Roots of unity — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Roots of unity — 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.
AMC 10
AMC 12
1957 AMC 12 Problem 42 • 1964 AMC 12 Problem 34 • 1971 AMC 12 Problem 22 • 1977 AMC 12 Problem 28 • 1980 AMC 12 Problem 28 • 1984 AMC 12 Problem 30 • 1985 AMC 12 Problem 23 • 1989 AMC 12 Problem 29 • 2002 AMC 12A Problem 24 • 2005 AMC 12B Problem 22 • 2008 AMC 12A Problem 23 • 2009 AMC 12A Problem 21 • 2011 AMC 12A Problem 23 • 2011 AMC 12B Problem 24 • 2012 AMC 12B Problem 23 • 2015 AMC 12B Problem 25 • 2017 AMC 12A Problem 17 • 2017 AMC 12B Problem 12 • 2018 AMC 12B Problem 16 • 2019 AMC 12A Problem 21 • 2020 AMC 12B Problem 17 • 2020 AMC 12B Problem 23 • 2021 AMC 12A Spring Problem 15 • 2021 AMC 12A Spring Problem 22 • 2021 AMC 12B Spring Problem 20 • 2021 AMC 12A Fall Problem 25 • 2022 AMC 12A Problem 21 • 2022 AMC 12B Problem 11 • 2022 AMC 12B Problem 24 • 2023 AMC 12A Problem 14 • 2023 AMC 12B Problem 19
AIME
1984 AIME Problem 8 • 1990 AIME Problem 10 • 1994 AIME Problem 13 • 1996 AIME Problem 11 • 1997 AIME Problem 14 • 2003 AIME II Problem 15 • 2004 AIME I Problem 13 • 2008 AIME II Problem 9 • 2009 AIME II Problem 13 • 2011 AIME II Problem 8 • 2012 AIME I Problem 6 • 2014 AIME II Problem 10 • 2019 AIME II Problem 8 • 2023 AIME II Problem 8 • 2024 AIME II Problem 13