What are the different tournaments that a student can participate?

Elementary School Tournaments

1. AMC 8: A 25-problem, 40-minute multiple choice examination in middle school mathematics promoting problem-solving skills.
2. Berkeley Mini Math Tournament (BMMT): Hosted by UC Berkeley, attracting elementary and middle school participants.
3. Exeter Math Competition (EMCC): An annual competition held at Phillips Exeter Academy.
4. Continental Math League (CML): Designed to maximize student participation and improve problem-solving capabilities.
5. Centre for Education in Mathematics and Computing (CEMC): A selection of contests for students in elementary and middle school.
6. Math League: A series of contests culminating in a National or International Championship.
7. Mathematical Olympiads for Elementary and Middle Schools (MOEMS): Focuses on multiple strategies for problem-solving.
8. Math Kangaroo: An international mathematics competition with six levels of participation, ranging from grade 1 to grade 12.
9. Noetic Learning Math Contest (NLMC): A semiannual problem-solving contest for elementary and middle school students.

Middle School Tournaments

1. AMC 8: A 25-problem, 40-minute multiple choice examination in middle school mathematics promoting problem-solving skills.
2. AMC 10/12: A 25-question, 75-minute multiple choice examination designed for middle and high school mathematics.
3. American Invitational Mathematics Examination (AIME): The second exam in the series of exams leading to the International Mathematics Olympiad (IMO).
4. Berkeley Mini Math Tournament (BMMT): Hosted by UC Berkeley for elementary and middle school students.
5. Exeter Math Competition (EMCC): Held at Phillips Exeter Academy.
6. Continental Math League (CML): Designed to improve problem-solving capabilities.
7. Purple Comet Math Meet: A team mathematics competition for middle and high school students.
8. Centre for Education in Mathematics and Computing (CEMC): Contests for elementary and middle school students.
9. Math League: A series of contests with a National or International Championship.
10. Mathematical Olympiads for Elementary and Middle Schools (MOEMS): Focuses on problem-solving strategies.
11. Mathcounts: A nationwide middle school competition series.
12. Math Kangaroo: An international competition with levels for grades 1 to 12.
13. Noetic Learning Math Contest (NLMC): A problem-solving contest for elementary and middle school students.
14. Silicon Valley Math Tournament (SVMT): An annual competition organized by Random Math for middle school students, featuring individual and team events​ (Random Math)​.

High School Tournaments

1. AMC 10/12: A 25-question, 75-minute multiple choice examination in high school mathematics.
2. AIME: The second exam in the series leading to the IMO.
3. USA(J)MO: The third test in the series for selecting the US IMO team.
4. Berkeley Math Tournament (BMT): Hosted by UC Berkeley for high school students.
5. Harvard-MIT Math Tournament (HMMT): One of the largest high school competitions globally.
6. Stanford Math Tournament (SMT): Organized by Stanford students, includes individual and team portions.
7. Caltech Harvey Mudd Math Competition (CHMMC): Hosted by Caltech and Harvey Mudd College.
8. Carnegie Mellon Informatics and Mathematics Competition (CMIMC): Held at Carnegie Mellon University.
9. Math Majors of America Tournament for High Schools (MMATHS): Hosted by Yale University.
10. Duke Math Meet (DMM): Hosted by Duke University.
11. Princeton University Mathematics Competition (PUMaC): Organized by the Princeton University Math Club.
12. Purple Comet Math Meet: A team competition for middle and high school students.
13. Centre for Education in Mathematics and Computing (CEMC): Contests for high school students.
14. Math League: A series culminating in a National or International Championship​