| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2021 |
| Session | June |
| 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 formula and basic algebraic manipulation. Part (a) is routine application of the formula, and part (b) involves setting up and solving a simple quadratic equation. The question requires no problem-solving insight and is a standard textbook exercise testing basic binomial expansion skills. |
| 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]
\end{enumerate}
Given that in the expansion of $(1 + kx)^{10}$ the coefficient $x^3$ is 3 times the coefficient of $x$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the possible values of $k$. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q6 [6]}}