A Level Maths: Differentiation 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.
- Differentiation (Mixed) (OCR)
- Differentiation From First Principles (OCR)
- Stationary Points (OCR)
- Stationary Points (Edexcel)
- Tangents and Normals to Curves (OCR)
- Tangents and Normals to Curves (Edexcel)
- Practical Applications of Differentiation (OCR)
- Practical Applications of Differentiation (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:
- Indices — essential for rewriting expressions in differentiable form
- Quadratic Equations — needed for solving dy/dx = 0
- Straight Line Geometry — tangents and normals are straight-line equations
A Level Maths differentiation is the Year 1 introduction to calculus — the mathematics of rates of change. Given a function $y = f(x)$, differentiation finds the gradient function $\frac{dy}{dx}$, which gives the gradient of the curve at any point. This is used everywhere: finding tangents and normals, locating maxima and minima for optimisation, classifying stationary points, and modelling rates of change in physics and economics. The Year 2 extensions are covered in Further Differentiation.
In Year 1 you differentiate any rational power of $x$ using $\frac{d}{dx}(x^n) = nx^{n-1}$, extending to sums, differences, and constant multiples. You also differentiate from first principles using the limit definition for small positive integer powers and for $\sin(x)$ and $\cos(x)$. You use the derivative to find equations of tangents and normals at specific points, locate stationary points by setting $\frac{dy}{dx} = 0$, and classify them as maxima, minima, or points of inflection using the second derivative. Practical applications include optimisation problems (maximum volume, minimum surface area) and modelling rates of change in real contexts.
Differentiation is part of the Pure Maths strand of A Level Maths and underpins material throughout the rest of the course for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: simplify expressions using Indices BEFORE differentiating — terms like $3/x^2$ should be rewritten as $3x^{-2}$ first; the gradient of a normal is the negative reciprocal of the tangent gradient, not the negative; at a stationary point $\frac{dy}{dx} = 0$, but $f''(x) = 0$ does NOT automatically mean a point of inflection — check whether the second derivative changes sign; and when finding maxima in modelling, check the physical context for restrictions on the domain.