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</div><h2>SL Paper 1</h2><div class="specification">
<p>The vertices A, B, C of an acute angled triangle have position vectors <strong><em>a</em></strong>, <strong><em>b</em></strong>, <strong><em>c </em></strong>with respect to an origin O.</p>
</div>
<div class="specification">
<p>The mid-point of [BC] is denoted by D. The point E lies on [AD] such that \({\text{AE}} = 2{\text{DE}}\).</p>
</div>
<div class="specification">
<p>The perpendiculars from B to [AC] and C to [AB] meet at the point F.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the position vector of E is</p>
<p style="text-align: center;">\(\frac{1}{3}\) (<em><strong>a</strong></em> + <em><strong>b</strong></em> + <em><strong>c</strong></em>).</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain briefly why this result shows that the three medians of a triangle are concurrent.</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>Show that the position vector <strong><em>f </em></strong>of F satisfies the equations</p>
<p style="text-align: center;">(<strong><em>b </em></strong>– <strong><em>f </em></strong>) \( \bullet \) (<strong><em>c </em></strong>– <strong><em>a</em></strong>) = 0</p>
<p style="text-align: center;">(<strong><em>c </em></strong>– <strong><em>f </em></strong>) \( \bullet \) (<strong><em>a </em></strong>– <strong><em>b</em></strong>) = 0.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show, by expanding these equations, that</p>
<p style="text-align: center;">(<strong><em>a</em></strong> – <strong><em>f </em></strong>) \( \bullet \) (<strong><em>c</em></strong> – <strong><em>b</em></strong>) = 0.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain briefly why this result shows that the three altitudes of a triangle are concurrent.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-08-17_om_14.20.30.png" alt="M17/5/FURMA/HP1/ENG/TZ0/12.a.i/M"></p>
<p><strong><em>d</em></strong> = <strong><em>b</em></strong> + \(\frac{1}{2}\)(<strong><em>c</em></strong> – <strong><em>b</em></strong>) = \(\frac{1}{2}\)(<strong><em>b</em></strong> + <strong><em>c</em></strong>) <strong><em>(M1)A1</em></strong></p>
<p><strong><em>e</em></strong> = <strong><em>d</em></strong> + \(\frac{1}{3}\)(<strong><em>a</em></strong> – <strong><em>d</em></strong>) <strong><em>M1</em></strong></p>
<p>= \(\frac{1}{2}\)(<strong><em>b</em></strong> + <strong><em>c</em></strong>) + \(\frac{1}{3}\)(<strong><em>a</em></strong> - \(\frac{1}{2}\)(<strong><em>b</em></strong> + <strong><em>c</em></strong>)) <strong><em>A1</em></strong></p>
<p>= \(\frac{1}{3}\)(<strong><em>a</em></strong> + <strong><em>b</em></strong> + <strong><em>c</em></strong>) <strong><em>AG</em></strong></p>
<p><strong><em>[??? marks]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(because of the symmetry of the result), the other two medians also pass through E. <strong><em>R1</em></strong></p>
<p><strong><em>[??? marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-08-17_om_14.32.54.png" alt="M17/5/FURMA/HP1/ENG/TZ0/12.b.i/M"></p>
<p>\(\overrightarrow {{\text{BF}}} \) = <strong><em>f</em></strong> – <strong><em>b</em></strong> and \(\overrightarrow {{\text{AC}}} \) = <strong><em>c</em></strong> – <strong><em>a</em></strong> <strong><em>A1</em></strong></p>
<p>since FB is perpendicular to AC, (<strong><em>b</em></strong> – <strong><em>f</em></strong>) \( \bullet \) (<strong><em>c</em></strong> – <strong><em>a</em></strong>) = 0 <strong><em>R1AG</em></strong></p>
<p>similarly since FC is perpendicular to BA, (<strong><em>c</em></strong> – <strong><em>f</em></strong>) \( \bullet \) (<strong><em>a</em></strong> – <strong><em>b</em></strong>) = 0 <strong><em>R1AG</em></strong></p>
<p><strong><em>[??? marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>expanding these equations and adding, <strong><em>M1</em></strong></p>
<p><strong><em>b</em></strong> \( \bullet \) <strong><em>c</em></strong> – <strong><em>b</em></strong> \( \bullet \) <strong><em>a</em></strong> – <strong><em>f</em></strong> \( \bullet \) <strong><em>c</em></strong> + <strong><em>f</em></strong> \( \bullet \) <strong><em>a</em></strong> + <strong><em>c</em></strong> \( \bullet \) <strong><em>a</em></strong> – <strong><em>c</em></strong> \( \bullet \) <strong><em>b</em></strong> – <strong><em>f</em></strong> \( \bullet \) <strong><em>a</em></strong> + <strong><em>f</em></strong> \( \bullet \) <strong><em>b</em></strong> = 0 <strong><em>A1</em></strong></p>
<p>– <strong><em>b</em></strong> \( \bullet \) <strong><em>a</em></strong> – <strong><em>f</em></strong> \( \bullet \) <strong><em>c</em></strong> + <strong><em>c</em></strong> \( \bullet \) <strong><em>a</em></strong> + <strong><em>f</em></strong> \( \bullet \) <strong><em>b</em></strong> = 0 <strong><em>A1</em></strong></p>
<p>leading to (<strong><em>a</em></strong> – <strong><em>f</em></strong>) \( \bullet \) (<strong><em>c</em></strong> – <strong><em>b</em></strong>) = 0 <strong><em>AG</em></strong></p>
<p><strong><em>[??? marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>this result shows that AF is perpendicular to BC so that the three altitudes are concurrent (at F) <strong><em>R1</em></strong></p>
<p><strong><em>[??? marks]</em></strong></p>
<div class="question_part_label">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The point \({\rm{T}}(a{t^2},2at)\) lies on the parabola \({y^2} = 4ax\) . Show that the tangent to </span><span style="font-family: times new roman,times; font-size: medium;">the parabola at T has equation \(y = \frac{x}{t} + at\) .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The distinct points \({\rm{P}}(a{p^2}, 2ap)\) and \(Q(a{q^2}, 2aq)\) , where \(p\), \(q \ne 0\) , also lie on </span><span style="font-family: times new roman,times; font-size: medium;">the parabola \({y^2} = 4ax\) . Given that the line (PQ) passes through the focus, show </span><span style="font-family: times new roman,times; font-size: medium;">that</span></p>
<p style="margin-left: 30px;" align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"> (i) \(pq = - 1\) ;</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (ii) the tangents to the parabola at P and Q, intersect on the directrix.</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">\(2y\frac{{{\rm{d}}y}}{{{\rm{d}}x}} = 4a\) <strong><em>M1</em></strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\rm{d}}y}}{{{\rm{d}}x}} = \frac{{2a}}{y} = \frac{1}{t}\) <strong><em>A1</em></strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Accept parametric differentiation.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">the equation of the tangent is</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(y - 2at = \frac{1}{t}(x - a{t^2})\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(y = \frac{x}{t} + at\) <em><strong>AG</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Accept equivalent based on \(y = mx + c\) .</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(i) the focus F is (\(a\), \(0\)) <em><strong>A1</strong></em></span></p>
<p><strong> <span style="font-family: times new roman,times; font-size: medium;">EITHER</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">the gradient of (PQ) is \(\frac{{2a(p - q)}}{{a({p^2} - {q^2})}} = \frac{2}{{p + q}}\) </span><strong><em><span style="font-family: times new roman,times; font-size: medium;">M1A1</span></em></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">the equation of (PQ) is \(y = \frac{{2x}}{{p + q}} + \frac{{2apq}}{{p + q}}\) </span><strong><em><span style="font-family: times new roman,times; font-size: medium;">A1</span></em></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">substitute \(x = a\) , \(y = 0\) <em><strong> M1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(pq = - 1\) <strong><em>AG</em></strong></span></p>
<p><strong> <span style="font-family: times new roman,times; font-size: medium;">OR</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">the condition for PFQ to be collinear is</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> \(\frac{{2a(p - q)}}{{a({p^2} - {q^2})}} = \frac{{2ap}}{{a{p^2} - a}}\) </span><strong><em><span style="font-family: times new roman,times; font-size: medium;">M1A1</span></em></strong></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\(\frac{2}{{p + q}} = \frac{{2p}}{{{p^2} - 1}}\) </span><strong><em><span style="font-family: times new roman,times; font-size: medium;">A1</span></em></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({p^2} - 1 = {p^2} + pq\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(pq = - 1\) <em><strong>AG</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: There are alternative approaches.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) the equations of the tangents at P and Q are</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(y = \frac{x}{p} + ap\) and \(y = \frac{x}{q} + aq\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">the tangents meet where</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\frac{x}{p} + ap = \frac{x}{q} + aq\) <em><strong>M1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(x = apq = - a\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">the equation of the directrix is \(x = - a\) <strong><em>R1</em></strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">so that the tangents meet on the directrix <strong><em>AG</em></strong></span></p>
<p><strong><em><span style="font-family: times new roman,times; font-size: medium;"> </span></em></strong></p>
<p><strong><em><span style="font-family: times new roman,times; font-size: medium;">[8 marks]</span></em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The normal at the point \({\text{T}}(a{t^2},{\text{ }}2at),{\text{ }}t \ne 0\), on the parabola \({y^2} = 4ax\) meets the parabola again at the point \({\text{S}}(a{s^2},{\text{ }}2as)\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \({t^2} + st + 2 = 0\).</p>
<div class="marks">[7]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that \({\rm{S\hat OT}}\) is a right-angle, where O is the origin, determine the possible values of \(t\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{\frac{{{\text{d}}y}}{{{\text{d}}t}}}}{{\frac{{{\text{d}}x}}{{{\text{d}}t}}}}\) <strong><em>(M1)</em></strong></p>
<p>\( = \frac{{2a}}{{2at}} = \frac{1}{t}\) <strong><em>A1</em></strong></p>
<p>the gradient of the normal \( = - t\) <strong><em>(A1)</em></strong></p>
<p>the equation of the normal at T is \(y - 2at = - t(x - a{t^2})\) <strong><em>A1</em></strong></p>
<p>substituting the coordinates of S, <strong><em>M1</em></strong></p>
<p>\(2as - 2at = - t(a{s^2} - a{t^2})\)</p>
<p>\(2a(s - t) = - at(s - t)(s + t)\) <strong><em>A1</em></strong></p>
<p>\(2 = - t(s + t) = - st - {t^2}\) <strong><em>A1</em></strong></p>
<p>\({t^2} + st + 2 = 0\) <strong><em>AG</em></strong></p>
<p><strong><em>[7 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>gradient of \({\text{OT}} = \frac{{2at}}{{a{t^2}}} = \frac{2}{t}\) <strong><em>A1</em></strong></p>
<p>gradient of \({\text{OS}} = \frac{{2as}}{{a{s^2}}} = \frac{2}{s}\) <strong><em>(A1)</em></strong></p>
<p>the condition for perpendicularity is \(\frac{2}{t} \times \frac{2}{s} = - 1\) <strong><em>M1</em></strong></p>
<p>\({t^2} - 4 + 2 = 0\) <strong><em>A1</em></strong></p>
<p>\(t = \pm \sqrt 2 \) <strong><em>A1</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The triangle ABC is isosceles and AB = BC = 5. D is the midpoint of AC and BD = 4.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Find the lengths of the tangents from A, B and D to the circle inscribed in </span><span style="font-family: times new roman,times; font-size: medium;">the triangle ABD.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/bush.png" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">AD \( = 3\) <em><strong> (A1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let the lengths of the tangents be as shown.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Then,</span></p>
<p style="margin-left: 30px;" align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(x + y = 3\)</span></p>
<p style="margin-left: 30px;" align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(y + z = 4\)</span></p>
<p style="margin-left: 30px;" align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(x + z = 5\) <strong><em>(M1)A1</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Solving,</span></p>
