| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Partial Fractions |
| Type | Repeated linear factor with distinct linear factor – decompose and integrate |
| Difficulty | Standard +0.8 This is a substantial C4 question requiring partial fractions with a repeated linear factor, integration involving logarithms and a reciprocal linear term, and binomial expansions of two factors multiplied together. While each technique is standard C4 material, the combination of all three parts with the algebraic manipulation required (especially expanding and collecting terms to x² in part c) makes this moderately harder than average, though still within expected C4 scope. |
| Spec | 1.02y Partial fractions: decompose rational functions1.04c Extend binomial expansion: rational n, |x|<11.08j Integration using partial fractions |
$$\text{f}(x) = \frac{25}{(3 + 2x)^2(1 - x)}, \quad |x| < 1.$$
\begin{enumerate}[label=(\alph*)]
\item Express f(x) as a sum of partial fractions.
[4]
\item Hence find $\int \text{f}(x) \, dx$.
[5]
\item Find the series expansion of f(x) in ascending powers of $x$ up to and including the term in $x^2$. Give each coefficient as a simplified fraction.
[7]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q7 [16]}}