| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 2 (Further Pure Core 2) |
| Year | 2017 |
| Session | Specimen |
| Marks | 7 |
| Topic | Taylor series |
| Type | Direct multiplication of series |
| Difficulty | Challenging +1.2 This is a Further Maths question requiring multiplication of three Maclaurin series and careful coefficient tracking to x³, followed by solving a cubic approximation. While technically demanding with multiple series multiplications and algebraic manipulation, it's a fairly standard Further Maths exercise following established procedures without requiring novel insight. The surd form answer adds minor complexity but the method is straightforward once the series is obtained. |
| Spec | 4.08a Maclaurin series: find series for function4.08b Standard Maclaurin series: e^x, sin, cos, ln(1+x), (1+x)^n |
7 (i) Use the Maclaurin series for $\sin x$ to work out the series expansion of $\sin x \sin 2 x \sin 4 x$ up to and including the term in $x ^ { 3 }$.\\
(ii) Hence find, in exact surd form, an approximation to the least positive root of the equation $2 \sin x \sin 2 x \sin 4 x = x$.
\hfill \mbox{\textit{OCR Further Pure Core 2 2017 Q7 [7]}}