| Exam Board | OCR |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Polar coordinates |
| Type | Area enclosed by polar curve |
| Difficulty | Challenging +1.2 This is a multi-part Further Maths polar coordinates question requiring standard techniques: finding maxima (trivial), tangents at pole (routine), area integration (standard formula), and conversion to Cartesian form (algebraically involved but methodical). While Further Maths content is inherently harder, these are textbook exercises without novel insight, placing it moderately above average difficulty. |
| Spec | 4.09a Polar coordinates: convert to/from cartesian4.09b Sketch polar curves: r = f(theta)4.09c Area enclosed: by polar curve |
8 The equation of a curve, in polar coordinates, is
$$r = 1 + \cos 2 \theta , \quad \text { for } 0 \leqslant \theta < 2 \pi$$
(i) State the greatest value of $r$ and the corresponding values of $\theta$.\\
(ii) Find the equations of the tangents at the pole.\\
(iii) Find the exact area enclosed by the curve and the lines $\theta = 0$ and $\theta = \frac { 1 } { 2 } \pi$.\\
(iv) Find, in simplified form, the cartesian equation of the curve.
\hfill \mbox{\textit{OCR FP2 Q8 [13]}}