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LearnCambridge97092026–2027Paper 1 · Pure Mathematics 1Differentiation

Paper 1 · Module

Differentiation

5 subtopics≈ 220 min in total

Start the module: Gradients and the power rule Open graphing calculator

Gradients and the power rule
What the gradient of a curve means, how chords close in on the tangent, and the power rule $\dfrac{d}{dx}x^n=nx^{n-1}$ that makes differentiating fast, including roots, fractions and second derivatives.
≈ 45 min
The chain rule
How to differentiate a function of a function, such as $(2x-5)^4$ or $\sqrt{x^2+5}$ , without multiplying out: differentiate the outside, keep the inside, and multiply by the derivative of the inside.
≈ 40 min
Tangents and normals
Using $\dfrac{dy}{dx}$ to find the equation of the tangent and the normal to a curve at a point, points where the tangent has a given gradient, and the follow-on problems examiners love.
≈ 40 min
Stationary points and increasing functions
Where a curve turns: finding stationary points with $\dfrac{dy}{dx}=0$ , deciding whether each is a maximum or minimum with the second derivative, and finding where a function is increasing or decreasing.
≈ 45 min
Optimisation and rates of change
Using derivatives to answer real questions: the largest area, the smallest surface, the cheapest design, and how fast one quantity changes when another one does.
≈ 50 min