| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2024 |
| Session | October |
| Marks | 6 |
| Topic | Binomial Theorem (positive integer n) |
| Type | Binomial times linear coefficient |
| Difficulty | Moderate -0.8 Part (a) is a routine binomial expansion requiring direct application of the formula with no complications. Part (b) requires multiplying two expansions and equating coefficients, which is standard practice but involves slightly more algebraic manipulation. Both parts are straightforward textbook exercises with no problem-solving insight required, making this easier than average. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n1.04b Binomial probabilities: link to binomial expansion |
\begin{enumerate}[label=(\alph*)]
\item Find and simplify the first three terms in the expansion of $(2-5x)^5$ in ascending powers of $x$. [3]
\item In the expansion of $(1+ax)^2(2-5x)^5$, the coefficient of $x$ is 48.
Find the value of $a$. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2024 Q3 [6]}}