Edexcel C4 2014 June — Question 2 5 marks

Exam BoardEdexcel
ModuleC4 (Core Mathematics 4)
Year2014
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicGeneralised Binomial Theorem
TypeSingle unknown from one coefficient condition
DifficultyModerate -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.
Spec1.04c 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 $$1 - 6x + Ax^2 + \ldots$$
  1. [(a)] find the value of the constant \(k\), \hfill [2]
  2. [(b)] find the value of the constant \(A\), giving your answer in its simplest form. \hfill [3]

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]}}