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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;">A function is represented by the equation</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">\[f(x) = a{x^2} + \frac{4}{x} - 3\]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(f ′(x)\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The function \(f (x)\) has a local maximum at the point where \(x = −1\).</span></p>
<p><span>Find the value of <em>a</em>.</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;">The function \(f(x)\) is such that \(f'(x) < 0\) for \(1 < x < 4\). At the point \({\text{P}}(4{\text{, }}2)\) on the graph of \(f(x)\) the gradient is zero.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the equation of the tangent to the graph of \(f(x)\) at \({\text{P}}\).</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>State whether \(f(4)\) is greater than, equal to or less than \(f(2)\).</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>Given that \(f(x)\) is increasing for \(4 \leqslant x < 7\), what can you say about the point </span><span><span><span>\({\text{P}}\)</span></span>?</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function \(f\left( x \right) = \frac{{{x^4}}}{4}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <em>f'</em>(<em>x</em>)</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 gradient of the graph of <em>f</em> at \(x = - \frac{1}{2}\).</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 <em>x</em>-coordinate of the point at which the <strong>normal</strong> to the graph of <em>f</em> has gradient \({ - \frac{1}{8}}\).</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;">Consider the curve \(y = {x^2}\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).</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 point \({\text{P}}(3{\text{, }}9)\) lies on the curve \(y = {x^2}\) . Find the gradient of the tangent to the curve at 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>The point \({\text{P}}(3{\text{, }}9)\) lies on the curve \(y = {x^2}\) . Find the equation of the normal to the curve at P . Give your answer in the form \(y = mx + c\) .</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 equation of a curve is given as \(y = 2x^{2} - 5x + 4\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\)</span><span>.</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 equation of the line <em>L</em> is \(6x + 2y = -1\).</span></p>
<p><span>Find the <em>x</em>-coordinate of the point on the curve \(y = 2x^2 - 5x + 4\) where the tangent is parallel to <em>L</em>.</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;">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-size: medium; font-family: times new roman,times;">Let \(f (x) = 2x^2 + x - 6\)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(f'(x)\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of \(f'( - 3)\).</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>Find the value of \(x\) for which \(f'(x) = 0\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The coordinates of point A are \((6,{\text{ }} - 7)\) and the coordinates of point B are \(( - 6,{\text{ }}2)\). Point M is the midpoint of AB.</p>
</div>
<div class="specification">
<p>\({L_1}\) is the line through A and B.</p>
</div>
<div class="specification">
<p>The line \({L_2}\) is perpendicular to \({L_1}\) and passes through M.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates 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>Find the gradient of \({L_1}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the gradient of \({L_2}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, in the form \(y = mx + c\), the equation of \({L_2}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows part of the graph of a function \(y = f(x)\). The graph passes through point \({\text{A}}(1,{\text{ }}3)\).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_06.22.37.png" alt="M17/5/MATSD/SP1/ENG/TZ2/13"></p>
</div>
<div class="specification">
<p>The tangent to the graph of \(y = f(x)\) at A has equation \(y = - 2x + 5\). Let \(N\) be the normal to the graph of \(y = f(x)\) at A.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of \(f(1)\).</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 equation of \(N\). Give your answer in the form \(ax + by + d = 0\) where \(a\), \(b\), \(d \in \mathbb{Z}\).</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>Draw the line \(N\) on the diagram above.</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;">Consider the graph of the function \(y = f(x)\) defined below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Write down <strong>all</strong> the labelled points on the curve</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>that are local maximum points;</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>where the function attains its least value;</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>where the function attains its greatest value;</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>where the gradient of the tangent to the curve is positive;</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>where \(f(x) > 0\) and \(f'(x) < 0\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the function \(f(x) = \frac{1}{2}{x^3} - 2{x^2} + 3\).</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>Find \(f''(x)\).</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 equation of the tangent to the curve of \(f\) at the point \((1{\text{, }}1.5)\).</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>The point A has coordinates (4 , −8) and the point B has coordinates (−2 , 4).</p>
