AMC algebra problems

Equations and systems, polynomials, sequences, inequalities, functions and logarithms — plus the ratio, rate and average problems that open most contests.

1,403 problems in the archive use these ideas — 672 from the AMC 10 and 731 from the AMC 12.

Picks a problem you have not seen, at about the difficulty you are handling.

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Equations & Systems423
Linear equations, systems of equations, substitution and general algebraic manipulation.
Polynomials & Factoring270
Quadratics, polynomial roots, Vieta's formulas and the standard factoring identities.
Sequences & Series235
Arithmetic and geometric sequences, summation, telescoping and recursively defined terms.
Inequalities & Optimization250
Inequalities, AM-GM, and optimisation by bounding the extreme cases.
Functions, Exponents & Logs180
Function composition, functional equations, floor and ceiling, exponents and logarithms.
Complex Numbers59
Complex arithmetic, roots of unity and De Moivre's theorem.
Ratios, Rates & Word Problems388
Ratios and proportions, percentages, speed and distance, mixtures and unit conversion.
Averages & Statistics114
Mean, median, mode, range and weighted averages.

60 most recent problems

Newest contests first. Every problem opens with its answer choices, hints and a worked solution.

Use Start algebra practice above to keep going through the remaining 1,343, or browse them by contest in the AMC 12 and AMC 10 archives.

AMC algebra problems

Narrow it down

Equations & Systems423

Polynomials & Factoring270

Sequences & Series235

Inequalities & Optimization250

Functions, Exponents & Logs180

Complex Numbers59

Ratios, Rates & Word Problems388

Averages & Statistics114

60 most recent problems