| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Partial Fractions |
| Type | Repeated linear factor with distinct linear factor – decompose and integrate |
| Difficulty | Standard +0.3 This is a standard C4 partial fractions question with a repeated linear factor, followed by routine integration. Part (i) requires setting up and solving for three constants (standard technique), and part (ii) involves straightforward integration of partial fractions and simplifying logarithms. While it requires multiple steps and careful algebra, it follows a well-practiced procedure with no novel insight needed, making it slightly easier than average. |
| Spec | 1.02y Partial fractions: decompose rational functions1.08d Evaluate definite integrals: between limits1.08j Integration using partial fractions |
5.
$$f ( x ) = \frac { 7 + 3 x + 2 x ^ { 2 } } { ( 1 - 2 x ) ( 1 + x ) ^ { 2 } } , \quad | x | > \frac { 1 } { 2 }$$
(i) Express $\mathrm { f } ( x )$ in partial fractions.\\
(ii) Show that
$$\int _ { 1 } ^ { 2 } \mathrm { f } ( x ) \mathrm { d } x = p - \ln q$$
where $p$ is rational and $q$ is an integer.\\
\hfill \mbox{\textit{OCR C4 Q5 [10]}}