| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2018 |
| Session | December |
| Marks | 12 |
| Topic | Partial Fractions |
| Type | Simplify then show identity |
| Difficulty | Standard +0.3 This is a straightforward multi-part question requiring algebraic manipulation to combine fractions (part a) and then solving a definite integral equation using partial fractions and logarithm properties (part b). While it involves multiple techniques, each step follows standard procedures with no novel insight required, making it slightly easier than average. |
| Spec | 1.02y Partial fractions: decompose rational functions1.08j Integration using partial fractions |
11 In this question you must show detailed reasoning.
A function f is given by $\mathrm { f } ( x ) = \frac { x - 4 } { ( x + 2 ) ( x - 1 ) } + \frac { 3 x + 1 } { ( x + 3 ) ( x - 1 ) }$.
\begin{enumerate}[label=(\alph*)]
\item Show that $\mathrm { f } ( x )$ can be written as $\frac { 2 ( 2 x + 5 ) } { ( x + 2 ) ( x + 3 ) }$.
\item Given that $\int _ { a } ^ { a + 4 } \mathrm { f } ( x ) \mathrm { d } x = 2 \ln 3$, find the value of the positive constant $a$.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 2018 Q11 [12]}}