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<!DOCTYPE html>
<html>
<head>
<title>
Advanced Mathematics 1
</title>
<link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/bootstrap/4.3.1/css/bootstrap.min.css">
<link rel="stylesheet" href="styles.css">
<style>
@media (min-width: 490px) {
body {
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<body >
<div class="container"><br>
<h1><b>Advanced </b></h1>
<b>M a t h e m a t i c s - 1</b>
<br>
<br>
<ul>
<b>Unit 1a Complex Numbers (6 or 7 Marks)</b>
<br>
<br>
<li><a href="solved question/Γ3+i(polar form).pdf" width="100%" height="500px">Express the complex number √3+i in the polar form</a>
<img src="img/√3+i.png" alt="√3+i" width="40" height="20"></li>
<li><a href="solved question/1-iΓ3(polar form).pdf" width="100%" height="500px">Express the complex number 1-i√3 in the polar form</a>
<img src="img/1-i√3.png" alt="1-i√3" width="40" height="20"></li>
<li><a href="solved question/1 + cosθ + isinθ.pdf" width="100%" height="500px">Find the modulus and amplitude of the complex number 1+cosθ+isinθ</a>
<img src="img/1+cosθ+isinθ.png" alt="1+cosθ+isinθ" width="85" height="20"></li>
<li><a href="solved question/1 - cosθ + isinθ.pdf" width="100%" height="500px">Find the modulus and amplitude of the complex number 1-cosθ+isinθ</a>
<img src="img/1-cosθ+isinθ.png" alt="1-cosθ+isinθ" width="90" height="20"></li>
<li><a href="solved question/(3 - Γ2i)2 | 1+2i.pdf" width="100%" height="500px">Find the modulus and amplitude of the complex number (3-√2i)² / 1+2i</a>
<img src="img/(3-√2i)² | 1+2i.png" alt="(3-√2i)² / 1+2i" width="55" height="24"></li>
<li><a href="solved question/3+i | 2+i.pdf" width="100%" height="500px">Find the modulus and amplitude of the complex number 3+i / 2+i</a>
<img src="img/3+i | 2+i.png" alt="3+i / 2+i" width="45" height="20"></li>
<li><a href="solved question/5+3i | 4-2i.pdf" width="100%" height="500px">Find the modulus and amplitude of the complex number 5+3i / 4-2i</a>
<img src="img/5+3i | 4-2i.png" alt="5+3i / 4-2i" width="40" height="20"></li>
</ul>
<br>
<ul>
<b>Unit 1b Complex Numbers (6 or 7 Marks)</b>
<br>
<br>
<li><a href="solved question/1 |(2+i)2 - 1 | (2-1)2.pdf" width="100%" height="500px">Express : 1 / (2+i)² - 1 /(2-1)² in the form of a+ib</a>
<img src="img/1 | (2+i)² - 1 |(2-1)².png" alt="1 / (2+i)² - 1 /(2-1)²" width="70" height="20"></li>
<li><a href="solved question/3 | 1+i - 1 | 2-i + 1 | 1-i.pdf" width="100%" height="500px">Express : 3 / 1+i - 1 / 2-i + 1 / 1-i in the form of a+ib</a>
<img src="img/3 | 1+i - 1 | 2-i + 1 | 1-i.png" alt="3 / 1+i - 1 / 2-i + 1 / 1-i" width="70" height="20"></li>
<li><a href="solved question/(1+i) (1+3i) | (1+5i).pdf" width="100%" height="500px">Express : (1+i)(1+3i) / (1+5i) in the form of a+ib</a>
<img src="img/(1+i)(1+3i) | (1+5i).png" alt="(1+i)(1+3i) / (1+5i)" width="70" height="20"></li>
<li><a href="solved question/(5-3i)(2+i) | 4+2i.pdf" width="100%" height="500px">Express : (5-3i)(2+i) / 4+2i in the form of a+ib</a>
<img src="img/(5-3i)(2+i) | 4+2i.png" alt="(5-3i)(2+i) / 4+2i" width="70" height="20"></li>
<li><a href="solved question/(1+i) (2+i) | 3+i.pdf" width="100%" height="500px">Express : (1+i)(2+i) / 3+i in the form of a+ib</a>
<img src="img/(1+i)(2+i) | 3+i.png" alt="(1+i)(2+i) / 3+i" width="70" height="20"></li>
</ul>
<br>
<ul>
<b>Unit 1c Complex Numbers (6 or 7 Marks)</b>
<br>
<br>
<li><a href="solved question/1 + i cube root.pdf" width="100%" height="500px">Find the cube root of 1+i</a>
<img src="img/1+i.png" alt="1+i" width="25" height="15"></li>
<li><a href="solved question/1 - i cube root.pdf" width="100%" height="500px">Find the cube root of 1-i</a>
