| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2020 |
| Session | June |
| Marks | 5 |
| Topic | Generalised Binomial Theorem |
| Type | State validity only |
| Difficulty | Moderate -0.8 Part (a) is a routine application of the binomial expansion for fractional powers requiring recall of the formula and simplification of coefficients. Part (b) tests understanding of the validity condition |x| < 1 for convergence, which is a standard conceptual check. This is easier than average as it involves straightforward computation and basic theoretical knowledge without problem-solving. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
1.
\begin{enumerate}[label=(\alph*)]
\item Find the first 4 terms, in ascending powers of $x$, of the binomial expansion of
$$\sqrt { 1 + 4 x }$$
giving each coefficient in its simplest form.
The expansion can be used to find an approximation for $\sqrt { 26 }$
\item Explain why $x = \frac { 25 } { 4 }$ should not be used in the expansion to find an approximation for $\sqrt { 26 }$
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2020 Q1 [5]}}