| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2020 |
| Session | February |
| Marks | 8 |
| Topic | Generalised Binomial Theorem |
| Type | Expand and state validity |
| Difficulty | Moderate -0.5 This is a straightforward application of the binomial expansion for fractional powers with standard follow-up parts: expand (4+x)^(1/2), state validity |x|<4, and substitute x=0.9 to approximate √36.9. All steps are routine and commonly practiced, making it slightly easier than average but still requiring proper technique. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
5
\begin{enumerate}[label=(\alph*)]
\item Find the first three non-zero terms of the expansion, in ascending powers of $x$, of $( 4 + x ) ^ { \frac { 1 } { 2 } }$.
\item State the range of values of $x$ for which your expansion in part (a) is valid. [1]
\item Use your expansion to determine an approximation to $\sqrt { } 36.9$, showing all the figures on your calculator.
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2020 Q5 [8]}}