</div>
<div class="specification">
<p>The point D has coordinates (−3 , 1).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of C, the midpoint of line segment AB.</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 gradient of the line DC.</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 equation of the line DC. Write your answer in the form <em>ax</em> + <em>by</em> + <em>d</em> = 0 where <em>a</em> , <em>b</em> and <em>d</em> are integers.</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 sketch of the function \(f(x) = 5{x^3} - 3{x^5} + 1\) is shown for \( - 1.5 \leqslant x \leqslant 1.5\) and \( - 6 \leqslant y \leqslant 6\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down \(f'(x)\) .</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>Find the equation of the tangent to the graph of \(y = f(x)\) at \((1{\text{, }}3)\) .</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>Write down the coordinates of the second point where this tangent intersects the graph of \(y = f(x)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A quadratic function \(f\) is given by \(f(x) = a{x^2} + bx + c\). The points \((0,{\text{ }}5)\) and \(( - 4,{\text{ }}5)\) lie on the graph of \(y = f(x)\).</p>
</div>
<div class="specification">
<p>The \(y\)-coordinate of the minimum of the graph is 3.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the axis of symmetry of the graph of \(y = f(x)\).</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>Write down the value of \(c\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(a\) and of \(b\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the curve \(y = {x^2} + \frac{a}{x} - 1,{\text{ }}x \ne 0\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The gradient of the tangent to the curve is \( - 14\) when \(x = 1\).</p>
<p class="p1">Find the value of \(a\).</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>The equation of line \({L_1}\) is \(y = 2.5x + k\). Point \({\text{A}}\) \(\,(3,\, - 2)\) lies on \({L_1}\).</p>
<p>Find the value of \(k\).</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 line \({L_2}\) is perpendicular to \({L_1}\) and intersects \({L_1}\) at point \({\text{A}}\).</p>
<p>Write down the gradient of \({L_2}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of \({L_2}\). Give your answer in the form \(y = mx + c\) .</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write your answer to part (c) in the form \(ax + by + d = 0\) where \(a\), \(b\) and \(d \in \mathbb{Z}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A small manufacturing company makes and sells \(x\) machines each month. The monthly cost \(C\) , in dollars, of making \(x\) machines is given by</span><br><span style="font-family: times new roman,times; font-size: medium;">\[C(x) = 2600 + 0.4{x^2}{\text{.}}\]</span><span style="font-family: times new roman,times; font-size: medium;">The monthly income \(I\) , in dollars, obtained by selling \(x\) machines is given by</span><br><span style="font-family: times new roman,times; font-size: medium;">\[I(x) = 150x - 0.6{x^2}{\text{.}}\]</span><span style="font-family: times new roman,times; font-size: medium;">\(P(x)\) is the monthly profit obtained by selling \(x\) machines.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(P(x)\) .</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>Find the number of machines that should be made and sold each month to maximize \(P(x)\) .</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>Use your answer to part (b) to find the selling price of</span> <span><strong>each machine</strong> in order to maximize \(P(x)\) .</span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The equation of line \({L_1}\) is \(y = - \frac{2}{3}x - 2\).</p>
</div>
<div class="specification">
<p>Point P lies on \({L_1}\) and has \(x\)-coordinate \( - 6\).</p>
</div>
<div class="specification">
<p>The line \({L_2}\) is perpendicular to \({L_1}\) and intersects \({L_1}\) when \(x = - 6\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the gradient of \({L_1}\).</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 \(y\)-coordinate of P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the equation of \({L_2}\). Give your answer in the form \(ax + by + d = 0\), where \(a\), \(b\) and \(d\) are integers.</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><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="question" style="padding-left: 20px; padding-right: 20px;">
<p>Consider the function \(f(x) = a{x^2} + c\).</p>
<p>Find \(f'(x)\)</p>
<p> </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>Point \({\text{A}}( - 2,\,5)\) lies on the graph of \(y = f(x)\) . The gradient of the tangent to this graph at \({\text{A}}\) is \( - 6\) .</p>
<p>Find the value of \(a\) .</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(c\) .</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Maria owns a cheese factory. The amount of cheese, in kilograms, Maria sells in one week, \(Q\), is given by</p>
<p style="text-align: center;">\(Q = 882 - 45p\),</p>
<p>where \(p\) is the price of a kilogram of cheese in euros (EUR).</p>
</div>
<div class="specification">
<p>Maria earns \((p - 6.80){\text{ EUR}}\) for each kilogram of cheese sold.</p>
</div>
<div class="specification">
