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Functional equation — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses functional equation — 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 10

2002 AMC 10B Problem 23 · 2016 AMC 10A Problem 23 · 2021 AMC 10A Spring Problem 18

AMC 12

2001 AMC 12 Problem 9 · 2004 AMC 12A Problem 17 · 2006 AMC 12A Problem 18 · 2016 AMC 12A Problem 20 · 2021 AMC 12A Spring Problem 18 · 2023 AMC 12B Problem 22

AIME

1997 AIME Problem 12 · 2000 AIME I Problem 12 · 2001 AIME II Problem 8 · 2007 AIME II Problem 14 · 2016 AIME I Problem 11

More algebra concepts

absolute valueagesalgebraic manipulationAM-GM Inequalityarithmetic sequencebinomial theoremcalculusCauchy-Schwarz Inequalitycompleting the squarecomplex numbercustom operationDe Moivre’s Theoremdeterminantdifference of squaresfactoringFibonaccifloor and ceiling functionsfunctiongeometric 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