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M a t h e m a t i c s - 1-
Unit 1a Complex Numbers (6 or 7 Marks)
- Express the complex number √3+i in the polar form
- Express the complex number 1-i√3 in the polar form
- Find the modulus and amplitude of the complex number 1+cosθ+isinθ
- Find the modulus and amplitude of the complex number 1-cosθ+isinθ
- Find the modulus and amplitude of the complex number (3-√2i)² / 1+2i
² | 1+2i.png)
- Find the modulus and amplitude of the complex number 3+i / 2+i
- Find the modulus and amplitude of the complex number 5+3i / 4-2i
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Unit 1b Complex Numbers (6 or 7 Marks)
- Express : 1 / (2+i)² - 1 /(2-1)² in the form of a+ib
² - 1 |(2-1)².png)
- Express : 3 / 1+i - 1 / 2-i + 1 / 1-i in the form of a+ib
- Express : (1+i)(1+3i) / (1+5i) in the form of a+ib
(1+3i) | (1+5i).png)
- Express : (5-3i)(2+i) / 4+2i in the form of a+ib
(2+i) | 4+2i.png)
- Express : (1+i)(2+i) / 3+i in the form of a+ib
(2+i) | 3+i.png)
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Unit 1c Complex Numbers (6 or 7 Marks)
- Find the cube root of 1+i
- Find the cube root of 1-i
- Find the fourth root 1-i√3
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Unit 2a & 2b Differential Calculus (6 or 7 Marks)
- Find the nth derivative of eax cos(bx+c)
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- Find the nth derivative of eax sin(bx+c)
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- Find the nth derivative of y=cos2xcos3x
- Find the nth derivative of y=log(ax+b)
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- Find the nth derivative of y=sin(ax+b)
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Unit 2c Differential Calculus (6 or 7 Marks)
- Find the nth derivative of x ∕ (x-1)(2x+3)
(2x+3).png)
- Find the nth derivative of y = x / x²-5x+6
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Unit 3c Differential Calculus(6 or 7 Marks)
- Find the pedal equation to the curve r=a(1-cosθ)
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- Find the pedal equation to the curve r=a(1+cosθ)
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- Find the pedal equation to the curve r=a(1+sinθ)
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- Find the pedal equation to the curve r(1-cosθ)=2a
=2a.png)
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Unit 5a Integral Calculus (6 or 7 Marks)
- obtain the reduction formula for ∫sinnx dx
- obtain the reduction formula for ∫cosnx dx
- obtain the reduction formula for ∫sinmx cosnx dx
- obtain the reduction formula for 0∫π∕2 sinnx dx
- obtain the reduction formula for 0∫π∕2 cosnx dx
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Unit 5b Integral Calculus (6 or 7 Marks)
- Evaluate 1∫2 0∫2-y xy dxdy
- Evaluate 0∫2a 0∫√2a-x2 xy dxdy
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Unit 5c Integral Calculus (6 or 7 Marks)
- Evaluate 0∫1 0∫1 0∫1 (x+y+z)dxdydz
dxdydz.png)
- Evaluate 0∫3 0∫2 0∫1 (x+y+z) dzdxdy
 dzdxdy.png)
- Evaluate 0∫a 0∫x 0∫x+y ex+y+z dzdydx
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Unit 6b Integral Calculus (6 or 7 Marks)
- Prove that β(m,n) = ΓmΓn ∕ Γ(m+n)
 = ΓmΓn ∕ Γ(m+n).png)
- Prove that Γ[½] = √π
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