<p>When I took AIMEs back in 05-07, the averages used to be 2.x on the AIMEs, now, I think due to the restructuring of the AIME that happened in either 07 or 08, the averages have risen to 4.x (AIME 2009).</p>
<p>Just take a look at the [AIME</a> I & II 2008 Statistics](<a href=“http://www.unl.edu/amc/e-exams/e7-aime/e7-1-aimearchive/2009-aa/09-AIMEstats.shtml]AIME”>http://www.unl.edu/amc/e-exams/e7-aime/e7-1-aimearchive/2009-aa/09-AIMEstats.shtml) score distribution yourself.</p>
<p>IMO (pun not intended :P), doing well on the AIME is a very good way to distinguish yourself, since I consider it akin to a national competition. If you can say, “well, I was within the top 500 scorers of the AIME nationally,” I think that’s a very legit accomplishment, especially if you come from a school district that doesn’t traditionally offer a lot of opportunities in the form of academic competitions.</p>
<p>Therefore, any score above the average on the AIME is just not a decent score, but a great score. Even if you just qualified for the AIME (but got a 0 on it), still put the qualification down. It still represents that you are near top 5% of the people who took AMC12 nationally. </p>
<p>You guys should check out [USA</a> Mathematical Talent Search](<a href=“http://www.usamts.org/]USA”>http://www.usamts.org/) if you are into math. It’s a NSA-sponsored math competition that can be done at home, and is a great enrichment resource for math students. If you qualified for the AIME, you should be able to get decently far in USAMTS. Even if you didn’t, you can also qualify for the AIME via USAMTS, so if you’re not great on the whole AMC multiple choice thing (or your school doesn’t offer the AMC!) this is also an excellent alternative.</p>