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</div><h2>SL Paper 1</h2><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The first term of a geometric sequence is 2 and the third term is 2.205.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the common ratio of the sequence;</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>Calculate the eleventh term of the sequence;</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 sum of the first 23 terms of the sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>In this question give all answers correct to two decimal places.</strong></p>
<p>Diogo deposited \(8000\) Argentine pesos, \({\text{ARS}}\), in a bank account which pays a nominal annual interest rate of \(15\% \), <strong>compounded monthly</strong>.</p>
<p>Find how much <strong>interest</strong> Diogo has earned after \(2\) years.</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>Carmen also deposited \({\text{ARS}}\) in a bank account. Her account pays a nominal annual interest rate of \(17\% \), <strong>compounded yearly</strong>. After three years, the total amount in Carmen’s account is \({\text{10}}\,{\text{000}}\,{\text{ARS}}\).</p>
<p>Find the amount that Carmen deposited in the bank account.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The exchange rate between Indian rupees (INR) and Singapore dollars (S$) is \(100{\text{ INR}} = {\text{S\$ }}3.684\) <br></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Kwai Fan changes \({\text{S\$ }}500\) to Indian rupees.</span></p>
<p><span>Calculate the number of Indian rupees she will receive using this exchange rate. <strong>Give your answer correct to the nearest rupee.</strong></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>On her return to Singapore, Kwai Fan has \(2500\) Indian rupees left from her trip. She wishes to exchange these rupees back to Singapore dollars. There is a \(3\% \) commission charge for this transaction and the exchange rate is \(100{\text{ INR}} = {\text{S\$}}3.672\).</span></p>
<p><span>Calculate the commission in Indian rupees that she is charged for this exchange.</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 her return to Singapore, Kwai Fan has \(2500\) Indian rupees left from her trip. She wishes to exchange these rupees back to Singapore dollars. There is a \(3\% \) commission charge for this transaction and the exchange rate is \(100{\text{ INR}} = {\text{S\$}}3.672\).</span></p>
<p><span>Calculate the amount of money she receives in Singapore dollars, <strong>correct to two decimal places</strong>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A store sells bread and milk. On Tuesday, 8 loaves of bread and 5 litres of milk were sold for $21.40. On Thursday, 6 loaves of bread and 9 litres of milk were sold for $23.40. </span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">If \(b =\) the price of a loaf of bread and \(m =\) the price of one litre of milk, Tuesday’s sales can be written</span> <span style="font-size: medium; font-family: times new roman,times;">as \(8b + 5m = 21.40\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using simplest terms, write an equation in <em>b</em> and <em>m</em> for Thursday’s sales.</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>Find <em>b</em> and <em>m</em>.</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>Draw a sketch, in the space provided, to show how the prices can be found graphically.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The annual fees paid to a school for the school years 2000, 2001 and 2002 increase as a geometric progression. The table below shows the fee structure.</span></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,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the common ratio for the increasing sequence of fees.</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><strong><span>Give your answer correct to 2 decimal places.</span></strong></p>
<p><span>The fees continue to increase in the same ratio.</span></p>
<p><span>Find the fees paid for 2006.</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><strong>Give your answer correct to 2 decimal places.</strong></span></p>
<p><span>The fees continue to increase in the same ratio.</span></p>
<p><span>A student attends the school for eight years, starting in 2000.</span></p>
<p><span>Find the <strong>total</strong> fees paid for these eight years.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">An amount, <em>C</em>, of Australian Dollars (AUD) is invested for 5 years at 2.5 % yearly simple interest. The interest earned on this investment is 446.25 AUD.</span></p>
</div>
<div class="question">
<p><span>5000 AUD is invested at a nominal annual interest rate of 2.5 % <strong>compounded half yearly</strong>.</span></p>
<p><span>Calculate the length of time in years for the interest on this investment to exceed 446.25 AUD.</span></p>
</div>
<br><hr><br><div class="specification">
<p><em><span style="font-size: medium; font-family: times new roman,times;"><strong>In this question give all answers correct to two decimal places.</strong> </span></em></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Chiara is an Italian tourist visiting Sweden. The exchange rate for changing euros (€) into Swedish Krona (SEK) is 1€ = 10.275 SEK. She converts 350 euros into Swedish Krona at a bank which charges 2 % commission.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the amount of commission charged in <strong>SEK</strong>.</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 the amount of money she receives from the bank after commission.</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>Chiara returns to Italy with 296 SEK. She changes this money back into euros at a bank and receives 32€. The bank does not charge commission.</span></p>
<p><span>Calculate the value in SEK of 1€.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the function \(f (x) = ax^3 − 3x + 5\), where \(a \ne 0\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(f ' (x) \). </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 the value of \(f ′(0)\).</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 function has a local maximum at <em>x</em> = −2.</span></p>
<p><span>Calculate the value of <em>a</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Given that \(z = \frac{{12\cos (A)}}{{4q + r}}\) and that \(A = {60^ \circ }\), \(q = 8\) and \(r = 32\);</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the <strong>exact </strong>value of \(z\).</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 your answer to part (a) correct to 2 decimal places.</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 your answer to part (a) correct to three significant figures.</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><span>Write your answer to part (a) in the form \(a \times {10^k}\), where </span><span><span><span>1 ≤ <em>a</em> < 10, \(k \in {\mathbb{Z}}\) .</span></span></span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>When Bermuda \({\text{(B)}}\), Puerto Rico \({\text{(P)}}\), and Miami \({\text{(M)}}\) are joined on a map using straight lines, a triangle is formed. This triangle is known as the Bermuda triangle.</p>
<p>According to the map, the distance \({\text{MB}}\) is \(1650\,{\text{km}}\), the distance \({\text{MP}}\) is \(1500\,{\text{km}}\) and angle \({\text{BMP}}\) is \(57^\circ \).</p>
<p><img src="data:image/png;base64,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" alt></p>
<p>Calculate the distance from Bermuda to Puerto Rico, \({\text{BP}}\).</p>
<p> </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 area of the Bermuda triangle.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The fifth term of an arithmetic sequence is 20 and the twelfth term is 41.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Find the common difference. </span></p>
<p><span>(ii) Find the first term of the sequence.</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 eighty-fourth term.</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>Calculate the sum of the first 200 terms.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The second term of an arithmetic sequence is <span class="s1">30</span>. The fifth term is <span class="s1">90</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>the common difference of the sequence;</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>the first term of the sequence.</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 first, second and fifth terms of this arithmetic sequence are the first three terms of a geometric sequence.</p>
<p class="p1">Calculate the seventh term of the <strong>geometric </strong>sequence.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The length of a square garden is (<em>x</em> + 1) m. In one of the corners a square of 1 m length is used only for grass. The rest of the garden is only for planting roses and is shaded in the diagram below.</span></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>
<p><span style="font-size: medium; font-family: times new roman,times;">The area of the shaded region is <em>A</em> .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down an expression for <em>A</em> in terms of <em>x</em>.</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 <em>x</em> given that <em>A</em> = 109.25 m<sup>2</sup>.</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 owner of the garden puts a fence around the shaded region. Find the length of this fence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Factorise the expression \({x^2} - kx\) .</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>Hence solve the equation \({x^2} - kx = 0\) .</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 diagram below shows the graph of the function \(f(x) = {x^2} - kx\) for a particular value of \(k\).<br></span></p>
<p><br><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Write down the value of \(k\) for this function.</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 diagram below shows the graph of the function \(f(x) = {x^2} - kx\) for a particular value of \(k\).<br></span></p>
<p><br><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Find the minimum value of the function \(y = f(x)\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Minta deposits <span class="s1">1000 </span>euros in a bank account. The bank pays a nominal annual interest rate of <span class="s1">5</span>%, <strong>compounded quarterly</strong>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the amount of money that Minta will have in the bank after <span class="s1">3 </span>years. Give your answer correct to two decimal places.</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">Minta will withdraw the money from her bank account when the interest earned is <span class="s1">300 </span>euros.</p>
<p class="p1">Find the time, in years, until Minta withdraws the money from her bank account.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The tenth term of an arithmetic sequence is 32 and the common difference is –6.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the first term of the sequence.</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>Find the 21<sup>st</sup> term of the sequence.</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 sum of the first 30 terms of the sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The first three terms of a geometric sequence are \({u_1} = 486,{\text{ }}{u_2} = 162,{\text{ }}{u_3} = 54\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(r\), the common ratio of the sequence.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(n\) for which \({u_n} = 2\).</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 sum of the first 30 terms of the sequence.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Javier starts training for a running race.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">On the first day he runs 1.5 km. Every day he runs 10 % more than the day before.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the distance he runs on the second day of training.</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 <strong>total</strong> distance Javier runs in the first seven days of training.</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>Javier stops training on the day his total distance exceeds 100 km.</span></p>
<p><span>Calculate the number of days Javier has trained for the running race.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Claudia travels from Buenos Aires to Barcelona. She exchanges 8000 Argentine Pesos (ARS) into Euros (EUR).</p>
<p>The exchange rate is 1 ARS = 0.09819 EUR. The bank charges a 2% commission on the exchange.</p>
</div>
<div class="specification">
<p>When Claudia returns to Buenos Aires she has 85 EUR left and exchanges this money back into ARS. The exchange rate is 1 ARS = 0.08753 EUR. The bank charges \(r\)% commission. The commission charged on this exchange is 14.57 ARS.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the amount of Euros that Claudia receives. Give your answer correct to two decimal places.</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 value of \(r\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The first term of an arithmetic sequence is 3 and the sum of the first two terms is 11.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the second term of this sequence.</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>Write down the common difference of this sequence.</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>Write down the fourth term of this sequence.</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 <em>n</em><sup>th</sup> term is the first term in this sequence which is greater than 1000. Find the value of <em>n</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">In a television show there is a transparent box completely filled with identical cubes. Participants have to estimate the number of cubes in the box. The box is 50 cm wide, 100 cm long and 40 cm tall.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the volume of the box.</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>Joaquin estimates the volume of one cube to be 500 cm<sup>3</sup>. He uses this value to estimate the number of cubes in the box.</span></p>
<p><span>Find Joaquin’s estimated number of cubes in the box.</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 actual number of cubes in the box is 350.</span></p>
<p><span>Find the percentage error in Joaquin’s estimated number of cubes in the box.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Pietro arrives in Singapore and, at the airport, changes 800 euros (EUR) to Singapore dollars (SGD).</p>
<p class="p1">The bank rates quoted at the airport for exchanging EUR with SGD are given in the following table. Also given are the rates for exchanging SGD with British pounds (GBP) and US dollars (USD<span class="s1">). There is no commission charged on exchanges.</span></p>
<p class="p1" style="text-align: center;"><span class="s1"><img src="images/Schermafbeelding_2015-12-19_om_17.06.44.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the number of <span class="s1">SGD </span>Pietro receives.</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">Pietro also has <span class="s1">100 GBP </span>that he wishes to change to <span class="s1">USD </span>for a trip to Cambodia.</p>
<p class="p1">To perform this transaction, the <span class="s1">GBP </span>must first be converted to <span class="s1">SGD </span>and then to <span class="s1">USD</span>.</p>
<p class="p1">Calculate the number of <span class="s1">USD </span>Pietro receives.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The number of apartments in a housing development has been increasing by a constant amount every year.</p>
<p class="p1">At the end of the first year the number of apartments was 150, and at the end of the sixth year the number of apartments was 600.</p>
<p class="p1">The number of apartments, \(y\), can be determined by the equation \(y = mt + n\), where \(t\)<em> </em>is the time, in years.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(m\).</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">State what \(m\) represents <strong>in this context</strong>.</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">Find the value of \(n\).</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">State what \(n\) represents <strong>in this context</strong>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate exactly \(\frac{{{{(3 \times 2.1)}^3}}}{{7 \times 1.2}}\).</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>Write the answer to part (a) correct to 2 significant figures.</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>Calculate the percentage error when the answer to part (a) is written correct to 2 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 your answer to <strong>part (c)</strong> in the form \(a \times {10^k}\) where \(1 \leqslant a < 10{\text{ and }}k \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>For a study, a researcher collected 200 leaves from oak trees. After measuring the lengths of the leaves, in cm, she produced the following cumulative frequency graph.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_17.29.13.png" alt="M17/5/MATSD/SP1/ENG/TZ2/06"></p>
</div>
<div class="specification">
<p>The researcher finds that 10% of the leaves have a length greater than \(k\) cm.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the median length of these leaves.</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 number of leaves with a length less than or equal to 8 cm.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the graph to find the value of \(k\).</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>Before measuring, the researcher estimated \(k\) to be approximately 9.5 cm. Find the percentage error in her estimate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Shiyun bought a car in 1999. The value of the car \(V\) , in USD, is depreciating according to the exponential model</span><br><span style="font-family: times new roman,times; font-size: medium;">\[V = 25000 \times {1.5^{ - 0.2t}}{\text{, }}t \geqslant 0\]</span><br><span style="font-family: times new roman,times; font-size: medium;">where \(t\) is the time, in years, that Shiyun has owned the car.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of the car when Shiyun bought it.</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 value of the car three years after Shiyun bought it. Give your answer correct to <strong>two decimal places</strong>.</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 time for the car to depreciate to half of its value since Shiyun bought it.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The fourth term, <em>u</em><sub>4</sub>, of a geometric sequence is 135. The fifth term, <em>u</em><sub>5</sub>, is 101.25 .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the common ratio of the sequence.</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>Find <em>u</em><sub>1</sub>, the first term of the sequence.</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 sum of the first 10 terms of the sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">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;">A quadratic function \(f:x \mapsto a{x^2} + b\), where \(a\) and \(b \in \mathbb{R}\) and \(x \geqslant 0\), is represented by the mapping diagram.</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_08.19.32.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using the mapping diagram, write down two equations in terms of \(a\) and \(b\).</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>Solve the equations to find the value of</span></p>
