| Exam Board | Edexcel |
|---|---|
| Module | P4 (Pure Mathematics 4) |
| Year | 2022 |
| Session | October |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Partial Fractions |
| Type | Partial fractions with linear factors – decompose and integrate (definite) |
| Difficulty | Moderate -0.3 Part (a) is a standard partial fractions decomposition with linear factors requiring routine algebraic manipulation. Part (b) involves integrating the partial fractions to get logarithms and simplifying using log laws—straightforward application of technique with clear structure. The 'show that' format and specific limits make it slightly more demanding than pure routine practice, but this remains a typical textbook-style question testing standard A-level integration methods without requiring problem-solving insight. |
| Spec | 1.02y Partial fractions: decompose rational functions1.08j Integration using partial fractions |
\begin{enumerate}[label=(\alph*)]
\item Express $\frac{3x}{(2x-1)(x-2)}$ in partial fraction form. [3]
\item Hence show that
$$\int_5^{25} \frac{3x}{(2x-1)(x-2)} \, dx = \ln k$$
where $k$ is a fully simplified fraction to be found.
(Solutions relying entirely on calculator technology are not acceptable.) [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel P4 2022 Q2 [7]}}