| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2014 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Single unknown from one coefficient condition |
| Difficulty | Moderate -0.3 This is a straightforward application of the binomial expansion formula for negative powers. Part (a) requires equating the coefficient of x from the general expansion to -6 to find k, then part (b) uses this k value to find the x² coefficient. Both parts are routine calculations with no conceptual difficulty beyond knowing the formula, making it slightly easier than average. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
Given that the binomial expansion of $(1 + kx)^{-4}$, $|kx| < 1$, is
$$1 - 6x + Ax^2 + \ldots$$
\begin{enumerate}
\item[(a)] find the value of the constant $k$, \hfill [2]
\item[(b)] find the value of the constant $A$, giving your answer in its simplest form. \hfill [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 2014 Q2 [5]}}