Partial fractionsAQA A-Level Maths: Flashcards

What these 13 flashcards ask

What are partial fractions?
Form for \dfrac{px+q}{(x+a)(x+b)}?
Form for \dfrac{px+q}{(x+a)^2}?
Form for \dfrac{c}{(x+a)(x+b)(x+d)}?
Form for \dfrac{px+q}{(x+a)(x+b)^2}?
First step before decomposing?
What do you do after writing the form?
How do you find a constant by substitution?
When is equating coefficients needed?
Find A in \dfrac{9}{(x+1)(x-2)}\equiv\dfrac{A}{x+1}+\dfrac{B}{x-2}.
Which x do you substitute to find the constant of \dfrac{A}{2x-1}?
How can you check partial fractions?
Decompose \dfrac{4x+9}{(x+2)(x+3)}.

Exam questions on Partial fractions

It is given that $\dfrac{7x+1}{(x-1)(x+2)}\equiv\dfrac{A}{x-1}+\dfrac{B}{x+2}$ for all $x\neq1,-2$ , where $A$ and $B$ are constants.
Verify that the partial fractions you found for $A$ and $B$ are correct by substituting $x=0$ into both sides of the identity.2 marks
It is given that $\dfrac{5x+3}{(x+1)^2}\equiv\dfrac{P}{x+1}+\dfrac{Q}{(x+1)^2}$ for all $x\neq-1$ , where $P$ and $Q$ are constants.
Use the partial fractions to evaluate $\dfrac{5x+3}{(x+1)^2}$ when $x=1$ .2 marks
Let $\mathrm{f}(x)=\dfrac{4x+9}{(x+2)(x+3)}$ and $\mathrm{g}(x)=\dfrac{5x+4}{(x-1)(x+2)^2}$ , defined for values of $x$ where the denominators are non-zero.
Express $\mathrm{f}(x)$ in partial fractions.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).