Cambridge A Level Mathematics Syllabus
The A Level Mathematics syllabus is split into Pure Mathematics, Mechanics, and Statistics. Most students take two papers for the AS Level and two further papers for the full A Level.
Modular Structure
The qualification is modular. Students can complete the AS Level (Paper 1 and an applied paper) in the first year and the A2 Level (Paper 3 and a second applied paper) in the second. This staged approach allows you to build your qualification over two examination series. The most common combination is Pure Mathematics 1 & 3, with one Mechanics and one Statistics paper.
Pure Mathematics (Papers 1 & 3)
- Algebra Covers quadratics, functions, coordinate geometry, series, and the binomial expansion.
- Logarithmic & Exponential Functions Includes their graphs, properties, and use in modelling real-world phenomena.
- Trigonometry Extends to reciprocal functions, compound angles, and solving trigonometric equations.
- Calculus Involves differentiation and integration of various functions, including applications.
- Numerical Solutions Methods for finding approximate solutions to equations that cannot be solved algebraically.
- Vectors Covers vector geometry and algebra in two and three dimensions, including scalar products.
- Complex Numbers Introduces the algebra of complex numbers, including the Argand diagram and polar form.
Mechanics (e.g., Paper 4)
- Forces and Equilibrium Analysing particles and rigid bodies at rest under a system of forces.
- Kinematics Describes motion in a straight line with constant or variable acceleration.
- Newton's Laws of Motion Applying F=ma to various scenarios, including connected particles and friction.
- Energy, Work and Power Using the principles of conservation of energy and the work-energy principle.
- Momentum Covers the principle of conservation of linear momentum in collisions.
Statistics (e.g., Paper 5)
- Representation of Data Using histograms, stem-and-leaf diagrams, and calculating measures of central tendency and spread.
- Permutations and Combinations Methods for counting arrangements and selections, forming the basis of probability.
- Probability Calculating probabilities of events, including conditional probability and mutual exclusivity.
- Discrete Random Variables Understanding probability distributions, expectation, and variance, including the binomial distribution.
- The Normal Distribution Using the normal distribution as a model and for approximating the binomial distribution.