Completing the square — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Completing the square — 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
2013 AMC 10B Problem 11 • 2015 AMC 10A Problem 12 • 2016 AMC 10B Problem 16 • 2020 AMC 10B Problem 9
AMC 12
1950 AMC 12 Problem 41 • 1952 AMC 12 Problem 13 • 1954 AMC 12 Problem 42 • 1955 AMC 12 Problem 24 • 1955 AMC 12 Problem 39 • 1957 AMC 12 Problem 10 • 1957 AMC 12 Problem 36 • 1959 AMC 12 Problem 8 • 1962 AMC 12 Problem 26 • 1962 AMC 12 Problem 37 • 1964 AMC 12 Problem 24 • 1965 AMC 12 Problem 9 • 1969 AMC 12 Problem 12 • 1970 AMC 12 Problem 6 • 1978 AMC 12 Problem 1 • 1984 AMC 12 Problem 22 • 1998 AMC 12 Problem 23 • 2002 AMC 12B Problem 25 • 2005 AMC 12B Problem 20 • 2006 AMC 12A Problem 21 • 2010 AMC 12A Problem 21 • 2010 AMC 12B Problem 23 • 2013 AMC 12B Problem 6 • 2016 AMC 12B Problem 18 • 2020 AMC 12B Problem 8 • 2021 AMC 12B Spring Problem 18 • 2024 AMC 12B Problem 13