Question 1

Resolve the algebraic fraction $\frac{5x-3}{(x-3)(x+3)}$ into partial fractions

Accepted Answer

$\frac{2}{x-3}+\frac{3}{x+3}$

Answer

$\frac{5}{x-3}+\frac{3}{x+3}$

Answer

$\frac{1}{x-3}+\frac{2}{x+3}$

Answer

$\frac{4}{x-3}+\frac{3}{x+3}$

Question 2

Resolve the algebraic fraction $\frac{10x-13}{(2x-3)^{2}}$ into partial fractions

Accepted Answer

$\frac{5}{2x-3}+\frac{2}{(2x-3)^{2}}$

Answer

$\frac{3}{2x-3}+\frac{2}{(2x-3)^{2}}$

Answer

$\frac{4}{2x-3}+\frac{3}{(2x-3)^{2}}$

Answer

$\frac{3}{2x-3}-\frac{3}{(2x-3)^{2}}$

Question 3

Resolve the algebraic fraction $\frac{8x^{2}-12}{x(x^{2}+2x-6)}$ into partial fractions

Accepted Answer

$\frac{2}{x}+\frac{6x-4}{x^{2}+2x-6}$

Answer

$\frac{2}{x}+\frac{5x-4}{x^{2}+2x-6}$

Answer

$\frac{2}{x}+\frac{4x+4}{x^{2}+2x-6}$

Answer

$\frac{2}{x}+\frac{3x+4}{x^{2}+2x-6}$

Question 4

Convert $3-5i$ into polar form]

Accepted Answer

$5.83  \angle\ -59^{0}$

Answer

$4.83  \angle\ 49^{0}$

Answer

$4.83  \angle\ 159^{0}$

Answer

$5.83  \angle\ -49^{0}$

Question 5

Rationalise (by writing  in the form $a+bi$) the ratio $\frac{2+4i}{1-3i}$

Accepted Answer

$-1+i$

Answer

$-2+i$

Answer

$3-i$

Answer

$3+i$

Question 6

Expand the following expression $(3+2i)(5-i)$

Accepted Answer

$17+7i$

Answer

$17-7i$

Answer

$15+7i$

Answer

$15+4i$

Question 7

Find the Modulus and argument on the Argand Diagram shown

Accepted Answer

Modulus = $\sqrt{13}$, Argument = $0.98$ radinas

Answer

Modulus = $\sqrt{12}$, Argument = $0.58$ radinas

Answer

Modulus = $\sqrt{12}$, Argument = $1.98$ radinas

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