A Level Maths: Parametric Equations Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
- Parametric Equations and Differentiation (OCR)
- Parametric Equations and Differentiation (Edexcel)
- Integrating Parametric Functions (Edexcel)
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Differentiation — needed for parametric differentiation
- Integration — needed for parametric integration
- Trigonometry — Radians, Circle Sectors and Triangles}}: parametric forms often use trig
A Level Maths parametric equations describe curves where $x$ and $y$ are both functions of a third variable (the parameter, typically $t$). This is enormously flexible — it lets you describe curves that cannot be written as $y = f(x)$, and is essential for Vector Mechanics, modelling motion, and Connected Rates of Change.
Given parametric equations $x = f(t)$, $y = g(t)$, you convert to Cartesian form by eliminating $t$ — usually by rearranging one equation for $t$ and substituting into the other. Common parametric forms include the circle ($x = r\cos(t), y = r\sin(t)$) and the ellipse. You differentiate parametrically using $\frac{dy}{dx} = \frac{dy/dt}{dx/dt}$, and use this to find tangents, normals, and stationary points of parametric curves. You integrate parametrically, finding areas under parametric curves using $\int y \cdot \frac{dx}{dt} \, dt$ with the limits in $t$-form. You apply parametric equations to model motion in two dimensions, projectile paths, and other contexts where the natural variable is time.
Parametric equations is part of the Pure Maths strand of A Level Maths for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: when eliminating $t$, watch out for restrictions on the domain — parametric curves often describe only PART of the corresponding Cartesian curve; $\frac{dy}{dx}$ is $\frac{dy/dt}{dx/dt}$, NOT $\frac{dx/dt}{dy/dt}$; for parametric integration, the limits must be in the PARAMETER variable $t$, not $x$; and when integrating to find area, $\frac{dx}{dt}$ may be negative for parts of the curve, which can require splitting the integral.