| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Product with linear term |
| Difficulty | Moderate -0.3 This is a standard binomial expansion question requiring the formula for negative integer powers followed by algebraic manipulation. Part (i) is routine application of $(1+x)^n$ with $n=-2$. Part (ii) requires recognizing that $(2-x)^2 = 4(1-x/2)^2$ and combining expansions, which is a common C4 technique but involves careful coefficient arithmetic across multiple terms. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
\begin{enumerate}[label=(\roman*)]
\item Expand $(1 - 3x)^{-2}, |x| < \frac{1}{3}$, in ascending powers of $x$ up to and including the term in $x^3$, simplifying each coefficient. [4]
\item Hence, or otherwise, show that for small $x$,
$$\left(\frac{2-x}{1-3x}\right)^2 \approx 4 + 20x + 85x^2 + 330x^3.$$ [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C4 Q4 [7]}}