| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2024 |
| Session | October |
| Marks | 6 |
| Topic | Binomial Theorem (positive integer n) |
| Type | Coefficient zero after multiplying binomial |
| Difficulty | Moderate -0.3 Part (a) is a straightforward binomial expansion requiring routine application of the binomial theorem. Part (b) requires identifying terms from the product and solving an equation, but the algebra is manageable and the approach is standard. This is slightly easier than average due to being a familiar exam technique with clear structure, though it does require careful coefficient tracking. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
\begin{enumerate}[label=(\alph*)]
\item Find and simplify the first three terms in the expansion, in ascending powers of $x$, of $\left(2 + \frac{1}{3}kx\right)^6$, where $k$ is a constant.
[3]
\item In the expansion of $(3 - 4x)\left(2 + \frac{1}{3}kx\right)^6$, the constant term is equal to the coefficient of $x^2$.
Determine the exact value of $k$, given that $k$ is positive.
[3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2024 Q3 [6]}}