn/pU7vaUTensZJ97jzfyxaKDneRu8mUM7eRndJ3hLw1cXHqqcnzSQj8QxNcX19zCNoYF8pKuNGw3kY3OzsbVpku2iwbVNHNPjx2Y+LnK1ieMiVz+OKd9kudnEMeWaTDeTv4tcbUxMediYuMjVJo6LXG2uWVOcVGwgXzUwZbr/7OZ//0fjJv1LoyfdGJH2/eecqPvbDC94ljOjY1e11oriY0KbtGrhdrW+qL0yip4FLT6EewgggAACCCCAAAKJEwhQ4ZmmWp1H6IuVI8I0SnupXVJGe/XIekEzcjarc+e6+8bnfadluS3Uo2MTUXeGEbKIAAIIIIAAAggkSaBy1mBpWbp4eHfljByrWet3SaF1mvXIGOX0G6yLC94HmiRdwiCAAAIIIIAAAggUCVSwwtN/BnO4Tjr+t7p/wQ7teL6v2jYt7eswi/IvYyFN6W0H6Jn7jtKLXU5Q5vGDNCPzDj0zuF0p7ZfKOASrEUAAAQQQQAABBJwKVLCX2kt7Ob28+RaOL23MoWrQbqCylwwsbSPrEEAAAQQQQAABBJIsUMGe8Uzy7AmHAAIIIIAAAgggkDSBitnHM2nTtwuU2bSZsidMsht8kEeNyx6rfv0HHOQs7MIvXrSoYGDLVq3sdjjIo4JkG6Rc/dMapHzJNXEPRGwTY4trYlyD+LuLPp5+E6wA3OjjGXmSTL3J/D1MY+jjGelq40Yfz9jcbGxtehW66DNoE8f0+LGZj4tcbeK4yNWPY8o3WW42cUy5JtPN5O8iVxsTUx42Ji5ytYnjIleba9YUJxX7ePJSe+L+EOLICCCAAAIIIIAAAmECFJ5hGCwigAACCCCAAAIIJE6AwjNxthwZAQQQQAABBBBAIEyAwjMMg0UEEEAAAQQQQACBxAlQeCbOliMjgAACCCCAAAIIhAlQeIZhsIgAAggggAACCCCQOAEKz8TZcmQEEEAAAQQQQACBMAEayIdhlLVIA/myZOJbTwP5+PzK2ztIDaP9eQQpX3It78qLbxu28fmVtTeuZcnEvz5otjSQ97uvBuBGA/nIk2RqiuvvYRpDA/lIVxs3GsjH5mZja9Mk20WDa5s4psePzXxc5GoTx0WufhxTvslys4ljyjWZbiZ/F7namJjysDFxkatNHBe52lyzpjg0kI+/+OcICCCAAAIIIIAAAgiUKsB7PEtlYSUCCCCAAAIIIICAawEKT9eiHA8BBBBAAAEEEECgVAEKz1JZWIkAAggggAACCCDgWoDC07Uox0MAAQQQQAABBBAoVYDCs1QWViKAAAIIIIAAAgi4FqDwdC3K8RBAAAEEEEAAAQRKFaCBfKksxVfSQL64h6t7NJB3JRl5nCA1NfazD1K+5Bp5vblag60ryeLHwbW4h8t7QbOlgbzffTUANxrIR54kU1Ncfw/TGBrIR7rauNFAPjY3G1ubJtkuGlzbxDE9fmzm4yJXmzgucvXjmPJNlptNHFOuyXQz+bvI1cbElIeNiYtcbeK4yNXmmjXFoYG8yz8DOBYCCCCAAAIIIIAAAmECvMczDINFBBBAAAEEEEAAgcQJUHgmzpYjI4AAAggggAACCIQJUHiGYbCIAAIIIIAAAgggkDgBCs/E2XJkBBBAAAEEEEAAgTABCs8wDBYRQAABBBBAAAEEEidAH08LW/p4WiDFMIQ+njGgWe4SpN5y/pSClC+5Wl6EMQzDNgY0i11wtUCKcUjQbOnj6TfBCsCNPp6RJ8nUm8zfwzSGPp6RrjZu9PGMzc3G1qZXoYs+gzZxTI8fm/m4yNUmjotc/TimfJPlZhPHlGsy3Uz+LnK1MTHlYWPiIlebOC5ytblmTXHo4xljxc9uCCCAAAIIIIAAAgiYBHiPp0mI7QgggAACCCCAAAJOBCg8nTByEAQQQAABBBBAAAGTAIWnSYjtCCCAAAIIIIAAAk4EKDydMHIQBBBAAAEEEEAAAZMAhadJiO0IIIAAAggggAACTgQoPJ0wchAEEEAAAQQQQAABkwAN5PcL9erVu0yr+fPmql37DmVuZwMCCCCAAAIIIFDRBWgg73dfDcCNBvKRJ8nUFNffwzSGBvKRrjZuNJCPzc3G1qZJtosG1zZxTI8fm/m4yNUmjotc/TimfJPlZhPHlGsy3Uz+LnK1MTHlYWPiIlebOC5ytblmTXFoIF/RS3XyQwABBBBAAAEEEAisAO/xDOypI3EEEEAAAQQQQCBYAhSewTpfZIsAAggggAACCARWgMIzsKeOxBFAAAEEEEAAgWAJUHhWkPO1efNmrV27Vjt37qwgGZEGAggggAACCCDgVoDC061nTEdbsGCBTmt7ikYMu0sXdOtWUIDGdCB2QgABBBBAAAEEKrAAhWcFODmvvvJKURarV67Siy+8UHSfBQQQQAABBBBAoLII0EDe4kxmNm2m7AmTLEbGNmTShGc158MPinY+p1s3/fGSS4vuR7MwLnus+vUfEM0uB23s4kWLCmK3bNXqoOUQTeAg2QYpV/8cBClfco3mURPdWGyj87IdjautVPTjgmZLA3m/+2oAboluIP/55597fgz/31lnnumtWbOmVJVkNQ63iWNqiutPwDSGBvKlnmajm835SbUmzDbXm80YmybZLmxt4pgePzbzcZGrTRwXufpxTPkmy80mjinXZLqZ/F3kamNiysPGxEWuNnFc5GpzzZripGID+arR1/fs4VqgTZs2+iTnU7097V1dcP55qlOnjusQHA8BBBBAAAEEEDjoArzH86Cfgn0J+MVmo0aNKDoryPkgDQQQQAABBBBwL0Dh6d6UIyKAAAIIIIAAAgiUIkDhWQoKqxBAAAEEEEAAAQTcC1B4ujfliAgggAACCCCAAAKlCFB4loLCKgQQQAABBBBAAAH3AvTxtDBNdB9PixSshwSppxh9PK1Pa9QDg3Qd+JMLUr7kGvXlaL0DttZUUQ3ENSquqAYHzZY+nn4TrADcEt3Hs5DA1O8rWf0bbeKYcvXnZBpDH8/CM1/8p8nN5vykWi88m+vNZoxNr0IXtjZxTNeBzXxc5GoTx0WufhxTvslys4ljyjWZbiZ/F7namJjysDFxkatNHBe52lyzpjip2MeTl9qj+tuGwQgggAACCCCAAAKxClB4xirHfggggAACCCCAAAJRCVB4RsXFYAQQQAABBBBAAIFYBSg8Y5VjPwQQQAABBBBAAIGoBCg8o+JiMAIIIIAAAggggECsAhSescqxHwIIIIAAAggggEBUAhSeUXExGAEEEEAAAQQQQCBWARrIW8jRQN4CKYYhNJCPAc1ylyA1NfanFKR8ydXyIoxhGLYxoFnsgqsFUoxDgmZLA3m/+2oAbjSQjzxJpqa4/h6mMTSQj3S1caOBfGxuNrY2TbJdNLi2iWN6/NjMx0WuNnFc5OrHMeWbLDebOKZck+lm8neRq42JKQ8bExe52sRxkavNNWuKQwP5GCt+dkMAAQQQQAABBBBAwCTAezxNQmxHAAEEEEAAAQQQcCJA4emEkYMggAACCCCAAAIImAQoPE1CbEcAAQQQQAABBBBwIkDh6YSRgyCAAAIIIIAAAgiYBCg8TUJsRwABBBBAAAEEEHAiQOHphJGDIIAAAggggAACCJgEaCBvEpJEA3kLpBiG0EA+BjTLXYLU1NifUpDyJVfLizCGYdjGgGaxC64WSDEOCZotDeT97qsBuNFAPvIkmZri+nuYxtBAPtLVxo0G8rG52djaNMl20eDaJo7p8WMzHxe52sRxkasfx5Rvstxs4phyTaabyd9FrjYmpjxsTFzkahPHRa4216wpDg3kY6z42Q0BBBBAAAEEEEAAAZMA7/E0CbEdAQQQQAABBBBAwIlABSw8tyl31lua/Gg/nTpslrZFTHObcmeMUf8WzQree5nZbZiez1mvUMS4XVqf86Lu7tZSmU3bq//j87Q+clDEXqxAAAEEEEAAAQQQSIxABSs885U78Xb94/kXNXz0dO2KmPMurXvrRf2vfqtRS1Zo2Tfz9O9u3+vBntfp8ZytYaNDyssZq6uHrtDZEz7Tsm9e12WbHtbVo+crL2wUiwgggAACCCCAAALJE6hghWd1ZfV5Ws9m36shbWpGKoTWatkRv9N1Z2cp3d+a1kCnXn+LhrT5Ss++8fmBZ0dDuXp9xFS1vX2AOjc4VEprqM5DblDbcaP1em5+5HFZgwACCCCAAAIIIJBwgQpWeBrmm9ZMnTo1VrGk045Sk9Z1i+0YWj5PUxbUV2ajgvJ037ZarXR2z+81Zc6qUl6WL7Y7dxBAAAEEEEAAAQQSIFAx+3iGvtaki3rqkdZPavZfO6tWuRPfqFnDrtYrp47REz2OU5r8l+uvUbcHMzT+o+HqXKuwTPXHXaxrFvbVO5P7KKtw9f5j9+rVu8wo8+fNVbv2HcrczgYEEEAAAQQQQKCiC9DH02+CVdpt71fexO4tvNZDZ3o/lrY9fN2PM71h3R/3Pt2+d//aDd7MoZ28jO4TvKWFqwq2lLU+/GClL9PHM9LF1JvM38M0hj6eka42bvTxjM3NxtamV6GLPoM2cUyPH5v5uMjVJo6LXP04pnyT5WYTx5RrMt1M/i5ytTEx5WFj4iJXmzgucrW5Zk1x6ONZ0Uv1iPy2KueZt3XU8CvUNr3EU5gRY1mBAAIIIIAAAgggcDAFAlyt+Z9cf1WTa/fRNW2PDDNMV6PMY6XcFVqbR/+kMBgWEUAAAQQQQACBgyoQ2MIztO49TVjcQbf3abnvE+5FjNWV0bGrWhfd378Q2qRVC7er9UXtlRHYWZecFPcRQAABBBBAAIHgCASyBAutn6UnX6uuP/YuLDpDyvv6DU36cGOBfFpGe/XImqsZOZsPnIm877Qst4V6dGxS/FPxB0awhAACCCCAAAIIIJBAgYAVniHl5U7R8L7XafSovvr18fu/vahphn513hvSMfvbJ6Vl6eLh3ZUzcqxmrd8lhdZp1iNjlNNvsC7Oqp5ATg6NAAIIIIAAAgggUJZABSs8Q9o2a7hOOv63un/BDu14vq/aNr1ck/Y3fQ+tm6rbLrxZL325I3I+bbqqQ0ZhUZmm9LYD9Mx9R+nFLico8/hBmpF5h54Z3K7Ey/KRh2ENAggggAACCCCAQGIEqibmsLEeNU21Oo/QFytHlHqAtIY99NSSHqVui1x5qBq0G6jsJQMjN7EGAQQQQAABBBBAIOkCFbOBfNIZyg+Y2bSZsidMKn9QBdk6Lnus+vUfUEGyKT+NxYsWFQxo2apV+QMryNYg2QYpV//0Bilfck3cAxLbxNjimhjXIP7uooG83301ADcayEeeJFNTXH8P0xgayEe62rjRQD42NxtbmybZLhpc28QxPX5s5uMiV5s4LnL145jyTZabTRxTrsl0M/m7yNXGxJSHjYmLXG3iuMjV5po1xaGBfOL+KODICCCAAAIIIIAAAikuUME+XJTiZ4PpI4AAAggggAAClViAwrMSn1ymhgACCCCAAAIIVCQBCs+KdDbIBQEEEEAAAQQQqMQCFJ6V+OQyNQQQQAABBBBAoCIJUHhWpLNBLggggAACCCCAQCUWoPCsxCeXqSGAAAIIIIAAAhVJgAbyFmeDBvIWSDEMoYF8DGiWuwSpYbQ/pSDlS66WF2EMw7CNAc1iF1wtkGIcEjRbGsj73VcDcKOBfORJMjXF9fcwjaGBfKSrjRsN5GNzs7G1aZLtosG1TRzT48dmPi5ytYnjIlc/jinfZLnZxDHlmkw3k7+LXG1MTHnYmLjI1SaOi1xtrllTnFRsIF/Bvqs9xj852M1KYOfOnZo0cZLmzftI23/crAt72H7vvdXhGYQAAggggAACCJQrQOFZLk/l2vjEmDEa+9TTBZOa8+EHOiw9XV27dq1ck2Q2CCCAAAIIIFBhBfhwUYU9Ne4TKyw6C488a+bMwkV+IoAAAggggAACCReg8Ew4ccUJMODaQcWS6XzWWcXucwcBBBBAAAEEEEikAC+1J1K3gh37+htuKMho0aIlOvfcrrzMXsHOD+kggAACCCBQ2QUoPCv7GQ6bX40aNXTrbbfp/ZkfqstZncK2sIgAAggggAACCCRegD6eFsb08bRAimEIfTxjQLPcJUi95fwpBSlfcrW8CGMYhm0MaBa74GqBFOOQoNnSx9NvghWAG308I0+SqTeZv4dpDH08I11t3OjjGZubja1Nr0IXfQZt4pgePzbzcZGrTRwXufpxTPkmy80mjinXZLqZ/F3kamNiysPGxEWuNnFc5GpzzZripGIfTz5cFONfOeyGAAIIIIAAAgggEJ0AhWd0XoxGAAEEEEAAAQQQiFGAwjNGOHZDAAEEEEAAAQQQiE6AwjM6L0YjgAACCCCAAAIIxChA4RkjHLshgAACCCCAAAIIRCdA4RmdF6MRQAABBBBAAAEEYhSg8IwRjt0QQAABBBBAAAEEohOggbyFFw3kLZBiGEID+RjQLHcJUlNjf0pBypdcLS/CGIZhGwOaxS64WiDFOCRotjSQ97uvBuBGA/nIk2RqiuvvYRpDA/lIVxs3GsjH5mZja9Mk20WDa5s4psePzXxc5GoTx0WufhxTvslys4ljyjWZbiZ/F7namJjysDFxkatNHBe52lyzpjg0kI+x4mc3BBBAAAEEEEAAAQRMArzH0yTEdgQQQAABBBBAAAEnAhSeThg5CAIIIIAAAggggIBJgMLTJMR2BBBAAAEEEEAAAScCFJ5OGDkIAggggAACCCCAgEmAwtMkxHYEEEAAAQQQQAABJwL08dzP2KtX7zJB58+bq3btO5S5nQ0IIIAAAggggEBFF6CPp98EKwA3+nhGniRTbzJ/D9MY+nhGutq40cczNjcbW5tehS76DNrEMT1+bObjIlebOC5y9eOY8k2Wm00cU67JdDP5u8jVxsSUh42Ji1xt4rjI1eaaNcWhj2dFL9XJDwEEEEAAAQQQQCCwArzHM7CnjsQRQAABBBBAAMg0RoUAACAASURBVIFgCVB4But8kS0CCCCAAAIIIBBYAQrPwJ46EkcAAQQQQAABBIIlQOEZrPNFtggggAACCCCAQGAFKDwDe+pIHAEEEEAAAQQQCJYAhWewzhfZIoAAAggggAACgRWggbzFqcts2kzZEyZZjDz4Q8Zlj1W//gMOfiIWGSxetKhgVMtWrSxGH/whQbINUq7+mQ1SvuSauMcitomxxTUxrkH83UUDeb/7agBuNJCPPEmmprj+HqYxNJCPdLVxo4F8bG42tjZNsl00uLaJY3r82MzHRa42cVzk6scx5ZssN5s4plyT6Wbyd5GrjYkpDxsTF7naxHGRq801a4pDA/nE/VHAkRFAAAEEEEAAAQRSXID3eKb4BcD0EUAAAQQQQACBZAlQeCZLmjgIIIAAAggggECKC1B4pvgFwPQRQAABBBBAAIFkCVB4JkuaOAgggAACCCCAQIoLUHim+AXA9BFAAAEEEEAAgWQJUHgmS5o4CCCAAAIIIIBAigvQQN7iAqCBvAVSDENoIB8DmuUuQWoY7U8pSPmSq+VFGMMwbGNAs9gFVwukGIcEzZYG8n731QDcaCAfeZJMTXH9PUxjaCAf6WrjRgP52NxsbG2aZLtocG0Tx/T4sZmPi1xt4rjI1Y9jyjdZbjZxTLkm083k7yJXGxNTHjYmLnK1ieMiV5tr1hSHBvIxVvzshgACCCCAAAIIIICASYD3eJqE2I4AAggggAACCCDgRIDC0wkjB0EAAQQQQAABBBAwCVB4moTYjgACCCCAAAIIIOBEgMLTCSMHQQABBBBAAAEEEDAJUHiahNiOAAIIIIAAAggg4ESAPp4WjPTxtECKYQh9PGNAs9wlSL3l/CkFKV9ytbwIYxiGbQxoFrvgaoEU45Cg2dLH02+CFYAbfTwjT5KpN5m/h2kMfTwjXW3c6OMZm5uNrU2vQhd9Bm3imB4/NvNxkatNHBe5+nFM+SbLzSaOKddkupn8XeRqY2LKw8bERa42cVzkanPNmuKkYh/PqjEW+eyGQCAEdu7cqZycnIJcjz66rmrUqBGIvEkSAQQQQACByihA4VkZzypzKhK4ZcgQvTvtnYL70//TTU8+9VTRNhYQQAABBBBAILkCfLgoud5ES6JAbm5uUdHph/ULUH8dNwQQQAABBBA4OAIUngfHnahJEKhZs2ZElNLWRQxiBQIIIIAAAggkRIDCMyGsHLQiCDRq1Ei33H57USr+sr+OGwIIIIAAAggcHAHe43lw3ImaJIGBgwaqQ4eOBdFOatM6SVEJgwACCCCAAAKlCVB4lqbCukolcMSRR1aq+TAZBBBAAAEEgipAA3mLM0cDeQukGIbQQD4GNMtdgtTU2J9SkPIlV8uLMIZh2MaAZrELrhZIMQ4Jmi0N5P3uqwG40UA+8iSZmuL6e5jG0EA+0tXGjQbysbnZ2No0yXbR4NomjunxYzMfF7naxHGRqx/HlG+y3GzimHJNppvJ30WuNiamPGxMXORqE8dFrjbXrClOKjaQ58NFMf6Vw24IIIAAAggggAAC0QlQeEbnxWgEEEAAAQQQQACBGAUqYOG5Tbmz3tLkR/vp1GGztK20iYXWK+e5YbqgaTNltuinMfPXKxQxbpfW57you7u1VGbT9ur/+DytjxwUsRcrEEAAAQQQQAABBBIjUMEKz3zlTrxd/3j+RQ0fPV27Sp3zVuWMvll3LztLz3yzQkvfv1Sb7rlZj+dsDRsdUl7OWF09dIXOnvCZln3zui7b9LCuHj1feWGjWEQAAQQQQAABBBBInkAFKzyrK6vP03o2+14NaRP5rTM+Syh3iu4f11y3DjlLDdKktAZn6S+3N9ezI6Yot/AZzVCuXh8xVW1vH6DODQ6V0hqq85Ab1HbcaL2em588XSIhgAACCCCAAAIIFAlUsMKzKK8yFvK1fM50LcxqpkbphamnqVbbs3Rh7nTNXb6vqAwtn6cpC+ors1H6gePUaqWze36vKXNWlfKy/IFhLCGAAAIIIIAAAggkRqCwekvM0V0fNbRKcyd/ppqtm6p+ROaf7S8q9xenNTPUpP6hJTLYpYWT52l54TOjJbZyFwEEEEAAAQQQQCBxAhWzgXzoa026qKceaf2kZv+1s2oVzn/bLN19xnVadNsber3PCSqqPYutP0ofDrtY1yzsq3cm91FW0aCNmlXq+n0H79Wrd2GUiJ/z581Vu/YdItazAgEEEEAAAQQQCIoADeT97qul3fZ+5U3s3sJrPXSm92P49h9nesNObOH1mPCVt7fM9Ru8mUM7eRndJ3hLiw0qa334gUpfpoF8pIupKa6/h2kMDeQjXW3caCAfm5uNrU2TbBcNrm3imB4/NvNxkatNHBe5+nFM+SbLzSaOKddkupn8XeRqY2LKw8bERa42cVzkanPNmuLQQL6il+zpxygzS1q+7LtyPp2erkaZx0q5K7Q2j9fUK/opJT8EEEAAAQQQSB2BoheiAzHltCbqcNHJEamGvl+pRTtOVo+OTZSm6sro2FWtS44KbdKqhdvV+qL2ygjWrEvOhPsIIIAAAggggEAgBQJWgu0rKjPemKmcbYXPZoaUt3aFlrfpqg4Z1QtOQlpGe/XImqsZOZsPnJS877Qst8X+4vTAapYQQAABBBBAAAEEkiMQsMJTSsvqobv7LdVDj8ws+Cai0PqZGjVyqf48vMeBDxKlZeni4d2VM3KsZq3fJYXWadYjY5TTb7AuztpXnCaHlygIIIAAAggggAAChQIVrPAMadus4Trp+N/q/gU7tOP5vmrb9HJNKtb0/Ui1HfyoRhz1b517fDM17ztTmX97VDe2PbJwTpLSlN52gJ657yi92OUEZR4/SDMy79Azg9sprLNn2HgWEUAAAQQQQAABBBItUDXRAaI7fppqdR6hL1aOKH+3tAY69cZx+uLG8oYdqgbtBip7ycDyBrENAQQQQAABBBBAIEkCFewZzyTNmjAIIIAAAggggAACSReomA3kk85QfsDMps2UPWFS+YMqyNZx2WPVr/+ACpJN+WksXrSoYEDLVq3KH1hBtgbJNki5+qc3SPmSa+IekNgmxhbXxLgG8XcXDeT97qsBuNFAPvIkmZri+nuYxtBAPtLVxo0G8rG52djaNMl20eDaJo7p8WMzHxe52sRxkasfx5Rvstxs4phyTaabyd9FrjYmpjxsTFzkahPHRa4216wpDg3kE/dHAUdGAAEEEEAAAQQQSHEB3uOZ4hcA00cAAQQQQAABBJIlQOGZLGniIIAAAggggAACKS5A4ZniFwDTRwABBBBAAAEEkiVA4ZksaeIggAACCCCAAAIpLkDhmeIXANNHAAEEEEAAAQSSJUDhmSxp4iCAAAIIIIAAAikuQAN5iwuABvIWSDEMoYF8DGiWuwSpYbQ/pSDlS66WF2EMw7CNAc1iF1wtkGIcEjRbGsj73VcDcKOBfORJMjXF9fcwjaGBfKSrjRsN5GNzs7G1aZLtosG1TRzT48dmPi5ytYnjIlc/jinfZLnZxDHlmkw3k7+LXG1MTHnYmLjI1SaOi1xtrllTHBrIx1jxsxsCCCCAAAIIIIAAAiYB3uNpEmI7AggggAACCCCAgBMBCk8njBwEAQQQQAABBBBAwCRA4WkSYjsCCCCAAAIIIICAEwEKTyeMHAQBBBBAAAEEEEDAJEDhaRJiOwIIIIAAAggggIATAfp4WjDSx9MCKYYh9PGMAc1ylyD1lvOnFKR8ydXyIoxhGLYxoFnsgqsFUoxDgmZLH0+/CVYAbvTxjDxJpt5k/h6mMfTxjHS1caOPZ2xuNrY2vQpd9Bm0iWN6/NjMx0WuNnFc5OrHMeWbLDebOKZck+lm8neRq42JKQ8bExe52sRxkavNNWuKQx/PGCt+dkMAAQQQQAABBBBAwCTAezxNQmxHAAEEEEAAAQQQcCJA4emEkYMggAACCCCAAAIImAQoPE1CbEcAAQQQQAABBBBwIkDh6YSRgyCAAAIIIIAAAgiYBKqaBpS73cvXxmVfKOe/n2vB4sXKXb9DUk3Vz2quzBNaqe2pJ+vExrUUX5ByM2AjAgggUExg586dmjRxkh4eOVLtTj9ND48apUaNGhUbwx0EEEAAgYMjEFtN6O3Qmrmva+yoMXrp0w2RmU8vXHWUTux+lQYO7K3zWtShAC1k4ScCCCRMYM6cOQVFpx9g/sef6Ja//EUvvfxywuJxYAQQQAABe4EoG8h72rMhR688NEIjXlmvky65Qhd3PVUnZTXV0fXqqW66X8eGlL/1B61ft0JLF3yq/3v7Nb0ye7faD75Xw/t1UbP0Q+yzqyAjaSCfmBNBA/nEuPpHDVJTY9f5zps7RxPGZRfDzZ4wqdj9eO4EyTZIubq+DuI5xzb7BsmWXG3OaGxjgmYbvAbye77yJl7Yybvkvte8T9f95IX87qmmW+gn77sv3vWyrz/PO33o+95m0/gKuJ0G8pEnxdQU19/DNIYG8pGuNm40kC/fbenSpZ7/mC38N/Suu4p2MF2TNk2yXTS4toljytXmWnGRq00cF7n6cUz5JsvNJo4p12S6mfxd5GpjYsrDxsRFrjZxXORqc82a4qRiA/noXmpPq6eOI19T7xPq2b9sXqWmGrQ+V/0e/7XOX/6jasT2RwV7IYAAAlYCWVlZeuc/72nJ4sU6LD1dHTt2tNqPQQgggAACiRewKDxDyl+fqy+3HKETf1lbR/z8H018bIW8Y09TtwvaqXF1yw/GV6mpRpk1Ez8jIiCAQMoL+MWn/48bAggggEDFEjAUnp52r3hdN//hIa0+8RS1bVVLX42brcP6D1SP0GfKfniLBg39rY6pUrEmRTYIIIAAAggggAACFU/AUHju1aYF87T5huf0Zp/m0uo3dOPq9rr7th46pspunfrqY3pvWWddlVW94s2MjBBAAAEEEEAAAQQqlIDhdfKqqn/6OWqxdaO275GqHtdNw+46Uw0KnuH8Seu+Waot/gZuCCCAAAIIIIAAAggYBAyFp1TlmN9qaO8G2vTj3oLm8A0b19a+V9arqvYpl+uCFocZQrAZAQQQQAABBBBAAAHJWHhKVVS1XoYyj9r/qry3QQvnr1K+0pXV9UxlVecNnlxICCCAAAIIIIAAAmaBKBvIS9qTo8duXq1Lx/RQA/PxAzOiV6/eZeY6f95ctWvfocztbEAAAQQQQAABBCq6QPAayPvdUnd/6j16/WTvO385RW40kI880aamuP4epjE0kI90tXGjgXxsbja2Nk2yXTS4toljevzYzMdFrjZxXOTqxzHlmyw3mzimXJPpZvJ3kauNiSkPGxMXudrEcZGrzTVrikMD+YpeqpMfAgjELbBz505NmjhJ8+Z9pO0/btaFPXrEfUwOgAACCCCAgI2AoZ2SzSEYgwACQRJ4YswYjX3q6YKU53z4QcG3+3Tt2jVIUyBXBBBAAIGAClh8uCigMyNtBBAoVaCw6CzcOGvmzMJFfiKAAAIIIJBQgegLz0Oa64+3/EZ1bdLa8onenLPBZiRjEEAgSQIDrh1ULFLns84qdp87CCCAAAIIJEog+pfaq6SrUZP0/fl42rN1mT76zwf6dM12ecWy9PTzNx9pxdmjdGGx9dxBAIGDKXD9DTfo8MNrFbzHs2fPHuJl9oN5NoiNAAIIpJZA9IVnuM/Oz5V95ZUa9UVe+Nqw5drqcnbYXRYRQOCgC9SoUUMDBw1U81+2UJezOh30fEgAAQQQQCB1BKLv4xlmsyfnUZ3R83/U5R8P6trOjVS8l7yn3csna9yG7rqvR+OwvYK3mNm0mbInTApE4uOyx6pf/wGByHXxokUFebZs1SoQ+QbJNki5+ic/SPmSa+IertgmxhbXxLgG8XdXMPt4+o2r9t9CP7ztDc4c4L367a7CVcV/7t7sfbcxv/i6AN6jj2fkSTP1JvP3MI2hj2ekq40bfTxjc7OxtelV6KLPoE0c0+PHZj4ucrWJ4yJXP44p32S52cQx5ZpMN5O/i1xtTEx52Ji4yNUmjotcba5ZU5xU7OMZ/YeLwv5wqFLvbN2enaU5//uV8sPWFy56Gz7W5E82F97lJwIIIIAAAggggEAKC8T3Hk9V1eGNMnT4o7foinnHqXaxr233lL92maoPeD6FeZk6AggggAACCCCAQKFAXIWnt2GG7u91i17ftFfS0sJjhv2srS5h91hEAAEEEEAAAQQQSF2BuArPvd8u1oxNLdRn/BO65ezjIj5ctCf333pgceriMnMEEEAAAQQQQACBAwJxFZ5VT+ykyzOW6OiM+iWKTj9AFVXN/L1uqF/9QDSWEEAAAQQQQAABBFJWIK4PF6nGr3TNmM5aOPVzbS/ePV6Spz3L3tKY99enLC4TRwABBBBAAAEEEDggENcznqHc53TF+SO0UNKrjx446IGl2ury2G8O3GUJAQQQQAABBBBAIGUF4mogr91fatLlvTVm24lq26hmCcQDn2rPpoF8CZvE3Q1So2AayHMdFAoE6bol18Kz5v4ntu5N/SPimhjXINoGvoG85+3y1k17zpu2brffRzXiFlr3jvfUtHUR64O2ggbykWfM1BTX38M0hgbyka42bjSQj83NxtamSbaLBtc2cUyPH5v5uMjVJo6LXP04pnyT5WYTx5RrMt1M/i5ytTEx5WFj4iJXmzgucrW5Zk1xUrGBfFwvtUvVdEy3y3VMGX9MVDnmtxpU1sYy9mE1AggggAACCCCAQOUUiO/DRZXThFkhgAACCCCAAAIIJEAgzsJzhxY+9bDe2eA3kC9585SfO0X3XNJdf7phuJ6a9rXyIj75XnIf7iOAAAIIIIAAAghUVoE4C8+Qdv+8TDOfe1C3DRigwXeP1/QV21VQX3or9T9/u08v1/6zHnv8VnXdMEF/e2e19lRWSeaFAAIIIIAAAgggUK5AfO/x9HZq2+av9MZz7+4P8p7enrZID7z2D/3h2C1as2CLDr/yONWrkq4G556hLT2f08e/uVMdD4+z3i13SmxEAAEEEEAAAQQQqIgCcVWA3vo5enlBVz0y9f/0+bJvtGzZAs185FhNfuUL7dixTZt+PjDlKvWO0y/zP9ScJXkHVrKEAAIIIIAAAgggkDICcfXx3JPzhK5f/ns9/ccmqlJItidHj928WpcOle4542blDH5dH93cVlX99e2u0ZLhUxW0vp6ZTZspe8KkwhlW6J9B6tdGH8/EXUpBug58hSDlS65ct1yzXAOFAkH7fRD4Pp6hb170rh76nvfD7pDfzsrzQj95q6cN97qNmO399N1kr1+TVt6lLyzzCrZufs+7NfNkr9/kb/eNDdD/9PGMPFmm3mT+HqYx9PGMdLVxo49nbG42tja9Cl30GbSJY3r82MzHRa42cVzk6scx5ZssN5s4plyT6Wbyd5GrjYkpDxsTF7naxHGRq801a4pDH8/CEt7yZ5WmnfWn3Zfr113+qU7Na2nr0k/02domOuv8vcp+bYeWKaTDvt+grXuayPvvLP3v7izdcMJRlkdnGAIIIIAAAggggEBlEojrPZ6qcoy63v2UHut5rNZ/OkcrDj9XQyaN09OPDtSvdnyv0GnX6IZTv9KIyy7RFbe9rJ9PP1+dM6tXJj/mggACCCCAAAIIIGApEN+n2iVVST9B3W56rOBfeMzOtz2vWQUrQurUrLmmTF2pYy+6WFnVit4NGj6cZQQQQAABBBBAAIFKLhB34Vm6z09a+fHn2nx0C53UrLaqN+6gS6/tUPpQ1iKAAAIIIIAAAgikhEB8L7WXSVRDDY7brRmDr9WjH2/c11C+zLFsQAABBBBAAAEEEEgFgfie8cz7Qq+Nn6E1pXwVprdtid5Z/JG2zV2tm0+vq/gCpcKpYI4IIIAAAggggEDlFoivHsz7Ru899rjeL8PokKZ/0F8vaE7RWYYPqxFAAAEEEEAAgVQSiKuBvLx8/fjDVu2MeMbzZ619a5zebTFYd3asd6C5fEBlaSCfmBNHA/nEuPpHDVJT46DlGyTbIOXKdcDvg6BdA0HL1/99EPgG8n7z1DJvP33kjTzndm/aul1lDgnKBhrIR54pU1Ncfw/TGBrIR7rauNFAPjY3G1ubJtkuGlzbxDE9fmzm4yJXmzgucvXjmPJNlptNHFOuyXQz+bvI1cbElIeNiYtcbeK4yNXmmjXFScUG8gn6cJGkGg10/DHvK/vdbxRK3B9yHBkBBBBAAAEEEEAgIALxvcdzz0blfrFa2yMmu1vbvvwfTZq9Vbt/vZdPtUf4sAIBBBBAAAEEEEg9gfgKz42z9VDPm8v8cJHUWF3ycvTyuLe15IO39fqadrove7j+2Dw9DumQ8nJnaPzIe/TE9PWSGqjL4Pt0a7+zlZUe/gTuLq3PeU1PDv2bXvqylrr8ZZTuu769GoQPiSMLdkUAAQQQQAABBBCITiC+wvPINrrq8Ud1Qbmvpe/QDyvylb8r4hNI0WW6f3Ro3VTdduFI7bltvD4f31LpoXWaNWKQLn6gmmb/tbNqFYwLKS9nrK4euk23TvhM9x+9UbNG3KCrR9+hl29up3jK3piSZicEEEAAAQQQQACBaDsd7dWePWmqWnX/115Wb6aO3ZvZMd48TCP3hJRW9RC78aWOytfy917TezpX43ueuK+ATGuoTpdfpIwLZyrntk7qXCtNCuXq9RFT1fb2l9S5waGSGqrzkBs044zRev1343VVFt8XXyovKxFAAAEEEEAAgQQKRPfC854FevJPd2jSnNXKj+YJzD2bteTt0brurmn6Pq7JHKr6TTNUc8cifb5s2/4jhZS3doW+7XmW2vpFp6TQ8nmasqC+MhuFPbdZq5XO7vm9psxZxYed4joH7IwAAmUJTJ8+XX77tf59r9ILzz9f1jDWI4AAAikrEF3hWbWlLrm5sWbeeIHO7/eAXpy+QKu25Jfx4aE9ylvzhWa98ogGdv2NLnpig7r27aT6cVGnqdapv9OfT/xKT1x+pyZ9vU2h9TM1enpj/fP6DvtfZs/X8jnTtbBmhprU95/tDL/t0sLJ87S83LcGhI9nGQEEELAT2Lx5swZe069o8PBhd2vt2rVF91lAAAEEEJBiaCDvac+GBXrznw/qH8/M01bVVONTTlebE5ur2VG/kLRX29d9rS8+nqvPVu+QDmmuC26/Xddf8htlHVnNiXlo/Tw9OewvGu1/uKjNcL0zuY+yikrojZo17GJds7Cv5fp9KfXq1bvM3ObPm6t27TuUuZ0NCCCAwI6fftLiLxYUg2h5UhvVPOywYuu4gwACCBwsgYA3kN/lbf3mY2/ahJHekD928po3aer5jdb3/TvFO//qu70nX/nQ+3LDTi/kd1l1edv+lTdl1Cjv0aHdvYwmLbzz75nufbe3MMAGb+bQTl