| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 7 |
| Topic | Partial Fractions |
| Type | Partial fractions with linear factors – decompose and integrate (definite) |
| Difficulty | Moderate -0.3 This is a straightforward two-part question combining partial fractions (a standard algebraic technique) with integration. Part (a) is routine A-level algebra, and part (b) requires integrating the partial fractions to get logarithms, then evaluating and simplifying. While it requires multiple steps and careful algebraic manipulation, both techniques are standard textbook exercises with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02y Partial fractions: decompose rational functions1.08j Integration using partial fractions |
\begin{enumerate}[label=(\alph*)]
\item Express $\frac{1}{(x-1)(x+2)}$ in partial fractions [2]
\item In this question you must show detailed reasoning.
Hence find $\int_2^3 \frac{1}{(x-1)(x+2)} dx$.
Give your answer in its simplest form. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2017 Q4 [7]}}