| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Coefficient relationship between terms |
| Difficulty | Moderate -0.8 This is a straightforward C2 binomial expansion question requiring direct application of the binomial theorem formula with a simple constraint. Part (a) is routine calculation, part (b) involves equating two coefficients to solve for k (basic algebra), and part (c) is substitution. No problem-solving insight needed, just methodical application of a standard technique. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
\begin{enumerate}[label=(\alph*)]
\item Find the first four terms, in ascending powers of $x$, in the bionomial expansion of $(1 + kx)^8$, where $k$ is a non-zero constant.
[3]
\end{enumerate}
Given that, in this expansion, the coefficients of $x$ and $x^2$ are equal, find
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item the value of $k$,
[2]
\item the coefficient of $x^3$.
[1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q3 [6]}}