CAIE A-Level Mathematics A2 3.1.4 Partial Fractions Questions

Practise decomposing rational expressions into partial fractions and using the resulting forms.

Exam points

decompose rational expressions into partial fractions
determine unknown constants in partial-fraction forms
use partial fractions in algebraic and integration problems

[Maximum number: 5]

$8 \quad$ Let $\mathrm{f}(x)=\frac{3-3 x^{2}}{(2 x+1)(x+2)^{2}}$ .

Express f(x) in partial fractions.

State or imply the form $\frac{A}{2 x+1}+\frac{B}{x+2}+\frac{C}{(x+2)^{2}}$
Marking guidance:

Accept $\frac{A}{2 x+1}+\frac{D x+E}{(x+2)^{2}}$ .

Use a correct method for finding a constant
Obtain one of A=1, B=-2, C=3
For alternative form: A=1, D=-2, E=-1.

Obtain a second value
Obtain the third value

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CAIE A-Level Mathematics A2 3.1.4 Partial Fractions Questions question 1