| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem and Partial Fractions |
| Type | Partial fractions then binomial expansion |
| Difficulty | Standard +0.8 This is a two-part question requiring partial fractions followed by binomial expansion of each fraction. While the techniques are standard C4 content, the question demands careful factorization, correct setup of partial fractions, then applying binomial expansion to two separate terms and combining results—multiple steps with opportunities for algebraic errors. The coefficient simplification adds computational demand beyond routine exercises. |
| Spec | 1.02y Partial fractions: decompose rational functions1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
\begin{enumerate}[label=(\roman*)]
\item Express $\frac{2 + 20x}{1 + 2x - 8x^2}$ as a sum of partial fractions. [3]
\item Hence find the series expansion of $\frac{2 + 20x}{1 + 2x - 8x^2}$, $|x| < \frac{1}{4}$, in ascending powers of $x$ up to and including the term in $x^3$, simplifying each coefficient. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR C4 Q5 [8]}}