| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find stationary points |
| Difficulty | Challenging +1.2 This question requires implicit differentiation to find dy/dx, setting it to zero for stationary points, then solving the resulting system of equations. While it involves multiple steps (implicit differentiation, algebraic manipulation, and solving a cubic), the techniques are standard A-level fare. The cubic factorization is manageable and the question provides clear direction, making it moderately above average difficulty but not requiring exceptional insight. |
| Spec | 1.07s Parametric and implicit differentiation1.08k Separable differential equations: dy/dx = f(x)g(y) |
13 In this question you must show detailed reasoning.
Find the exact values of the $x$-coordinates of the stationary points of the curve $x ^ { 3 } + y ^ { 3 } = 3 x y + 35$.
\hfill \mbox{\textit{OCR H240/01 Q13 [9]}}