The New York City Math Team participates as a team in the following competitions
The Princeton University Mathematics Competition (PUMaC) is an annual competition in November run by the students of the Princeton University Math Club. Teams come from all over the US and various countries to participate in the contest.
The Harvard-MIT Math Tournament is held each February. It is jointly organized by Harvard and MIT students. It attracts teams from around the world and is highly competitive.
The New York State Mathematics League is a state-wide team competition closely related to ARML, and having the same format. It takes place usually in April, traveling each year to a different region of New York State.
American Regions Mathematics League is a nationwide team competition. It always takes place at the end of the school year, in four locations around the US, and serves as the high point and the conclusion of the year for the math team.
There are also a number of contests that students take part in as individuals or as part of their school math teams
The NYC Interscholastic Math League offers several levels of contests for high school students, competing in teams to solve individual questions. Contests are administered in schools by a math teacher several times each semester. Most members of NYC Math Team participate in IML contests. If your school doesn’t offer it, it’s easy for a coach to start it.
AMC & co www.maa.org/math-competitions
AMC is a national competition with individual questions. It offers multiple levels, for grades 8 (November), 10 and 12 (February). Top performers are invited to continue with AIME, then USAMO, culminating with the IMO (International Math Olympiad).
There are many more great contests, including SBIMC (South Brooklyn Invitational Math Competition).
See our Resources page for other resources.