Math team in my school consists of about 40 people assembling on Saturdays and Sundays, from 1 to 4. During that time students read various books from the math library, eat donuts, and solve math problem. Most of the problems are taken from previous math competitions such as AHSME, AIME, USAMO, IMO, mandelbrot, Harvard, and MIT.

This is a quick run down of our study materials

The Art of Problem Solving is a two volume book that deals with all topics ranging from Algebra to Trigonometry, Probability, and Pre-Calculus. It composes the bulk of out studies.
Previous competitions compose the other half. We usually try to solve a problem for a reasonable amount of time, and if unable to, we look in the solutions sheet.
  • AHSME competition is target at high school seniors and juniors from normal schools. Most math teams folks use these to study in their freshmen and sophomore years. This completion takes 1.5 hours and consists of 30 multiple choice questions. Recently it has been renamed and split into AMC-10 and AMC-12.
  • AIME is targeted at people who come in the first 1% of AHSME. It is 3 hours long and has 15 questions with answers integer ranging from 000 to 999.
  • USAMO is the hardest completion in America. A few students who do really well on it are sent to international mathematical olympiad.
  • IMO is an international competition. Follow the hard link to learn more.
  • Mandelbrot is a combination, team and individual completion carrying Mandelbrot’s name. It takes place 4 times a year, while all others are annual.
  • Havard is a high school competions that takes place at Harvard. I will add details when I ask my math coach, or take the competition in about a month.
  • MIT is a competition that takes place at MIT. I have no details about it

Please note that even thought it is called “math team”, most competitions and results are individual. Most math competitions publish their previous competitions with complete solutions in books and other releases.