| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 9 |
| Topic | Implicit equations and differentiation |
| Type | Find stationary points |
| Difficulty | Challenging +1.8 This implicit differentiation problem requires multiple sophisticated steps: differentiating implicitly to find dy/dx, setting the numerator to zero for stationary points, substituting back into the original cubic equation, and solving the resulting system. The algebraic manipulation is non-trivial and the question demands extended reasoning beyond standard textbook exercises, though it uses core A-level techniques. |
| Spec | 1.07s Parametric and implicit differentiation |
In this question you must show detailed reasoning.
Find the exact values of the x-coordinates of the stationary points of the curve $x^3 + y^3 = 3xy + 35$.
[9]
\hfill \mbox{\textit{OCR H240/01 2017 Q13 [9]}}