<p>It depends on your index. There is a huge range of USAMO indices that will qualify you for AIME.</p>
<p>Take 100.5 AMC 12 and 1 AIME. Now, take 114.5 AMC 12 and 7 AIME (my indices in 10th and 11th grade, respectively).</p>
<p>The first one was awful, the second one was not that far off from USAMO qualification. In terms of proving your ability to do math, AIME qualifying is less than USAMO qualifying. But if you have a high index, then that’s significant as well. Remember, though, that there are a lot of USAMO qualifiers applying to MIT.</p>