Edexcel P2 2020 January — Question 2 7 marks

Exam BoardEdexcel
ModuleP2 (Pure Mathematics 2)
Year2020
SessionJanuary
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeProduct with unknown constant to determine
DifficultyStandard +0.3 This is a straightforward binomial expansion question requiring students to (a) equate a given term to find a constant using the binomial coefficient formula, then (b) identify which terms multiply to give x^0. Both parts follow standard procedures taught in P2 with no novel insight required, making it slightly easier than average.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

2. One of the terms in the binomial expansion of \(( 3 + a x ) ^ { 6 }\), where \(a\) is a constant, is \(540 x ^ { 4 }\)
  1. Find the possible values of \(a\).
  2. Hence find the term independent of \(x\) in the expansion of $$\left( \frac { 1 } { 81 } + \frac { 1 } { x ^ { 6 } } \right) ( 3 + a x ) ^ { 6 }$$

2. One of the terms in the binomial expansion of $( 3 + a x ) ^ { 6 }$, where $a$ is a constant, is $540 x ^ { 4 }$
\begin{enumerate}[label=(\alph*)]
\item Find the possible values of $a$.
\item Hence find the term independent of $x$ in the expansion of

$$\left( \frac { 1 } { 81 } + \frac { 1 } { x ^ { 6 } } \right) ( 3 + a x ) ^ { 6 }$$

\begin{center}

\end{center}
\end{enumerate}

\hfill \mbox{\textit{Edexcel P2 2020 Q2 [7]}}