| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2010 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find normal line equation at given point |
| Difficulty | Moderate -0.8 This is a straightforward application of differentiation to find a normal line. It requires finding dy/dx, evaluating at x=2, taking the negative reciprocal for the normal gradient, then using point-slope form and rearranging to the required format. All steps are routine C1 techniques with no problem-solving insight needed, making it easier than average but not trivial since it involves multiple standard steps. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07m Tangents and normals: gradient and equations |
Question 3:
$3 \mid x^2 + 5x$3 Find the equation of the normal to the curve $y = x ^ { 3 } - 4 x ^ { 2 } + 7$ at the point $( 2 , - 1 )$, giving your answer in the form $a x + b y + c = 0$, where $a , b$ and $c$ are integers.
\hfill \mbox{\textit{OCR C1 2010 Q3 [7]}}