Logo for LIVE by Po-Shen Loh

LIVE

English

Symmetry (algebra) — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses symmetry (algebra) — 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

2006 AMC 10B Problem 14 · 2007 AMC 10A Problem 20 · 2008 AMC 10B Problem 5 · 2015 AMC 10A Problem 16 · 2021 AMC 10B Spring Problem 15 · 2021 AMC 10A Fall Problem 16

AMC 12

2000 AMC 12 Problem 20 · 2002 AMC 12B Problem 19 · 2005 AMC 12B Problem 23 · 2007 AMC 12A Problem 7 · 2010 AMC 12B Problem 23 · 2014 AMC 12B Problem 16 · 2019 AMC 12B Problem 8 · 2025 AMC 12A Problem 19

AIME

2000 AIME I Problem 7 · 2000 AIME II Problem 7 · 2001 AIME I Problem 9 · 2014 AIME I Problem 14 · 2015 AIME II Problem 14 · 2021 AIME II Problem 7 · 2023 AIME II Problem 4 · 2024 AIME II Problem 11

More algebra concepts

absolute valueagesalgebraic manipulationAM-GM Inequalityarithmetic sequencebinomial theoremcalculusCauchy-Schwarz Inequalitycompleting the squarecomplex 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 squaressummationsystem of equationstelescopingVieta’s Formulas