The 8 Best Math Competitions for High School Students
As you’re advancing in your school years, and you are learning new things everyday, it is just as important to simultaneously put your abilities to the test and challenge yourself. With such complex subjects as math, it is often not enough to simply learn; you need to push yourself to use what you learn in different settings.
Math competitions are a great way to go up against fellow high schoolers that also share an interest in mathematics, and if you do well, receive national/international recognition in high school. Still, no matter whether you do well or not, math competitions are also a great thing to put in your college applications!
Math competitions can be helpful for all students who have an interest in mathematics: in this post, we will talk about the 10 best math competitions for high school students that can cater a wide range of students– we will show some math competitions that offer individual/team options, ones that encompass different fields of mathematics, ones with awards and prizes, and more!
Keep in mind that this list is not in order of best to worst; all of these math competitions are specialized for a specific audience and all have their own host of benefits for the students that participate in them! This is just a list that showcases the various options available for mathematics-oriented students with different goals.
The 8 Best Math Competitions
American Mathematics Competition (AMC) 10/12
Where: Online
When: Mid-November
Who: Anyone up to 10th grade for AMC 10, up to 12th grade for AMC 12
Cash Prize: None
The AMC 10/12 is an annual exam geared towards high school students, deriving from a typical high school curriculum but excluding calculus, but middle and elementary school students who are interested in math are also welcome to participate. The AMC is a highly prestigious test that over 300,000 students take annually. It is a 75 minute, 25 question exam that increases in difficulty as you get further in the test, and is scored out of 150. A score higher than 100 usually places one in the higher end of participants. The AMC 10 is for participants in the 10th grade or below, and the AMC 12 is for students in the 12th grade or below. Since the AMC 12 is for a higher age group, the questions are significantly more difficult.
What makes the AMC 10/12 so special is that the highest scorers receive commendations and opportunities to advance farther in the AMC series. The top 2.5% of AMC 10 scorers and top 5% of AMC 12 advance to the next stage, which is called AIME: American Invitational Mathematics Examination. Very high scorers on this exam get to proceed to the next level of tests, an incredibly prestigious one: the ones who took the AMC 10 get to advance to the USAJMO, which is the United States of America Junior Mathematics Olympiad, and those who took the AMC 12 get to go to the USAMO, which is the same as above but not Junior.
The AMCs are a huge stepping stone to any difficult mathematics competitions, and performing successfully can be a great look for getting into more math competitions and applying for college and scholarships. Since it is such an open exam, the AMCs are a great foundational base for students who want to further their experience with math competitions.
American Invitational Mathematics Examination (AIME)
Where: School-based: if your school offers the exam, they will host it for all participants
When: Early February
Who: Up to 12th grade, only for those who qualify through AMC 10/12
Cash Prize: None
The AIME, as was mentioned before, is a highly prestigious exam occurring annually that can be taken by all high schoolers that perform well enough on the AMC exams to qualify. The AIME is a 15-question exam with all answers being integers falling between 0 and 999. Despite this, the questions on the AIME are highly difficult and guessing will not get you anywhere. The questions on that AIME cover a variety of topics, like algebra, geometry, trigonometry, number theory, etc. Similar to the AMC 10/12, the AIME exam does not include any calculus topics.
As was also mentioned in the previous section, the AIME is extra special because the scorers that get the highest combined scores on the AMC 10/12 and AIME get the opportunity to advance to the USA(J)MO, the USA (Junior) Mathematics Olympiad, which is arguably the country’s most prestigious exam. Students who get the chance to participate in AIME and have the good fortune of performing well on it will very much reap the benefits, and this is an incredibly valuable experience for any student who wants to challenge themselves and achieve a lot in the math world.
American Regions Mathematics League (ARML)
Where: Various sites – Penn State, University of Alabama Huntsville, University of Iowa, and University of Nevada Reno
When: Early June
Who: Non-graduated high school students, and rarely middle school students
Cash Prize: Yes
ARML is an annual competition for high school students that requires that participants compete in teams of 15 members, though there are both individual and team questions. Registration for ARML can be done online by any group of students that has managed to form a team and has managed to acquire two coaches as well.
ARML covers a variety of mathematical topics similar to the AMC exams, containing problems on algebra, geometry, trigonometry, number theory, combinatorics, and more. Also similar to the AMCs, calculus knowledge is not required for ARML, though it may come in handy.
The top teams and individual participants receive cash prizes in the form of gift cards. The top two teams in different divisions get their own prize, while the top 20 individual competitors each get individual prizes and the top performer receives an extra $100 in prize money.
