A Level Mathematics: Year 1

A free, complete set of notes, worked examples and practice questions for the first year of A Level Mathematics, following the Department for Education’s GCE AS and A level subject content for mathematics.

The first year covers the AS content, which every exam board (AQA, Edexcel, OCR and OCR MEI) teaches: about two thirds pure mathematics, with the remaining third shared between statistics and mechanics. It builds directly on Higher tier GCSE (9–1) Mathematics.

Use the menu on the left, or the links below, to reach any topic.

Summary notes: download the PDF covering the whole of Year 1 (AS) in one document.

Pure mathematics

Proof — A · deduction, exhaustion and disproof by counter-example
Algebra and Functions — B, D · indices, surds, quadratics, inequalities, polynomials, graphs, the binomial expansion
Coordinate Geometry — C · straight lines and circles
Trigonometry — E · sine and cosine rules, graphs, identities and equations
Exponentials and Logarithms — F · e^x, log laws, equations and modelling
Differentiation — G · first principles, the power rule, tangents, stationary points
Integration — H · indefinite and definite integrals, areas under curves
Vectors — J · vectors in two dimensions and vector geometry

Statistics

Statistics — K, L · sampling, presenting data, measures of location and spread, correlation
Probability and Distributions — M, N · Venn diagrams, independence and the binomial distribution
Hypothesis Testing — O · the language of testing, and binomial tests

Mechanics

Mechanics — P, Q, R · units, motion graphs, suvat, variable acceleration and Newton’s laws

When you have finished Year 1, carry on with A Level Maths Year 2.

About these pages

Every topic has an overview page covering the big picture, the language, the key formulae and the common mistakes, plus a page for each group of content statements. Each page contains step-by-step explanations, several fully worked examples, a quick-reference summary, and ten practice questions with complete worked solutions that you can reveal one at a time.

The bold letters are the content areas of the DfE subject content (A Proof, B Algebra and functions, and so on), which every exam board’s specification is built from.

All pages are self-contained HTML files, so they can be downloaded and used offline.

Subject content reference: DfE GCE AS and A level subject content for mathematics