| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2002 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Parametric curves and Cartesian conversion |
| Type | Tangent/normal intersection problems |
| Difficulty | Challenging +1.8 This question requires finding the normal at a given point on a parametric curve, then solving a system where this normal intersects the curve again. Students must: (1) find which t-value gives (14,1), (2) compute dy/dx using parametric differentiation, (3) find the normal equation, (4) substitute parametric equations into the normal to get a cubic in t, and (5) solve this cubic knowing one root. The multi-step nature, parametric context, and need to solve a cubic equation make this substantially harder than typical A-level questions, though it's more computational than conceptually deep for an AEA problem. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07m Tangents and normals: gradient and equations1.07s Parametric and implicit differentiation |
The curve $C$ has parametric equations
$$x = 15t - t^3, \quad y = 3 - 2t^2.$$
Find the values of $t$ at the points where the normal to $C$ at $(14, 1)$ cuts $C$ again.
[11]
\hfill \mbox{\textit{Edexcel AEA 2002 Q3 [11]}}