Substitution — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Substitution — 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).
Filter by difficulty
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.
AMC 8
1985 AMC 8 Problem 8 • 1990 AMC 8 Problem 24 • 1998 AMC 8 Problem 1 • 2023 AMC 8 Problem 3 • 2024 AMC 8 Problem 21
AMC 10
2000 AMC 10 Problem 15 • 2000 AMC 10 Problem 24 • 2002 AMC 10A Problem 16 • 2003 AMC 10A Problem 13 • 2005 AMC 10A Problem 3 • 2006 AMC 10B Problem 12 • 2007 AMC 10A Problem 2 • 2016 AMC 10B Problem 1 • 2018 AMC 10A Problem 21 • 2019 AMC 10A Problem 15 • 2019 AMC 10A Problem 19 • 2023 AMC 10A Problem 21 • 2023 AMC 10B Problem 22 • 2025 AMC 10B Problem 9
AMC 12
1950 AMC 12 Problem 2 • 1950 AMC 12 Problem 6 • 1950 AMC 12 Problem 17 • 1950 AMC 12 Problem 20 • 1950 AMC 12 Problem 24 • 1953 AMC 12 Problem 20 • 1953 AMC 12 Problem 38 • 1954 AMC 12 Problem 3 • 1954 AMC 12 Problem 28 • 1954 AMC 12 Problem 40 • 1955 AMC 12 Problem 16 • 1956 AMC 12 Problem 1 • 1956 AMC 12 Problem 8 • 1956 AMC 12 Problem 41 • 1957 AMC 12 Problem 9 • 1958 AMC 12 Problem 11 • 1958 AMC 12 Problem 20 • 1958 AMC 12 Problem 23 • 1958 AMC 12 Problem 40 • 1959 AMC 12 Problem 17 • 1959 AMC 12 Problem 38 • 1960 AMC 12 Problem 1 • 1960 AMC 12 Problem 18 • 1960 AMC 12 Problem 22 • 1961 AMC 12 Problem 5 • 1961 AMC 12 Problem 22 • 1962 AMC 12 Problem 19 • 1962 AMC 12 Problem 28 • 1963 AMC 12 Problem 1 • 1963 AMC 12 Problem 2 • 1963 AMC 12 Problem 21 • 1964 AMC 12 Problem 3 • 1964 AMC 12 Problem 4 • 1964 AMC 12 Problem 5 • 1964 AMC 12 Problem 11 • 1964 AMC 12 Problem 19 • 1964 AMC 12 Problem 20 • 1964 AMC 12 Problem 21 • 1965 AMC 12 Problem 14 • 1965 AMC 12 Problem 27 • 1965 AMC 12 Problem 34 • 1966 AMC 12 Problem 17 • 1966 AMC 12 Problem 36 • 1967 AMC 12 Problem 4 • 1967 AMC 12 Problem 22 • 1968 AMC 12 Problem 4 • 1969 AMC 12 Problem 7 • 1969 AMC 12 Problem 17 • 1969 AMC 12 Problem 26 • 1969 AMC 12 Problem 29 • 1969 AMC 12 Problem 32 • 1969 AMC 12 Problem 34 • 1970 AMC 12 Problem 3 • 1970 AMC 12 Problem 11 • 1970 AMC 12 Problem 16 • 1972 AMC 12 Problem 6 • 1972 AMC 12 Problem 11 • 1972 AMC 12 Problem 29 • 1973 AMC 12 Problem 10 • 1974 AMC 12 Problem 4 • 1974 AMC 12 Problem 12 • 1974 AMC 12 Problem 30 • 1975 AMC 12 Problem 14 • 1975 AMC 12 Problem 21 • 1976 AMC 12 Problem 6 • 1976 AMC 12 Problem 19 • 1977 AMC 12 Problem 1 • 1977 AMC 12 Problem 10 • 1977 AMC 12 Problem 22 • 1978 AMC 12 Problem 1 • 1978 AMC 12 Problem 3 • 1978 AMC 12 Problem 17 • 1979 AMC 12 Problem 25 • 1981 AMC 12 Problem 1 • 1981 AMC 12 Problem 15 • 1981 AMC 12 Problem 30 • 1982 AMC 12 Problem 3 • 1982 AMC 12 Problem 17 • 1983 AMC 12 Problem 1 • 1983 AMC 12 Problem 18 • 1984 AMC 12 Problem 14 • 1984 AMC 12 Problem 21 • 1985 AMC 12 Problem 1 • 1985 AMC 12 Problem 15 • 1988 AMC 12 Problem 8 • 1991 AMC 12 Problem 1 • 1993 AMC 12 Problem 1 • 1998 AMC 12 Problem 4 • 1998 AMC 12 Problem 17 • 2000 AMC 12 Problem 11 • 2000 AMC 12 Problem 15 • 2001 AMC 12 Problem 9 • 2003 AMC 12B Problem 20 • 2005 AMC 12A Problem 2 • 2006 AMC 12A Problem 2 • 2006 AMC 12A Problem 18 • 2006 AMC 12B Problem 8 • 2007 AMC 12B Problem 9 • 2009 AMC 12A Problem 6 • 2009 AMC 12A Problem 9 • 2009 AMC 12B Problem 8 • 2011 AMC 12A Problem 6 • 2012 AMC 12B Problem 10 • 2016 AMC 12A Problem 16 • 2017 AMC 12B Problem 3 • 2018 AMC 12B Problem 22 • 2019 AMC 12A Problem 9 • 2020 AMC 12A Problem 10 • 2020 AMC 12B Problem 21 • 2020 AMC 12B Problem 22 • 2021 AMC 12B Fall Problem 18 • 2022 AMC 12A Problem 2 • 2022 AMC 12B Problem 16 • 2023 AMC 12A Problem 10 • 2024 AMC 12A Problem 2
AIME
1983 AIME Problem 3 • 1986 AIME Problem 1 • 1988 AIME Problem 3 • 1990 AIME Problem 4 • 1998 AIME Problem 7 • 2000 AIME I Problem 9 • 2002 AIME I Problem 6 • 2005 AIME I Problem 8 • 2009 AIME II Problem 14 • 2010 AIME I Problem 3 • 2010 AIME I Problem 9 • 2012 AIME I Problem 9 • 2014 AIME I Problem 14 • 2015 AIME II Problem 14 • 2016 AIME I Problem 11 • 2016 AIME II Problem 3 • 2016 AIME II Problem 6 • 2019 AIME I Problem 8 • 2019 AIME II Problem 6 • 2022 AIME I Problem 15 • 2023 AIME I Problem 2 • 2025 AIME II Problem 13