Polygence blog / Research Opportunities and Ideas

The 20 Best Math Competitions for High School Students

13 minute read

Math contests are a great way to build your problem-solving muscles, engage in some healthy competition, build your mathematical knowledge, enhance your college applications, and perhaps win cash, an incredible scholarship, or a magic hat. They are also a great way to build resilience, make some math-loving friends, and get inspired by experts. You don’t have to win 1st place to have a great time and get a lot out of the experience.

Want to hone your higher math skills with expert advice on a mathematics-focused project? Learn more about Polygence’s high school research project program and our team of exceptional research mentors.

What are the Best Math Contests, Meets, and Challenges for Teens?

Most of these math competitions and tournaments are group efforts, organized with team, individual, relay, and other themed rounds. Some are individual only and one is strictly virtual. Some are higher stakes (e.g., the International Mathematical Olympiad) and others let you tap into your goofier, more creative side (looking at you Mu Alpha Theta Mathematical Minutes Video Contest). To address the gender disparity in the field of mathematics, we’ve listed two contests (InteGIRLS and Math Prize for Girls) specifically for female and female-identifying teens.

As entry requirements and specific deadlines may change year to year, be sure to refer to the specific contest websites for those that interest you.

These 20 math competitions for high schoolers are sorted in alphabetical order.

1. American Mathematics Competition (AMC 10, AMC 12)

Hosting institution: Mathematical Association of America

Awards: Pins and ribbons, entry into larger competitions

Entry deadline: Early October

Competition date: Early November

Dating back to the 1950s, the AMC is now one of the most prestigious international math competitions. Both AMC 10 and AMC 12 are 75-minute competitions of 25 multiple-choice questions. The AMC page on MMA’s website offers a zip-code-based test location finder. AMC 10 covers the high school math curriculum up to the tenth grade. AMC 12 covers all of high school math. The competitions cover a wide range of topics (e.g., algebra, geometry, number theory) and are the qualifying tests for the Math Olympiad (and also for the Math Prize for Girls listed in this post). Scoring highly (top 2.5% for AMC 10 or top 5% for AMC 12) qualifies you for the American Invitational Mathematics Examination (AIME). Based on your AMC and AIME scores, you can then be eligible for the USA Mathematical Olympiad, and ultimately the equivalent of the Olympics for math: the International Mathematical Olympiad. You can purchase AMC preparation materials online.

2. American Regions Mathematics League (ARML)

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

Awards: A wide array of trophies and cash prizes change annually

Entry deadlines: Early May

Competition date: Friday and Saturday following Memorial Day

This is a prestigious international mathematics competition for high school students at 4 different hosting institutions in the United States. Teams made up of up to 15 students (typically from the same geographic region such as a state or district) compete against other teams on a range of math topics. There are 5 rounds: team, power, individual, relay, and tiebreaker. The competition is sponsored by many companies that provide internship and fellowship opportunities. You can see past contest questions on the ARML website, as well as instructions on how to form a team and raise funds to attend the event.

3. Caltech Harvey Mudd Math Competition (CHMMC)

Hosting institutions: Caltech

Awards: Medals, plaques, trophies, and one magic hat

Entry deadlines: Early December

Competition date: Mid-January

Heads up, California students: this math competition for high school is organized by the students at Caltech and Harvey Mudd College for teams of 2-6 students. It consists of various rounds, including team, power, and tiebreaker. The event also features an esteemed guest speaker. Get more information, including the math competition problems from prior years, on the CHMMC website.

4. Caribou Math Contests

Hosting institution: Caribou (online)

Awards: Cash prizes

Entry deadline: N/A, sign up to compete

Competition date: Contest schedules of bimonthly challenges are released in September.

This is strictly a virtual, no-stress, fun online math competition (you probably won’t be adding it to your college application), but it has great problems and has grown to incorporate students from 34 different countries. It covers a very wide range of math topics including Calcrostic puzzles, chess, math history, logic problems, and other interactive math games. 

