CAIE A-Level Mathematics 3.1.4 Partial Fractions

CAIE A-Level Mathematics 3.1.4 Partial Fractions
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

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

How this is tested

  • 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

Question 10(a)

[Maximum number: 6]

Let f(x)=x3+2x−11(3+x)(2+x2)\mathrm{f}(x)=\frac{x^{3}+2 x-11}{(3+x)\left(2+x^{2}\right)}.

Express f(x) in partial fractions.