• Stephen Turban

10 Best Math Competitions for High School Students

Math competitions are a great way to gain recognition in high school and see how you stack up against your peers nationally. They can also look good on your college applications (whether you win or not)! In this article, we outline 10 of the most popular math competitions for students. Math competitions have been around for a while - so many of these are highly competitive competitions that require months of concerted prep.

If competitions aren’t your thing, then another valuable experience is to deep-dive into a challenging and innovative research project you can call your own - Lumiere had 2100 students apply this past year and over 100 students do math-based research projects with us!

10 Best Math Competitions for High School Students

  1. American Mathematics Competition (AMC): 10/12

Location: Virtual

Eligibility: AMC 10: Must be in grade 10 or below and under 17.5 years of age on the day of the contest. AMC 12: must be in grade 12 or below and under 19.5 years of age on the day of the contest.

Prize: Certificates and award pins.

Registration: To be announced for 2023. Please check here for updates.

Competition dates: November 2023 (Tentatively, based on previous year’s schedule).

AMC is one of the largest and most prestigious math competitions globally. Each year, over 300,000 students compete in AMC. Scoring in the 120 range (out of 150) is considered to be a high achievement and it allows for you to enter into the USA Mathematical Olympiad. The competition locations are available here.

Pro tip: AMC 10/12 is the first in a series of competitions that eventually lead all the way to the International Mathematical Olympiad. The invitational competitions include the American Invitational Mathematics Examination which is an intermediate examination between the AMC 10 or AMC 12 and the USA Mathematical Olympiad. Other competitions / awards which are open to AMC participants are the Math Prize for Girls. It can be super helpful to map out which competitions are right for you in terms of the structure and how they are spread through the year!

2. The American Regions Mathematics League

Location: University of Iowa, Penn State, University of Nevada at Las Vegas, and the University of Alabama in Huntsville.

Eligibility: Students from all over the world may compete. Teams can have up to 15 members. Cannot have turned 19 before the December 31 immediately preceding the ARML Competition. If a student turns 19 between January 1 and the competition dates, they would be eligible as long as they have not graduated high school (K-12) prior to March 1 of the year of the competition.

Prize: Gift cards are given to top teams and individual performers (around $2,000 collectively to the top 20 performers)

Registration: To be announced for 2023, but likely to close by May 1, 2023. Please check here for updates.

Competition dates: June 2023 (Tentatively, based on previous year's schedule).

The ARML is a highly competitive, international high school mathematics competition which covers a wide range of topics such as algebra, geometry, number theory, combinatorics, probability, and inequalities. The focus is to check speed and accuracy in mathematical problem-solving. Members will answer questions in teams and individually.

For the 2022 competition, 120 teams and over 1800 students participated from the United States, Canada, China, Taiwan, Hong Kong, South Korea, Thailand, Iran, and Colombia. Please visit here for practice questions.

Pro tip: Keep an eye out for competition sponsors (for instance, you’ll notice that D.E. Shaw is fairly prominent across many math competitions). Participating and winning competitions attract excellent internship and work opportunities since employers are impressed to see credentials from competitions they like (hence, they sponsor them)!

3. Harvard/MIT Mathematics Tournament (HMMT)

Location: 1 Tournament at Harvard and 1 tournament at MIT. Each student may only compete in any one tournament each season.

Eligibility: High school students around the world can compete individually or in teams of 4-6.

Prize: Prizes are awarded to the ten highest-scoring individuals overall, the top ten scorers on each of the individual tests, the five highest-scoring teams on the Team Round, and the five highest-scoring teams on the Guts Round. The top ten teams overall are named the Sweepstakes winners.

Registration: To be announced for 2023-24.

There is an $80 registration fee for a team and a $10 registration fee for an unaffiliated individual.

Competition dates: November 2023 and February 2024 (Tentatively, based on previous year’s schedule)

HMMT is one of the largest and most prestigious high school competitions in the world, often attracting winners from other math competitions! Each tournament draws close to 1,000 students from around the globe, including top scorers at national and international olympiads.

