Summation — AMC & AIME Problems

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

1996 AMC 8 Problem 16 1998 AMC 8 Problem 12 2013 AMC 8 Problem 3 2015 AMC 8 Problem 9 2020 AMC 8 Problem 16 2025 AMC 8 Problem 20

AMC 12

1950 AMC 12 Problem 39 1950 AMC 12 Problem 43 1952 AMC 12 Problem 30 1952 AMC 12 Problem 50 1956 AMC 12 Problem 25 1957 AMC 12 Problem 35 1958 AMC 12 Problem 26 1958 AMC 12 Problem 37 1959 AMC 12 Problem 39 1959 AMC 12 Problem 49 1960 AMC 12 Problem 36 1961 AMC 12 Problem 26 1962 AMC 12 Problem 12 1962 AMC 12 Problem 14 1962 AMC 12 Problem 32 1962 AMC 12 Problem 40 1963 AMC 12 Problem 20 1963 AMC 12 Problem 27 1964 AMC 12 Problem 34 1965 AMC 12 Problem 20 1965 AMC 12 Problem 24 1965 AMC 12 Problem 36 1966 AMC 12 Problem 18 1966 AMC 12 Problem 19 1967 AMC 12 Problem 20 1967 AMC 12 Problem 39 1968 AMC 12 Problem 17 1968 AMC 12 Problem 27 1970 AMC 12 Problem 22 1970 AMC 12 Problem 33 1972 AMC 12 Problem 19 1973 AMC 12 Problem 7 1974 AMC 12 Problem 21 1974 AMC 12 Problem 29 1975 AMC 12 Problem 9 1975 AMC 12 Problem 15 1975 AMC 12 Problem 16 1977 AMC 12 Problem 16 1977 AMC 12 Problem 24 1979 AMC 12 Problem 6 1979 AMC 12 Problem 11 1980 AMC 12 Problem 11 1980 AMC 12 Problem 13 1984 AMC 12 Problem 12 1989 AMC 12 Problem 27 1990 AMC 12 Problem 13 1999 AMC 12 Problem 1 2002 AMC 12A Problem 21 2003 AMC 12A Problem 1 2004 AMC 12A Problem 17 2006 AMC 12A Problem 12 2007 AMC 12A Problem 24 2008 AMC 12B Problem 12 2008 AMC 12B Problem 24 2009 AMC 12A Problem 11 2010 AMC 12A Problem 2 2010 AMC 12A Problem 22 2010 AMC 12B Problem 10 2014 AMC 12A Problem 15 2018 AMC 12A Problem 19 2018 AMC 12B Problem 9 2020 AMC 12A Problem 22 2020 AMC 12A Problem 25 2021 AMC 12A Spring Problem 14 2024 AMC 12B Problem 18 2025 AMC 12B Problem 2

More algebra concepts

absolute valueagesalgebraic manipulationAM-GM Inequalityarithmetic sequencearithmetico-geometric seriesbinomial 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 squaressymmetry (algebra)system of equationstelescopingVieta’s Formulaszero product property