Custom operation — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Custom operation — 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 problems are used with official legal permission of the Mathematical Association of America (MAA).

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AMC 8

1986 AMC 8 Problem 11 1987 AMC 8 Problem 21 1992 AMC 8 Problem 6 1993 AMC 8 Problem 9 1998 AMC 8 Problem 2 2000 AMC 8 Problem 17 2001 AMC 8 Problem 12 2007 AMC 8 Problem 10 2010 AMC 8 Problem 2 2016 AMC 8 Problem 10 2022 AMC 8 Problem 2

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absolute valueagesalgebraic manipulationAM-GM Inequalityarithmetic sequencearithmetico-geometric seriesbinomial theoremcalculusCauchy-Schwarz Inequalitycompleting the squarecomplex numberDe 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 Formulaszero product property