| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Polar coordinates |
| Type | Polar curve intersection points |
| Difficulty | Standard +0.8 This FP2 polar coordinates question requires converting between polar and cartesian forms, sketching curves, and finding intersections. Part (a) involves standard conversions but the secant form requires trigonometric manipulation. Part (c) requires solving a non-trivial trigonometric equation from equating the two polar forms. While systematic, it demands fluency with multiple techniques and careful algebraic work across several steps, placing it moderately above average difficulty. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^24.09a Polar coordinates: convert to/from cartesian4.09b Sketch polar curves: r = f(theta) |
The curve $C$ has polar equation $r = 6 \cos \theta$, $-\frac{\pi}{2} \leq \theta < \frac{\pi}{2}$,
and the line $D$ has polar equation $r = 3 \sec\left(\frac{\pi}{3} - \theta\right)$, $-\frac{\pi}{6} \leq \theta \leq \frac{5\pi}{6}$.
\begin{enumerate}[label=(\alph*)]
\item Find a cartesian equation of $C$ and a cartesian equation of $D$. [5]
\item Sketch on the same diagram the graphs of $C$ and $D$, indicating where each cuts the initial line. [3]
The graphs of $C$ and $D$ intersect at the points $P$ and $Q$.
\item Find the polar coordinates of $P$ and $Q$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q40 [13]}}