Logo for LIVE by Po-Shen Loh

LIVE

English

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

AMC 10

2013 AMC 10B Problem 11 · 2015 AMC 10A Problem 12 · 2016 AMC 10B Problem 16 · 2020 AMC 10B Problem 9

AMC 12

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

AIME

1999 AIME Problem 3 · 2005 AIME I Problem 4 · 2005 AIME II Problem 15 · 2008 AIME I Problem 4 · 2010 AIME I Problem 6 · 2017 AIME II Problem 6

More algebra concepts

absolute valueagesalgebraic manipulationAM-GM Inequalityarithmetic sequencebinomial theoremcalculusCauchy-Schwarz Inequalitycomplex numbercustom operationDe Moivre’s Theoremdeterminantdifference of squaresfactoringFibonaccifloor and ceiling functionsfunctionfunctional equationgeometric sequenceinequalitylinear equationlogarithmmatrixmixtureNewton’s Sumspartial fractionspolynomialquadraticradicalrational equationrationalizing denominatorrecursionroots of unitySimon’s Favorite Factoring Trickslopesubstitutionsum and difference of cubessum of first n cubessum of first n odd numberssum of first n squaressummationsymmetry (algebra)system of equationstelescopingVieta’s Formulas