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Algebra

Algebraic techniques at contest depth: solving equations and systems, polynomials and their roots, sequences and series, inequalities and optimization, logarithms and exponents, and trigonometric identities and complex numbers treated as algebraic objects. Topics: Equation-Solving Techniques, Rates, Ratios, and Numerical Word Problems, Polynomials, Roots, and Vieta's Formulas, Factoring and Algebraic Manipulation, Sequences, Series, and Recursions, Inequalities and Optimization, Floor Functions, Radicals, and Absolute Value, Logarithms and Exponents, Trigonometric Identities and Complex Numbers.

Counting and Probability

Counting and probability techniques, organized the way experienced problem solvers name them: casework, permutations and combinations, overcounting corrections, inclusion-exclusion, distributions, recursive counting and states, bijective and identity-based arguments, and probability including expected value. Topics: Casework, Permutations and Combinations, Overcounting and Complementary Counting, Inclusion-Exclusion, Stars and Bars and Distributions, Recursion, States, and Random Walks, Bijections, Identities, and Pigeonhole, Probability and Expected Value.

Number Theory

Integer structure: divisibility and prime factorization, greatest common divisor and least common multiple, modular arithmetic through orders and the Chinese Remainder Theorem, number bases and digit problems, Diophantine equations, and the structural arguments, perfect powers, Legendre's formula, prime properties, that pin down an unknown integer. Topics: Divisibility and Prime Factorization, GCD, LCM, and the Euclidean Algorithm, Modular Arithmetic, Bases, Digits, and Place Value, Diophantine Equations, Perfect Powers and Number Structure.

Geometry

Geometry techniques across three complementary approaches: synthetic relationships in triangles, circles, and polygons; trigonometric methods including the Law of Sines and Cosines; and analytic methods using coordinates, complex numbers, and vectors. Topics: Triangle Area and Length Relations, Triangle Centers and Special Segments, Similarity and Homothety, Circles, Chords, and Tangents, Quadrilaterals and Polygons, Trigonometric Methods in Geometry, Coordinate and Analytic Geometry, Three-Dimensional Geometry.

Past Contests

Real past editions of this contest, organized by decade so a specific year and division can be found directly. Topics: 2020s Contests, 2010s Contests, 2000s Contests, 1990s Contests.