<p>To calculate her weekly profit \(W\), in EUR, Maria multiplies the amount of cheese she sells by the amount she earns per kilogram.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down how many kilograms of cheese Maria sells in one week if the price of a kilogram of cheese is 8 EUR.</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 how much Maria earns in one week, from selling cheese, if the price of a kilogram of cheese is 8 EUR.</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 an expression for \(W\) in terms of \(p\).</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 price, \(p\), that will give Maria the highest weekly profit.</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;">Consider the curve \(y = {x^3} + kx\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).</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 curve has a local minimum at the point where \(x = 2\).</span></p>
<p><span>Find the value of \(k\).</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 curve has a local minimum at the point where \(x = 2\).</span></p>
<p><span>Find the value of \(y\) at this local minimum.</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;"><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="question" style="padding-left: 20px; padding-right: 20px;">
<p>The equation of the straight line \({L_1}\) is \(y = 2x - 3.\)</p>
<p>Write down the \(y\)-intercept of \({L_1}\) .</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 gradient of \({L_1}\) .</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>The line \({L_2}\) is parallel to \({L_1}\) and passes through the point \((0,\,\,3)\) .</p>
<p>Write down the equation of \({L_2}\) .</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>The line \({L_3}\) is perpendicular to \({L_1}\) and passes through the point \(( - 2,\,\,6).\)</p>
<p>Write down the gradient of \({L_3}.\)</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of \({L_3}\) . Give your answer in the form \(ax + by + d = 0\) , where \(a\) , \(b\) and \(d\) are integers.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A company sells fruit juices in cylindrical cans, each of which has a volume of \(340\,{\text{c}}{{\text{m}}^3}\). The surface area of a can is \(A\,{\text{c}}{{\text{m}}^2}\) and is given by the formula</p>
<p>\(A = 2\pi {r^2} + \frac{{680}}{r}\) ,</p>
<p>where \(r\) is the radius of the can, in \({\text{cm}}\).</p>
<p>To reduce the cost of a can, its surface area must be minimized.</p>
<p>Find \(\frac{{{\text{d}}A}}{{{\text{d}}r}}\)</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 value of \(r\) that minimizes the surface area of a can.</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;">Consider the function \(f(x) = 2{x^3} - 5{x^2} + 3x + 1\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(f'(x)\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of \(f'(2)\).</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 equation of the tangent to the curve of \(y = f(x)\) at the point \((2{\text{, }}3)\).</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 equation of a curve is \(y = \frac{1}{2}{x^4} - \frac{3}{2}{x^2} + 7\).</p>
</div>
<div class="specification">
<p class="p1">The gradient of the tangent to the curve at a point <span class="s1">P </span>is \( - 10\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).</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 class="p1">Find the coordinates of <span class="s1">P</span><span class="s2">.</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;">The table given below describes the behaviour of <em>f</em> ′(<em>x</em>), the derivative function of <em>f</em> (<em>x</em>), in the domain −4 < <em>x</em> < 2.</span></p>
<p style="text-align: center;"><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State whether<em> f</em> (0) is greater than, less than or equal to <em>f</em> (−2). Give a reason for your answer.</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 P(−2, 3) lies on the graph of <em>f</em> (<em>x</em>).</span></p>
<p><span>Write down the equation of the tangent to the graph of <em>f</em> (<em>x</em>) at the point 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><span>The point P(−2, 3) lies on the graph of <em>f</em> (<em>x</em>).</span></span></p>
<p><span>From the information given about <em>f</em> ′(<em>x</em>), state whether the point (−2, 3) is a maximum, a minimum or neither. Give a reason for your answer.</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 straight line, <em>L</em>, has equation \(2y - 27x - 9 = 0\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the gradient of <em>L</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>Sarah wishes to draw the tangent to \(f (x) = x^4\) parallel to <em>L</em>.</span></p>
<p><span>Write down \(f ′(x)\).</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 <em>x</em> coordinate of the point at which the tangent must be drawn.<br></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c, i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of \(f (x)\) at this point.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c, ii.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the graph of the function \(f(x) = {x^3} + 2{x^2} - 5\).</span></p>