<p style="margin-left: 30px;" align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(x = 2\) , \(y = 1\) , \(z = 3\) <strong><em>A1A1A1</em></strong></span></p>
<p><strong><em><span style="font-family: times new roman,times; font-size: medium;">[6 marks]</span></em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>Given that the tangents at the points P and Q on the parabola \({y^2} = 4ax\) are perpendicular, find the locus of the midpoint of PQ.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><strong>EITHER</strong></p>
<p>attempt to differentiate <em><strong>(M1)</strong></em></p>
<p>let \(y = 2at \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}t}} = 2a\) and \(x = a{t^2} \Rightarrow \frac{{{\text{d}}x}}{{{\text{d}}t}} = 2at\) <em><strong>A1</strong></em></p>
<p>hence \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{{\text{d}}y}}{{{\text{d}}t}} \times \frac{{{\text{d}}t}}{{{\text{d}}x}} = \frac{{2a}}{{2at}} = \frac{1}{t}\) <em><strong>A1</strong></em></p>
<p>let P have coordinates \(\left( {at_1^2,\,2a{t_1}} \right)\) and Q have coordinates \(\left( {at_2^2,\,2a{t_2}} \right)\) <em><strong> (M1)</strong></em></p>
<p>therefore gradient of tangent at P is \(\frac{1}{{{t_1}}}\) and gradient of tangent at Q is \(\frac{1}{{{t_2}}}\) <em><strong>A1</strong></em></p>
<p>since these tangents are perpendicular \(\frac{1}{{{t_1}}} \times \frac{1}{{{t_2}}} = - 1 \Rightarrow {t_1}{t_2} = - 1\) <em><strong>A1</strong></em></p>
<p>mid-point of PQ is \(\left( {\frac{{a\left( {t_1^2 + t_2^2} \right)}}{2},\,\,a\left( {{t_1} + {t_2}} \right)} \right)\) <em><strong>A1</strong></em></p>
<p>\({y^2} = {a^2}\left( {t_1^2 + 2{t_1}{t_2} + t_2^2} \right)\) <em><strong>M1</strong></em></p>
<p>\({y^2} = {a^2}\left( {\frac{{2x}}{a} - 2} \right)\,\,\,\left( { \Rightarrow {y^2} = 2ax - 2{a^2}} \right)\) <em><strong>A1</strong></em></p>
<p><strong>OR</strong></p>
<p>attempt to differentiate <em><strong> (M1)</strong></em></p>
<p>\(2y\frac{{{\text{d}}y}}{{{\text{d}}x}} = 4a\) <em><strong>A1</strong></em></p>
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{2a}}{y}\)</p>
<p>let coordinates of P be \(\left( {{x_1},\,{y_1}} \right)\) and the coordinates of Q be \(\left( {{x_2},\,{y_2}} \right)\) <em><strong> (M1)</strong></em></p>
<p>coordinates of midpoint of PQ are \(\left( {\frac{{{x_1} + {x_2}}}{2},\,\,\frac{{{y_1} + {y_2}}}{2}} \right)\) <em><strong>M1</strong></em></p>
<p>if the tangents are perpendicular \(\frac{{2a}}{{{y_1}}} \times \frac{{2a}}{{{y_2}}} = - 1\) <em><strong>A1</strong></em></p>
<p>\( \Rightarrow {y_1}{y_2} = - 4{a^2}\)</p>
<p>\(y_1^2 + y_2^2 = 4a\left( {{x_1} + {x_2}} \right)\) <em><strong>A1</strong></em></p>
<p>\(\frac{{y_1^2 + 2{y_1}{y_2} + y_2^2}}{4} = \frac{{4a\left( {{x_1} + {x_2}} \right) + 2{y_1}{y_2}}}{4}\) <em><strong>M1</strong></em></p>
<p>\(\left( {\frac{{{y_1} + {y_2}}}{2}} \right) = 2a\frac{{{x_1} + {x_2}}}{2} - \frac{{8{a^2}}}{4}\) <em><strong>A1</strong></em></p>
<p>hence equation of locus is \({y^2} = 2ax - 2{a^2}\) <em><strong>A1</strong></em></p>
<p><em><strong>[9 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
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<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{ABCDEF}}\) is a hexagon. A circle lies inside the hexagon and touches each of the six sides.</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;">Show that \({\text{AB}} + {\text{CD}} + {\text{EF}} = {\text{BC}} + {\text{DE}} + {\text{FA}}\).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/hex.jpg" alt> <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the lengths of the two tangents from a point to a circle are equal <strong><em>(R1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so that</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{AG}} = {\text{LA}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{GB}} = {\text{BH}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{CI}} = {\text{HC}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{ID}} = {\text{DJ}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{EK}} = {\text{JE}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{KF}} = {\text{ FL}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">adding,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{(AG}} + {\text{GB)}} + {\text{(CI}} + {\text{ID)}} + {\text{(EK}} + {\text{KF)}} = {\text{(BH}} + {\text{HC)}} + {\text{(DJ}} + {\text{JE)}} + {\text{(FL}} + {\text{LA)}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{AB}} + {\text{CD}} + {\text{EF}} = {\text{BC}} + {\text{DE}} + {\text{FA}}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
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<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p class="p1">Consider the curve C given by \(y = {x^3}\).</p>
<p class="p1">The tangent at a point <span class="s1">P </span>on \(C\) meets the curve again at <span class="s1">Q</span>. The tangent at <span class="s1">Q </span>meets the curve again at <span class="s1">R</span>. Denote the \(x\)-coordinates of \({\text{P, Q}}\) and <span class="s1">R</span>, by \({x_1},{\text{ }}{x_2}\) and \({x_3}\) respectively where \({x_1} \ne 0\). Show that, \({x_1},{\text{ }}{x_2},{\text{ }}{x_3}\) form the first three elements of a divergent geometric sequence.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1">attempt to find the equation of the tangent at P <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\(y - x_1^3 = 3x_1^2(x - {x_1})\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">the tangent meets \(C\) when</p>
<p class="p2"><span class="Apple-converted-space">\({x^3} - x_1^3 = 3x_1^2(x - {x_1})\) </span><strong><em>M1</em></strong></p>
<p class="p2">attempt to solve the cubic <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p2">the \(x\)<span class="s2">-coordinate of Q </span>satisfies</p>
<p class="p2"><span class="Apple-converted-space">\({x^2} + x{x_1} - 2x_1^2 = 0\) </span><strong><em>A1</em></strong></p>
<p class="p2">hence \({x_2} = - 2{x_1}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2">hence \({x_3} = 4{x_1}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2">hence \({x_1},{\text{ }}{x_2},{\text{ }}{x_3}\) form the first three terms of a geometric sequence with common ratio \( - 2\) so the sequence is divergent <span class="Apple-converted-space"> </span><strong><em>R1AG</em></strong></p>
<p class="p3"> </p>
<p class="p2"><strong>Note: <span class="Apple-converted-space"> </span></strong>Final <strong><em>R1 </em></strong>is not dependent on final 3 <strong><em>A1</em></strong>s providing they form a geometric sequence.</p>
<p class="p3"> </p>
<p class="p2"><strong><em>Total [8 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">This question caused a problem for many candidates and only a small number of fully correct answers were seen. Most candidates were able to find a generalised equation of a tangent, but were then unable to see what could be replaced in order to find a quadratic equation that could be solved.</p>
</div>
<br><hr><br><div class="question">
<p class="p1">The points <span class="s1">P, Q </span>and <span class="s1">R</span>, lie on the sides <span class="s1">[AB], [AC] </span>and <span class="s1">[BC]</span>, respectively, of the triangle <span class="s1">ABC</span>. The lines <span class="s1">(AR), (BQ) </span>and <span class="s1">(CP) </span>are concurrent.</p>
<p class="p1">Use Ceva’s theorem to prove that <span class="s1">[PQ] </span>is parallel to <span class="s1">[BC] </span>if and only if <span class="s1">R </span>is the midpoint of <span class="s1">[BC]</span>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1">suppose R is the midpoint of BC <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>The first mark is for initiating a relevant discussion for “if” or “only if” by Ceva’s theorem.</p>
<p class="p2"> </p>
<p class="p3"><span class="Apple-converted-space">\(\frac{{{\text{AP}}}}{{{\text{PB}}}} \times \frac{{{\text{BR}}}}{{{\text{RC}}}} \times \frac{{{\text{CQ}}}}{{{\text{QA}}}} = 1\) </span><strong><em>A1</em></strong></p>
<p class="p3"><span class="s2">\( \Rightarrow \frac{{{\text{AP}}}}{{{\text{PB}}}} = \frac{{{\text{AQ}}}}{{{\text{QC}}}}\) </span>or equivalent <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p4"><span class="Apple-converted-space">\( \Rightarrow \frac{{{\text{PB}}}}{{{\text{AP}}}} + 1 = \frac{{{\text{QC}}}}{{{\text{AQ}}}} + 1\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p4">\( \Rightarrow \frac{{{\text{AP}} + {\text{PB}}}}{{{\text{AP}}}} = \frac{{{\text{AQ}} + {\text{QC}}}}{{{\text{AQ}}}}\)</p>
<p class="p4"><span class="Apple-converted-space">\( \Rightarrow \frac{{{\text{AB}}}}{{{\text{AP}}}} = \frac{{{\text{AC}}}}{{{\text{AQ}}}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p3"><span class="s3">\( \Rightarrow \) triangles APQ and ABC </span>are similar with common base angles <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">so PQ is parallel to BC <span class="Apple-converted-space"> </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p3">statement of the converse <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p3">the argument is reversible <span class="Apple-converted-space"> </span><strong><em>R1AG</em></strong></p>
<p class="p5"><strong><em>[8 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">This was again a question which a significant number of students were unable to start. For those who did start only a small number understood the significance of “if and only if” meaning that wholly correct answers were not often seen.</p>
</div>
<br><hr><br><div class="specification">
<p class="p1">The points <span class="s1">A, B </span>have coordinates \(( - 3,{\text{ }}0)\), \((5,{\text{ }}0)\) respectively. Consider the Apollonius circle \(C\) which is the locus of point <span class="s1">P </span><span class="s2">where</span></p>
<p class="p2">\[\frac{{{\text{AP}}}}{{{\text{BP}}}} = k{\text{ for }}k \ne 1.\]</p>
<p class="p1">Given that the centre of \(C\) has coordinates \((13,{\text{ }}0)\), find</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>the value of \(k\)<span class="s1">;</span></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>the radius of \(C\)<span class="s1">;</span></p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>the \(x\)-intercepts of \(C\).</p>
<div class="marks">[11]</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">Let </span><span class="s2">M </span>be any point on \(C\) and <span class="s2">N </span>be the \(x\)-intercept of \(C\) between <span class="s2">A </span>and <span class="s2">B</span>.</p>
<p class="p1">Prove that \({\rm{A\hat MN}} = {\rm{N\hat MB}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1">(i) <span class="Apple-converted-space"> </span>let \((x,{\text{ }}y)\) </span>be a point on \(C\)</p>
<p class="p2">then \({(x + 3)^2} + {y^2} = {k^2}\left( {{{(x - 5)}^2} + {y^2}} \right)\) <span class="Apple-converted-space"> </span><span class="s2"><strong><em>M1A1A1</em></strong></span></p>
<p class="p3"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong>for form of an Apollonius circle, <strong><em>A1 </em></strong>for each side.</p>
<p class="p3"> </p>
<p class="p1">rearrange, for example,</p>
<p class="p1"><span class="Apple-converted-space">\(({k^2} - 1){x^2} - (10{k^2} + 6)x + ({k^2} - 1){y^2} + 25{k^2} - 9 = 0\) </span><strong><em>A1</em></strong></p>
<p class="p2"><span class="s2">equate the \(x\)</span>-coordinate of the centre as given by this equation to 13<span class="s2">:</span></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{5{k^2} + 3}}{{{k^2} - 1}} = 13\) </span><strong><em>M1A1</em></strong></p>
<p class="p1">obtain \({k^2} = 2 \Rightarrow k = \sqrt 2 \) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span><strong>METHOD 1</strong></p>
<p class="p2"><span class="s2">with this value of \(k\)</span>, the equation can be reduced to the form</p>
<p class="p2"><span class="Apple-converted-space">\({(x - 13)^2} + {y^2} = 128\) </span><span class="s2"><strong><em>M1A1</em></strong></span></p>
<p class="p1">obtain the radius \(\sqrt {128} {\text{ }}\left( { = 8\sqrt 2 } \right)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1"><span class="s1">assuming N </span>is the \(x\)-intercept of \(C\) <span class="s1">between A and B</span></p>
<p class="p2"><span class="Apple-converted-space">\(\frac{{{\text{AB}}}}{{{\text{BN}}}} = \frac{{16 - r}}{{r - 8}} = \sqrt 2 \) </span><span class="s2"><strong><em>M1A1</em></strong></span></p>
