Algebra

Algebra is where most competition problems begin. Polynomials, inequalities, sequences, functional equations — the objects are familiar from school, but a contest asks you to manipulate them rather than merely evaluate them.

The problems here run from a single-step factorisation up to identities that only fall to a well-chosen substitution. Expect Vieta’s formulas, AM–GM, and the recurring lesson that the right rearrangement does most of the work.