Edexcel C2 — Question 27 6 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Marks6
PaperDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeCoefficient relationship between terms
DifficultyModerate -0.3 This is a straightforward binomial theorem question requiring standard application of the formula and simple algebraic manipulation. Part (a) is direct recall, part (b) involves setting up and solving a linear equation from coefficients, and part (c) is routine substitution. The multi-step nature and algebraic work make it slightly easier than average but still representative of typical C2 examination questions.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

  1. Write down the first four terms of the binomial expansion, in ascending powers of \(x\), of \((1 + 3x)^n\), where \(n > 2\). [2]
Given that the coefficient of \(x^3\) in this expansion is ten times the coefficient of \(x^2\),
  1. find the value of \(n\), [2]
  2. find the coefficient of \(x^4\) in the expansion. [2]

\begin{enumerate}[label=(\alph*)]
\item Write down the first four terms of the binomial expansion, in ascending powers of $x$, of $(1 + 3x)^n$, where $n > 2$. [2]
\end{enumerate}

Given that the coefficient of $x^3$ in this expansion is ten times the coefficient of $x^2$,

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the value of $n$, [2]

\item find the coefficient of $x^4$ in the expansion. [2]
\end{enumerate}

\hfill \mbox{\textit{Edexcel C2  Q27 [6]}}