Pro tip: There are two competitions each year (November and the following February) and the competitions are significantly different from one another - be sure to pick wisely! Here are the test formats. Also, be sure to check out the 2022 problem, solution and results here.

4. TrigStar

Location: Varies since there are local chapters before the national round.

Eligibility: High students in the U.S.

Prize: Cash prizes between $500 to $2,000 are awarded to the top 3 performers.

Registration: To be announced for 2023.

Competition dates: July 2023 (tentatively, based on previous year’s schedule)

The purpose of this competition is to test and recognize excellence in trigonometry and its practical applications. Since this competition is sponsored by the National Society of Professional Surveyors, an important objective of the competition is also to grow awareness of surveying as a profession among mathematically skilled high school students. The competition has local chapters and then a national-level competition among top performers from the local chapters.

If competitions which test deep knowledge of specific topics / skills interest you, then be sure to check out the MathWorks Math Modelling Challenge or SIMIODE SCUDEM which is based on differential equations modeling.

Pro tip: Application-oriented competitions can be a great experience because the topics being tested are less, which allows you to deep-dive during prep! These types of competitions are also great for you if you are more interested in real-world application of mathematics (as opposed to just theory).

5. Stanford Math Tournament

Location: Stanford University campus

Eligibility: High school students in the U.S. can form 8-member teams. There may be an additional restriction on students being from Bay area high schools (changes year to year)

Prize: Not known.

To be announced. To be up to date, please join their Registration: To be announced. To be up to date, please join their mailing list. mailing list.To be announced. To be up to date, please join their mailing list.

Competition dates: Already passed for 2022 (April). For 2023, it is likely to be April (based on previous year’s schedule)

The Stanford Math Tournament (SMT) is an annual, student-run math competition for high school students. SMT aims to encourage interest in math by providing students an opportunity to work on fun and challenging problems and to meet other students interested in math.

Students can choose subject tests (up to 2) and general tests. The Subject Tests are 50-minute exams with 10 short answer questions. The subjects covered are algebra, combinatorics, number theory and geometry. The General Tess are 110-minute exams with 25 short answer questions and designed for a wider pool of students who may not have subject-level mastery but would like a more well-rounded question paper. To view past competition questions and results, please visit here.

Pro tip: Other universities have student-run math competitions which you should be sure to check out! These are not only incredible opportunities to compete, but also get a feel for ‘college fit’ and for networking! Berkeley Math Tournament, Caltech Harvey Mudd Math Competition, Princeton University Math Competition, Carnegie Mellon Informatics and Mathematics Competition, Duke Math Meet.

6. Caribou Math Contests

Location: Virtual

Eligibility: High school students for the levels 9/10 and 11/12.

Prize: Certificates and cash prizes.

Registration: Register here.

Competition dates: Since there are multiple competitions through the year, please check the schedule to find a convenient date.

The Caribou Mathematics Competition or Caribou Cup is the largest online math contest that is conducted globally and is held six times over the school year, typically over 2 days in October, November, January, February, April, and May. Each contest is run at the 7 contest levels and there are levels for grades 9/10 and 11/12.

Pro tip: If you like to have fun with math then gear up to solve some incredible logic-oriented questions and puzzles. This contest is not based purely on concepts or memorizing formulas but instead on flexible thinking, creativity, logic, and common sense, applicable in the real world.

7. Math League High School Contest

Location: Virtual

Eligibility: In addition to being in high school, there may be different requirements for local, state and national chapters. Please visit here for more information. Students from other countries are welcome to apply.

Prize: Not known

Registration: Rolling, please visit here for dates.

Competition dates: May 2023 (Tentatively, based on previous year's schedule)

This is a high school program that consists of a series of contests held throughout the school year, culminating in a National/International Championship.