5G9wne0qJ1/ray1hfuV/ZPGshH2pia4vp7mMbQQD7S1caNBvKxudnY2jTJLqvB9Y4dO7xLL7mk6PfgWWee6fnrSrvZxDE9fmzmU1au4Tm5iOPiGH5OpnyT5WYTx5Srzflx5WY6jotcbUxMediYuMjVJo6LXG2uWVOcVGwgH8en2qvpiGanqZv/r8+teiBvszbm7ZZUTel16yi98ANIrsv6vMWadOtLOvLue3RTw+t0adeHdHWfG3X1kRP3f2I9XY0yj5XeWKG1eSFl7X/fp+s0OB4CCCAQLlCjRg09+fTT+r8PP9SixV9q0KAB8tdxQwABBBA4IFD0AvWBVbEsVVHV9KPUoEEDNWhwVOKKTuUr97V/6P51mWpR8Gn1Q9Wg8516+Y2B0ujRej03X1J1ZXTsqtYlpxHapFULt6v1Re2V4WjWJUNwHwEEUlugTp06urBHD7Xv0FH+MjcEEEAAgeICASvB8rR22bfFZ6A0pWe2VtuaB1anZbRXj6y5mpGz+cDKvO+0LLeFenRsooBN+sAcWEIAAQQQQAABBAIsELAarI5O7fkHnbBgrB7612LlFcBv09dvvKx3zvyDzsnY358zLUsXD++unJFjNWv9LslvMv/IGOX0G6yL6eEZ4MuV1BFAAAEEEEAgyAIBKzzTlN52gJ554wbVf/kS/appM2U2PU+PbOmplx7qroZFs9k/7r6j9GKXE5R5/CDNyLxDzwzmW4uCfLGSOwIIIIAAAggEWyCODxcdrIkfqgZtL9P971ym+8tN4VA1aDdQ2UsGljuKjQgggAACCCCAAALJEYihj2dhYnuUt36lvlm+Qis3/FTQRL7KYfXUuHFTNc9qmMAPGBXGT95P/5tIsidMSl7AOCKNyx6rfv0HxHGE5O26eNGigmAtW7VKXtA4IgXJNki5+qckSPmSaxwPIsOu2BqAYtyMa4xwFrsFzTagfTz3eNu/+Y/35A3dvVOK+nYW9u/c97P5mQO9Ryd/7v2w23kHT79tVtJv9PGMJDf1JvP3MI2hj2ekq40bfTxjc7OxtelV6KLPoE0c0+PHZj4ucrWJ4yJXP44p32S52cQx5ZpMN5O/i1xtTEx52Ji4yNUmjotcba5ZUxz6eBqr+73KW/KSbrlipL7K6KoLB/9OGc3q6cD3cuzQDyvXaf3aRfrPiKs0Y+Ejyr6zi45JVE9PY74MQAABBBBAAAEEEKgoAtG9x3PXIv3rr8vU7aUP9UTz2ipvZy9/reb+82E98/HJGtaRfnYV5YSTBwIIIIAAAgggcLAEij4HbpXA5hX6ul13XWAoOv1jVaneSB3+0EFrPlmpPVYHZxACCCCAAAIIIIBAZRaIrvA86gS1XfiyXvx0nfK98lg87clbrY+nzlbNExrokPKGsg0BBBBAAAEEEEAgJQTKe7U8EqBac118S2vdckVnPX50B3Vp30qNjmmoJvVqqkrB6JB+2rBKy7/6RDOmLNLhfR5Tdv9j9m+LPBxrEEAAAQQQQAABBFJHILrCU4covcVleuzNZnrln4/r8Wef1NZSrA5p+lsNeuR59f7dSarHB4tKEWIVAggggAACCCCQegJRFp4+UJqqN+6oK//aXpcMWaMVOdjQvAAAIABJREFUud9o5bqt2uW/r7OS9vFMvcuCGSOAAAIIIIAAAu4F4mgg7z6ZinpEGsgn5szQQD4xrv5Rg9TUOGj5Bsk2SLlyHfD7IGjXQNDy9X8fBLSBvN8yNbVuNJCPPN+mprj+HqYxNJCPdLVxo4F8bG42tjZNsl00uLaJY3r82MzHRa42cVzk6scx5ZssN5s4plyT6Wbyd5GrjYkpDxsTF7naxHGRq801a4qTig3ko/tUe7R/kG2YoXHvfBftXoxHAAEEEEAAAQQQqIQC0b3HM3+F5ry3QBtDdhI/f/2Ock64224woxBAAAEEEEAAAQQqtUB0hech+Vr2wr26/+MfLVFqq8tjlkMZhgACCCCAAAIIIFCpBaIrPKs1V/dBPTW+Wi0Nu+E3qldtX/fO0oU87fpqil4ufSNrEUAAAQQQQAABBFJMILrCU4eodsc/qt+cb3TSaafomPLqTh+y2V59v+QXKUbKdBFAAAEEKqrA5s2btX379oqaHnkhUOkFoiw8JVX7pXrf3lxppqLTp6t9mi7sWOkNmSACCCCAQAAE/vn0P/XwyJEFmX639lsNHDQwAFmTIgKVSyCGT7VX0SFVD+FrMCvXdcBsEEAAgUotkJubW1R0+hP1C9C1a9dW6jkzOQQqogAN5C3OCg3kLZBiGEID+RjQLHehcbglVAzDgmQbpFz9U5HIfP0ic8Swu4qd8eF//bsaNWpUbJ3tnUTmapuD7ThytZWKflzQbIPXQH7PUu/Vm/t7/a6+xvLfjd6js3/we6wG+kYD+cjTZ2qK6+9hGkMD+UhXGzcayMfmZmNr0yTbRYNrmzimx4/NfFzkahPHRa5+HFO+8bjt2LHDu3bQIM//fe7/85fLutnEMeWaTDeTv4tcbUxMediYuMjVJo6LXP04pnxNcVKxgXx07/H0tmvNzPf0/hbbvwpqS7/72XYw4xBAAAEEEEiIQI0aNfTwI4/o8iuuUE7O5/rzn/skJA4HRQCB8gWiKzyLHaumGp92ns4//2z9+rQWalanRinv+0xTjSPrFtuLOwgggAACCBwMAb/4bN++vXbm75a/zA0BBJIvEF3hWbW1+r7xhn7137ma8earemX2ZGV/MlnZOkon/r6HunfqoFNObq0WGfVU3eZT78mfLxERQAABBBBAAAEEDpJAdIWnqumIZiers//vj4M0dONyfZHzqf774Tt65aVnNPKtZyQdoiNPPEvn/+5cdWnfVq1aNFPd6jF8eP4ggRAWAQQQQAABBBBAIDECURae4UmkqXrdLJ12rv/vT+p/x/dasThH8+b+n6ZPnqoXH5quF+V/ZeZUZfdoHL4jywgggAACARXwPx3+3/nz1aJlS2VlZQV0FqSNAAIHSyCOwjM85Sqqml5XxzRqrCbNmqtVm0wtWf2FtoYPYRkBBBBAINACCxYs0MUX9iiaw3MvvVjwnsmiFSwggAACBoH4+nju2aY1Sz7Tpzkf6f1XX9XbizftD1f4ns/f6NdnnaET6wb7azPp42m4imLcTB/PGOEsdgtSbzl/OkHKN5VznTThWc358IOiK7BjpzN1Vd8/F92PdyGVbeO1K29/XMvTiW9b0GyD18fTC3m7t3/rfTFrsjfhgRu83/0qo6gnWsavuns3PvCsN2XWAm/l5p1eyG9wVUlu9PGMPJGm3mT+HqYx9PGMdLVxo49nbG42tja9Ck19+1zFMT1+bOK4yDU8zoMjRx74nd+kqTf0rrv8zcbHuu0YU74258eFm00cU642c3aRq00cF7namLiYj4tcbUxc5OrHMeVrikMfT1Phv3ehsn/bU6PW7JXkt1Pqrv7nd9LpbU/VKS0aKb0qH2U3EbIdAQQQCKrAZb17651p07R65Sod17SJBl17bVCnQt4IIHCQBKJ7j6e3R7t+8otO/7ZDa/xWSgXtlPavivhRTxc89aZGn39MxBZWIIAAAggES8D/esn3Z82S/73nfLAoWOeObBGoKALR9TmqUlWHHnZIRcmdPBBAAAEEDoIARedBQCckApVEILpnPA85SdfOXiZeXKkkZ59pIIAAAggggAACSRSI7hnPJCZGKAQQQAABBBBAAIHKJRDdM56Fc/d2aP2i/+qz5Zu1+7CGOvHkk5RZt3op39VeuAM/EUAAAQQQQAABBFJdIOrC08tbpJfuGqIRU5eq8GNGOuRk9Rk/Rnec1UhRHzDVzwDzRwABBBBAAAEEUkQgygbyO5Q78Tr97t5P1Kjr5bryvF8q/adFmjpmkuZu7az7pj+py5oFs1l8r169yzzl8+fNVbv2HcrczgYEEEAAAQQQQKCiCwSvgXxomffCJa28jDMe9D7+qbBF/B5v03t3ea2btPGuemVlpWoc7zeH9W80kN8PEfbD1BTXH2oaQwP5MNCwRZMbDeTDsMIWTW7+UNMYmybZpobRruKYcrWJ4yJXmzgucvXjmPK1OT8ucrGJY8o1mW6mObvI1cbElIeNiYtcbeK4yNXmmjXFScUG8tF9uGjvj/phaZ7UMkvH1SxsFn+I6rRupzP0oxat2XTg5feKXvaTHwIIIIAAAggggEBSBaIrPJOaGsEQQAABBBBAAAEEKpMAhWdlOpvMBQEEEEAAAQQQqMACsX0IPX+rNqxff2BaP2xVvqTQ9k36fv16HfhuozTVOLKujqhOfXsAiyUEEEAAAQQQQCA1BWIrPGeP0EVnjIgUe7a/znw2fHVtdXlsqrJ7NA5fyTICCCCAAAIIIIBACgpEV3hWOVyNzzpXXbaFLKlqqkW9YLZXspwgwxBAAAEEEEAAAQQsBaIrPA/J0h9GjdUfLA/OMAQQQAABBBBAAAEECgWibCBfuFtq/cxs2kzZEyYFYtLjsseqX/8Bgch18aJFBXm2bNUqEPkGyTZIufonP0j5kmviHq7YJsYW18S4BvF3V/AayPvdUlPwRgP5yJNuaorr72EaQwP5SFcbNxrIx+ZmY2vTJNtFg2ubOKbHj818XORqE8dFrn4cU77JcrOJY8o1mW4mfxe52piY8rAxcZGrTRwXudpcs6Y4NJBP3B8FHBkBBBBAAAEEEEAgxQWi63PkbVbu/E+1cE2evBSHY/oIIIAAAggggAAC0QlEV3hu/EhPXPoH9X11qfYqX7mv3q3+A8Zozpa90UVlNAIIIIAAAggggEDKCUT3qfa9u7Rzr7RrxXIt/+5Irf7yI73/bhN1vG69Mn4+0Db+gCIN5A9YsIQAAggggAACCKS2QHSF59En64JujfX+1Nt0wdRCuGW6v/sM3V94t9hPGsgX4+AOAggggAACCCCQwgLRFZ5pTdT9ofE69JT39PX2HVo3+2W98Wltdfnz+WpxeGmv2h+qxsenpzAvU0cAAQQQQAABBBAoFIijj+cOLXyyty4adbzGfPSgutUr7aX2wjDB/kkfz8ScP/p4JsbVP2qQ+vYFLd8g2QYpV64Dfh8E7RoIWr7+74PK0ccztM1bMfs1L/u+W7wBV1/j9et/i3ffmOe8aQu+93b7Ta4qwY0+npEn0dSbzN/DNIY+npGuNm708YzNzcbWplehiz6DNnFMjx+b+bjI1SaOi1z9OKZ8k+VmE8eUazLdTP4ucrUxMeVhY+IiV5s4LnK1uWZNcVKxj2d0L7WX/IPM+16z/zZIV4//TMU+1/7ua5r08Fh1/Xu2HrvsRFUvuR/3EUAAAQQQQAABBFJOoLQ3Zloi7NWWD8bqlvGLdEz3e/XizE+1aMUKLVu2ULOnPaX+p/2k6Xc/qJeX7rA8HsMQQAABBBBAoKILzJs3T106dy7498Lzz1f0dMmvggnEUXhu0YLpM7Sx2oW6/e7eOq1ZHVWvIqlquhq0+K1uGnaNMvZ+oilzv1Wogk2adBBAAAEEEEAgeoGdO3fqil6XafXKVQX/hg+7W7m5udEfiD1SViCOwjNfP67fLqU3VP3aJV+xr6JDj26oJtqhb7f8ROGZspcXE0cAAQQQqEwCa9asiZjOqlWrItaxAoGyBOIoPI/QsS0bS1s+0kdLtpc4/h79kDNXH+kondqsnirv591LTJu7CCCAAAIIVGKBrKwstTv9tKIZHte0idq2bVt0nwUETAIln6o0jQ/bnq7WF/bSb566S6P63qi8IX9SxxOOVo09P+rbBe8oe+Sr2lGvry49s6H8V+C5IYAAAggggEDwBZ6dOFHvvftuwURObddOderUCf6kmEHSBOIoPKuo2vE99fcJG3Xn4NHKvmuWssPSPuTEy/TAqME6szbPd4axsIgAAggggECgBWrUqKELe/QI9BxI/uAJxNFAvjBpT3vy1il3Sa5WrtuqXWmHqW7TDJ3QvKnqVo/jlfzCw1eAnzSQT8xJoIF8Ylz9o9I4HFuug8RdA0GzDdLvgyDlGsTroHI0kPc7qFbyGw3kI0+wqSmuv4dpDA3kI11t3GggH5ubja1Nk2wXDa5t4pgePzbzcZGrTRwXufpxTPkmy80mjinXZLqZ/F3kamNiysPGxEWuNnFc5GpzzZripGID+crxlGRi/7Dl6AgggAACCCCAAAIOBCg8HSByCAQQQAABBBBAAAGzAIWn2YgRCCCAAAIIIIAAAg4EKDwdIHIIBBBAAAEEEEAAAbNAHO2U9h98T57Wr1ihddt3lxLtEB1+3C+VVfcXpWxjFQIIIIAAAggggEAqCcRVeHp5C/XckGt137uRX6G1D7G2ujw2Vdk9GqeSKXNFAAEEEEAAgRQW2Lx5s64bNEjzP/6k4JueHh41So0aNUphkQNTj6PwzNOiSffqvnc367iu/XXleSeqdrUDB963VE1129QuuZL7CCCAAAIIIIBApRV45eVXCopOf4J+8fn0U0/pr3/7W6WdbzQTi6OB/Bq9eU13DZnbTU/Pvk/n1Km831BEA/loLin7sTSQt7eKdiRNmKMVsx8fJNsg5eqfgSDlS672j5loRgbJtbxrdtKEZzXnww+Kpt6x05m6qu+fi+4fjAXfNuAN5Dd4M4d28jJa3e/N/ink91GttDcayEeeWlNTXH8P0xgayEe62rjRQD42NxtbmybZLhpc28QxPX5s5uMiV5s4LnL145jyTZabTRxTrsl0M/m7yNXGxJSHjYmLXG3iuMi1vGv2888/9/zaofDflMmT/eERNxrIR1WCH6UzLrtSp+yYqanTVyjfi2pnBiOAAAIIIIAAApVSoE2bNnrnP++pb7/+eu6lF/lu+7CzHMd7PH/Wt4u/Ul6tVXr9xrM15eG26tS8jqqEHVyqqRZ9h+mmjvWKrXV2J7ReOW9/oA/ffExPTD9UvSa+rvs7191/+F1an/Oanhz6N730ZS11+cso3Xd9ezWggZQzfg6EAAIIIIAAAqULZGVlqX2Hjmrfvn3pA1J0bRyFZ0j5PyzT11v2FtDtXZ2jmatLKtZTjZ57Sq50cj+0fp6eHPYXjdMlGnH5v/T5+CylFx05pLycsbp66DbdOuEz3X/0Rs0acYOuHn2HXr65Xdi4oh1YQAABBBBAAAEEEEiwQByFZ021vm6yll2X4AxLO3zefD3e9w4t6TZK75X2LGYoV6+PmKq2t7+kzg0OldRQnYfcoBlnjNbrvxuvq7Kql3ZU1iGAAAIIIIAAAggkUCCALzxvVc64B/Rs05t1b2lFp6TQ8nmasqC+MhsdeA5UtVrp7J7fa8qcVQolEJRDI4AAAggggAACCJQuEMcznvsP6G3Xyrnv6T/vf6RPV21V6JAjdWzrNjq107k656SjFX+A4omHcqfo/tF7dOG9O/RK//Z6Yvp61ez6Fz12+1XqklVLUr6Wz5muhTUzNLi+/2xn+G2XFk6ep+VXnqCsAJbc4TNhGQEEEEAAAQQQCJpAHH08JXnfa/bfBunq8Z9p3zs9w6ffWF3/nq3HLjtR7l7YzlfuxGvU7eWmuvdv1+uytg2UlrdYk266RvevvUyvvHqd2qZv1qxhF+uahX31zuQ+YQXmxjLW78u5V6/e4ckXW54/b67ate9QbB13EEAAAQQQQACBIAkEvI/nHm/zzBHe6U2yvDNvmOh9/M0mb6ffznP3du+7xdO8kX882cs4vo838eufIvpWxb5iX+/Q1kNnej+GHWTv0glejyYtvB4TvvL2evv7i3af4C3dGzaozPXhY0pfpo9npIuLHmj08Yx09deYbOnjGZubja1Nr0IXfQZt4piuA5v5uMjVJo6LXP04pnyT5WYTx5RrMt1M/i5ytTEx5WFj4iJXmzgucrW5Zk1x6OMZVdm+RQumz9DGahfq9rt767RmdVTd76VUNV0NWvxWNw27Rhl7P9GUud+6e09laJNWLdwYkWVaRnv1aCMtX/ad8pSuRpnHSrkrtDaPd3NGYLECAQQQQAABBBA4SAJxvNMxXz+u3y6lN1T92iXfyVlFhx7dUE20Q99u+cld4Zl2lJq0rqsdC1fq+4ia8hfKyDxG6aqujI5d1bokaEHRul2tL2qvjDhmXfKw3EcAAQQQQAABBBCwE4ijBDtCx7ZsLG35SB8t2V4i2h79kDNXH+kondqsntx9i3sdte3aWTVzF2jJ+l0HYuZ9p2W5LdSjYxP5Eyp4BjRrrmbkbC5zzIENLCGAAAIIIIAAAggkQyCOwjNdrS/spd9U+0Sj+t6oB1/8X835NEc5H8/Um9l3qe8Nr2pHve669MyGJb7NKJ5ppalWp6t1/5kf6e57XtHX/kvpofX678SXtajfYF1c2J8zLUsXD++unJFjNcsvUEPrNOuRMcoJHxNPGuyLAAIIIIAAAgggELVAydfIozhAFVU7vqf+PmGj7hw8Wtl3zVJ22N6HnHiZHhg1WGfWdvd8Z8Hh047ThQ/9S4ePe1B/bHW3dugk9bp/mJ7uHf6NRGlKbztAz9z3rO7pcoKu2bFvzDPFxoQlyyICCCCAAAIIIIBAwgXiKDz93H6hY359vcZ/0FO5S3K1ct1W7Uo7THWbZuiE5k1Vt3ocT6iWN/X0LHW5eZy+uLm8QYeqQbuByl4ysLxBbEMAAQQQQAABBBBIkkB0hefeXL1268OafuyV+sfNp2jjq3/TQ++uLyfVmmrRd5hu6livnDFsQgABBBBAAAEEEEgFgegayO/9Qk+d2VOjT35cs8d01vone+uihz4vx6meLnjqTY0+/5hyxlT8TZlNmyl7wqSKn6ikcdlj1a//gEDkunjRooI8W7ZqFYh8g2QbpFz9kx+kfMk1cQ9XbBNji2tiXIP4uyvgDeT91qmpcaOBfOR5NjXF9fcwjaGBfKSrjRsN5GNzs7G1aZLtosG1TRzT48dmPi5ytYnjIlc/jinfZLnZxDHlmkw3k7+LXG1MTHnYmLjI1SaOi1xtrllTHBrIR/VHwR5t/GK63pw6Vyvzvcg981do9ksT9XLOJpWyNXI8axBAAAEEEEAAAQQqtUAcn/7J1+oZozTkxn9rwdbIb2r3Nv5X4+8coYc+WFXK97hXalMmhwACCCCAAAIIIFCKQHQfLtIebZh2pzpd+5p2Fx3sSw054y0NKbofvnCETqtfq6Cpe/halhFAAAEEEEAAAQRSTyDKwrOq6p0zUA9c+ZPeXrdTW5Z+os9W19AJv/6VGhV8UXs4YE01aNtNV3RvRuEZzsIyAggggAACCCCQogJRFp6SqmXowvue0oXaoYX+p9pHHa/rH31Q3eo5bhSfoieEaSOAAAIIIIAAApVVIPrCs0iiplpfN1nLBmzTmtyFyvk2VLSlYMHbqY1Ll2j98RfpytPrFt/GPQQQQAABBBBAAIGUE4ij8JS8LR/p8QE3aswnG8qA8/t4/k5XlrGV1QgggAACCCCAAAKpIxBdA/liLvnKnXiNut37mY7rerHOrfGpJry1Wpm//6PO0Kd6860vVeuKJ/TC8HN0TNUqxfYM2h0ayCfmjNFAPjGu/lGD1DA6aPkGyTZIuXId8PsgaNdA0PL1fx8EvIH8Om/a9e28jMxbvGk/7PZC37zgXdqkhddjwlfe3tAWb8GTvb3mbW/zpq3b5fdYDfSNBvKRp8/UFNffwzSGBvKRrjZuNJCPzc3G1qZJtosG1zZxTI8fm/m4yNUmjotc/TimfJPlZhPHlGsy3Uz+LnK1MTHlYWPiIlebOC5ytblmTXFoIB/VH1x7tWvnHim9oerXrqoq9ZuoxeE7tHzZd8qrcqRadztfbTdN079mrqaBfFSuDEYAAQQQQAABBCqnQBwN5A9T3eNqS3nr9P2WPVL1ujru+JrakbtOm/2vKqpWTb9QnnK//5EG8pXz2mFWCCCAAAIIIIBAVAJxFJ5H6KSzu6ju7ml6aNgz+nhTHZ3YoYn037f0yrTZmvnmO/pYtdW6cW3RaCmqc8JgBBBAAAEEEECgUgrEUXim6fAO/TT65tOV9+7/6auth6vtlUPU55eLlH3dFer/0EyFWl6ugV2PU7A/WlQpzzuTQgABBBBAAAEEki4QVzslVTlapw/O1vt/+F4/1/+FqlbtojteeFPnzl+s9Wqok9v/Ssem83xn0s8qARFAAAEEEEAAgQooEEfh+bNWvDRMI5a205DBF6v1/pZJVY88Xqedc3wFnCopIYAAAggggAACCBxMgTj6eK7Rm9d015D5l+rFT27Vab+ovC+o08czMZcofTwT4+oflf6N2HIdJO4aCJptkH4fBCnXIF4HAe/jucP75pXBXrvje3tPfvSdtzPkd7SqnDf6eEaeV1NvMn8P0xj6eEa62rjRxzM2Nxtbm16FLvoM2sQxPX5s5uMiV5s4LnL145jyTZabTRxTrsl0M/m7yNXGxJSHjYmLXG3iuMjV5po1xUnFPp5xvNSepmp1G+uXR/6PRv2pvUYf11admtcp8UGimmrRd5hu6lgvsX96cnQEEEAAAQQQQACBCi8QR+G5V1uWzNHcTXsLJrl3dY5mri4533qq0XNPyZXcRwABBBBAAAEEEEhBgTgKz5pqfd1kLbsuBdWYMgIIIIAAAggggEDUAnH08dyjjV9M15tT52plvv9VRSVu+Ss0+6WJejlnE1+ZWYKGuwgggAACCCCAQCoKxFF45mv1jFEacuO/tWDrvpfbwwG9jf/V+DtH6KEPVvGVmeEwLCOAAAIIIIAAAikqEOVL7Xu0Ydqd6nTta9pdBPalhpzxloYU3Q9fOEKn1a+lOKrb8IOxjAACCCCAAAIIIBBggSgLz6qqd85APXDlT3p73U5tWfqJPltdQyf8+ldqVL1kH8+aatC2m67o3ozCM8AXCKkjgAACCCCAAAKuBOJoIL9DC5/srYtGHa8xHz2obvUq71dj0kDe1eVW/Dg0kC/u4fIeTZhdahY/VpBsg5SrrxykfMm1+OPC1b0guQbxmg14A3m/darnebu3e98t/cL79NNPS/n3ubd0Q/7+gcH9QQP5yHNnaorr72EaQwP5SFcbNxrIx+ZmY2vTJNtFg2ubOKbHj818XORqE8dFrn4cU77JcrOJY8o1mW4mfxe52piY8rAxcZGrTRwXudpcs6Y4NJCP8k8WL2+hnhtyre57d00Ze9ZWl8emKrtH4zK2sxoBBBBAAAEEEEAgVQSifI9nOEueFk26V/e9u1nHde2vK887UbWrhW/3l6upbpvaJVdyHwEEEEAAAQQQQCAFBeIoPLfqm89WSDV76M4Hb9M5dSrvezxT8LpgyggggAACCCCAgHOBODodVdcRDQ6XDqmhmtXjOIzzKXFABBBAAAEEEEAAgYooEEfFeJTOuOxKnbJjpqZOX6HSvryoIk6YnBBAAAEEEEAAAQQOjkAcL7X/rG8Xf6W8Wqv0+o1na8rDbdWpeR0V7+ZZUy36DtNNHesdnNkRFQEEEEAAAQQQQKDCCMRReIaU/8Myfb1l39dl7l2do5mrS86rnmr03FNyJfcRQAABBBBAAAEEUlAgjgbylUurV6/eZU5o/ry5ate+Q5nb2YAAAv/f3p3AR1Xd/R//Gi0iT0QRFxbZTCKVVYNUEf9ABRcerWx9tCBqkAAqClirWAWBglatyuJSWRSoiLWyBLXVIkj0YatIFFl8IERAa4CKQjFGijLzf90skGRmck5mTsbc5DOvFy8mc885v9993zvDj5k7vyCAAAIIIFDVBapHA/nAt8Hc9W8G5z45Jjhi8Ijg5JX/Cv6Q/WZwxuKPgv/6PuD1V/X9jQbyoYfQ1BTXm2EaQwP5UFcbNxrIR+dmY2vTJNtFg2ubOKbnj83+uMjVJo6LXL04pnzj5WYTx5RrPN1M/i5ytTEx5WFj4iJXmzgucrU5Z01xaCBf0VI9uE/vTx2l26es0oGCufV02TX5Opj/rp4c9YZe2zhFM357mRqeUPrKz4qGYTwCCCCAAAIIIICA/wVi+Fb7Ee1/91mNmLJJSaP+pBXzhuvUAo/jVe/nwzXtxib65Pkn9OL6f/tfiT1AAAEEEEAAAQQQiFkghsJzvzYsW659P7lcaTd0UsM6JRrIn3C2ut90ndpqu975OFeFXz+KOVcWQAABBBBAAAEEEPCxQAyF5yH9e883UmIjnVUv9MvxCSefqjP0vfblHVLQx0CkjgACCCCAAAIIIOBGIIbCM1ENUxpIB7fp092Hy2RzRF9vXKe1qq8LW5yhEu+FlhnHjwgggAACCCCAAAI1RSCGwvMUtftFP3XQ23ps0ov6x2cHFFBAhw7s0sa3n9N9972i/Prd1euiBmWaytcUWvYTAQQQQAABBBBAoKRAjH08/6PdKyZraPp0fVL2Qs76P9edzz6iERed6fvCM7l5C82YPbekW5W9P3PGdA0ZOqzK5lcysc2bNhX82LpNm5IPV9n7frL1U67eAfdTvuRaeU9RbCvHFtfKcfXja1f16OMZPBL8bvfGYObiOcFnnnwyOHnyjOBLb6wKbtt/2GtxVS1u9PEMPYym3mTeDNMY+niGutq40cczOjcbW5tehS76DNrEMT1/bPbHRa42cVzk6sUx5RsvN5s4plzj6Wbyd5GrjYkpDxsTF7naxHGRq805a4pDH89o/1NwQj217DFQXROtgYgKAAAgAElEQVS9qzm/1a6sLco/9L2C+onv3+2MloR5CCCAAAIIIIAAAqUFYrjGU1Lw39oy/x7990UD9MwH+wtXPrJLS++7Qb/oPFAPrfhC/Kb20uD8hAACCCCAAAII1FSBGApPr4H8VN1y/xLlXXqt/l+zkwoNE5ro8nEPqv9PszUnfYxe2pZfU23ZbwQQQAABBBBAAIESAjEUnsUN5K/RA4+M0BUt/qtw2eNOVvPON2js729T0pH3lbH6cwVKBOQuAggggAACCCCAQM0UiKHwLG4g30xNzvhJGb3jVOvMRmqmfH2+/1sKzzI6/IgAAggggAACCNREgRgKz1PUpPXZ0v51Wp9d9uN0GsjXxJOJfUYAAQQQQAABBMoTCP1dl+WNLrUtUW2v7qeOT4/X47fdrbzbf6nOyfV0QjBfez98Sy8884ryz7hJv+raiG+2l3LjBwQQQAABBBBAoGYKxN5AfuUM/XbkVK38qnQH+ePPG6CHnrxX/c47xfeFJw3kK+fJQQP5ynH1VvVTw2i/5esnWz/lynnA64HfzgG/5eu9HlSTBvLBYOC73cFP/rEi+LfFi4MZS5YGV27ICX753RGvt2q1uNFAPvQwmpriejNMY2ggH+pq40YD+ejcbGxtmmS7aHBtE8f0/LHZHxe52sRxkasXx5RvvNxs4phyjaebyd9FrjYmpjxsTFzkahPHRa4256wpDg3ko/kP1w952vv5l8o/oa7Oalq3cIUfDuizLR/pMx2vk5v+VCmnnxjNysxBAAEEEEAAAQQQqEYCMVzjKQXzNurFu2/X7/7+zwgk9XTZlNc0o/fZEbbzMAIIIIAAAggggEBNEYih8MzTprnj9bu/f62mPYbqpivPU72yXZX0E53evl5NsWQ/EUAAAQQQQAABBMoRiKHwPKBPP9wh1emt3z52ry4/zfs97dwQQAABBBBAAAEEEAgvEEMfz9o6pcHJ0vEnqU7tGJYJnxePIoAAAggggAACCFQzgRgqxvq6eMBN6pC/Qq8t26FDwWomw+4ggAACCCCAAAIIOBWIoY/nIWW/OlajHl6srfuP6Pimqepy7mllenbWUatBYzSq8xlOk473YvTxrBxx+nhWjqu3Kv0bseU8qLxzwG+2fno98FOufjwPfN7H89vgx0/3Dno9LiP/6Rgc8ddcr9WVr2/08Qw9fKbeZN4M0xj6eIa62rjRxzM6Nxtbm16FLvoM2sQxPX9s9sdFrjZxXOTqxTHlGy83mzimXOPpZvJ3kauNiSkPGxMXudrEcZGrzTlrikMfzwr9B7GO2g5frO3DKzSJwQgggAACCCCAAAI1VCCGb7UXiQW/0c7VS/X2O2u1ftcBBY4/VU3atteFXa7Q5e3OVOwBauiRYbcRQAABBBBAAIFqJhBbXRjcq5UP3abBsz5Uqd/U/vcFmvv4dPV4eIamDDhPtasZGruDAAIIIIAAAgggUHGBGL7VfkT7352u38zapIbXjtf8Feu1accObd++USv/9qyG/uxbLRv7mF7Zll/xrJiBAAIIIIAAAgggUO0EYig892vDsuXa95NeGj32Bv2sxWmqfZykExLVoNVVGjUmXUlH3lfG6s8VqHZs7BACCCCAAAIIIIBARQViKDwP6d97vpESG+msemU/sT9Otc5spGbK1+f7v6XwrOhRYTwCCCCAAAIIIFANBWIoPE9Rk9ZnS/vXau2Wb8rQ/KB/Za3WWtXXhS3OEL9MswwPPyKAAAIIIIAAAjVQIIYG8kF9/+mfNfTK+/W/dbtp6N3Xq3PLM3XSD//W5xve1IxHX9XW0wZp1tIH1K2ev0tPGshXzjODBvKV4+qtShNmbDkPKu8c8Jutn14P/JSrH88DnzeQ91qnHgrm/u+04M2pSSFN5M+96v7gq1sOBAPeMJ/faCAfegBNTXG9GaYxNJAPdbVxo4F8dG42tjZNsl00uLaJY3r+2OyPi1xt4rjI1YtjyjdebjZxTLnG083k7yJXGxNTHjYmLnK1ieMiV5tz1hSHBvIV/g/iiWp46R2a9W5fZW/J1s7cAzqc8F86vXmSWp7bXKfXjuGT/ArnwgQEEEAAAQQQQACBqixQ9ltBUeR6nE5IbKzzftZY50UxmykIIIAAAggggAACNUMghrckA/rPocMKlnL6VruyspS971CZx0sNcvpDIDdDt7caqLnZh8qse1h7suZrbM/WSm7eSUOnrdEe+jqVMeJHBBBAAAEEEEAgfgJRFJ5B/fDlev15bH91vnmBdpWsPI/s0tL7fqWeF/XSXXPW6csfSm6shJ0KfKbXJz6qpSE96gPKy5quwQ/sUPfZH2r7pws14KvHNXjqOuVVQhosiQACCCCAAAIIIGAWqHDhGfzyPT2alqYxL76vb/Yf0MHDJYrL72uree8+uqBujt4Yf4vSn/5A35TYbE6nIiMOKGvqZK2t/1PVKTstkK2FE15T6uhh6taglpTQSN3uvlOpM6dqYcg7o2Un8zMCCCCAAAIIIIBAZQhUsPD8Wqv/+LBmbz5VPca8rMzXblW7E71fV1R0q32OLr/9Eb38zsv69c+O1+anntWi7JC3I4tHx/C3947mS3pOv9KdPZqGrBPIWaOMDWcpuXHisW1126h7373KWLWLhvbHVLiHAAIIIIAAAgjETaBihWf+J3rn1W06vtsIPTD4YjUM+63143RCvQuVNvKXSjzygd76YLf76z3z1mvWs9KtQzqoRGlZhHZIOauWaWOdJDU7q1YZyMPauHiNcrjWs4wLPyKAAAIIIIAAApUvULEG8nsyNPTiu5Q1cqHW3pWqcr8SX5GxFdrPA8qa/JDe6/qARqXW1cHMCbo0LUd3vz1LN6fUlrRPmWP6KX3jIL25OE0pR0vrSI8XBu/f/4aIWaxbs1odO10ScTsbEEAAAQQQQACBqi7gvwbyXy8N3pPcPNh+wsrgt17n1HJuR7bNDvZulhTs8vSG4A/ljKvYpiPBb9bPCI5bvCt4pGDikeC/VzwYbNvshuCcbd8VLfVlcMUDXYJJ184ObiscZHjcnAEN5EONTE1xvRmmMTSQD3W1caOBfHRuNrY2TbJdNLi2iWN6/tjsj4tcbeK4yNWLY8o3Xm42cUy5xtPN5O8iVxsTUx42Ji5ytYnjIlebc9YUpyY2kD/6fqBVlX5qsn7WuZ7yXl+u9/cfKWdKvnJWvastaqwurRu5+13tees1e0kDDb22qSInnqjGyU2k7B36Io/P1Ms5SGxCAAEEEEAAAQTiKhC5fguXxnFN1T2tt07/8k+69745en93fsj1m8FD/9LGjMf064mZUrtf6X8uqh9upSgeC+jgB29o5twR6nJOC3m/Pz25eZJS0/6kfK3SxMvPU3KvOcoO1FZS5x5qWzZC4Cvt2viN2vbppKSK7XXZlfgZAQQQQAABBBBAIAqBci/TDF3veNXrOlIvTNirtHGTNODvT+rsn12h7hc31cnHHdE3uZu0dtlKbfXeDa3/33rwkQFqe1KJb72HLliBRxJUt9sEfbxzQok5gTDXeEpK6qTeKS9pedbX6tbt9MLxebu1PbuVenduVs67pSWW5i4CCCCAAAIIIICAU4EKFp6SjjtFrW56RH9p3lHPT3tWL7+fobnvl8ipXjtdM2qwbrnhSrU748QSG+J4NyFF/cZdq+sfmK7Mn96jbmfuU+YTTylryH0aXfAFpDjmQigEEEAAAQQQQACBAoGKF57etONOVvOuaZrY5Vf6zd7dys3dr++UoJPqNVCjhmfqlLBtluIpnqDE1GF6/ncv6MHLWio9v536Txyj52/oGKb9UjzzIhYCCCCAAAIIIFBzBaIrPIu9jqutUxq0KPhT/FB8/y7++D1c1Fpq0PFWzdhya7iNPIYAAggggAACCCAQZ4GK9fGMc3JVJZz3RaYZs+dWlXTKzWPmjOkaMnRYuWOqysbNmzYVpNK6TZuqklK5efjJ1k+5euh+ypdcy32axLQR25j4Ik7GNSJNzBv8Zuu/Pp5e06oaeKOPZ+hBN/Um82aYxtDHM9TVxo0+ntG52dja9Cp00WfQJo7p+WOzPy5ytYnjIlcvjinfeLnZxDHlGk83k7+LXG1MTHnYmLjI1SaOi1xtzllTHPp4xlz7swACCCCAAAIIIIAAAuEF6GgZ3oVHEUAAAQQQQAABBBwLUHg6BmU5BBBAAAEEEEAAgfACFJ7hXXgUAQQQQAABBBBAwLEAhadjUJZDAAEEEEAAAQQQCC9A4RnehUcRQAABBBBAAAEEHAtQeDoGZTkEEEAAAQQQQACB8AI0kA/vUupRGsiX4nD2Aw3knVGGLOSnpsZe8n7Kl1xDTjdnD2DrjLLUQriW4nD6g99saSDvdV/1wY0G8qEHydQU15thGkMD+VBXGzcayEfnZmNr0yTbRYNrmzim54/N/rjI1SaOi1y9OKZ84+VmE8eUazzdTP4ucrUxMeVhY+IiV5s4LnK1OWdNcWgg7/T/ASyGAAIIIIAAAggggMAxAa7xPGbBPQQQQAABBBBAAIFKFKDwrERclkYAAQQQQAABBBA4JkDhecyCewgggAACCCCAAAKVKEDhWYm4LI0AAggggAACCCBwTIDC85gF9xBAAAEEEEAAAQQqUYDCsxJxWRoBBBBAAAEEEEDgmAAN5I9ZRLxHA/mINDFtoIF8THzlTvZTU2NvR/yUL7mWe+rFtBHbmPgiTsY1Ik3MG/xmSwN5r/uqD240kA89SKamuN4M0xgayIe62rjRQD46NxtbmybZLhpc28QxPX9s9sdFrjZxXOTqxTHlGy83mzimXOPpZvJ3kauNiSkPGxMXudrEcZGrzTlrikMD+ZhrfxZAAAEEEEAAAQQQQCC8ANd4hnfhUQQQQAABBBBAAAHHAhSejkFZDgEEEEAAAQQQQCC8AIVneBceRQABBBBAAAEEEHAsQOHpGJTlEEAAAQQQQAABBMILUHiGd+FRBBBAAAEEEEAAAccC9PG0AKWPpwVSFEPo4xkFmuUUP/WW83bJT/mSq+VJGMUwbKNAs5iCqwVSlEP8ZksfT68Jlg9u9PEMPUim3mTeDNMY+niGutq40cczOjcbW5tehS76DNrEMT1/bPbHRa42cVzk6sUx5RsvN5s4plzj6Wbyd5GrjYkpDxsTF7naxHGRq805a4pDH88oK36mIYAAAggggAACCCBgEuAaT5MQ2xFAAAEEEEAAAQScCFB4OmFkEQQQQAABBBBAAAGTAIWnSYjtCCCAAAIIIIAAAk4EKDydMLIIAggggAACCCCAgEmAwtMkxHYEEEAAAQQQQAABJwIUnk4YWQQBBBBAAAEEEEDAJEAD+SKh/v1viGi1bs1qdex0ScTtbEAAAQQQQAABBKq6AA3kve6rPrjRQD70IJma4nozTGNoIB/qauNGA/no3GxsbZpku2hwbRPH9Pyx2R8XudrEcZGrF8eUb7zcbOKYco2nm8nfRa42JqY8bExc5GoTx0WuNuesKQ4N5Kt6qU5+CCCAAAIIIIAAAr4V4BpP3x46EkcAAQQQQAABBPwlQOHpr+NFtggggAACCCCAgG8FKDx9e+hIHAEEEEAAAQQQ8JcAhae/jhfZIoAAAggggAACvhWg8PTtoSNxBBBAAAEEEEDAXwIUnv46XmSLAAIIIIAAAgj4VoAG8haHLrl5C82YPddi5I8/ZOaM6RoydNiPn4hFBps3bSoY1bpNG4vRP/4QP9n6KVfvyPopX3KtvOcitpVji2vluPrxtYsG8l73VR/caCAfepBMTXG9GaYxNJAPdbVxo4F8dG42tjZNsl00uLaJY3r+2OyPi1xt4rjI1YtjyjdebjZxTLnG083k7yJXGxNTHjYmLnK1ieMiV5tz1hSHBvKV958CVkYAAQQQQAABBBCo4QJc41nDTwB2HwEEEEAAAQQQiJcAhWe8pImDAAIIIIAAAgjUcAEKzxp+ArD7CCCAAAIIIIBAvAQoPOMlTRwEEEAAAQQQQKCGC1B41vATgN1HAAEEEEAAAQTiJUAfTwtp+nhaIEUxhD6eUaBZTvFT3z5vl/yUL7lanoRRDMM2CjSLKbhaIEU5xG+29PH0mmD54EYfz9CDZOpN5s0wjaGPZ6irjRt9PKNzs7G16VXoos+gTRzT88dmf1zkahPHRa5eHFO+8XKziWPKNZ5uJn8XudqYmPKwMXGRq00cF7nanLOmOPTxjLLiZxoCCCCAAAIIIIAAAiYBrvE0CbEdAQQQQAABBBBAwIkAhacTRhZBAAEEEEAAAQQQMAlQeJqE2I4AAggggAACCCDgRIDC0wkjiyCAAAIIIIAAAgiYBCg8TUJsRwABBBBAAAEEEHAiQOHphJFFEEAAAQQQQAABBEwCNJA3CUmigbwFUhRDaCAfBZrlFD81NfZ2yU/5kqvlSRjFMGyjQLOYgqsFUpRD/GZLA3mv+6oPbjSQDz1Ipqa43gzTGBrIh7rauNFAPjo3G1ubJtkuGlzbxDE9f2z2x0WuNnFc5OrFMeUbLzebOKZc4+lm8neRq42JKQ8bExe52sRxkavNOWuKQwP5KCt+piGAAAIIIIAAAgggYBLgGk+TENsRQAABBBBAAAEEnAhQeDphZBEEEEAAAQQQQAABkwCFp0mI7QgggAACCCCAAAJOBCg8nTCyCAIIIIAAAggggIBJgMLTJMR2BBBAAAEEEEAAAScCFJ5OGFkEAQQQQAABBBBAwCRAA3mTEA3kLYSiG0ID+ejcbGb5qamxtz9+ypdcbc7A6MZgG52baRauJqHot/vNlgbyXvdVH9xoIB96kExNcb0ZpjE0kA91tXGjgXx0bja2Nk2yXTS4toljev7Y7I+LXG3iuMjVi2PKN15uNnFMucbTzeTvIlcbE1MeNiYucrWJ4yJXm3PWFIcG8tEX/cxEAAEEEEAAAQQQQKBcAR9e43lQ2cuf0tBWLQp+h3pyzzGal7VHgZDdPKw9WfM1tmdrJTfvpKHT1mhP6KCQWTyAAAIIIIAAAgggUDkCPis8Dyv39fl6S1fpyS07tP3TNfpzz716rO9wTcs6UEIooLys6Rr8wA51n/2htn+6UAO+elyDp65TXolR3EUAAQQQQAABBBCIn4C/Cs/AF9p+yjUa3j1FiZ5RQgNdeMdvdHf7/9MLiz7SwWK3QLYWTnhNqaOHqVuDWlJCI3W7+06lzpyqhdmHikfxNwIIIIAAAggggEAcBfxVeCa0UJcuZ6tU0gn11azt6aXIAjlrlLHhLCU3LihPC7fVbaPuffcqY9WuMB/Ll5rODwgggAACCCCAAAKVIFCqhquE9eO05Km69MJzCt8F1SHlrFqmjXWS1OysWmXiH9bGxWuUw7WeZVz4EQEEEEAAAQQQqHwB//fxPJipsTduVJ+Xhis10auj9ylzTD+lbxykNxenKeVoaR3p8ULk/v1viKi9bs1qdex0ScTtbEAAAQQQQAABBKq6AH08vSZYMd32B9c/+Zvg5PX7S6zyZXDFA12CSdfODm47UuLhYKTHS44Jf58+nqEupt5k3gzTGPp4hrrauNHHMzo3G1ubXoUu+gzaxDE9f2z2x0WuNnFc5OrFMeUbLzebOKZc4+lm8neRq42JKQ8bExe52sRxkavNOWuKQx/Pql6ql8rP++b6q1pcL03pqaeW2JKoxslNpOwd+iKPz9RLwHAXAQQQQAABBBD4UQWOfhD9o2YRRfBA7lLN3nyJRqe1Lrq2s3iR2krq3ENti38s/jvwlXZt/EZt+3RSkm/3unhn+BsBBBBAAAEEEPCfgC9LsMCeTD2zoLb+54biojOgvK2LNPe9fQVHICGpk3qnrNbyrK+PHZG83dqe3Uq9Ozcr/a34YyO4hwACCCCAAAIIIFCJAj4rPAPKy87QuEHDNfXJQbr0nKLfXtQ8SedfuUhqWNQ+KSFF/cZdq6xHpytzz2EpkKvMJ55S1pCR6pdSuxI5WRoBBBBAAAEEEEAgkoCvCs9A7mu6t9ddevmT/ND9ad9DlyQVF5UJSkwdpud/V1/zL2up5HNu0/Lk+/T8yI5lPpYPXYZHEEAAAQQQQAABBCpH4ITKWbZyVk1o1FvPbultuXgtNeh4q2ZsudVyPMMQQAABBBBAAAEEKlPAV+94ViYEayOAAAIIIIAAAghUroD/G8hXrk/B6snNW2jG7LlxiBR7iJkzpmvI0GGxLxSHFTZv2lQQpXWbNnGIFnsIP9n6KVfvyPgpX3KN/bkUaQVsI8nE9jiusfmVN9tvtjSQ97qv+uBGA/nQg2RqiuvNMI2hgXyoq40bDeSjc7OxtWmS7aLBtU0c0/PHZn9c5GoTx0WuXhxTvvFys4ljyjWebiZ/F7namJjysDFxkatNHBe52pyzpjg0kC+vrGcbAggggAACCCCAAAIxCHCNZwx4TEUAAQQQQAABBBCwF6DwtLdiJAIIIIAAAggggEAMAhSeMeAxFQEEEEAAAQQQQMBegMLT3oqRCCCAAAIIIIAAAjEIUHjGgMdUBBBAAAEEEEAAAXsBCk97K0YigAACCCCAAAIIxCBAA3kLPBrIWyBFMYQG8lGgWU7xU1Njb5f8lC+5Wp6EUQzDNgo0iym4WiBFOcRvtjSQ97qv+uBGA/nQg2RqiuvNMI2hgXyoq40bDeSjc7OxtWmS7aLBtU0c0/PHZn9c5GoTx0WuXhxTvvFys4ljyjWebiZ/F7namJjysDFxkatNHBe52pyzpjg0kI+y4mcaAggggAACCCCAAAImAa7xNAmxHQEEEEAAAQQQQMCJAIWnE0YWQQABBBBAAAEEEDAJUHiahNiOAAIIIIAAAggg4ESAwtMJI4sggAACCCCAAAIImAQoPE1CbEcAAQQQQAABBBBwIkAfTwtG+nhaIEUxhD6eUaBZTvFTbzlvl/yUL7lanoRRDMM2CjSLKbhaIEU5xG+29PH0mmD54EYfz9CDZOpN5s0wjaGPZ6irjRt9PKNzs7G16VXoos+gTRzT88dmf1zkahPHRa5eHFO+8XKziWPKNZ5uJn8XudqYmPKwMXGRq00cF7nanLOmOPTxjLLiZxoCCCCAAAIIIIAAAiYBrvE0CbEdAQQQQAABBBBAwIkAhacTRhZBAAEEEEAAAQQQMAlQeJqE2I4AAggggAACCCDgRIDC0wkjiyCAAAIIIIAAAgiYBCg8TUJsRwABBBBAAAEEEHAiQOHphJFFEEAAAQQQQAABBEwCNJA3CUmigbwFUhRDaCAfBZrlFD81NfZ2yU/5kqvlSRjFMGyjQLOYgqsFUpRD/GZLA3mv+6oPbjSQDz1Ipqa43gzTGBrIh7rauNFAPjo3G1ubJtkuGlzbxDE9f2z2x0WuNnFc5OrFMeUbLzebOKZc4+lm8neRq42JKQ8bExe52sRxkavNOWuKQwP5KCt+piGAAAIIIIAAAgggYBLgGk+TENsRQAABBBBAAAEEnAhQeDphZBEEEEAAAQQQQAABkwCFp0mI7QgggAACCCCAAAJOBCg8nTCyCAIIIIAAAggggIBJgMLTJMR2BBBAAAEEEEAAAScCFJ5OGFkEAQQQQAABBBBAwCRAA/kiof79b4hotW7NanXsdEnE7WxAAAEEEEAAAQSqugAN5L3uqz640UA+9CCZmuJ6M0xjaCAf6mrjRgP56NxsbG2aZLtocG0Tx/T8sdkfF7naxHGRqxfHlG+83GzimHKNp5vJ30WuNiamPGxMXORqE8dFrjbnrCkODeSreqlOfggggAACCCCAAAK+FeAaT98eOhJHAAEEEEAAAQT8JUDh6a/jRbYIIIAAAggggIBvBSg8fXvoSBwBBBBAAAEEEPCXAIWnv44X2SKAAAIIIIAAAr4VoPD07aEjcQQQQAABBBBAwF8C9PG0OF7JzVtoxuy5FiN//CEzZ0zXkKHDfvxELDLYvGlTwajWbdpYjP7xh/jJ1k+5ekfWT/mSa+U9F7GtHFtcK8fVj69d9PH0mmD54EYfz9CDZOpN5s0wjaGPZ6irjRt9PKNzs7G16VXoos+gTRzT88dmf1zkahPHRa5eHFO+8XKziWPKNZ5uJn8XudqYmPKwMXGRq00cF7nanLOmOPTxrLz/FLAyAggggAACCCCAQA0X4BrPGn4CsPsIIIAAAggggEC8BCg84yVNHAQQQAABBBBAoIYLUHjW8BOA3UcAAQQQQAABBOIlQOEZL2niIIAAAggggAACNVyAwrOGnwDsPgIIIIAAAgggEC8BCs94SRMHAQQQQAABBBCo4QI0kLc4AWggb4EUxRAayEeBZjnFTw2jvV3yU77kankSRjEM2yjQLKbgaoEU5RC/2dJA3uu+6oMbDeRDD5KpKa43wzSGBvKhrjZuNJCPzs3G1qZJtosG1zZxTM8fm/1xkatNHBe5enFM+cbLzSaOKdd4upn8XeRqY2LKw8bERa42cVzkanPOmuLQQD7Kip9pCCCAAAIIIIAAAgiYBLjG0yTEdgQQQAABBBBAAAEnAhSeThhZBAEEEEAAAQQQQMAkQOFpEmI7AggggAACCCCAgBMBCk8njCyCAAIIIIAAAgggYBKg8DQJsR0BBBBAAAEEEEDAiQCFpxNGFkEAAQQQQAABBBAwCdBA3iQkiQbyFkhRDKGBfBRollP81NTY2yU/5UuulidhFMOwjQLNYgquFkhRDvGbLQ3kve6rPrjRQD70IJma4nozTGNoIB/qauNGA/no3GxsbZpku2hwbRPH9Pyx2R8XudrEcZGrF8eUb7zcbOKYco2nm8nfRa42JqY8bExc5GoTx0WuNuesKQ4N5KOs+JmGAAIIIIAAAggggIBJgGs8TUJsRwABBBBAAAEEEHAiQOHphJFFEEAAAQQQQAABBEwCFJ4mIbYjgAACCCCAAAIIOBGg8HTCyCIIIIAAAggggAACJgEKT5MQ2xFAAAEEEEAAAQScCNDH04KRPp4WSFEMoY9nFGiWU/zUW87bJT/lS66WJ2EUw7CNAs1iCq4WSFEO8ZstfTy9Jlg+uNHHM/QgmbuWxRYAABX5SURBVHqTeTNMY+jjGepq40Yfz+jcbGxtehW66DNoE8f0/LHZHxe52sRxkasXx5RvvNxs4phyjaebyd9FrjYmpjxsTFzkahPHRa4256wpDn08o6z4mYYAAggggAACCCCAgEmAazxNQmxHAAEEEEAAAQQQcCJA4emEkUUQQAABBBBAAIHqJ/DcH5/TsmXLnO0YhaczShZCAAEEEEAAAQSql0DDhg10a/oQ9b/+emVnZ8e8cxSeMROyAAIIIIAAAgggUD0FevXurfez1ispOVk9L79Cf3jsMX399ddR7yyFZ9R0TEQAAQQQQAABBKq/wGmnnaZJDz2kN99eqqz16/Wz1A5akpGh7777rsI7T+FZYTImIIAAAggggAACNU8gJSVFL7/yip6bNVNTp0zR1T17as2aNRWCoIF8EZfXJJ4bAggggAACCCBQHQU6drpE69asrpRd8wrRHj162K3tNUDlVr6ATQP58ldws/X7778Pen/Ku9k03y1vvrfNJo5pDZvtNg3kbdaxGWNys1nDZBsvN5s4plxt9jeeY6pKvocOHTLutotcbeIYE7EY4CJXizDOhpjyjZebTRxTrs5QHCzkIlcbEwepGn+JgIsYLteI1dZ7PfebbX5+fnDeiy8Gvdro9ttuC27btq1CpCfYlaeMqgoCJ5wQn8MVrzjxNI3HPsUjhmcWrzjxPD5VJdaJJ54Yl1TiFScuOxPHIPFyi1ecONLFHAqTmAnDLuC9nvvpNd1rq/TwpEkF+/Liy/PVqVOnsPtV3oPxqWTKy4BtCCCAAAIIIIAAAlVWwGuj9OCYMVr3j/f1xJTJuuLKK3XSSSdFlS9fLoqKjUkIIIAAAggggED1FxjzwAMFbZRSO3QoaKvktVeKtuj0tHjHs/qfM+whAggggAACCCAQlUDHjh11c1qavG+0u7hReLpQZA0EEEAAAQQQQKAaCnjvcLq88VG7S03WqpBAmzZtdPbZjSs0h8EIIIAAAgggUBUE/qkl6any2lEmt7pLS3IPS4E9+mDaELVr3kIXTs7SD2HSpI9nGBQeQgABBBBAAAEEEDALBHIzdEePu7Sy72OacuY2fX7lnbq5Zd2IE2vIO56HtSdrvsb2bK3k5p00dNoa7QlENGEDAggggAACCCCAgIVAQqNLdV3fpsqf96QWNL1RN5ZTdHrL1YDCM6C8rOka/MAOdZ/9obZ/ulADvnpcg6euU54FKEMQQAABBBBAAAEEIgmcptQe3VRHSbqo9ZnGwrL6F56BbC2c8JpSRw9Ttwa1pIRG6nb3nUqdOVULsw9FUuRxBBBAAAEEEEAAAWuBD5WxapdMHyhX+8IzkLNGGRvOUnLjxGN0dduoe9+9VkDHJnHPjUBAedlva0p6p8ILkpv30tgX13HpgxvcEqscVm7GXWrXa46yTa8CJWZx10bAu3TnLS2eXHgBfbsxmTpoM40xkQXysvVOkaf3RYV26U/pnWxUI4NF2nJQ2ZmvF5ybF0Y8L7n0LJJexMfzspWZ8YqmpPfS2Mx9ocNKnb+tdfWY+craczh0XDV9JLBnhaYuO6Krz5Nytu82fppczQvPQ8pZtUwb6ySp2Vm1yhzyw9q4eI1y+Ee5jEvl/hjIXarZb0pXT1ml7Tu3auWrPbX392lc+uCYPZD7N026P0P5jtet8csVfGNzuK4YuFC7mt2ohZty9PGkbop8GX2NFzMDBD7Tkntu0qjNXfXqppyC14WlAw/qiV5PKPMgL9BmwOIRh5Q9Z7R+P2++xk1dpvBlD5eeFWtZ/x3Yqrk3T9D8JVP09LIDodMCn+mNFzKla57Qxzt3aNvaWbpqz1O6btB0ZeXVgPM38Jlef2iF2t1+r265/gLlL1qhrNyPNW/aW8qNsPvVvPDM0xfbP5dSWqhxYjXf1dCnQxV85JB2bq+nfndcrpSC41FLDTqm6Z57L9DWmW/oA/6RcXPM8tZp2oOrVP+SBm7WY5UigQPKmjpct3zcQS+884xG9e1SdB4DFItAIOcdzXmzlnoNvEoti18XuvxS16Ws1vKsr2NZuobNra2UtD/qhRnjdXf7OuH3nUvPwruU92hCS928cJ6eu3+Y2oYZF9j5her+8mZdllL438+EBp00fPQwtf1kgRZ/UI3PX68g79VayVc/L424V70aJaphu4vUMn+B/vDsp7rolivUKELZRQP5MCcSD1WWQG2d0+WiMovX0lnNkxThZbLMWH40CxxQ1sy/SLcPVfdF7+vlL80zGGEj4L1T9KLGzmyqictu0YXe9eLcnAgknNVcbersU9aHO5TX7XQVXBSVt1vbP7tE3VNPcxKDRQoFii896x3m0rOpq3bpxpSWxi+GYFlaIOGcTupS+iEVntNlHqxuP3oF+ZLNurnEfiWm3qm/7ryzxCPh70aoR8MP9t+jiWqc3ETK3qEvasJb3v47QEczrtX1Ap3Lu9JHPaK74xVHL+k5Xaf01HrRLcGs8AIF7xTNlvq2VeCV4QXNkZNbDdGU5dnG65nCL8ijRwXqnq8+Q36qrVNH6NdzNisvkKvMKSt05ozb1KVuNf8n6ihCPO5w6Vk8lI/GODFVF57LRThHPUrcqebP6tpK6twj9O3xwFfatfEbte3TSUnVXKDEsa6id79W1rJcDRzSLeLb8lU08aqXVt56zXpWunVIh8J3japehr7NqPCdoiZKbdlWnUbO1Mc7N+iv956gFwbfp1lZYa778u2e/hiJn6rUkc/oz79uo7Xjr9H559yrXf1/qzs7NuDdN6eHg0vPnHJGXCygg1n/q003DVD3RnwyEo6p2pddCUmd1LvstULexzjZrdS7czNe2MKdFXF7zHuH7hXNrz9U6amnxi1q9Qx0QFkvvKsWvxuiVN45dnyIA8r7Yody6pyv7r06qEHBq2ZdtbxplO5u/396ekIGnQNiFU+oo1Oanq9bRl6vllqliSOeUGYN+lZwrHzMr0ICeev1wrzTNJY3ACIelGpfeCohRf3GXausR6cXvpB5H+M88ZSyhoxUv5TaEWHYEAeBvPWavaie7uYJGiO2V8C/qteaXqdf8D/sGC3DTT+svTtzQjsEJDTTJX0u4FKecGQVeuygts6ZqKf1C4246xG9vnaWBmq+0mvKt4IrZBXLYC49i0XPbq73BsBS1bvnRt4AKAes+heeSlBi6jA9/7v6mn9ZSyWfc5uWJ9+n50d25OPIck6MSt9U0IJip66471dF32St9IjVOMDX+mDRPM0b1VXnNm9R1B+1o9LnfSZtmKCe57RWnzlbjU19qzFQjLtW9AW4/Bzt2humSQ1dM2LyDWQv0n3jdyu16DeeJDTorvGvztEdmq2JC7I5b2PSLTmZS89Kari/f1i5r7+qLYbfU+4+rv9WrAGFp3dQvLY9t2rGlh3avnOJJt7YsejjMv8dsGqRsfeu89N/V+J1vY4VnXmbNW/OGhpxR3WAT1e3Se9q+07v/C7+s06zBjaV2o/Tm59u1uI0vq0aFW3BpATVTf25etXJ0T82/6tEIeRdM7eXa8Wjh5VUdBlD2TUSW+j8DvXLPsrPMQpw6VmMgBGnH9aezLlaePLVGnD095Qf1NYX5+s92gSGqNWQwjNkv3ngxxLI26olD96m9CcfVvrFLYvenWuh5DbXaaFO413oH+u4ELd8gbqX6LaHL9bK+3+vF7d6v1HnsPasW6D5G6/V2F+mcK14+XrlbE1Q3Quv0S3nfagnHl2grQXdRwLK2/qW5v+1jdKuaIFtOXoV3sSlZxUmM084qOyMhzQ47WFNTetc4lOn9rp6wWE15Jr7EEIKzxASHqg0gYLfUJKmu+d9HCbEBXzZK4wKD1UVgVpq1HuCFj7VSqv6tFdy8ws0eEld3Tp9GNdyxXqIEjtqxOw5urfBq7q6TZKSmyfpkj/s16/+MkG9uGa5AroBHcwcp3bnXKWJG/KVP2+QUpsP1NzsQyXW4NKzEhiWd/cpc0xXnXv5BG3UZ3o5raOSj/4qYu9XE49Tv1F/0taQ1erwaUiISeEDxwWDwWCEbTyMAAIIIIAAAggggIAzAd7xdEbJQggggAACCCCAAALlCVB4lqfDNgQQQAABBBBAAAFnAhSezihZCAEEEEAAAQQQQKA8AQrP8nTYhgACCCCAAAIIIOBMgMLTGSULIYAAAggggAACCJQnQOFZng7bEEAAAQQQQAABBJwJUHg6o2QhBBBAAAEEEEAAgfIEKDzL02EbAggggAACCCCAgDMBCk9nlCyEAAIIIIAAAgggUJ4AhWd5OmxDAAEEEEAAAQQQcCZA4emMkoUQQAABBBBAAAEEyhOg8CxPh20IIIBANRQI7MnSG4sma+gF45R5MFAN95BdQgCBqipA4VlVjwx5IYCAQ4GADmaOU7vmAzU3+5CkQ8qeM1DJrSpSeB1U9vJnNP7FrfJlqZa3TlPSn1FW3pd67+m7NOrX0/TOfxwSH10qoLysp9Tntgzl+hLq6I5wBwEEKkGAwrMSUFkSAQSqukBtpaTN0/YtE9StruXL4MEs/enOZ7XhSFXft3D57VPmI5O07Zpf6PzEM9Rt0kLNGtg03EAHjyUoMbW/RtafrUmvfebPIt2BAksggEB4ActX3PCTeRQBBBBAoKoLeO9Avqw/bOyju65tqvi86J+uLjf30e77n9d7fJRf1U8Q8kMgrgLxeQ2K6y4RDAEEarxAYI+yMiZraKsWSm7eQu3Sp2rph7klWMp+1B5QXnam5o7pVTDem5Pcc4zmZmYrz5t1MFNjLx6kl/PztXH8VTr36Ef0h7UnK0NT0juFn6djH/HPznxP846u30lDJ7+t7LySn0V7a83X2J6tC9dqNURTlhfFL8o8sGddiTVa6+oxc5SZfbDEfoW5G/inls9coFp9Oikpjq/4CUmXKa1rpqYuyuZdzzCHhYcQqKkCcXwZqqnE7DcCCMRX4ICypg7XddMP6OolG7R9Z45Wj26hDUtXKz9SInnrNWvEOK1Kflgf7dyh7Tu3auXok/SXtAla6F0TWrebJq6drf516qjt+Le0reAjeikva7oGD/yrjh+2WNtKzbtPs7IOlIi2Sg89ulwn3/yitu/coW1rJ6nR0tEaNXN9YWGrw8rNGK0r+r4iDVukj3bm6KPFXbXlzpt0b0bhx9WB3AzdcdkIvXfmfVr5qZfjGj2Z/A+N6DVOS3IPl4hV+m4g5x3NebOJenduVs67nfuUOaZrUfHcVWMz90l52cos/gLSgVx9MG2I2hUU5A8pc89hlSyC26XP09ZSRbSkhDPV6qIm2rh4jXJK1tel0+MnBBCoYQIUnjXsgLO7CFR7gYMfafHMfeo/+k71SqnrVUBKTLlW94z+pepE2PnA7s1695Mm6tw5SYkFY2qpQbcH9Ned83RzSu0Is77WB4sW6PO+N+jmjg2KirpaatDll7qu/Q69+/HeEu/0NS2Rj5TQoL26dThZWzM3a7dXlAV26O3ZS6WBd+me3i2V6OXc8ioN6FtLS2e/o5zAPr337GQtTRmme+7opAYFr9x11TJtoqb1zdLYZ1cr/PueAeV9sUM5dZLU7KxaEfbDe7iuftprkO64Z75WfvquJnaTMh9JV3rBF5By9VHmHp19x0x9vOkvukPzNWLMM1ryf6eq96Ql2rZ2lvp+8aTuW1D2nc1aOqt5kupsWKbVOd4XurghgAAC3isyNwQQQKDaCAR0MGuFluQ3UXLjwhKycNcSlNi4hZIi7GdCw9bqet6HemLu3/RB5t/MH18XrHO6uk16Vx9PStXezNe1JCNDSzJe0Nir+2riBtPXxRPVOLmJlL1DX+QFFMhZo4wNUlJyw6LC1wtQuP72JWlKyduk5Ys+U522zXVWqVftwnXyF61QVthrKQ9r784c5ae0UOPEUhNLSBzU1jmP6rkvOil9eHFR68X+u94c31lSI51/2fmFxW5iC53f4XTlf1lPbbqkFOSacObZalHrP8rZvrvo3dvipYvNP9f2LwouWCjewN8IIFCDBSK9EtVgEnYdAQT8K1BUaFV0BxI7atSrGZp24QEtefQepV/eXsnNe2nsnMwy12GWXDigvK3zNLRVe/VMm6UPDnhvXZ6h7lNe0Nj2ClOIlZwb3f38eYOU6n3cffTPeeo5flU5i+Xpi+2fl7M9Vx9Mv0c3bP9/+nXBO63lDGUTAggg4EDgBAdrsAQCCCBQRQSKPt5VTsXzSUxRt97en1s00fty0msv67n7B6nf9tlaOambvA/tS90C2Vp47++1tutkvfdMbzUq/m+890Wk7HypbanRDn7wri9dpIVpLSvwUVXRO6sbyw9/eN5kPdnjXD3YrVEF1i5/TbYigAAC4QSKXyrDbeMxBBBAwGcCCaqb+nP1qlP2492iax1t9yahgVJ736gBfZsqf+NO7Q335Zi83dqeLSVddF7RNZeFiwfyDugr2zhF4xKSOql3yLukRd+895re701W976nK+cfn2hPqVwOKGtyPyX3mqPsUo8XJ1BUiBd9pF/86LG/G+nCYX/Qq+MbadHtE/Xi1vBXih4bX5F7xeZlL3uoyBqMRQCB6iZA4Vndjij7g0BNF6h7iW57OFVLbh+ruQWFlNcq6TX94dEFEb/VHsieoz7eR+sZW4uuU/TmrNTy9dIVgy4rbEOU2FDJKScW6ubnKS+xTUExuPGVBXpvT+G3ygN71uiZBx/V0ohfn49wcBJa6Mq7BqiJ985jZm7Bl5ICe1bppVe2qOXIkeqXcra63H6XLn33UY1/ek1R8XlQ2RmTNXaqdMe43koJ+2pedJ1lfo527Y30zfe6annTWE37n1xN7DO6yCxCnhV6uOiyh/Y9dElSpC9oVWhBBiOAQDUQCPtSVQ32i11AAIEaK1BLjXpP0MKnWmlVH+9azSSdP+JDpQ4bFPHT74SUAfrjokGq/0aazi+4fjJJ5/f6q+oPm6wHi5uuFxSH/XS4oI/nrVqYk6gudzyu8R3eV/rFLQuuuzx/zFqdPfBxPVHh3wrkfYv+Hj2/6HodefRyndu8hc69eJqODJiu50d2LPwST6Nr9diS36vzvx7Rped413m2V783TtXQRc9oROqpEY92Qso1GjlwrzJW7Sr8ln1gq+b26qr0eZ9J+X9SerubNNfrd3TkgJT/liZe2V7t7ntCj/fqUHj9aPGYrR8dm7dhgnq2GafMfy7X2DZXaeKGfBVcf3q0v6n3Tf1dWr14i9rGuX9oRAg2IIBAlRA4LhgMBqtEJiSBAAIIIFAJAt5vLnpG1z8gTXx1uFIjfrvdbWjvXeR+vXZo5Npx9r+W1G0KrIYAAlVQgHc8q+BBISUEEEDAnUDh706/p8MyzVr2zxK9Rd1FCF1pn96bu1gNHx6sLnX5ZybUh0cQqLkCvCLU3GPPniOAQI0ROF1d7hihM994XR+V/Q1Dzg0Kfzf81K8GaUzxZQrOY7AgAgj4VYCP2v165MgbAQQQQAABBBDwmQDvePrsgJEuAggggAACCCDgVwEKT78eOfJGAAEEEEAAAQR8JkDh6bMDRroIIIAAAggggIBfBf4/AWfySevhrkEAAAAASUVORK5CYII=" alt></p>
<p>His data are also listed in the following table.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p>Use the scatter diagram to find the value of \(a\) and of \(b\) in the table.</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</p>
<p>i) \({\bar x}\) , the mean distance from the power plant;</p>
<p>ii) \({\bar y}\) , the mean concentration of \({\text{PM}}10\) ;</p>
<p>iii) \(r\) , the Pearson’s product–moment correlation coefficient.</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 equation of the regression line \(y\) on \(x\) .</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>Ernesto’s school is located \(14\,{\text{km}}\) from the power plant. He uses the equation of the regression line to estimate the concentration of \({\text{PM}}10\) in the air at his school.</p>
<p>i) Calculate the value of Ernesto’s estimate.</p>
<p>ii) State whether Ernesto’s estimate is reliable. Justify your answer.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Throughout this question <em>all</em> the numerical answers must be given correct to the nearest whole number.</strong></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Park School started in January 2000 with \(100\) students. Every full year, there is an increase of \(6\% \) in the number of students.</span></p>
<p><span>Find the number of students attending Park School in</span></p>
<p><span>(i) January 2001;</span></p>
