A-level · Algebra & functions

Partial fractionsExam-style questions

Splitting one fraction into a sum of simpler ones. Partial fractions as adding fractions run backwards, and why the pieces are worth having; distinct linear factors, found by substituting the values that make brackets vanish; factorising the denominator first, including factors like (2x + 1); the extra piece a repeated factor needs, and equating coefficients for it; and dividing out a top-heavy fraction first.

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26 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
Express $\dfrac{9x + 17}{(2x + 1)(x + 3)}$ in partial fractions.

(3 marks)
Level 2 · 3 marksTry it
2
Express $\dfrac{5x + 1}{(x - 1)(x + 2)}$ in partial fractions.
Level 3 · 3 marksTry it
3
Express $\dfrac{3x + 2}{x(x + 1)^2}$ in partial fractions.
Level 3 · 5 marksTry it
4
Given that $\dfrac{7x^2 + 2x - 2}{(x + 1)(x - 2)(2x + 1)} \equiv \dfrac{A}{x + 1} + \dfrac{B}{x - 2} + \dfrac{C}{2x + 1}$ , find the values of the constants $A$ , $B$ and $C$ .
Level 3 · 4 marksTry it
5
Express $\dfrac{6x^2 + 14x - 11}{(x - 1)(x + 2)(2x - 1)}$ in partial fractions.
Level 3 · 4 marksTry it

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