| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2010 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find stationary points |
| Difficulty | Moderate -0.8 This is a straightforward two-part question requiring basic differentiation using the power rule, then solving a simple quadratic equation (dy/dx = 0) to find stationary points. Both are routine C2-level techniques with no problem-solving insight required, making it easier than average but not trivial since it requires correct execution of multiple steps. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07n Stationary points: find maxima, minima using derivatives |
| Answer | Marks | Guidance |
|---|---|---|
| \(3x^2 - 12x - 15\) | 2 marks | M1 if one term incorrect or an extra term is included |
| Answer | Marks |
|---|---|
| Their \(\frac{dv}{dx} = 0\) s.o.i. | M1 |
| \(x = 5\) | B1 |
| \(x = -1\) | B1 |
## (i)
$3x^2 - 12x - 15$ | 2 marks | M1 if one term incorrect or an extra term is included
## (ii)
Their $\frac{dv}{dx} = 0$ s.o.i. | M1 |
$x = 5$ | B1 |
$x = -1$ | B1 |\begin{enumerate}[label=(\roman*)]
\item Differentiate $x^3 - 6x^2 - 15x + 50$. [2]
\item Hence find the $x$-coordinates of the stationary points on the curve $y = x^3 - 6x^2 - 15x + 50$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2010 Q3 [5]}}