<p>For the record, as a freshman, I did make it to the AIME (and got a 1.5), but was then sick and missed the AMC for the next 2 years (well, I may as well have done - I just did really badly). But frankly, I find these math competitions distasteful and pointless. Being able to do random algebra very well has no relation to, well, anything. You’re never going to be doing anything at all like that in the real world. And yes, linear algebra can help solve a lot of those problems, but expecting high schoolers to have already taken what is normally a second or third year college course in order to be able to do the problems sensibly is just silly. Which means that you’re left doing the problems by ridiculous elementary methods which, as I said, serve no purpose to anything.</p>
<p>I beg to differ that it relates to do with problem solving ability. Sure, being able to do well on these means that you are above some threshold for problem solving ability, but I don’t believe it necessarily means you are very good at it. I have a “friend” who is able to place in the top handful in state math competitions, and all he can do is memorize formulas (according to himself).</p>
<p>[/bitter rant] ;)</p>