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Parametric differentiation finds the gradient of a curve defined by x = f(t), y = g(t) using dy/dx = (dy/dt)/(dx/dt), then finds tangents, normals and stationary points on parametric curves. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive eClassroom course walks through each step with worked examples and instant-feedback questions, so you can practise until it's secure.
How you do it
Differentiate x and y separately with respect to the parameter, then divide dy by dt by dx by dt. The parameter cancels, leaving the gradient in terms of t. Substitute the t value to get the gradient at a particular point.
Before you start
You will want the chain rule and parametric equations at your fingertips first. Pure 4 is where it is assessed. Expect to use it again in parametric curve sketching and areas. It is part of the Differentiation strand.
What you learn
The course works through the parametric derivative, evaluating at a parameter value, gradients and tangents, stationary points and exponential and logarithmic curves. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
We teach Parametric Differentiation as one of the Differentiation topics in our A-level course library, at the second year of A-level. You work through 5 concepts and 5 worked examples, testing yourself at 5 points. Nearby topics in the same strand are Product Rule, Quotient Rule, Reciprocal Trig and Second Derivatives & Stationary Points. The Differentiation revision engine gives you as many extra questions as you want, tracked on your skill tree.
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