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 of these problems are used with official legal permission of the Mathematical Association of America (MAA).
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
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
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