| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2024 |
| Session | September |
| Marks | 3 |
| Topic | Partial Fractions |
| Type | Repeated linear factor with distinct linear factor – decompose only |
| Difficulty | Moderate -0.8 This is a standard partial fractions decomposition with a repeated linear factor. The method is routine: set up the form A/(x-2) + B/(x-1) + C/(x-1)², multiply through, and solve for coefficients. It's a textbook exercise requiring only procedural knowledge with no problem-solving insight needed, making it easier than average but not trivial due to the algebraic manipulation required. |
| Spec | 1.02y Partial fractions: decompose rational functions |
\begin{enumerate}
\item Express
\end{enumerate}
$$f ( x ) = \frac { x ^ { 2 } + x - 5 } { ( x - 2 ) ( x - 1 ) ^ { 2 } }$$
in partial fractions.
\section*{(Total for Question 1 is 3 marks)}
\hfill \mbox{\textit{SPS SPS SM Pure 2024 Q1 [3]}}