| Exam Board | Edexcel |
|---|---|
| Module | P4 (Pure Mathematics 4) |
| Year | 2022 |
| Session | October |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Non-zero terms only |
| Difficulty | Standard +0.3 This is a standard binomial expansion question requiring the generalised binomial theorem with fractional/negative powers. Part (a) involves routine application of the formula with some algebraic manipulation to extract the correct form. Part (b) tests understanding of validity conditions (|x/2| < 1). Part (c) requires choosing an appropriate x-value and algebraic manipulation to obtain √3, which is slightly more demanding but still follows a familiar pattern for this topic. Overall, this is slightly easier than average as it follows a well-practiced template with no novel insights required. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
$$g(x) = \frac{1}{\sqrt{4-x^2}}$$
\begin{enumerate}[label=(\alph*)]
\item Find, in ascending powers of $x$, the first four non-zero terms of the binomial expansion of $g(x)$. Give each coefficient in simplest form. [5]
\item State the range of values of $x$ for which this expansion is valid. [1]
\item Use the expansion from part (a) to find a fully simplified rational approximation for $\sqrt{3}$
Show your working and make your method clear. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel P4 2022 Q4 [8]}}