<p>Yeah, like joeman said you must remember that the applicant pool for Caltech is full of science and math students, so qualifying for the AIME is nothing really special. However, I think a general rule is that 4 or 5 on the AIME looks good to colleges. However, if you get above the mean score of like 2 point something, then you should prolly report it. I don’t think ARML is incredibly useful for college apps. The only other one I’ve heard of on that list is HMMT and I can’t imagine that that’s too useful either. AMC/AIME is the premiere high school math competition I think.</p>