<p class="p4"><span class="Apple-converted-space">\( \Rightarrow r = 8\sqrt 2 \) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p3"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Accept answers given in terms of \(k\), if no value of \(k\) found in (a)(i).</p>
<p class="p3"> </p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>\(x\)-intercepts are \(13 \pm 8\sqrt 2 \) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[11 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1">because N </span>lies on the circle it satisfies the Apollonius property</p>
<p class="p1">hence \({\text{AN}} = \sqrt 2 {\text{NB}}\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">but as \({\text{AM}} = \sqrt 2 {\text{MB}}\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">by the converse to the angle-bisector theorem <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\({\rm{A\hat MN}} = {\rm{N\hat MB}}\) </span><span class="s2"><strong><em>AG</em></strong></span></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">This question was the first one on the paper to cause a significant problem for the majority of candidates. Many were unable to start and a small number were unable to successfully deal with the algebraic manipulation required from the method they had embarked upon. For those who were successful at part (a), part (b) was often not fully correct, again due to the degree of formality required from the command term “prove”.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">This question was the first one on the paper to cause a significant problem for the majority of candidates. Many were unable to start and a small number were unable to successfully deal with the algebraic manipulation required from the method they had embarked upon. For those who were successful at part (a), part (b) was often not fully correct, again due to the degree of formality required from the command term “prove”.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The point \({\rm{P}}(x,y)\) moves in such a way that its distance from the point (\(1\) , \(0\)) is three </span><span style="font-family: times new roman,times; font-size: medium;">times its distance from the point (\( -1\) , \(0\)) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the equation of the locus of P.</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Show that this equation represents a circle and state its radius and the coordinates </span><span style="font-family: times new roman,times; font-size: medium;">of its centre.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">We are given that</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(\sqrt {{{(x - 1)}^2} + {y^2}} = 3\sqrt {{{(x + 1)}^2} + {y^2}} \) <strong><em> M1A1</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\({x^2} - 2x + 1 + {y^2} = 9({x^2} + 2x + 1 + {y^2})\) <strong><em>A1</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(8{x^2} + 8{y^2} + 20x + 8 = 0\) <em><strong>A1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Rewrite the equation in the form</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\({\left( {x + \frac{5}{4}} \right)^2} + {y^2} = - 1 + \frac{{25}}{{16}} = \frac{9}{{16}}\) <strong><em>M1A1</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">This represents a circle with radius \( = \frac{3}{4}\) ; centre \(\left( { - \frac{5}{4},0} \right)\) </span><strong><em><span style="font-family: times new roman,times; font-size: medium;">A1A1</span></em></strong></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Allow <em><strong>FT</strong></em> from the line above.</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<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 parabola \(P\) has equation \({y^2} = 4ax\). The distinct points \({\text{U}}\left( {a{u^2},{\text{ }}2au} \right)\) and \({\text{V}}\left( {a{v^2},{\text{ }}2av} \right)\) lie on \(P\), where \(u,{\text{ }}v \ne 0\). Given that \({\rm{U\hat OV}}\) is </span><span style="font-family: 'times new roman', times; font-size: medium;">a right angle, where \({\text{O}}\) denotes the origin,</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">(a) show that \(v = - \frac{4}{\mu }\);</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">(b) find expressions for the coordinates of \({\text{W}}\), the midpoint of \([{\text{UV}}]\), in terms of \(a\) and \(u\);</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">(c) show that the locus of \({\text{W}}\), as \(u\) varies, is the parabola \({P'}\) with equation \({y^2} = 2ax - 8{a^2}\);</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">(d) determine the coordinates of the vertex of \({P'}\).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) gradient of \({\text{OU}} = \frac{{2au}}{{a{u^2}}} = \frac{2}{u}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">gradient of \({\text{OV}} = \frac{{2av}}{{a{v^2}}} = \frac{2}{v}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">since the lines are perpendicular,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{2}{u} \times \frac{2}{v} = - 1\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so \(v = - \frac{4}{u}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">(b) coordinates of \({\text{W}}\) are \(\left( {\frac{{a({u^2} + {v^2})}}{2},{\text{ }}\frac{{2a(u + v)}}{2}} \right)\) <em><strong>M1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \left( {\frac{a}{2}\left( {{u^2} + \frac{{16}}{{{u^2}}}} \right),{\text{ }}a\left( {u - \frac{4}{u}} \right)} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) putting</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \frac{a}{2}\left( {{u^2} + \frac{{16}}{{{u^2}}}} \right);{\text{ }}y = a\left( {u - \frac{4}{u}} \right)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">it follows that</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({y^2} = {a^2}\left( {{u^2} + \frac{{16}}{{{u^2}}} - 8} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 2ax - 8{a^2}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Accept verification.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(d) since \({y^2} = 2a(x - 4a)\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the vertex is at \((4a,{\text{ }}0)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Prove the internal angle bisector theorem, namely that the internal bisector of an </span><span style="font-family: times new roman,times; font-size: medium;">angle of a triangle divides the side opposite the angle into segments proportional </span><span style="font-family: times new roman,times; font-size: medium;">to the sides adjacent to the angle.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The bisector of the exterior angle \(\widehat A\) of the triangle ABC meets (BC) at P. </span><span style="font-family: times new roman,times; font-size: medium;">The bisector of the interior angle \(\widehat B\) meets [AC] at Q. Given that (PQ) meets </span><span style="font-family: times new roman,times; font-size: medium;">[AB] at R, use Menelaus’ theorem to prove that (CR) bisects the angle \({\rm{A}}\widehat {\rm{C}}{\rm{B}}\) .</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong><span style="font-family: times new roman,times; font-size: medium;">EITHER</span></strong></p>
<p><br><img src="images/bella.png" alt></p>
<p><span style="font-family: times new roman,times; font-size: medium;">let [AD] bisect A, draw a line through C parallel to (AD) meeting (AB) at E <strong><em>M1</em></strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">then \({\rm{B}}\widehat {\rm{A}}{\rm{D}} = {\rm{A}}\widehat {\rm{E}}{\rm{C}}\) and \({\rm{D}}\widehat {\rm{A}}{\rm{C}} = {\rm{A}}\widehat {\rm{C}}{\rm{E}}\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">since \({\rm{B}}\widehat {\rm{A}}{\rm{D}} = {\rm{D}}\widehat {\rm{A}}{\rm{C}}\) it follows that \({\rm{A}}\widehat {\rm{E}}{\rm{C}} = {\rm{A}}\widehat {\rm{C}}{\rm{E}}\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">triangle AEC is therefore isosceles and \({\rm{AE}} = {\rm{AC}}\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">since triangles BAD and BEC are similar</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\rm{BD}}}}{{{\rm{DC}}}} = \frac{{{\rm{AB}}}}{{{\rm{AE}}}} = \frac{{{\rm{AB}}}}{{{\rm{AC}}}}\) <strong><em>M1A1</em></strong></span></p>
<p><strong> <span style="font-family: times new roman,times; font-size: medium;">OR</span></strong></p>
<p><br><img src="images/alice2.png" alt></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\rm{AB}}}}{{\sin \beta }} = \frac{{{\rm{BD}}}}{{\sin \alpha }}\) <em><strong>M1A1</strong></em></span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\(\frac{{{\rm{AC}}}}{{\sin (180 - \beta )}} = \frac{{{\rm{DC}}}}{{\sin \alpha }}\) </span><strong><em><span style="font-family: times new roman,times; font-size: medium;">M1A1</span></em></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\sin \beta = \sin (180 - \beta )\) <em><strong>R1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> \( \Rightarrow \frac{{{\rm{AB}}}}{{{\rm{BD}}}} = \frac{{{\rm{AC}}}}{{{\rm{DC}}}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( \Rightarrow \frac{{{\rm{BD}}}}{{{\rm{DC}}}} = \frac{{{\rm{AB}}}}{{{\rm{AC}}}}\) <strong><em>A1</em></strong></span></p>
<p><strong><em><span style="font-family: times new roman,times; font-size: medium;"> [6 marks]</span></em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/half.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">using the angle bisector theorem, <strong><em>M1</em></strong></span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\(\frac{{{\rm{AQ}}}}{{{\rm{QC}}}} = \frac{{{\rm{AB}}}}{{{\rm{BC}}}}\) and \(\frac{{{\rm{BP}}}}{{{\rm{PC}}}} = \frac{{{\rm{AB}}}}{{{\rm{BC}}}}\) </span><strong><em><span style="font-family: times new roman,times; font-size: medium;">A1</span></em></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">using Menelaus’ theorem with (PR) as transversal to triangle ABC <em><strong>M1</strong></em></span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\(\frac{{{\rm{BR}}}}{{{\rm{AR}}}} \times \frac{{{\rm{AQ}}}}{{{\rm{QC}}}} \times \frac{{{\rm{PC}}}}{{{\rm{BP}}}} = ( - )1\) </span><strong><em><span style="font-family: times new roman,times; font-size: medium;">A1</span></em></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">substituting the above results, <em><strong>M1</strong></em></span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\(\frac{{{\rm{BR}}}}{{{\rm{AR}}}} \times \frac{{{\rm{AB}}}}{{{\rm{BC}}}} \times \frac{{{\rm{AC}}}}{{{\rm{AB}}}} = ( - )1\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">giving</span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\(\frac{{{\rm{BR}}}}{{{\rm{AR}}}} = \frac{{{\rm{BC}}}}{{{\rm{AC}}}}\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">[CR] therefore bisects angle C by (the converse to) the angle bisector </span><span style="font-family: times new roman,times; font-size: medium;">theorem <strong><em>R1AG</em></strong></span></p>
<p><strong><em><span style="font-family: times new roman,times; font-size: medium;"> [8 marks]</span></em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Triangle ABC has points D, E and F on sides [BC], [CA] and [AB] respectively; </span><span style="font-family: times new roman,times; font-size: medium;">[AD], [BE] and [CF] intersect at the point P. If 3BD = 2DC and CE = 4EA , </span><span style="font-family: times new roman,times; font-size: medium;">calculate the ratios</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">AF : FB .</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 style="font-family: times new roman,times; font-size: medium;">AP : PD</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="images/south.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">using Ceva's theorem, </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\rm{BD}}}}{{{\rm{DC}}}} \times \frac{{{\rm{CE}}}}{{{\rm{EA}}}} \times \frac{{{\rm{AF}}}}{{{\rm{FB}}}} = 1\) <em><strong>M1A1 </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\frac{2}{3} \times \frac{4}{1} \times \frac{{{\rm{AF}}}}{{{\rm{FB}}}} = 1\) <strong><em>A1</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\rm{AF}}}}{{{\rm{FB}}}} = \frac{3}{8}\) or AF : FB \( = 3 : 8\) <strong><em>A1 </em></strong></span></p>
