| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2022 |
| Session | February |
| Marks | 7 |
| Topic | Generalised Binomial Theorem |
| Type | Product with linear term |
| Difficulty | Moderate -0.3 Part (i) is a standard binomial expansion with negative index requiring straightforward application of the formula. Part (ii) requires multiplying two expansions and collecting terms, which is routine but involves more algebraic manipulation than a basic recall question. This is slightly easier than average A-level difficulty as it follows a predictable pattern with no conceptual challenges. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
\begin{enumerate}[label=(\roman*)]
\item Expand $(1 - 3x)^{-2}$ in ascending powers of $x$, up to and including the term in $x^2$. [3]
\item Find the coefficient of $x^2$ in the expansion of $\frac{(1 + 2x)^2}{(1 - 3x)^2}$ in ascending powers of $x$. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2022 Q8 [7]}}