A-Level Mathematics
What Is A-Level Mathematics?
A-Level Mathematics develops advanced mathematical reasoning through pure mathematics and selected applied topics, including mechanics and probability and statistics. It prepares learners for university-level mathematics, science and engineering.
This independent study guide introduces common topics. Exact examination requirements vary by examination board, route and syllabus year; always check the official syllabus for your examination.
Topic-Wise Mathematics Guide
Pure Mathematics: Algebra and Functions
Quadratic expressions, inequalities, transformations, functions and inverse functions.
Coordinate Geometry and Trigonometry
Lines and curves, circular measure, trigonometric identities and equations.
Sequences and Series
Arithmetic and geometric progressions, sums and binomial expansions.
Differentiation
Rules of differentiation, tangents, normals, stationary points and rates of change.
Integration
Indefinite and definite integration, area problems and integration techniques.
Advanced Pure Mathematics
Exponential and logarithmic functions, numerical methods, vectors, differential equations and complex numbers, according to level.
Mechanics
Kinematics, forces and equilibrium, Newton’s laws, work, energy, power and momentum.
Probability and Statistics
Data representation, permutations and combinations, probability, discrete distributions and normal distribution.
Further Statistics
Continuous random variables, Poisson distribution, sampling, estimation and hypothesis testing for relevant routes.
A Simple Worked Example
Differentiate f(x) = x³ − 4x² + 5x.
Solution: Using the power rule, f′(x) = 3x² − 8x + 5.
Study Resources
Read the definitions, practise worked examples and revise each topic regularly. Topic-wise MCQs, short questions and step-by-step solutions will be added to this section.
Official Syllabus Reference
Cambridge International AS & A Level Mathematics (official syllabus)