| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2025 |
| Session | February |
| Marks | 5 |
| Topic | Generalised Binomial Theorem |
| Type | Product with linear term |
| Difficulty | Moderate -0.3 Part (i) is a straightforward binomial expansion using the formula for negative integer powers, requiring only direct application of the standard result. Part (ii) requires multiplying two series and collecting terms, which adds a modest layer of algebraic manipulation but remains a standard textbook exercise with clear methodology. The question is slightly easier than average due to its routine nature and limited conceptual demand. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
\begin{enumerate}[label=(\roman*)]
\item Find the first three terms in the expansion of $(1-2x)^{-1}$ in ascending powers of $x$, where $|x| < \frac{1}{2}$.
[3]
\item Hence find the coefficient of $x^2$ in the expansion of $\frac{x+3}{\sqrt{1-2x}}$.
[2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2025 Q2 [5]}}