| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2024 |
| Session | October |
| Marks | 7 |
| Topic | Binomial Theorem (positive integer n) |
| Type | Product with unknown constant to determine |
| Difficulty | Moderate -0.3 This is a straightforward binomial expansion question requiring standard application of the formula for (2+ax)^6, then multiplying by (3-5x) and equating coefficients. The algebra is routine with no conceptual challenges, making it slightly easier than average but not trivial due to the multi-step nature and algebraic manipulation required. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
3.\\
\begin{enumerate}[label=(\roman*)]
\item Find and simplify the first three terms in the binomial expansion of $( 2 + a x ) ^ { 6 }$ in ascending powers of $x$.
\item In the expansion of $( 3 - 5 x ) ( 2 + a x ) ^ { 6 }$, the coefficient of $x$ is 64 . Find the value of $a$.\\[0pt]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2024 Q3 [7]}}