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AMC 12 tutor

Algebra

Algebraic reasoning at contest speed and depth: solving and modeling with linear and quadratic equations and systems, polynomial roots and identities, factoring and manipulation techniques, sequences and series, functions, inequalities, and data reasoning. Topics: Linear Equations, Systems, and Contextual Modeling, Ratios, Percents, and Proportional Reasoning, Quadratics and Vieta's Formulas, Polynomials: Roots, Division, and Identities, Algebraic Manipulation and Factoring Techniques, Sequences and Series, Functions and Functional Equations, Inequalities, Optimization, and Bounding, Statistics and Data Reasoning.

Counting and Probability

The techniques used to count outcomes and compute probabilities without brute-force enumeration: casework, complementary counting, correcting for overcounting, inclusion-exclusion, stars and bars, combinatorial identities, probability and expected value, and recursion with states. Topics: Permutations, Combinations, and Arrangements, Casework, Complementary Counting, Overcounting and Symmetry Correction, Principle of Inclusion-Exclusion, Stars and Bars and Distributions, Combinatorial Identities, Probability, Expected Value, and Geometric Probability, Recursion and States.

Number Theory

Integer structure and arithmetic: primes and factorization, divisors, GCD and LCM, divisibility and digit reasoning, number bases, modular arithmetic, and the deeper congruence tools, the Chinese Remainder Theorem, linear congruences, Fermat's Little Theorem, and Euler's theorem, that come up often on this exam and go well beyond typical school number theory. Topics: Primes and Prime Factorization, Divisors, GCD, and LCM, Divisibility and Digit Reasoning, Number Bases, Modular Arithmetic, Congruences: CRT and Linear Congruences, Fermat, Euler, and Multiplicative Order, Diophantine Equations.

Geometry

Plane and solid geometry built from angle chasing, triangle relationships, similarity and transformations, quadrilaterals and polygons, circles, coordinate methods, and three-dimensional solids. Topics: Angle Chasing, Triangles: Area, Length, and Special Triangles, Similarity, Congruence, and Transformations, Quadrilaterals and Polygons, Circles and Power of a Point, Cyclic Quadrilaterals and Ptolemy's Theorem, Area and Length of Composite Figures, Coordinate Geometry, Three-Dimensional Geometry.

Advanced Topics: Trigonometry, Logarithms, and Complex Numbers

The material most students have not yet seen when they start preparing for this exam: logarithm properties and equations, trigonometric functions, identities, and equations, the Law of Sines and Law of Cosines, and complex numbers in rectangular and polar form, including De Moivre's theorem and roots of unity. Topics: Logarithm Properties and Equations, Trigonometric Functions and the Unit Circle, Trigonometric Identities, Solving Trigonometric Equations, Law of Sines and Law of Cosines, Complex Number Arithmetic, Polar Form and De Moivre's Theorem, Roots of Unity, Trigonometry in 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.