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AMC 10 tutor

Algebra

Algebra at contest grain: setting up and solving linear equations and systems, working ratio, percent, and rate word problems, solving and reasoning about quadratics including Vieta's formulas, manipulating and factoring algebraic expressions, working with sequences and series, evaluating functions including floor, ceiling, and absolute value, summarizing data with mean and median, and reasoning with inequalities and bounding arguments. Topics: Linear Equations and Systems, Fractions, Ratios, and Percents, Rate and Word-Problem Modeling, Quadratics and Vieta's Formulas, Algebraic Manipulation, Factoring, and Radicals, Sequences and Series, Functions, Floor/Ceiling, and Absolute Value, Statistics: Mean, Median, and Averages, Inequalities and Bounding.

Counting and Probability

Counting and probability, organized the way contest problems actually get solved: by naming the technique first. Topics: Foundational Counting Principles, Permutations and Combinations, Casework, Complementary Counting and Overcounting Correction, Inclusion-Exclusion and Stars and Bars, Probability Fundamentals, Geometric Counting, Geometric Probability, and Expected Value, Recursion and States.

Number Theory

The structure of integers: primes and factorization, divisibility, greatest common divisor and least common multiple, digit and place-value reasoning, number bases, modular arithmetic, parity arguments, and Diophantine equations. Topics: Primes and Prime Factorization, Divisibility, GCD and LCM, Digits, Place Value, and Units Digits, Number Bases, Modular Arithmetic, Parity Arguments, Diophantine Equations.

Geometry

Plane and solid geometry: angle chasing and polygon angle sums, triangle area and the Pythagorean theorem, triangle centers and special segments, similarity and area ratios, quadrilaterals and regular polygons, circle relationships including power of a point, composite-area decomposition, coordinate geometry and transformations, and three-dimensional volume and surface area. Topics: Angle Chasing and Polygon Angle Sums, Triangle Area, the Pythagorean Theorem, and Special Triangles, Triangle Centers, Cevians, and Special Segments, Similarity and Area Ratios, Quadrilaterals and Regular Polygons, Circles: Chords, Tangents, Angles, and Power of a Point, Composite Area and Length by Decomposition, Coordinate Geometry and Transformations, 3D Geometry and Volume.

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.