<p><span>(ii) January 2003.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Park School started in January 2000 with \(100\) students. Every full year, there is an increase of \(6\% \) in the number of students.</span></p>
<p><span>Show that the number of students attending Park School in January 2007 is \(150\).</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><span>Grove School had \(110\) students in January 2000. Every full year, the number of students is \(10\) more than in the previous year.</span></p>
<p><span>Find the number of students attending Grove School in January 2003.</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><span>Grove School had \(110\) students in January 2000. Every full year, the number of students is \(10\) more than in the previous year.</span></p>
<p><span>Find the year in which the number of students attending Grove School will be first \(60\% \) <strong>more than</strong> in January 2000.</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><span>Each January, one of these two schools, the one that has more students, is given extra money to spend on sports equipment.</span></p>
<p><span>(i) Decide which school gets the money in 2007. Justify your answer.</span></p>
<p><span>(ii) Find the first year in which Park School will be given this extra money.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A parcel is in the shape of a rectangular prism, as shown in the diagram. It has a length \(l\) cm, width \(w\) cm and height of \(20\) cm.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The total volume of the parcel is \(3000{\text{ c}}{{\text{m}}^3}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Express the volume of the parcel in terms of \(l\) and \(w\).</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><span>Show that \(l = \frac{{150}}{w}\).</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><span>The parcel is tied up using a length of string that fits <strong>exactly </strong>around the parcel, as shown in the following diagram.</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_11.55.29_3.png" alt><br></span></p>
<p><span>Show that the length of string, \(S\) cm, required to tie up the parcel can be written as</span></p>
<p><span>\[S = 40 + 4w + \frac{{300}}{w},{\text{ }}0 < w \leqslant 20.\]</span></p>
<p><span> </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><span>The parcel is tied up using a length of string that fits <strong>exactly </strong>around the parcel, as shown in the following diagram.</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_11.55.29_5.png" alt><br></span></p>
<p><span>Draw the graph of \(S\) for \(0 < w \leqslant 20\) and \(0 < S \leqslant 500\), clearly showing the local minimum point. Use a scale of \(2\) cm to represent \(5\) units on the horizontal axis \(w\)<em> </em>(cm), and a scale of \(2\) cm to represent \(100\) units on the vertical axis \(S\) (cm).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The parcel is tied up using a length of string that fits <strong>exactly </strong>around the parcel, as shown in the following diagram.</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_11.55.29_4.png" alt><br></span></p>
<p><span>Find \(\frac{{{\text{d}}S}}{{{\text{d}}w}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The parcel is tied up using a length of string that fits <strong>exactly </strong>around the parcel, as shown in the following diagram.</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_11.55.29.png" alt><br></span></p>
<p><span>Find the value of \(w\) for which \(S\) is a minimum.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The parcel is tied up using a length of string that fits <strong>exactly </strong>around the parcel, as shown in the following diagram.</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_11.55.29_1.png" alt><br></span></p>
<p><span>Write down the value, \(l\), of the parcel for which the length of string is a minimum.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The parcel is tied up using a length of string that fits <strong>exactly </strong>around the parcel, as shown in the following diagram.</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_11.55.29_2.png" alt><br></span></p>
<p><span>Find the minimum length of string required to tie up the parcel.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">On the coordinate axes below, \({\text{D}}\) is a point on the \(y\)-axis and \({\text{E}}\) is a point on the \(x\)-axis. \({\text{O}}\) is the origin. The equation of the line \({\text{DE}}\) is \(y + \frac{1}{2}x = 4\).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the coordinates of point \({\text{E}}\).</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><span>\({\text{C}}\) is a point on the line </span><span><span>\({\text{DE}}\)</span>. </span><span><span>\({\text{B}}\)</span> is a point on the \(x\)-axis such that </span><span><span>\({\text{BC}}\)</span> is parallel to the \(y\)-axis. The \(x\)-coordinate of </span><span><span>\({\text{C}}\)</span> is \(t\).</span></p>
<p><span>Show that the \(y\)-coordinate of </span><span><span>\({\text{C}}\)</span> is \(4 - \frac{1}{2}t\).</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><span><span>\({\text{OBCD}}\) </span>is a trapezium. The \(y\)-coordinate of point </span><span><span>\({\text{D}}\)</span> is \(4\).<br></span></p>
<p><span>Show that the area of </span><span><span><span>\({\text{OBCD}}\) </span></span>is \(4t - \frac{1}{4}{t^2}\).</span></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><span>The area of </span><span><span><span>\({\text{OBCD}}\) </span></span>is \(9.75\) square units. Write down a quadratic equation that expresses this information.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Using your graphic display calculator, or otherwise, find the two solutions to the quadratic equation written in part (d).</span></p>
<p><span>(ii) Hence find the correct value for \(t\). Give a reason for your answer.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A surveyor has to calculate the area of a triangular piece of land, DCE.</p>
<p class="p1">The lengths of CE and DE cannot be directly measured because they go through a swamp.</p>
<p class="p1">AB, DE, BD and AE are straight paths. Paths AE and DB intersect at point C.</p>
<p class="p1">The length of AB is 15 km, BC is 10 km, AC is 12 km, and DC is 9 km.</p>
<p class="p1">The following diagram shows the surveyor’s information.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-04_om_11.57.28.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Find the size of angle \({\rm{ACB}}\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Show that the size of angle \({\rm{DCE}}\) is \(85.5^\circ\), correct to one decimal place.</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 class="p1">The surveyor measures the size of angle \({\text{CDE}}\) to be twice that of angle \({\text{DEC}}\).</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Using angle \({\text{DCE}} = 85.5^\circ \), <span class="s1">find </span>the size of angle \({\text{DEC}}\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find the length of \({\text{DE}}\).</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 class="p1">Calculate the area of triangle \({\text{DEC}}\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following table shows the number of bicycles, \(x\), produced daily by a factory and their total production cost, \(y\)<span class="s1">, in US dollars (USD)</span>. The table shows data recorded over seven days.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-22_om_10.06.31.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) Write down the Pearson’s product–moment correlation coefficient, \(r\), for these data.</p>
<p class="p1">(ii) Hence comment on the result.</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 class="p1">Write down the equation of the regression line \(y\) on \(x\) for these data, in the form \(y = ax + b\).</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 class="p1">Estimate the total cost, <strong>to the nearest </strong><span class="s1"><strong>USD</strong></span>, of producing \(13\)<span class="s1"> </span>bicycles on a particular day.</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 class="p1">All the bicycles that are produced are sold. The bicycles are sold for <span class="s1">304 USD </span><strong>each</strong>.</p>
<p class="p1">Explain why the factory does <strong>not </strong>make a profit when producing \(13\)<span class="s1"> </span>bicycles on a particular day.</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 class="p1">All the bicycles that are produced are sold. The bicycles are sold for <span class="s1">304 USD </span><strong>each</strong>.</p>
<p class="p1">(i) Write down an expression for the total selling price of \(x\) bicycles.</p>
<p class="p1">(ii) Write down an expression for the <strong>profit </strong>the factory makes when producing \(x\) bicycles on a particular day.</p>
<p class="p1">(iii) Find the least number of bicycles that the factory should produce, on a particular day, in order to make a profit.</p>
<div class="marks">[5]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Give all answers in this question correct to two decimal places.</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Arthur lives in London. On \({1^{{\text{st}}}}\) August 2008 Arthur paid \({\text{37}}\,{\text{500}}\) euros (\({\text{EUR}}\)) for a new car from Germany. The price of the same car in London was \({\text{34}}\,{\text{075}}\) British pounds (\({\text{GBP}}\)).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The exchange rate on \({1^{{\text{st}}}}\) August 2008 was \({\text{1}}\,{\text{EUR = 0.7234}}\,{\text{GBP}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate, <strong>in GBP</strong>, the price that Arthur paid for the car.</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><span>Write down, in \({\text{GBP}}\), the amount of money Arthur saved by buying the car in Germany.</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><span>Between \({1^{{\text{st}}}}\) August 2008 and \({1^{{\text{st}}}}\) August 2012 Arthur’s car depreciated at an annual rate of \(9\%\) of its current value.</span></p>
<p><span>Calculate the value, in \({\text{GBP}}\), of Arthur’s car on \({1^{{\text{st}}}}\) August <strong>2009</strong>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Between \({1^{{\text{st}}}}\) August 2008 and \({1^{{\text{st}}}}\) August 2012 Arthur’s car depreciated at an annual rate of \(9\%\) of its current value.</span></p>
<p><span>Show that the value of Arthur’s car on \({1^{{\text{st}}}}\) August <strong>2012 </strong>was \({\text{18}}\,{\text{600}}\,{\text{GBP}}\), correct to the nearest \({\text{100}}\,{\text{GBP}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the functions \(f(x) = \frac{{2x + 3}}{{x + 4}}\) and \(g(x) = x + 0.5\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sketch the graph of the function \(f(x)\), for \( - 10 \leqslant x \leqslant 10\) . Indicating clearly the axis intercepts and any asymptotes.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the equation of the vertical asymptote.</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><span>On the same diagram as part (a) sketch the graph of \(g(x) = x + 0.5\) .</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><span>Using your graphical display calculator write down the coordinates of <strong>one</strong> of the points of intersection on the graphs of \(f\) and \(g\), <strong>giving your answer correct to five decimal places</strong>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the gradient of the line \(g(x) = x + 0.5\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The line \(L\) passes through the point with coordinates \(( - 2{\text{, }} - 3)\) and is perpendicular to the line \(g(x)\) . Find the equation of \(L\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The table shows the distance, in km, of eight regional railway stations from a city centre terminus and the price, in \($\), of a return ticket from each regional station to the terminus.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/Schermafbeelding_2014-09-03_om_09.54.14.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a scatter diagram for the above data. Use a scale of \(1\) cm to represent \(10\) km on the \(x\)-axis and \(1\) cm to represent \(\$10\) on the \(y\)-axis.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find</span></p>
<p><span>(i) \(\bar x\), the mean of the distances;</span></p>
<p><span>(ii) \(\bar y\), the mean of the prices.</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><span>Plot and label the point \({\text{M }}(\bar x,{\text{ }}\bar y)\) on your scatter diagram.</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><span>Use your graphic display calculator to find</span></p>
<p><span>(i) the product–moment correlation coefficient, \(r\,;\)</span></p>
<p><span>(ii) the equation of the regression line \(y\) on \(x\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw the regression line \(y\) on \(x\) on your scatter diagram.</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><span>A ninth regional station is \(76\) km from the city centre terminus.</span></p>
<p><span><span><span>Use the equation of the regression line to estimate the price of a return ticket to the city centre terminus from this regional station. </span></span><span><span><strong>Give your answer correct to the nearest </strong></span><span><span>\({\mathbf{\$ }}\).</span></span></span></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Give a reason why it is valid to use your regression line to estimate the price of this return ticket.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The actual price of the return ticket is \(\$80\).</span></p>
<p><span><strong>Using your answer to part (f)</strong>, calculate the percentage error in the estimated price of the ticket.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>Give your answers to parts (b), (c) and (d) to the nearest whole number.</strong></p>
<p>Harinder has 14 000 US Dollars (USD) to invest for a period of five years. He has two options of how to invest the money.</p>
<p><strong>Option A:</strong> Invest the full amount, in USD, in a fixed deposit account in an American bank.</p>
<p>The account pays a nominal annual interest rate of <em>r </em>% , <strong>compounded yearly</strong>, for the five years. The bank manager says that this will give Harinder a return of 17<em> </em>500 USD.</p>
</div>
<div class="specification">
<p><strong>Option B:</strong> Invest the full amount, in Indian Rupees (INR), in a fixed deposit account in an Indian bank. The money must be converted from USD to INR before it is invested.</p>
<p>The exchange rate is 1 USD = 66.91 INR.</p>
</div>
<div class="specification">
<p>The account in the Indian bank pays a nominal annual interest rate of 5.2 % <strong>compounded monthly</strong>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of <em>r</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>Calculate 14 000 USD in INR.</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>Calculate the amount of this investment, in INR, in this account after five years.</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>Harinder chose option B. At the end of five years, Harinder converted this investment back to USD. The exchange rate, at that time, was 1 USD = 67.16 INR.</p>
<p>Calculate how much <strong>more</strong> money, in USD, Harinder earned by choosing option B instead of option A.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Daniel grows apples and chooses at random a sample of <span class="s1">100 </span>apples from his harvest.</p>
<p class="p1">He measures the diameters of the apples to the nearest <span class="s1">cm</span>. The following table shows the distribution of the diameters.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-22_om_08.48.03.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Using your graphic display calculator, write down the value of</p>
<p class="p1">(i) the mean of the diameters in this sample;</p>
