| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2010 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Find stationary point then sketch curve |
| Difficulty | Moderate -0.8 This is a straightforward curve sketching question covering standard C2 content: differentiation of polynomials, finding stationary points using the second derivative test, solving a cubic by factoring, and sketching. All techniques are routine with no problem-solving insight required. The 11 marks reflect multiple steps rather than difficulty, making this easier than average for A-level. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.07i Differentiate x^n: for rational n and sums1.07n Stationary points: find maxima, minima using derivatives |
\begin{enumerate}[label=(\roman*)]
\item Differentiate $x^3 - 3x^2 - 9x$. Hence find the $x$-coordinates of the stationary points on the curve $y = x^3 - 3x^2 - 9x$, showing which is the maximum and which the minimum. [6]
\item Find, in exact form, the coordinates of the points at which the curve crosses the $x$-axis. [3]
\item Sketch the curve. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2010 Q10 [11]}}