Math team is an entertaining extracurricular activity at some high schools. I'm sure there are different versions in different areas and whatnot, but this is how we play it at my school.

Teams consist of eight individuals (any mix of male/female). Team One, the only team that actually counts for consideration in the team competition, has an additional restriction: there may be no more than four seniors on this team. The competition consists of five rounds, four individual and one team. All rounds last 15 minutes. All individual rounds have four questions, numbered sequentially, with values equal to their numbers. The first three individual rounds are conducted without the aid of calculators, with the last individual round and the team round allowing calculator use. The team round has six questions, each worth ten points. The entire team of eight can work together on these problems, turning in one answer sheet.

Questions are generally from the areas of problem solving, algebra, geometry, and logic. Winners in the individual contest are determined purely by their scores on the individual rounds, with separate prizes for freshmen, sophomores, juniors, and seniors. The team prizes are figured by adding the individual scores of all team members and the results of the team round.

Some people might not immediately think that math team would be a lot of fun. They have not experienced the social joys that is the math team meal that preceeds each monthly meet.

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.