Learning pathways
Mathematics is cumulative. These pathways show how each course feeds the next, so you can see where a gap today shows up two years from now.
Recommended sequences
A guide, not a rule — students join at the point that matches their current work.
United States core sequence
Grades 6–12 into first-year university
- 1Middle School Math
Ratios, proportional reasoning, negative numbers, first equations.
- 2Algebra I
Linear equations, systems, quadratics, function notation.
- 3Geometry
Proof, similarity, trigonometric ratios, coordinate geometry.
- 4Algebra II
Polynomials, rational and exponential functions, logarithms.
- 5Precalculus
Trigonometry, sequences, limits as an idea before the machinery.
- 6Calculus (AP or university)
Derivatives, integrals, applications.
UK sequence
KS3 through A-Level and admissions tests
- 1KS3 Mathematics
Number, algebraic notation, geometry foundations.
- 2GCSE Mathematics
Higher-tier algebra, geometry, statistics and problem solving.
- 3A-Level Mathematics
Pure, mechanics and statistics.
- 4Further Mathematics
Complex numbers, matrices, differential equations.
- 5TMUA / STEP
Admissions-test reasoning and proof under time pressure.
University mathematics
Undergraduate students
- 1Calculus sequence
Single and multivariable calculus.
- 2Linear Algebra
Vector spaces, eigenvalues, diagonalisation.
- 3Probability & Statistics
Distributions, inference, statistical modelling.
- 4Proof-based courses
Real analysis, abstract algebra, discrete mathematics.