| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Direct single expansion substitution |
| Difficulty | Standard +0.3 This is a structured multi-part question testing standard binomial expansion with negative/fractional powers. Part (a) requires simple substitution and recognizing √3/2, part (b) is routine application of the binomial formula, and parts (c)-(d) involve straightforward substitution and arithmetic. While it requires multiple techniques, each step follows a predictable pattern with no novel insight needed, making it slightly easier than average. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.05g Exact trigonometric values: for standard angles |
\begin{enumerate}[label=(\alph*)]
\item Prove that, when $x = \frac{1}{12}$, the value of $(1 + 5x)^{-\frac{1}{2}}$ is exactly equal to $\sin 60°$. [3]
\item Expand $(1 + 5x)^{-\frac{1}{2}}$, $|x| < 0.2$, in ascending powers of $x$ up to and including the term in $x^3$, simplifying each term. [4]
\item Use your answer to part $(b)$ to find an approximation for $\sin 60°$. [2]
\item Find the difference between the exact value of $\sin 60°$ and the approximation in part $(c)$. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q21 [10]}}