<p>Okay, so I don’t want to sound all negative and pessimistic. </p>
<p>Honestly, it’s really hard. Even the IMO Gold Medalist, Xioayu He, only got a 87/100. </p>
<p>Getting 68 points, even if you do all 4 sets, is pretty darn hard. The AMC 10 equivalent of a 68/75 is definitely not 90, more like 140+. There’s a reason you get a month to solve 5 problems. </p>
<p>If you’re aiming for the AIME, definitely don’t depend on the USAMTS. The USAMTS is more of a more-practice-with-really-hard-proof-problems-for-fun. Just keep working on AMC, is my best advice. </p>
<p>However, if you really can get a 68/75 by the first three sets, then you should be aiming for USAMO and potentially MOP. </p>
<p>Also, on the Mathematica thing, a lot of competitions give away free licenses. </p>
<p>And MIT isn’t the only school you’re applying to either. Would schools like Cornell know about it? Maybe. Would they consider it much? Perhaps. </p>
<p>Keep working on other stuff too. Pretty soon, you’ll want to start developing an area that’s of incredible interest to you (if you haven’t already), and you should pursue that. Colleges like to see passion.</p>