| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2012 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find stationary points |
| Difficulty | Standard +0.8 This question requires implicit differentiation of a cubic curve (moderately challenging), algebraic manipulation to reach a specific form, then solving dy/dx=0 which leads to a system involving the original curve equation. The multi-step nature, need for careful algebra, and solving the resulting system elevates this above standard C3 fare, though it remains within reach of strong students using systematic techniques. |
| Spec | 1.07s Parametric and implicit differentiation |
Fig. 7 shows the curve $x^3 + y^3 = 3xy$. The point P is a turning point of the curve.
\includegraphics{figure_7}
\begin{enumerate}[label=(\roman*)]
\item Show that $\frac{dy}{dx} = \frac{y - x^2}{y^2 - x}$. [4]
\item Hence find the exact $x$-coordinate of P. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 2012 Q7 [8]}}