5. Duke Math Meet (DMM)

Hosting institution: Duke University

Awards: Undisclosed

Entry deadline: Mid-October

Competition date: Early November

Duke University hosts 45 high school teams (made up of 6 students each) from around the country. Registration happens on a first come, first served basis - so register early. The event is made up of a Power Round, Team Round, Individual Round, Relay Round, and Devil Round (a fun final round meant simply to decompress).

6. Harvard/MIT Mathematics Tournament (HMMT)

Hosting institutions: Harvard University and Massachusetts Institute of Technology (MIT)

Awards: Undisclosed

Entry deadlines: varies by year; the registration window is typically three weeks in September and October

Competition date: Early November at Harvard and early February at MIT

This naturally very prestigious math competition attracts nearly 1,000 high school students globally. Teams are selected via a lottery system. Hosted at both Harvard and MIT in different months, each of the two competitions focuses on different areas. The Harvard tournament is more generally focused, with a short answer round, smaller teams, and less difficulty. The MIT version has a higher difficulty rating, involves writing proofs, and focuses on algebra, geometry, and combinatorics. HMMT also offers an unofficial online tournament.

You can check out past tests on HMMT’s site to help prepare for the event. While you’re there, see if you can solve the HMMT problem of the week.

7. InteGIRLS Math Competitions

Hosting institution: InteGIRLS

Awards: Cash prizes

Entry deadline: Depends on the local chapter

Competition date: Winter and spring, dates depend on location

Led by teens, InteGIRLS chapters throughout the country host winter and spring math competitions for middle and high school girls and non-binary students comfortable being grouped with girls. Most of these math competitions are virtual, although some may take place in person. You can register alone or with a group of up to 4 people. Get more details, including past InteGRALS math competition problems, on the non-profit’s site.

8. MathCON

Hosting institution: MathCON

Awards: Undisclosed

Entry deadline: Early March

Competition date: Between Mid-January and Early March; Finals are in Mid-May

MathCON is an online competition run in 2 rounds. If you score in the top 628 students, you qualify for the MathCON Finals Competition. That final competition will be held in person in Chicago. Starting in September, weekly practice tests in algebra, combinatorics, geometry, and number theory are released on the MathCon site to help you prepare for the competition. These weekly practice tests run until May 31st. The competition is available to students in grades 4 through 12. Talk to your teacher if you’re interested in participating in MathCon, because you must register for the competition through your school. Homeschooled students are also eligible to compete.

9. Math League High School Contest

Hosting institution: Math League

Awards: Medals

Entry deadline: varies; local qualifying rounds take place between October and March

Competition date: April (State Championship), May (Nationals), and July (International)

This competition is run through participating high schools and follows a tiered science-fair style run through local, state, national, and international championships. In order to qualify for subsequent tournaments, you need to earn certain percentages of the total points available or place among the top individuals. But the place to start is at the local level. If you’re interested, you can check to see if your school is already a Math League member. If not, encourage it to join for no cost. Get a free contest problem set (i.e., sneak peek questions) by signing up for Math League’s mailing list; you can also buy problem sets from prior contests in Math League’s virtual store.

10. Math Majors of America Tournament for High Schools (MMATHS) and Girls in Math (GiM)

Hosting institutions: Yale University (but changes annually)

Awards: Undisclosed

Entry deadline: Generally a month before the event

Competition dates: October (MMATHS) and February (GiM)

MMATHS follows a tournament structure with various rounds, starting with an Individual Round, followed by a Team Round, a Tiebreaker Round, and a Lightning Finals. Algebra, geometry, number theory, and combinatorics will be covered. No math beyond precalculus will be tested. You can come join with your own team of 6 or contest organizers will group you with other students for the team round if you do not have a full team.

Girls in Math is a one-day math competition that follows a similar format as MMATHS. This event takes place at Yale University in February and there is an option to join via Zoom. Refer to the MMATHS site’s GiM page for more information, including prior competition questions.

