| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2018 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Finding unknown constant from coefficient |
| Difficulty | Standard +0.3 Part (i) is a standard application of the binomial expansion for negative/fractional powers requiring recall of the formula and careful arithmetic. Part (ii) requires multiplying the result from (i) by (a+bx) and equating coefficients, which is a routine technique. This is slightly easier than average as it follows a predictable two-part structure with no novel insight required. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
8 (i) Find the first three terms in the expansion of $( 4 - x ) ^ { - \frac { 1 } { 2 } }$ in ascending powers of $x$.\\
(ii) The expansion of $\frac { a + b x } { \sqrt { 4 - x } }$ is $16 - x \ldots$. Find the values of the constants $a$ and $b$.
\hfill \mbox{\textit{OCR H240/01 2018 Q8 [7]}}