CAIE A-Level Mathematics 3.1.4 Partial Fractions

Practise selecting the full partial-fraction form for distinct, repeated or irreducible factors and determining all constants by substitution or coefficient comparison.

Exam points

write one constant term per linear factor and a linear numerator over an irreducible quadratic
include separate terms for every power of a repeated factor before clearing denominators
substitute convenient roots and compare remaining coefficients to determine every constant

[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 $\frac{A}{2 x+1}+\frac{B}{x+2}+\frac{C}{(x+2)^{2}}$

B1

Marking guidance:

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

Use a correct method for finding a constant

M1

Obtain one of A=1, B=-2, C=3

A1

For alternative form: A=1, D=-2, E=-1.

Obtain a second value

A1

Obtain the third value

A1

All question bank results loaded

3.1.4—Partial fractions question 1