| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find stationary points |
| Difficulty | Standard +0.3 This is a straightforward implicit differentiation question requiring students to find dy/dx, set it equal to zero for horizontal tangents, then solve the resulting system. While it involves multiple steps (implicit differentiation, solving simultaneous equations), each step uses standard C4 techniques without requiring novel insight or particularly complex algebra. |
| Spec | 1.07s Parametric and implicit differentiation |
2. A curve has the equation
$$2 x ^ { 2 } + x y - y ^ { 2 } + 18 = 0$$
Find the coordinates of the points where the tangent to the curve is parallel to the $x$-axis.\\
\hfill \mbox{\textit{OCR C4 Q2 [7]}}