Top-scoring students in qualifying rounds are invited to compete in their State Championship contest (or their National Championship, for schools outside the US), held in April. Winners of each State Championship are invited to compete in the US National High School Championship in May. Winners of each non-US National Championship are invited to compete in the International Championship in May. Problems draw from a wide range of high school topics: geometry, algebra, trigonometry, logarithms, series, sequences, exponents, roots, integers, real numbers, combinations, probability, coordinate geometry, and more. No knowledge of calculus is required to solve any of these problems.

There are several rounds with different structures, details of which are available here. Please see the free practice problems that are available here.

Pro tip: The questions from this contest are known to be great for SAT prep!

8. Math Majors of America Tournament for High Schools (MMATHS)

Location: Changes yearly. In 2022, the tournaments were held in Yale University, the University of Texas at Dallas, and Coralville Public Library (University of Iowa)

Eligibility: High school students can participate individually or in teams of up to 6 (from the same or different high schools).

Prize: Not known

Registration: To be announced for 2023. Please keep checking here for updates or sign up for the mailing list.

Competition dates: April or October 2023 (Tentatively, based on previous year’s schedule)

The MMATHS aims to assess problem-solving abilities in areas such as algebra, geometry, probability, and combinatorics. The individual round is a 12-question, 75-minute test. All of the questions are weighted equally and have only numerical answers. In the mathathon round, teams work together to solve small packets of questions. Upon submitting final answers to one packet, the team can move to the next one. The point values for each question increase, and so does the difficulty. The team will have 75 minutes to get through as many packets as it can. For the mixer round, teams are randomly formed.

9. Purple Comet Math Meet

Location: Virtual

Eligibility: High school students across the world can compete as individuals or in teams.

Prize: Certificates

Registration: To begin on February 1, 2023. Please look out here for registration-related updates.

Competition dates: April 18, 2023, to April 27, 2023.

This is an international math competition with a dedicated track for high school students. The competition has 30 problems that need to be solved in 90 minutes! The questions range from very easy to extremely difficult, but students can pick a convenient start time within a 10-day competition window and participate!

This competition is known for its flexibility in having competitive and non-competitive teams. Students competing on a competitive team must qualify by satisfying age, grade, and school criteria. Competitive teams are eligible for award certificates, and winning teams have their team name and results posted on the contest website. Non-competitive teams have no age, grade, or school restrictions. Members of non-competitive teams only receive certificates of participation, and their team results are never posted on the contest website.

In 2022, over 12,000 students competed on over 3998 teams from 62 countries. Here are the problems from the previous competitions.

Pro tip: If you feel overwhelmed by the idea of jumping into something super competitive right away, try checking out flexible competitions such as this one and assessing yourself. These are great skill and confidence boosting competitions!

10. Mu Alpha Theta Mathematical Minutes Video Contest

Location: Virtual

Eligibility: High school students who are members of Mu Alpha Theta.

Prize: $3,000 award will be split up among these eight finalists

Registration: To be announced for 2023 (Tentatively, January 2023 to February 2023)

Competition dates: April 2023 (Tentatively, based on previous year’s schedule)

This competition combines a solid understanding of math with creativity. Students select a math topic and create a fun, informative, 2–5-minute video that would be relevant for other high school students. The videos are submitted on YouTube and judged on quality of information and video.

An excellent complement to competitions – Lumiere Research Scholar Program

Competitions go hand-in-hand with great research skills and projects. Great research skills often groom you to problem-solve during competitions and they both add their own value to college applications because admissions officers love seeing academic focus with a competitive appetite!

If you are passionate about research and want to work on a stellar project of your own with mentorship from top PhDs in the world then you could also consider applying to the Lumiere Research Scholar Program, a selective online high school program for students that I founded with researchers at Harvard and Oxford. Last year, we had over 2100 students apply for 500 spots in the program! You can find the application form here.

Stephen is one of the founders of Lumiere and a Harvard College graduate. He founded Lumiere as a PhD student at Harvard Business School. Lumiere is a selective research program where students work 1-1 with a research mentor to develop an independent research paper.


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