<p><span>(i) \(a\);</span></p>
<p><span>(ii) \(b\).</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>Find the value of \(c\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The planet Earth takes one year to revolve around the Sun. Assume that a year is 365 days and the path of the Earth around the Sun is the circumference of a circle of radius \(150000000{\text{ km}}\).</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>Calculate the distance travelled by the Earth in <strong>one day</strong>.</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>Give your answer to part (a) in the form \(a \times {10^k}\) where \(1 \leqslant a \leqslant 10\) and \(k \in \mathbb{Z}\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Albena travels to Bulgaria on a business trip. She is paid 3550 Bulgarian levs (BGN) at the end of her trip. She converts all her BGN into euros (EUR), at an exchange bureau that sells 1 EUR for 1.95 BGN and charges 3 % commission.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the amount that Albena receives in EUR.</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">At the airport shop, Albena buys chocolates that cost 34.50 BGN. She uses 20 EUR to pay for the chocolates but receives her change in BGN. The shop’s exchange rate is 1 EUR = 1.90 BGN.</p>
<p class="p1">Find how many BGN she receives as change.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A concert choir is arranged, per row, according to an arithmetic sequence. There are 20 singers in the fourth row and 32 singers in the eighth row.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the common difference of this arithmetic sequence.</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>There are 10 rows in the choir and 11 singers in the first row.</span></p>
<p><span>Find the <strong>total</strong> number of singers in the choir.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A building company has many rectangular construction sites, of varying widths, along a road.</p>
<p class="p1">The area, \(A\), of each site is given by the function</p>
<p class="p1">\[A(x) = x(200 - x)\]</p>
<p class="p1">where \(x\) is the <strong>width </strong>of the site in metres and \(20 \leqslant x \leqslant 180\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Site <span class="s1">S </span>has a width of \(20\)<span class="s1"> m</span>. Write down the area of <span class="s1">S</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 class="p1">Site <span class="s1">T </span>has the same area as site <span class="s1">S</span>, but a different width. Find the width of <span class="s1">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 class="p1">When the width of the construction site is \(b\) metres, the site has a maximum area.</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Write down the value of \(b\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Write down the maximum area.</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 range of \(A(x)\) is \(m \leqslant A(x) \leqslant n\).</p>
<p class="p1">Hence write down the value of \(m\) and of \(n\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The exchange rates between the British pound (GBP) and the United States dollar (USD) and between the USD and the Euro (EUR) are given below.</span></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 exchange rate between GBP and EUR in the form 1 GBP = <em>k</em> EUR,</span> <span>where <em>k</em> is a constant. Give your answer correct to <strong>two decimal places</strong>.</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>Isabella changes 400 USD into Euros and is charged 2 % commission.</span></p>
<p><span>Calculate how many Euros she receives. Give your answer correct to <strong>two decimal places</strong>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider <em>c</em> = 5200 and <em>d</em> = 0.0000037.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of <em>r</em> = <em>c </em></span><span><span>× </span><em>d</em>.</span></p>
<p><span> </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>Write down your value of <em>r</em> in the form </span><span><span><em>a</em> × </span>10<em><sup>k</sup></em>, where 1 </span><span><span>≤ </span></span><span><span><span><em>a</em> < </span></span>10 and \(k \in \mathbb{Z}\).</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>Consider the following statements about <em>c</em>, <em>d</em> and <em>r</em>. Only <strong>three</strong> of these statements are true.</span></p>
<p><span>Circle the true statements.</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>
<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 average radius of the orbit of the Earth around the Sun is 150 million kilometres.</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_14.06.16.png" alt></span></p>
</div>
<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 average radius of the orbit of the Earth around the Sun is 150 million kilometres.</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_14.06.16_1.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down this radius, in kilometres, in the form \(a \times {10^k}\), where \(1 \leqslant a < 10,{\text{ }}k \in \mathbb{Z}\).</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 Earth travels around the Sun in one orbit. It takes one year for the Earth to complete one orbit.</span></p>
<p><span>Calculate the distance, in kilometres, the Earth travels around the Sun in one orbit, assuming that the orbit is a circle.</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>Today is Anna’s 17th birthday.</span></p>
<p><span>Calculate the total distance that Anna has travelled around the Sun, since she was born.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A function <em>f</em> (<em>x</em>) = <em>p</em>×2<em><sup>x</sup></em> + <em>q</em> is defined by the mapping diagram below.</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>Find the value of</span></p>
<p><span>(i) <em>p</em> ;</span></p>
<p><span>(ii) <em>q</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>Write down the value of <em>r </em>.</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>Find the value of <em>s </em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Given the arithmetic sequence: \({u_1} = 124{\text{, }}{u_2} = 117{\text{, }}{u_3} = 110{\text{, }}{u_4} = 103, \ldots \)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the common difference of the sequence.</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 sum of the first \(50\) terms of the sequence.</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>\({u_k}\) is the first term in the sequence which is negative. </span></p>
<p><span>Find the value of \(k\).</span></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 ladder is standing on horizontal ground and leaning against a vertical wall. The length of the ladder is \(4.5\) metres. The distance between the bottom of the ladder and the base of the wall is \(2.2\) metres.</p>
<p>Use the above information to sketch a labelled diagram showing the ground, the ladder and the wall.</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>Calculate the distance between the top of the ladder and the base of the wall.</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>obtuse</strong> angle made by the ladder with the ground.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Gabriella purchases a new car.</p>
<p class="p1">The car’s value in dollars, \(V\), is modelled by the function</p>
<p class="p1">\[V(t) = 12870 - k{(1.1)^t},{\text{ }}t \geqslant 0\]</p>
<p class="p1">where \(t\) is the number of years since the car was purchased and \(k\) is a constant.</p>
</div>
<div class="specification">
<p class="p1">After two years, the car’s value is <span class="s1">$9143.20</span>.</p>
</div>
<div class="specification">
<p class="p1">This model is defined for \(0 \leqslant t \leqslant n\). At \(n\) years the car’s value will be zero dollars.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down, and simplify, an expression for the car’s value when Gabriella <span class="s1">purchased it.</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">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 class="p1">Find the value of \(n\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">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;">The following Venn diagram shows the relationship between the sets of numbers</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;">\[\mathbb{N},{\text{ }}\mathbb{Z}{\text{, }}\mathbb{Q}{\text{ and }}\mathbb{R}{\text{.}}\]</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 number –3 belongs to the set of \(\mathbb{Z}{\text{, }}\mathbb{Q}\) and \(\mathbb{R}\), but not \(\mathbb{N}\), and is placed in the appropriate position on the Venn diagram as an example.</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_14.14.57.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;">Write down the following numbers in the appropriate place in the Venn diagram.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>4</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>\(\frac{1}{3}\)</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>\(\pi \)</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>\(0.38\)</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>\(\sqrt 5 \)</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>\(-0.25\)</span></p>
<div class="marks">[1]</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;">A satellite travels around the Earth in a circular orbit \(500\) kilometres above the Earth’s surface. The radius of the Earth is taken as \(6400\) kilometres.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the radius of the satellite’s orbit.</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 distance travelled by the satellite in one orbit of the Earth. Give your answer correct to the nearest km.</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>Write down your answer to (b) in the form \(a \times {10^k}\) , where \(1 \leqslant a < 10{\text{, }}k \in \mathbb{Z}\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">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;">\(U\) is the set of <strong>positive </strong>integers less than or equal to \(10\).</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;">\(A\), \(B\) and \(C\) are subsets of \(U\).</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;"><em> </em>\(A = \left\{ {{\text{even integers}}} \right\}\)</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;"><em> </em>\(B = \left\{ {{\text{multiples of }}3} \right\}\)</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;"><em> </em>\(C = \left\{ {6,{\text{ }}7,{\text{ }}8,{\text{ }}9} \right\}\)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of \(A\).</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>List the elements of \(B\).</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>Complete the Venn diagram with <strong>all </strong>the elements of \(U\).</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-02_om_17.36.22.png" alt></span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the universal set \(U = \{ x \in \mathbb{N}|3 < x < 13\} \), and the subsets \(A = \{ {\text{multiples of 3}}\} \) and \(B = \{ 4,{\text{ }}6,{\text{ }}12\} \).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of the following set.</span></p>
<p><span><em>A</em></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>List the elements of the following set.</span></p>
<p><span>\(A \cap B'\)</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>Write down one element of \((A \cup B)'\).</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>One of the statements in the table below is false. Indicate with an <strong>X</strong> which statement is false. Give a reason for your answer.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A manufacturer in England makes \(16 000\) garden statues. \(12\% \) are defective and cannot be sold.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of statues that are non-defective.</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 manufacturer sells each non-defective statue for \(5.25\) British pounds (GBP) to an American company. The exchange rate from GBP to US dollars (USD) is \(1{\text{ GBP}} = 1.6407{\text{ USD}}\).</span></p>
<p><span>Calculate the amount in USD paid by the American company for all the non-defective statues. Give your answer correct to <strong>two decimal places</strong>.</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 American company sells one of the statues to an Australian customer for \(12{\text{ USD}}\). The exchange rate from Australian dollars (AUD) to USD is \(1{\text{ AUD}} = 0.8739{\text{ USD}}\) .</span></p>
<p><span>Calculate the amount that the Australian customer pays, in AUD, for this statue. Give your answer correct to <strong>two decimal places</strong>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The diagram shows triangle ABC in which angle BAC \( = 30^\circ \), BC \( = 6.7\) cm and AC \( = 13.4\) cm.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"> </span></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,iVBORw0KGgoAAAANSUhEUgAAAe8AAACbCAIAAADEL4T5AAAU+UlEQVR4nO3d72vb9qLH8fwbfSSDHtkcw0qf5FHcwCieByaE3VAIlN055sS9t9AHo7u1fNN7Rx/cLmDTMGK4kNkspzAGqUzLGDQpInAxXVrRDMrmCnpYT+OIQzA+RhwHE77oPvhKsmTLP5LYsX58XuRJZklRnO7tr7+SpSkVwEUaQiYYYJnOr3Ai+1iQlEnvHcAETU16BwBOizSElTCzWJSOte/lvU0uzjLTycIbBB18CzUH1+msuaqqKqkU4yE2uCI0yOR2DGCSUHNwHdQcwAZqDq7TVXMii99zMcy0gL+h5uA6tOZdB0I5oTHpPQOYINQcXKf7KKhYyi6FmUA4sVlRMNMCPoWag+vYzZurx1JhkWVCc4UKcg7+hJqD69jWXJt+wXwL+BZqDq5jW/NWlb8dxtgcfAw1B9exO6eFzyaDATZ6X5BbE903gIlBzcFVenyyn2XimcJPIlIOPoaaAwB4AWoOAOAFqDm4UrPZfPnyZbPZnPSOADgFag4u02w2Szw/G4n8+81/u5lKIegAFGoOrmF0nEuna7Waqqr59TyCDkCh5uAC5o5LkmR+CEEHoFBzcLQ+HTcg6AAqag6ONUzHDQg6AGoOjnOqjhsQ9BEhirRb2somg7dK8omqqqTKp4KhWHYP146fqJYs/vw4uxRO8HKPJVBzcJCzddyAoI+AzCfpx2vjBYmoqnoi87dYJsB+lBVPJr1v/qX/FfpeiQg1B6col8vXFxbO1nEDDTo94wXOpPP6ZX4amxOl8kPuyYcejzYqhfxTeVKvaYqY/YTtvNicBWoOkzeSjhvy6/nZSOTg4OD8m/KlD6XEZZb5JCf6oN4WDYlfifXKpVIpcXH9/cpEfCglLvd/h4SawySNtuMGBP20iLy3ycVZJhT76qtkMKDfL7sliz+XClzMFBF9yenURv4/ggFT4FqyyOcS09pF0PhK+9VAkYStbPKjFaFRrxSWw+2bcbdk8VEmGmKDt77b+NL0hoAo0m6pwM1xQkOLLH2IKBKfiYbY6Jpof5MpbYfnOKFhbNy6MJHFpwUuxgRYJhTjeEkhqkqUymayfTU37YCBrlEpLLfvXKhPW9ttpxvd+QDLTCezPzz+lt9vP43G6tPJh2W5/RzaPiHa9easl+9vyeJPRS7OMgE2uFysNFBzmAza8esLC6PtuAFBHx6Rd+5FQ2z0viA3pMKifpPV9v1XjYjoS66Jyt8FboZlAle0zrdk4X5Mz0r7UpfBFaHxRylxmWUCYW6nKq7FmIA+XUBXCcWye4q2vP6GQJu7v5zk31X523QfrmTFVpVPBW2DqzkRs1e0yeVfq3R/LAtr1Q4v81VCfzsjl/TeVcav0/EEVYrxkOn9Sp/tWNeTCnPaQy1ZuB/TXgno6vQ14FgW7se0Pez9hGh/i5mMcKRvuiqsxNnofUH+p8zfovPpqDlcNKPj5XJ5rD/oL5ubCPpg5H1peZrVSnFipIGoqv6tHhHLknQa13iI9k5fkebYGIPLfJIJzW38+F08xDI0gnQ6Xl/mRMx9ZFpe2/j1XCGbKeyJhUWWmcnwT9a4R5XqTsbyhqDjd6G7sfjdzg/3/ntHrgvmhfWfeLtUbbWPK9LCaiuacmneqlSYM/06/bZjRV9d9NvV1vbF98RYnb5jIJViPDTEE3IkcDOmSfO6mJ1nmfmcWNf/KItF6Rg1h4tzYR03/0QEvS99AK5NR3RUg35LR45EoSNrbUk6va4Pey2jV32bWozot9dXs1yq8EaffqE90g+u0vq3g/ihlLjMBj9JZgX5hG75ciyxJsgtrY897heoZZeZmVv5qWvUTH+XHt/SsXC7njZPkf5D+26nc1WaWvN9VOjy3S8bfZ+QhvllSftDhDnhH9qsV/yeUCWYN4eLcfEdN/9oBL03u6gZs+SWiByZp1a0gaRp0rzK3w7T0aKyl4uG2mGikxjBj+e4J1UjeJaZhK67AJrbqi05nxPr+nyI/Qja9CpCR83Wbmrb0V+oLN/qK9oP+e2eIvvt2FHeFBPT7dmqXi8b/Z4Q25clm5u0oOYwXhPsuHkfEHR79B29ljw6PAyEuZ0Pr1+/6xjbaqPvy0n+g7HklWz5/W75HU2OvLeZ5ZLREMsE2OBSjhe1I3t0Ra2wGn0Qfaskn+j1/yS399vu7l+JJV7WcbG2KdsRtDpguE1Hu9oLFX1VMF5v+o6vO3rdbzsWRHr2lK5Cf0G6imV1+ry92ZdbfZ8Q62tY96SQ8ttT4a8Ym8MYOaHj5p1B0G20a16VxWdF7mOWCYQ///rx67ppbPtO2n2tz3jMZIS/K9Izeu6KviR97x/PFLZK/G7H2R20Ux1zI6aZ6Lq0s5YMBlhm+l+5H/c7Z3sss/PaWvENsfLC5q6B+qQ5za52RDSxJUkvRLllivuJ6SAkMa34SU6sSruvZWvRtR/6UVasS7uiTPpsx7peQ1i5ksi/lFt0vkV7BrRSTycLbxSVKNLuU1Em/Z+Q9mvYsSw+E6R39LWHvoQQWXz6RHvhRM1h9CRJ4tJph3TcgKDb0d7Ux7hHovx3MTtvOrmQVnU6mX0mKcS0ZEEPirFkxxl+ATa6UpJovem4ko7oTbQJ5XimIEj0wKaxinlMbQ20fvzQ2Lh1kx3HKum37YVb8l5e28koVxQkpXNnjN/Uulnt4ORSboeu0ns7FsfvdsuVCn3ZM29ZP8mSCYQT2ZL+BqbfE6JPvocTa8+lhnkLlvdAqDmMljM7bkDQx4HIYim7co9/IQpPHmeXwpYLA8DFQc1hNBzecQOCPmpHAjdjabd5mhguEGoO50U7PhuJbG9vT3pfhoKgjxSdS2l/+JPIO/eil/1xXRdnQc3h7IyOl3jeXVcuRNBHicgin23Pm/ebTYYxQs3hLNzbcQMNusPnhQCGh5rD6Xig44ZyucwyAQQdvAE1h2F5qeMGBB08AzWHwTzZcQOCDt6AmkM/tVqNXlrWkx037O/vYw4d3A41B3s+6bjh4OAAQQdXQ82hk986bkDQwdVQc2ijHWeZgN86bkDQwb1Qc1BVU8fz63mf3/AeQQeXQs39Dh3vhqCDG6Hm/oWO94Ggg+ug5n6Ejg8DQQd3Qc39BR0/FQQdXAQ194tms1nieXT8tBB0cAvU3Ptox2cjEXT8bGjQ8+v5Se8IQD+ouZeh46OCoIPzoebeZHT8mwcP0PGRQNDB4VBzrzE6zqXTkiRNenc8BUEHJ0PNvQMdvwDNZvNmKoWggwOh5l6Ajl8kBB2cCTV3N3R8IhB0cCDU3K3Q8clC0MFpUHNXovebR8cnC0EHR0HNXaZcLl9fWEDHHQJBB+dAzV0DHXem0QW9JYs/P84uhZlAmBMaNgscCdwMywQsX/GCRM79k8ETUHMXoB2/mUqh4840gqAT+eXDpXBwKbe1Kyk98twQMkFrypnQXKGCmAOFmjsa7fj1hQVc9cnhzhf0upidDyfyL+VW72VIQ/j2a6FqaveRwN0qSsdn+ongQai5Q6HjrmME/ZS3VCWKuBYL3i5V+6RcVdWWLL1XzKtJhTlMs4AJau446Lh70aDfTKVOEXRSKcYvx7gNOmPOBpdyO5IyeLVjqbCc4t/3iDlRpGe5xDTLBNjg0tqeTFRVVRuS8GMuEc8IVXkvnwwGWCZ+T6gSIovfczEmwAaXixW76XpwCdTcQdBxDzht0IlUmGPime9pcRuVwnKYmc+J9UGrVYrzXwsN25gTRVyLRe8LcktVW1X+dphZLEr/bAgrYSbAMtPJLC/KLTq9wxoz9aQqrMRxTNXVUHNHQMe95DRBJw1hJRxcaXeZVIrx0MCqEqnwmf15L6qqHgncfEY40paUy2uJz+nLA5EKc8yM/hBpCCthZlGfeT+WCouseU/AbVDzCZMk6WYqhY57TLPZ5NLpIYLe3dBhqnosFW4Zve7UEDLBGdtHUXNvQ80nRpIkLp1Gxz0sv54fFPSOpKpaVfuPzftNs9Cah2LZve7Jd9Tc21DzCUDH/WNw0BtCJjhtOp55JHAf9z+LvO80iz5Xw8QzfEUPen1f+LWBmnsdan6h0HEfGhT0VpW/HdbOJ2nJe/lkfE3UPkDUqvK3w1HjW6rvNIuqakdBLR8ymse8uR+g5heEdnw2Einx/CnPRwbXGxT0hrSzlgwGWCYU4x6J7c8Q2dWcVIrL34q9Pi+qryiLjzLREMsE2ChXFCSFxrr9CdLXlfa3MxnhN9M1A+zn3MH5UPOxQ8dBHWoOHeBcUPMxQsfBDEGHsULNxwIdB1sIOowPaj5i6Dj0h6DDmKDmI1Or1dBxGAaCDuOAmo9ArVbLr+fRcRhefj1/fWHh4OBg0jsC3oGanws6DmdG/+Ug6DAqqPkZoeNwfgg6jBBqfmq04ywTyK/na7XapHcH3A1Bh1FBzU8BHYdx2N7eRtDh/FDzoaDjMFblchlBh3NCzQdAx+FiIOhwTqh5T+g4XDAEHc4DNbfRbDb/srmJjsPFQ9DhzFBzi2azWeL52UgEHYdJQdDhbFBzDToOzoGgwxmg5ug4OBGCDqfl65obHefSaUmSJr07ABYIOpyKT2uOjoMrIOgwPN/VHB0HdymXyywTwG3BYSAf1RwdB5dC0GEYvqg5Og5uh6DDQN6vOb2kEToOboegQ39ernm5XL6+sICOg2ccHBzMRiIIOtjyZs3RcfAqBB168VrN0XHwPAQdbHmn5rTj1xcW9vf3uXT6ZiqFe7yBVyHo0M0LNTc6bv7Hvb+//82DB7gtOngVgg4d3F1z2453LICP0oFXIehg5taaD+y4ecnZSARTLuBJCDoY3Ffz4Ttu+ObBg28ePBjrXgFMCoIOlJtqvr+/f9qOU81mczYSwVku4FUIOqhuqbkkSVw6fYaOG7a3t7l0erR7BeAcNOglnp/0jsDEOL3m5++4AcNz8DYa9Px6ftI7ApPh3JqPsONUiefxDx28DUH3MyfWnHZ85G8ba7UaywRwcgt4G4LuW86qubnj48juzVQKR4rA8w4ODm6mUgi63zil5uPuOLW9vY1TFcEPms0mgu43k6/5aDtODp/dvXppaura3ecHpOvRWq02G4mc80cAuAKC7jeTrPkYxuPHbzfurL6qq8ovq18U33bnXFVx5RbwDwTdVyZT84ODg2E7Tg5/yd64NDU1NTV16Ub22duG3UPX7hR/OSTqMDXPr+e3t7dH++sAOBaC7h8XXfNarZZfzw89Hq+/yv5n9pdDYkyhXNvQG11/tfrp1NX/en7YIofP7l698sXWH2TQTIuqqtvb2/iXDb6CoPvExdX8lB3vdnK49eepS3efN4iqquTtxrWpK3eeH6mqqqrHbzf+xXioPzq9c/qfDuBiCLofXETNz91x6uj5nWt0AK7le+rPW4cn9DFr3PtpNpssEzjrPgC4FYLueeOtOe04ywTy6/lzHedU3j5bvcHeea7Pmh89v3Nlil19daIvcLh1Y+rStY3fBw/OVXU2EqnVamffGQB3QtC9bVw1N3f8nOk8ebXKTmkufbF1QFRV/dvWDbar5pb/0AfuGgq+haB72OhrPsKOm7QOX22t3vjTlDadYlvzYcfmXDq9v78/oh0DcBkadC6dHuLtcksWf36cXQozAZYJsFGu+ESUT6SnT6Rh/keDCzbKmo+n423k7ca1KfbG1t+6D3uevFplh5s3V1W1xPO4cCj4GQ36zVSqX9CJ/PLhUji4lONFmWj/ReSzyWBorlBBzR3IWnPyvrQ8c4Y/1bg7rmk8v3Pp09VXdfUc57SoqDnA4KC3qvztMDOfE+vW/04UcW2OExp268BkWWpOpMIcE2DjheHfRzWbzYvouKqq5OD53U+v3n12qA0T/tj64k+XbhR/V06Ut1t39PPNh4GaA6j9g94QMsFA2L7aR7v8C9Tcgcw1r4vZr1azt8PMYlE6Hrhms9ks8Ty99ua4Oq78snr1knYA9OqdjdKrQ3Owld+37lybop8F3fpdGXqr+AARAEVHY11BP5YKiyyDGRWXMdW8IWTmC1K9z2uy5iI6Pk74ABGAWVfQjwRuhmVmMsJQB6LAIYyaH0uFWxnhSPtDBlcEuzlot3ecQs0BOliDjpq7kl5zUikufysqRNVmz23+kNvb27ORCJdOu7fjVLPZxGUUATrQoKuqqs+0oOYuQ2tOGsLXnxlzZKRSjIfCy3zVOjpn6Tmn+MIXvjz9peonRPSfcQWnoTWnb6w6/qhDHQsFAC+iTeg+Q1FViSzuSsOfdAAXZkpVVSIVPrO+CJMqn8JnBAD8THlTTEyzTDxTECRFOy9YkYTNwk8VBWFwoilVrYtZrmsYfiRwM6c68RwAvIbI4pONTDSkvV+nn+xHE5xqShbux2zOYNFOOI2t7OCPBwDgfFN2s+Q05foEeo+zFQEAwDkmeZdnAAAYFdQcAMALUHMAAC9AzQEAvAA1BwDwAtQcAMALUHMAAC9AzQEAvAA19xlFEvgfcol498VOiVxeS0yzTICNrpSkYa6d16ryt8O4/AOAM6DmfkIqxfnF5OfTNpeuVn4tff9CJsad2gd/AJhU+VTwdHeRBYDxQc19x+5uJMfvdl+0L2ffEDLBQXcqUPZyiS8ziWnUHMAhUHPf6XVvKcsC0TWx31VP62L2y5wo4UKbAM6BmvtO35o3JKGQSfyPILf6bEARv01m95SBl01WpOfZpTATYJnp5MOydjFORRK2ssmPVoR69eXDpTATYKP3BblF5L1NLs4ygXBiE5fPBjgD1Nx3eta8IWSC9MKZ8Qxf6XlzGWUvl6C3kO1bc2UvF52/J1SJ5eYn+l2ugks5XpQJXSwUTmQfC5KiqkTeuRe9jNukAJwBau47/Wda9DHydIp/b5fUuvhwtVSlI/c+NScNYeWKcUMrIr98uDyX3VNUVbvecvsoq3Uj9J60uB0lwOmh5r4zcN68d1KJIv7vvXbl+9T8SOBmekQZNQcYC9TcdwbXXD2WCot2SbW9G3iAZbpvIXskcDOs/aFU1BxgLFBz3xmi5kcCF+8x09KxWK+xuX4nQo5v3yD49f+JDYKaA4wJau47NjUn70vLMzHukSi3VLUlC/fnTCeWkCqfCs7nxHrXlgYeBQ2Zx+8xzJsDjBNq7ivWqZJ2iBuVwnJYuw2sfraJ7ow1bx9QDbBMPFMQJIXQWLdvRVt53f42uCJ82NFPqsHdaAFODTUHAPAC1BwAwAtQcwAAL/h/AcDHBlS23JIAAAAASUVORK5CYII=" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the size of angle ACB.</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>Nadia makes an accurate drawing of triangle ABC. She measures angle BAC and finds it to be 29°.</span></p>
