| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2011 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find dy/dx at a point |
| Difficulty | Standard +0.3 This is a straightforward implicit differentiation question with standard verification. Part (i) is trivial substitution (1 mark). Part (ii) requires applying implicit differentiation to sin 2x + cos y = √3, which is a routine C3 technique, followed by substituting coordinates to find a numerical gradient. The chain rule application is standard and the algebra is clean, making this slightly easier than the average A-level question. |
| Spec | 1.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^21.07s Parametric and implicit differentiation |
A curve is defined by the equation $\sin 2x + \cos y = \sqrt{3}$.
\begin{enumerate}[label=(\roman*)]
\item Verify that the point P $(\frac{\pi}{6}, \frac{\pi}{6})$ lies on the curve. [1]
\item Find $\frac{dy}{dx}$ in terms of $x$ and $y$.
Hence find the gradient of the curve at the point P. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 2011 Q6 [6]}}