| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2011 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Ratio of coefficients condition |
| Difficulty | Moderate -0.8 Part (a) is trivial recall of the binomial coefficient formula (b=36). Part (b) requires writing the ratio of consecutive binomial coefficients and simplifying, which is a standard textbook exercise with minimal problem-solving. The calculation is straightforward: q/p = C(40,5)/C(40,4) = 36/5. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
\begin{enumerate}
\item Given that $\binom { 40 } { 4 } = \frac { 40 ! } { 4 ! b ! }$,\\
(a) write down the value of $b$.
\end{enumerate}
In the binomial expansion of $( 1 + x ) ^ { 40 }$, the coefficients of $x ^ { 4 }$ and $x ^ { 5 }$ are $p$ and $q$ respectively.\\
(b) Find the value of $\frac { q } { p }$.\\
\hfill \mbox{\textit{Edexcel C2 2011 Q5 [4]}}