| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2018 |
| Session | September |
| Marks | 9 |
| Topic | Binomial Theorem (positive integer n) |
| Type | Standard binomial expansion coefficient |
| Difficulty | Standard +0.3 Part (i) is a routine binomial coefficient calculation. Part (ii) requires equating coefficients and solving, which is standard but involves some algebraic manipulation. Part (iii) requires recognizing the binomial expansion for negative/fractional powers, which is slightly beyond basic A-level but still a standard technique in Stats 1/FP1. Overall, this is slightly easier than average due to being mostly procedural with well-practiced techniques. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
6 (i) Find the coefficient of $x ^ { 4 }$ in the expansion of $( 3 x - 2 ) ^ { 10 }$.\\
(ii) In the expansion of $( 1 + 2 x ) ^ { n }$, where $n$ is a positive integer, the coefficients of $x ^ { 7 }$ and $x ^ { 8 }$ are equal. Find the value of $n$.\\
(iii) Find the coefficient of $x ^ { 3 }$ in the expansion of $\frac { 1 } { \sqrt { 4 + x } }$.
\hfill \mbox{\textit{OCR H240/02 2018 Q6 [9]}}