<p><span>Calculate the percentage error in Nadia’s measurement of angle BAC.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Passengers of Flyaway Airlines can purchase tickets for either Business Class or Economy Class.</p>
<p class="p2">On one particular flight there were <span class="s1">154 </span><span class="s2">passengers.</span></p>
<p class="p2">Let \(x\) be the number of Business Class passengers and \(y\) be the number of Economy Class passengers on this flight.</p>
</div>
<div class="specification">
<p class="p1">On this flight, the cost of a ticket for each Business Class passenger was <span class="s1">320 </span>euros and the cost of a ticket for each Economy Class passenger was <span class="s1">85 </span>euros. The total amount that Flyaway Airlines received for these tickets was \({\text{14}}\,{\text{970 euros}}\).</p>
</div>
<div class="specification">
<p class="p1">The airline’s finance officer wrote down the total amount received by the airline for these tickets as \({\text{14}}\,{\text{270 euros}}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use the above information to write down an equation in \(x\) <span class="s1">and \(y\).</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 class="p1">Use the information about the cost of tickets to write down a second equation <span class="s1">in \(x\) and \(y\).</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 class="p1">Find the value of \(x\) <span class="s1">and the value of \(y\).</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">Find the percentage error.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Let \(f (x) = x^2 - 6x + 8\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Factorise \(x^2 - 6x + 8\).</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>Hence, or otherwise, solve the equation \(x^2 - 6x + 8 = 0\).</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>Let \(g(x) = x + 3\).</span></p>
<p><span>Write down the solutions to the equation \(f (x) = g(x)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Given that \(h = \sqrt {{\ell ^2} - \frac{{{d^2}}}{4}} \) ,</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the <strong>exact</strong> value of \(h\) when \(\ell = 0.03625\) and \(d = 0.05\) .</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 the answer to part (a) correct to three decimal places.</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>Write down the answer to part (a) correct to three significant figures.</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>Write down the answer to part (a) in the form \(a \times {10^k}\) , where \(1 \leqslant a < 10{\text{, }}k \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The following table gives the exchange rate from US dollars to euros and from US dollars to Japanese Yen.<strong> Give all answers in this question correct to two decimal places</strong>.</span></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>Enrico has 475 USD.</span></p>
<p><span>How many euros is this worth?<br></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a, i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Enrico has 475 USD.</span></p>
<p><span>Enrico goes to a bank to exchange his dollars. The bank charges 3 % commission.</span></p>
<p><span>How many euros does Enrico receive?</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a, ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the exchange rate from euros to yen.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Astrid invests 1200 Euros for five years at a nominal annual interest rate of 7.2 %, <strong>compounded monthly</strong>.</span></p>
</div>
<div class="question">
<p><span>Find the interest Astrid has earned during the five years of her investment. <strong>Give your answer correct to two decimal places.</strong></span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Neung is going home to Vietnam after working in Singapore.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">She has 5000 Singapore dollars (SGD) and changes these into American dollars (USD)</span><br><span style="font-size: medium; font-family: times new roman,times;">to take home.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The exchange rate between Singapore dollars (SGD) and American dollars (USD) is</span></p>
<p style="text-align: left; margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">1 USD = 1.2945 SGD.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">There is also a 2.4 % commission on the exchange.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the amount of commission on the exchange <strong>in SGD</strong>.</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>Calculate the number of American dollars (USD) Neung takes home. <strong>Give your answer correct to 2 decimal places.</strong></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>At the airport in Vietnam, Neung changes 150 USD into Vietnamese dong (VND) to pay for her transport home.</span></p>
<p><span>The exchange rate between American dollars (USD) and Vietnamese dong (VND) is</span></p>
<p><span>1 USD = 19 495 VND.</span></p>
<p><span><span><span>There is no commission.</span></span></span></p>
<p><span><span>Calculate the number of Vietnamese dong that Neung receives.</span><strong> Give your answer correct to the nearest thousand dong.</strong></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the sequence</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">\[{\text{512, 128, 32, 8, }} \ldots \]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the exact value of the ninth term of the sequence.</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 least number of terms required for the sum of the sequence to be greater than 682.6</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A tree begins losing its leaves in October. The number of leaves that the tree loses each day increases by the same number on each successive day.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAgwAAABJCAIAAADe7umuAAASaklEQVR4nO2cz4vbSNrH9z+RQCcbBGly8alPw+L4YJrmvfUl4DZ0w5slh0AONg475LDsgE2bLIHAIJMmsMySyCTMBkKHomFpZh1ELmEwghloghEvfegROjSmKfQe6ockq9xtW5b9xDwfCmaI7NJX8qPnW/VUqf8UIgiCIMgU/sT+Y2g6NmzYsGHDJtukSazHpJCNA04swVEigSMJghIIGhAl8Z8GTQJZMnBiCY4SCRxJEJRA0IAoQZNAcgROLMFRIoEjCYISCBoQJWgSSI7AiSU4SiRwJEFQAkEDogRNAskROLEER4kEjiQISiBoQJSgSSA5AieW4CiRwJEEQQkEDYgSNAkkR+DEEhwlEjiSICiBoAFRgiaB5AicWIKjRAJHEgQlEDQgStAkkByBE0twlEjgSIKgBIIGRAmaBJIjcGIJjhIJHEkQlEDQgChBk0ByBE4swVEigSMJghIIGhAlC5jEtWc/UP1xj1K9/c93jkfzlBuGYRheOu1do3DQG/qL9jD2nJ97jWokvtzovV2+9GunfZef4kHfu15y798CWZ/8wCX2Pzu1apNcrFlJ6Lsn3XqBR8vxMoIlm6SxN3heL+iGVqw0bDfIJGcZCXo8sh+aVctdVAiaBFgWnUnQYa9ajKU/GbKl+tHZPA/QpfPslTNX/rx2Ond0Q9Pvtuf7nsAfWgemppu17kfXD8MwpN6no31T043yU+KNZ+tkRtnSUNEk5ocOe7t79fslQ9tet0mMR2+fd0/cIJTRsttxLtcniQaf3x4PPBqG1Dvr1kpmgyw8YsqmRAga2YcF3UCT2EQWLjd97de2kumPBk63oumGVjq0z2cLFRo43cqdeZN9lpnEeGQ/NDXdKDzsj+J+cOm0dw1NN8pd5/ZB2eyy0SQyZx/X2lm7SdDfT0+/RmFBh71qMWNeziQpoYf6pGUWWsRffDKRecI36NQeNWslNImNZIkmEZtezBSyNBge1wu6MbdJZMAnzYJuaHr6CaeutTOTw80lG01iI0xikgvS2F6nSSS4cq37lfYgWJuSS6f9qOO4pLGNJrGRLNUkwivX2jM03dDudRwWtDRwT9+0901topjru3arEl/SqNke+3de+S1WGq+cdPFH1JoMbatufw3DwGnfYz3c/bv935eNiqYbWrVpD1XPDPVJy4y+m0ThH+ky9K2ydaPc6BFXnF2axEGP/NyplQxNN2vPP0XXRQP3A/v32M2JXVR78Af7QLah4rrYXJOozjxdnsoSJAUusVr11knGFZJMhS/nWb09CMILNIlNZbkmIXMiz8JseG42iC/rPNpez70KwzBKhdGQnK0WlA7tc8pm9Af2KB1znl2PJ3o5fSk/Jd6VsAHlyF3KUyUdaT9cDxNT3LGGlPsHU56WzS6tWGkPAv7/pbr1JUickfkWXw4RRS0+KTEP7BG9cq29qAgmLsq8//2bz55r7cV891tiM03CJ83qLGXJW8gmSY54dKPc6ruZZjWLKwkGndozJ6AhmsTmkrNJsOWsQov4VGz1kckulW15LmYdsqOqzDhhEkIJW8dOnSXObCbBAj1hDGwVhGXwabL5GXnZig/8J8tNoqjFBFyQxra8EKZcrMaL21u1XBpS19rBmcS6lQhYdSXrqnW4pD1FnvOqWS6m1thWo+TSOfpBnBdNYmPJu9wUhiGbFHd/aNw3bzSJ2IZR2VR1ocVNYo5yk+gnPSOZJlt8kstjAlJrEnHxUeksXb/iF5W98L1eNs4kaOC8aPJpYlaWlRaz36KFlNDAefEkqrmhSWwsyzUJNjSOL1yzYn3p0D4f3zaTENlW1qOmsLhJzLJwzR42aSfpfpZiEttNciFMorhjDVNPVuKivl02zCTo6H335XIcIlxiWqTDXvW7lZuEeNgnmzKec9KArIJlmgQvLkUbhMSm2NnKTbPuL8piErdtgZWrIEJMMbVvZFq5iXsbFzBZbuJHRbd7PfcqWnhQLL2gSXDgmAT1SPeIiCViGgxf904zqVpaWvRJ885ayk1xcCaxsSxqEpMv09HAtZvlYvJlOrlLZ6/nevxFhCh9i9pUoUUuz09Pf6f0vH9QMjRdvAMx9hyi2ODETUIMWGSqbRD/phmARL5MJ3YZiZfpzNrxMFqNFG9OFPa7A4+GNHD/Q1xfIVust9etLwH/VnrhmjkfOyqNRy7m889Tz/k32+CUuKhvmE0xCRne8SHzbVPe3CTRkX1YqDZfsrfpRqS1V89WAftWTIKO7MOCeI2RnvcPtuUYLnGIPVnynafEJ284dFMnM/e/TpE5sYBJTPuzHNWmZZPELgvxSoFWbVpk6H54Ui4m/opA8KVXKxlasSL38AXuR7FfNnojOnHyeB3/Xsfx5G5RQ9uqt/9Wj/Tc8GpCcmOuppu19pv0n+WgnsP31Opmrd2Xx9Oy41tgC/udk/gW2Mf1o7PR6KzL9rkmjk77YhC7KLlK8U2SLfskCxoZElBGJWKKnGzZ9GSSxCMwFZmrVxKBJoEmgSDzAyeW4CiRwJEEQQkEDYgSNAkkR+DEEhwlEjiSICiBoAFRgiaB5AicWIKjRAJHEgQlEDQgStAkkByBE0twlEjgSIKgBIIGRAmaBJIjcGIJjhIJHEkQlEDQgChBk0ByBE4swVEigSMJghIIGhAlaBJIjsCJJThKJHAkQVACQQOiBE0CyRE4sQRHiQSOJAhKIGhAlKBJIDkCJ5bgKJHAkQRBCQQNiBI0CSRH4MQSHCUSOJIgKIGgAVGCJoHkCJxYgqNEAkcSBCUQNCBK1CaBDRs2bNiwyTZpEit2KmRTgRNLcJRI4EiCoASCBkSJgeUmJD/gxBIcJRI4kiAogaABUYImgeQInFiCo0QCRxIEJRA0IErQJJAcgRNLcJRI4EiCoASCBkQJmgSSI3BiCY4SCRxJEJRA0IAoQZNAcgROLMFRIoEjCYISCBoQJWgSSI7AiSU4SiRwJEFQAkEDogRNAskROLEER4kEjiQISiBoQJSgSSA5AieW4CiRwJEEQQkEDYgSNAkkR+DEEhwlEjiSICiBoAFRsohJXDvtu/J17cLD/mgsD3TuiH+/03aulyk0dtIHfW+pXc8A9QbHjaqh6YZWqh+deVQe+dqvbRmabmhbdfvrilXdgmfX13fHGHCefDhKJHAkQVACQQOiZOGZxAVpbDM/MA/sUZQ0xyO78Rf7nN7w1QW59uwH60l5waBTLhraXs91+7UtQ9vruVfRUZ80CyBNIqQ+aZnZ71gw+If1ebHvz/nk++5Jt17QDU03yo1jx1NHET3vH2zvWMO5YixbDhqP7Idm1XJjp5TjBrP2/JM3nv7dJUqSP6huaLqR1MN0es77N+19U9PNBvHzUMKjPd6K4reggfuhUysZmm5o1ebLwZTfL7MGZLUsbBKBc/S4+VgMrq0vgThw7Vj/cIKbvrogazMJ6lo7/LweaWwb5a4TxMKfz58AmoScfmW5Y5dOe/fuotPCeZ788ejt8+6JG4RhSL1PR/umtttxLhUfsx+aUWLKQ8kkdGQfFpJJORh0yrtPyIiGY488rUyERE6S6Hn/oJRKzfKo9+lo3yzsd16funOKmVlJ0qV442MmOnrfPfrgBjQMx97geb1QrLQHsycCNAmwZDCJZ5Zz+aXHBw7R87x5JnFLqt1kk/CH1oGp6aswCfr76enXKLfRYa9aTA2HaeA8qz9+XC+s0CSCQaf2qFkrxUziyrX2YtouSOO7efXML4kGTndn6vzg0mnv5j+nuSDtLomfwifNXXZbrn47/SVWUbhyrT2j0CL+rHcFTQIs2UziOqTeyZNy0dB0Ob6OmYSs1+t32851VCK/13GCMLHMcNAjP/OJavkp8QKPPK2wWlbteMiHRdIkog8nn4rYbDcqVgRO+57QMPiDfUAdu4laR4+47BoSCzBKJ1CYhOyqWGm8cqTCwCWv2/wU0Xw8ukuiE/EvNdubel0h9c66NTmuVNtAyiSSBQGLyCGnordg2OfLMNOv/TYyPPkXpLE9aRLBoFN75oxOmqsziUun/ajjuKSxHZkEHfaqWzEB1CctU1H8Wa4kVuCtNi2buBNOQQOnW4mvDs7JrEro/7m/xU995Vr3p/wQ1CctE01iI8hqEmFIg+ExT4jtQTAxkxBL2XfbznU0V+UmwYcbsmAlZtNm+d6fCwe9X143C/FptTSJatMeBmKQK8yJyzAP7BFloxjxzNBhr1o0NN28//2bz55r7cUESHgRo9IeBPz/oxqaSLXpb8WvUeZQJqx0aJ9TNhxmazZMRqFFfMrLF/LSAjEhk4nm+nPv6YlHw+nXdRGlrcD92H72bgaT4Octd52AaxAePKW3xM+3CNlMonqYWNxi+foy9MmqTIIGzrN6exDE7w8vP243yYX8mE9a5sRK1bIliZqnHnsE5LFhr7pVafzIViOMwn7nxJ1rLr/gz0SHvd1HU5yJ+qR1N7FamY8GJH+ym0QoMqxuaKVD+3w81STS2XaigiRG/YWD3tCXA2qRoSbLTeKxYY8rG2fxTM1OJL4oBuZVy6Uhda2d9ACHL8dxYbxn8bH5TIJ3Fb+iex0nEAXl7Sa5SCdfcS2sakd98uMxzzjTrotdVDJZKKTFTYLvNeAn5d7J7t6U3tZoEj5pVuOFfpmvw9WZBJu4TJiowhJWYRL8TJ7zzmpUkgVe6lo70cSUjVGUyznLVMLO+z9Ty18XpLG/Ag3ICliKSYSsJMp2xP7r9fOsJsHLLLeYhNjiuVW3vyZ238qW7OeG/R6TZRne80RZbCaTSJan0oUa3yXHnb83WNEpSr5yutMgfnhxav/iJ29g6rpo4HRFRa77cbL+oLquyRlP/PZO6W1tJiEmDZJg0G295cPSFZnEpXP0gxgmQzEJfj7v5ElZLtikCjssluYpfy2k5Mq1HsSmUwmBkaPPDJoEWJZlEvGtF7FkugqTiI/Nlbljoh8FN5uEGObPZRLplMHXA8wDezROJ19Riyu0Pv76/vj0Itm5OidGb2/wudeN13WTSUzpbT0mQQPnRTO2Xy6Zr1djEjRwXjyJil3rLzdNyIsZQ3qJeCWLxnTY2/1efYpg0G28Gua1wwpZNcsziVC+TxBLpmKAvFSTEFvueO7e67lX0UhcUQa93SREjYj3zHXKxyzpGZMkk69QVTqceFmE3xx1uSmmYatS+zEqs9x0XYwxW+RXXp2q3CTSK9ewnRwMJntbh0nQ0fvuyy+JG63Ym5/YfJmDkug1oGQr7lhDSoe96nex+3blWntzjdwXkpSAutbO1JnN3HoW+Zmm1Zro+bujn+Z1iMU0IKthUZOg5/3/baTXrOjIPizEkyl/2MwG8emItKrJqYZcuE4UzXl8JyowYcwkWP5lBS65FztaF2ELztRz/s02Ak32o4SvNtetLwHvOVq4Ti5+pL9KEgvsckbFx+NjzyGONxb5urhj/eqL2k4y+bK7MTFGnnZdX9+1n/Udj/J7nvKkMIztamcZRKyB146HwTWrL4mF6ym9xW7dH6NfTn+bb6Qczv/kU490j4h4CYsGw9e909Q9X93CtSQxk1jTFtg41Cc/PJHR6JNmIgDm1jO/kim1JjoiRy+iPbLBl2PrbMZ3+tAkwLKIScTL7qkxJg2c415kEjRw7Wa5aGi6WXt+Zj/lX7zTdq6T5fs7f+v/9MCIuv3pX5MbQ689+3H96Gw0Eps1J3dxxPawRoeiLbCxOYoS5ddv3QIb38AqzC9wP7J9JvESP9/CVKw0LDL8lftludWPLSdQ19pRjI6VwkanxPX5vZ3ydmu051j+lZT4FthSvf1BbIGd1pvculZ9QmbfqBIxz5Mfhcotc4X1m8TqX6Ybe877d3z389gbvGj+9ST2i49H9kNTDkoGz+vV+fTMfXOUtabJPdNTy6QLa6Aj+7Ag1uTpef9gW76vlzjEboj8URKfvOHQTZ3M3P86RebEwuUmBLmd2WNJbAtONmXNBIJJRG+WJF+FyUvSOPbmUPsNSe9wnfJqzvKVhGEYUvf4cGJdOvE2eF71QDSJWzrJBzQJJEfgxBIcJRI4kiAogaABUYImgeQInFiCo0QCRxIEJRA0IErQJJAcgRNLcJRI4EiCoASCBkQJmgSSI3BiCY4SCRxJEJRA0IAoQZNAcgROLMFRIoEjCYISCBoQJWgSSI7AiSU4SiRwJEFQAkEDogRNAskROLEER4kEjiQISiBoQJSgSSA5AieW4CiRwJEEQQkEDYgSNAkkR+DEEhwlEjiSICiBoAFRgiaB5AicWIKjRAJHEgQlEDQgStQmgQ0bNmzYsMmWMAkEQRAESYMmgSAIgkzl/wHqUsPlUrrcCAAAAABJRU5ErkJggg==" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the number of leaves that the tree loses on the 21st October.</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 total number of leaves that the tree loses in the 31 days of the month of October.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A cuboid has the following dimensions: length = 8.7 cm, width = 5.6 cm and height = 3.4 cm.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the <strong>exact</strong> value of the volume of the cuboid, in cm<sup>3</sup>.</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 your answer to part (a) correct to</span></p>
<p><span>(i) one decimal place;</span></p>
<p><span>(ii) 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>Write your answer to <strong>part (b)(ii)</strong> in the form \(a \times 10^k\), where \(1 \leqslant a < 10 , k \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The first term of an arithmetic sequence is \(0\) and the common difference is \(12\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of the \({96^{{\text{th}}}}\) term of the sequence.</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 first term of a geometric sequence is \(6\). The \({6^{{\text{th}}}}\) term of the geometric sequence is equal to the </span><span><span>\({17^{{\text{th}}}}\)</span> term of the arithmetic sequence given above.</span></p>
<p><span>Write down an equation using this information.</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 first term of a geometric sequence is \(6\). The \</span><span><span>\({6^{{\text{th}}}}\)</span> term of the geometric sequence is equal to the </span><span><span>\({17^{{\text{th}}}}\)</span> term of the arithmetic sequence given above.</span></p>
<p><span>Calculate the common ratio of the geometric sequence.<br></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">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;">\(512\) competitors enter round 1 of a tennis tournament, in which each competitor plays a match against one other competitor.</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 winning competitor progresses to the next round (round 2); the losing competitor leaves the tournament.</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 tournament continues in this manner until there is a winner.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of competitors who play in round 6 of the tournament.</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 total number of matches played in the tournament.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Only one of the following four sequences is arithmetic and only one of them is geometric.</p>
<p class="p1"><span class="Apple-converted-space"> </span>\({a_n} = 1,{\text{ }}2,{\text{ }}3,{\text{ }}5,{\text{ }} \ldots \)</p>
<p class="p1"><span class="Apple-converted-space"> </span>\({b_n} = 1,{\text{ }}\frac{3}{2},{\text{ }}\frac{9}{4},{\text{ }}\frac{{27}}{8},{\text{ }} \ldots \)</p>
<p class="p1"><span class="Apple-converted-space"> </span>\({c_n} = 1,{\text{ }}\frac{1}{2},{\text{ }}\frac{1}{3},{\text{ }}\frac{1}{4},{\text{ }} \ldots \)</p>
<p class="p1"><span class="Apple-converted-space"> </span>\({d_n} = 1,{\text{ }}0.95,{\text{ }}0.90,{\text{ }}0.85,{\text{ }} \ldots \)</p>
<p class="p1">State which sequence is</p>
<p class="p1">(i) arithmetic;</p>
<p class="p1">(ii) geometric.</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 <strong>another </strong>geometric sequence \({e_n} = - 6,{\text{ }} - 3,{\text{ }} - \frac{3}{2},{\text{ }} - \frac{3}{4},{\text{ }} \ldots \)</p>
<p>write down the common ratio;</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>For <strong>another </strong>geometric sequence \({e_n} = - 6,{\text{ }} - 3,{\text{ }} - \frac{3}{2},{\text{ }} - \frac{3}{4},{\text{ }} \ldots \)</p>
