| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Find constants from coefficient conditions on terms |
| Difficulty | Standard +0.3 This is a straightforward binomial expansion problem requiring students to equate coefficients and solve simultaneous equations. While it involves multiple steps and algebraic manipulation, the techniques are standard C2 fare with no novel insight required. The constraint that coefficients of x² and x³ are equal provides a clear path to the solution, making it slightly easier than average. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks | Guidance |
|---|---|---|
| 7 | 3.2 | 4 |
Question 7:
7 | 3.2 | 4 | 4 | 8The first four terms, in ascending powers of $x$, of the binomial expansion of $(1 + kx)^n$ are
$$1 + Ax + Bx^2 + Bx^3 + \ldots,$$
where $k$ is a positive constant and $A$, $B$ and $n$ are positive integers.
\begin{enumerate}[label=(\alph*)]
\item By considering the coefficients of $x^2$ and $x^3$, show that $3 = (n - 2) k$. [4]
\end{enumerate}
Given that $A = 4$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the value of $n$ and the value of $k$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q7 [8]}}