| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2013 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Normal meets curve/axis — further geometry |
| Difficulty | Standard +0.3 This is a standard C2 calculus question combining differentiation (finding normal), coordinate geometry (line equations), and integration (area under curve). All techniques are routine: find derivative, use perpendicular gradient, integrate polynomial. The multi-step nature and 11 marks elevate it slightly above average, but no novel insight is required—it's a textbook exercise testing standard methods. |
| Spec | 1.07m Tangents and normals: gradient and equations1.08e Area between curve and x-axis: using definite integrals |
Fig. 10 shows a sketch of the curve $y = x^2 - 4x + 3$. The point A on the curve has $x$-coordinate 4. At point B the curve crosses the $x$-axis.
\includegraphics{figure_10}
\begin{enumerate}[label=(\roman*)]
\item Use calculus to find the equation of the normal to the curve at A and show that this normal intersects the $x$-axis at C$(16, 0)$. [6]
\item Find the area of the region ABC bounded by the curve, the normal at A and the $x$-axis. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2013 Q10 [11]}}