<p class="p1">(ii) the standard deviation of the diameters in this sample.</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 class="p1">Daniel assumes that the diameters of all of the apples from his harvest are normally distributed with a mean of <span class="s1">7 cm </span>and a standard deviation of <span class="s1">1.2 cm</span>. He classifies the apples according to their diameters as shown in the following table.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-22_om_08.50.32.png" alt></p>
<p class="p1">Calculate the percentage of <strong>small </strong>apples in Daniel’s harvest.</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 class="p1">Daniel assumes that the diameters of all of the apples from his harvest are normally distributed with a mean of <span class="s1">7 cm </span>and a standard deviation of <span class="s1">1.2 cm</span>. He classifies the apples according to their diameters as shown in the following table.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-22_om_08.50.32.png" alt></p>
<p class="p1">Of the apples harvested, <span class="s1">5</span>% are <strong>large </strong>apples.</p>
<p class="p1">Find the value of \(a\).</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="p1">Daniel assumes that the diameters of all of the apples from his harvest are normally distributed with a mean of <span class="s1">7 cm </span>and a standard deviation of <span class="s1">1.2 cm</span>. He classifies the apples according to their diameters as shown in the following table.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-22_om_08.50.32.png" alt></p>
<p class="p1">Find the percentage of <strong>medium </strong>apples.</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 class="p1">Daniel assumes that the diameters of all of the apples from his harvest are normally distributed with a mean of <span class="s1">7 cm </span>and a standard deviation of <span class="s1">1.2 cm</span>. He classifies the apples according to their diameters as shown in the following table.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-22_om_08.50.32.png" alt></p>
<p class="p1">This year, Daniel estimates that he will grow <span class="s1">\({\text{100}}\,{\text{000}}\) </span>apples.</p>
<p class="p1">Estimate the number of <strong>large </strong>apples that Daniel will grow this year.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A boat race takes place around a triangular course, \({\text{ABC}}\), with \({\text{AB}} = 700{\text{ m}}\), \({\text{BC}} = 900{\text{ m}}\)<span class="s1"> </span>and angle \({\text{ABC}} = 110^\circ \). The race starts and finishes at point \({\text{A}}\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-21_om_07.47.08.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the total length of the course.</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 class="p1">It is estimated that the fastest boat in the race can travel at an average speed of \(1.5\;{\text{m}}\,{{\text{s}}^{ - 1}}\)<span class="s1">.</span></p>
<p class="p2">Calculate an estimate of the winning time of the race. Give your answer to the nearest minute.</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 class="p1">It is estimated that the fastest boat in the race can travel at an average speed of \(1.5\;{\text{m}}\,{{\text{s}}^{ - 1}}\)<span class="s1">.</span></p>
<p class="p1">Find the size of angle \({\text{ACB}}\).</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 class="p1">To comply with safety regulations, the area inside the triangular course must be kept clear of other boats, and the shortest distance from \({\text{B}}\)<span class="s1"> </span>to \({\text{AC}}\)<span class="s1"> </span>must be greater than \(375\)<span class="s1"> </span>metres.</p>
<p class="p1">Calculate the area that must be kept clear of boats.</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 class="p1">To comply with safety regulations, the area inside the triangular course must be kept clear of other boats, and the shortest distance from \({\text{B}}\)<span class="s1"> </span>to \({\text{AC}}\)<span class="s1"> </span>must be greater than \(375\)<span class="s1"> </span>metres.</p>
<p class="p1">Determine, giving a reason, whether the course complies with the safety regulations.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The race is filmed from a helicopter, \({\text{H}}\), which is flying vertically above point \({\text{A}}\).</p>
<p class="p1">The angle of elevation of \({\text{H}}\)<span class="s1"> </span>from \({\text{B}}\)<span class="s1"> </span>is \(15^\circ\).</p>
<p class="p1">Calculate the vertical height, \({\text{AH}}\), of the helicopter above \({\text{A}}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The race is filmed from a helicopter, \({\text{H}}\), which is flying vertically above point \({\text{A}}\).</p>
<p class="p1">The angle of elevation of \({\text{H}}\)<span class="s1"> </span>from \({\text{B}}\)<span class="s1"> </span>is \(15^\circ\).</p>
<p class="p1">Calculate the maximum possible distance from the helicopter to a boat on the course.</p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The front view of the edge of a water tank is drawn on a set of axes shown below.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The edge is modelled by \(y = a{x^2} + c\).</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-02_om_11.23.28.png" alt><br></span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: left; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">Point \({\text{P}}\) has coordinates \((-3, 1.8)\), point \({\text{O}}\) has coordinates \((0, 0)\) and point \({\text{Q}}\) has coordinates \((3, 1.8)\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of \(c\).</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><span>Find the value of \(a\).</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><span>Hence write down the equation of the quadratic function which models the edge of the water tank.</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><span>The water tank is shown below. It is partially filled with water.</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-02_om_10.48.45_1.png" alt></span></p>
<p><span>Calculate the value of <em>y </em>when \(x = 2.4{\text{ m}}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The water tank is shown below. It is partially filled with water.</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-02_om_10.48.45_3.png" alt></span></p>
<p><span>State what the value of \(x\) and the value of \(y\) represent for this water tank.</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><span>The water tank is shown below. It is partially filled with water.</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-02_om_10.48.45.png" alt></span></p>
<p><span>Find the value of \(x\) when the height of water in the tank is \(0.9\) m.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The water tank is shown below. It is partially filled with water.</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-02_om_10.48.45_2.png" alt></span></p>
<p> </p>
<p><span>The water tank has a length of 5 m.</span></p>
<p> </p>
<p><span>When the water tank is filled to a height of \(0.9\) m, the front cross-sectional area of the water is \({\text{2.55 }}{{\text{m}}^2}\).</span></p>
<p><span>(i) Calculate the volume of water in the tank.</span></p>
<p><span>The total volume of the tank is \({\text{36 }}{{\text{m}}^3}\).</span></p>
<p><span>(ii) Calculate the percentage of water in the tank.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Tepees were traditionally used by nomadic tribes who lived on the Great Plains of North America. They are cone-shaped dwellings and can be modelled as a cone, with vertex O, shown below. The cone has radius, \(r\), height, \(h\), and slant height, \(l\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-04_om_10.28.13.png" alt></p>
<p class="p1">A model tepee is displayed at a Great Plains exhibition. The curved surface area of this tepee is covered by a piece of canvas that is \(39.27{\text{ }}{{\text{m}}^2}\), and has the shape of a semicircle, as shown in the following diagram.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-04_om_10.29.53.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that the slant height, \(l\), is \(5\) m, correct to the nearest metre.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Find the circumference of the base of the cone.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find the radius, \(r\), of the base.</p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>Find the height, \(h\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">A company designs cone-shaped tents to resemble the traditional tepees.</p>
<p class="p1">These cone-shaped tents come in a range of sizes such that the sum of the diameter and the height is equal to <strong>9.33 m</strong>.</p>
<p class="p1">Write down an expression for the height, \(h\), in terms of the radius, \(r\), of these cone-shaped tents.</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 class="p1">A company designs cone-shaped tents to resemble the traditional tepees.</p>
<p class="p1">These cone-shaped tents come in a range of sizes such that the sum of the diameter and the height is equal to <strong>9.33 m</strong>.</p>
<p class="p1">Show that the volume of the tent, \(V\), can be written as</p>
<p class="p1">\[V = 3.11\pi {r^2} - \frac{2}{3}\pi {r^3}.\]</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">A company designs cone-shaped tents to resemble the traditional tepees.</p>
<p class="p1">These cone-shaped tents come in a range of sizes such that the sum of the diameter and the height is equal to <strong>9.33 m</strong>.</p>
<p class="p1">Find \(\frac{{{\text{d}}V}}{{{\text{d}}r}}\).</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 class="p1">A company designs cone-shaped tents to resemble the traditional tepees.</p>
<p class="p1">These cone-shaped tents come in a range of sizes such that the sum of the diameter and the height is equal to <strong>9.33 m</strong>.</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Determine the exact value of \(r\) for which the volume is a maximum.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find the maximum volume.</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>A manufacturer makes trash cans in the form of a cylinder with a hemispherical top. The trash can has a height of 70 cm. The base radius of both the cylinder and the hemispherical top is 20 cm.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>A designer is asked to produce a new trash can.</p>
<p>The new trash can will also be in the form of a cylinder with a hemispherical top.</p>
<p>This trash can will have a height of <em>H</em> cm and a base radius of <em>r</em> cm.</p>
<p style="text-align: center;"><img 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"></p>
<p>There is a design constraint such that <em>H</em> + 2<em>r</em> = 110 cm.</p>
<p>The designer has to maximize the volume of the trash can.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the height of the cylinder.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total volume of the trash can.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the height of the <strong>cylinder</strong>, <em>h</em> , of the new trash can, in terms of <em>r</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the volume, <em>V</em> cm<sup>3</sup> , of the new trash can is given by</p>
<p>\(V = 110\pi {r^3}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your graphic display calculator, find the value of <em>r</em> which maximizes the value of <em>V</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The designer claims that the new trash can has a capacity that is at least 40% greater than the capacity of the original trash can.</p>
<p>State whether the designer’s claim is correct. Justify your answer.</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram shows an office tower of total height 126 metres. It consists of a square based pyramid VABCD on top of a cuboid ABCDPQRS.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">V is directly above the centre of the base of the office tower.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The length of the sloping edge VC is 22.5 metres and the angle that VC makes with the base ABCD (angle VCA) is 53.1°.</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the length of VA in metres.<br></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><span>Sketch the triangle VCA showing clearly the length of VC and the size of angle VCA.</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><span>Show that the height of the pyramid is 18.0 metres correct to 3 significant figures.</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><span>Calculate the length of AC in metres.</span></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><span>Show that the length of BC is 19.1 metres correct to 3 significant figures.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the volume of the tower.</span></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><span>To calculate the cost of air conditioning, engineers must estimate the weight of air in the tower. They estimate that 90 % of the volume of the tower is occupied by air and they know that 1 m<sup>3</sup> of air weighs 1.2 kg.</span></p>
<p><span>Calculate the weight of air in the tower.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sketch the graph of <em>y</em> = 2<sup><em>x</em></sup> for \( - 2 \leqslant x \leqslant 3\). Indicate clearly where the curve intersects the <em>y</em>-axis.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">A, a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the equation of the asymptote of the graph of <em>y</em> = 2<sup><em>x</em></sup>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A, b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>On the same axes sketch the graph of <em>y</em> = 3 + 2<em>x</em> − <em>x</em><sup>2</sup>. Indicate clearly where this curve intersects the <em>x</em> and <em>y</em> axes.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">A, c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using your graphic display calculator, solve the equation 3 + 2<em>x</em> − <em>x</em><sup>2</sup> = 2<sup><em>x</em></sup>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A, d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the maximum value of the function <em>f</em> (<em>x</em>) = 3 + 2<em>x</em> − <em>x</em><sup>2</sup>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A, e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use Differential Calculus to verify that your answer to (e) is correct.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">A, f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The curve <em>y</em> = <em>px</em><sup>2</sup> + <em>qx</em> − 4 passes through the point (2, –10).</span></p>
<p><span>Use the above information to write down an equation in <em>p</em> and <em>q</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B, a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The gradient of the curve \(y = p{x^2} + qx - 4\) at the point (2, –10) is 1.</span></p>
<p><span>Find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B, b, i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The gradient of the curve \(y = p{x^2} + qx - 4\) at the point (2, –10) is 1.</span></p>
<p><span>Hence, find a second equation in <em>p</em> and <em>q</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B, b, ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The gradient of the curve \(y = p{x^2} + qx - 4\) at the point (2, –10) is 1.</span></p>
<p><span>Solve the equations to find the value of <em>p</em> and of <em>q</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">B, c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A shipping container is to be made with six rectangular faces, as shown in the diagram.</span></p>
<p> </p>
