UKMT Senior Mathematical Challenge Syllabus
The SMC tests mathematical reasoning and problem-solving skills rather than advanced curriculum knowledge. The syllabus is based on standard school mathematics up to and including the first year of A-level or equivalent.
An Exam of Application, Not Rote Learning
There is no formal syllabus for the SMC. The challenge tests your ability to apply familiar mathematical concepts in unfamiliar contexts. Questions are designed to be solved with logic and ingenuity, not by recalling complex theorems. The material is accessible to anyone studying mathematics in their final two years of school, but the problems require a deeper level of thinking than standard exams.
Number Theory and Algebra
- Primes and Divisibility Properties of prime numbers, factors, multiples, and remainders (modular arithmetic).
- Sequences and Series Arithmetic and geometric progressions, and recognising other numerical patterns.
- Polynomials Roots of quadratics and cubics, factorisation, and algebraic manipulation.
- Indices and Logarithms Rules of indices and logarithms, and solving related equations.
- Inequalities Solving and manipulating algebraic inequalities.
Geometry
- Euclidean Geometry Properties of triangles, circles (including circle theorems), and polygons.
- Coordinate Geometry Equations of lines and circles, distances, gradients, and points of intersection.
- Mensuration Areas and volumes of 2D and 3D shapes, including sectors, segments, and cones.
- Trigonometry Ratios, identities, and solving problems in triangles using the sine and cosine rules.
Combinatorics and Logic
- Counting Principles Systematic counting methods, including simple permutations and combinations.
- Logic Puzzles Deductive reasoning and interpreting complex conditional statements.