| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Direct single expansion substitution |
| Difficulty | Moderate -0.3 This is a structured multi-part question that guides students through binomial expansion and approximation. Part (a) is straightforward substitution and simplification, part (b) is standard binomial expansion with negative fractional index (core C4 content), parts (c) and (d) are routine applications. While it requires multiple techniques, the question provides clear scaffolding and involves no novel problem-solving—slightly easier than average due to its guided nature. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.05a Sine, cosine, tangent: definitions for all arguments1.05g Exact trigonometric values: for standard angles |
\begin{enumerate}[label=(\alph*)]
\item Prove that, when $x = \frac{1}{15}$, the value of $(1 + 5x)^{-\frac{1}{3}}$ is exactly equal to $\sin 60°$. [3]
\item Expand $(1 + 5x)^{-\frac{1}{3}}$, $|x| < 0.2$, 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 Q5 [10]}}