Bounding to limit cases — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses bounding to limit cases — a problem-solving techniques 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 10
2000 AMC 10 Problem 10 · 2000 AMC 10 Problem 11 · 2000 AMC 10 Problem 22 · 2001 AMC 10 Problem 14 · 2002 AMC 10A Problem 11 · 2002 AMC 10B Problem 7 · 2004 AMC 10B Problem 4 · 2004 AMC 10B Problem 13 · 2007 AMC 10A Problem 25 · 2009 AMC 10A Problem 2 · 2009 AMC 10A Problem 12 · 2010 AMC 10A Problem 8 · 2010 AMC 10A Problem 9 · 2010 AMC 10B Problem 12 · 2011 AMC 10A Problem 6 · 2017 AMC 10B Problem 6 · 2017 AMC 10B Problem 25 · 2018 AMC 10A Problem 14 · 2018 AMC 10A Problem 22 · 2019 AMC 10B Problem 24 · 2020 AMC 10B Problem 9 · 2021 AMC 10A Fall Problem 20 · 2021 AMC 10B Fall Problem 19 · 2023 AMC 10A Problem 4 · 2023 AMC 10B Problem 14 · 2023 AMC 10B Problem 22 · 2024 AMC 10A Problem 4 · 2024 AMC 10B Problem 5 · 2025 AMC 10B Problem 17
AMC 12
1999 AMC 12 Problem 7 · 1999 AMC 12 Problem 9 · 1999 AMC 12 Problem 14 · 2000 AMC 12 Problem 13 · 2001 AMC 12 Problem 7 · 2002 AMC 12A Problem 9 · 2002 AMC 12B Problem 4 · 2002 AMC 12B Problem 24 · 2003 AMC 12B Problem 7 · 2004 AMC 12B Problem 11 · 2005 AMC 12A Problem 8 · 2005 AMC 12A Problem 21 · 2007 AMC 12A Problem 14 · 2007 AMC 12A Problem 22 · 2009 AMC 12A Problem 10 · 2009 AMC 12A Problem 12 · 2009 AMC 12A Problem 13 · 2010 AMC 12A Problem 5 · 2010 AMC 12A Problem 6 · 2010 AMC 12B Problem 13 · 2010 AMC 12B Problem 19 · 2011 AMC 12A Problem 7 · 2011 AMC 12A Problem 20 · 2011 AMC 12B Problem 7 · 2013 AMC 12A Problem 21 · 2013 AMC 12B Problem 15 · 2014 AMC 12A Problem 19 · 2014 AMC 12B Problem 13 · 2015 AMC 12A Problem 2 · 2017 AMC 12A Problem 11 · 2017 AMC 12B Problem 21 · 2018 AMC 12A Problem 21 · 2018 AMC 12B Problem 17 · 2019 AMC 12B Problem 6 · 2019 AMC 12B Problem 22 · 2020 AMC 12B Problem 8 · 2021 AMC 12B Spring Problem 21 · 2023 AMC 12B Problem 22 · 2024 AMC 12A Problem 3 · 2024 AMC 12A Problem 8 · 2024 AMC 12A Problem 21 · 2025 AMC 12B Problem 14
AIME
1998 AIME Problem 8 · 1998 AIME Problem 14 · 2001 AIME I Problem 8 · 2001 AIME II Problem 2 · 2003 AIME I Problem 1 · 2003 AIME I Problem 14 · 2007 AIME I Problem 14 · 2007 AIME II Problem 12 · 2007 AIME II Problem 14 · 2008 AIME I Problem 10 · 2010 AIME I Problem 5 · 2011 AIME II Problem 9 · 2013 AIME II Problem 6 · 2013 AIME II Problem 14 · 2016 AIME I Problem 12 · 2017 AIME I Problem 13 · 2018 AIME II Problem 3 · 2018 AIME II Problem 15 · 2020 AIME I Problem 3 · 2020 AIME I Problem 10 · 2021 AIME I Problem 15 · 2022 AIME I Problem 7 · 2025 AIME I Problem 1