IB Math RevisionOlympiad-style competition-style problems (ages 15 to 18)
120 problems in the style of national maths olympiad first rounds. Fewer, harder problems where the answer is only half the work: you have to find an argument that settles every case. Number theory, inequalities, invariants, extremal arguments and clever counting. 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.
Every question is free to read. Hints, answer checking and full solutions for Olympiad-style problems are included with every A Level, IB, IGCSE and CBSE plan. See plans.
Answer a problem to track what you have solved.
Choose a topic
Number theory
Divisibility, primes, remainders and digits.
Questions free; solutions with a plan
24 problems →Combinatorics
Counting arrangements, paths, subsets and tilings.
Questions free; solutions with a plan
22 problems →Geometry
Angles, areas, circles, lattice points and solids.
Questions free; solutions with a plan
18 problems →Algebra
Equations, sequences, functions and inequalities.
Questions free; solutions with a plan
22 problems →Probability
Dice, cards, areas and expected values.
Questions free; solutions with a plan
10 problems →Logic
Truth-tellers, calendars, games and reasoning puzzles.
Questions free; solutions with a plan
8 problems →Calculus and functions
Limits, derivatives, integrals and functional equations used cleverly rather than routinely.
Questions free; solutions with a plan
16 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) · Senior problems (ages 16 to 18) · Where next after these? · Competitions, past papers and problem of the week