IB Math RevisionProblem-solving strategies
Hard problems are rarely solved by knowing more content. They are solved by trying the right idea: split into cases, count the opposite, look at the extreme case, find what never changes. Each guide explains one idea, shows when to reach for it, works through two examples and lists original problems to practise on, at every level.
Ten strategies
Organised cases
Split a problem into cases that cannot overlap and together cover everything, then deal with each small case.
Guide and 180 problems →Count the opposite
When the cases you want are messy, count or find the ones you don't want and subtract.
Guide and 58 problems →Working backwards
Start from the end state or the answer you want and undo each step.
Guide and 114 problems →Invariants
Find a quantity that never changes (or only changes one way) however the moves are made.
Guide and 38 problems →Extremal principle
Look at the largest, smallest, first or last object: it often has to behave in a special way.
Guide and 70 problems →Pigeonhole principle
More pigeons than holes means two share a hole: a guarantee that needs no searching.
Guide and 16 problems →Parity and remainders
Odd and even, or remainders on dividing by a small number, rule out whole families of answers at once.
Guide and 45 problems →Symmetry
Use a reflection, rotation or swap that leaves the problem unchanged to halve the work or pin down the answer.
Guide and 114 problems →Spot the pattern and generalise
Try small cases, spot the pattern, then explain why it must continue.
Guide and 118 problems →Proof techniques
Contradiction, contrapositive, induction and construction: ways to be certain, not just convinced.
Guide and 55 problems →Put them to work
Junior problems · Intermediate problems · Senior problems · Olympiad-style problems · Maths club sessions · Extension & competition maths