| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 2 (Further Pure Core 2) |
| Year | 2021 |
| Session | June |
| Marks | 11 |
| Topic | Polar coordinates |
| Type | Polar curve with exponential function |
| Difficulty | Challenging +1.3 This is a Further Maths polar coordinates question requiring standard techniques: part (a) uses the polar area formula ∫½r²dθ with substitution (u = sin θ), while part (b) requires differentiation using product and chain rules, then solving dr/dθ = 0. The algebra is moderately involved but follows established methods without requiring novel insight. The 11-mark allocation and 'show detailed reasoning' requirement indicate substantial working, but the techniques are direct applications of FP2 content. |
| Spec | 1.07n Stationary points: find maxima, minima using derivatives1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates4.09c Area enclosed: by polar curve |
In this question you must show detailed reasoning.
The diagram below shows the curve $r = \sqrt{\sin\theta}e^{\cos\theta}$ for $0 \leq \theta < \pi$.
\includegraphics{figure_5}
\begin{enumerate}[label=(\alph*)]
\item Find the exact area enclosed by the curve. [4]
\item Show that the greatest value of $r$ on the curve is $\sqrt{\frac{3}{2}}e^{\frac{1}{2}}$. [7]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Pure Core 2 2021 Q5 [11]}}