Algebra on the AMC 10

|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