<img src="img/1-i.png" alt="1-i" width="25" height="15"></li>
<li><a href="solved question/1 - iΓ3 fourth root.pdf" width="100%" height="500px">Find the fourth root 1-i√3</a>
<img src="img/1-i√3.png" alt="1-i√3" width="25" height="15"></li>
</ul>
<br>
<ul>
<b>Unit 2a & 2b Differential Calculus (6 or 7 Marks)</b>
<br>
<br>
<li><a href="solved question/eax cos (bx+c).pdf" width="100%" height="500px">Find the nth derivative of eax cos(bx+c)</a>
<img src="img/eax cos(bx+c).png" alt="eax cos (bx+c)" width="80" height="20"></li>
<li><a href="solved question/eax sin (bx+c).pdf" width="100%" height="500px">Find the nth derivative of eax sin(bx+c)</a>
<img src="img/eax sin(bx+c).png" alt="eax sin (bx+c)" width="80" height="20"></li>
<li><a href="solved question/y=cos2xcos3x.pdf" width="100%" height="500px">Find the nth derivative of y=cos2xcos3x</a>
<img src="img/y=cos2xcos3x.png" alt="y=cos2xcos3x" width="80" height="20"></li>
<li><a href="solved question/y = log(ax+b).pdf" width="100%" height="500px">Find the nth derivative of y=log(ax+b)</a>
<img src="img/y=log(ax+b).png" alt="y = log(ax+b)" width="80" height="20"></li>
<li><a href="solved question/y= sin(ax+b).pdf" width="100%" height="500px">Find the nth derivative of y=sin(ax+b)</a>
<img src="img/y=sin(ax+b).png" alt="y= sin(ax+b)" width="80" height="20"></li>
</ul>
<br>
<ul>
<b>Unit 2c Differential Calculus (6 or 7 Marks)</b>
<br>
<br>
<li><a href="solved question/x | (x-1) (2x+3).pdf" width="100%" height="500px">Find the nth derivative of x ∕ (x-1)(2x+3)</a>
<img src="img/x | (x-1)(2x+3).png" alt="x ∕ (x-1)(2x+3)" width="50" height="20"></li>
<li><a href="solved question/y = x | x2 - 5x + 6.pdf" width="100%" height="500px">Find the nth derivative of y = x / x²-5x+6</a>
<img src="img/y = x | x²-5x+6.png" alt="y = x / x²-5x+6" width="50" height="20"></li>
</ul>
<br>
<ul>
<b>Unit 3c Differential Calculus(6 or 7 Marks)</b>
<br>
<br>
<li><a href="solved question/r=a(1-cosθ).pdf" width="100%" height="500px">Find the pedal equation to the curve r=a(1-cosθ)</a>
<img src="img/r=a(1-cosθ).png" alt="r=a(1-cosθ)" width="80" height="20"></li>
<li><a href="solved question/r=a(1+cosθ).pdf" width="100%" height="500px">Find the pedal equation to the curve r=a(1+cosθ)</a>
<img src="img/r=a(1+cosθ).png" alt="r=a(1+cosθ)" width="80" height="20"></li>
<li><a href="solved question/r=a(1+sinθ).pdf" width="100%" height="500px">Find the pedal equation to the curve r=a(1+sinθ)</a>
<img src="img/r=a(1+sinθ).png" alt="r=a(1+sinθ)" width="80" height="20"></li>
<li><a href="solved question/r(1-cosθ)=2a.pdf" width="100%" height="500px">Find the pedal equation to the curve r(1-cosθ)=2a</a>
<img src="img/r(1-cosθ)=2a.png" alt="r(1-cosθ)=2a" width="80" height="20"></li>
</ul>
<br>
<ul>
<b>Unit 5a Integral Calculus (6 or 7 Marks)</b>
<br>
<br>
<li><a href="solved question/∫sinnx dx.pdf" width="100%" height="500px">obtain the reduction formula for ∫sinnx dx</a>
<img src="img/∫sinnx dx.png" alt="∫sinnx dx" width="60" height="20"></li>
<li><a href="solved question/∫cosnx dx.pdf" width="100%" height="500px">obtain the reduction formula for ∫cosnx dx</a>
<img src="img/∫cosnxdx.png" alt="cosnx dx" width="60" height="20"></li>
<li><a href="solved question/∫sinmx cosnx dx.pdf" width="100%" height="500px">obtain the reduction formula for ∫sinmx cosnx dx</a>
<img src="img/∫sinmx cosnx dx.png" alt="∫sinmx cosnx dx" width="80" height="20"></li>
<li><a href="solved question/0∫π∕2sinnx dx.pdf" width="100%" height="500px">obtain the reduction formula for 0∫π∕2 sinnx dx</a>
