Differentiation

DfE content area G: the mathematics of rate of change. Year 1 builds the derivative from first principles, then differentiates xⁿ for rational n and uses the result for tangents, normals, stationary points and optimisation.

• An Overview — the big idea, the notation, the five core techniques and the common mistakes

The content statements

• Differentiation from First Principles — gradients of chords, the limit definition, and proofs for x² and x³
• Differentiating Powers of x — the rule for kxⁿ, rewriting roots and fractions, and the second derivative
• Tangents and Normals — equations of tangents and normals, and working backwards from a gradient
• Stationary Points and Optimisation — increasing and decreasing functions, maxima and minima, gradient graphs and optimisation in context

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Each page has step-by-step notes, several worked examples, a quick-reference grid and ten practice questions with fully worked solutions.