| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Integration with Partial Fractions |
| Type | Partial fractions with repeated linear factor |
| Difficulty | Standard +0.3 This is a standard partial fractions question with a repeated linear factor, followed by routine integration using logarithms and the reverse chain rule. The algebraic manipulation is straightforward for C4 level, and the integration techniques are directly applicable without requiring novel insight. Slightly above average difficulty due to the repeated factor and careful arithmetic required, but remains a textbook exercise. |
| Spec | 1.02y Partial fractions: decompose rational functions1.08j Integration using partial fractions |
$$f(x) = \frac{15-17x}{(2+x)(1-3x)^2}, \quad x \neq -2, \quad x \neq \frac{1}{3}.$$
\begin{enumerate}[label=(\roman*)]
\item Find the values of the constants $A$, $B$ and $C$ such that
$$f(x) = \frac{A}{2+x} + \frac{B}{1-3x} + \frac{C}{(1-3x)^2}.$$ [5]
\item Find the value of
$$\int_{-1}^{0} f(x) \, dx,$$
giving your answer in the form $p + \ln q$, where $p$ and $q$ are integers. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR C4 Q5 [10]}}