<p><strong><em><span style="font-family: times new roman,times; font-size: medium;">[4 marks] </span></em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">using Menelaus' theorem in triangle ACD with BPE as transversal </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\rm{AE}}}}{{{\rm{EC}}}} \times \frac{{{\rm{CB}}}}{{{\rm{BD}}}} \times \frac{{{\rm{DP}}}}{{{\rm{PA}}}} = - 1\) <strong><em>M1A1</em></strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\frac{1}{4} \times - \frac{5}{2} \times \frac{{{\rm{DP}}}}{{{\rm{PA}}}} = - 1\) <strong><em>A1</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\rm{DP}}}}{{{\rm{PA}}}} = \frac{8}{5}\) or AP : PD = 5 : 8 <em><strong>A1</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 marks] </span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">This proved difficult for many candidates and often the ratios and negative signs were "blurred". </span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">This proved difficult for many candidates and often the ratios and negative signs were "blurred". </span></p>
<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;"><img style="display: block; margin-left: auto; margin-right: auto;" src="images/energy.png" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The figure shows a circle C<sub>1</sub> with centre O and diameter [PQ] and a circle C<sub>2</sub> which </span><span style="font-family: times new roman,times; font-size: medium;">intersects (PQ) at the points R and S. T is one point of intersection of the two circles </span><span style="font-family: times new roman,times; font-size: medium;">and (OT) is a tangent to C<sub>2</sub> .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that \(\frac{{{\rm{OR}}}}{{{\rm{OT}}}} = \frac{{{\rm{OT}}}}{{{\rm{OS}}}}\) .</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 style="font-family: times new roman,times; font-size: medium;">(i) Show that \({\rm{PR}} - {\rm{RQ}} = 2{\rm{OR}}\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Show that \(\frac{{{\rm{PR}} - {\rm{RQ}}}}{{{\rm{PR}} + {\rm{RQ}}}} = \frac{{{\rm{PS}} - {\rm{SQ}}}}{{{\rm{PS}} + {\rm{SQ}}}}\) .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">by the tangent – secant theorem, <strong><em>M1</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({\rm{O}}{{\rm{T}}^2} = {\rm{OR}} \bullet {\rm{OS}}\) <strong><em>A1</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">so that \(\frac{{{\rm{OR}}}}{{{\rm{OT}}}} = \frac{{{\rm{OT}}}}{{{\rm{OS}}}}\) <strong><em>AG </em></strong></span></p>
<p><strong><em><span style="font-family: times new roman,times; font-size: medium;">[2 marks] </span></em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(i) \({\rm{PR}} - {\rm{RQ}} = {\rm{PO}} + {\rm{OR}} - ({\rm{OQ}} - {\rm{OR}})\) <strong><em>A1</em> </strong></span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\( = 2{\rm{OR}}\) </span><em><span style="font-family: times new roman,times; font-size: medium;"><strong>AG</strong> </span></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) attempt to continue the process set up in (b)(i) <em><strong>(M1) </strong></em></span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\({\rm{PR + RQ}} = {\rm{PO}} + {\rm{OR + OQ}} - {\rm{OR}} = 2{\rm{OT}}\) </span><em><span style="font-family: times new roman,times; font-size: medium;"><strong>A1</strong> </span></em></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\({\rm{PS}} - {\rm{SQ}} = {\rm{PQ}} + {\rm{QS}} - {\rm{SQ}} = 2{\rm{OT}}\) </span><strong><span style="font-family: times new roman,times; font-size: medium;"><em>A1</em> </span></strong></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\({\rm{PS + SQ}} = {\rm{PO}} + {\rm{OS}} - {\rm{OQ}} = 2{\rm{OS}}\) </span><em><span style="font-family: times new roman,times; font-size: medium;"><strong>A1</strong> </span></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">it now follows that </span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\(\frac{{{\rm{PR}} - {\rm{RQ}}}}{{{\rm{PR}} + {\rm{RQ}}}} = \frac{{{\rm{OR}}}}{{{\rm{OT}}}}\) </span><span style="font-family: times new roman,times; font-size: medium;">and \(\frac{{{\rm{PS}} - {\rm{SQ}}}}{{{\rm{PS}} + {\rm{SQ}}}} = \frac{{{\rm{OT}}}}{{{\rm{OS}}}}\) so using the result in part (a) <strong><em>R1</em> </strong></span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\(\frac{{{\rm{PR}} - {\rm{RQ}}}}{{{\rm{PR}} + {\rm{RQ}}}} = \frac{{{\rm{PS}} - {\rm{SQ}}}}{{{\rm{PS}} + {\rm{SQ}}}}\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">AG </span></strong></em></p>
<p> </p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> </span></strong></em></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[6 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates solved (a) correctly although some used similar triangles instead of the more obvious tangent-secant theorem. </span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Although (b) and then (c) were fairly well signposted, many candidates were unable to cope with the required algebra. </span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">A triangle \(T\) has sides of length \(3\), \(4\) and \(5\).</span></p>
<p style="margin-left: 30px;" align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"> (i) Find the radius of the circumscribed circle of \(T\) .</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (ii) Find the radius of the inscribed circle of \(T\) .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">A triangle \(U\) has sides of length \(4\), \(5\) and \(7\).</span></p>
<p style="margin-left: 30px;" align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"> (i) Show that the orthocentre, H, of \(U\) lies outside the triangle.</span></p>
<p style="margin-left: 30px;" align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"> (ii) Show that the foot of the perpendicular from H to the longest side divides </span><span style="font-family: times new roman,times; font-size: medium;">it in the ratio \(29:20\).</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(i) \(T\) is a right angled triangle \( \Rightarrow \) the hypotenuse is a diameter <strong><em>(M1)</em></strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">circumradius \( = 2.5\) <em><strong>A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em><strong> </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) diagram seen with some sensible unknown(s) given <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/windmill.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">need to solve \(3 - r + 4 - r = 5\) (or equivalent) <em><strong>M1A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(r = 1\) <em><strong>A1 </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em><strong> </strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[6 marks] </span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(i) recognition that \({7^2} > {4^2} + {5^2}\) <strong><em>M1 </em></strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">therefore one of the angles is obtuse <em><strong>R1 </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">so the orthocentre, H, of \(U\) lies outside of the triangle <strong><em>AG </em></strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong><em> </em></strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) foot of perpendicular from H to longest side is the foot of the perpendicular from A to the longest side <strong><em>(R1) </em></strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/lawrue.png" alt></span></p>
<p><strong><span style="font-family: times new roman,times; font-size: medium;">EITHER </span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to solve \({4^2} - {x^2} = {5^2} - {(7 - x)^2}\) or \({4^2} - {(7 - y)^2} = {5^2} - {y^2}\) <strong><em>M1A1</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">obtain \(x = \frac{{20}}{7}\) or \(y = \frac{{29}}{7}\) <strong><em> A1</em> </strong></span></p>
<p><strong><span style="font-family: times new roman,times; font-size: medium;">OR </span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">if \(\hat B\) is the smallest angle </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\cos \hat B = \frac{{25 + 49 - 16}}{{2 \times 5 \times 7}}\) <strong><em>M1</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( = \frac{{58}}{{70}} = \frac{{29}}{{35}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(y = 5 \times \frac{{29}}{{35}} = \frac{{29}}{7}\) <strong><em>A1</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(x = 7 - \frac{{29}}{7} = \frac{{20}}{7}\) <strong><em>A1</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>THEN</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">ratio \(29:20\) (accept \(20:29\)) <em><strong> AG</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Accept the use of Stewart’s theorem. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><strong><span style="font-family: times new roman,times; font-size: medium;"><em>[6 marks]</em> </span></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A few fully correct answers were seen to this question, but many candidates were unable to make much progress after part a) (i) and a significant minority made no attempt at all. A few fully correct answers were seen to part a) (ii) and part b) (i). In both part a) (ii) and part b) (ii) a majority of candidates were unable to draw a meaningful diagram to enable them to start the question.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A few fully correct answers were seen to this question, but many candidates were unable to make much progress after part a) (i) and a significant minority made no attempt at all. A few fully correct answers were seen to part a) (ii) and part b) (i). In both part a) (ii) and part b) (ii) a majority of candidates were unable to draw a meaningful diagram to enable them to start the question.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1"><span class="s1">A wheel of radius \(r\) </span>rolls, without slipping, along a straight path with the plane of the wheel remaining vertical. A point \({\text{A}}\) on the circumference of the wheel is initially at \({\text{O}}\)<span class="s1">. When the wheel is rolled, the radius rotates through an angle of \(\theta \) </span>and the point of contact is now at \({\text{B}}\), where the length of the arc \({\text{AB}}\) is equal to the distance \({\text{OB}}\)<span class="s1">. This is shown in the following diagram.</span></p>
<p class="p2" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-15_om_09.43.46.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Find the coordinates of \({\text{A}}\) </span>in terms of \(r\) and \(\theta \).</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"><span class="s1">As the wheel rolls, the point A </span>traces out a curve. Show that the gradient of this curve is \(\cot \left( {\frac{1}{2}\theta } \right)\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the tangent to the curve when \(\theta = \frac{\pi }{3}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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" alt></p>
<p>\({\text{OX}} = {\text{OB}} - {\text{XB}} = r\theta - r\sin \theta = x\) <em>(</em><strong><em>M1)A1</em></strong></p>
<p>\({\text{OY}} = {\text{ZB}} - {\text{ZC}} = r - r\cos \theta = y\) <strong><em>A1</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{{\text{d}}x}}{{{\text{d}}\theta }} = r - r\cos \theta \) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\(\frac{{{\text{d}}y}}{{{\text{d}}\theta }} = r\sin \theta \) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{r\sin \theta }}{{r - r\cos \theta }}\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\( = \frac{{2\sin \frac{\theta }{2}\cos \frac{\theta }{2}}}{{2{{\sin }^2}\frac{\theta }{2}}}\) <span class="Apple-converted-space"> </span><strong><em>M1A1A1</em></strong></p>
<p class="p1">\( = \frac{{\cos \frac{\theta }{2}}}{{\sin \frac{\theta }{2}}}\)</p>
<p class="p1">\( = \cot \frac{\theta }{2}\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>when \(\theta = \frac{\pi }{3}\), gradient \( = \sqrt 3 \) <strong><em>A1</em></strong></p>
<p>\(x = \frac{\pi }{3}r - r\frac{{\sqrt 3 }}{2},{\text{ }}y = r - \frac{r}{2} = \frac{r}{2}\) <strong><em>A1</em></strong></p>
