algebra
Roots of unity — AMC & AIME Problems
47 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.
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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
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