| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 7 |
| 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 straightforward two-part question requiring basic differentiation to find the gradient, then using perpendicular gradient rules to find the normal equation, followed by solving a quadratic to find the intersection point. All steps are routine C1 techniques with no conceptual challenges, making it slightly easier than average. |
| Spec | 1.02q Use intersection points: of graphs to solve equations1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.07m Tangents and normals: gradient and equations |
6. The curve with equation $y = x ^ { 2 } + 2 x$ passes through the origin, $O$.\\
(i) Find an equation for the normal to the curve at $O$.\\
(ii) Find the coordinates of the point where the normal to the curve at $O$ intersects the curve again.\\
\hfill \mbox{\textit{OCR C1 Q6 [7]}}