https://www.maa.org/math-competitions/invitational-competitions
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Q. How do I qualify for the AIME?
A. Qualification parameters for AIME vary with the results of the AMC 10/12 competitions. For AMC 10, invitations are issued to at least the top 2.5% of all scorers. For AMC 12, invitations are issued to at least the top 5% of all scorers. The exact cutoffs will depend on the difficulty of each competition.