SPS SPS FM 2023 January — Question 3 5 marks

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2023
SessionJanuary
Marks5
TopicPartial Fractions
TypeRepeated linear factor with distinct linear factor – decompose and integrate
DifficultyStandard +0.8 This is a Further Maths partial fractions question requiring handling of a repeated linear factor (x-1)² and an improper fraction (degree 2 over degree 3). Students must recognize the need for terms A/(x-1) + B/(x-1)² + C/(x-2), then solve a system of equations. More challenging than standard A-level partial fractions due to the repeated factor and algebraic manipulation required, but still a recognizable technique-based question.
Spec1.02y Partial fractions: decompose rational functions

Express \(\frac{x^2}{(x-1)^2(x-2)}\) in partial fractions. [5]

Express $\frac{x^2}{(x-1)^2(x-2)}$ in partial fractions. [5]

\hfill \mbox{\textit{SPS SPS FM 2023 Q3 [5]}}