| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2013 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Factoring out constants first |
| Difficulty | Standard +0.3 This is a standard C4 binomial expansion question with routine factoring of constants. Part (a) is direct application of the formula, part (b)(i) requires factoring out 27 = 3³ before applying the expansion (a common textbook technique), and part (b)(ii) involves straightforward substitution of a given value. The question tests procedural fluency rather than problem-solving insight, making it slightly easier than average for A-level. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
3
\begin{enumerate}[label=(\alph*)]
\item Find the binomial expansion of $( 1 + 6 x ) ^ { - \frac { 1 } { 3 } }$ up to and including the term in $x ^ { 2 }$.
\item \begin{enumerate}[label=(\roman*)]
\item Find the binomial expansion of $( 27 + 6 x ) ^ { - \frac { 1 } { 3 } }$ up to and including the term in $x ^ { 2 }$, simplifying the coefficients.
\item Given that $\sqrt [ 3 ] { \frac { 2 } { 7 } } = \frac { 2 } { \sqrt [ 3 ] { 28 } }$, use your binomial expansion from part (b)(i) to obtain an approximation to $\sqrt [ 3 ] { \frac { 2 } { 7 } }$, giving your answer to six decimal places.\\
(2 marks)
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA C4 2013 Q3 [7]}}