| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2021 |
| Session | May |
| Marks | 8 |
| Topic | Generalised Binomial Theorem |
| Type | Direct quotient expansion |
| Difficulty | Standard +0.3 This question requires binomial expansion of (1+x)^{-1/2} and (1-x)^{1/2}, then multiplication of series—standard A-level techniques. Part (ii) is straightforward substitution and arithmetic. While it involves multiple steps, it's a routine application of the binomial theorem without requiring problem-solving insight or novel approaches. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
\begin{enumerate}[label=(\roman*)]
\item Show that $\sqrt{\frac{1-x}{1+x}} \approx 1 - x + \frac{1}{2}x^2$, for $|x| < 1$. [5]
\item By taking $x = \frac{2}{7}$, show that $\sqrt{5} \approx \frac{111}{49}$. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q5 [8]}}