<p>find the <strong>exact </strong>value of the tenth term. Give your answer as a fraction.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b(ii).</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">\(80\) matches were played in a football tournament. The following table shows the number of goals scored in all matches.</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 mean number of goals scored per match.</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>Find the median number of goals scored per match.</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>A local newspaper claims that the mean number of goals scored per match is two. Calculate the percentage error in the local newspaper’s claim.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate \(\frac{{77.2 \times {3^3}}}{{3.60 \times {2^2}}}\).</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>Express your answer to part (a) 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">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Juan estimates the length of a carpet to be 12 metres and the width to be 8 metres. He then estimates the area of the carpet.</span></p>
<p><span>(i) Write down his estimated area of the carpet.</span></p>
<p><span>When the carpet is accurately measured it is found to have an area of 90 square metres.</span></p>
<p><span>(ii) Calculate the percentage error made by Juan.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The following diagram shows a rectangle with sides of length 9.5 ×10<sup>2</sup> m and 1.6 ×10<sup>3</sup> m.</span></p>
<p style="text-align: center;"> <span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAlIAAACCCAIAAAACHLEiAAART0lEQVR4nO3d/2sbd57H8fkX9kf9JMFQqI0NKeYg5IfgwCKcBEwoGJYWhM9JIEsp1x8O7Rm7Ttnr7RYEMhcKvVuYWuSuELaoEsntLfg8pzOUo06lTUuza0uQI9naEtQEr5gfXOF+MvvDzEgz+uIoHyenfvJ5PvAvsmdGI+X91qufz2dGNVwAALRhjPoEVGXGE/zwo+3PqPsPkEfsSaLzoS2K33WbtdLtz7JXJi8XGq7ruq29wjuT8ddXKwejPjG9iUbl9q3Vyz+9Wvj2mK2IPUl0PrSlffEfNQpvm/GEGR+/tLYjXNd1vy1efs2MJ6aylaNRn5zG/H8FM/5mrnZ4zHbEniTtOx/6ovhd8ah47XTo41Wr0V5zZ+2jO40B+e7cz2V/3/j/PaGOo8rqqYQ5u1YTx21F7Emi86Etit9tFK7GE+Yp/QZ3zk5xaXZArginVlieeS0YAY9Co3B1iDE3sSeJzoe2dC3+VqPyyfLMuBmf/Yel+cl4YnKp1HS99aR8bmk29GkbbDn29sfW30925kJdVzQqhezVsYQZT5gzK8VaMzi4cGqbn2WvTC2Vms793OXT/sG9XW4uXYgnJq99+PEvzoaGmM1aqZBbml8u7ftp5P+pWSusXIiPX8jedfq+Dv+E55dL+8HBuzZuNSq/yy3NmvGEGZ9dLuw4ruu6zZ21a5Pty5r8Rc2Acz93+XRwxdNrwdJa3+N0n41TKyzPjJvxxOTl7Gf5teK99lah3ceu3Ljb6LyH/d8Q0SytTMbPLpf2oy/WCo7/bzuOcIk9abp2PqBn8bcapfcvxMcvrGw0jnZys+Om//G6X1o6a8YTZufTNtgye9dplpbHEmb8/GrFcV3XFXulldng8/eoWVrxUmRyqdT0ho/xs8ulWiX7uhkPZur8XV5frTz2t/eHmO31xbeLew+K17zIOb9aebxXeGeybzL5nEr2vL8AtvPAO5/oxl68nf554ZHwX12QK8J74cHLiRK1tUuREfDg40R228nNjnsvVjQ2rs+8U/SnT73dZ5cLO473JnhnOPANcf1/i7GVUrOdjxvXZ167sLLREN6yn38CxJ4kLTsfcF0ti1/sFX4+lgg+UiOfof7D4NM2sqW31NT+kxcM/o5+bgWjOu/hmx8XPrwUT5h+WnhLhv42R5XsVGf79jrWB7ns+7k/fZGbHTfHloobHy2vfb1XWokMMbtei3casx/Z+Q9+Wfr2L5GNg2e8VtgTwUsLRm/+jqFcCTmsrb0ZejnHHSfCf4uu5Xaariua9+49EO3d/TGoqK1dGuYN8f4joz0B69xdnRk3Z25UHOH/owR/IvYkadj5gEe/4vcGK8FMYNfHq/fQHy0dVLKvd7b0xnDBQCo6HvKHicGn9n5p6aw5+8vVpV/kdoKZT++D279SxsvFUHI0ClfjicmZa6ulvSM/kM5fzZYawhvPRef6Ovx8Mn/6s+u3e8Zh/vC070NvCjEUM33eouBJjztOl1YwPJ29Xtrz49Tbvjdfj3tDvNNr57f3D3F2ubTnTzjPvF9qtLzDEHuS9Ot8wKdd8ff79A9W8qKftpFZTX/IElrYe1S8dtqcuVFxjpzKjQvxhNm++FPs5GbHJ2d+tlx4FHzSi8gkXve1o+EQCracuVFxhD9t2H9M5nbi1huHRQImOI6f6F0P/ezvP4js9xYNOE6fnf1Vw+hp9OTr8W9I3/z21lCXcrcrjdBTE3uStOt8IKBb8XuTaf6Hsj/gOLtc2vmq0j1aCqYx3y42joItz6/e/dPm5v95U4iNyq3VpSsXvCW9y9li8Gns7RhMCXqCYdnlQsMVfkyeyn756IvNB4fRT/nISMs/VP8x2fEDOH/e1U90fyUvCObjRmxdwXbscSL71e7croUGZ95/LkR39963e/cb4tg3JBr2PfOxwtnZKD3wz5zYk6Rb5wNtuhV/J/YO9ioba8unEmb89N8u/fYrR3RGS3s7m5XGUefT9qC2cePqWGhL75N9ZilXKBRLteg1Id4Hete0ZGi1zKnZ2SuT8YQ59uZy/uvuidbICqK31/iltS92Nu81ekZXwcKel0/edOhrVwv3a5v3GiKcgqErSsI7nspWDmqbla4D+6c6lb37l9oXlcbhMceJaJaWT3mXaLb2Cu9MBqM9P9L8Bb9mrbReabSOf0M6YS8aldubtb2N5bH2YLrVqPz+TuiciT1JunU+0KZd8fvzabPLN+82mt6FEsG9B37sXVndqDnhLddK/idv5y6F6A0A8fELS4WaI1y3PR56uxi9B9y/EGNmKVfa8a5SCXaJjNKiSRZcDNI+eETXhSd+RobOpPHlP1+Z9E9vrdS5v6J9qU7wSiOCK00u37C9XQYfJ/ICH/zv5s59L8A6+7pucA9GwoyfvpotVII1ucFvSPCn+Omr2fWaI0JHiIyqPcSeJO06HwhQ/M+u1agUVpc+KFbulgq3Vv1b3AZebIkXitiTROdDWxT/M2uWlsfCIefP4/EdniNB7Emi86Etiv+ZedOYnQlP75Z2Tb7D80eH2JNE50NbFL8E0agUvaswnrbihReN2JNE50NbFD+URuxJovOhLYofSiP2JNH50BbFD6URe5LofGiL4ofSiD1JdD60RfFDacSeJDof2qL4oTRiTxKdD21R/FAasSeJzoe2KH4ojdiTROdDWxQ/lEbsSaLzoS2KH0oj9iTR+dAWxQ+lEXuS6Hxoi+KH0og9SXQ+tEXxQ2nEniQ6H9qi+KE0Yk8SnQ9tUfxQmlKxJ+pb2VTMMIzYgrU94v9VFZ0PbVH8UJpKsSeqnyxa3zjuQTlz0UhaVTHKk6HzoS2KH0pTKfbaRNVKxhbt5ihzj86Htih+KE3V2Lu4kN9ltAeMAsUPpXViT9S3cumkYRhGLJVZrzrH7bVvp6cMXyxpbUsFkHCqpfynmZTZO25r1cs309Mxw5hIZT+vdx/9oJz5u0z5QOY5nx86H9qi+KG0IPacrUxyIbtVF65wtnOp2MRC/uGgMBO7+YVYkHrGnFU9lHhiUbUuvpF6I2YY3dOVwilnp6ffs+stV+zaixenM1uhDG7V7Y+y9mhHeq5L50NjFD+U5sXeYdWai6Xt4OLI1m7+rdjAxbODciaVtvcHHPAH535x7b+/PRrq94dVa6479sS2lTzTOX7TTsfaySqc7VvZ4kPhuqL+h1J1lBdz0vnQFsUPpRmu6yWNGZ6rFFUraUz1z7amnY4ZxnTaypeqTm8ufv/dl7+Zf/XiykY44X5w7ufmX7347p2a8yS8cZ/YE1UrGRlB7tvpM0lrW7it+taHqROPMp8XOh/aovihNMN1vSSLLtH1/sZ3WLXm2sljTC/m+wy5/JALkq/rYc/RIrHX+5t9Oz019O0KwqmWPs2kzLR9UP88m5owjNj04npdhBYLrW+OXbYcFp0PbVH8UFp7tBeLREvTTscGjPZc13Vb9fIdy7v+ZTpb7jPmO/pu85/O/eT8ysbDx/dz869Mzd/8Y7+h2TAh9yyx541EDSOWyuTLdeEtExoTqcwtu9p03Vbdfm/6OQ0T6Xxoi+KH0ry1PdG0F2PtkZCol3PpIeLBS5FB6fh9feMfz/0kYSam5q2vo3Obbc879lw/wjvrlNFh63GTt8+Izoe2KH4orX0DQ7O67n3x10Qqc9NKJ4dLmn07PRW6FibMm9s0TbPv9KbnuU9yEnvAC0fxQ2n9blfvupbyOIdV641+S4Dt9byHjwcu7LkDL2kJ/6bncpunIPaAF4zih9J6Yq/PrXLH2LcXf91zn8NJLmk5/gaGIRB7wAtG8UNp4dhrVu1bmdR09xejiIf5hSk/CEW9XPxdud5yXe//h7D4bved431DblDy9Yu9p9yu/jTEHvCCUfxQmhd73peNxabTlt17Q0Ik9nbtxaRheEuAt/ps7H5f37jxq/941Od29a9y19dC17YEV132+4az9i16yXRuq+fLyQYSVSvZPmTS2t7uPIyl1/9sL8Y6D/uuRz4DOh/aovihNCW/ivrHgM6Htih+KI3Yk0TnQ1sUP5RG7Emi86Etih9KI/Yk0fnQFsUPpRF7kuh8aIvih9KIPUl0PrRF8UNpxJ4kOh/aovihNGJPEp0PbVH8UBqxJ4nOh7YofiiN2JNE50NbFD+URuxJovOhLYofSiP2JNH50BbFD6URe5LofGiL4ofSiD1JdD60RfFDacSeJDof2qL4oTRiTxKdD21R/FAasSeJzoe2KH4ojdiTROdDWxQ/lEbsSaLzoS2KH0oj9iTR+dAWxQ+lEXuS6Hxoi+KH0og9SXQ+tEXxQ2nEniQ6H9qi+KE0Yk8SnQ9tUfxQGrEnic6Htih+KI3Yk0TnQ1sUP5RG7Emi86Etih9KI/Yk0fnQFsUPpRF7kuh8aIvih9KIPUl0PrRF8UNpxJ4kOh/aovihNGJPEp0PbVH8UBqxJ4nOh7YofiiN2JNE50NbFD+URuxJovOhLYofSiP2JNH50BbFD6URe5LofGiL4ofSiD1JdD60RfFDacSeJDof2qL4oTRiTxKdD21R/FAasSeJzoe2KH4ojdiTROdDWxQ/lEbsSaLzoS2KH0oj9iTR+dAWxQ+lEXuS6Hxoi+KH0og9SXQ+tEXxQ2nEniQ6H9qi+KE0Yk8SnQ9tUfxQGrEnic6Htih+KI3Yk0TnQ1sUP5RG7Emi86Etih9KI/Yk0fnQFsUPpRF7kuh8aIvih9KIPUl0PrRF8UNpxJ4kOh/aovihNGJPEp0PbVH8UBqxJ8mMJ/jhR9ufUfcfII/YAwBohNgDAGiE2AMAaITYAwBohNgDAGiE2AMAaITYw8utVbffmzYMI7ZgbTdHfTIARo/Yw0utWcpktxy3tZt/ayJTPhr16QAYOWIPGnC28+m3MuWDUZ8HgNEj9vCyq+dThhFLfbhVb436VACMHrGHk2hW7eKnmZSZtodaNxP1cvGTTGrCMKbS9r7MEzpVO/9JJpXs3V3Ut3LppNE34UR9K5uKJa2qkHlOAC8TYg/yqtbCG6lLMcOIDRF7ov55NjURS2U+tauO3POJbeviXOqNfqnpbGWmLy7au8K7hmU6W3aiEVfPp0wW9wAQezghsW0lY0+PPWcrMz2Vyn5e7zfeeuJ889u1/6kfPRnm96JqJbtj77BqzYXOYd9On0la26GnatXt95JDDkkBvNSIPZzMULF3UM5cjC3kd/vPMT45+u6Lf5k/c25lPZxwT5yvrfkz596988D5IfKEvbEntq2kGco50bQXvSlNUbWShmEYsen0zTJrewCIPZzUELEnqlbSSKatm5nUhGEYsVR2vdq9uR9yQfJ1Pew5WiT2en4jmvZizJizqodDvIBm1b6VSSXT9m5968NUzDCM5KK9K0S9nEtzwx/w8iH2cDJPj73DqjVnTKdz5bpwXdf5xkpNGL1rb6775LvS9XOvnltZ33v8lTU/9cr8v1cPuzPPHSrkho89b0vDMCZSmXy53vIGpkYslfm0VHWEK3btxaTBtTDAS4TYw8k8Pfb27fRUeANRtZJGLLr25nlyVF9fOWeaZuKV+dz96Nxm5wmfZ+z1HrBr38OqNWfEFu0muQe8JIg9nMxTY693g8G7PHG+tub/xjRf7Tu96e/9nCc5iT1AL8QeTma40V5knrD7ChRfez1v7/FXgxb23IGXtJwJ/eawas0NPzNJ7AFaIfZwMk+PPdG0F2Oxt/K7wYWUTTsd6x6KneSSliFuYDj2FRB7gE6IPZxM39gTD/MLU9OZLafzcCKWym07whX1rexCsv0n13UHhNyg5OsXe0Pcrn7MKyD2AJ0Qe5AXXAbpCQ3gumLPdV2nup5JxQzDMJLp3Fb0pvUnR/X/+vWv/nOvz+3qlX+9/kno2pZ9Oz3VecLoNKb3LTDPeIveYdWaCw4XS1p/2O48nErbfww9ney3qQH4kSH2AAAaIfYAABr5K+W+AtazdSNpAAAAAElFTkSuQmCC" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the area of the rectangle in the form <em>a</em> × 10<sup><em>k</em></sup>, where 1 ≤ <em>a</em> < 10, <em>k</em> ∈ \(\mathbb{Z}\).</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>Helen’s estimate of the area of the rectangle is \(1\,600\,000{\text{ }}{{\text{m}}^2}\).</span></p>
<p><span>Find the percentage error in Helen’s estimate.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">\(z = \frac{{17{x^2}}}{{a - b}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of <em>z </em>when <em>x</em> = 12.5, <em>a</em> = 0.572 and <em>b</em> = 0.447. Write down your full calculator display.</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 your answer to part (a)</span></p>
<p><span>(i) correct to the nearest 1000 ;</span></p>
<p><span>(ii) 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>Write your answer to <strong>part (b)(ii)</strong> in the form <em>a</em> × 10<sup><em>k</em></sup>, where 1 ≤ <em>a</em> < 10, \(k \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Water has a lower boiling point at higher altitudes. The relationship between the boiling point of water (<em>T</em>) and the height above sea level (<em>h</em>) can be described by the model \(T = -0.0034h +100\) where <em>T</em> is measured in degrees Celsius (</span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">°</span>C) and <em>h</em> is measured in metres from sea level.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the boiling point of water at sea level.</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>Use the model to calculate the boiling point of water at a height of 1.37 km above sea level.</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>Water boils at the top of Mt. Everest at 70 </span><span><span>°</span>C.</span></p>
<p><span>Use the model to calculate the height above sea level of Mt. Everest.<br></span></p>
<p><span> </span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: 'times new roman', times;">The length, in cm, of six baseball bats was measured. The lengths are given below.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: 'times new roman', times;">104.5, 105.1, 104.8, 105.2, 104.9, 104.9</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the <strong>exact value</strong> of the mean length.</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 your answer to part (a) in the form <em>a</em> × 10<sup><em>k</em></sup> where 1 ≤ <em>a</em> < 10 and \(k \in \mathbb{Z}\).</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>Marian calculates the mean length and finds it to be 105 cm.</span></p>
<p><span>Calculate the percentage error made by Marian.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>In the Canadian city of Ottawa:</p>
<p>\[\begin{array}{*{20}{l}} {{\text{97% of the population speak English,}}} \\ {{\text{38% of the population speak French,}}} \\ {{\text{36% of the population speak both English and French.}}} \end{array}\]</p>
</div>
<div class="specification">
<p>The total population of Ottawa is \(985\,000\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the percentage of the population of Ottawa that speak English but not French.</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 number of people in Ottawa that speak both English and French.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down your answer to part (b) in the form \(a \times {10^k}\) where \(1 \leqslant a < 10\) and <em>k </em>\( \in \mathbb{Z}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>In this question, give all answers correct to 2 decimal places.</strong></p>
<p>Jose travelled from Buenos Aires to Sydney. He used Argentine pesos, ARS, to buy 350 Australian dollars, AUD, at a bank. The exchange rate was 1 ARS = 0.1559 AUD.</p>
</div>
<div class="specification">
<p>The bank charged Jose a commission of 2%.</p>
</div>
<div class="specification">
<p>Jose used his credit card to pay his hotel bill in Sydney. The bill was 585 AUD. The value the credit card company charged for this payment was 4228.38 ARS. The exchange rate used by the credit card company was 1 AUD = \(x\) ARS. No commission was charged.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use this exchange rate to calculate the amount of ARS that is equal to 350 AUD.</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 <strong>total </strong>amount of ARS Jose paid to get 350 AUD.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(x\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">\(U\) is the set of all the <strong>positive</strong> integers less than or equal to \(12\).</span><br><span style="font-size: medium; font-family: times new roman,times;">\(A\) , \(B\) and \(C\) are subsets of \(U\) .</span><br><span style="font-size: medium; font-family: times new roman,times;">\[A = \{ 1{\text{, }}2{\text{, }}3{\text{, }}4{\text{, }}6{\text{, }}12\} \]</span><span style="font-size: medium; font-family: times new roman,times;">\[B = \{ {\text{odd integers}}\} \]</span><span style="font-size: medium; font-family: times new roman,times;">\[C = \{ 5{\text{, }}6{\text{, }}8\} \]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of elements in \(A \cap C\) .</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>List the elements of \(B\) .</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>Complete the following Venn diagram with <strong>all</strong> the elements of \(U\) .</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The diagram below represents a rectangular flag with dimensions 150 cm by 92 cm. The flag is divided into three regions A, B and C.</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>Write down the total area of the flag.</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>Write down the value of <em>y</em>.</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 areas of regions A, B, and C are equal.</span></p>
<p><span>Write down the area of region A.</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>Using your answers to <strong>parts (b) and (c)</strong>, find the value of <em>x</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A snack container has a cylindrical shape. The diameter of the base is \(7.84\,{\text{cm}}\). The height of the container is \(23.4\,{\text{cm}}\). This is shown in the following diagram.</p>
<p><img 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" alt></p>
<p>Write down the radius, in \({\text{cm}}\), of the base of the container.</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>Calculate the area of the base of the container.</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>Dan is going to paint the curved surface and the base of the snack container.</p>
<p>Calculate the area to be painted.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The first term of an arithmetic sequence is 7 and the sixth term is 22.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find </span><span>the common difference.</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>Find </span><span>the twelfth term.</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 </span><span>the sum of the first 100 terms.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the arithmetic sequence</span><br><span style="font-size: medium; font-family: times new roman,times;">\[{\text{326, 321, 316, 311, }} \ldots {\text{, 191.}}\]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of the common difference of this sequence.</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>Calculate the sum of the first 10 terms of this sequence.</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 number of terms in this sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Factorise the expression \({x^2} - 3x - 10\).</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>A function is defined as \(f(x) = 1 + {x^3}\) for \(x \in \mathbb{Z}{\text{, }} {- 3} \leqslant x \leqslant 3\).</span></p>
<p><span>(i) List the elements of the domain of \(f(x)\).</span></p>
<p><span>(ii) Write down the range of \(f(x)\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Daniela is going for a holiday to South America. She flies from the US to Argentina stopping in Peru on the way.</p>
<p>In Peru she exchanges 85 United States dollars (USD) for Peruvian nuevo sol (PEN). The exchange rate is 1 USD = 3.25 PEN and a flat fee of 5 USD commission is charged.</p>
</div>
<div class="specification">
<p>At the end of Daniela’s holiday she has 370 Argentinean peso (ARS). She converts this back to USD at a bank that charges a 4% commission on the exchange. The exchange rate is 1 USD = 9.60 ARS.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the amount of PEN she receives.</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 amount of USD she receives.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Assume the Earth is a perfect sphere with radius <span class="s1">6371 km</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the volume of the Earth in \({\text{k}}{{\text{m}}^3}\)<span class="s1">. Give your answer in the form \(a \times {10^k}\)</span>, where \(1 \leqslant a < 10\) <span class="s1">and \(k \in \mathbb{Z}\).</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 class="p1">The volume of the Moon is \(2.1958 \times {10^{10}}\;{\text{k}}{{\text{m}}^3}\)<span class="s1">.</span></p>
<p class="p2">Calculate how many times greater in volume the Earth is compared to the Moon.</p>
<p class="p2">Give your answer correct to the nearest <strong>integer</strong>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>In this question, give all answers to two decimal places.</strong></p>
<p>Karl invests 1000 US dollars (USD) in an account that pays a nominal annual interest of 3.5%, <strong>compounded quarterly</strong>. He leaves the money in the account for 5 years.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the amount of money he has in the account after 5 years.</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>Write down the amount of <strong>interest</strong> he earned after 5 years.</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>Karl decides to donate this <strong>interest</strong> to a charity in France. The charity receives 170 euros (EUR). The exchange rate is 1 USD = <em>t</em> EUR.</p>
<p>Calculate the value of <em>t</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the following four numbers.</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;">\(p = 0.00314{\text{ ; }}q = 0.00314 \times {10^2}{\text{ ; }}r = \frac{\pi }{{1000}}{\text{ ; }}s = 3.14 \times {10^{ - 2}}\)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>One of these numbers is written in the form \(a \times {10^k}\) where \(1 \leqslant a < 10\) and \(k \in \mathbb{Z}\). Write down this number.</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>Write down the smallest of these numbers.</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 value of <strong><em>q</em> + <em>s</em></strong>.</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>Give your answer to part (c) 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>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Susi travels from Singapore to Thailand and changes 1500 Singapore dollars (SGD) to Thai baht (THB). The exchange rate is 1 SGD buys 21.03464 THB.</span></p>
</div>
