Past papers are mostly for when you understand the material and want to optimise your exam technique. (Especially past HSC papers.)
First step is to make sure you understand the theory of the course, why things are true, how the proofs of things in the course work etc. (Try to prove some of them yourself, although for some things like the fundamental theorem of algebra, this is a bit unrealistic.)
Definitely don't look at the answer to a question if you can't get in in a few mins. Move on to another question and return to the one that was troubling you later. Sometimes you might get fresh ideas. If you are stumped by most of the questions in a section, you probably don't understand the theory.
It is infinitely easier to follow someone elses proof than construct your own, so people who look at answers too quickly often hoodwink themselves into believing that they understand the mathematics better than they actually do. One of the most important skills is to be honest and self-critical.
Even if you eventually give up and ask someone for help, or read the answers, I guarantee you will get a lot more out of it if you bashed your head against it for a bit and tried some stuff.
Returning to the first point about past papers. You should really stress accuracy over speed at the start of the year. You should take your time and learn to be so careful that when you finish a problem, you can be almost certain that you are right. (Being self-critical helps develop this confidence funnily enough). When you have reached this point, or close to it, then you can worry about speeding up, which is a lot easier than you might think. Too many people skip the first step of developing accuracy and then these are the people who struggle with the harder questions in the paper, even if mechanically they are very fast.
