| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2023 |
| Session | October |
| Marks | 6 |
| Topic | Binomial Theorem (positive integer n) |
| Type | Coefficient relationship between terms |
| Difficulty | Moderate -0.8 This is a straightforward binomial expansion question requiring recall of the binomial theorem for n=3, followed by a simple algebraic equation. Part (i) is routine manipulation, and part (ii) involves equating two terms and solving a quadratic—both are standard textbook exercises with no problem-solving insight required. The low power (n=3) and direct application make this easier than average. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
\begin{enumerate}[label=(\roman*)]
\item Find the binomial expansion of $(3 + kx)^3$, simplifying the terms. [4]
\item It is given that, in the expansion of $(3 + kx)^3$, the coefficient of $x^2$ is equal to the constant term. Find the possible values of $k$, giving your answers in an exact form. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2023 Q5 [6]}}