<div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Susi leaves Thailand and travels to Indonesia. She has \(20\,000\) THB and uses these to </span><span style="font-family: 'times new roman', times; font-size: medium;">buy Indonesian rupiah (IDR). The exchange rate is 3.28352 THB buys 1000 IDR.</span></p>
</div>
<div class="specification">
<p><span style="font-family: 'times new roman', times; font-size: medium;">Susi wants to find the approximate exchange rate between Singapore dollars and Indonesian rupiah and uses the exchange rates for Thai baht to do this.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the number of Thai baht Susi buys. Give your answer <strong>correct to the</strong></span> <span><strong>nearest baht</strong>.</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><span>Calculate the <strong>total</strong> number of Indonesian rupiah Susi receives, <strong>correct to the</strong></span> <span><strong>nearest thousand rupiah</strong>.</span></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>Calculate Susi’s exchange rate between Singapore dollars and Indonesian rupiah.</span> <span>Give your answer in the form 1 SGD buys <em>x</em> IDR, where <em>x</em> is given correct to the </span><span>nearest rupiah.</span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">\(T = \frac{{\left( {\tan (2z) + 1} \right)\left( {2\cos (z) - 1} \right)}}{{{y^2} - {x^2}}}\), where \(x = 9\), \(y = 41\) and \(z = 30^\circ \).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the <strong>exact </strong>value of \(T\).</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">Give your answer to \(T\) correct to</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>two significant figures;</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>three decimal places.</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">Pyotr estimates the value of \(T\) <span class="s1">to be \(0.002\)</span>.</p>
<p class="p1">Calculate the percentage error in Pyotr’s estimate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">56 students were given a test out of 40 marks. The teacher used the following box and whisker plot to represent the marks of the students.</span></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>Write down </span><span>the median mark</span><span>.</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>Write down</span><span> the 75<sup><span>th</span></sup> percentile mark</span><span>.</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>Write down the range of marks.</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>Estimate the number of students who achieved a mark greater than 32.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A comet orbits the Sun and is seen from Earth every <span class="s1">37 </span>years. The comet was first seen from Earth in the year <span class="s1">1064</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the year in which the comet was seen from Earth for the fifth time.</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">Determine how many times the comet has been seen from Earth up to the year <span class="s1">2014</span><span class="s2">.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p><span>Kunal borrows 200 000 Indian rupees (INR) from a money lender for 18 months at a nominal annual interest rate of \(15\% \), <strong>compounded monthly</strong>.</span></p>
<p><span>Calculate the <strong>total amount</strong> that Kunal must repay at the end of the 18 months. Give your answer to the nearest rupee.</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Sasha travelled from the USA to Mexico and converted 650 US dollars (USD) to Mexican pesos (MXN). Her bank offered an exchange rate of 1 USD = 12.50 MXN.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of MXN that Sasha received.</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>Before her return to the USA, Sasha exchanged 2300 MXN back into USD. The bank charged a commission of 1 %. The exchange rate was still 1 USD = 12.50 MXN. </span></p>
<p><span>Write down the commission charged by the bank in MXN.</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><span>Before her return to the USA, Sasha exchanged 2300 MXN back into USD. The bank charged a commission of 1 %. The exchange rate was still 1 USD = 12.50 MXN. </span></span></p>
<p><span>Calculate the amount of USD that Sasha received after commission. Give your answer correct to the nearest USD.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Julio is making a wooden pencil case in the shape of a large pencil. The pencil case consists of a cylinder attached to a cone, as shown.</p>
<p>The cylinder has a radius of <em>r</em> cm and a height of 12 cm.</p>
<p>The cone has a base radius of <em>r</em> cm and a height of 10 cm.</p>
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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the slant height of the cone <strong>in terms of <em>r</em></strong>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The total external surface area of the pencil case rounded to 3 significant figures is 570 cm<sup>2</sup>.</p>
<p>Using your graphic display calculator, calculate the value of <em>r</em>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Matryoshka dolls, or Russian dolls, are similarly designed dolls which open up and fit inside each other.</p>
<p>The largest set of these type of dolls is a 51 piece set which was completed in 2003. The height of the largest piece in this set is 54 cm. The heights of successive smaller dolls are 94 % of the preceding larger doll, as shown.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the height of the smallest doll in this set.</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 <strong>total</strong> height if all 51 dolls were placed one on top of another.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the following numbers in increasing order.</span></p>
<p><span>\(3.5\), \(1.6 \times 10^{−19}\), \(60730\), \(6.073 \times 10^{5}\), \(0.006073 \times 10^6\), \(\pi\), \(9.8 \times 10^{−18}\).</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 the median of the numbers in part (a).</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>State which of the numbers in part (a) is irrational.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the function \(f(x) = 1.25 - {a^{ - x}}\) , where a is a positive constant and \(x \geqslant 0\). The diagram shows a sketch of the graph of \(f\) . The graph intersects the \(y\)-axis at point A and the line \(L\) is its horizontal asymptote.</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 \(y\)-coordinate of A .</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 point \((2{\text{, }}1)\) lies on the graph of \(y = f(x)\) . Calculate 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>The point \((2{\text{, }}1)\) lies on the graph of \(y = f(x)\) . Write down the equation of \(L\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>In this question give all answers correct to the nearest whole number.</strong></p>
<p>Loic travelled from China to Brazil. At the airport he exchanged 3100 Chinese Yuan, \({\text{CNY}}\), to Brazilian Real, \({\text{BRL}}\), at an exchange rate of \({\text{1}}\,{\text{ CNY = 0}}{\text{.3871 BRL}}\).</p>
<p>No commission was charged.</p>
<p>Calculate the amount of \({\text{BRL}}\) he received.</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>When he returned to China, Loic changed his remaining \({\text{BRL}}\) at a bank. The exchange rate at the bank was \({\text{1}}\,{\text{ CNY = 0}}{\text{.3756 BRL}}\) and a commission of \(5\% \) was charged. He received \(285\,\,{\text{CNY}}\).</p>
<p>i) Calculate the amount of \({\text{CNY}}\) Loic would have received if no commission was charged.</p>
<p>ii) Calculate the amount of \({\text{BRL}}\) Loic exchanged when he returned to China.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the geometric sequence 16, 8, <em>a</em>, 2, <em>b</em>, …</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the common ratio.</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>Write down the value of</span><span> <em>a</em>.</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 the value of <em>b</em>.</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>The sum of the first <em>n</em> terms is 31.9375. Find the value of <em>n</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Mr Tan invested 5000 Swiss Francs (CHF) in Bank A at an annual simple interest rate of <em>r</em> %, for four years. The total interest he received was 568 CHF.</span></p>
</div>
<div class="question">
<p><span>Mr Black invested 5000 CHF in Bank B at a nominal annual interest rate of 3.6 %, </span><span><strong>compounded quarterly</strong> for four years.</span></p>
<p><span>Calculate the total interest he received at the end of the four years. Give your answer correct to <strong>two decimal places</strong>.</span></p>
</div>
<br><hr><br><div class="specification">
<p>Each year the soccer team, Peterson United, plays 25 games at their home stadium. The owner of Peterson United claimed that last year the mean attendance per game at their home stadium was 24500.</p>
</div>
<div class="specification">
<p>The actual total attendance last year was 617700.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Based on the owner’s claim, calculate the total attendance for the games at Peterson United’s home stadium last year.</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 percentage error in the owner’s claim.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down your answer to <strong>part (b)</strong> in the form <em>a</em> × 10<em><sup>k</sup></em> where 1 ≤ a < 10, \(k \in \mathbb{Z}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The population of big cats in Africa is increasing at a rate of 5 % per year. At the beginning of 2004 the population was \(10\,000\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the population of big cats at the beginning of 2005.</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 population of big cats at the beginning of 2010.</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 number of years, from the beginning of 2004, it will take the population of big cats to exceed \(50\,000\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the numbers \(p = 2.78 \times {10^{11}}\) and \(q = 3.12 \times {10^{ - 3}}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate \(\sqrt[3]{{\frac{p}{q}}}\). Give your full calculator display.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down your answer to part (a) correct to two decimal places;</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down your answer to part (a) correct to three significant figures.</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>Write your answer to <strong>part (b)(ii) </strong>in the form \(a \times {10^k}\), where \(1 \leqslant a < 10,{\text{ }}k \in \mathbb{Z}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Veronica wants to make an investment and accumulate 25 000 EUR over a period of 18 years. She finds two investment options.</span></p>
</div>
<div class="question">
<p><span>Option 2 offers a nominal annual interest rate of 4 %, <strong>compounded monthly</strong>.</span></p>
<p><span>Find the amount that Veronica has to invest with option 2 to have 25 000 EUR in her account after 18 years. Give your answer correct to <strong>two decimal places</strong>.</span></p>
</div>
<br><hr><br><div class="specification">
<p>Consider the geometric sequence \({u_1} = 18,{\text{ }}{u_2} = 9,{\text{ }}{u_3} = 4.5,{\text{ }} \ldots \).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the common ratio of the sequence.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \({u_5}\).</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 smallest value of \(n\) for which \({u_n}\) is less than \({10^{ - 3}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(p = \frac{{\cos x + \sin y}}{{\sqrt {{w^2} - z} }}\),</p>
<p class="p1">where \(x = 36^\circ ,{\text{ }}y = 18^\circ ,{\text{ }}w = 29\) and \(z = 21.8\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Calculate the value of \(p\)</span>. Write down your full calculator display.</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">Write your answer to part (a)</p>
<p class="p2">(i) <span class="Apple-converted-space"> </span>correct to two decimal places;</p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>correct to three significant figures.</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"><span class="s1">Write your answer to </span><strong>part (b)(ii) </strong>in the form \(a \times {10^k}\), where \(1 \leqslant a < 10,{\text{ }}k \in \mathbb{Z}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: 'times new roman', times;">The first term of an arithmetic sequence is 3 and the seventh term is 33.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the common difference;</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>Calculate the 95<sup>th</sup> term of the sequence;</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 sum of the first 250 terms.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Yun Bin invests \(5000{\text{ euros}}\) in an account which pays a nominal annual interest rate of \(6.25\% \) , <strong>compounded monthly</strong>.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Give all answers correct to two decimal places.</strong></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of the investment after 3 years.</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 difference in the final value of the investment if the interest was compounded quarterly at the same nominal rate.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">In the diagram, triangle ABC is isosceles. AB = AC and angle ACB is 32°. The length of side AC is <em>x</em> cm.</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>Write down the size of angle CBA.</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>Write down the size of angle CAB.</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 area of triangle ABC is 360 cm<sup>2</sup>. Calculate the length of side AC. Express your answer in <strong>millimetres</strong>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">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;">The first term, \({u_1}\), of an arithmetic sequence is \(145\). The fifth term, \({u_5}\), of the sequence is \(113\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the common difference of the sequence.</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 \({n^{{\text{th}}}}\) term, \({u_n}\), of the sequence is \(–7\).</span></p>
<p><span>Find the value of \(n\).</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 \({n^{{\text{th}}}}\) term, \({u_n}\), of the sequence is \(–7\).</span></p>
<p><span>Find \({S_{20}}\), the sum of the first twenty terms of the sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A rumour spreads through a group of teenagers according to the exponential model</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;">\(N = 2 \times {(1.81)^{0.7t}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">where <em>N</em> is the number of teenagers who have heard the rumour <em>t</em> hours after it is first started.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of teenagers who started the rumour.</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 the number of teenagers who have heard the rumour five hours after it is first started.</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>Determine the length of time it would take for 150 teenagers to have heard the rumour. <strong>Give your answer correct to the nearest minute.</strong></span></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>The golden ratio, \(r\) , was considered by the Ancient Greeks to be the perfect ratio between the lengths of two adjacent sides of a rectangle. The exact value of \(r\) is \(\frac{{1 + \sqrt 5 }}{2}\).</p>
<p>Write down the value of \(r\)</p>
<p>i) correct to \(5\) significant figures;</p>
<p>ii) correct to \(2\) decimal places.</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>Phidias is designing rectangular windows with adjacent sides of length \(x\) metres and \(y\) metres. The area of each window is \(1\,{{\text{m}}^2}\).</p>
<p>Write down an equation to describe this information.</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>Phidias designs the windows so that the ratio between the longer side, \(y\) , and the shorter side, \(x\) , is the golden ratio, \(r\).</p>
<p>Write down an equation in \(y\) , \(x\) and \(r\) to describe this information.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(x\) .</p>
<div class="marks">[2]</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;">The surface of a red carpet is shown below. The dimensions of the carpet are in metres.</span></p>
<div style="text-align: center;"><img src="images/Schermafbeelding_2014-09-02_om_14.31.51.png" alt></div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down an expression for the area, \(A\), in \({{\text{m}}^2}\), of the carpet.</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>The area of the carpet is \({\text{10 }}{{\text{m}}^2}\).</span></p>
<p><span>Calculate the value of \(x\).</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>The area of the carpet is \({\text{10 }}{{\text{m}}^2}\).</span></p>
<p><span>Hence, write down the value of the length and of the width of the carpet, in metres.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Solve the following equation for <em>x</em></span></p>
<p><span>\(3(2x +1) − 2(3 − x)=13\).</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>Factorize the expression \(x^2 + 2x − 3\).</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 <strong>positive</strong> solution of the equation</span></p>
<p><span>\(x^2 + 2x − 6 = 0\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Yoshi is spending a year travelling from Japan to Italy and then to the United States of America.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Before Yoshi leaves Japan he changes 100 000 Japanese Yen (JPY) into euro (EUR). The exchange rate is 1 JPY = 0.006 EUR.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the amount Yoshi receives, in EUR.</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>Yoshi spends 426.70 EUR in Italy. In an American bank he changes the remaining</span> <span>amount, into US dollars (USD), at an exchange rate of 1 USD = 0.673 EUR.</span></p>
<p><span>The bank charges 1.5 % commission.</span></p>
<p><span>Calculate the amount, in USD, Yoshi receives after commission.</span> <strong><span>Give your answer correct to the nearest USD.</span></strong></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Consider the following statements</p>
<p>\(z\,:\,x\) is an integer<br>\(q\,:\,x\) is a rational number<br>\(r\,:\,x\) is a real number.</p>
