resources
Like many other disciplines, the most important thing in competition math is practice. With very few exceptions, the people who perform better than everyone else are the ones who do the more problems than everyone else. The reason why is because competitive math is highly intuition based, and the simplest and most straightforward way to build intuition is to solve more problems.
Hence, problem dispensers are indispensable (pun intended):
Alcumus - Alcumus is a problem dispenser created by AoPS targeted towards middle school aged students looking to prepare for MATHCOUNTS and AMC competitions. It provides problems based on subject and level (1 being the easiest, 25 being the hardest).
MATHCOUNTS Trainer - MATHCOUNTS Trainer is a problem dispenser created by AoPS designed specifically to train students for the MATHCOUNTS competitions.
AMCTrivial - A personal favorite! This program is a problem dispenser made by searching the AoPS Wiki for problems. For more info on the difficulty scale, please visit the AoPS Difficulty Ratings page.
Summer Programs:
For students who would like to better prepare for state-level competitions, we highly recommend FrostMath (http://www.frostmath.com). Coach Frost runs online classes on Wednesday nights (6:15-8:45 pm) and in person classes on Saturday mornings in Lexington (9-11:30 am).
Students are also encouraged to prepare for and participate in AMC 8, AMC 10, and MOEMS.