| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2012 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Factoring out constants first |
| Difficulty | Moderate -0.3 This is a standard C4 binomial expansion question with straightforward steps: part (a) is direct application of the formula, part (b) requires factoring out 8 first (a common textbook technique), and part (c) involves substituting a value to approximate a cube root. The question tests routine application of the generalized binomial theorem with minimal problem-solving required, making it slightly easier than average. |
| 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 $( 1 + 6 x ) ^ { \frac { 2 } { 3 } }$ up to and including the term in $x ^ { 2 }$.\\
(2 marks)
\item Find the binomial expansion of $( 8 + 6 x ) ^ { \frac { 2 } { 3 } }$ up to and including the term in $x ^ { 2 }$.\\
(3 marks)
\item Use your answer from part (b) to find an estimate for $\sqrt [ 3 ] { 100 }$ in the form $\frac { a } { b }$, where $a$ and $b$ are integers.\\
(2 marks)
\end{enumerate}
\hfill \mbox{\textit{AQA C4 2012 Q3 [7]}}