<p>i) Write down, in words, \(\neg q\).</p>
<p>ii) Write down a value for \(x\) such that the statement \(\neg q\) is true.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write the following argument in symbolic form:<br>“If \(x\) is a real number and \(x\) is not a rational number, then \(x\) is not an integer”.</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>Phoebe states that the argument in part (b) can be shown to be valid, without the need of a truth table.</p>
<p>Justify Phoebe’s statement.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The volume of a sphere is \(V{\text{ = }}\sqrt {\frac{{{S^3}}}{{36\pi }}} \), where \(S\) is its surface area.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The surface area of a sphere is 500 cm<sup>2</sup> .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Calculate the volume of the sphere. Give your answer correct to <strong>two decimal</strong></span> <span><strong>places</strong>.</span></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 your answer to (a) correct to the nearest integer.</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>Write down your answer to (b) in the form \(a \times {10^n}\), where \(1 \leqslant a < 10\) and \(n \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Five pipes labelled, “6 metres in length”, were delivered to a building site. The contractor measured each pipe to check its length (in metres) and recorded the following;</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">5.96, 5.95, 6.02, 5.95, 5.99.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Find the mean of the contractor’s measurements.</span></p>
<p><span>(ii) Calculate the percentage error between the mean and the stated, <strong>approximate</strong> length of 6 metres.</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 \(\sqrt {{{3.87}^5} - {{8.73}^{ - 0.5}}} \), giving your answer</span></p>
<p><span>(i) correct to the nearest integer,</span></p>
<p><span>(ii) in the form \(a \times 10^k\), where 1 ≤ <em>a</em> < 10, \(k \in {\mathbb{Z}}\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A rectangle is 2680 cm long and 1970 cm wide.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the perimeter of the rectangle, giving your answer in the form \(a \times {10^k}\), where \(1 \leqslant a \leqslant 10\) and \(k \in \mathbb{Z}\).</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 area of the rectangle, giving your answer correct to the nearest thousand square centimetres.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><em><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></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Isabel is travelling from Geneva to Toronto via Amsterdam.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">She changes 1240 Swiss francs (CHF) to Euros (EUR).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The exchange rate is 1 CHF = 0.7681 EUR.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the amount of Euros Isabel receives.</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>Isabel then changes 750 EUR into Canadian dollars (CAD) and is charged 3.12 % commission.</span></p>
<p><span>The exchange rate is 1 CAD = 0.7470 EUR .</span></p>
<p><span>Calculate the amount of Canadian dollars she receives.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A type of candy is packaged in a right circular cone that has volume \({\text{100 c}}{{\text{m}}^{\text{3}}}\) and vertical height 8 cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_11.14.55.png" alt="M17/5/MATSD/SP1/ENG/TZ1/09"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the radius, \(r\), of the circular base of the cone.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the slant height, \(l\), of the cone.</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 curved surface area of the cone.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Sergei is training to be a weightlifter. Each day he trains at the local gym by lifting a metal bar that has heavy weights attached. He carries out successive lifts. After each lift, the same amount of weight is <strong>added</strong> to the bar to increase the weight to be lifted.</p>
<p>The weights of each of Sergei’s lifts form an arithmetic sequence.</p>
<p>Sergei’s friend, Yuri, records the weight of each lift. Unfortunately, last Monday, Yuri misplaced all but two of the recordings of Sergei’s lifts.</p>
<p>On that day, Sergei lifted 21 kg on the third lift and 46 kg on the eighth lift.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For that day find how much weight was added after each lift.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For that day find the weight of Sergei’s first lift.</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>On that day, Sergei made 12 successive lifts. Find the total combined weight of these lifts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The table below shows the frequency distribution of the number of dental fillings for a group of \(25\) children.</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 value of \(q\) .</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>Use your graphic display calculator to find</span><br><span>(i) the mean number of fillings;</span><br><span>(ii) the median number of fillings;</span><br><span>(iii) the standard deviation of the number of fillings.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Jane plans to travel from Amsterdam to Chicago. She changes \(1500\) Euros (\({\text{EUR}}\)) to US Dollars </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">(\({\text{USD}}\))</span> at an exchange rate of \(1{\text{ EUR}}\) to \(1.33{\text{ USD}}\). Give all answers in this question <strong>correct to two decimal places</strong>.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the number of </span><span><span>\({\text{USD}}\) </span>Jane receives.</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>Jane spends \(1350{\text{ USD}}\) and then decides to convert the remainder back to \({\text{EUR}}\) </span><span>at a rate of \(1{\text{ EUR}}\) to \(1.38{\text{ USD}}\).</span></p>
<p><span>Calculate the amount of </span><span><span>\({\text{EUR}}\) </span>Jane receives.</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>If Jane had waited until she returned to Amsterdam she could have changed her \({\text{USD}}\) at a rate of \(1{\text{ EUR}}\) to \(1.36{\text{ USD}}\) but the bank would have charged \(0.8\% \) commission.</span></p>
<p><span>Calculate the amount of \({\text{EUR}}\) Jane gained or lost by changing her money in Chicago.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>One of the locations in the \(2016\) Olympic Games is an amphitheatre. The number of seats in the first row of the amphitheatre, \({u_1}\) , is \(240\). The number of seats in each subsequent row forms an arithmetic sequence. The number of seats in the sixth row, \({u_6}\) , is \(270\).</p>
<p>Calculate the value of the common difference, \(d\).</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>There are \(20\) rows in the amphitheatre.</p>
<p>Find the <strong>total</strong> number of seats in the amphitheatre.</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>Anisha visits the amphitheatre. She estimates that the amphitheatre has \(6500\) seats.</p>
<p>Calculate the percentage error in Anisha’s estimate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The table below shows some exchange rates for the Japanese Yen (\({\text{JPY}}\)).</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>Minbin has \(1250\) Japanese Yen which she wishes to exchange for Chinese Yuan.</span></p>
<p><span>Calculate how many Yuan she will receive. Give your answer to the nearest Yuan.</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>Rupert has \(855\) Canadian Dollars which he wishes to exchange for Japanese Yen. </span></p>
<p><span>Calculate how many Yen he will receive. Give your answer to the nearest Yen.</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 how many Norwegian Kroner there are to the Euro. Give your answer correct to 2 decimal places.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Pierre invests <span class="s1">5000 </span>euros in a fixed deposit that pays a nominal annual interest rate of <span class="s1">4.5%</span>, compounded <strong>monthly</strong>, for seven years.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the value of Pierre’s investment at the end of this time. Give your answer correct to two decimal places.</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">Carla has <span class="s1">7000 </span>dollars to invest in a fixed deposit which is compounded <strong>annually</strong>.</p>
<p class="p1">She aims to double her money after 10 years.</p>
<p class="p1">Calculate the minimum annual interest rate needed for Carla to achieve her aim.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Juan buys a bicycle in a sale. He gets a discount of 30% off the original price and pays 560 US dollars (USD).</p>
</div>
<div class="specification">
<p>To buy the bicycle, Juan takes a loan of 560 USD for 6 months at a nominal annual interest rate of 75%, <strong>compounded monthly</strong>. Juan believes that the total amount he will pay will be less than the original price of the bicycle.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the original price of the bicycle.</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 difference between the original price of the bicycle and the total amount Juan will pay.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1"><span class="s1">The distance \(d\) </span>from a point \({\text{P}}(x,{\text{ }}y)\) to the point \({\text{A}}(1,{\text{ }} - 2)\) <span class="s1">is given by \(d = \sqrt {{{(x - 1)}^2} + {{(y + 2)}^2}} \)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the distance from \({\text{P}}(100,{\text{ }}200)\) to \({\text{A}}\)<span class="s1">. Give your answer correct to two decimal places.</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 class="p1">Write down your answer to <strong>part (a) </strong>correct to three significant figures.</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">Write down your answer to <strong>part (b) </strong>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">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Expand the expression \(x(2{x^3} - 1)\).</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>Differentiate \(f(x) = x(2{x^3} - 1)\).</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>Find the \(x\)-coordinate of the local minimum of the curve \(y = f(x)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Marcus has been given 500 Australian dollars (AUD) by his grandmother for his 18th birthday.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">He plans to deposit it in a bank which offers a nominal annual interest rate of 6.0 %, <strong>compounded quarterly</strong>, for three years.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the total amount of interest Marcus would earn, in AUD, over the three years. <strong>Give your answer correct to two decimal places.</strong></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>Marcus would earn the same amount of interest, <strong>compounded annually</strong>, for three years if he deposits the 500 AUD in a second bank.</span></p>
<p><span>Calculate the interest rate the second bank offers.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p><span>Charles invests \(3000{\text{ USD}}\) in a bank that offers compound interest at a rate of \(3.5\% \) per annum, compounded half-yearly.</span></p>
<p><span>Calculate the number of years that it takes for Charles’s money to double.</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">In the diagram, \({\text{B}}\hat {\text{A}}{\text{C}} = {90^ \circ }\) . The length of the three sides are \(x{\text{ cm}}\), \((x + 7){\text{ cm}}\) and \((x + 8){\text{ cm}}\).</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 and <strong>simplify</strong> a quadratic equation in \(x\) which links the three sides of the triangle.</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>Solve the quadratic equation found in part (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>Write down the value of the perimeter of the triangle.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A teacher earns an annual salary of \(45 000\) USD for the first year of her employment. Her annual salary increases by \(1750\) USD each year.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the annual salary for the fifth year of her employment.</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>She remains in this employment for 10 years. Calculate the <strong>total</strong> salary she earns in this employment during these 10 years.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;"><em><strong>In this question give all answers correct to 2 decimal places.</strong></em></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">George travelled from the USA to Europe and changed \(1200\) dollars (USD) into</span> <span style="font-size: medium; font-family: times new roman,times;">Euros (EUR). The exchange rate was \(1{\text{ USD}} = 0.8154{\text{ EUR}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the number of EUR George received.</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>On his return, George had \(160\) EUR to change back into USD. There was \(4.5\% \) commission charged on the exchange. The exchange rate was \(1\) USD = \(0.8202\) EUR. </span></p>
<p><span>Calculate the value, in EUR, of the commission that George paid.</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 his return, George had \(160\) EUR to change back into USD. There was \(4.5\% \) commission charged on the exchange. The exchange rate was \(1\) USD = \(0.8202\) EUR.</span></p>
<p><span>Calculate the number of dollars George received.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">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;">Ludmila takes a loan of 320 000 Brazilian Real (BRL) from a bank for two years at a nominal annual interest rate of 10%, <strong>compounded half yearly</strong>.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of times interest is added to the loan in the two years.</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 <strong>exact </strong>amount of money that Ludmila must repay at the end of the 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>Ludmila estimates that she will have to repay \({\text{360}}\,{\text{000}}\) BRL at the end of the two years.</span></p>
<p><span>Calculate the percentage error in her estimate.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A cuboid has a rectangular base of width \(x\)<span class="s1"><em> </em>cm </span>and length <span class="s1">2\(x\) cm </span>. The height of the cuboid is \(h\) <span class="s1">cm </span>. The total length of the edges of the cuboid is \(72\)<span class="s1"> cm</span>.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-20_om_08.27.58.png" alt></p>
<p class="p1">The volume, \(V\), of the cuboid can be expressed as \(V = a{x^2} - 6{x^3}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(a\).</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">Find the value of \(x\) that makes the volume a maximum.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Emma places \({\text{€}}8000\) in a bank account that pays a nominal interest rate of \(5\% \) per annum, compounded quarterly.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the amount of money that Emma would have in her account after 15 years. Give your answer correct to the nearest Euro.</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>After a period of time she decides to withdraw the money from this bank. There is \({\text{€}}9058.17\) in her account. Find the number of months that Emma had left her money in the account.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A liquid is heated so that after \(20\) seconds of heating its temperature, \(T\) , is \({25^ \circ }{\text{C}}\) and after \(50\) seconds of heating its temperature is \({37^ \circ }{\text{C}}\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The temperature of the liquid at time \(t\) can be modelled by \(T = at + b\) , where \(t\) is the time in seconds after the start of heating.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Using this model one equation that can be formed is \(20a + b = 25\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using the model, write down a second equation in \(a\) and \(b\) .</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>Using your graphic display calculator or otherwise, find the value of \(a\) and of \(b\) .</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>Use the model to predict the temperature of the liquid \(60{\text{ seconds}}\) after the start of heating.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The seventh term, \({u_7}\) , of a geometric sequence is \(108\). The eighth term, \({u_8}\) , of the sequence is \(36\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the common ratio of the sequence.</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 \({u_1}\) .</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>The sum of the first \(k\) terms in the sequence is \(118 096\) . Find the value of \(k\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A shipping container is a cuboid with dimensions \({\text{16 m}}\), \({\text{1}}\frac{{\text{3}}}{{\text{4}}}{\text{ m}}\) and \({\text{2}}\frac{{\text{2}}}{{\text{3}}}{\text{ m}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the <strong>exact</strong> volume of the container. Give your answer as a fraction.</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>Jim estimates the dimensions of the container as 15 m, 2 m and 3 m and uses these to estimate the volume of the container.</span></p>
<p><span>Calculate the percentage error in Jim’s estimated volume of the container.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">\(10 000\) people attended a sports match. Let \(x\) be the number of adults attending the sports match and \(y\) be the number of children attending the sports match.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down an equation in \(x\) and \(y\) .</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>The cost of an adult ticket was \(12\) Australian dollars (AUD). The cost of a child ticket was \(5\) Australian dollars (AUD).</span></p>
<p><span> Find the total cost for a family of 2 adults and 3 children.</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 total cost of tickets sold for the sports match was \(108800{\text{ AUD}}\).</span></p>
<p><span>Write down a second equation in \(x\) and \(y\) .</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>Write down the value of \(x\) and the value of \(y\) .</span></p>
