| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2011 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Parametric differentiation |
| Difficulty | Moderate -0.3 This is a straightforward parametric differentiation question requiring standard techniques: substituting a value to find coordinates, using the chain rule dy/dx = (dy/dθ)/(dx/dθ) for the gradient, and eliminating the parameter using the double angle formula cos 2θ = 1 - 2sin²θ. All steps are routine C4 content with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07s Parametric and implicit differentiation |
A curve has parametric equations
$$x = 2 \sin \theta, \quad y = \cos 2\theta.$$
\begin{enumerate}[label=(\roman*)]
\item Find the exact coordinates and the gradient of the curve at the point with parameter $\theta = \frac{1}{4}\pi$. [5]
\item Find $y$ in terms of $x$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C4 2011 Q4 [7]}}