Useful techniques for mathematical competitions I did a research about mathematical competitions and I came to a conclusion that in order to do well, one needs to master a set of particular techniques and shortcuts. I was struggling with math pretty much my entire life and I generally hated it. However, a few months ago, it was brought to my attention a different perspective about the subject and I decided to give myself a second shot with it. I dedicated 4 hours a day, 5 days a week for study and practice, and I went from Algebra I all the way to Calculus II in a matter of 6 months. I did all the exercises in the 3 textbook manuals I was working with, and generally, I was pretty satisfied with the outcome. As I was gaining more and more confidence, I was attempting more and more challenging problems and I was getting them right most of the time. At some point, I picked up several sample AMO problems and as I was attempting to work them out, I realized that I wasn't even able to understand the questions let alone to solve them. Although, they cover topics from basic Algebra and Geometry (which I thought I have mastered), out of 12 questions I managed to answer 3, needless to say, I was very disappointed at myself. And if it wasn't for the fact that I am able to solve most of the problems in regular high school math textbooks, I would probably have given up already.  I googled my issue and I was suggested to buy a copy of The Art of Problem Solving Volume I and II which I did. But sadly, it did not help me at all. I am still incapable of tackling problems from Olympiads. I will greatly appreciate it if anyone out there can recommend techniques and approaches for solving such problems, and also, books and study materials which could eventually help me build up my skills. So basically, my question boils down to - how to prepare myself for such mathematical contest?
Thanks in advance!
 A: 
I went from Algebra 1 all the way to Calculus II in a matter of 6 months

You probably realized that didn't help much by now. Competition math doesn't require much mathematical knowledge to understand the questions or answers, in the sense of high school or college courses.
In competitions, an entirely different skillset has the main focus: the ability to find proofs to completely unique problems. You'll need to learn about basic proof techniques, which the Art of Problem Solving book does a very good job of explaining. You should definitely give it another try.
A big part of solving a problem is experience: It's a lot easier to solve a problem if you can tell at first glance which methods are promising to approach that problem. The only way to gain experience is by working through a ton of problems, peeking at the solutions only if you're stuck. It helps if you do problems grouped by proof technique, so you can immediately apply the ideas you see.
I suggest that you start out by tackling problems of lower grades and/or early rounds of contests, until you're confident you can solve 99% of them, in order to build a strong foundation. Once you're at that point, you'll be accustomed to the necessary thought processes that allow you to have those brilliant ideas that are absolutely mandatory to solve the more difficult problems.
