| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2018 |
| Session | December |
| Marks | 9 |
| Topic | Generalised Binomial Theorem |
| Type | Multiply by polynomial |
| Difficulty | Standard +0.3 This is a standard binomial expansion question with routine polynomial division. Part (a) is direct application of the formula with n=1/2, part (b) requires multiplying by (1+9x²)^(-1) which only affects the x² and x³ terms minimally, and part (c) is straightforward validity condition from combining two ranges. Slightly above average due to the multi-step nature and fractional index, but still a textbook exercise requiring no novel insight. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<1 |
8
\begin{enumerate}[label=(\alph*)]
\item Expand $\sqrt { 1 + 2 x }$ in ascending powers of $x$, up to and including the term in $x ^ { 3 }$.
\item Hence expand $\frac { \sqrt { 1 + 2 x } } { 1 + 9 x ^ { 2 } }$ in ascending powers of $x$, up to and including the term in $x ^ { 3 }$.
\item Determine the range of values of $x$ for which the expansion in part (b) is valid.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 2018 Q8 [9]}}