AMC, AIME, etc.

AMC

The American Mathematics Competition (AMC) are a set of annual mathematics competitions offered by the Mathematical Association of America. There are three different tests in three different levels: AMC 8, AMC 10, and AMC 12, the number is the highest grade level that can take that test. (In other words, juniors and seniors cannot take the AMC 10, and so on.)

AIME

The American Invitational Mathematics Examination is an invitation-only competition for students who score well on the AMC 10 or 12.

USA(J)MO