<div class="marks">[2]</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;"><em>f</em> (<em>x</em>) = 5<em>x</em><sup>3</sup> − 4<em>x</em><sup>2</sup> + <em>x</em></span></p>
</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">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find using your answer to part (a) the <em>x</em>-coordinate of</span></p>
<p><span>(i) the local maximum point;</span></p>
<p><span>(ii) the local minimum point.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">José stands 1.38 kilometres from a vertical cliff.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Express this distance in metres.</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>José estimates the angle between the horizontal and the top of the cliff as 28.3° and uses it to find the height of the cliff.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span><span>Find the height of the cliff according to José’s calculation.<strong> Express your answer in metres, to the nearest whole metre.</strong></span></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>José estimates the angle between the horizontal and the top of the cliff as 28.3° and uses it to find the height of the cliff.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>The actual height of the cliff is 718 metres. Calculate the percentage error made by José when calculating the height of the cliff.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Ross is a star that is 82 414 080 000 000 km away from Earth. A spacecraft,</span> <span style="font-size: medium; font-family: times new roman,times;">launched from Earth, travels at 48 000 kmh<sup>–1</sup> towards Ross.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the <strong>exact</strong> time, in hours, for the spacecraft to reach the star Ross.</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>Give your answer to part (a) in years. (Assume 1 year = 365 days)</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>Give your answer to part (b) in the form <em>a</em>×10<em><sup>k</sup></em>, where 1 ≤ <em>a</em> < 10 and \(k \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">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;">Dumisani has received a scholarship of 5000 US dollars (USD) to study in Singapore.</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;">He has to travel from South Africa and must change USD for his air fare of 6600 South African rand (ZAR).</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 is 1USD = 8.2421 ZAR.</span></p>
<p><em><strong><span style="font-family: 'times new roman', times; font-size: medium;">In this question give all answers correct to two decimal places.</span></strong></em></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the number of USD that Dumisani must change to pay for his air fare.</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>On arrival in Singapore, Dumisani changes 3000 USD to Singapore dollars (SGD) to pay for his school fees. There is a 2.8% commission charged on the exchange.</span></p>
<p><span>Calculate the value, <strong>in USD</strong>, of the commission that Dumisani has to pay.</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 exchange rate is \(1{\text{ USD }} = 1.29903{\text{ SGD}}\).</span></p>
<p><span>Calculate the number of SGD Dumisani receives.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p><span>The sets \(P\), \(Q\) and \(U\) are defined as</span></p>
<p><span><span><em>U</em> = {Real Numbers} , <em>P</em> = {Positive Numbers} and <em>Q</em> = {Rational Numbers}.</span></span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Write down in the correct region on the Venn diagram the numbers</span></p>
<p><span>\(\frac{{22}}{7}\) , \(5 \times {10^{ - 2}}\) , \(\sin (60^\circ )\) , \(0\) , \(\sqrt[3]{{ - 8}}\) , \( - \pi \).</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1"><strong>In this question give all answers correct to two decimal places.</strong></p>
<p class="p1">Javier takes <span class="s1">5000 </span>US dollars (<span class="s1">USD</span>) on a business trip to Venezuela. He exchanges <span class="s1">3000 USD </span>into Venezuelan bolívars (<span class="s1">VEF</span>).</p>
<p class="p2"><span class="s2">The exchange rate is </span>1 USD \( = \) 6.3021 VEF<span class="s2">.</span></p>
</div>
<div class="specification">
<p class="p1">During his time in Venezuela, Javier spends <span class="s1">1250 USD </span>and <span class="s1">12 000 VEF</span>. On his return home, Javier exchanges his remaining <span class="s1">VEF </span>into <span class="s1">USD</span>.</p>
<p class="p2"><span class="s2">The exchange rate is </span>1 USD \( = \) 8.7268 VEF<span class="s2">.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the amount of <span class="s1">VEF </span><span class="s2">that Javier receives.</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"><span class="s1">Calculate the total amount, in </span><span class="s2">USD</span>, that Javier has remaining from his <span class="s2">5000 USD </span>after his trip to Venezuela.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The length of one side of a rectangle is 2 cm longer than its width.</span></p>
<p><span>If the smaller side is <em>x</em> cm, find the perimeter of the rectangle in terms of <em>x</em>.</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>The length of one side of a rectangle is 2 cm longer than its width.</span></p>
<p><span>The perimeter of a square is equal to the perimeter of the rectangle in part (a).</span></p>
<p><span>Determine the length of each side of the square in terms of <em>x</em>.</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 length of one side of a rectangle is 2 cm longer than its width.</span></p>
<p><span>The perimeter of a square is equal to the perimeter of the rectangle in part (a).</span></p>
<p><span>The sum of the areas of the rectangle and the square is \(2x^2 + 4x +1\) (cm<sup>2</sup>).</span></p>
<p><span>(i) Given that this sum is 49 cm<sup>2</sup>, find <em>x</em>.</span></p>
<p><span>(ii) Find the area of the square.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A hydraulic hammer drives a metal post vertically into the ground by striking the top of the post. The distance that the post is driven into the ground, by the \(n{\text{th}}\) strike of the hammer, is \({d_n}\).</p>
<p class="p2"><span class="s1">The distances \({d_1},{\text{ }}{d_2},{\text{ }}{d_3}{\text{ }} \ldots ,{\text{ }}{d_n}\) </span>form a geometric sequence.</p>
<p class="p1">The distance that the post is driven into the ground by the first strike of the hammer, \({d_1}\), is <span class="s2">64 cm</span>.</p>
<p class="p1">The distance that the post is driven into the ground by the second strike of the hammer, \({d_2}\), is <span class="s2">48 cm</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of the common ratio for this sequence.</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 distance that the post is driven into the ground by the eighth strike of the <span class="s1">hammer.</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"><span class="s1">Find the </span><strong>total depth </strong>that the post has been driven into the ground after <span class="s2">10 </span>strikes of the hammer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">In an arithmetic sequence, the fifth term, <em>u</em><sub>5</sub>, is greater than the first term, <em>u</em><sub>1</sub>. The difference between these terms is 36.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the common difference, <em>d</em>.</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 tenth term of the sequence is double the seventh term.</span></p>
<p><span>(i) Write down an equation in <em>u</em><sub>1</sub> and <em>d</em> to show this information.</span></p>
<p><span>(ii) Find <em>u</em><sub>1</sub>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Obi travels from Dubai to Pretoria and changes \(2000\) United Arab Emirates Dirham \(({\text{AED}})\) at a bank. He receives \(6160\) South African Rand \(({\text{ZAR}})\).</p>
<p>The exchange rate is \(1\;{\text{AED}} = x\,{\text{ZAR}}\).</p>
<p>Calculate the value of \(x\) .</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>Obi decides to invest half of the money he receives, \(3080\,\,{\text{ZAR}}\), in an account which pays a nominal interest rate of \(9\,\% \), <strong>compounded monthly</strong>.</p>
<p>The amount of money in the account will have doubled before the end of the \(n{\text{th}}\) year of the investment.</p>
<p>Calculate the minimum value of \(n\) .</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the following sequence:</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;">57, 55, 53 ..., 5, 3</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of terms of the sequence.</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 sequence.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Given \(p = x - \frac{{\sqrt y }}{z}\) , \(x = 1.775\) , \(y = 1.44\) and \(z = 48\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the value of \(p\).</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>Barry <strong>first</strong> writes \(x\) , \(y\) and \(z\) correct to one significant figure and <strong>then</strong> uses these values to estimate the value of \(p\) .</span><br><span>(i) Write down \(x\) , \(y\) and \(z\) each correct to one significant figure.</span><br><span>(ii) Write down Barry’s estimate of the value of \(p\) .</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 percentage error in Barry’s estimate of the value of \(p\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The \(x\)-coordinate of the minimum point of the quadratic function \(f(x) = 2{x^2} + kx + 4\) is \(x =1.25\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Find the value of \(k\) .</span></p>
<p><span>(ii) Calculate the \(y\)-coordinate of this minimum point.</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>Sketch the graph of \(y = f(x)\) for the domain \( - 1 \leqslant x \leqslant 3\).</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Tomás is playing with sticks and he forms the first three diagrams of a pattern. These diagrams are shown below.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_17.25.44.png" alt="M17/5/MATSD/SP1/ENG/TZ2/05"></p>
<p>Tomás continues forming diagrams following this pattern.</p>
</div>
<div class="specification">
<p>Tomás forms a total of 24 diagrams.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Diagram \(n\) is formed with 52 sticks. Find the value of \(n\).</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 total number of sticks used by Tomás for all 24 diagrams.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The company Snakezen’s Ladders makes ladders of different lengths. All the ladders that the company makes have the same design such that:</p>
<p style="padding-left: 90px;">the first rung is 30 cm from the base of the ladder,</p>
<p style="padding-left: 90px;">the second rung is 57 cm from the base of the ladder,</p>
<p style="padding-left: 90px;">the distance between the first and second rung is equal to the distance between all adjacent rungs on the ladder.</p>
<p>The ladder in the diagram was made by this company and has eleven equally spaced rungs.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_10.59.54.png" alt="M17/5/MATSD/SP1/ENG/TZ1/05"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the distance from the base of this ladder to the top rung.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The company also makes a ladder that is 1050 cm long.</p>
<p>Find the maximum number of rungs in this 1050 cm long ladder.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Inge borrows € 4500 for 2 years.</span></p>
</div>
<div class="question">
<p><span>Bank 1 charges compound interest at a rate of 15 % per annum, compounded quarterly.</span></p>
<p><span>Calculate the <strong>total</strong> amount to be repaid at the end of the 2 years.<strong> Give your answer correct to two decimal places</strong>.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">Mandzur, a farmer, takes out a loan to buy a buffalo. He borrows 900 000 Cambodian riels (KHR) for 2 years. The nominal annual interest rate is 15%, compounded <strong>monthly</strong>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the amount of the <strong>interest </strong>that Mandzur must pay. Give your answer correct to the nearest 100 KHR.</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 your answer to part (a) in the form \(a \times {10^k},{\text{ where }}1 \leqslant a < 10,{\text{ }}k \in \mathbb{Z}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p><span>Consider the numbers \(\sqrt 3 \), \(6\), \(2\frac{1}{2}\), \(\pi \), \( - 5\), and the sets \(\mathbb{N}\), \(\mathbb{Z}\), and \(\mathbb{Q}\). Complete the following table by placing a tick in the appropriate box if the number is an element of the set.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
</div>
<br><hr><br><div class="specification">
<p style="text-align: left;"><span style="font-size: medium; font-family: times new roman,times;">A quadratic function, \(f(x) = a{x^2} + bx\), is represented by the mapping diagram below.</span></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>Use the mapping diagram to write down <strong>two</strong> equations in terms of <em>a</em> and<em> b</em>.</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>Find the value of</span><span> <em>a</em>.</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>Find the value of <em>b</em>.</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 <em>x</em>-coordinate of the vertex of the graph of <em>f </em>(<em>x</em>).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The number of cells, <em>C</em>, in a culture is given by the equation \(C = p \times 2^{0.5t} + q\), where <em>t</em> is the time in hours measured from 12:00 on Monday and <em>p</em> and <em>q</em> are constants.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The number of cells in the culture at 12:00 on Monday is 47.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The number of cells in the culture at 16:00 on Monday is 53.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the above information to </span><span>write down two equations in <em>p</em> and <em>q</em> ;</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>Use the above information to </span><span>calculate the value of <em>p</em> and of <em>q</em> ;</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 above information to </span><span>find the number of cells in the culture at 22:00 on Monday.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The speed of light is \({\text{300}}\,{\text{000}}\) kilometres per second. The average distance from the Sun to the Earth is 149.6 million km.</p>
</div>
<div class="specification">
<p>A light-year is the distance light travels in one year and is equal to \({\text{9}}\,{\text{467}}\,{\text{280}}\) million km. Polaris is a bright star, visible from the Northern Hemisphere. The distance from the Earth to Polaris is 323 light-years.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the time, <strong>in minutes</strong>, it takes for light from the Sun to reach the Earth.</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 distance from the Earth to Polaris in millions of km. Give your answer in the form \(a \times {10^k}\) with \(1 \leqslant a < 10\) and \(k \in \mathbb{Z}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</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><em>In this question give all answers correct to the nearest whole number.</em></strong></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Fumie is going for a holiday to Great Britain. She changes \({\text{100}}\,{\text{000}}\) Japanese Yen (JPY) into British Pounds (GBP) with no commission charged.</span></p>
<p><span>The exchange rate between GBP and JPY is</span></p>
<p><span>1 GBP = 129 JPY.</span></p>
<p><span>Calculate the value of \({\text{100}}\,{\text{000}}\) JPY in GBP.</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>At the end of Fumie’s holiday in Great Britain she has 239 GBP. She converts this back to JPY at a bank, which does not charge commission, and receives </span><span><span><span>30 200 JPY</span></span></span></p>
<p><span>(i) Find the exchange rate of this second transaction.</span></p>
<p><span>(ii) Determine, when changing GBP back to JPY, whether the exchange rate found in part (b)(i) is better value for Fumie than the exchange rate in part (a). Justify your answer.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Arthur and Jacob dream of owning a speedboat that costs \({\text{35}}\,{\text{300}}\) euros (EUR).</p>
<p>Arthur invested \(x\) EUR in an account that pays a nominal annual interest rate of 3.6%, compounded <strong>monthly</strong>. After 18 years he will have \({\text{35}}\,{\text{300}}\) EUR in the account.</p>
</div>
<div class="specification">
<p>Jacob invested 9000 EUR for \(n\) years. The investment has a nominal annual interest rate of 3.2% and is compounded <strong>quarterly</strong>. After \(n\) years, the investment will be worth \({\text{35}}\,{\text{300}}\) EUR.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of Arthur’s initial investment, \(x\). Give your answer to two decimal places.</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 value of \(n\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The graph of the quadratic function \(f (x) = c + bx − x^2\) intersects the <em>y</em>-axis at point A(0, 5) and has its vertex at point B(2, 9).</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>Write down the value of <em>c</em>.</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 <em>b</em>.</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 <em>x</em>-intercepts of the graph of <em>f</em> .</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 down \(f (x)\) in the form \(f (x) = −(x − p) (x + q)\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The function \(g(x)\) is defined as \(g(x) = 16 + k({c^{ - x}})\) where \(c > 0\) .</span><br><span style="font-size: medium; font-family: times new roman,times;">The graph of the function \(g\) is drawn below on the domain \(x \geqslant 0\) .</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>
<p><span style="font-size: medium; font-family: times new roman,times;">The graph of \(g\) intersects the <em>y</em>-axis at (0, 80) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of \(k\) .</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 graph passes through the point (2, 48) . </span></p>
<p><span>Find the value of \(c\) .</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 graph passes through the point (2, 48) . </span></p>
