CAIE FP1 2018 June — Question 3

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2018
SessionJune
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPolar coordinates

3 The curve \(C\) has polar equation \(r = \cos 2 \theta\), for \(- \frac { 1 } { 4 } \pi \leqslant \theta \leqslant \frac { 1 } { 4 } \pi\).
  1. Sketch \(C\).
  2. Find the area of the region enclosed by \(C\), showing full working.
  3. Find a cartesian equation of \(C\).

3 The curve $C$ has polar equation $r = \cos 2 \theta$, for $- \frac { 1 } { 4 } \pi \leqslant \theta \leqslant \frac { 1 } { 4 } \pi$.\\
(i) Sketch $C$.\\
(ii) Find the area of the region enclosed by $C$, showing full working.\\

(iii) Find a cartesian equation of $C$.\\

\hfill \mbox{\textit{CAIE FP1 2018 Q3}}