| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2006 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Substitute expression for variable |
| Difficulty | Moderate -0.3 This is a standard C4 binomial expansion question with routine substitution and algebraic manipulation. Part (a) is direct application of the formula, (b) is straightforward substitution, (c) tests understanding of validity conditions (|5x/2| < 1), and (d) requires recognizing the connection and simplifying coefficients. While multi-part, each step follows predictable patterns with no novel insight required, making it slightly easier than average. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
2
\begin{enumerate}[label=(\alph*)]
\item Obtain the binomial expansion of $( 1 - x ) ^ { - 3 }$ up to and including the term in $x ^ { 2 }$.
\item Hence obtain the binomial expansion of $\left( 1 - \frac { 5 } { 2 } x \right) ^ { - 3 }$ up to and including the term in $x ^ { 2 }$.
\item Find the range of values of $x$ for which the binomial expansion of $\left( 1 - \frac { 5 } { 2 } x \right) ^ { - 3 }$ would be valid.
\item Given that $x$ is small, show that $\left( \frac { 4 } { 2 - 5 x } \right) ^ { 3 } \approx a + b x + c x ^ { 2 }$, where $a , b$ and $c$ are integers.
\end{enumerate}
\hfill \mbox{\textit{AQA C4 2006 Q2 [8]}}