| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chain Rule |
| Type | Inverse function differentiation |
| Difficulty | Standard +0.3 This question tests inverse trigonometric functions and implicit differentiation using dx/dy, which are standard C3 topics. Part (i) requires rearranging and differentiating (routine manipulation), while part (ii) needs substitution and exact value recall of cos(π/6). The multi-step nature and exact value requirement elevate it slightly above average, but it remains a straightforward application of taught techniques without requiring problem-solving insight. |
| Spec | 1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs1.07s Parametric and implicit differentiation |
Fig. 3 shows the curve defined by the equation $y = \arcsin(x - 1)$, for $0 \leqslant x \leqslant 2$.
\includegraphics{figure_7}
\begin{enumerate}[label=(\roman*)]
\item Find $x$ in terms of $y$, and show that $\frac{dx}{dy} = \cos y$. [3]
\item Hence find the exact gradient of the curve at the point where $x = 1.5$. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 Q7 [7]}}