AMC 12
Learn each topic from the ground up, study worked examples step by step, then practise by topic or sit a full timed paper. 360 original problems, with worked solutions. The method workshops add 24 guided examples across all 12 topics.
Know what to practise next.
Use the eight-week route to plan your sessions, or open a topic and work through its method workshop. Each workshop explains why the technique works, gives two fully worked examples, and includes a check or variation. Saved attempts are available in your history.
Full mock paper
Ordered easy → hard like the real contest, timed, scored 6 / 1.5 / 0.
Mixed drill
A random set across every topic, with hints and instant feedback.
Official contests
Real AMC 12 papers with community solutions on the AoPS wiki. Do them timed once you finish the mocks.
Algebraic Manipulation
Factoring and identities, Simon's Favourite Factoring Trick, symmetric systems, absolute value and piecewise equations, clever substitutions, nested radicals, telescoping sums, radical equations and word problems that reduce to algebra.
10 lessons · 6 examples · 30 problems · 3 videosPolynomials
Vieta's formulas and power sums, the remainder and factor theorems, rational roots, interpolation, transformed roots, and complex or unity roots.
10 lessons · 6 examples · 30 problems · 4 videosInequalities & Optimisation
Completing the square, AM-GM with equality cases and weighted forms, Cauchy–Schwarz in Titu form, the QM–AM–GM–HM chain, the rearrangement inequality, and bounding arguments for counting integer solutions.
9 lessons · 6 examples · 30 problems · 4 videosFunctions, Exponents & Logarithms
Composition, inverses and iteration, functional equations, floor and fractional part, exponent and logarithm laws with domain checks, comparing huge numbers, and graph transformations.
10 lessons · 6 examples · 30 problems · 3 videosSequences & Series
Arithmetic and geometric sums, infinite and arithmetico-geometric series, telescoping sums, linear recurrences, periodic sequences, power sums, and floor sums.
9 lessons · 6 examples · 30 problems · 4 videosNumber Theory
Divisibility and digit problems, primes and factorisation, gcd and lcm with the Euclidean algorithm, divisor counting and sums, modular arithmetic with inverses, Fermat, Euler and the Chinese Remainder Theorem, last digits and cycles, number bases, and Diophantine equations.
10 lessons · 6 examples · 30 problems · 4 videosCounting & Combinatorics
Counting tools for the AMC 12: multiplication and addition principles, permutations and combinations, arrangements with repeats, complementary counting, inclusion-exclusion, stars and bars, bijections, recursion, binomial identities, and casework.
10 lessons · 6 examples · 30 problems · 4 videosProbability & Expected Value
Equally likely outcomes, conditional probability and Bayes' theorem, independence, geometric probability, and expected value via linearity, symmetry, and state methods for repeated games and random walks.
9 lessons · 6 examples · 30 problems · 3 videosPlane Geometry
Similar triangles and Pythagoras, area methods (base-height, sine, Heron, shoelace and ratios of areas), medians, bisectors and altitudes, circle theorems and power of a point, incircle and circumcircle, cyclic quadrilaterals with Ptolemy, and special triangles.
9 lessons · 6 examples · 30 problems · 4 videosCoordinate & Solid Geometry
Coordinates, lines and circles, conics, shoelace areas, transformations, loci, solids and sections, and 3D distances as they appear on the AMC 12.
9 lessons · 6 examples · 30 problems · 3 videosTrigonometry
Exact values on the unit circle, the standard identities, triangle laws, and solving, counting and optimizing trigonometric expressions at AMC 12 level.
10 lessons · 6 examples · 30 problems · 4 videosComplex Numbers
Cartesian and polar form, De Moivre's theorem, roots of unity and their sums and products, rotations and loci in the complex plane, and polynomials with complex roots.
9 lessons · 6 examples · 30 problems · 3 videos