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AMC inequalities & optimization problems

Inequalities, AM-GM, and optimisation by bounding the extreme cases.

250 problems in the archive use these ideas — 116 from the AMC 10 and 134 from the AMC 12.

Picks a problem you have not seen, at about the difficulty you are handling.

60 most recent problems

Newest contests first. Every problem opens with its answer choices, hints and a worked solution.

Use Start inequalities & optimization practice above to keep going through the remaining 190, or browse them by contest in the AMC 12 and AMC 10 archives.

Back to all algebra problems.