| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2006 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Standard product of two binomials |
| Difficulty | Moderate -0.3 This is a straightforward binomial expansion question requiring routine application of the binomial theorem. Part (a) involves simple expansion of a small power with pattern matching, part (b) is direct application of the binomial coefficient formula, and part (c) requires multiplying terms from two expansions—a standard technique. While multi-part, each step is procedural with no novel insight required, making it slightly easier than average. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
4
\begin{enumerate}[label=(\alph*)]
\item The expression $( 1 - 2 x ) ^ { 4 }$ can be written in the form
$$1 + p x + q x ^ { 2 } - 32 x ^ { 3 } + 16 x ^ { 4 }$$
By using the binomial expansion, or otherwise, find the values of the integers $p$ and $q$.
\item Find the coefficient of $x$ in the expansion of $( 2 + x ) ^ { 9 }$.
\item Find the coefficient of $x$ in the expansion of $( 1 - 2 x ) ^ { 4 } ( 2 + x ) ^ { 9 }$.
\end{enumerate}
\hfill \mbox{\textit{AQA C2 2006 Q4 [8]}}