| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795/1 (Pre-U Further Mathematics Paper 1) |
| Year | 2013 |
| Session | November |
| Marks | 8 |
| Topic | Polar coordinates |
| Type | Tangent parallel/perpendicular to initial line |
| Difficulty | Challenging +1.2 This is a polar curves question requiring differentiation to find stationary points and sketching. While polar coordinates are a Further Maths topic (making it inherently harder on an absolute scale), the actual techniques are straightforward: differentiate a simple trigonometric expression, solve cos θ + 2sin θ cos θ = 0 using standard identities, then sketch using the found points. The 8 marks reflect moderate length rather than exceptional difficulty. Comparable to a solid A-level FM question but not requiring deep insight or extended reasoning. |
| Spec | 1.07i Differentiate x^n: for rational n and sums4.09b Sketch polar curves: r = f(theta) |
The curve $S$ has polar equation $r = 1 + \sin \theta + \sin^2 \theta$ for $0 \leqslant \theta < 2\pi$.
\begin{enumerate}[label=(\roman*)]
\item Determine the polar coordinates of the points on $S$ where $\frac{dr}{d\theta} = 0$. [5]
\item Sketch $S$. [3]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9795/1 2013 Q5 [8]}}