| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Session | Specimen |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Polar coordinates |
| Type | Tangent parallel/perpendicular to initial line |
| Difficulty | Challenging +1.2 This is a multi-part Further Maths polar coordinates question requiring sketching, tangent conditions using dr/dθ, and area integration. While it involves several techniques, the curve is a standard lemniscate form, the tangent condition (dy/dθ = 0) is a textbook application, and the integration is straightforward with the given bounds. The Further Maths context elevates it above average A-level difficulty, but it remains a standard exercise without requiring novel insight. |
| Spec | 4.09a Polar coordinates: convert to/from cartesian4.09b Sketch polar curves: r = f(theta)4.09c Area enclosed: by polar curve |
6. The curve $C$ has polar equation
$$r ^ { 2 } = a ^ { 2 } \cos 2 \theta , \quad \frac { - \pi } { 4 } \leq \theta \leq \frac { \pi } { 4 }$$
\begin{enumerate}[label=(\alph*)]
\item Sketch the curve $C$.
\item Find the polar coordinates of the points where tangents to $C$ are parallel to the initial line.
\item Find the area of the region bounded by $C$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q6 [12]}}