Linear equation — AMC & AIME Problems

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

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These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.

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AMC 10

2000 AMC 10 Problem 4 2000 AMC 10 Problem 8 2001 AMC 10 Problem 9 2001 AMC 10 Problem 16 2001 AMC 10 Problem 22 2002 AMC 10A Problem 6 2002 AMC 10A Problem 12 2002 AMC 10B Problem 12 2003 AMC 10A Problem 22 2003 AMC 10B Problem 2 2003 AMC 10B Problem 3 2003 AMC 10B Problem 11 2004 AMC 10A Problem 14 2004 AMC 10A Problem 21 2004 AMC 10B Problem 7 2005 AMC 10A Problem 3 2005 AMC 10A Problem 7 2006 AMC 10B Problem 3 2007 AMC 10A Problem 4 2007 AMC 10A Problem 7 2007 AMC 10A Problem 10 2007 AMC 10B Problem 6 2007 AMC 10B Problem 12 2007 AMC 10B Problem 14 2008 AMC 10A Problem 8 2008 AMC 10A Problem 13 2008 AMC 10B Problem 18 2009 AMC 10A Problem 7 2009 AMC 10A Problem 11 2009 AMC 10A Problem 14 2009 AMC 10B Problem 5 2009 AMC 10B Problem 15 2010 AMC 10A Problem 3 2010 AMC 10A Problem 11 2010 AMC 10A Problem 13 2010 AMC 10B Problem 9 2010 AMC 10B Problem 10 2010 AMC 10B Problem 14 2010 AMC 10B Problem 15 2011 AMC 10A Problem 12 2011 AMC 10A Problem 15 2011 AMC 10B Problem 7 2012 AMC 10B Problem 5 2012 AMC 10B Problem 7 2013 AMC 10A Problem 9 2013 AMC 10A Problem 18 2013 AMC 10B Problem 3 2013 AMC 10B Problem 10 2014 AMC 10A Problem 15 2014 AMC 10A Problem 21 2014 AMC 10B Problem 1 2014 AMC 10B Problem 3 2014 AMC 10B Problem 5 2015 AMC 10A Problem 6 2015 AMC 10B Problem 3 2016 AMC 10B Problem 7 2017 AMC 10B Problem 5 2017 AMC 10B Problem 7 2018 AMC 10A Problem 6 2019 AMC 10B Problem 3 2019 AMC 10B Problem 4 2019 AMC 10B Problem 18 2020 AMC 10A Problem 1 2021 AMC 10A Spring Problem 2 2021 AMC 10A Spring Problem 3 2021 AMC 10B Fall Problem 4 2021 AMC 10B Fall Problem 9 2022 AMC 10A Problem 3 2023 AMC 10A Problem 2 2023 AMC 10A Problem 8 2024 AMC 10A Problem 2 2025 AMC 10A Problem 1 2025 AMC 10A Problem 2

AMC 12

1950 AMC 12 Problem 2 1950 AMC 12 Problem 14 1950 AMC 12 Problem 23 1950 AMC 12 Problem 31 1950 AMC 12 Problem 36 1951 AMC 12 Problem 17 1951 AMC 12 Problem 30 1952 AMC 12 Problem 4 1954 AMC 12 Problem 18 1954 AMC 12 Problem 50 1956 AMC 12 Problem 16 1956 AMC 12 Problem 28 1956 AMC 12 Problem 41 1956 AMC 12 Problem 47 1957 AMC 12 Problem 8 1957 AMC 12 Problem 37 1958 AMC 12 Problem 7 1958 AMC 12 Problem 9 1958 AMC 12 Problem 14 1958 AMC 12 Problem 27 1958 AMC 12 Problem 34 1958 AMC 12 Problem 45 1958 AMC 12 Problem 50 1959 AMC 12 Problem 9 1959 AMC 12 Problem 29 1959 AMC 12 Problem 35 1960 AMC 12 Problem 1 1960 AMC 12 Problem 14 1960 AMC 12 Problem 19 1960 AMC 12 Problem 22 1961 AMC 12 Problem 3 1961 AMC 12 Problem 16 1961 AMC 12 Problem 23 1962 AMC 12 Problem 3 1963 AMC 12 Problem 7 1964 AMC 12 Problem 8 1965 AMC 12 Problem 6 1965 AMC 12 Problem 15 1965 AMC 12 Problem 27 1966 AMC 12 Problem 1 1966 AMC 12 Problem 7 1966 AMC 12 Problem 26 1966 AMC 12 Problem 28 1967 AMC 12 Problem 12 1967 AMC 12 Problem 27 1967 AMC 12 Problem 30 1968 AMC 12 Problem 2 1968 AMC 12 Problem 3 1970 AMC 12 Problem 9 1970 AMC 12 Problem 15 1970 AMC 12 Problem 29 1971 AMC 12 Problem 3 1972 AMC 12 Problem 2 1972 AMC 12 Problem 9 1972 AMC 12 Problem 15 1973 AMC 12 Problem 10 1973 AMC 12 Problem 12 1974 AMC 12 Problem 7 1975 AMC 12 Problem 2 1975 AMC 12 Problem 5 1976 AMC 12 Problem 10 1976 AMC 12 Problem 14 1976 AMC 12 Problem 19 1976 AMC 12 Problem 29 1977 AMC 12 Problem 3 1978 AMC 12 Problem 5 1979 AMC 12 Problem 11 1980 AMC 12 Problem 3 1980 AMC 12 Problem 22 1981 AMC 12 Problem 4 1981 AMC 12 Problem 10 1983 AMC 12 Problem 7 1984 AMC 12 Problem 20 1985 AMC 12 Problem 1 1985 AMC 12 Problem 8 1986 AMC 12 Problem 2 1989 AMC 12 Problem 6 1989 AMC 12 Problem 17 1991 AMC 12 Problem 16 1992 AMC 12 Problem 10 1999 AMC 12 Problem 8 2000 AMC 12 Problem 13 2001 AMC 12 Problem 3 2001 AMC 12 Problem 4 2002 AMC 12A Problem 2 2002 AMC 12A Problem 4 2003 AMC 12A Problem 2 2003 AMC 12B Problem 2 2003 AMC 12B Problem 9 2004 AMC 12A Problem 11 2004 AMC 12B Problem 5 2004 AMC 12B Problem 15 2005 AMC 12A Problem 1 2005 AMC 12A Problem 2 2006 AMC 12A Problem 7 2007 AMC 12A Problem 3 2007 AMC 12B Problem 8 2008 AMC 12A Problem 6 2008 AMC 12A Problem 10 2008 AMC 12B Problem 10 2009 AMC 12B Problem 3 2010 AMC 12B Problem 5 2010 AMC 12B Problem 7 2010 AMC 12B Problem 10 2012 AMC 12B Problem 3 2013 AMC 12B Problem 1 2014 AMC 12B Problem 1 2014 AMC 12B Problem 3 2014 AMC 12B Problem 4 2014 AMC 12B Problem 5 2014 AMC 12B Problem 6 2015 AMC 12A Problem 4 2017 AMC 12B Problem 1 2017 AMC 12B Problem 4 2018 AMC 12B Problem 3 2021 AMC 12A Spring Problem 3 2021 AMC 12A Spring Problem 5 2023 AMC 12A Problem 2 2024 AMC 12A Problem 5 2025 AMC 12A Problem 1 2025 AMC 12A Problem 2 2025 AMC 12B Problem 4

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 sequenceinequalitylogarithmmatrixmixtureNewton’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