shravas

It's a lot harder to qualify for USAMO though through USAMTS though, since if you do qualify for the AIME, they just treat it as if you got a 100 on the AMC (AMC is out of 150), and AMC scores will matter if you're a senior (and a junior, and maybe if you're a sophomore or below).

anotherparent

^^ Actually, it is the top 350ish kids, then the fill out the rest of the 500 with sophomores and below.

You can take the AMC even ifyour shcool does not organize it. My son homeschools and has taken the test 7 times in the past 4 years, plus the aime and the USAMO three times. He has taken these tests at 6 different locations. Two were local private schools that were willing to allow him to take it as a guest (I had to organize that through the AMC office), twice thru local math circles. and twice with local colleges who were offering it on the b date. This is last years list:
Additional Locations for the AMC 10B/12B at Higher Education Sites

And Shavras is correct - if you qualify for AIME through the USAMTS, you would probably need a 9-11 on the AIME to move up.