| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2021 |
| Session | June |
| Marks | 5 |
| Topic | Generalised Binomial Theorem |
| Type | Expand and state validity |
| Difficulty | Moderate -0.3 Part (a) is a standard binomial expansion with fractional power requiring routine application of the formula to find one coefficient. Part (b) tests basic understanding of validity conditions (|x| < 4). This is straightforward bookwork with minimal problem-solving, making it slightly easier than average but not trivial since it involves fractional indices. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
\begin{enumerate}[label=(\alph*)]
\item Use the binomial expansion, in ascending powers of $x$, to show that
$$\sqrt{4-x} = 2 - \frac{1}{4}x + kx^2 + ...$$
where $k$ is a rational constant to be found.
[4]
A student attempts to substitute $x = 1$ into both sides of this equation to find an approximate value for $\sqrt{3}$.
\item State, giving a reason, if the expansion is valid for this value of $x$.
[1]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Pure 2021 Q6 [5]}}