| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Two unknowns from two coefficient conditions |
| Difficulty | Standard +0.3 This is a standard binomial expansion problem requiring systematic application of the binomial theorem formula. Students must set up two equations from given coefficients, solve simultaneously for parameters, then apply the formula again. While it involves algebraic manipulation across multiple steps, it follows a well-practiced procedure with no novel insight required, making it slightly easier than average. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<1 |
When $(1 + ax)^n$ is expanded as a series in ascending powers of $x$, the coefficients of $x$ and $x^2$ are $-6$ and $27$ respectively.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $a$ and the value of $n$. [5]
\item Find the coefficient of $x^3$. [2]
\item State the set of values of $x$ for which the expansion is valid. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q6 [8]}}