<p> </p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The dimensions of the container are</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">length 2<em>x</em></span><br><span style="font-size: medium; font-family: times new roman,times;">width <em>x</em></span><br><span style="font-size: medium; font-family: times new roman,times;">height <em>y</em>.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">All of the measurements are in metres. The total length of all twelve edges is 48 metres.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that <em>y</em> =12 − 3<em>x </em>.</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><span>Show that the volume <em>V</em> m<sup>3</sup> of the container is given by</span></p>
<p><span><em>V</em> = 24<em>x</em><sup>2</sup> − 6<em>x</em><sup>3</sup></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><span>Find \( \frac{{\text{d}V}}{{\text{d}x}}\).</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><span>Find the value of <em>x</em> for which <em>V</em> is a maximum.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the maximum volume of the container.</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><span>Find the length and height of the container for which the volume is a maximum.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The shipping container is to be painted. One litre of paint covers an area of 15 m<sup>2</sup> .</span> <span>Paint comes in tins containing four litres.</span></p>
<p><span>Calculate the number of tins required to paint the shipping container.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Beartown has three local newspapers: <em>The Art Journal</em>, <em>The Beartown News</em>, and <em>The Currier</em>.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">A survey shows that</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">32 % of the town’s population read <em>The Art Journal</em>,</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">46 % read <em>The Beartown News</em>,</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">54 % read <em>The Currier</em>,</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">3 % read <em>The Art Journal</em> and <em>The Beartown News</em> <strong>only</strong>,</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">8 % read <em>The Art Journal</em> and <em>The Currier</em> <strong>only</strong>,</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">12 % read <em>The Beartown News</em> and <em>The Currier</em> <strong>only</strong>, and</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">5 % of the population reads <strong>all</strong> three newspapers.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a Venn diagram to represent this information. Label<em> A</em> the set that represents <em>The Art Journal</em> readers, <em>B</em> the set that represents <em>The Beartown News</em> readers, and <em>C</em> the set that represents <em>The Currier</em> readers.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the percentage of the population that does not read any of the three newspapers.</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><span>Find the percentage of the population that reads exactly one newspaper.</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><span>Find the percentage of the population that reads <em>The Art Journal</em> or <em>The Beartown News</em> but not <em>The Currier</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A local radio station states that 83 % of the population reads either <em>The Beartown News</em> or <em>The Currier</em>.</span></p>
<p><span>Use your Venn diagram to decide whether the statement is true. Justify your answer.</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><span>The population of Beartown is 120 000. The local radio station claimed that 34 000 of the town’s citizens read at least two of the local newspapers.</span></p>
<p><span>Find the percentage error in this claim.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A chocolate bar has the shape of a triangular right prism ABCDEF as shown in the diagram. The ends are equilateral triangles of side 6 cm and the length of the chocolate bar is 23 cm.</span></p>
<p style="text-align: center;"><img 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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the size of angle BAF.<br></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><span>Hence or otherwise find the area of the triangular end of the chocolate bar.</span></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><span>Find the total surface area of the chocolate bar.</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><span>It is known that 1 cm<sup>3</sup> of this chocolate weighs 1.5 g. Calculate the weight of the chocolate bar.</span></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><span>A different chocolate bar made with the same mixture also has the shape of a triangular prism. The ends are triangles with sides of length 4 cm, 6 cm and 7 cm.</span></p>
<p><span>Show that the size of the angle between the sides of 6 cm and 4 cm is 86.4° correct to 3 significant figures.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The weight of this chocolate bar is 500 g. Find its length.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Pauline owns a piece of land ABCD in the shape of a quadrilateral. The length of BC is \(190{\text{ m}}\) , the length of CD is </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(120{\text{ m}}\)</span> , the length of AD is </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(70{\text{ m}}\)</span> , the size of angle BCD is \({75^ \circ }\) and the size of angle BAD is \({115^ \circ }\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Pauline decides to sell the triangular portion of land ABD . She first builds a straight fence from B to D .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the length of the fence.</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><span>The fence costs \(17\) USD per metre to build. </span></p>
<p><span>Calculate the cost of building the fence. Give your answer correct to the </span><span>nearest USD.</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><span>Show that the size of angle ABD is \({18.8^ \circ }\) , correct to three significant figures.</span></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><span>Calculate the area of triangle ABD .</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><span>She sells the land for \(120\) USD per square metre. </span></p>
<p><span>Calculate the value of the land that Pauline sells. Give your answer correct </span><span>to the nearest USD.</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><span>Pauline invests \(300 000\) USD from the sale of the land in a bank that pays compound interest compounded annually. </span></p>
<p><span>Find the interest rate that the bank pays so that the investment will double in value in 15 years.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">ABCDV is a solid glass pyramid. The base of the pyramid is a square of side 3.2 cm. The vertical height is 2.8 cm. The vertex V is directly above the centre O of the base.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the volume of the pyramid.</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><span>The glass weighs 9.3 grams per cm<sup>3</sup>. Calculate the weight of the pyramid.</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><span>Show that the length of the sloping edge VC of the pyramid is 3.6 cm.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the angle at the vertex, \({\text{B}}{\operatorname {\hat V}}{\text{C}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the total surface area of the pyramid.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram shows part of the graph of \(f(x) = {x^2} - 2x + \frac{9}{x}\) , where \(x \ne 0\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down</span></p>
<p><span>(i) the equation of the vertical asymptote to the graph of \(y = f (x)\) ;</span></p>
<p><span>(ii) the solution to the equation \(f (x) = 0\) ;</span></p>
<p><span>(iii) the coordinates of the local minimum point.</span></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><span>Find \(f'(x)\) . </span></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><span>Show that \(f'(x)\) can be written as \(f'(x) = \frac{{2{x^3} - 2{x^2} - 9}}{{{x^2}}}\) .</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><span>Find the gradient of the tangent to \(y = f (x)\) at the point \({\text{A}}(1{\text{, }}8)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The line, \(L\), passes through the point A and is perpendicular to the tangent at A. </span></p>
<p><span>Write down the gradient of \(L\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The line, \(L\) , passes through the point A and is perpendicular to the tangent at A. </span></p>
<p><span>Find the equation of \(L\) . Give your answer in the form \(y = mx + c\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>The line, \(L\) , passes through the point A and is perpendicular to the tangent at A. </span></span></p>
<p><span>\(L\) also intersects the graph of \(y = f (x)\) at points B and C . Write down the <strong><em>x</em>-coordinate</strong> of B and of C .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A solid metal <strong>cylinder</strong> has a base radius of 4 cm and a height of 8 cm.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the area of the base of the cylinder.</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><span>Show that the volume of the metal used in the cylinder is 402 cm<sup>3</sup>, given correct to three significant figures.</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><span>Find the total surface area of the cylinder.</span></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><span>The cylinder was melted and recast into a solid cone, shown in the following diagram. The base radius OB is 6 cm.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Find the height, OC, of the cone.</span></p>
<p> </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><span>The cylinder was melted and recast into a solid cone, shown in the following diagram. The base radius OB is 6 cm.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Find the size of angle BCO.</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><span>The cylinder was melted and recast into a solid cone, shown in the following diagram. The base radius OB is 6 cm.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Find the slant height, CB.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The cylinder was melted and recast into a solid cone, shown in the following diagram. The base radius OB is 6 cm.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Find the total surface area of the cone.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Alex and Kris are riding their bicycles together along a bicycle trail and note the following distance markers at the given times.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a scatter diagram of the data. Use 1 cm to represent 1 hour and 1 cm to represent 10 km.</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><span>Write down for this set of data </span><span>the mean time, \(\bar t\).</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><span>Write down for this set of data the mean distance, \(\bar d\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Mark and label the point \(M(\bar t,{\text{ }}\bar d)\) on your scatter diagram.</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><span>Draw the line of best fit on your scatter diagram.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><strong>Using your graph</strong>, estimate the time when Alex and Kris pass the 85 km distance marker. Give your answer correct to <strong>one decimal place</strong>.</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><span>Write down the equation of the regression line for the data given.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><strong>Using your equation</strong> calculate the distance marker passed by the cyclists at 10.3 hours.<br></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Is this estimate of the distance reliable? Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.ii.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">A gardener has to pave a rectangular area 15.4 metres long and 5.5 metres wide using rectangular bricks. The bricks are 22 cm long and 11 cm wide.</span></p>
</div>
<div class="specification">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">The gardener decides to have a triangular lawn ABC, instead of paving, in the middle of the rectangular area, as shown in the diagram below.</span></p>
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><img src="onbekend.html" alt="onbekend.png"></span></p>
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">The distance AB is 4 metres, AC is 6 metres and angle BAC is 40°.</span></p>
</div>
<div class="specification">
<div style="color: #3f3f3f; font: normal normal normal 14px/1.5em 'Lucida Grande', Helvetica, Arial, sans-serif; padding-top: 40px; padding-right: 10px !important; padding-bottom: 10px !important; padding-left: 10px !important; background-image: url('body-bg.html'); background-attachment: initial; background-origin: initial; background-clip: initial; background-color: #f7f7f7; height: 94% !important; font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px; display: inline; float: none; background-position: 50% 0%; background-repeat: no-repeat repeat; margin: 0px;">
<p style="margin-top: 0px; margin-right: 0px; margin-bottom: 10px; margin-left: 0px; font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif;"><span style="font-family: times new roman,times; font-size: medium;">In another garden, twelve of the same rectangular bricks are to be used to make an edge around a small garden bed as shown in the diagrams below. FH is the length of a brick and C is the centre of the garden bed. M and N are the midpoints of the long edges of the bricks on opposite sides of the garden bed.</span></p>
<p style="margin-top: 0px; margin-right: 0px; margin-bottom: 10px; margin-left: 0px; font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif;"><span style="font-family: times new roman,times; font-size: medium;"><img style="border-style: initial; border-color: initial; max-width: 100%; vertical-align: middle; border-width: 0px;" 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" alt></span></p>
</div>
</div>
<div class="specification">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">The garden bed has an area of 5419 cm<sup>2</sup>. It is covered with soil to a depth of 2.5 cm.</span></p>
</div>
<div class="specification">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">It is estimated that 1 kilogram of soil occupies 514 cm<sup>3</sup>.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the total area to be paved. Give your answer in cm<sup>2</sup>.</span></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><span>Write down the area of each brick.</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><span>Find how many bricks are required to pave the total area.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the length of BC.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Hence write down the perimeter of the triangular lawn.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the area of the lawn.</span></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><span>Find the percentage of the rectangular area which is to be lawn.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the angle FCH.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the distance MN from one side of the garden bed to the other, passing through C.</span></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><span>Find the volume of soil used.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of kilograms of soil required for this garden bed.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram shows a Ferris wheel that moves with constant speed and completes a rotation every 40 seconds. The wheel has a radius of \(12\) m and its lowest point is \(2\) m above the ground.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt></span></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Initially, a seat C is vertically below the centre of the wheel, O. It then rotates in an anticlockwise (counterclockwise) direction.</span></p>