<p>\(y - \frac{r}{2} = \sqrt 3 \left( {x - \frac{\pi }{3}r + r\frac{{\sqrt 3 }}{2}} \right)\;\;\;{\text{or}}\;\;\;y = \sqrt 3 x + 2r - \frac{{\pi r}}{{\sqrt 3 }}\) <strong><em>A1</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Many candidates were unable to find the coordinates of the point A which made (b) inaccessible. Many candidates reached the halfway point in (b) but were then unable to use the half angle formulae to obtain the required result. Many of the candidates who failed to solve (b) picked up the A1 in (c) for finding the gradient.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Many candidates were unable to find the coordinates of the point A which made (b) inaccessible. Many candidates reached the halfway point in (b) but were then unable to use the half angle formulae to obtain the required result. Many of the candidates who failed to solve (b) picked up the A1 in (c) for finding the gradient.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Many candidates were unable to find the coordinates of the point A which made (b) inaccessible. Many candidates reached the halfway point in (b) but were then unable to use the half angle formulae to obtain the required result. Many of the candidates who failed to solve (b) picked up the A1 in (c) for finding the gradient.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) The function \(g\) is defined by \(g(x,{\text{ }}y) = {x^2} + {y^2} + dx + ey + f\) and the circle \({C_1}\) has equation \(g(x, y) = 0\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Show that the centre of \({C_1}\) has coordinates \(\left( { - \frac{d}{2}, - \frac{e}{2}} \right)\) and the radius of \({C_1}\) is \(\sqrt {\frac{{{d^2}}}{4} + \frac{{{e^2}}}{4} - f} \).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) The point \({\text{P}}(a, b)\) lies outside \({C_1}\). Show that the length of the tangents from \({\text{P}}\) to \({C_1}\) is equal to \(\sqrt {g(a,{\text{ }}b)} \).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) The circle \({C_2}\) has equation \({x^2} + {y^2} - 6x - 2y + 6 = 0\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The line \(y = mx\) meets \({C_2}\) at the points </span><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{R}}\) and \({\text{S}}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Determine the quadratic equation whose roots are the <em>x</em>-coordinates of </span><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{R}}\) and \({\text{S}}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) <strong>Hence</strong>, given that \(L\) denotes the length of the tangents from the origin </span><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{O}}\) to \({C_2}\), show that \({\text{OR}} \times {\text{OS}} = {L^2}\).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) completing the square,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\left( {x + \frac{d}{2}} \right)^2} + {\left( {y + \frac{e}{2}} \right)^2} - \frac{{{d^2}}}{4} - \frac{{{e^2}}}{4} + f = 0\) <strong><em>M1A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">whence the centre \({\text{C}}\) is the point \(\left( { - \frac{d}{2}, - \frac{e}{2}} \right)\) and the radius is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sqrt {\frac{{{d^2}}}{4} + \frac{{{e^2}}}{4} - f} \) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \({\text{C}}{{\text{P}}^2} = {\left( {a + \frac{d}{2}} \right)^2} + {\left( {b + \frac{e}{2}} \right)^2}\) (<strong><em>A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let \({\text{Q}}\) denote the point of contact of one of the tangents from</span><span style="font-family: 'times new roman', times; font-size: medium;"> \({\text{P}}\) to the circle.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{C}}{{\text{Q}}^2} = \frac{{{d^2}}}{4} + \frac{{{e^2}}}{4} - f\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">using Pythagoras’ Theorem in triangle</span><span style="font-family: 'times new roman', times; font-size: medium;"> \({\text{CPQ}}\), <em><strong>M1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({L^2} = {\left( {a + \frac{d}{2}} \right)^2} + {\left( {b + \frac{e}{2}} \right)^2} - \left( {\frac{{{d^2}}}{4} + \frac{{{e^2}}}{4} - f} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {a^2} + {b^2} + da + eb + f = g(a, b)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore \(L = \sqrt {g(a,{\text{ }}b)} \) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) (i) the <em>x</em>-coordinates </span><span style="font-family: 'times new roman', times; font-size: medium;">of \({\text{R, S}}\) satisfy</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^2} + {(mx)^2} - 6x - 2mx + 6 = 0\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((1 + {m^2}){x^2} - (6 + 2m)x + 6 = 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \({L^2} = g(0,{\text{ }}0) = 6\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let \({x_1},{x_2}\) denote the two roots. Then \({x_1}{x_2} = \frac{6}{{1 + {m^2}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{OR}} = \sqrt {x_1^2 + {{(m{x_1})}^2}} = {x_1}\sqrt {1 + {m^2}} \) and \({\text{OS}} = {x_2}\sqrt {1 + {m^2}} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{OR}} \times {\text{OS}} = {x_1}{x_2}(1 + {m^2}) = 6\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so that \({\text{OR}} \times {\text{OS}} = {L^2}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The diagram below shows a quadrilateral ABCD and a straight line which intersects </span><span style="font-family: times new roman,times; font-size: medium;">(AB), (BC), (CD), (DA) at the points P, Q, R, S respectively.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/puck.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Using Menelaus’ theorem, show that \(\frac{{{\rm{AP}}}}{{{\rm{PB}}}} \times \frac{{{\rm{BQ}}}}{{{\rm{QC}}}} \times \frac{{{\rm{CR}}}}{{{\rm{RD}}}} \times \frac{{{\rm{DS}}}}{{{\rm{SA}}}} = 1\) .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p align="LEFT"><br><img src="images/tesco.png" alt></p>
<p><span style="font-family: times new roman,times; font-size: medium;">join BD and let the transversal meet (BD) at T <em><strong>(A1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">apply Menelaus’ theorem to triangle ABD with transversal (RS) : <strong><em>M1</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\rm{AP}}}}{{{\rm{PB}}}} \times \frac{{{\rm{BT}}}}{{{\rm{TD}}}} \times \frac{{{\rm{DS}}}}{{{\rm{SA}}}} = ( - )1\) <strong><em>A1</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">apply Menelaus’ theorem to triangle CBD with transversal (RS) : <em><strong>M1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\rm{AP}}}}{{{\rm{PB}}}} \times \frac{{{\rm{BQ}}}}{{{\rm{QC}}}} \times \frac{{{\rm{CR}}}}{{{\rm{RD}}}} \times \frac{{{\rm{DT}}}}{{{\rm{TB}}}} = ( - )1\) <strong><em> A1</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">multiplying these two results,</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\rm{AP}}}}{{{\rm{PB}}}} \times \frac{{{\rm{BT}}}}{{{\rm{TD}}}} \times \frac{{{\rm{DS}}}}{{{\rm{SA}}}} \times \frac{{{\rm{BQ}}}}{{{\rm{QC}}}} \times \frac{{{\rm{CR}}}}{{{\rm{RD}}}} \times \frac{{{\rm{DT}}}}{{{\rm{TB}}}} = 1\) </span><strong><em><span style="font-family: times new roman,times; font-size: medium;">M1A1</span></em></strong></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">whence</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\rm{AP}}}}{{{\rm{PB}}}} \times \frac{{{\rm{BQ}}}}{{{\rm{QC}}}} \times \frac{{{\rm{CR}}}}{{{\rm{RD}}}} \times \frac{{{\rm{DS}}}}{{{\rm{SA}}}} = 1\) </span><strong><em><span style="font-family: times new roman,times; font-size: medium;">AG</span></em></strong></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: The question can also be solved by joining AC and letting the transversal meet </span><span style="font-family: times new roman,times; font-size: medium;">(AC) at T. Menelaus’ Theorem then has to be applied to triangles ABC and ACD.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The relevant equations are \(\frac{{{\rm{AP}}}}{{{\rm{PB}}}} \times \frac{{{\rm{BQ}}}}{{{\rm{QC}}}} \times \frac{{{\rm{CT}}}}{{{\rm{TA}}}} = ( - )1\) </span><span style="font-family: times new roman,times; font-size: medium;">and \(\frac{{{\rm{CT}}}}{{{\rm{TA}}}} \times \frac{{{\rm{AS}}}}{{{\rm{SD}}}} \times \frac{{{\rm{DR}}}}{{{\rm{RC}}}} = ( - )1\) .</span></p>
<p><strong><em><span style="font-family: times new roman,times; font-size: medium;">[7 marks]</span></em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">Questions on pure geometry which require an initial construction to be made are usually either well done or not done at all and this was no exception. The obvious construction was to draw the line BD and use Menelaus’ Theorem twice although some candidates took the more difficult route by joining AC which also leads to the solution. However, many candidates did not start the question at all or tried to apply Menelaus’ Theorem to existing triangles which was not a successful approach. The examiners saw a number of candidates who produced well set out and well-explained solutions, but there were still a significant number of cases where diagrams were not fully labelled and points were referred to in the working that were not on the diagram. Candidates should realise that to ensure full marks on questions involving geometric proof that there is a certain degree of formality required in the solution. </span></p>
</div>
<br><hr><br><div class="question">
<p class="p1">A circle \({x^2} + {y^2} + dx + ey + c = 0\) and a straight line \(lx + my + n = 0\) intersect. Find the general equation of a circle which passes through the points of intersection, justifying your answer.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p1">\({x^2} + {y^2} + dx + ey + c + \lambda (lx + my + n) = 0\) <span class="Apple-converted-space"> </span><strong><em>M1 A1</em></strong></p>
<p class="p2"><em>ie</em>\(\;\;\;\)\({x^2} + {y^2} + x(d + \lambda l) + y(e + \lambda m) + c + \lambda n = 0\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">since \({x^2}\) and \({y^2}\) have the same coefficients and there is no \(xy\) term, this is a circle <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">we know the pair of points fit the equation. <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">hence this is the required equation.</p>
<p class="p1"> </p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1">Let the general equation be</p>
<p class="p1">\({x^2} + {y^2} + ax + by + q = 0\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">The intersection with the given circle satisfies</p>
<p class="p1">\((a - d)x + (b - e)y + (q - c) = 0\) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p1">This must be the same line as \(lx + my + n = 0\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">Therefore</p>
<p class="p1">\(a - d = \lambda l\;\;\;{\text{giving}}\;\;\;a = d + \lambda l\)</p>
<p class="p1">\(b - e = \lambda m\;\;\;{\text{giving}}\;\;\;b = e + \lambda m\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\(q - c = \lambda n\;\;\;{\text{giving}}\;\;\;q = c + \lambda n\)</p>
<p class="p3">leading to the required general equation</p>
<p class="p4"> </p>
<p class="p1"><strong>Note: </strong>Award <strong><em>M1 </em></strong>to candidates who only attempt to find the points of intersection of the line and circle</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">This was the worst answered question on the paper and indeed no complete solution was seen with no candidate having the required insight to write down the solution. Most candidates who attempted the question tried to find the points of intersection of the line and circle which led nowhere.</p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Two line segments [\(\rm{AB}\)] and [\(\rm{CD}\)] meet internally at the point \(\rm{Y}\). Given that</p>
<p class="p1">\({\text{YA}} \times {\text{YB}} = {\text{YC}} \times {\text{YD }}\) show that \(\rm{A}\), \(\rm{B}\), \(\rm{C}\) and \(\rm{D}\) <span class="s1">all lie on the circumference of a circle.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Explain why the result also holds if the line segments meet externally at \(\rm{Y}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-15_om_10.50.57.png" alt></p>
<p class="p1">Consider the triangles \(\rm{ACY}\)<span class="s1"> </span>and \(\rm{DBY}\)<span class="s1"> <span class="Apple-converted-space"> </span></span><strong><em>M1</em></strong></p>
<p class="p1">Then \({\text{YA}} \times {\text{YB}} = {\text{YC}} \times {\text{YD }}\)</p>
