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SMO Open – Selected topics

12 topics built from Singapore Mathematical Olympiad (SMO) Open Section papers 2005–2026, Round 1 and Round 2: key ideas with pictures, 60 fully worked examples, real practice questions and a 15-question, 30-minute Mock for every topic.

Algebraic expressions, radicals, exponents and logarithms

Equations, systems and word problems

Polynomials, functional equations and sequences

Inequalities, extreme values and the integer part

Trigonometry

Divisibility, remainders and digits

Primes, divisors, perfect squares and integer equations

Triangles, similarity and lengths

Areas, coordinates and vectors

Circles, tangents and cyclic quadrilaterals

Counting and probability

Combinatorics: games, invariants and the pigeonhole principle

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