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Ages — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses ages — a algebra concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.

All of these problems are used with official legal permission of the Mathematical Association of America (MAA).

AMC 8

1995 AMC 8 Problem 2 · 2000 AMC 8 Problem 1 · 2014 AMC 8 Problem 10 · 2022 AMC 8 Problem 5

AMC 10

2004 AMC 10B Problem 17 · 2006 AMC 10A Problem 3 · 2007 AMC 10B Problem 12 · 2009 AMC 10B Problem 6 · 2010 AMC 10A Problem 8 · 2015 AMC 10A Problem 8 · 2019 AMC 10A Problem 3 · 2021 AMC 10B Spring Problem 5 · 2025 AMC 10A Problem 4

AMC 12

1999 AMC 12 Problem 8 · 2004 AMC 12B Problem 15 · 2006 AMC 12A Problem 3 · 2007 AMC 12B Problem 8 · 2015 AMC 12A Problem 6 · 2025 AMC 12A Problem 3

AIME

2002 AIME I Problem 3

More algebra concepts

absolute valuealgebraic manipulationAM-GM Inequalityarithmetic sequencebinomial theoremcalculusCauchy-Schwarz Inequalitycompleting the squarecomplex numbercustom operationDe Moivre’s Theoremdeterminantdifference of squaresfactoringFibonaccifloor and ceiling functionsfunctionfunctional equationgeometric sequenceinequalitylinear equationlogarithmmatrixmixtureNewton’s Sumspartial fractionspolynomialquadraticradicalrational equationrationalizing denominatorrecursionroots of unitySimon’s Favorite Factoring Trickslopesubstitutionsum and difference of cubessum of first n cubessum of first n odd numberssum of first n squaressummationsymmetry (algebra)system of equationstelescopingVieta’s Formulas