<p class="p1">It follows that \(\frac{{{\text{YA}}}}{{{\text{YD}}}} = \frac{{{\text{YC}}}}{{{\text{YB}}}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">Also \({\rm{A\hat YC}} = {\rm{D\hat YB}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">The triangles \(\rm{ACY}\)<span class="s1"> </span>and \(\rm{DBY}\)<span class="s1"> </span>are therefore similar <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">So \({\rm{A\hat CY}} = {\rm{D\hat BY}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">Therefore by the converse to the angles subtended by a chord theorem,</p>
<p class="p1">the points \(\rm{A}\), \(\rm{B}\), \(\rm{C}\), \(\rm{D}\)<span class="s1"> </span>lie on a circle. <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1"> </p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1"><img src="data:image/png;base64,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" alt></p>
<p class="p1">consider the circle passing through \(\rm{ABC}\)<span class="s1"> <span class="Apple-converted-space"> </span></span><strong><em>M1</em></strong></p>
<p class="p1">the circle then cuts the line \((\rm{CD})\) at \(\rm{K}\)<span class="s1"> <span class="Apple-converted-space"> </span></span><strong><em>M1</em></strong></p>
<p class="p1"><strong>Note: </strong>May be seen on diagram</p>
<p class="p2"> </p>
<p class="p1">since \(\rm{Y}\)<span class="s1"> </span>lies inside the circle, \(\rm{Y}\)<span class="s1"> </span>divides the chord \(\rm{CK}\)<span class="s1"> </span>internally</p>
<p class="p1">hence \(\rm{K}\)<span class="s1"> </span>and \(\rm{D}\)<span class="s1"> </span>are on the same side of \(\rm{Y}\)<span class="s1"> <span class="Apple-converted-space"> </span></span><strong><em>(R1)</em></strong></p>
<p class="p1">\({\text{YA}} \times {\text{YB}} = {\text{YC}} \times {\text{YK}}\) since \(\rm{A}\), \(\rm{B}\), \(\rm{C}\)<span class="s1"> </span>and \(\rm{K}\)<span class="s1"> </span>are concyclic <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\({\text{YA}} \times {\text{YB}} = {\text{YC}} \times {\text{YD }}\) given</p>
<p class="p1">\( \Rightarrow {\text{YC}} \times {\text{YK}} = {\text{YC}} \times {\text{YD }}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">hence \(\rm{K}\)<span class="s1"> </span>and \(\rm{D}\)<span class="s1"> </span>are the same point <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">the circle passes through \(\rm{D}\)</p>
<p class="p1"><strong>Note: </strong>Allow an argument based on similar triangles and angles in the segment</p>
<p class="p1" style="padding-left: 30px;">Do not allow the use of the converse of the intersecting chords theorem in either (a) or (b)</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-15_om_11.39.50.png" alt></p>
<p>Since the triangles \(\rm{ACY}\) and \(\rm{DBY}\) are still similar \({\rm{A\hat CY}} = {\rm{D\hat BY}}\) <strong><em>A1</em></strong></p>
<p>Therefore \({\rm{A\hat CY}} + {\rm{D\hat BA}} = {\rm{A\hat CY}} + 180^\circ - {\rm{D\hat BY}}\)</p>
<p style="padding-left: 60px;">\( = 180^\circ \) <strong><em>A1</em></strong></p>
<p>\(\rm{ACDB}\) is therefore a cyclic quadrilateral so the points \(\rm{A}\), \(\rm{B}\), \(\rm{C}\), \(\rm{D}\) lie on a circle. <strong><em>R1</em></strong></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAswAAAF9CAYAAAAQrz5XAAAgAElEQVR4Ae2dO7bcyHZtyfeuI1M0ZYqmTNGUKTbhsgksUyZpPpNsQrEJVBMoVx7lyqNceZQrr17NrLFObYLITGQmPhHAjDFw8Dn4RMwAAgsLG5HPf/s9PTNJoGEC//M///OsDmSV+f/6r/86jZlnOmP+l5TlmZ86/vu///unVf/2b//2WebrmOUMpCyvy5524IQEJCABCUhAAl0TeK5g7rr+dpX5iGBE7n/8x388CeKIZQpbp1spfETycIyI/sd//MeTqGZskoAEJCABCUigTwIK5j7rrdtcxxVmXIUxAvlaGgpS1mcZKQ4v4yzL8jp/WvnKnwj3rJY8M880iXVIdT7LTv8Y+UM+EM4M5DN5zXhkExdJQAISkIAEJNAAAQVzA5Ww5ywghDNEeGZ8rtwRk3WM2MzAdnX63H6WXB5xzHg4TfkoM8szPpeXiOWU9Z//+Z+fXOlz27hcAhKQgAQkIIF1CSiY1+W926MhDhGKEYv/9m//dhKLYwVG7A6FYnVdx7bpfVmEM1zCKWI7gruWET4wQUBHTDM2SUACEpCABCSwPgEF8/rMd3NEhN6//uu/PjnIEc3DAkb8JRwh7vCRBWDEMuKZ6bjwCOqxBDu4xYFmbJKABCQgAQlIYB0CCuZ1OHd/lAg8hB2iDqHMspqqcxxhF6FX13P6MgFEdBz6ONMsGyYYy3lIxXkJSEACEpDA/AQUzPMz3dUeI5BrKEEtYFxPhJuhA5XMPNP1QSV1wbimPKjA/69//etJRLPMJAEJSEACEpDAPAQUzPNw3M1ecDIjzMZcZBxjhFnczSOHVWxZ6TzAZEhYR81P6icOdP2f0xKQgAQkIAEJ3EZAwXwbr92ujTiuAqwWFJEcARYXuf7f6e0I4EDXhxzqsIbKpL5wnhl0nrerK48sAQlIQAL9ElAw91t3D+U8IitCeSiyIpIVWQ9h3mRjRDP1ypuCYfhGHnx0njepGg8qAQlIQAKdElAwd1px92Y7YooxorkmRNTbt2+fflij/s/p/gjwEEQ9I5o/ffo06jxT3zwUmSQgAQlIQAISOE9AwXyezW7+g2DCcWSoIpnX9TjJeV2/mwJbkFECEc6MGWqKcOZ8MGyjknFaAhKQgAQk8OyZgnnHZwHu4sePH0/iqIZcIIoQSDjKfrS34xPgTNHiPHN+4DwnIZQTisP5oXAOGccSkIAEJHB0AgrmnZ0BcZOHr+Crk6xI3lmlP1CciGfOF86dPFghlmuIjuL5AchuKgEJSEAC3RNQMHdfhX8UALcwYRcRPfwn4RaIH0XPTip7oWIgmBHOnEc5hzhn8kbCWOeFwLtbCUhAAhJonoCCufkqOp9BRA3iJu5g1oyb7Gv1EHF8K4EIZx7EkhDP7969OznPnGMmCUhAAhKQwFEIKJg7rWlikxHL9eMtRAyChrFhF51WbEPZ5oGshvgka5xbuM08kHmehYpjCUhAAhLYMwEFc0e1Sw8XOH8MeWWOYEEgf/jwQfHSUV32llXOvbzNqD2tIJoRz4T8mCQgAQlIQAJ7JaBg7qBmEcdxlCNWeD0el8/X4x1U4k6yyPmX3lfquYhgztuNnRTVYkhAAhKQgASeCCiYn1C0N4EgGTrKiGPECY6ySQJbEsi5WcOC8hCn47xlzXhsCUhAAhKYm4CCeW6iM+xvzFEm9CKvv40bnQGyu5iFAOcqjvP79++ffhQnbz9wnD1XZ8HsTiQgAQlIYGMCCuaNK6AeHkeZOFHCLxKjjKOMa4f4MEmgZQIJ1ag9a/CQx2DYUMs1Z94kIAEJSOAaAQXzNUIr/X/4ehuXLmJDl26lSvAwDxMYc5zzdoTzmfPaJAEJSEACEuiNgIJ54xqLo5w4UMQFjrIxyhtXjId/mAAPgbwtqR8Hcl5zfiucH8brDiQgAQlIYEUCCuYVYddDISIQE4iKpAhlHeUQcdw7gYQZEeOclI9WDdMIEccSkIAEJNA6gS4EMzddhsT1AhVRiUtVxSUubes3YQVE65eE+VuCAOd9ukbMdewD4hKk3acEJCABCSxBoGnBjADOK91zghmBnNjIN2/ePPvy5Uuzr3sJv6i9CSD2eUWN4+Yr6iVOb/fZGoHhh4FcA1y/ftTaWk2ZHwlIQAISqASaFMyIY4QlAhMhiaDkplr7dkVMc/MlpIH1k759+/aD65zlW47JK+VJ7wERCRH6W+bNY0tgCwLDj1x58EU04zqbJCABCUhAAq0RaE4wI35/+eWXk7hELH/+/PkHoTwEWMU1//v69WtTYRmJU46oRxAgDFoPHRlydl4CcxPgmsj1wb653uM2+8ZlbtruTwISkIAEHiHQlGDmBvr69euTYzxFLNeCsx0OLiEZ1Ymu66w5TV5wlXGXSTpoa9L3WD0RGL6B4dr/9ddfdZt7qkTzKgEJSGDnBP5PS+VLvDJ5GoZgXMsnscCEOuSDomvrL/V/jk85iKeOWKYsCHlfNy9F3f32TICHSd4kIZIRy1xDvGXiGtr6eu6Zq3mXgAQkIIH5CDTjMBPTyE2SxE3z+/fvN5cSRzfxwTdvPMMGuMqUIeEXCAFEgOEXM8B1F4cgMBamwcMwD50mCUhAAhKQwFYEmnGYa3/E94ZUcFPdypGKqxyxzE0eV1mxvNWp7XF7JMADLw+ZQ7eZB9Gtru0eOZpnCUhAAhKYl0ATDjOhC69evXoqGa9newlfwFVGLDMmIfYRywrlp+p0QgJ3EUhoBr3lkG79ruGug7qRBCQgAQlIYIRAEw5zYn3JHzdFXKYeEjdy4iwRy+Qbhxuxr1juofbMY+sEuKZwmrmmSAhorjdCr0wSkIAEJCCBNQk0IZjjzlJwbpIMLSfCLrhx56MkBDLhF3mN3HLezZsEeiJAW8DbJvpXZ4xo5o0Ob6Rqu9FTmcyrBCQgAQn0R6AJwVxjE1sXy9ykEcp5Tayr3N9Jb477I5DYZvowp43grVS9DvsrkTmWgAQkIIGeCGwumBHLVTC3Ci/OFv09c7PODRxXuZcQklbZmi8JTCGAUK4f03JN1jc9U/bhOhKQgAQkIIF7CGwumLkJtu4qA5av9BM7SQgGcZV2dXXPKec2EniMQK6/fBicbwnqtxCPHcGtJSABCUhAAj8S2Fwwk50qmFtzmwnBIF4yIRi8Era7uB9PIucksDYB3urw0IrjTPvBdcrbn1yna+fH40lAAhKQwL4JNCGYa68SCOZWRDM3X5xlnCtuytycc4Pe92lh6STQB4E8wHJ90m7UN0F9lMBcSkACEpBADwSaEMz1h0q46eXHP7YESPgF8ZHkJb1gcHM2SUACbRHg+hz2opFrt62cmhsJSEACEuiVQBOCmRte/XBuy9eqcanouopEnKR9K/d6epvvoxDAYeYD3HxXQBuiaD5K7VtOCUhAAssTaEIwU8zq3nKzu9dlRujeG9LBMYlX5me6uQGTJ8RyFfPLV4lHkIAE7iEQ0cw1yzShVPX7g3v26TYSkIAEJCABCDQjmHFya2hGHN5bqolt2Ac3y1tT+leOUE+88q37cX0JSGBbAnkrxINu3hjxEGySgAQkIAEJ3Evg+W+/p3s3nns7xCpfuke08nqV16xTEmIZoZxXslO2yTp5fcs8N1mOWcV71nMsAQn0QwCxTFgGD8OkW9qTfkppTiUgAQlIYA0C//f//Z7WONCUYyB4/+Ef/uHZv//7v5+cIV6p/ud//udJxP7d3/3d6C4Q13ygx7b/8i//MrrOpYUIbbb/3//939NxeJ37T//0T5c28X8SkEAHBP7mb/7mdC3/93//96kdoT1hmuub/5kkIAEJSEACUwk05TAn0zhDiFic38Qj4/jWjwNZzg0QwYxzdKuzzPaIZQYSr3EJwzBeObXgWAL7IUB7kmudtsRf6NxP3VoSCUhAAmsQaFIwp+AIYl6nMkY8J+EmI3AR0IyZvzXRX2viGtkHN9B79nPrcV1fAhLYhgDXO9c9SdG8TR14VAlIQAK9EmhaMC8BNSEcEeC4yrWHjiWO6T4lIIE2CCCacZppB3ibZJeRbdSLuZCABCTQOoHDCWY+KsS1xk0mjAPBbJKABI5DgOufdoDkR77HqXdLKgEJSOARAs10K/dIIaZsS1hHxDLrE4KhWJ5CznUksC8ChGN8/fr1FNKF00xPGrQPJglIQAISkMA5AocQzHzgR+xinGWEMnHLJglI4JgE+P4h3y3QPiCaE6Z1TCKWWgISkIAELhHYvWCOs8yYMAxiFo1ZvnRK+D8JHIMAovnLly+nDwDjNCuaj1H3llICEpDArQR2LZjjHOV1K/GKiGaWmyQgAQnEaWZM4k2UotnzQgISkIAEhgR2+9EfIpmbX8TysODplo4bJUKawSQBCRyTAA5zwrYgwJsow7aOeS5YaglIQAJjBHYpmHGQX716deo6CkeZmGVuiIhn4phr4v+IZYQzAx8EKZ4rIaclcAwCtBt8GEw7QbtAjLOi+Rh1byklIAEJXCOwO8GcWMTc9HCKEMFJ3BT5H69dI6KHIRoIZrZhiAOd7R1LQAL7JTB0mhPjvN8SWzIJSEACEphCYHeCOV3HTXGIEMrcIBkQ0LjPY+KZfSWEo4rvKYBdRwIS6IsAbUCcZh6ecZq97vuqQ3MrAQlIYG4CuxHMczlDuM8MiGf2yXRNiGdcZwR0QjlYZpKABPZDgGs//TNzfeM0c92bJCABCUjgmAR2I5jTjyo3N7qNm6PrOG6aEc040GPiGdFcQziYNklAAv0T4HrHacZxRiwT3uX13X+9WgIJSEAC9xDoXjBzM3v//v2zT58+ncq/5NftHAvnmRtpBpbVxI2VgVe43Fx1pSodpyXQFwGucx7GeXDmesZpVjT3VYfmVgISkMAcBLoXzIjljx8/nli8ffv2FG84B5hr+0Aox33mpooDPRTP3FgjmhPCYfjGNbL+XwJtEeAhGaeZxIMwD+Vex23VkbmRgAQksDSBrgUzQhnBTCIEg+7jtkwI6IRuIKKZr4mbLDfcuNCMvfFWQk5LoE0CiGacZh6KuYZxmk0SkIAEJHAcAt0KZoQpPzTADQz3FtenpYRYZuBGmzCOmj+EchxobsCUQfFcCTktgbYIEPZFm0Nq4QG9LTrmRgISkMC+CXQpmHFv8zEOQpNun1oXmwj7iGeENGUYC+GgPHGgjZXc98Vn6foj0Npbrf4ImmMJSEACfRLoTjAjNtPdE4Ly69evzYvl4amBUI4DjVOOkB4Tz5QP9zlhHMP9OC8BCaxPAJd5jY+M1y+ZR5SABCQggXMEuhLMiMr6gwKEYeylFwoc5+pAI6hrwkGPeEZIG/9c6TgtgXUJ0A5xvXJd+hPa67L3aBKQgAS2INCNYEYs1+7j9vyTtXGfq4CuDjQ3aUQzAyEcCOnWQ1K2OLk9pgSWIrCHN11LsXG/EpCABPZIoBvBXLuPw9GhC7mjJMRyxHN636gCGg44zgndYBoxbZKABJYjgGh+9erVU88Zdje3HGv3LAEJSGBrAl0IZsRi+kFds6/lrStn7PgIZW7UNYRjKJ7jPtcQDh3oMZouk8BjBFrvreex0rm1BCQgAQmEQPOCGbHMRzaIRASg/Z+m6v4cRzwzjgP953+fncI1Ip7jPiugKyGnJXA/gdrd3NHeft1PzS0lIAEJ9EWgecHMK09EIK7pnj7yW+o04cGCoYZw1GMl/jkhHAhpxXMl5LQEbidAzz24zVxLtFNcVyYJSEACEtgPgaYFc7pv4iaEs4zIM91GoIZvZHoYwhHxzJjB+OfbGLu2BLimEM08qNJe0d2l15HnhQQkIIH9EGhWMNfXnPzkNb+sZXqMQI1/xg3DuR+K52H8sw8pjzF36+MQ4IE0HwH28oNKx6kdSyoBCUjgMQJNCmaEHDce0tE/8nuseq9vjSMG7wzc9GvCLUv8M2IaAc0ykwQk8DOB+hGgP5/9Mx+XSEACEuiVQHOCGcFGKAZCDoHW4y/59XoywJ4B9tz4x8RzRHN+wlvx3Gttm++lCNQuMPfcX/xS/NyvBCQggRYJNCeY68czxi1ve8pEPFf3eRjCgeOMA82YAUFtksDRCeSXALkeaMe8Lo5+Rlh+CUigdwJNCWZcTQQzye6Z2jq1avwzDjTDUDwjChgQ0DjQioS26tDcrEeAh0zaMh46uRboOcMkAQlIQAL9EmhGMHuD6e8kos7y8SDCYBjCEfFc3WdDOPqrZ3N8HwENgPu4uZUEJCCBFgk0I5jzChNxhRujO9ni6XI+TxHMEdCI6ZoQytQp9ZuPCBXPlZDTeySQEDPOffuR32MNWyYJSOAoBJoQzB8/fnzGhzIkP5LZx6mHgEY0E7rBmPlhCAfiOaEbTPuQtI+6txR/EuCcxwzgGuAc5yNmkwQkIAEJ9Edgc8HMjYQbCjcWu5Dr7wSakmPqNgI6DvRQPCOWGdL7BuLCJIE9EKCNSzeZ9im/hxq1DBKQwBEJbC6Y89PXCCTcZV/TH+M0jPPMOOEcteSIZ86J9MDBvOdGJeR0TwTS1RznsD+d3VPNmVcJSEACfxDYVDDXUAxeVeoqHu+0xGlmwIVjwIFGQNeEyIiAjgOteK6EnG6dAOe4oRmt15L5k4AEJHCewGaCGWeRD2K4kfiLWOcr6Ij/QTDHgY6QHnKI88wYMc1gkkDLBAzNaLl2zJsEJCCBywQ2E8z2inG5YvzvHwQQz3GgEdEMzCfhNDPwdoIhHxHm/44l0BKBGprhDzO1VDPmRQISkMBlApsIZkMxLleK/71MIMI5TnQV0GyJ2xwHOkL68h79rwTWIcC5yps1zmHOTXvNWIe7R5GABCTwKIHVBTOvJfMLWPaK8Wj1uT2imYHYZ0QI0zXV+GdENIPxz5WQ02sT4DzlDRvJXzRdm77Hk4AEJHAfgdUFczryx13xB0ruqzS3Ok8grnPEMw9owxThHCdaAT0k5PzSBH755Zdnnz59Or0N8QdNlqbt/iUgAQk8TmBVwVydFW4SxJuaJLAUAV5/I6ARzVP6f0ZI+/HgUrXhfisBzktcZsa0g7SHJglIQAISaJfAaoKZGwPuMuLFG0S7J8Tec8ZDGwPnIeckQ01xnSOeeRNiksASBHiIo00k+QunSxB2nxKQgATmI7CaYM6HfggSX0HOV4Hu6T4CuM8MCOeI6KF4rvHPPOQhng3fuI+3W40TSG9BPKDRLnp+jXNyqQQkIIGtCawimBEiL1++PJXVn4bduso9/jkCnKdxnxHSDMOEsEE4x4E2hGNIyPlbCHCOIZp5eLNtvIWc60pAAhJYl8Aqgrl+4EI3Sroo61ayR7udAOIZERP3GWHDfBLnMEPEcwR0/u9YAlMJ1L6Zv337Zvs4FZzrSUACEliRwOKCmTg9BDNiwy6UVqxZDzUrAc5fRHN1oKuA5mCJf0ZEZ5g1E+5slwQ4j3gDx9iuNndZxRZKAhLYAYHFBfOrV69OQsMYvR2cLRbhRABhwxABjYgexj8jnnGgOe8ZENC+WfEEOkcg33hwjvgLgOcouVwCEpDAdgQWFcz1K3BCMRANJgnskQDiOQIa8cx0TTV8I+6zAroSOvY0D2D0mMHDFw9YiGaTBCQgAQm0Q2AxwcwNgI9ZEA52I9dOhZuT5QnEfebc56Ex8dA5MkK5CmgEkh8Phs5xx4hl2kyS3cwd9zyw5BKQQJsEFhPMecWIELAbuTYr31ytQwABXWOfEdIsqymuc8Szb2MqneNM283ccerakkpAAn0RWEwwv3jx4iQK3r17d+ouqS8s5lYCyxBAKMeBRkQzZFmOGPcZ0czbmcRD5/+O90uA84HQDM4JjAbq3yQBCUhAAtsTWEQwx13mxm83SdtXsjlomwAhGwndQDANPyDkOsqHg3GiWWbaJ4HaDSftp0kCEpCABLYnMLtg5nUzDgk3fTvi376CzUFfBBLvjIDmWhqGbyCUGRDOiGiGLOurpOb2HAHOgfzQky7zOUoul4AEJLAugdkFczrh54ZOY+/HTOtWqEfbFwFezeM6RzwPBTSl5RpL6EZioPdF4XilictMO8oHgL5RON45YIklIIG2CMwqmLm5E7tM0l1uq6LNTf8EuL5wHxniQDNdU+KdEdCGb1QyfU3zYJSfzPYHn/qqO3MrAQnsk8CsgjnuMm7I9+/f90nMUkmgIQJxnhP7zHxNNXxDAV3JtD8dl5mHIGOZ268vcygBCeybwGyCGacLR4Sx7vK+TxpL1yYBrj0GRHM+IsSVTkqsM8I5DrQhU6HT3pi6NJa5vXoxRxKQwDEJzCaY4y5zMzZ2+Zgnk6Vui8CU+Oe4zol9Zt7UDoG4zNSLsczt1Is5kYAEjkdgFsHMjRknhLHu8vFOIkvcPgGuzSqgcaBJLEvCbWZAnCGgGfuxWehsM66xzPaYsU0deFQJSEACEJhFMNvvsieTBPojgBirPXAQAlATYjnCGfGsgK501pumm04ecOD/9evXhw5MHVPn19Lbt2+fVuE8YTiXcm6c+7/LJSABCeyBwMOCGYeK2GUaVH/Vbw+nhGU4IgGEFEMV0dV9rvHPiOj8Ap0O9PJnC3Xy6tWr04EQzAjUexN1Sj0jwD99+vTDGwbqlTacOq3HyHlB2B3TSayPsGbseRAqjiUggb0SeFgw0+gSZ8erXF4Z1oZ2r9AslwT2TgBhhRNZe9+oApryc60jlhgz+AHhcmcFghnhzIMK7ewcKW8G2Rd1R4z0pTqM0404pqu7PDTNkRf3IQEJSKB1Ag8L5jTkOA00oiYJSGBfBOJKxplEuFWnkdIitBBSCOiI6HtcR/aN+8mY47Jf9oc4u2d/e6kJmCBYYYCwncOYyD5hBGOE+DnGPDhxfOqD71RY3yQBCUjgSAQeEsw0ooRjkOgn9JI7cSSollUCeyeAoOX6Z8wwFNAIL0QVA+0CAu+cGIMV2+N48sZqLLEPwgVqbO3YentdxsMDghXmc5kTtf2mnhDiY4m6STt/zYUe295lEpCABPZA4CHBnFd03Awf/RhlDzAtgwSOSABBxYBwxrVkuoZvIJQRvAw4xcPwDdbNdxDX+B25F54aQsEPQ116ALnGkf9PEczUJSF31JHO8hSqriMBCeyVwN2CmZsjNzkaUrs72uvpYbkkcDsB2oS4z4yHApo9IppxNRkjshmmJEQi7Q3bHjG9ePHiSbziuD+Srglm6g1ThPrUWX6EtNtKQAJ7IPCXewvBDY6GlBseg0kCEpAABBC1OMkMtBER0Ag0BlJCOU4zN/xhXzitRxXMMCVsBY6EZjzqMp9DH2eZ//NtCm8HTBKQgASOTOBuh3lOp+PIFWDZJXA0AohlBF/GiOBb0xwhCbces4X153yzRx0kNrnGMCOWs1xnuYVaNw8SkEALBP7PPZmIu8y2R/0I5x5ubiMBCfwRjkE4AaEV976dukdk74E9vOKuTw1juaXcCHLCMHCudZZvIee6EpDA3gncJZjzJTuvB5d6Jbh38JZPAhL4I3zjHg6EZSAYcUOPlmJSVONiDgbsLx9f+oHfHETdhwQksCcCNwtmHAgGEoLZJAEJSOBeAvc+cPPQjhOKwGNAQNMuHcF5xmEOt7lcZtjxS37hB98jPozcex67nQQksH8CNwvmuBr11eD+MVlCCUhgCQIJL7hl34hFHtb5EA1RRywuYo8fUWJASOfDuAjAW/bfw7pxmSnnHGVMl38pO+08HBXNIeJYAhI4OoG7BDPQDMc4+qlj+SXwOAEevG+NYyb+mfhaPkhjYJ59IKQReIg9+g6OA800y/Yk/uIyU6a88XukNmAHR4Yk9gu7PXFL2RxLQAISuJXATb1k1K+qj/qV+q2AXV8CErhMoLYrl9f840EdsZyQhLp+xCP7Q+wxP3RfEZoR6Yx77S6NcvFAQFlxm2Fya6rc4cLDBwnXGqGcBCN7ywgNxxKQwFEJ3CSYaURpTGvjelRwllsCEpiPAO1KjaEd2zPtDj1rjInl4foIyiqgEYdD8YwQZGC/DExP2ffwWFvNR9iSZwyMW9M5wcx+iAlnCDMeLvwQ8FbCri8BCeyJwGTBzM2Hj2sY42Ykhm5PMCyLBCSwHQHaFkQaQo5pEmIQIUt782gYGPvFec6QY6TEHAdhiHiO+9yygEbM0h8+CQeYfN+SLglm9pPQlohmWBz5VxZvYeu6EpDA/ghMFsz5CISbiq/n9nciWCIJtEIAIVtFGkJtbuHKMRgQjRHoOSYccsy4zxGjc+fjUeaYGOSfhwnE7C3pmmBmX0PRTPuP08zxTBKQgASORGCyYCZejsbznob5SEAtqwQk0B8BxDPOMyIyDvSwFHGecZ/jQA/XWXv+ESNjimCmPPBAmNcHCsS5onnt2vZ4EpDAlgT+MuXgNJQ0zCRDMaYQcx0JSKAnAjinDIhA2rsIaNq9oRtNubJ+HGjmt3CfI9yTX/IxNVUBzDbMj5WBYyCQa48ZTLO+94OptF1PAhLoncAkh/nRj0t6h2T+JSCBYxOozjOOKwK1JoQqwrK60PX/S07f+/aPeHE+tCSR/2uhdrkP1LIQnoFoHhPadT2nJSABCfROYJJgToNMw3hP90W9QzL/EpDAZQJDt/Ly2n/8t0eRRTkZEMyIaAama/kpVwQ0jjXTDEulhGWw/99+++3qYcgr+UYsV+FPXhHA5H9YN6zH+nnTWA9C2ei/mYeFJctZj+m0BCQggbUJXBXMNJTpHcO4tbWrx+NJoA8C6RIOQVXF47nc48ZGWCasYSjSzm3b2nLayOpAMz9kUJ3nhFHMWY7nz5+fdnetjcYdHxO9w7wgnGuKE12XjU0Ptxtbx2USkIAEeiRwVTDHvcA5uPbKrkcA5lkCEpiPwPC1PW+lEIgMSYi2uLMRlvwfh7P+0lzW72lMeRhoN1POlJFyxL2lPc2DAtOPPiz4FrCns8S8SkACPRK4KpjTEHMzw70wSUACEjhHoL6RYp1v376dfU3PusTRIrKTENgJC8iynseI5QjnONFVQFO2iOc8WNwjoPOgwrYaGz2fMeZdAhJolcDVXjJwgnKDiGsAACAASURBVEgIZpMEJCCBawSmuqWIO76JQCjmp5gRfgjKvTycwyJOMuViiHCmbWWaIQ8NcaCzDWPSNaYwhGf2x7RJAhKQgATmI3DRYaZBJ36ZxE+vXmu058uWe5KABHokgGDjrRSuKumSw1zLV3tsYPlRfk0UXrSz8MpQudDmxnlmjIA+1w7nR0wIazGWuFJ0WgISkMDjBC46zHGXaajPNdKPZ8E9SEACRydAKAbtTdocHFfE4d6dUspH2UlxnxHOiYFmWbjQBjOwTRxoptM2s4x12VbBfPQryvJLQAJzEzgrmNNQc0DDMebG7v4kIIFKANGHMxrBjGhkOmKyrrvXaRjETabctMHhEPc5IRfhFPFcTQ3WYdsI6b3yslwSkIAE1iRwVjCnYU4jvmamPJYEJHA8AjikNR1NMNeyM03bGycZAcyQEA5c5MzX+OfsgxAXHkAUzSHiWAISkMBjBM7GMNMI8yEOzgVfXdvwPgbarSVwBAIIuntimMMmcbjM0+bw7YRpnEDEc9xnxjXBL441wru60HU9pyUgAQlI4DqBsw5zXvnZyF6H6BoSkMA8BOqDeVzVumyeo+xjL2PxzxgdcZzhRzvOwDI4JoSDMDvmZbuPc8FSSEACyxO4KpiHr0mXz5JHkIAEjkpAAXdfzcMNcyMfT+I+50dg4kCzLK40v9wX8RwXmrFJAhKQgATGCYwKZhpY3AmSgnkcnEslIAEJtEYAEcyAMEZEI5rj1LOM2GccZ5YxHzeadSOgDd9orVbNjwQk0AKBUcGccAwaUB2fFqrJPEjgGATyoJ7S2v6ExLQxvHCKE4qRD/+qIGZPcZ1ZD+GcecZ8MJj9RDyzT+tiWh24lgQksE8Co4KZRpOku7zPSrdUEmiVAOItiQd20+0EaLcRvWnHx/aQMIx0Xwf3iGy248El8wjlCG5in9l/lo3t22USkIAE9kjgJ8FMw5mbloJ5j1VumSTQJgFEWhV59v9+Xz0lFjk8M39ub4jfCOiEcCCWqYsMuS+wnJT1uUfwYHPtGOeO7XIJSEACvRD4STDTyNI4xlHopSDmUwIS6JsA8bVJtD8+sIfGbeO03bTjCN5bxSzb87DCwP0gwjuOc+bZ97D3DeqM47EPkwQkIIE9EfhJMNMI0iDS6PlKdE9VbVkk0C4BxB1hBEkRXpl3fBsB+CFmEbmP/FoiwjcCPI5/XGfG7D/CnPmx+GfuI95Lbqs/15aABNojMCqYySYNnC5BexVmjiSwRwJ0c4bwItHufPjwwfbngYqOqwxTDJA523L2nf2zb44R9zmGS+Y5LgPrI+IZsuyB4rmpBCQggdUJ/CSYaehINGwmCUhAAksSQHAhlhOOgZj69ddfdSQfhI5AhWUEbQTug7v9afOIYfaf+Oc4z4wZENQMqWPWzcB9Rvf5J6wukIAEGiTwk2CmYSMpmBusLbMkgcYJINAYkup0ljFmOWIKscyYhHBCLNv2nHA89AchC88I1qUE8zCTHJf6Y8i5QB4Qy4xT76nz5DPbJJ8sN0lAAhJoicDz335PyRCN2KtXr06zZXH+7VgCEpDAWQKIIWJYaywyAgjhFiHExjyU09ZENPF/4mOJtWXaNA+B169fn0IlcH4JcWkhpd5r7HPNF0KZcwUBzZhB8VwJOS0BCWxF4AfBzI0Ox4dG6uvXr1vlyeNKQAKdEXjz5s3JPcwbqmvZp41BHCOMGCuUrxG7/f+05bTpMP7y5cvtO1h4Cx6w8vDEB4pMsywJoczAucHDVMSzAjqEHEtAAmsS+EEwc9Pj1RmNE69GTRKQgAQk0CcB2nLadATm9+/fmy8EYhnnOS404yqgKQCimSEPWkybJCABCaxB4Ekw0zDRuNJgIZYf6YpojYx7DAlIQAISOE8Ax/bly5enFRDMPTmz3I8YEM3ckxiyLCWO+4xoTjhPT2VMORxLQAJ9EHgSzDRMCGYaWV7f8QRvkoAEJCCBfgk8f/78lPk9tOkRz4wZuFfVhFjmvhUXmrECuhJyWgISeITAUy8ZeXo3nvARnG4rAQlIoB0CiMYIzN5NkAhh6CbeOb1vUEbuYcwzIJQZ2IZyM2RZO7VjTiQggZ4IPAnmNEAIZp/Ke6pC8yoBCUhgnEAE89CNHV+7n6X5SJTykShfHgwyZhkDApoU8cyYIfs4/dM/EpCABK4Q+EEws66C+Qox/y0BCUigEwJVUOLA7tUM4b7FQPeEeVuKcK7xzxHSVF3uc3Gf4bRXNp2cqmZTAs0TeBLMNCYkGhKTBCQgAQn0TyDteUTkEUQhZWSIgKYWI54jmuO4M0/Xe6wb5znjI7Dq/wy3BBJYj8CTYE4DEkdivSx4JAlIQAISWIJAxCPtO6L5qCkimPLDAR64z4RrMJ3B+OejniGWWwLXCTz1kpGvqfnBEkXzdXCuIQEJSKB1AghBej/CSd1DTxlL8EZAI57jPjMePlxEcBPCETd6iby4TwlIoF0CJ8FMo9prf53tojVnEpCABLYlgPCzf/3pdQAvBkRzjX+uAjrhHohnYqYR0IZvTGfsmhLolcApJAPBTMrru14LY74lIAEJSOBPArVNTzv/53+dGhIIr2vxz3GjiX9mG8RzXGjGLDNJQAL7InASzFz8JBoJkwQkIAEJ7IdA2nUF8311GiHM1jDEbSbWGQe6zhv/fB9ft5JALwROgjmvm9Kw9pJ58ykBCUhAApcJpF1XMF/mNOW/YYmIJsE04RtxnbmfshwBTWLd6kBnH6d/+kcCEuiGwA8hGV7I3dSbGZWABCQwiUDa9bxJnLSRK00iAFuGYf/PiGV4I54jpNkh6xKuwfr5gNDwjUmoXUkCmxP4Cxe0DvPm9WAGJCABCSxCIIJ5kZ270ycCCF+GCGj+Mex9Iy5/Hl5YNw4004hokwQk0CaB59++ffst3Q59/vz59OTbZlbNlQQkIAEJ3EMg3Yb+3t77rco9AGfYBrHMkN43mI5Zxe4juBHQONCMs2yGw7sLCUjgQQJPMcxemA+SdHMJSEACjRKgfUecIdJ0nLepJLhXF5m6SLhGPiBkGUPin2vsMwLautum7jyqBCDwFJKhYPaEkIAEJLBPAhHM1dHcZ0n7KVUEdI1/jvuc+OfMUyrqMOEbxj/3U8/mdD8EToI5xeGCNElAAhKQwL4IIM7iaCLQTG0RiGH19u3bZwx5G4BgjgtN/VUBTZ0ioCOimfce3la9mpt9EXhymL3Y9lWxlkYCEpBACERI6TCHSNtj6itimJwmVCOCOfOMa//POM8J44gIb7uk5k4C/RA4xTCT3TSo/WTdnEpAAhKQwBQCGCIkBfMUWu2tQ/0xIIZJCGWcZwQ004yp20+fPp0G7udZP8I750B7pTNHEuiDwF+42Eg+jfZRYeZSAhKQwK0EYogomG8l1+b6EdCJf64COvHPCeWgBFk/DjTzOSfaLKG5kkB7BH6IYW4ve+ZIAhKQgAQeJVDdRUSzYulRou1sT13GRU78c8RyxgjqONHknPOhxj7HuW6nVOZEAu0ReHKYa4PaXjbNkQQkIAEJPEpAh/lRgu1vj4COk0x9M0QsJ4QjAjrxz9z/Gez/uf36NYfbEXiKYd4uCx5ZAhKQgASWJICIYoiAYtq0fwKpd8RwXOSI54zjQjOOgI5jnbGG2v7PFUt4ncBTSIYN6HVYriEBCUhAAhLomQDil9ANUh6gEMoRzixLbxxDwY3oZnv1Qs9ngHm/l4AhGfeSczsJSEACnRCoAgdBZJIABCKI3717dwLCuRHhzLiGcDBNiludMS60SQJHIGBIxhFq2TJKQAKHJhBhFEfx0DAs/FkCnCeJf2alGuuMgM483deRcl5lG8Rzlp1W8I8EdkRAwbyjyrQoEpCABCQggbkI4CLHSWafEc24zXGieQir/T8n7pkxQhoBbZLAHgg8hWR4Uu+hOi2DBCQgAQlIYBkCEcOX+n9O/DM5qILb+Odl6sS9rkfg+e+H+o3Dffv27XRyr3dojyQBCUhAAmsQ4FX6mzdvTq7gly9fnnpMWOPYHuMYBGr8c419rqVHcMexjviu/3daAi0TUDC3XDvmTQISkMAMBBAzr1+/Pgnmz58/n/rbnWG37kICowQSK5+u6+iFI8uyAW+1Ec8J3WBs/HPoOG6RgIK5xVoxTxKQgARmJIBYwWHG+VMwzwjWXU0mEPGc2GfGNSGW4zonfANBbZJAKwT86K+VmjAfEpCABCQggZ0SQPzW/p8R0IjmfEDIQ13in/mIMA404pmYad3nnZ4YHRVLh7mjyjKrEpCABO4hoMN8DzW3WYsA52fEc5xoltU0jH3GjTZJYE0COsxr0vZYEpCABCQgAQn8QAD3GCeZgYRoZsgvEGbe/p9/wObMygQUzCsD93ASkIAEJCABCZwngJscR5m1atxzpnGgh/0/J/aZMSLcJIE5CSiY56TpviQgAQlIQAISmJVAPgZkpwhlHGeEMw503OfEP7NOBDexz2zLvAIaMqZHCCiYH6HnthKQgAQkIAEJrEYA4RsBzUeECGjEMsI5HxBWEU3Gsn4dr5ZhD7QbAgrm3VSlBZGABCQgAQkciwACGieZFAGdDwgR0AjqhHGwDuvjOCOe2S5uNP8zSeASAQXzJTr+TwISkIAEJCCBLggghiOII6IjliOiE87BfLqvq7HPCGn2YZLAkICCeUjEeQlIQAISkIAEdkEgYRgUBreZgdjnhHFknv9HQLMNIpqx8c+QMUHgqR/mr1+/nk4OsUhAAhKQwL4IIAr8aex91amleZxAjXWOE821UlMEd0Q0Atp0TAJ/4dUDJwgnDieESQISkIAE9kWANp4hr6z3VTpLI4H7CCR+GTc510hCNxjX8A2OkOuHcI+EcWTZfTlwq54IPAnmnjJtXiUgAQlIQAISkMBcBCJ8EdHD+OeEbyCiEdYfP348DVVwx4lmP6Z9EjCGeZ/1aqkkIAEJSEACEniAQERwet/AcUY8R0DXkI6h4GZbBLUC+oEKaGzTk8NMnnhqMklAAhKQwP4I1PbdG/j+6tcSLU+A6yYC+t27dyfNhHBO7HNCOCKqyVHWT/gG86Z+CfyFJ6C8Zui3GOZcAhKQgAQuEUA0xwW7tJ7/k4AErhPgWiJ0g4FriyHimV446nx630BvIZrZJuEc14/kGq0QeArJoHJNEpCABCSwPwK27/urU0vUDoE8iCKCEcMfPnw4ieeEbmQcQR0Bna7r4kSzH1O7BAzJaLduzJkEJCCB2QggmrmhmyQggeUJRARzJK69hGpEPLMMJ5ohgjvbILqzbPmceoSpBBTMU0m5ngQkIIFOCcRh9ibcaQWa7a4JcN1FDBP/jHiO25xxPiBEQL9///5pfbZLDHTXEHaQeQXzDirRIkhAAhK4RCCC+dI6/k8CEliHQOKXh/HPiOUI5whpcoTgZhuEc8SzD7/r1FU9yumjvyygUaUSTBKQgAQksB8C3IRJ3mT3U6eWZB8Eck0m/plSJWyDMcK5OtL0Ac26cawzVrstfz784DArmJcH7hEkIAEJrE1Ah3lt4h5PAvcTwEUmXev/eRj/zHYIaAS1Avp+/ue2PPWSAVgb1HOIXC4BCUigbwJp37mRmiQggX4IoM/iIg/jn+NEJ4wDAU1K2EYV0P2UuN2cnhzmCOY0qu1m15xJQAISkMCtBGpIxq3bur4EJNAOAR56GYbxz4hnBnQcY1K6r2N9xHOEtA/O99XnTyEZ9+3GrSQgAQlIoFUCMUO8UbZaQ+ZLArcTwOxkqAKah2MEcz4aNP75dq7ntnhymFkhjeq5lV0uAQlIQAL9EYjDrGDur+7MsQSmEqjhG2yDpouARkQznWEs/hkHOiJ86jGPtN7z335Pr1+/Pj2R8Os0xMiYJCABCUhgHwS4ab548eJUmO/fv/sx0D6q1VJI4GYCiOU4z4wTupEdxa1O7HM+IMz/jz5++ugPEDrMRz8dLL8EJLA3Atwkk7ghmiQggWMS4A1TDd9A8yGccZsZZ55pUhXQPcQ/0+VenPRhDcc5pxznjOE3b96cHPiqhbMdPZacHGZ+VYYDsaMvX74Mj+O8BCQgAQl0SoCbITcCbpTfvn3rtBRmWwISWJpAxCZjRHN92ObYtCHpsYMxmrG1RJ7RtOkxJPlDJDNcMw0oO1EXJNYl8iI/VX5ymCk4aQjntNA/EpCABCTQLYG069zsTBKQgATOEYgAHvb/jPjEdaUtYWA+ziv6EUHJOMvO7X+N5bRzv/766ykv9BKSlPxl/twYBhHVGMjRx6x/cph5knj16tVp+99Dms/tx+USkIAEJNAZgV9++eXUvRQ3QW4kJglIQAK3EkAooxUZ4kAP94G4ZEB0Mt7yIR2B//Lly6dQY/I0JYIiepi2kjazppNgZsd+FFKxOC0BCUhgHwT8qHsf9WgpJNAKATQjA8I54jnLkkdcWgQzQjUhDWsL6ISjJU+fP38+5SXzwzFlIHyNvMelruucBDMLnj9/flqOAqeAJglIQAIS6JsANwAEM67JtZtF3yU19xKQwFYEaGfiPseBZllNiOWhA13/v9R03rCxf/KAxj0n3PmWjzCOc+s8CWasayz3MRt6qYK4XwlIQAISWI4ANy8cE25e3AS4YZkkIAEJLEmA9iaxzjjQTFcBnVhnzFkG2qUsmztfHLeGZuB2Yx4ME3kkNJmP/IahGFn3STBHhRvnFjSOJSABCfRNgJsVDvM1Z6XvUpp7CUigZQI8uCNI4z4zrgmxHPeZMSKaZXMlXGM0btIwkgJRnf+PhWJku1MvGczEoqZQJglIQAIS6J9A2nPa9zlvQP2TsQQSkMBaBCKGcXcRpwzD+OfMkyfaKtos1kc8P9p+YQSz/3Q1R7dzuMzRvSzn/1+/fr3YTv4kmCkIjWx2tBZQjyMBCUhAAvMSiJPDDUjBPC9b9yYBCdxOIG0RIpYBzUk7VYe40Wm/0KMR3QnhuPXIhFoginM84pVxk5lnmrxc070/CGYKQkbZgUkCEpCABPomEIeZm41JAhKQQGsE0J2IYAZSBG0cZ+Zpxxge6f8ZMYxoTugFYRock+Pwv3O//ld5PcUwkxk+DkHRD+M76gZOS0ACEpBAHwToLpQbjj1k9FFf5lICEviRANo07jPiNq5z1kJwx32+5hLTFiKYE5rBtqSpH0Q/CWY2sr9OKJgkIAEJ9E+Am0P61+cnsa+9buy/xJZAAhLYMwHEcpzmhFfU8k4xBtie3jBoH0nnes2o+830U0gGC9KgDhV8VnYsAQlIQAJ9EEg7jouStr2PnJtLCUhAAs9O4jgiOU4z44jdIaMp7RzrEIoRl3nKNjnOD4I5cW5paLOSYwlIQAIS6IsADgwp7XpfuTe3EpDAUQgggBkiimm7IoyH4jgGQA3FoI1D+CbEYiluo4I5GV364EsVyv1KQAISODoB2nGSgvnoZ4Lll0BbBCKMGdfpoTgm1whhhojiTG+hT0cFM5nEZc5Xi8ybJCABCUigDwJxa8itgrmPOjOXEtgbAdohhoRVTHGOI4hptxgQxluI47G6+EEwswIZpHAK5jFcLpOABCTQPoE4N9xouAGZJCABCSxNIMI447jHY8elXYo4rtOtiOOxPF8UzGMbuEwCEpCABNomwI0KZycOTdu5NXcSkEBPBG51jvPgHtc47VLL4nisPn4SzIRh0KFzHArdiTFsLpOABCTQLoF88Bfnpt2cmjMJSKB1AnGMM77mHCOI0/YwjkBupZwI/qQ6nWXnxj8JZgqH6o9DcW5Dl0tAAhKQQJsEuLGRuFGZJCABCUwh8KhznO/eWnaOKWPaR5gwzbIpeR4VzIhmdsJggzvlNHMdCUhAAm0QqDeE3MDayJm5kIAEWiFAO5FIArRenR7LY5ziOo7BOrZ+a8uInIiupexJLONXrtG6DPyQybn0k2BGZUcw81qPnxo0SUACEpBAHwS4ASRpeISEYwkckwDiMENCKdJbBUSqeGQeDRgdGBGZB+8pLiz7aDEhhFOOc/m7Vr6fBDM7Yqf8Ckri4M7t3OUSkIAEJNAWgbTb124ObeXa3EhAAnMQQADHLaYtYD4O8tj+q2OMQGa+J+d4rExjy/IgMPa/qcvOCmZ2EPDAM0lAAhKQQNsEcnMklwrmtuvK3EngEQJc6xkiiM85xxGLjOMao+vSRlxzVh/J5562HRXMebqgMqgAwzL2VOWWRQIS2CuBOEuUz3CMvday5ToiAfRYru8pznHc4ozRdbYJj505o4KZXRLvQZC0gvkxwG4tAQlIYC0CuaHmJrnWcT2OBCQwD4G4xoxxjjNwbZNYnjTmHHPtRxjrHIfUPOOzgjnA0wAbljEPcPciAQlIYCkCGBwk2mvb7KUou18JzEcgwhitldCK6K6xo+RhOGOd4zFKyyy7KJipiFScje8yFeBeJSABCcxFgI+1SYlNnGu/7kcCEniMgM7xY/xa2PqsYEYgM+BY8NRjA9xCdZkHCUhAAuMEMDfyutb2epyRSyWwFoFbnOPhx3jRX3nTv1aePc5lAmcFcyoQwYxr8e7du8t78r8SkIAEJLAZgbjLudlulhEPLIEDEbjkHOcBNjjQVVyfGfNgm9AK1mG5qV0CZwUzWebDv48fP54cZireymy3Is2ZBCRwbAKJX770S1XHJmTpJfA4gTjHw3hj3vAMU4RxRHHGiGZTfwQuCmYqlwrnBMG9sHu5/irYHEtAAvsnkJs3JTUcY//1bQmXJ4DuycD1lfDULKs5iDDOWOe40tnP9EXBTDGpeMQyJ4uCeT8Vb0kkIIH9EIhgNhxjP3VqSdYlgBDmOsq1hGPMNMuHKcI4jnHGOsdDUvuavyqYeb2HYM5J5AmxrxPA0khAAv0TSDgGBodtdP/1aQmWIxCHmHFc4wjjoTiOMGaMKM6Qa4zlpuMQuCqY8+SUp62cKMdBZEklIAEJtE0gH/wZjtF2PZm79QkgghHEMf2iZYbimJxFIOfBE72TYf2ce8TWCFwVzJwsiGZOMhplPyhprQrNjwQkcGQCEcswsH0+8plw7LIjgBkiiCOSs7zSiTDWOa5UnL5G4KpgZgcJy6gN87Ud+38JSEACElieQNplxfLyrD1COwQijDNGGCe0YpjLCGSd4yEZ528hMFkwZ6e6zCHhWAISkMC2BCIWyIWCedu68OjLEIhDnHNd53gZzu71OoFJgpndVJfZhvk6WNeQgAQksDSBxGUmdG7p47l/CSxNIMI440vOceKL861V5hmbJDA3gZsFc22g586M+5OABCQggekEPn36dFo5r5qnb+maEtiWwD3OcQQx5zsimVALBpME1iAwWTDnCY6nPvtkXqNqPIYEJCCB8wQQHOlOzrd+5zn5nzYIxDGO6cY8A+fxMEUYR3dkXud4SMr5NQlMFsycqDzV4WgQx+yPmKxZTR5LAhKQwI8E4i7jsNE2myTQAgEEcIQwD3RM58FuKI7zMV4Esc5xCzVoHs4RmCyY2QEuBo00Jz8nvq9CzmF1uQQkIIHlCND+RoToLi/H2T1fJ4Agzod4TGcYimP2FGGsc3ydq2u0R+AmwczTHyc8FwTC+d27d+2VyBxJQAIS2DmBCBRMCwXzziu7keIhgLn352GN6Ty0DcVxdY4RxxlYrtHWSIWajZsJ3CSY2TuN88ePH5/CMjz5b2buBhKQgAQeIpC3fHmF/dDO3FgCIwQSa5zxNec4rnHGmGvqgxGwLuqWwPPffk+35J6L5/Xr16enzM+fP+tu3ALPdSUgAQnMQODFixenNvjXX3/1e5IZeB51FzjDGRDEeXPBmDTmHCOCEcNxjRmzTHF81LPoOOW+WTCDBsGMw4HbjGg2SUACEpDAOgT46PrNmzeng33//l2hsg723RwlojgCGVEcgTwsZIRxHescDyk5fxQCN4dkAIYeMhDMNNxcbD5ZHuV0sZwSkMCWBGhv0zsGhoVt75a10e6xOU8yJNY4Aplc87+aEMGkCOO4xzrHlZLTRydwl2BOQ53G24//jn4aWX4JSGANAlX00A6bJBAC9zjHNd5Y5zgkHUtgnMBdgpld4TL78d84VJdKQAISWIIA7jJGBR/7MZiORSCuMeOpznFc4nwgGmHs24ljnTuW9nECd8Uwc1ieZv347/EKcA8SkIAEphBAJL18+fIkmP3Ybwqx/teJMOZ+m7cLjBnGUg2pYDqD4niMlsskcBuBuwUzh+HDE+KYeXL98uXLbUd2bQlIQAISmEyAN3rv378/xS3zsZ9pPwTGnOOIZP43THGJhwI5bvJwfeclIIHHCdwdksGhCctAMPMBIE+8XLwmCUhAAhKYlwCiibaWRLtr6ptAdY4jjC85x4k1zljnuO/6N/d9EnhIMCcmigse94PXhCYJSEACEpiXAKYE7SxCyY/95mW75N4edY65x8aIMqxiyZpy3xK4TuAhwczucTt++eWXk8tMg84TsEkCEpCABOYjgCFBon21jZ2P69x7QiBzH2SIY5zx2LFSn3GMmY9AHlvfZRKQwHYEHhbMuB18uU0DwStDG/PtKtMjS0AC+yMQd5mS2YVnG/Ub5zhimPsf9ZTlw1wignGIGXOP1DkeEnJeAu0TeOijvxTPj1FCwrEEJCCBeQn4cfW8PO/Zm87xPdTcRgL7IjCLYKYxSXdHHz580AXZ1zliaSQggY0I4FoimGljP3/+bPzywvUQhzjOcdz9LK+HT48UY86x8caVlNMS2AeBh0MywEDjUH/IhDAN47D2cYJYCglIYDsCvL1DrPEKn8E0LwHYTo05rsI4scbc57zXzVsn7k0CrRKYxWGmcDQ6OCE8mesyt1rd5ksCEuiFAG0pb+5I9HOvYL6/5uIQ3+ocI4wzIIx1ju+vA7eUQO8EZhPMgKBTfRwRGhU71u/91DD/EpDAlgTofYgPqhFsX79+3TIr3R07wri6x4hmlg8T96s4xhnrHA8pOS8BCcwqmGmQXrx4caKqy+zJJQEJSOA+AsYuT+NWneOIY8ZZXveCMM4Q1zgCmeUmCUhA0XsjgQAAGM1JREFUApcIzCqYOVBcZhoiPlIxvusSfv8nAQlI4GcCr1+/PnVTRhgG7aiC7g9GOsc/nysukYAE1iEwu2A2lnmdivMoEpDAPgnQhr569epUuKPGLschRiDf4hzzgIFJwzhu8j7PEkslAQmsTWB2wUwB4jLTYBnLvHaVejwJSKBnAul3mbd0R4ldrsI4LjKimelh4r6SUIqMjTkeUnJeAhKYm8AigpmGLv0y88tUxDObJCABCUjgMgF+LZWP/WhD99jv8tA5JlYbUZzllU4cYsY6x5WM0xKQwBYEFhHMFCS//seTP68VjWXeono9pgQk0BMBQjEIQaAv+19//bX72OUx5zgCeVgvOsdDIs5LQAItEVhMMNMo8moxjT9uiUkCEpCABMYJ0IUc7jKJUAzCDXpJtPekCOQ4x1leyxHnGBOFMmbI8rqu0xKQgARaIbCYYKaAPd8AWqkg8yEBCeyfACEJ9IzRi8EQYUx+mc5AOYaphlTUmGOWmyQgAQn0QmBRwQyE+opRl7mX08J8SkACaxLIh9K4rrSTrbjLCGFE8JhAHvKJQ6xzPCTjvAQksAcCiwtmPmIhNIO0x49Y9nASWAYJSGA7AgjSVj6SjmNcx+RP53i788MjS0ACbRBYXDBTzHSThPPw7du3NkpuLiQgAQk0QCA/gY1Du1Y3nEPnODHH54QxbTf5S7wx4zjKDSA0CxKQgAQWJ7CKYKZxxkEh+ZPZi9epB5CABDohUH8Cm14x3r59u0jOq2Oc8IpzznENqWA6AwLZJAEJSOCoBFYRzMBtNUbvqBVvuSUgge0J5BuPuX4C+xHnmDwkdlpxvP25YQ4kIIG2CKwmmGnI7Waurco3NxKQwHYE5uhFCOc4A44x0zrH29WpR5aABPZLYDXBDML6ASA/ZoKjYZKABCRwNAIIWwwEjATCMAjHOJcigCOI2WZqzHFc48QcnzuGyyUgAQlI4DKBVQUzWaGvURp7GnBEs6/+LleQ/5WABPZHoH4IPfZLqHGNGSOQM4yRMOZ4jIrLJCABCcxLYHXBfIuzMm9R3ZsEJCCB7QlgGGAckPgIGhc4wvicc5weKRhXgaxzvH19mgMJSOAYBFYXzGD9+PHj6SNApnv7CVjybJKABCRwDwEEMd3I4RiTEL+ZHu5vTBizzLdyQ1LOS0ACEliewCaCmWLl63BDM5avZI8gAQmsR2AYc5zwCoQx/6tJ57jScFoCEpBAuwQ2E8w4LcTxcQN59+7d6dVku5jMmQQkIIFxAvVjvIRWXIo5Zi+EYeSDvIRZ6ByP83WpBCQggRYIbCaYKbyhGS2cAuZBAhKYQmDMOebBP8vrPobOMfP0EsS6CGU+9DNJQAISkEA/BDYVzNw8CM3AjeEm8vnzZ+Pz+jl3zKkEdk2A9imOccaXnGPCyxgSe1yd4/rz14hl1jNJQAISkEA/BDYVzGDiRsQX49ycDM3o58QxpxLYCwHangy0RwxTneOEVVz6GI99pVeMJX/+ei/1YTkkIAEJtEhgc8EMFEMzWjw1zJME9kkgznHEMfO3OMeIY4Ypif3mF04NxZhCzHUkIAEJtEmgCcEMmtprBqEZU29IbWI1VxKQwNYE4hozxuWNQEbEDtMw5niKczzcx9h8/YES2jVDMcYouUwCEpBA+wSaEczczBKa8de//vUUz9w+PnMoAQm0QmBN53hKmT99+nTqc5l1Ecu0ayYJSEACEuiTQDOCGXx8RY4jQzLW74TBPxKQwIDAPc5xwihwjjONq7xUwtHOD5S8ffv21J4tdSz3KwEJSEACyxNoSjBTXF9hLl/pHkECPRG4xTlOzxRVGEcgr1lmQ8zWpO2xJCABCSxPoDnBXD+S4UbHT2cv6QQtj9gjSEACUwggjLn+q0BObxXD7RNzHDEcgdxCjLBdyA1ry3kJSEAC/RNoTjCDlHhmHBqSXc2dMPhHArsjgDBGECOSueYZRzAPC4tARgwzRCRnPFx3y/kat/zhw4dT+3UpP5SfULSpKRwoewsPB1Pz7XoSkIAEeifQpGAGau1qbsqNp/eKMP8S2CuBvTjH1+qnPugTt0y7NeXtWB4c3r9/f3pgyHGGDwSVI+vwfwwFPiaccpzs17EEJCABCdxOoFnBzM2BV5u4L9wM/HWs2yvXLSSwBYEIwD05x9c4Utb0t4yQvSeUrJoEuMd8+Dx0kRHltImsm2SvQiHhWAISkMByBJoVzBSZGy9dzXGTOHcDWQ6Ne5aABC4RqI4n1yjDLTHHXNOIyz2k+rEyQpeY6lsT7PKLgLDBJDjnHCOaMRSoA5Jv4W6l7foSkIAEbiPwl9tWX3dtbhbcCLgxcDPmlSU3EZMEJLA+gTjGXItMZ4hoqzni2kX0RRQnvGAvArmWFbc3cciESNwjluv+pkzjKlMPcZo5Psv2yHcKD9eRgAQksDSBpgUzhefmg2jGwcGBQTQzb5KABJYhEOe4CmTE2TlhXMUw12tE8jK5a2uvfOQX0UrcMsNaCYGcY+fhRcG8Fn2PIwEJHI1A84KZCuHGwI0oNyduCmvemI52UljeYxGowjjCi/GYQI44ru4xbvIRhRqMeICHUx7s1zxzarjGWF2tmRePJQEJSGDvBLoQzFRCXOV028QNeo1Xn3s/ASzfcQggqiKIcYwzjImthFRUgcz1VkXaccj9XFLYJYYYRvz09dpsyEMSx177+Dm2YwlIQAJHINCNYOZmgGjOTZ6bFTcpnC6TBCTwM4FcKxHJGY8J5AhjRHGmGSvCfubKEpxl+MKIj/zW5kQdJm6a/BwpDIbymiQgAQmsTaAbwQwYbkqI5HTfxPie7pvWhuzxJLAUAYRTBgQxcf4Zjx2TayjiCrGHQGZ+bcE3lrcelsEasQxnEg/xa77p4vjUb/3QkLojH9ZhD2eQeZSABHol0JVgBnIcHX4JkBsHTvMWDk+vFW6++ydQnWOmI6IYDxPXS4Rxphkrroakps0jVAkLI+VHQ6ZtedtaaduG9cTy1Dl75PsO8uGbttv4urYEJCCBWwl0J5gpIDcHnGbEcl5LMm+SwF4IIH4zIJKuOcdVDEcg6xzPezbko2P2ikjNdxXzHuXPvaX+/1zy7GQS5MEIMU1dZ76u57QEJCABCcxLoOkfLrlWVNweXo+S1riBXcuP/5fAIwRucY4Rw4iljCOYh47kI/lx2z8J8GCej/xwdZd4QOeh6NoPl3CO8ABF28c0iTqn1yDaQOv/zzpzSgISkMCcBLp0mAOAGwTuCjcPBqYJzzBJoFUCnKMZqkBOTOww3xHCEccIZJ3jIaVl56kbvpcgIZa3bGNS/8RN13bP9m/Zc8C9S0ACEujaYab6EB+4zIkrxPnhpmaSQCsEIozjDuIQMoylOMYZRzDrHI7RWn4ZdYZYpr6oiyU/Mp7iMA9L/PLlyx/OpW/fvp3yOVzPeQlIQAISeIxA1w4zRUdI4PggnPPalJsb7rNJAmsRiGvMuApkpscS4otzV+d4jE4by6g7QiSoUx5geBhv7cGFUIyEpUGNPHNOmSQgAQlIYF4C3Qvm4OADHG5suDTcQLhp6DSHjuMlCFRhHNf4knM8dI0jmpfIm/t8jAB1m5jlPJS3KESHeTp3/j1Gw60lIAEJSGA3gpkbx5cvX06OEKKZmx1J0exJ/giBR53j/BBIa87kI0z2vi2iM84y7QpvsHjYaTFxftbUaj5rHp2WgAQk0COB3QjmwOfmlh82QTQjVNb8YYHkw3GfBBAgcY6ra3zOuUOgZOBcY5qxArnP+qeeq7NMGEbLIjTfboR2y3lNHh1LQAIS6JFAV4I5bt/wNWQFH6c5P2yCeEZE6zRXSk7nXIoo5q0EQvmcMOa8QgQzRpToHO/vHOKcyMM29by2s8zxpybWJfSMczaJ/PqgFhqOJSABCcxLoCvBTNdJCJprfaBy02AdnKLEIrJMp3nek6envSEwdI57qrF18xpnOQJ07Z+8prT1YY3zlYc42qwqgrMcZ5n/J/GRMx8AmiQgAQlIYBkC3XQrx40M94cbBrHKU149sm6cZm46Os3LnEQt7ZU6Z0B8MFxyjjknGHAT4xxzXjFdRUpL5TMv8xPIQzXjtdsJzlWOy3mKCGZ+Ssq5y/mKUNYMmELNdSQgAQncT6Abh5kbShwYuo+bIpi5qQydZlAZnnH/CdPalhEciI6I5IzH8sp5kyFCmbHpmASqWIbA2g/VebjjHLzlp7Y5h2nfPHePed5aaglIYH0C3TjMtYN+bhTfv3+fTIubEu40optteX1pP82T8TWxYoRFFcgRycMMUscREwgKxEVijofrOn9cApw/w94wdGqPez5YcglIQAKXCHQhmBG63Nhqwjm+xSnGdSSmmX2RcJKM+atE25qOMM6bBeovonksp3GNGSOSM4yt6zIJcF7lozkerqaGeUlOAhKQgASOSaB5wYxIQuiSEEF8+EfCCUI0c7O7JSG8I5oRzAhn03YEIoIjkHH9dI63q48jHJnrPw/gtCm0ATrLR6h5yygBCUjgfgLNC+a8NkUcc3MjNIN0ryuEMMNZSv+lCc+4VXjfj/zYW0YYT3GOqZM4xgga5nWOj33+PFp6rvv0tsO5RLvCOWaSgAQkIAEJXCLQvGBO13Bfv349lWMuh5j9RjQT2oHLpGi+dKrc9r97neMqkBE0JgnMRYDrPW+reADjmvccm4uu+5GABCSwbwLNC+YXL1788JFevekhcG/5+K9WJYKOfeE2kxDNfKXuDbRSmj5NjHENp7gUc6xzPJ2ra85DgOu8hnMplufh6l4kIAEJHIVA04IZQcuQcAwqBSGWX+NinhvfIx/vRTQjoBFyfvwD1fOpCuEIZMbwGyZ4MvAQonM8pOP8GgQ4XxHLdEVJoq3gwZjz0iQBCUhAAhKYSqBZwYwAI/yCV6fD/kmHbtE9H/9VQMTT5kdREHcc75YeOOq+9jaN4IgwZjrDOYFchXHEsq793s6KPsrDOZruJMmxH/n2UW/mUgISkECLBJoVzDhCxBsSuzwUXIi2+vEfgvnRr9wRhYmXpqJwrhHNR3GiYIrAYByBfMk5pk5gA3emI5RbPMnN0/EI8BDM9cz5zHnKQ/Ajb6KOR9ASS0ACEpBAJdCsYI7jS4jEWKof/9HTxdCFHtvm2jJurjXcA8GMGN9jqsKY6QznnOOhMI5g3iMby9Q3gTxscy4jlvPw23epzL0EJCABCWxJoEnBjHjDQUYIn3OOuSkSf5zEx39zuMHcZAn5yL45PmIcB7XHBMvqHKc7t3PCOEI4ApnxHFx7ZGee+yIwvHa5Zuv3D32VxtxKQAISkEBLBJoUzDVGeSqsRz/+Gx6HL+oZuAkjItn/OfE+3HbLecIoEMkJq4hgPieQI4wTUhHBvGUZPLYEbiXA+U0IRj7us9ebWwm6vgQkIAEJXCLQnGBG4BFugbt8LeawCmuE36Mf/w1BDeMg84X9cL0t5iOEI44vOccRwTjFEciMdY63qDmPOTcBHg4JpeJa4Jxu6Tqdu6zuTwISkIAEtiHQnGBON2/fvn27Kui4Qc798d+wGrgZI8wRpKTcjNcWm/c4x9U1jmgels95CfRMIO1F3qDw0GwPNz3XqHmXgAQk0CaB5gQzAhj3kxCIKQlnqb6GXeojPV73Jq4Z8clxlohrvsc5Jj/kJcPaYn5KPbmOBOYkwHVCyFSuSdqMnr81mJON+5KABCQggfkJNCWYcXERwLf8eAhimW1ICMUpzvS9GLk5I5xzLMJGGB5JiTWOgxzBHMes7pvyIQx0jisVp49GgGuF65AxCUeZB2wfFI92JlheCUhAAusRaEYwIxAjfM91JTeGBYHJdrl5ImDn6GJu7Fgs4zg1RIObNce85jZHCLN9HcaOk/AJneMxOi47KgHaiLjKTCOQudavfetwVF6WWwISkIAE5iPQjGCOe4sAvSWsghsnHwlGMHMTZXuc2KUSx0Q053UwwnbYi0YVxYjlCGa2HSad4yER5yXwIwGuH665hF/xgIpYXvI6/zEHzklAAhKQwJEJbC6YCcPgJhjxSWUgmnGNuClees3KtmyXm2itSFxf9nPN+a3b3DrN8Xk1zM2clGNFvA/3N+Yce8MfUnJeAj8S4PrmOourzHU99RuHH/fknAQkIAEJSOA+Ak0I5jHXleIgJs8JZrZBsF5KcW4vrfPo/xDHvCYeE+1jIRURzY8e1+0lsHcCXOMI5VxbXM8IZQSzSQISkIAEJLAmgc0F85qFXfJYia2M24xDjsuNQDZJQAK3EeDNEddUvZ4IwTj3AH3b3l1bAhKQgAQkcBsBBfNtvC6ujdtcPwg0zvIiLv8pgZ8IIJDz8Mk/Ech+2PcTJhdIQAISkMDKBBTMCwDHHUM4J9SEV8jc9HWbF4DtLndBgGuF0IvhdWN3cbuoXgshAQlIoHsCCuaFqnDMbSZMwy6wFgLubrslgKtMrHK+SdBV7rYqzbgEJCCB3RJQMC9ctcNYTD5kJLbZ3jEWBu/umyeAq5zwC6YRynkbY6xy89VnBiUgAQkcioCCeYXqxkGrfcgiBvJRoMJghQrwEM0RIPwCsZwuGIn3T1eQzWXWDElAAhKQwOEJKJhXPAUQB7x6jkhALBPbjKumcF6xIjzUZgSGfacT15+Hx80y5YElIAEJSEACVwgomK8Amvvf+bgJ4ZyEu8bHTfnhkyx3LIG9EOAtC+FJDFwDJB4UcZU97/dSy5ZDAhKQwH4JKJg3qtt0n8Wr6QgI4ppxnBUQG1WKh52dAOd5wi9ynnN+c54bxz87bncoAQlIQAILEVAwLwR26m55RU0sZ+0hwA+fptJzvZYJxFE2BKnlWjJvEpCABCQwhYCCeQqlFdbBhUNgDIWzvxa4AnwPMRsBXGTOYT5yxV0mEZ/PeUyssrH6s6F2RxKQgAQksCIBBfOKsK8dCrGR19cRG3wUFcf52vb+XwJbEhi+LSEviGQGw4y2rBmPLQEJSEACjxJQMD9KcKHtCdNAPNfX2REf/mLgQtDd7c0EzjnK+aDPc/VmpG4gAQlIQAINElAwN1gpyRIuc+JA88EUAiQfB/p6O6Qcb0Egb0PyUEceEMo82PlB3xY14jElIAEJSGApAgrmpcjOuF/Ecj4MjDhBLEec+Lp7Rtju6iIBHuISepGwIc5FBLJdxF1E5z8lIAEJSKBjAgrmjioPgZKPAxUrHVXcDrI6du5RLNxkHtx0lHdQyRZBAhKQgATOElAwn0XT9j8I1UA8p1cNcku4Bi4f4sXY0bbrr4fc8WaDNxp5SEueObfydsPzLFQcS0ACEpDAngkomDuu3XxwVbujoziImDh/CpqOK3jDrI89kBF6kQcyw4A2rBwPLQEJSEACqxNQMK+OfJkD4gRGOCdcgyPhNucjLD8SXIb9HvbKwxfnTYQy8yTOGcRxHsD2UFbLIAEJSEACEriVgIL5VmKNr49wJkwD4VOFM6In4lnXufFKXDF7CGNCLhg4d6pQzvnCuePD1oqV4qEkIAEJSKA5Agrm5qpkvgxFOCOEhuIZxxAhxGA6FgHOBc6JCOWUPm4y8ckMiuSQcSwBCUhAAkcnoGA+wBlwznXGaUYwRyAdAMWhi8h5wJsHxgw11dhkhXIl47QEJCABCUjg2TMF88HOgkuiqb6CN2yj/xMjTnLqPOEWlCwPS4lv77+0lkACEpCABCSwHAEF83Jsm95zxBSv5QndGBNTuM8IKh3Hpqvyh8xRj9Qnw5iTzEMRA28VfCj6AZ0zEpCABCQggbMEFMxn0RzrHxHOCK0a7wwFhHOEFiJLodXOuYFApr4ikhnXlPpK2I0PP5WO0xKQgAQkIIFpBBTM0zgdZi3EF0M+CKvOMxAQz4iwKqAPA6eRgg5dZOprWE8IZOuokQozGxKQgAQk0D0BBXP3VbhsAXitH/cyYroeEfEcBzrTupiV0GPTcZATXjH2BgDeeZBJ7yePHdWtJSABCUhAAhKoBBTMlYbTZwlEuCGaEW040ENXE+GWEICIaMam2wjkIYVxHlLGWMdBjlj2QeU2zq4tAQlIQAISmEpAwTyVlOv9RAARh3CO+zkWGsBGCeGoDnTE9U87PciCPIAwrvyYHqawCkeEMtMmCUhAAhKQgATWIaBgXofz7o8SAYhoRvThQo+JP0Ag9hCBDHFHq5jeG6yI4rjFcGFZmI2VFy51CLOxdV0mAQlIQAISkMCyBBTMy/I9/N4RhxkiGCMWz8GJeI5IzDgim+3q9Ln9LLm8liHTEcApZ8bn8pEyUL6UOSL53DYul4AEJCABCUhgfQIK5vWZH/qIiMgqLBHTLGN8KSEuSRGZ5+YjrrOv4XyWnxsnf/l/na/CmP/XeaavpYjijClD8pfyXNuH/5eABCQgAQlIYH0CCub1mXvEMwQQnQjnjCNWI0zZrE6f2c2qiyPgOWimGeMUM67ieNWMeTAJSEACEpCABGYjoGCeDaU7WopARHLGHIfpMUGdZckL87cmRG5SRC/zWZ5ljEmM63Ba6B8JSEACEpCABHZD4P8DH32nteCELaEAAAAASUVORK5CYII=" alt></p>
<p>again consider the circle passing through \(\rm{ABC}\) and again let it cut the line \(\rm{CD}\) at \(\rm{K}\). <strong><em>M1</em></strong></p>
<p>in this case \(\rm{Y}\) lies outside the circle \(\rm{ABC}\) and therefore \(\rm{Y}\) divides the chord \(\rm{CK}\) externally. <strong><em>M1</em></strong></p>
<p>by the secant-secant theorem the same working applies as in part (a) <strong><em>R1</em></strong></p>
<p>and the proof follows identically. <strong><em>AG</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Many candidates made no significant attempt at this question. It was expected that solutions would use the intersecting chords theorem but in the event, the majority of candidates who answered the question used similar triangles successfully to prove the required result.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Many candidates made no significant attempt at this question. It was expected that solutions would use the intersecting chords theorem but in the event, the majority of candidates who answered the question used similar triangles successfully to prove the required result.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The rectangle ABCD is inscribed in a circle. Sides [AD] and [AB] have lengths \(3\) cm </span><span style="font-family: times new roman,times; font-size: medium;">and (\9\) cm respectively. E is a point on side [AB] such that AE is \(3\) cm. Side [DE] is </span><span style="font-family: times new roman,times; font-size: medium;">produced to meet the circumcircle of ABCD at point P. Use Ptolemy’s theorem to </span><span style="font-family: times new roman,times; font-size: medium;">calculate the length of chord [AP].</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">construct diagonal [DB] and the chords [AP] and [PB] <strong><em>M1</em></strong></span></p>
<p align="LEFT"><br><img src="data:image/png;base64,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" alt></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">since \({\rm{D}}\hat {\rm{A}}{\rm{B}} = {90^ \circ }\) , [DB] is the diameter of the circle and \({\rm{DB}} = \sqrt {{9^2} + {3^2}} = 3\sqrt {10} \) <em><strong>R1A1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">triangle AED is a right-angled, isosceles triangle so \({\rm{DE}} = 3\sqrt 2 \) <em><strong>R1A1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\({\rm{A}}\hat {\rm{E}}{\rm{D}} = {\rm{P}}\hat {\rm{E}}{\rm{B}} = {45^ \circ }\) <em><strong>M1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\( \Rightarrow {\rm{PB}} = {\rm{PE}} = 6\cos {\rm{P}}\hat {\rm{E}}{\rm{B}} = \frac{6}{{\sqrt 2 }} = 3\sqrt 2 \) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">M1A1</span></strong></em></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">using Ptolemy’s theorem in quadrilateral APBD</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\({\rm{PB}} \times {\rm{AD + AP}} \times {\rm{DB = DP}} \times {\rm{AB}}\) <strong><em> M1</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(3\sqrt 2 \times 3 + {\rm{AP}} \times 3\sqrt {10} = \left( {3\sqrt 2 + 3\sqrt 2 } \right) \times 9\) <strong><em>A1</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\({\rm{AP}} \times 3\sqrt {10} = 54\sqrt 2 - 9\sqrt 2 = 45\sqrt 2 \) <strong><em>A1</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"> \({\rm{AP}} = \frac{{45\sqrt 2 }}{{3\sqrt {10} }} = 3\sqrt 5 \) <em><strong>A1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[12 marks]</span></strong></em></p>
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<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagrams that some candidates drew were not always helpful to them and sometimes served to confuse what was required and make the problem harder than it was. Candidates were asked to use Ptolemy’s theorem but some ignored this request. Lengths of various segments were often written down without any evidence of where they came from. </span></p>
</div>
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