| Exam Board | Edexcel |
|---|---|
| Module | P2 (Pure Mathematics 2) |
| Year | 2020 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Product with unknown constant to determine |
| Difficulty | Standard +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. |
| Spec | 1.04a 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 $540 x ^ { 4 }$
\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]}}