| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Two equations from coefficients |
| Difficulty | Standard +0.3 This is a standard binomial expansion question requiring recall of the formula and solving simultaneous equations. While it involves multiple steps (writing expansion, forming equations from coefficients, solving for n and a, then finding x³ coefficient), these are routine C2 techniques with no novel insight required. Slightly above average difficulty due to the algebraic manipulation needed. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
\begin{enumerate}[label=(\alph*)]
\item Write down the first four terms of the binomial expansion, in ascending powers of x, of $(1 + ax)^n$, where $n > 2$. [2]
\end{enumerate}
Given that, in this expansion, the coefficient of x is 8 and the coefficient of x² is 30,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the value of n and the value of a, [4]
\item find the coefficient of x³. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q2 [8]}}