Partial fractionsEdexcel A-Level Maths: Flashcards

What these 13 flashcards ask

Form of partial fractions for \frac{\ldots}{(x-1)(x+2)}?
Form for \frac{\ldots}{(ax+b)(cx+d)^2}?
First step in finding A, B?
Cover-up/substitution method?
A and B for \frac{5x+1}{(x-1)(x+2)}?
\int\frac{1}{ax+b}\,dx?
\int\frac{1}{(x+2)^2}\,dx?
Why use partial fractions to differentiate?
Expansion of (1+x)^{-1}?
Expansion of (1-2x)^{-1} and its validity?
How do you expand \frac{1}{2-x}?
Validity of a sum of two expansions?
What does \equiv mean?

Exam questions on Partial fractions

$\frac{5x+1}{(x-1)(x+2)}\equiv\frac{A}{x-1}+\frac{B}{x+2}$ , where $A$ and $B$ are constants.
Hence find $\int\frac{5x+1}{(x-1)(x+2)}\,dx$ .2 marks
$f(x)=\frac{7x+4}{(x+1)(2x-1)}$ , $x\neq-1$ , $x\neq\frac12$ . It is given that $f(x)\equiv\frac{A}{x+1}+\frac{B}{2x-1}$ .
Find the coefficient of $x^2$ in the series expansion of $f(x)$ in ascending powers of $x$ , valid for $|x|<\frac12$ .2 marks
$g(x)=\frac{3x^2+7x+5}{(x+1)(x+2)^2}$ , $x>-1$ .
Find the values of the constants $A$ , $B$ and $C$ such that $g(x)\equiv\frac{A}{x+1}+\frac{B}{x+2}+\frac{C}{(x+2)^2}$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).