| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 8 |
| Topic | Generalised Binomial Theorem |
| Type | Two unknowns from two coefficient conditions |
| Difficulty | Standard +0.3 This is a standard binomial expansion question requiring the formula for fractional powers and coefficient matching. Part (a) is routine application of the binomial theorem. Part (b) involves algebraic manipulation to match coefficients, requiring careful arithmetic but no novel insight. The 8 marks and straightforward structure place it slightly above average difficulty. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
\begin{enumerate}[label=(\alph*)]
\item Find the first three terms in the expansion of $(1 + px)^{\frac{1}{3}}$ in ascending powers of $x$. [3]
\item The expansion of $(1 + qx)(1 + px)^{\frac{1}{3}}$ is $1 + x - \frac{2}{9}x^2 + ...$
Find the possible values of the constants $p$ and $q$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2017 Q5 [8]}}