| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find normal equation at point |
| Difficulty | Standard +0.3 This is a straightforward implicit differentiation question requiring students to differentiate implicitly, substitute a point to find the gradient, then find the perpendicular gradient and write the normal equation. It's slightly easier than average because it's a standard procedure with clear steps and no conceptual surprises, though implicit differentiation itself requires careful application of the chain rule. |
| Spec | 1.07m Tangents and normals: gradient and equations1.07s Parametric and implicit differentiation |
4. A curve has the equation
$$4 x ^ { 2 } - 2 x y - y ^ { 2 } + 11 = 0$$
Find an equation for the normal to the curve at the point with coordinates $( - 1 , - 3 )$.\\
\hfill \mbox{\textit{OCR C4 Q4 [7]}}