Harvard/MIT Mathematics Tournament (HMMT)
Where: 1 tournament at Harvard and 1 tournament at MIT
When: Around November and February
Who: 9th - 12th grade
Cash Prize: None
HMMT is a very competitive and prestigious math competition that attracts almost 1,000 students from around the globe. Students can compete in teams of 4-8 people, and there are also a limited number of seats for those students who wish to participate individually. Students are able to apply to take the November and February contests online.
Individual HMMT rounds are 50 minutes and consist of 10 questions, while team rounds are 60 minutes, allow teamwork, and also have 10 problems. It is very common for top scorers on national and international mathematics olympiads to attend the HMMT competitions, making it a highly competitive tournament.
The highest scoring individuals and teams from the various different question rounds offered at the HMMT are awarded prizes, though they are not cash prizes. The HMMT is a highly prestigious, student-organized mathematics competition that offers a competitive but also team-building environment where students can challenge themselves with the difficult problems offered in the competition.
TrigStar
Where: Various local chapter competitions at different locations before national tournament.
When: July
Who: High schoolers
Cash Prize: Yes
TrigStar is a competition sponsored by the National Society of Professional Surveyors that is intended to assess students’ proficiency in the field of trigonometry and its practical applications. Considering its sponsors, the competition is also meant to raise awareness of the surveying profession among high school students that are mathematically gifted.
There are two levels of the TrigStar competition. The first level is local, where each local high school has a winner. From these winners, an individual winner is selected from each state, and these state winners proceed to the second level, which is the national level. Participants at the national level get to compete for the national TrigStar title. First-place winners receive $2,000, second-place $1,000, and third $500. In addition, anyone who has participated in a TrigStar competition can apply for a special $5,000 scholarship.
Caribou Math Contests
Where: Online
When: Various competitions throughout the year, check this schedule for dates
Who: High schoolers
Cash Prize: Yes
The Caribou Math Contests, or Caribou Cup, is the largest global online math competition, and it is held 6 times a year. There are 7 contest levels and they are hosted for grades 9/10 and grades 11/12. Students that compete in all 6 contests can compete for the Caribou Cup. Each contest consists of 50 minutes of puzzles, interactive questions, and problem solving activities all concerning math.
The highest scoring students get cash prizes depending on their performances in the contests. The first place student gets $100 dollars times their percentage score, second gets $75 times their percentage, and etc. Cash prizes will be doled out to the students for as long as funds in the age group last.
Stanford Math Tournament
Where: Stanford University Campus
When: Likely April
Who: High school students that form 8-person teams
Cash Prize: N/A
The Stanford Math Tournament is an annual tournament run entirely by Stanford students for high schoolers. The aim of the tournament is to give students an opportunity to work on fun but difficult problems and meet peers who are similarly interested in mathematics. Students can take specific subject tests and/or general exams: the subject exams last 50 minutes with 10 short answer questions, and the general exams last 110 minutes with 25 questions.
The Stanford Math Tournament is a great way to get familiar with college and interact with intelligent high schoolers and college students that are assisting with the competition. Keep in mind, however, that Stanford is not the only college that hosts student-led math competitions. Some great other ones to check out are Princeton University Math Competition, Berkeley Math Tournament, Caltech Harvey Mudd Math Competition, and so many more!
Math Prize for Girls
Where: Massachusetts Institute of Technology (MIT) campus
When: Fall (around October)
Who: Students 11th grade and below who identify as female
Cash Prize: Yes
Math Prize for Girls is an annual math competition hosted by MIT for girls that consists of 20 challenging problems that test mathematical prowess and creativity for which you have 2 and a half hours to solve. Again, the test covers high school mathematics concepts, but excludes calculus. Students must apply online if they are interested, and a key requirement is that participants should have participated in the AMC 10 or 12.
Math Prize for Girls is a great opportunity for female high school students to push themselves in a mathematical capacity and also meet many students like themselves with whom they can interact and learn.
Conclusion
In conclusion, there are so many math competitions available nationally and internationally at all different times of the year, testing students on all different varieties of topics and testing their knowledge in so many creative ways. Some tests allow students to experience the opportunity to work with a team to work towards mathematical solutions, and some allow students to learn how to handle math contests individually. For those looking for a benefit, preferably in the form of awards or prizes, there are so many competitions that offer substantial prizes to top competitors, providing sufficient incentive to participants. There are so many ways that math competitions can help high school students to further their mathematics experience in high school, and I highly recommend that any high schooler that values their mathematics experience at least try their hand at a mathematics competition, possibly one of the ones listed in this post.
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