Topics

|x| equations, piecewise definitions, inequality solving, AM-GM, optimization by inequality

Factoring tricks (SFFT, difference of squares, sum of cubes), telescoping products, clever substitution, symmetric expressions

Complex arithmetic, modulus, roots of unity (rare on AMC 10)

Exponent rules, radicals, nested radicals, rationalizing, logarithms (rare)

Function evaluation, composition, inverses, functional equations, graphs and transformations

Linear equations/inequalities, word problems, rates, work, mixtures, distance-speed-time

Degree > 2: factor/remainder theorem, Vieta for higher degree, polynomial division, roots

Quadratic roots, Vieta's formulas, discriminant, completing the square, vertex form

Ratio, proportion, percent change, means/averages as arithmetic word problems

Arithmetic/geometric sequences, recursions, sums, telescoping sums

Multi-variable systems, substitution/elimination, symmetric systems

Non-decimal bases, digit manipulation, digit sums, palindromes

Integer solutions of equations, bounding, factoring integer equations

Divisors, number/sum of divisors, factorization, divisibility rules

Repeating decimals, unit fractions, rational number properties, terminating decimals

GCD/LCM computation, Euclidean algorithm, gcd*lcm = product

Remainders, congruences, last digits, cyclicity, Chinese-remainder style reasoning

Perfect squares/cubes, parity, consecutive integers, floor/ceiling, integer sequences

Prime properties, prime factorization, counting with primes

Permutations with constraints, adjacency, circular arrangements, forbidden positions

Multiplication principle, permutations, combinations, counting by listing

Sample-space probability: dice, coins, cards, random selection

Conditional probability, states/Markov-style processes, sequential random events

Distributing objects into bins, integer partitions, compositions

Expected value, linearity of expectation, fair games

Turn-based games, iterated processes, tournaments, scheduling

Probability as a ratio of lengths, areas, or volumes

Overlapping sets, Venn diagrams, PIE counting

Lattice paths, grid walks, board colorings and configurations

Counting via recurrences: tilings, Fibonacci-type, strings with no forbidden patterns

Angle chasing, polygon angle sums, regular polygons, parallel lines

Chords, tangents, inscribed angles, power of a point, arc length, sectors, inscribed/circumscribed circles

Distance, slope, lines, circles in the plane, reflections over lines, lattice points

Maximum/minimum length or area, shortest paths, extremal configurations

Areas of quadrilaterals/polygons, trapezoids, shoelace, decomposition, hexagons

Similarity ratios, congruence, proportional segments, area ratios of similar figures

Volume, surface area, cubes, cones, spheres, cylinders, cross-sections, nets

Rotations, reflections, folding, tessellations, symmetric figures

Medians, angle bisectors, altitudes, incenter/circumcenter/centroid, Heron, Stewart, angle bisector theorem

Triangle area, Pythagorean theorem, special right triangles, triangle inequality

Law of sines/cosines, trig values, trig identities (rare on AMC 10)

Clock angles, calendars, day-of-week, time-rate arithmetic

Truth-tellers/liars, deduction, self-referential statements, ordering puzzles

Set problems not primarily counting, estimation, pattern recognition, unit conversion

Mean, median, mode, range, data tables, charts, weighted averages