| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find normal line equation at given point |
| Difficulty | Standard +0.2 This is a straightforward C3 differentiation question requiring standard techniques: finding a derivative (including logarithm), evaluating at a point, finding the normal equation, and solving dy/dx=0 for stationary points. All steps are routine with no conceptual challenges, making it slightly easier than the average A-level question. |
| Spec | 1.07m Tangents and normals: gradient and equations1.07n Stationary points: find maxima, minima using derivatives |
The curve $C$ has the equation $y = x^2 - 5x + 2\ln \frac{x}{3}$, $x > 0$.
\begin{enumerate}[label=(\roman*)]
\item Show that the normal to $C$ at the point where $x = 3$ has the equation
$$3x + 5y + 21 = 0.$$ [5]
\item Find the $x$-coordinates of the stationary points of $C$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q6 [8]}}