Mathcounts is a math competition for sixth through eighth graders. It is held at four levels of competition: School, Chapter(Region), State, and National.
At the school level, the team members compete against one another. The players with the four highest scores are made the team and the next four make up the alternate members. The alternate members compete at the chapter competition, but they don't compete as a team, despite what some chapters wrongly do. The only rounds utilized in the School competition are the Sprint and Target rounds(the individual rounds). This level of the competition has the easiest questions of all the competitions.
The Chapter competition is held at a neutral site, frequently at colleges. At this level, the team round is also used, and some chapters use the Countdown and Masters rounds. What happens at this level is that the competitors are all removed from everyone else for the most part, and they are given the sprint and target rounds. Then, they let the teams get together and they have the team round. After that, it's just the awards, unless they have a Countdown round or Masters round. The scoring for the teams is done by averaging the four individual scores, and then adding the team round score. It varies from chapter to chapter how many advance to the state competition, but, at the least, 1 team and 2 individuals can advance. If the individuals are also on the team, then this is irrelevant, as they would advance anyways. This level of competition has harder questions than the School level.
The State Competition is normally held at a nice hotel. In most states, with websites of the competition, they take pictures of the competitors and coaches the first night, when there is no competition. The next morning is the actual competition. It is the same as the chapter competition, although more states have the Countdown and Masters rounds. The top 4 individuals are made the all-star team for the state, and the championship teams coach becomes the coach for the team of all-stars, even if no one on from their team is on the team. Here, the questions are still harder, and they have some strange ones, too.
The National competition is quite interesting, but, this year it is being held in Chicago, instead of Washington, D.C. Because of this, I'm not sure eactly what they are going to do. In the past, you get lots of sightseeing tours, and the competition is a bit of an afterthought. This year(according to my former coach) it is being held at Chicago University. Also, in the past, they gave out sizable scholarships to the top finishers. But, since they moved it to Chicago for monetary purposes, they might be cut back. At the nationals, every round is used. Here are the hardest questions of them all.
And here are all the different kinds of rounds.
The Sprint Round
The sprint round is, as the name implies, based on speed. There are thirty questions, for which you get 40 minutes to complete. In this round you can't use calculators, but they normally aren't useful. A common kind of question in this round regards the pythagorean theorem or patterns in exponents.
The Target Round
The Target Round consists of 4 sets of two questions each. You are given 6 minutes for each set, and the questions get progressively more challenging. Here, you can use calculators, and they are quite useful here. Frequently questions here have to be expressed in terms of pi.
The Team Round
The Team Round is very straightforward. The team works together, and they are given 20 minutes to solve 10 problems. The questions are very similar to those of the target round, just more difficult.
The Countdown Round
The Countdown round is a very fun round. The top finishers in the individual rounds are the only people who compete. Two people are called up at a time, and a question is flashed up on a screen. The competitors cannot use calculators, and are only given 45 seconds for each question. After three questions, the person with the most correct advances to the next round, and the loser does not. Most of the questions in this round are based on speed.
The Masters Round
The Masters Round is similar to the countdown round, in the sense that it is exclusive to the top finishers. Normally there aren't any awards associated with this round, it's just for fun. They give the top finishers(masters) a question, they get 5 minutes to work it out, then they present a solution the succeeds in perplexing everyone watching. Very fun stuff.