| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Topic | Polar coordinates |
| Type | Area of region with line boundary |
| Difficulty | Challenging +1.8 This is a Further Maths FP2 polar coordinates question requiring multiple advanced techniques: sketching a rose curve, computing area using polar integration with careful limits, and finding tangent lines parallel to the initial line (requiring implicit differentiation of polar equations and solving transcendental equations). The 8-mark part (c) demands substantial algebraic manipulation and geometric insight beyond standard exercises, though the overall structure follows recognizable FP2 patterns. |
| Spec | 1.07m Tangents and normals: gradient and equations4.09b Sketch polar curves: r = f(theta)4.09c Area enclosed: by polar curve |
\begin{enumerate}[label=(\alph*)]
\item Sketch the curve with polar equation
$$r = 3 \cos 2\theta, \quad -\frac{\pi}{4} \leq \theta < \frac{\pi}{4}.$$ [2]
\item Find the area of the smaller finite region enclosed between the curve and the half-line $\theta = \frac{\pi}{6}$. [6]
\item Find the exact distance between the two tangents which are parallel to the initial line. [8]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q28 [16]}}