| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2026 |
| Session | November |
| Marks | 6 |
| Topic | Binomial Theorem (positive integer n) |
| Type | Coefficient relationship between terms |
| Difficulty | Moderate -0.3 This is a straightforward binomial expansion question requiring recall of the binomial theorem formula and basic algebraic manipulation. Part (a) is routine application of nCr coefficients, while part (b) involves setting up and solving a simple equation by comparing coefficients—standard textbook fare with no novel insight required, making it slightly easier than average. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
\begin{enumerate}[label=(\alph*)]
\item Find the first 4 terms, in ascending powers of $x$, in the binomial expansion of
$$(1 + kx)^{10}$$
where $k$ is a non-zero constant. Write each coefficient as simply as possible.
[3]
Given that in the expansion of $(1 + kx)^{10}$ the coefficient $x^3$ is 3 times the coefficient of $x$,
\item find the possible values of $k$.
[3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2026 Q10 [6]}}