| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Generalised Binomial Theorem and Partial Fractions |
| Type | Partial fractions then binomial expansion |
| Difficulty | Moderate -0.3 This is a standard C4 question combining partial fractions (routine algebraic manipulation) with binomial expansion. Part (a) is straightforward cover-up method or substitution. Part (b) requires expanding two binomial series and combining terms, which is textbook procedure but involves careful arithmetic across multiple terms. Slightly easier than average due to being a well-practiced technique with clear steps. |
| Spec | 1.02y Partial fractions: decompose rational functions1.04c Extend binomial expansion: rational n, |x|<1 |
Given that
$$\frac{10(2 - 3x)}{(1 - 2x)(2 + x)} \equiv \frac{A}{1 - 2x} + \frac{B}{2 + x},$$
\begin{enumerate}[label=(\alph*)]
\item find the values of the constants $A$ and $B$. [3]
\item Hence, or otherwise, find the series expansion in ascending powers of $x$, up to and including the term in $x^3$, of $\frac{10(2 - 3x)}{(1 - 2x)(2 + x)}$, for $|x| < \frac{1}{2}$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q11 [8]}}