<div style="text-align: center;"><br><img src="images/Schermafbeelding_2014-09-02_om_15.08.15.png" alt></div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Label the local maximum as \({\text{A}}\) on the graph.</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>Label the local minimum as B on the graph.</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 interval where \(f'(x) < 0\).</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>Draw the tangent to the curve at \(x = 1\) on the graph.</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>Write down the equation of the tangent at \(x = 1\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A curve is described by the function \(f (x) = 3x - \frac{2}{{x^2}}\), \(x \ne 0\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(f ' (x) \).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The gradient of the curve at point A is 35.</span></p>
<p><span>Find the <em>x</em>-coordinate of point A.</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;">\[f(x) = \frac{1}{3}{x^3} + 2{x^2} - 12x + 3\]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(f'(x)\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the interval of \(x\) for which \(f(x)\) is decreasing.</span></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;">Let \(f(x) = {x^4}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down \(f'(x)\).</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>Point \({\text{P}}(2,6)\) lies on the graph of \(f\).</span></p>
<p><span>Find the gradient of the tangent to the graph of \(y = f(x)\) at \({\text{P}}\).</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>Point \({\text{P}}(2,16)\) lies on the graph of \(f\).</span></p>
<p><span>Find the equation of the normal to the graph at \({\text{P}}\). Give your answer in the form \(ax + by + d = 0\), where \(a\), \(b\) and \(d\) are integers.</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;">Consider \(f:x \mapsto {x^2} - 4\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(f ′(x)\).</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>Let <em>L</em> be the line with equation <em>y</em> = 3<em>x</em> + 2.</span></p>
<p><span>Write down the gradient of a line parallel to <em>L</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>Let <em>L</em> be the line with equation <em>y</em> = 3<em>x</em> + 2.</span></p>
<p><span>Let P be a point on the curve of <em>f</em>. At P, the tangent to the curve is parallel to <em>L</em>. Find the coordinates of P.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A function \(f\) is given by \(f(x) = 4{x^3} + \frac{3}{{{x^2}}} - 3,{\text{ }}x \ne 0\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the derivative of \(f\).</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 point on the graph of \(f\) at which the gradient of the tangent is equal to 6.</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 figure below shows the graphs of functions \(f_1 (x) = x\) and \(f_2 (x) = 5 - x^2\).</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>(i) Differentiate \(f_1 (x) \) with respect to <em>x</em>.</span></p>
<p><span>(ii) Differentiate \(f_2 (x) \) with respect to <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>Calculate the value of <em>x</em> for which the gradient of the two graphs is the same.</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 the tangent to the <strong>curved</strong> graph for this value of <em>x</em> on the figure, showing clearly the property in part (b).</span></p>
<div class="marks">[1]</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 function is given as \(f(x) = 2{x^3} - 5x + \frac{4}{x} + 3,{\text{ }} - 5 \leqslant x \leqslant 10,{\text{ }}x \ne 0\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the derivative of the function.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find the coordinates of the local minimum point of \(f(x)\) in the given domain.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Consider the function \(f(x) = {x^3} - 3{x^2} + 2x + 2\) . Part of the graph of \(f\) is shown below.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p>Find \(f'(x)\) .</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>There are two points at which the gradient of the graph of \(f\) is \(11\). Find the \(x\)-coordinates of these points.</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 figure shows the graphs of the functions \(f(x) = \frac{1}{4}{x^2} - 2\) and \(g(x) = x\) .</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>Differentiate \(f(x)\) with respect to \(x\) .</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>Differentiate \(g(x)\) with respect to \(x\) .</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 value of \(x\) for which the gradients of the two graphs are the same.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw the tangent to the parabola at the point with the value of \(x\) found in part (c).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A factory produces shirts. The cost, <em>C</em>, in Fijian dollars (FJD), of producing<em> x</em> shirts can be modelled by</p>
<p style="text-align: center;"><em>C</em>(<em>x</em>) = (<em>x</em> − 75)<sup>2</sup> + 100.</p>
</div>
<div class="specification">
<p>The cost of production should not exceed 500 FJD. To do this the factory needs to produce at least 55 shirts and at most <em>s</em> shirts.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the cost of producing 70 shirts.</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 <em>s</em>.</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 number of shirts produced when the cost of production is lowest.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br>