<p><span>Write down</span></p>
<p><span>(i) the height of O above the ground;</span></p>
<p><span>(ii) the maximum height above the ground reached by C .</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><span>In a revolution, C reaches points A and B , which are at the same height above the ground as the centre of the wheel. Write down the number of seconds taken for C to first reach A and then B .</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><span>The sketch below shows the graph of the function, \(h(t)\) , for the height above ground of C, where \(h\) is measured in metres and \(t\) is the time in seconds, \(0 \leqslant t \leqslant 40\) .</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span><strong>Copy</strong> the sketch and show the results of part (a) and part (b) on your diagram. Label the points clearly with their coordinates.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Farmer Brown has built a new barn, on horizontal ground, on his farm. The barn has a cuboid base and a triangular prism roof, as shown in the diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The cuboid has a width of 10 m, a length of 16 m and a height of 5 m.<br>The roof has two sloping faces and two vertical and identical sides, ADE and GLF.<br>The face DEFL slopes at an angle of 15° to the horizontal and ED = 7 m .</p>
</div>
<div class="specification">
<p>The roof was built using metal supports. Each support is made from <strong>five</strong> lengths of metal AE, ED, AD, EM and MN, and the design is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">ED = 7 m , AD = 10 m and angle ADE = 15° .<br>M is the midpoint of AD.<br>N is the point on ED such that MN is at right angles to ED.</p>
</div>
<div class="specification">
<p>Farmer Brown believes that N is the midpoint of ED.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the area of triangle EAD.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the <strong>total</strong> volume of the barn.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of MN.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of AE.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that Farmer Brown is incorrect.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the <strong>total</strong> length of metal required for one support.</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The Great Pyramid of Giza in Egypt is a right pyramid with a square base. The pyramid is made of solid stone. The sides of the base are \(230\,{\text{m}}\) long. The diagram below represents this pyramid, labelled \({\text{VABCD}}\).</p>
<p>\({\text{V}}\) is the vertex of the pyramid. \({\text{O}}\) is the centre of the base, \({\text{ABCD}}\) . \({\text{M}}\) is the midpoint of \({\text{AB}}\). Angle \({\text{ABV}} = 58.3^\circ \) .</p>
<p><img 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" alt></p>
<p>Show that the length of \({\text{VM}}\) is \(186\) metres, correct to three significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the height of the pyramid, \({\text{VO}}\) .</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 volume of the pyramid.</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>Write down your answer to part (c) in the form \(a \times {10^k}\) where \(1 \leqslant a < 10\) and \(k \in \mathbb{Z}\) .</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>Ahmad is a tour guide at the Great Pyramid of Giza. He claims that the amount of stone used to build the pyramid could build a wall \(5\) metres high and \(1\) metre wide stretching from Paris to Amsterdam, which are \(430\,{\text{km}}\) apart.</p>
<p>Determine whether Ahmad’s claim is correct. Give a reason.</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>Ahmad and his friends like to sit in the pyramid’s shadow, \({\text{ABW}}\), to cool down.<br>At mid-afternoon, \({\text{BW}} = 160\,{\text{m}}\) and angle \({\text{ABW}} = 15^\circ .\)</p>
<p><img 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" alt></p>
<p>i) Calculate the length of \({\text{AW}}\) at mid-afternoon.</p>
<p>ii) Calculate the area of the shadow, \({\text{ABW}}\), at mid-afternoon.</p>
<div class="marks">[6]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A contractor is building a house. He first marks out three points A , B and C on the ground such that AB = 5 m , AC = 7 m and angle BAC = 112 °.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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//T8r5IdJEAdEonV703TZOiL1bSdb3pys/8xemXn08o26SILD2QmV1o7q7S1Xd/sq+8pZq4fWXf+FtVmwleeevZvY9lL5bsy5NP3K2emmt9YACwmg7vIWOaJgsQooZlWU2fWZ+/9MGF4ieTh26uk6YN71r845E7Y48d/cPFhZK98NH00YNf2xCRN9w7/u4V52tnjjy4b/yd4qcfZB6477nTVusDA4DVdH5HNsuyxNriHrwuAm5JjaaGBgebfvi5zN6tK9K04V2LRnro2T9cdf679OfJQ/9Dlj5/z9EPnKPTUvHMsae+2Re959CL71Qds9qp0RRdJADr1639TUXRV9f1Lj0//MU0TVmKNH0lVWtpWipe/FOx+jTqwqz2gCxtHdDOrfmdxPoSdJEArFMXdwvXdZ2iLxxiQ7TmHttamq7w6bmj+2Rpz+HpYjPfLKYo/JUCWKcupqlt21NTU33RaCIep5cEcXja3EnK9aVp6U8nH71l+4P/eaHU8CHVRBeJP1EA69HdNLWrir5MpiE1moopShO5tZ40LX367njsi49kzl5t8IBadJEArF/X09S27UKhQNEXtm1bltUXjTax4+k60vRT48i9d3/7V+YqE8ErtViSAoBavUhTm53GUSHOpq/1uardNC1dzo3cv3/ZlaZNEV0kPu0BaFuP0lQQRd8mDk0QZIl4fK353rbStPSXd8Yf2f/8dKtRKtBFArAePU1Tu2qn8R5/X3iHmO9d9W+g9TQt/eWd8Ydjh165sOBk6fXLp/7jxMx8k6OiiwRgPXqdprZt5/N5FiAMOTGz2vBy5NIHP//G5xscgNa7q/SXd8aHtm/Y/eCT3x0ZHh4ZHh4Z/q4a/0b0S8nfXmn2QFVkPGciALTHhTS1q4q+nKkKLXECdUV6LVya/n9Hvv/w7g0RWfrS15944cXJmatr3DV/Vvun7Usr9Dq3z976bP5aK0OiiwSgbe6kqc1O47Dt1GjKU01vcUWsd8YDwEdcS1ObncbhvUAdGhzkpD6ANriZpsJEOi1LEbaZDC0RqB6ZohCrd3FGH0Cr3E9Tu6roy7tYOHlnioIuEoD2eCJNbds2DIOib5iJQPXCFIVY/tDtUQDwGa+kqW3bpmnGFCWmKN45i4ZeElMUru+R0OLmcQBg255KU7uq6MtO4+EkPlG5/gdAFwlAq7yVpoJ3zqKh9yzLEsW0pKq6te+QOErmpAOA5nkxTW3bzmgaCxCGmWEY4iA1o2m9T7VsNvvf/9vfNFyqCQBW8Gia2pXjg6SqcogQWhlN64tGe5mpU1NTMUWRpcg/PfwwXSQAzfNumtpVCxASqKFlWZaTqanRVJcaapZl6boucjQ1mioUCnSRALTE02lq27Zpmuw0DsuynKPGocFBXdc78vcgnlbsvNsXjU6k09VnahPxOOcaADTJ62lq27ZlWYl4nGvqYdu2aZoT6bSIVbEjqa7rLR1BFgqFfD4/kU4PDQ6K9fGTqlr3T4suEoDm+SBNBVH0pRgCwTRNXdeTqtoXjYpQjClKIh5PqmpG02puE+l0Ih5PxOPODjOJeHwinV7zOpy+aJQ/OQDN8E2a2pU9vJh8Q41CoWAYhq7rGU1LqqoIzpqbiNV8Pt/SFLE4Du7eyAEEhp/S1K4sSu76cjkIiUKhQBcJQDN8lqY2O42jt8TssdujAOB1/ktTu2oBQgIV3Sa6SG6tygTAL3yZprZtW5YlLmyg6ItuE8tHuD0KAJ7m1zQVRNGXdzp0FV0kAGvyd5raVTuNuz0QBJboIrGvEYBV+D5NbdvO5/MsQIiuoosEYHVBSFObncbRZXSRAKwuIGlqVxV9uToQ3RBTFM7QA2gkOGlq27ZlWew0ji7JaBpdJACNBCpNhYl0WpYiE+m02wNBoNBFArCKAKapXVX0pZeEDkqqKl0kAHUFM01t2zYMg6IvOiufz9NFAlBXYNPUZqdxdAFdJAB1BTlN7aqiL6e70BEZTeuLRt0eBQDPCXiaChR90Smii8TfEoAaoUhT27YzmsYChOgIsSG526MA4C1hSVO7UvRNqiq9JKwHXSQAK4UoTe2qncZ5K8R6xBSFC5oBVAtXmtq2XSgUKPpinegiAagRujS1bduyrEQ83heN0iVBe+giAagRxjQVRNFX13W3BwJfSo2m6CIBcIQ3TW3b1nWdoi/aYxgGXSQAjlCnqc1O41gHukgAHGFPU7uq6EsvCS3RdZ0uEgCBNLXtqgUICVQ0z7IsukgABNK0zLKspKry5oiWpEZTQ4ODbo8CgPtI02VE0ZdNQtAk0UViSgMAaVqLncbRkpiiUAsHQJrWwU7jaJ7oIvGnAoQcaVqfaZoxRYkpCpN4WB1dJAA2aboKp+hrGIbbY4Gn0UUCQJquxrIsdhrHmugiASBN1zaRTstShFVvsIqhwUG6SECYkaZNYadxrG5qaoouEhBmpGmznAUIecfESpZlsccfEGakaQtM02QBQjRCFwkIM9K0NU7RN5/Puz0WeItpmnSRgNAiTdtB0Rd10UUCQos0bVNG09hpHDVEW40z60AIkabtEzXORDzOuycE0UXSdd3tgQDoNdJ0XZyib6FQcHss8ITUaCqmKG6PAkCvkabrVSgUKPrCIbpIrEYJhA1p2gGWZSXicS43hEAXCQgh0rRj2GkcAl0kIIRI005ydhp3eyBwE10kIIRI0w7L5/MsQIiJdJouEhAqpGnnOUVfekmhVSgU6CIBoUKadoWzACGBGlqJeJw5fyA8SNNusSwrqaosQBhadJGAUCFNu4udxsOsLxql4w2EBGnadU7Rl8OUsKGLBIQHadoLhmFQ9A0h0UVi8z4gDEjTHjFNM6YoMUWhlxQqiXg8qapujwJA15GmveMUfblwIjzEPD+bIgCBR5r2lGVZ7DQeNnSRgDAgTV3ATuOhQhcJCAPS1B1iAjCpqvSSAo8uEhAGpKlrnAUICdTAo4sEBB5p6ibTNFmAMAzy+TxdJCDYSFOXOUVfZgKDLaYodJGAACNNPUEUfdkRM8AymkYXCQgw0tQrdF2n6BtgdJGAYCNNPWRqaqovGk3E4/SSAimpqol4vKUvKRWNXx/TMlrNTX/r0kKXBgmgPaSptzhFXxorwdN6F+nTC9pDN0kRuea2Yf/Pz17r4kABtI409ZxCoUDRN6hiitLC9nyLfzxy5x2P/p+fZV7K/jYn/Hr8H7904z1Hz5a6OUoArSNNvUjsNN4XjbIAYcBkNK0vGm3usaVr02P/U/tg2ZTutfzhndvvPTpDmAJeQ5p6lyj6cllFkIguUrsfkkrXpg/futo07/yl01O/nfnEtucvvftfJ0+8dvrSfPkri2d/n30lmztbJIeB7iBNPc3ZadztgaBj2ugiVRTfenZP/Wne0pyhv3Bgz3ZZ2jrws8msete28hlW5ek3L1x4/Zl7viDLUkSWbv6a+pvLBCrQBaSp1+XzeRYgDJL210VabZp3/s8X3js1cocsydv2HPxp7qMFe/5i9l93SpEbv3zbgyMnZ4rXS8V3frR3uyzdPW5cXf9PAaAGaeoDTtGXXlIwtNZFKltzmndhVntAlrYOaOfK/2P+lPq5iLxlOFc+9XrVGLtblr46kiu2OW4AjZGm/sBO40Gi63rTXSRH42neshVpupAb2VKdpuIBpCnQFaSpb7DTeGBYltXy73HtNi9pCriJNPWZiXRaliKtzxPCW1KjqVa6SGtO89qkKeAu0tR/nKIvvST/MgyjlS7SmtO8NmkKuIs09SXDMCj6+l0LXaRr+cM7v7Rf+3DVa1vWTNP59498U5ZuOZC9tJ5hA6iLNPUr0zRjihJTFIq+PiW6SE18Hipdmz5862ceOXFxlZXuP3n/9YlDd2yVpchNdxyaOJE/+97rPx3eH5Ui8obdD31fm7544a1jqUd33SxL8vZvPPXi9EUuOgU6izT1MXYa97Wmu0ilqzO/Of5rg2WMAC8jTX2Poq9/pUZTQ4ODbo8CQAeQpkGQ0TQWIPQj0UVirh4IANI0IETRN6mq9JL8JaYofAwCAoA0DQ5nAUIC1Uea7iIB8DTSNFBM02SncX9pZ10kAN5DmgaNZVmJeJydxn2ELhIQAKRpMImir67rbg8EazNNky4S4HekaWDpuk7R1y+GBgf5TQG+RpoG2dTUVF80mojHKbl4nPhN8WsC/Is0DTin6Nv0AutwgWVZnOoGfI00DT5nAULOzHlZajQVUxS3RwGgTaRpKFiWlVRVrsTwMtFFMgzD7YEAaAdpGiKi6JvRNLcHgvroIgH+RZqGi7PTuNsDQR3it0MXCfAj0jR08vk8CxB6k+gicZUw4EekaRix07hn0UUCfIo0DSmn6EvtxVPoIgE+RZqGl2VZ7DTuQYl4nBPbgO+QpmE3kU7LUmQinXZ7ICijiwT4EWmKpaIv7+AeQRcJ8B3SFLZt24ZhUPT1jol0mi4S4C+kKcrYadw7CoUCXSTAX0hTLHGKvvl83u2xhB1dJMBfSFPUoujrBeJkNjv/AH5BmqKOjKaxAKHr+qJRFlUG/II0RX3i2CipqvSS3EIXCfAR0hQNsdO4u0QXiXPYgC+QplhNoVCg6OuiRDyeVFW3RwFgbaQp1mBZViIe74tG6SX1Hl0kwC9IUzRFFH1ZoKf36CIBvkCaolm6rlP07b2MptFFAryPNEULpqam+qLRRDxO0bdn6CIBvkCaojVO0ZdeUs8kVZUuEuBxpCla5ixASKD2Rj6fp4sEeBxpinZYlpVUVRYg7JmYotBFAryMNEX7RNGXd/keyGhaXzTq9igANESaYl3Yabw3RBeJmQDAs0hTrBc7jfdGUlUT8bjbowBQH2mKDjBNM6YoMUWhl9Q9dJEALyNN0RlO0dcwDLfHElgxRZlIp90eBYA6SFN0jGVZ7DTeVXSRAM8iTdFhE+m0LEU4hOoGukiAZ5Gm6Dx2Gu+e1GiKLhLgQaQpusJZgJBA7SzDMOgiAR5EmqJbTNNkAcJuoIsEeBBpii5yir5sgdJBuq7TRQK8hjRF11H07SzLsng9Aa8hTdELGU1jp/EOoosEeA1pih5hp/EOEl0kTkgD3kGaonecoi+V1PWLKQrH+oB3kKboqUKhQNG3I0QXiQN9wCNIU/SaZVmJeLwvGqVHsx50kQBPIU3hDlH01XXd7YH4WGo0NTQ46PYoANg2aQoX6bpO0Xc96CIB3kGawk35fJ4FCNeDLhLgEaQpXOYUfTnGaoO47ojPIoDrSFO4z1mAkEBtlWVZ9LkALyBN4QmWZSVVlZJqG+giAV5AmsJD2Gm8DaZp0kUCXEeawlvETuOp0RTnAps3NDhIFwlwF2kKzzEMg6JvS8RHEF4uwEWkKbzINM2YosQUhQnMZoguEkthAC4iTeFRTtHXMAy3x+IDqdFUTFHcHgUQXqQpvMuyLHYab5LoIvHJA3ALaQqvY6fxJtFFAlxEmsIHRMsmqaoUbVZBFwlwEWkKf3AWICQtGqGLBLiINIVvmKbJAoSrm0in6SIBriBN4SdO0Tefz7s9Fi8qFAp0kQBXkKbwH3YaX0UiHqeLBPQeaQpfYqfxRugiAa4gTeFXYmvPRDxOctSgiwT0HmkKH3OKvoVCwe2xeAhdJKD3SFP4W6FQoOhbQ3SRKGoBvUSawvcsy0rE433RKAsQOhLxeFJV3R4FECKkKQJCFH0zmub2QDxBdJGYAAd6hjRFcDg7jbs9EE/oi0b5bAH0DGmKQMnn8yxAKNBFAnqJNEXQOEXfkPeS6CIBvUSaIoDYaVygiwT0DGmKYGKncdu28/k8XSSgN0hTBNlEOi1LkYl02u2BuCamKHSRgB4gTRFwTtE3nL2kjKbRRQJ6gDRF8BmGEdqiL10koDdIU4SCaZoxRYkpSgiLvklVTcTjbo8CCDjSFGER2p3G6SIBPUCaIlzCWfSNKUqYq1hAD5CmCJ2MpoVtAcKMpvVFo26PAggy0hRhJIq+SVUNSS9JdJHCdkQO9BJpipByFiAMSaDSRQK6ijRFeJmmGZ6dxukiAV1FmiLUQrXTOF0koBJoVxMAAAheSURBVHtIU6Bc9NV13e2BdJeu63SRgC4hTQHbtm1d1wNf9LUsiy4S0CWkKVA2NTXVF40m4vEA95JSoym6SEA3kKbAEqfoG9S2jmEYdJGAbiBNgWUKhUKwi750kYBuIE2BWpZlJVU1qKcYRRcpwLPZgCtIU6A+UfQN3lbbdJGAbiBNgYacncbdHkiHpUZTQ4ODbo8CCBTSFFhNPp8P3gKEoosU1BPDgCtIU2ANYqfxocHBIMVPTFGCd8wNuIg0Bdbm7DRuGIbbY+kMukhAZ5GmQFMsywrSTuN0kYDOIk2BFkyk07IUCcb1mnSRgA4iTYHWOEVfv0+TmqZJFwnoFNIUaJlhGMEo+g4NDtJFAjqCNAXaEYydxsVC/37/TAB4AWkKtMkp+ubzebfH0ibLskKyUzrQbaQpsC5+L/qmRlMxRXF7FIDvkabAemU0zb8LEIouUmCuowXcQpoCHSCKvklV9eM5SLpIwPqRpkBn+HencfFRwI+fAwDvIE2BjvHpTuOii6TrutsDAXyMNAU6ybKsRDzuu6IsXSRgnUhToPNE0ddHR3t0kYB1Ik2BrtB13V9FX7pIwHqQpkC3iJWGEvG4Lwo+dJGA9SBNgS5yir6+6CXRRQLaRpoC3eUsQOj9QJ1Ip+kiAe0hTYGusywrqareX4CwUCjQRQLaQ5oCPSKKvhlNc3sgq0nE43SRgDaQpkDvODuNuz2QhsQIfbecE+A60hToKe/vNN4XjXr8ABrwINIU6DXTNGOKElMUb/aS6CIBbSBNARc4RV8PVn5EF8m/W6ADriBNAXdYluXZncYT8XhSVd0eBeAnpCngpol0WpYiE+m02wNZhi4S0CrSFHCZN3cap4sEtIQ0BdznLEDonUDNaBpdJKB5pCngCaZpemoBQrpIQEtIU8ArnKKvRzIsqap0kYAmkaaAt3in6JvP5+kiAU0iTQHPyWiaRxYgjCkKXSSgGaQp4EUe2WmcLhLQJNIU8Cin6OviXKvoInlh2hnwONIU8K5CoeB60Tepqol43K3vDvgFaQp4mmVZiXi8Lxp16wCRLhLQDNIU8AFR9NV13ZXvHlMUr619CHgNaQr4g67rbhV9M5rWF432/vsCPkKaAr6Rz+ddWYCQLhKwJtIU8BOn6NvjXhJdJGB1pCngM84ChL0MVMMw6CIBqyBNAf+xLCupqj2efaWLBKyCNAX8ShR9e7byn67rdJGARkhTwMfETuOp0VQPekmWZdFFAhohTQF/MwyjZ0Xf1GiKLhJQF2kK+J5pmjFFiSlKt3tJoovkkf3MAU8hTYEgcIq+hmF09RvFFMULW8UBXkOaAgFhWVYPdhoXXSR394kDPIg0BQKl2zuN00UC6iJNgaARRd+kqnbpCDI1mhoaHOzGMwP+RZoCAeQsQNiNQKWLBKxEmgLBZJpm9xYgpIsE1CBNgcByir75fL6zzzw1NUUXCahGmgIB142dxi3L6otG6SIBDtIUCL5u7DROFwmoRpoCoSDmZhPxeKemZ03TpIsEOEhTICycom+ntikdGhykiwQIpCkQIoVCoYNFX7pIgIM0BcLFsqxEPN6RDpHoInW23wT4FGkKhFGndhpPjaZiitKRIQG+RpoCIeXsNL6eJxFdpG5vXAN4H2kKhFc+n1//AoR0kQCbNAVCzin6tt1LEse4dJEQcqQpEHbOAoTtBSpdJMAmTQHYtm1ZVlJV2964lC4SQJoCKJtIp2UpMpFOt/qFhUKBLhJCjjQFsMQp+rZ6HjQRj9NFQpiRpgCWMQyjjaIvXSSEHGkKoJZpmjFFiSlKS70kukgIM9IUQB1t7DQ+kU7TRUJokaYAGhILEDZZ9BVdpObTFwgS0hTAajKa1vwChIl4PKmq3R4S4EGkKYA1iIZRUlXXLBmJR3Zq/1TAR0hTAGtzFiBcM1D7otH1b00D+A5pCqAppmk2swAhXSSEE2kKoFnN7DROFwnhRJoCaI0o+q5yaSldJIQQaQqgZbqur1L0zefzdJEQNqQpgHZMTU31RaOJeLxuLymmKHSRECqkKYA2OUXflYehGU2ji4RQIU0BtK9QKNQt+tJFQtiQpgDWpdFO40lVpYuE8CBNAXSAKPpWnyuli4RQIU0BdIaz07jzf2KKMpFOuzgkoGdIUwAdk8/nqxcgzGhaXzTq9qCAXiBNAXSSU/Q1TVN0kZrc0A3wNdIUQIc5O40bhpFU1UQ87vaIgK4jTQF0nmVZopck6r50kRB4pCmAbplIp2UpIksRukgIPNIUQBeJoi9dJAQeaQqguwzD4NQpAo80BdBTpeLM5NHnkokHB/be/2Bi+EcvvXG2OH8xO/6icdXtoQHtI00B9Eppzjj2HWXLjtsTz5+YfPfSwvwl442TYwdu//K2bRu+OpIruj0+oH2kKYCeKP3lnfGh7dK2e56fLpaq77hefCe97wvbBrRzbg0NWD/SFEAPlKzp0f4NEfnvnz/9aWnFvVeMsf37SFP4GWkKoPtKH2b2bZelTbeNnVmse/+Fl7/74nsrYxbwC9IUQNeVLmj7NkRkiZOjCCzSFEDXLeSGt0kRWdr383Ofuj0WoCtIUwDdVpo/pW6VIrL0QGZ2we3BAF1BmgLousqx6TePzMy7PRagK0hTAF1XOW/6d4cmL7s9FqArSFMA3Vfu9MpfeurUlfqPuGLOXGQWGP5FmgLogdLVd15QNkTkz+w78p614t6Fi68f/s6xGdIU/kWaAugNa0b7Vt+GyI27/uVI7qOl4Cz9debEdx9Wf3lhgctN4WOkKYCemZ89lT6wZ7ssydt23bXvkYNPPHLf7bvueuwnb14kSuFzpCmAHrtePPfW5MnjGe1E9rfGJXIUgUCaAgCwXqQpAADr9f8BXA7Hs6g3CtMAAAAASUVORK5CYII=" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the length of BC.</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><span>He next marks a fourth point, D, on the ground at a distance of 6 m from B , such that angle BDC is 40° .</span></p>
<p> </p>
<p><span><img 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" alt></span></p>
<p><span>Find the size of angle DBC .</span></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><span>He next marks a fourth point, D, on the ground at a distance of 6 m from B , such that angle BDC is 40° .</span></p>
<p><img src="images/3c.png" alt> </p>
<p><span>Find the area of the quadrilateral ABDC.</span></p>
<p> </p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>He next marks a fourth point, D, on the ground at a distance of 6 m from B , such that angle BDC is 40° .</span></p>
<p> </p>
<p><span><img 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" alt></span></p>
<p><span> </span></p>
<p><span>The contractor digs up and removes the soil under the quadrilateral ABDC to a depth of 50 cm for the foundation of the house.</span></p>
<p><span>Find the volume of the soil removed. Give your answer in <strong>m<sup>3</sup></strong> .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>He next marks a fourth point, D, on the ground at a distance of 6 m from B , such that angle BDC is 40° .</span></p>
<p> </p>
<p><span><img 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" alt></span></p>
<p><span> </span></p>
<p><span>The contractor digs up and removes the soil under the quadrilateral ABDC to a depth of 50 cm for the foundation of the house.</span></p>
<p><span>To transport the soil removed, the contractor uses cylindrical drums with a diameter of 30 cm and a height of 40 cm.</span> </p>
<p><span>(i) Find the volume of a drum. Give your answer in <strong>m<sup>3</sup> </strong>.</span></p>
<p><span>(ii) Find the minimum number of drums required to transport the soil removed.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A random sample of 167 people who own mobile phones was used to collect data on the amount of time they spent per day using their phones. The results are displayed in the table below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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" alt></span></p>
</div>