<p><span>Write down the equation of the horizontal asymptote to the graph of \(y = g(x)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">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;">Let \(p = \frac{{2\cos x - \tan x}}{{\sqrt y - z}}.\)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the value of \(p\) when \(x = 45^\circ \), \(y = 8192\) and \(z = 64\). Write down your full calculator display.</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 your answer to part (a)</span></p>
<p><span>(i) correct to two decimal places;</span></p>
<p><span>(ii) correct to four significant figures;</span></p>
<p><span>(iii) in the form \(a \times {10^k}\), where \(1 \leqslant a < 10,{\text{ }}k \in \mathbb{Z}\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Jackson invested 12 000 Australian dollars (AUD) in a bank that offered simple interest at an annual interest rate of <em>r</em> %. The value of Jackson’s investment doubled after 20 years.</span></p>
</div>
<div class="question">
<p><span>Maddison invests 15 000 AUD in a bank that offers compound interest at a nominal annual interest rate of 4.44 %, <strong>compounded quarterly</strong>.</span></p>
<p><span>Calculate the number of years that it will take for Maddison’s investment to triple in value.</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The equation of a line <em>L</em><sub>1</sub> is \(2x + 5y = −4\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the gradient of the line <em>L</em><sub>1</sub>.</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>A second line <em>L</em><sub>2</sub> is perpendicular to <em>L</em><sub>1</sub>.</span></p>
<p><span>Write down the gradient of <em>L</em><sub>2</sub>.</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 point (5, 3) is on <em>L</em><sub>2</sub>.</span></p>
<p><span>Determine the equation of <em>L</em><sub>2</sub>.</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>Lines <em>L</em><sub>1</sub> and <em>L</em><sub>2</sub> intersect at point P.</span></p>
<p><span>Using your graphic display calculator or otherwise, find the coordinates of P.</span></p>
<div class="marks">[2]</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;">Consider the function \(f(x) = p{(0.5)^x} + q\) where <em>p</em> and <em>q</em> are constants. The graph of <em>f</em> (<em>x</em>) passes through the points \((0,\,6)\) and \((1,\,4)\) and is shown below.</span></p>
<p style="text-align: center;"><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 two equations relating <em>p</em> and <em>q</em>.</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>Find the value of <em>p</em> and of <em>q</em>.</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 equation of the horizontal asymptote to the graph of <em>f</em> (<em>x</em>).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Eva invests \({\text{USD}}2000\) at a nominal annual interest rate of \(8\% \) <strong>compounded half-yearly</strong>.</span></p>
<p><span>Calculate the value of her investment after \(5\) years, correct to the nearest dollar.</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>Toni invests \({\text{USD}}1500\) at an annual interest rate of \(7.8\% \) <strong>compounded yearly</strong>.</span></p>
<p><span>Find the number of <strong>complete</strong> years it will take for his investment to double in value.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p><span>1 Brazilian Real (BRL) = 2.607 South African Rand (ZAR). Giving answers <strong>correct to two decimal places</strong>,</span></p>
<p><span>(i) convert 300 BRL to ZAR,</span></p>
<p><span>(ii) find how many Real it costs to purchase 300 Rand.</span></p>
</div>
<br><hr><br><div class="question">
<p><span>Consider the numbers 3, −5 , \(\sqrt{7}\), \(2^{−3}\) and 1.75.</span></p>
<p><span>Complete the table below, placing a tick (</span><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAPCAIAAABm5AhFAAAA5ElEQVQokWP4TxZgIFLd+/fv79+/T5q2Y0cmyrNyWbZMJUHb1HpXdR5Vi5IW4h35e1KNgSOLt355O5oEHm2/J9UYuDGZK2S3YMrh1NZVru/PLC8YW/f682cC2vbv3w9h7NuckaHFwulWvObufayGQrVdvjg33oKDQdhbr2bCg7tLcqxYGUyK45eux+UWhG1d5frBogwMxtl+brziDG5S8WW49KA58ktDtIgkAwMDAwOTY+n2l6+J1PZ//6bYTDEGBgYfvbqpuDRg0fb16zkvBRHzqr7379+ToO3////ICY8EbUQCAMRdzWFSum9AAAAAAElFTkSuQmCC" alt><span>) to show which of the number sets, \(\mathbb{N}, \mathbb{Q} {\text{ and }} \mathbb{R}\)</span><span> these numbers belong to. The first row has been completed as an example.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Ben inherits $6500. Ben invests his money in a bank that pays compound interest at a rate of 4.5% per annum.</span></p>
</div>
<div class="question">
<p><span>Calculate the value of <strong>Ben’s</strong> investment at the end of 6 years. Give your answer <strong>correct to 2 decimal places</strong>.</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Jenny invested $20 000 in a bank account that paid 3.5 % annual simple interest. She withdrew her investment from the account when its value was $31 200.</span></p>
</div>
<div class="question">
<p><span>Ramón invests $18 000 in a bank account that pays 3.4 % nominal annual interest, <strong>compounded quarterly</strong>.</span></p>
<p><span>Find the minimum number of years that Ramón must invest the money for his investment to be worth $27 000.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">A hotel has a rectangular swimming pool. Its length is \(x\) metres, its width is \(y\) metres and its perimeter is \(44\) metres.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down an equation for \(x\) and \(y\).</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 area of the swimming pool is \({\text{112}}{{\text{m}}^2}\).</p>
<p class="p1">Write down a second equation for \(x\) and \(y\).</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">Use your graphic display calculator to find the value of \(x\) and the value of \(y\).</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">An Olympic sized swimming pool is \(50\) m long and \(25\) m wide.</p>
<p class="p1">Determine the area of the hotel swimming pool as a percentage of the area of an Olympic sized swimming pool.</p>
<div class="marks">[2]</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;">The graph of the quadratic function \(f(x) = a{x^2} + bx + c\) intersects the <em>y</em>-axis at point A (0, 5) and has its vertex at point B (4, 13).</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><img src="images/Schermafbeelding_2014-09-20_om_14.11.23.png" alt></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>By using the coordinates of the vertex, B, or otherwise, write down <strong>two </strong>equations in \(a\) and \(b\).</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 value of \(a\) and of \(b\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A race track is made up of a rectangular shape \(750{\text{ m}}\) by \(500{\text{ m}}\) with semi-circles at each end as shown in the diagram.</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;">Michael drives around the track once at an average speed of \(140{\text{ km}}{{\text{h}}^{ - 1}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the distance that Michael travels.</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><span>Calculate how long Michael takes in</span> <span><strong>seconds</strong>.</span></span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</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;">Chocolates in the shape of spheres are sold in boxes of 20.</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;">Each chocolate has a radius of 1 cm.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the volume of 1 chocolate.</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 the volume of 20 chocolates.</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 diagram shows the chocolate box from above. The 20 chocolates fit perfectly in the box with each chocolate touching the ones around it or the sides of the box.</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_14.27.38.png" alt><br></span></p>
<p><span>Calculate the volume of the box.</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 diagram shows the chocolate box from above. The 20 chocolates fit perfectly in the box with each chocolate touching the ones around it or the sides of the box.</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_14.27.38_1.png" alt><br></span></p>
<p><span>Calculate the volume of empty space in the box.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">An iron bar is heated. Its length, \(L\), in millimetres can be modelled by a linear function, \(L = mT + c\), where \(T\) <span class="s1">is the temperature measured in degrees Celsius (°C)</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">At <span class="s1">150°</span><span class="s1">C </span>the length of the iron bar is <span class="s1">180 mm</span>.</p>
<p class="p1">Write down an equation that shows this information.</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">At <span class="s1">210°</span><span class="s1">C </span>the length of the iron bar is <span class="s1">181.5 mm</span>.</p>
<p class="p1">Write down an equation that shows this second piece of information.</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">At <span class="s1">210°</span><span class="s1">C </span>the length of the iron bar is <span class="s1">181.5 mm</span>.</p>
<p class="p1">Hence, find the length of the iron bar at <span class="s1">40°</span><span class="s1">C</span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the truth table.</span></p>
<p><img src="data:image/png;base64,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" alt></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>Consider the propositions <em>p</em> and <em>q</em>:</span></p>
<p><em><span>p: x is a number less than 10.</span></em></p>
<p><span><em><span><span>q: x2 is a number greater than 100.</span></span></em></span></p>
<p><span><span>Write in words the compound proposition \(\neg p \vee q\).</span></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>Using part (a), determine whether \(\neg p \vee q\) is true or false, for the case where \(x\) is a number less than 10 and \(x^2\) is a number greater than 100.</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>Write down a value of \(x\) for which \(\neg p \vee q\) is false.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A solid right circular cone has a base radius of 21 cm and a slant height of 35 cm.<br>A smaller right circular cone has a height of 12 cm and a slant height of 15 cm, and is removed from the top of the larger cone, as shown in the diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the radius of the base of the cone which has been removed.</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 curved surface area of the cone which has been removed.</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 curved surface area of the remaining solid.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Last year a South American candy factory sold 4.8 × 10<sup>8</sup> spherical sweets. Each sweet has a diameter of 2.5 cm.</p>
<p>The factory is producing an advertisement showing all of these sweets placed in a straight line.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The advertisement claims that the length of this line is <em>x</em> times the length of the Amazon River. The length of the Amazon River is 6400 km.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length, in cm, of this line. Give your answer in the form <em>a</em> × 10<sup><em>k</em></sup> , where 1 ≤ <em>a</em> < 10 and k ∈ \(\mathbb{Z}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the length of the Amazon River in cm.</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>Find the value of <em>x</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A park in the form of a triangle, ABC, is shown in the following diagram. AB is 79 km and BC is 62 km. Angle A\(\mathop {\text{B}}\limits^ \wedge \)C is 52°.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of side AC in km.</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 area of the park.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider the numbers \(2\), \(\sqrt 3 \), \( - \frac{2}{3}\) and the sets \(\mathbb{N}\), \(\mathbb{Z}\), \(\mathbb{Q}\) and \(\mathbb{R}\).</span></p>
<p><span>Complete the table below by placing a tick in the appropriate box if the number is an element of the set, and a cross if it is not.<img src="data:image/png;base64,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" alt></span></p>
<p> </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>A function \(f\) is given by \(f(x) = 2{x^2} - 3x{\text{, }}x \in \{ - 2{\text{, }}2{\text{, }}3\} \).</span></p>
<p><span>Write down the range of function \(f\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Fabián stands on top of a building, <span class="s1">T</span>, which is on a horizontal street.</p>
<p class="p1">He observes a car, <span class="s1">C</span>, on the street, at an angle of depression of <span class="s1">30°</span>. The base of the building is at <span class="s1">B</span>. The height of the building is <span class="s1">80 </span>metres.</p>
<p class="p1">The following diagram indicates the positions of <span class="s1">T</span>, <span class="s1">B </span>and <span class="s1">C.</span></p>
<p class="p1" style="text-align: center;"><span class="s1"><img src="images/Schermafbeelding_2015-12-20_om_09.20.36.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show, in the appropriate place on the diagram, <strong>the values </strong>of</p>
<p class="p1">(i) the height of the building;</p>
<p class="p1">(ii) the angle of depression.</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 distance, <span class="s1">BC</span>, from the base of the building to the car.</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">Fabián estimates that the distance from the base of the building to the car is <span class="s1">150 </span>metres. Calculate the percentage error of Fabián’s estimate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Assume that the Earth is a sphere with a radius, \(r\) , of \(6.38 \times {10^3}\,{\text{km}}\) .</p>
<p><img 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" alt></p>
<p>i) Calculate the surface area of the Earth in \({\text{k}}{{\text{m}}^2}\).</p>
<p>ii) Write down your answer to part (a)(i) in the form \(a \times {10^k}\) , where \(1 \leqslant a < 10\) and \(k \in \mathbb{Z}\) .</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The surface area of the Earth that is covered by water is approximately \(3.61 \times {10^8}{\text{k}}{{\text{m}}^2}\) .</p>
<p>Calculate the percentage of the surface area of the Earth that is covered by water.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>Consider the numbers \( - 1,\,\,4,\,\,\frac{2}{3},\,\,\sqrt 2 ,\,\,0.35\) and \( - {2^2}\).</p>
<p>Complete the following table by placing a tick (<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABUAAAASCAYAAAC0EpUuAAABLElEQVQ4EdWTP2vCQBjGX539AG4pZIogOGbuUFIHFT9BB4Pp5t61s1KhdMwQdwU/QOkaydYh6OQgcZOSKcP5yPkHgpfTHLr04OB4797f+zx39xYAgO48infm7XE3QbfrGY2GU1psz6Rx++ojQeR/4dXxEMZMSCchcjWQIPp+R90aIsgA8nRF6BFo9DBZJdLyCtAjUGtjEGykQAWlDHHowTZM2O4v4ovITPuHR7CNlKLYx8CqoOqMsRLfRSgh2mcRZh8dVLUH6A0Xc7ZB0G9Dv3KPabII5btsiYljQtdM2G891LUKWm6IHCL37Gwo585dtLhaPi98n7TC01raUUX9kV6ey0RUpqduk2ol6dGzdiKSKgUY/n48fPpRbtsnpQW+EEvdFlHwlL/Q/4HuAAoRIMzxYx0jAAAAAElFTkSuQmCC" alt>) to indicate if the number is an element of the number set. The first row has been completed as an example.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p> </p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">\(U = \{ x|x{\text{ is an integer, }}2 < x < 10\}\)</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><em>A</em> and <em>B</em> are subsets of <em>U</em> such that <em>A</em> = {multiples of 3}, <em>B</em> = {factors of 24}.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of</span></p>
<p><span>(i) <em>U</em> ;</span></p>
<p><span>(ii) <em>B</em> .</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 the elements of <em>U</em> on the Venn diagram.</span></p>
<p><img src="data:image/png;base64,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" alt></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>Write down \(n (A \cap B)\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p><span>The Venn diagram shows the number sets \(\mathbb{N}\), \(\mathbb{Z}\), \(\mathbb{Q}\) and \(\mathbb{R}\). Place each of the following</span> <span>numbers in the appropriate region of the Venn diagram.</span></p>
<p><span>\(\frac{{1}}{{4}}\), −3, π, cos 120°, 2.7 × 10<sup>3</sup>, 3.4 × 10<sup>–2</sup></span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
</div>
<br><hr><br><div class="specification">
<p>The following table shows four different sets of numbers: \(\mathbb{N}\), \(\mathbb{Z}\), \(\mathbb{Q}\) and \(\mathbb{R}\).</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the second column of the table by giving <strong>one</strong> example of a number from each set.</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>Josh states: “Every integer is a natural number”.</p>
<p>Write down whether Josh’s statement is correct. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Temi’s sailing boat has a sail in the shape of a right-angled triangle, \({\text{ABC}}{\text{.}}\,\,\,{\text{BC}} = \,\,5.45{\text{m}}\),<br>angle \({\text{CAB}} = {76^{\text{o}}}\) and angle \({\text{ABC}} = {90^{\text{o}}}\).</p>
<p>Calculate \({\text{AC}}\), the height of Temi’s sail.</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><img 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" alt></p>
<p>William also has a sailing boat with a sail in the shape of a right-angled triangle, \({\text{TRS}}\).<br>\({\text{RS}}\,\,{\text{ = }}\,\,{\text{2}}{\text{.80m}}\). The area of William’s sail is \({\text{10}}{\text{.7}}\,{{\text{m}}^2}\).</p>
<p>Calculate \({\text{RT}}\), the height of William’s sail.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Each day a supermarket records the midday temperature and how many cold drinks are sold on that day. The following table shows the supermarket’s data for the last 6 days. This data is also shown on a scatter diagram.</p>
<p><img 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" alt></p>
<p><img 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" alt></p>
<p>Write down</p>
<p>i) the mean temperature, \({\bar x}\) ;</p>
<p>ii) the mean number of cold drinks sold, \({\bar y}\) .</p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the line of best fit on the scatter 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>Use the line of best fit to estimate the number of cold drinks that are sold on a day when the midday temperature is \(10\,^\circ {\text{C}}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br>