IGCSE Math RevisionSenior competition-style problems (ages 16 to 18)
150 problems in the age band of the UKMT Senior Mathematical Challenge and the MAA AMC 12. A Level / IB / Class 11–12 ideas: recurrences, inclusion–exclusion, Vieta, expectation, 3D geometry and harder logic. Every problem is original — written by us, not taken from a real paper — with two hints, a full solution, a note on why the method works and where the idea leads.
92 of these problems are free with full solutions; the rest are marked ‘With a plan’ (included with every A Level, IB, IGCSE and CBSE plan).
Answer a problem to track what you have solved.
Choose a topic
Number theory
Divisibility, primes, remainders and digits.
15 free, 7 with a plan
22 problems →Combinatorics
Counting arrangements, paths, subsets and tilings.
15 free, 7 with a plan
22 problems →Geometry
Angles, areas, circles, lattice points and solids.
15 free, 7 with a plan
22 problems →Algebra
Equations, sequences, functions and inequalities.
15 free, 7 with a plan
22 problems →Probability
Dice, cards, areas and expected values.
13 free, 7 with a plan
20 problems →Logic
Truth-tellers, calendars, games and reasoning puzzles.
12 free, 6 with a plan
18 problems →Calculus and functions
Limits, derivatives, integrals and functional equations used cleverly rather than routinely.
7 free, 17 with a plan
24 problems →Stuck? Learn a strategy
Each problem is tagged with the strategy that cracks it. The problem-solving strategy guides explain ten of them with worked examples: organised cases, count the opposite, working backwards, invariants, extremal principle and more.
Junior problems (ages 11 to 13) · Intermediate problems (ages 13 to 16) · Olympiad-style problems (ages 15 to 18) · Where next after these? · Competitions, past papers and problem of the week