| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2015 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Parametric curves and Cartesian conversion |
| Type | Convert to Cartesian (tan/sec/cot/cosec identities) |
| Difficulty | Standard +0.3 This is a standard parametric equations question with routine techniques: (i) uses chain rule with given derivative, (ii) applies sec²θ - tan²θ = 1 identity, (iii) requires volume of revolution formula. All parts follow textbook methods with no novel problem-solving, making it slightly easier than average. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07s Parametric and implicit differentiation4.08d Volumes of revolution: about x and y axes |
**Question 5(i):** [3 marks]
Complete table for Car C using Strategy 3
**Question 5(ii):** [1 mark]
Time for Car C to transport people from floors 7 and 8 and return5 A curve has parametric equations $x = \sec \theta , y = 2 \tan \theta$.\\
(i) Given that the derivative of $\sec \theta$ is $\sec \theta \tan \theta$, show that $\frac { \mathrm { d } y } { \mathrm {~d} x } = 2 \operatorname { cosec } \theta$.\\
(ii) Verify that the cartesian equation of the curve is $y ^ { 2 } = 4 x ^ { 2 } - 4$.
Fig. 5 shows the region enclosed by the curve and the line $x = 2$. This region is rotated through $180 ^ { \circ }$ about the $x$-axis.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{132ae754-bd4c-4819-80ef-4823ac2ead4f-02_545_853_1738_607}
\captionsetup{labelformat=empty}
\caption{Fig. 5}
\end{center}
\end{figure}
(iii) Find the volume of revolution produced, giving your answer in exact form.
\hfill \mbox{\textit{OCR MEI C4 2015 Q5 [8]}}