<div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Manuel conducts a survey on a random sample of 751 people to see which television programme type they watch most from the following: Drama, Comedy, Film, News. The results are as follows.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Manuel decides to ignore the ages and to test at the 5 % level of significance whether the most watched programme type is independent of <strong>gender.</strong></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State the modal group.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to calculate approximate values of the mean and standard deviation of the time spent per day on these mobile phones.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>On graph paper, draw a fully labelled histogram to represent the data.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a table with 2 rows and 4 columns of data so that Manuel can perform a chi-squared test.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State Manuel’s null hypothesis and alternative hypothesis.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the expected frequency for the number of females who had ‘Comedy’ as their most-watched programme type. Give your answer to the nearest whole number.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using your graphic display calculator, or otherwise, find the chi-squared statistic for Manuel’s data.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) State the number of degrees of freedom available for this calculation.</span></p>
<p><span>(ii) State his conclusion.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.e.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A group of <span class="s1">100 </span>customers in a restaurant are asked which fruits they like from a choice of mangoes, bananas and kiwi fruits. The results are as follows.</p>
<p class="p1"><span class="s1"> 15 </span>like all three fruits</p>
<p class="p1"><span class="s1"> 22 </span>like mangoes and bananas</p>
<p class="p1"><span class="s1"> 33 </span>like mangoes and kiwi fruits</p>
<p class="p1"><span class="s1"> 27 </span>like bananas and kiwi fruits</p>
<p class="p1"><span class="s1"> 8 </span>like none of these three fruits</p>
<p class="p1"> \(x\) like <strong>only </strong>mangoes</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><strong>Copy </strong>the following Venn diagram and correctly insert all values from the above information.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-22_om_06.31.28.png" alt></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 class="p1">The number of customers that like <strong>only </strong>mangoes is equal to the number of customers that like <strong>only </strong>kiwi fruits. This number is half of the number of customers that like <strong>only </strong>bananas.</p>
<p class="p1">Complete your Venn diagram from part (a) with this additional information <strong>in terms </strong><strong>of</strong> \(x\).</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 class="p1">The number of customers that like <strong>only </strong>mangoes is equal to the number of customers that like <strong>only </strong>kiwi fruits. This number is half of the number of customers that like <strong>only </strong>bananas.</p>
<p class="p1">Find the value of \(x\).</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="p1">The number of customers that like <strong>only </strong>mangoes is equal to the number of customers that like <strong>only </strong>kiwi fruits. This number is half of the number of customers that like <strong>only </strong>bananas.</p>
<p class="p1">Write down the number of customers who like</p>
<p class="p1">(i) mangoes;</p>
<p class="p1">(ii) mangoes or bananas.</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 class="p1">The number of customers that like <strong>only </strong>mangoes is equal to the number of customers that like <strong>only </strong>kiwi fruits. This number is half of the number of customers that like <strong>only </strong>bananas.</p>
<p class="p1">A customer is chosen at random from the <span class="s1">100 </span>customers. Find the probability that this customer</p>
<p class="p1">(i) likes none of the three fruits;</p>
<p class="p1">(ii) likes only two of the fruits;</p>
<p class="p1">(iii) likes all three fruits given that the customer likes mangoes and bananas.</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 class="p1">The number of customers that like <strong>only </strong>mangoes is equal to the number of customers that like <strong>only </strong>kiwi fruits. This number is half of the number of customers that like <strong>only </strong>bananas.</p>
<p class="p1">Two customers are chosen at random from the <span class="s1">100 </span>customers. Find the probability that the two customers like none of the three fruits.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>A new café opened and during the first week their profit was $60.</p>
<p>The café’s profit increases by $10 every week.</p>
</div>
<div class="specification">
<p>A new tea-shop opened at the same time as the café. During the first week their profit was also $60.</p>
<p>The tea-shop’s profit increases by 10 % every week.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the café’s profit during the 11th week.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the café’s <strong>total</strong> profit for the first 12 weeks.</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 tea-shop’s profit during the 11th week.</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>Calculate the tea-shop’s <strong>total</strong> profit for the first 12 weeks.</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>In the <em>m</em>th week the tea-shop’s <strong>total</strong> profit exceeds the café’s <strong>total</strong> profit, for the first time since they both opened.</p>
<p>Find the value of <em>m</em>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The Tower of Pisa is well known worldwide for how it leans.</p>
<p>Giovanni visits the Tower and wants to investigate how much it is leaning. He draws a diagram showing a non-right triangle, ABC.</p>
<p>On Giovanni’s diagram the length of AB is 56 m, the length of BC is 37 m, and angle ACB is 60°. AX is the perpendicular height from A to BC.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>Giovanni’s tourist guidebook says that the actual horizontal displacement of the Tower, BX, is 3.9 metres.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Giovanni’s diagram to show that angle ABC, the angle at which the Tower is leaning relative to the<br>horizontal, is 85° to the nearest degree.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Giovanni's diagram to calculate the length of AX.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Giovanni's diagram to find the length of BX, the horizontal displacement of the Tower.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the percentage error on Giovanni’s diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Giovanni adds a point D to his diagram, such that BD = 45 m, and another triangle is formed.</p>
<p><img 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"></p>
<p>Find the angle of elevation of A from D.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A distress flare is fired into the air from a ship at sea. The height, \(h\) , in metres, of the flare above sea level is modelled by the quadratic function</p>
<p>\[h\,(t) = - 0.2{t^2} + 16t + 12\,,\,t \geqslant 0\,,\]</p>
<p>where \(t\) is the time, in seconds, and \(t = 0\,\) at the moment the flare was fired.</p>
<p>Write down the height from which the flare was fired.</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 height of the flare \(15\) seconds after it was fired.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The flare fell into the sea \(k\) seconds after it was fired.</p>
<p>Find the value of \(k\) .</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \(h'\,(t)\,.\)</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>i) Show that the flare reached its maximum height \(40\) seconds after being fired.</p>
<p>ii) Calculate the maximum height reached by the flare.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The nearest coastguard can see the flare when its height is more than \(40\) metres above sea level.</p>
<p>Determine the total length of time the flare can be seen by the coastguard.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">George leaves a cup of hot coffee to cool and measures its temperature every minute. His results are shown in the table below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the decrease in the temperature of the coffee</span></p>
<p><span>(i) during the first minute (between <em>t</em> = 0 and <em>t</em> =1) ;</span></p>
<p><span>(ii) during the second minute;</span></p>
<p><span>(iii) during the third minute.</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><span>Assuming the pattern in the answers to part (a) continues, show that \(k = 19\).</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><span>Use the <strong>seven</strong> results in the table to draw a graph that shows how the temperature of the coffee changes during the first six minutes.</span></p>
<p><span>Use a scale of 2 cm to represent 1 minute on the horizontal axis and 1 cm to represent 10 °C on the vertical axis.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>The function that models the change in temperature of the coffee is <em>y</em> = <em>p</em> (2<sup>−<em>t</em></sup> )+ <em>q</em>.</span></span></p>
<p><span>(i) Use the values <em>t</em> = 0 and <em>y</em> = 94 to form an equation in <em>p</em> and <em>q</em>.</span></p>
<p><span>(ii) Use the values <em>t</em> =1 and <em>y</em> = 54 to form a second equation in <em>p</em> and <em>q</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Solve the equations found in part (d) to find the value of <em>p</em> and the value of <em>q</em>.</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><span>The graph of this function has a horizontal asymptote.</span></p>
<p><span>Write down the equation of this asymptote.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>George decides to model the change in temperature of the coffee with a linear function using correlation and linear regression.</span></p>
<p><span>Use the <strong>seven</strong> results in the table to write down</span></p>
<p><span>(i) the correlation coefficient;</span></p>
<p><span>(ii) the equation of the regression line <em>y</em> on <em>t</em>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the equation of the regression line to estimate the temperature of the coffee at <em>t</em> = 3.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the percentage error in this estimate of the temperature of the coffee at <em>t</em> = 3.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the function \(f(x) = - \frac{1}{3}{x^3} + \frac{5}{3}{x^2} - x - 3\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sketch the graph of <em>y</em> = <em>f</em> (<em>x</em>) for −3 ≤ <em>x</em> </span><span><span>≤</span> 6 and −10 </span><span><span>≤</span> <em>y</em> </span><span><span>≤ </span>10 showing clearly the axes intercepts and local maximum and minimum points. Use a scale of 2 cm to represent 1 unit on the <em>x</em>-axis, and a scale of 1 cm to represent 1 unit on the <em>y</em>-axis.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of <em>f</em> (−1).</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><span>Write down the coordinates of the <em>y</em>-intercept of the graph of <em>f</em> (<em>x</em>).</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><span>Find <em>f '</em>(<em>x</em>).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that \(f'( - 1) = - \frac{{16}}{3}\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Explain what <em>f</em> <em>'</em>(−1) represents.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the equation of the tangent to the graph of <em>f</em> (<em>x</em>) at the point where <em>x</em> is –1.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sketch the tangent to the graph of <em>f</em> (<em>x</em>) at <em>x</em> = −1 on your diagram for (a).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>P and Q are points on the curve such that the tangents to the curve at these points are horizontal. The <em>x</em>-coordinate of P is <em>a</em>, and the <em>x</em>-coordinate of Q is <em>b</em>, <em>b</em> > <em>a</em>.</span></p>
<p><span>Write down the value of</span></p>
<p><span>(i) <em>a</em> ;</span></p>
<p><span>(ii) <em>b</em> .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>P and Q are points on the curve such that the tangents to the curve at these points are horizontal. The <em>x</em>-coordinate of P is <em>a</em>, and the <em>x</em>-coordinate of Q is <em>b</em>, <em>b</em> > <em>a</em>.</span></span></p>
<p><span>Describe the behaviour of <em>f</em> (<em>x</em>) for <em>a</em> < <em>x</em> < <em>b</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">j.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A biologist is studying the relationship between the number of chirps of the Snowy Tree cricket and the air temperature. He records the chirp rate, \(x\), of a cricket, and the corresponding air temperature, \(T\), in degrees Celsius.</p>
<p class="p1">The following table gives the recorded values.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-04_om_08.39.25.png" alt></p>
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<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Draw the scatter diagram for the above data. Use a scale of 2 cm for 20 chirps on the horizontal axis and 2 cm for 4<span class="s1"><strong>°</strong></span>C on the vertical axis.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
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<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use your graphic display calculator to write down the Pearson’s product–moment correlation <span class="s1">coefficient, \(r\)</span>, between \(x\) and \(T\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
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<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Interpret the relationship between \(x\) and \(T\) using your value of \(r\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
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<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use your graphic display calculator to write down the equation of the regression line \(T\) on \(x\). Give the equation in the form \(T = ax + b\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
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<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the air temperature when the cricket’s chirp rate is \(70\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
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<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Given that \(\bar x = 70\), draw the regression line \(T\) on \(x\) on your scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
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<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">A forest ranger uses her own formula for estimating the air temperature. She counts the number of chirps in 15 seconds, \(z\), multiplies this number by \(0.45\) and then she adds \(10\).</p>
<p class="p1">Write down the formula that the forest ranger uses for estimating the temperature, \(T\).</p>
<p class="p1">Give the equation in the form \(T = mz + n\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">g.</div>
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<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">A cricket makes 20 chirps in <strong>15</strong> seconds.</p>
<p class="p1">For this chirp rate</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>calculate an estimate for the temperature, \(T\), <strong>using the forest ranger’s formula</strong>;</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>determine the actual temperature recorded by the biologist, <strong>using the table above</strong>;</p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>calculate the percentage error in the forest ranger’s estimate for the temperature, compared to the actual temperature recorded by the biologist.</p>
<div class="marks">[6]</div>
<div class="question_part_label">h.</div>
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