| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem and Partial Fractions |
| Type | Simplification then binomial expansion |
| Difficulty | Standard +0.3 This question involves algebraic manipulation with partial fractions (factoring the denominator, combining fractions) followed by a standard binomial expansion. Part (i) requires careful algebra but is methodical; part (ii) is a routine C4 binomial series application once simplified. The work is somewhat lengthy but uses only standard techniques with no novel insight required, making it slightly easier than average. |
| Spec | 1.02k Simplify rational expressions: factorising, cancelling, algebraic division1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
$$f(x) = 3 - \frac{x-1}{x-3} + \frac{x+11}{2x^2-5x-3}, \quad |x| < \frac{1}{2}.$$
\begin{enumerate}[label=(\roman*)]
\item Show that
$$f(x) = \frac{4x-1}{2x+1}.$$ [4]
\item Find the series expansion of $f(x)$ 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 Q3 [9]}}