<p>"Besides, I can do some of the exam problems even though i’m not in Caltech and that means something. "</p>
<p>I personally find the exam problems to be like two levels below the hw problems. In the exams you’re on the whole mostly expected to regurgitate and apply concepts. On the hw, you’re expected to synthesize.</p>
<p>"It seems quite easy for a mediocre student to copy off the solutions off an advanced student for the homework problems. "</p>
<p>Well, straight copying is against the honor code, but the math 1a policy is that if you can reproduce the work you write, then it’s fine to get help. And if you’re really lazy, it’s easy to just get a friend to show you the proof. The steps of proofs are never particularly hard, it’s just seeing how they fit all together, and so it’s not that hard once you have all the steps. So I know that a lot of frosh will just wait until the TA office hours or after their friends have finished to just learn the proofs and write them down, but I personally don’t do that. And if you don’t do that, the math hw can be a pain. Math 1a hw isn’t necessarily long. If you’re an IMO team member and you see it immediately, it’s rather short. For us normal people though, it takes more than no time. However, I haven’t given up on trying to learn all my hw on my own even though they warned us at frosh camp not to try it and numerous people have called me a moron.</p>