| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2012 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Product of separate expansions |
| Difficulty | Standard +0.3 This is a structured multi-part question on binomial expansions with fractional powers. Parts (a) and (b)(i) are routine applications of the formula, (b)(ii) tests understanding of validity conditions, and (c) requires multiplying two expansions—all standard C4 techniques with no novel problem-solving required. Slightly above average due to the algebraic manipulation in part (c), but still a textbook exercise. |
| 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 $( 1 + 4 x ) ^ { \frac { 1 } { 2 } }$ up to and including the term in $x ^ { 2 }$.\\
(2 marks)
\item \begin{enumerate}[label=(\roman*)]
\item Find the binomial expansion of $( 4 - x ) ^ { - \frac { 1 } { 2 } }$ up to and including the term in $x ^ { 2 }$.
\item State the range of values of $x$ for which the expansion in part (b)(i) is valid.
\end{enumerate}\item Find the binomial expansion of $\sqrt { \frac { 1 + 4 x } { 4 - x } }$ up to and including the term in $x ^ { 2 }$.\\
(2 marks)
\end{enumerate}
\hfill \mbox{\textit{AQA C4 2012 Q3 [8]}}