| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2016 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find dy/dx at a point |
| Difficulty | Standard +0.3 This question involves standard implicit differentiation using the chain rule (part i) and transformations of the arcsin function (part ii). Both parts require routine C3 techniques with no novel problem-solving. The implicit differentiation is straightforward, and identifying transformations from y = arcsin x is a standard exercise, making this slightly easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs1.07s Parametric and implicit differentiation |
Fig. 6 shows part of the curve $\sin 2y = x - 1$. P is the point with coordinates $(1.5, \frac{1}{12}\pi)$ on the curve.
\includegraphics{figure_6}
\begin{enumerate}[label=(\roman*)]
\item Find $\frac{dy}{dx}$ in terms of $y$.
Hence find the exact gradient of the curve $\sin 2y = x - 1$ at the point P. [4]
\end{enumerate}
The part of the curve shown is the image of the curve $y = \arcsin x$ under a sequence of two geometrical transformations.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find $y$ in terms of $x$ for the curve $\sin 2y = x - 1$.
Hence describe fully the sequence of transformations. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 2016 Q6 [8]}}