| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Topic | Polar coordinates |
| Type | Tangent parallel/perpendicular to initial line |
| Difficulty | Challenging +1.8 This is a substantial Further Maths polar coordinates question requiring: (a) finding tangent conditions using dr/dθ and the polar tangent formula, (b) using the chord length formula between polar points, and (c) computing area using the polar area integral. While the techniques are standard for FP2, the multi-step nature, algebraic complexity with √5, and need to correctly apply multiple polar formulas makes this significantly harder than average A-level questions but still within expected Further Maths scope. |
| Spec | 4.09a Polar coordinates: convert to/from cartesian4.09b Sketch polar curves: r = f(theta)4.09c Area enclosed: by polar curve |
\includegraphics{figure_1}
The curve $C$ shown in Fig. 1 has polar equation
$$r = a(3 + \sqrt{5} \cos \theta), \quad -\pi \leq \theta < \pi$$
\begin{enumerate}[label=(\alph*)]
\item Find the polar coordinates of the points $P$ and $Q$ where the tangents to $C$ are parallel to the initial line. [6]
The curve $C$ represents the perimeter of the surface of a swimming pool. The direct distance from $P$ to $Q$ is $20$ m.
\item Calculate the value of $a$. [3]
\item Find the area of the surface of the pool. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q8 [15]}}