Although all math competitions require knowledge of math to do well in, there are certain ways to do slightly better than normally using some contest strategies.
It's a bad idea to stay up all night solving problems or playing video games because it's easy to get drowsy during the test. Getting a good night sleep can help refresh the brain, so it can be ready for the test.
Studying is important but don't forget to leave room to exercise. Exercise can help refresh the brain, allowing problem solvers to prepare for tests more effectively.
Problem Solving Strategies
In many geometry problems, a visual aid can help solvers visualize and look for clues. Even in non-geometry problems, drawing pictures can help formulate ideas.
Patterns are everywhere in mathematics, and successful problem solvers look for patterns to get information. Many patterns can then be proved by induction.
In some problems, estimation can narrow down the possible values. It can also be used to check if an answer is reasonable.
Test Taking Strategies
Instead of spending twenty minutes on a problem, some people choose to spend thirty seconds reading the problem, then skip it. The time saved skipping the problem can help you check and solve other problems, and you can always return to the problem that you skipped. This concept helps double where you are rewarded for a blank answer, such as the SAT, the AMC 10, and the AMC 12.
In the MathCounts Sprint competition of 2006, many of the harder problems were presented earlier on in the test, putting people who did not skip problems at a large disadvantage - Daesun Yim, the 5th place written finisher, skipped five out of thirty problems on the Sprint round, and he received a 23/30 on the Sprint round.
Part of the strategy of skipping problems after reading them is that you often work on problems subconciously. An insight might hit you about a particular problem while you're not working on it. You can then go back and work through the problem.
Educated guessing is the art of taking a, well, educated guess. An educated guess takes less time than completely solving the problem, especially when the problem stumps you, and if you can narrow the problem down to a couple of choices, you may be able to take a good guess, saving you time and giving you a chance of getting the answer correct. This tactic helps the most in competitions with multiple choice answers. It also helps where a wrong answer and an answer left blank are counted as the same amount of points, such as the AMC 8 and MathCounts.
Reflecting on Past Problems
Sometimes, harder problems are really multi-layered easy problems in disguise. Also, one can look at strategies from past problems and try to use that here. Also, Rusczyk talked about “wishful thinking” — trying to make a problem look like a similar one solved before.