| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Show specific gradient value |
| Difficulty | Standard +0.3 This is a straightforward implicit differentiation question requiring students to differentiate, substitute a point to find the gradient, then find the perpendicular gradient and write the normal equation. All steps are routine C4 techniques with no conceptual challenges, making it slightly easier than average. |
| Spec | 1.07m Tangents and normals: gradient and equations1.07s Parametric and implicit differentiation |
2. A curve has the equation
$$x ^ { 3 } + 2 x y - y ^ { 2 } + 24 = 0$$
Show that the normal to the curve at the point $( 2 , - 4 )$ has the equation $y = 3 x - 10$.\\
\hfill \mbox{\textit{OCR C4 Q2 [7]}}