<img src="img/0∫π|2 sinnx dx.png" alt="0∫π∕2sinnx dx" width="80" height="20"></li>
<li><a href="solved question/0∫π∕2cosnx dx.pdf" width="100%" height="500px">obtain the reduction formula for 0∫π∕2 cosnx dx</a>
<img src="img/0∫π|2 cosnx dx.png" alt="0∫π∕2cosnx dx" width="80" height="20"></li>
</ul>
<br>
<ul>
<b>Unit 5b Integral Calculus (6 or 7 Marks)</b>
<br>
<br>
<li><a href="solved question/1∫2 0∫2-y xy dxdy.pdf" width="100%" height="500px">Evaluate 1∫2 0∫2-y xy dxdy</a>
<img src="img/1∫2 0∫2-y xy dxdy.png" alt="1∫2 0∫2-y xy dxdy" width="80" height="20"></li>
<li><a href="solved question/0∫2a 0∫Γ2a-x2 xy dydx.pdf" width="100%" height="500px">Evaluate 0∫2a 0∫√2a-x2 xy dxdy</a>
</ul>
<br>
<ul>
<b>Unit 5c Integral Calculus (6 or 7 Marks)</b>
<br>
<br>
<li><a href="solved question/0∫1 0∫1 0∫1 dxdydz.pdf" width="100%" height="500px">Evaluate 0∫1 0∫1 0∫1 (x+y+z)dxdydz</a>
<img src="img/0∫1 0∫1 0∫1 (x+y+z)dxdydz.png" alt="0∫1 0∫1 0∫1 dxdydz" width="110" height="20"></li>
<li><a href="solved question/0∫3 0∫2 0∫1 (x+y+z) dzdxdy.pdf" width="100%" height="500px">Evaluate 0∫3 0∫2 0∫1 (x+y+z) dzdxdy</a>
<img src="img/0∫3 0∫2 0∫1 (x+y+z) dzdxdy.png" alt="0∫3 0∫2 0∫1 (x+y+z) dzdxdy" width="110" height="20"></li>
<li><a href="solved question/0∫a 0∫x 0∫x+y ex+y+z dzdydx.pdf" width="100%" height="500px">Evaluate 0∫a 0∫x 0∫x+y ex+y+z dzdydx</a>
<img src="img/0∫a 0∫x 0∫x+y ex+y+z dzdydx.png" alt="0∫a 0∫x 0∫x+y ex+y+z dzdydx.pdf" width="110" height="20"></li>
</ul>
<br>
<ul>
<b>Unit 6b Integral Calculus (6 or 7 Marks)</b>
<br>
<br>
<li><a href="solved question/β(m,n).pdf" width="100%" height="500px">Prove that β(m,n) = ΓmΓn ∕ Γ(m+n)</a>
<img src="img/β(m,n) = ΓmΓn ∕ Γ(m+n).png" alt="β(m,n)" width="65" height="25"></li>
<li><a href="solved question/Γ[½]=Γπ.pdf" width="100%" height="500px">Prove that Γ[½] = √π </a>
<img src="img/Γ[½] = √π .png" alt="Γ[½]=Γπ" width="55" height="20"></li>
</ul>
<br>
<table>
<b>2010 Scheme</b>
<tr>
<td><a href="qp 2010 scheme/1 jun2010.pdf" width="100%" height="500px">Jun 2010</a></td>
<td><a href="qp 2010 scheme/2 dec2010.pdf" width="100%" height="500px">Dec 2010</a></td>
<td><a href="qp 2010 scheme/3 jun2011.pdf" width="100%" height="500px">Jun 2011</a></td>
<td><a href="qp 2010 scheme/4 Dec2011.pdf" width="100%" height="500px">Dec 2011</a></td>
<td><a href="qp 2010 scheme/5 jun2012.pdf" width="100%" height="500px">Jun 2012</a></td>
<td><a href="qp 2010 scheme/6 Dec2012.pdf" width="100%" height="500px">Dec 2012</a></td>
<td><a href="qp 2010 scheme/8 dec2013.pdf" width="100%" height="500px">Dec 2013</a></td>
<td><a href="qp 2010 scheme/9 jun2014.pdf" width="100%" height="500px">Jun 2014</a></td>
<td><a href="qp 2010 scheme/10 dec2014.pdf" width="100%" height="500px">Dec 2014</a></td>
</tr>
<tr>
<td><a href="qp 2010 scheme/11 jun2015.pdf" width="100%" height="500px">Jun 2015</a></td>
<td><a href="qp 2010 scheme/12 dec2015.pdf" width="100%" height="500px">Dec 2015</td>
<td><a href="qp 2010 scheme/13 jun2016.pdf" width="100%" height="500px">Jun 2016</a></td>
<td><a href="qp 2010 scheme/14 dec2016.pdf" width="100%" height="500px">Dec 2016</a></td>
<td><a href="qp 2010 scheme/14 dec2016.pdf" width="100%" height="500px">Dec 2016</a></td>
<td><a href="qp 2010 scheme/15 jun2017.pdf" width="100%" height="500px">Jun 2017</a></td>
<td><a href="qp 2010 scheme/16 Dec2017.pdf" width="100%" height="500px">Dec 2017</a></td>
<td><a href="qp 2010 scheme/17 June2018.pdf" width="100%" height="500px">Jun 2018</a></td>
<td><a href="qp 2010 scheme/17 Dec2018.pdf" width="100%" height="500px">Dec 2018</a></td>
</tr>
</table>
<br><br>
</div>
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