| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2023 |
| Session | January |
| Marks | 5 |
| Topic | Partial Fractions |
| Type | Repeated linear factor with distinct linear factor – decompose and integrate |
| Difficulty | Standard +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. |
| Spec | 1.02y Partial fractions: decompose rational functions |
Express $\frac{x^2}{(x-1)^2(x-2)}$ in partial fractions. [5]
\hfill \mbox{\textit{SPS SPS FM 2023 Q3 [5]}}