A Level Mathematics: Year 2

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

The second year completes the full A Level. It assumes everything in A Level Maths Year 1, deepens each pure topic, and adds new ones such as parametric equations, sequences and series, and numerical methods. Statistics moves on to the normal distribution, and mechanics adds moments, friction and projectiles.

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

Summary notes: download the PDF covering the full A Level in one document.

Pure mathematics

Proof — A · proof by contradiction
Algebra and Functions — B · partial fractions, modulus, composite and inverse functions, combined transformations
Parametric Equations — C · converting between forms, and modelling with parameters
Sequences and Series — D · sigma notation, arithmetic and geometric series, the general binomial expansion
Trigonometry — E · radians, small angles, reciprocal functions, compound angles, R cos(x + α)
Differentiation — G · exponentials and trig, chain, product and quotient rules, implicit and parametric
Integration — H · substitution, by parts, partial fractions and differential equations
Numerical Methods — I · locating roots, iteration, Newton–Raphson and the trapezium rule
Vectors — J · vectors in three dimensions

Statistics

Statistics — L, M, N · regression, conditional probability and the normal distribution
Hypothesis Testing — O · tests for correlation and for a normal mean

Mechanics

Mechanics — Q, R, S · moments, resolving forces, friction, projectiles and kinematics with vectors

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