11. Math Prize for Girls

Hosting institution: Massachusetts Institute of Technology (MIT)

Awards: $100,000 in cash prizes, with 1st prize being $50,000

Entry deadline: Late May

Competition date: Early October

This annual competition held at MIT is for high school students who are female in gender identity and are juniors or below. Also, you must have taken an official administration of the AMC 10 or 12 exam. Students are selected on the basis of their official AMC scores. The top 300 applicants are admitted. Past Math Prize for Girls problems and solutions are available for review on the event’s site.

12. MathWorks Math Modeling (M3) Challenge

Hosting institution: Society for Industrial and Applied Mathematics (SIAM)

Awards: Scholarships totaling $100,000

Entry deadline: Late February

Competition date: March

If you’re mostly interested in how math can be applied to the real world, this completely virtual math competition should interest you. The M3 Challenge is unique in that it focuses on the real-world applications of mathematics. Open to high school juniors and seniors in the US and sixth-form students in England and Wales, the contest invites teams of 3-5 students and one teacher/coach to submit solution papers for the year’s math modeling problem. Past scenarios include volcanic eruption fallout; budgeting time and money; the cost of connectivity; and affordable, delicious, and nutritious lunches.

13. Mu Alpha Theta Mathematical Minutes Video Contest

Hosting institution: Mu Alpha Theta

Awards: $3,000 divided among the finalists

Entry deadline: Late February

Competition date: Late March (the first round of online judging)

Where else can you write a catchy song about the fundamental theorem of calculus and win a cash award? The winning videos of this Mu Alpha Theta contest are always amusing and educational. The only eligibility requirement for this contest is that your high school student team be made up of active members of Mu Alpha Theta, the national math honor society. Videos should teach a math lesson in a creative way and be 2-5 minutes long. They are submitted on YouTube. Here’s a good list of dos and don’ts to create a winning video entry.

14. Pi Math Contest – Gauss (PiMC)

Hosting institution: AlphaStar Academy

Awards: Trophies

Entry deadline: Mid-February (for in-person); Mid-March (for online)

Competition date: Early March (in-person); Mid-March (online)

The topics in this math competition include algebra, geometry, and number theory. It consists of 25 multiple-choice questions, and you have 75 minutes to complete the test. PiMC Gauss is for high school grades; Euler and Fermat are for elementary and middle schoolers. Check out the PiMC sample archive for past problems and solutions.

View the Pi Math contest website for more detailed registration information.

15. Purple Comet Math Meet

Hosting institution: AwesomeMath

Awards: Certificates

Entry deadline:

Competition date: Mid to Late April

Location: Virtual

This is a purely virtual contest in which you compete as a team with an adult supervisor. Each team has 90 minutes to solve as many of the 30 problems as they can. It’s cool to see all the different teams from all 67 countries, and some of the team names are pretty hilarious. You can review Purple Comet problems and solutions from previous years online. Purple Comet is a fun, low-stress competition and a great way to prepare yourself for higher-stakes contests.

16. SIMIODE Challenge Using Differential Equations Modeling (SCUDEM)

Hosting institution: QUBES

Awards: Recognition

Entry deadline: Late October

Competition date: Late October to Mid-November

This competition challenges you to use math to solve real-life problems. Teams of 3 high school students with one coach are asked to use differential equations and create a MATLAB model to solve one challenge in either physics/engineering, chemistry/life, or social sciences/humanities. You and your team will have one week to build and defend a model and then prepare a 10-minute video for judging.

You can view more information on SIMIODE’s YouTube channel.

17. Stanford Math Tournament (SMT, SMT Online, and SMT Asynchronous)

Hosting institution: Stanford University

Awards: Undisclosed

Entry deadline: Mid-March (in-person), Late March (online), Mid-April (asynchronous)

Competition date: Mid-April (in-person)

Run by Stanford students, the in-person tournament invites up to 25 teams of 5 to 6 high school students through a mixed merit-based lottery system. There’s a Power Round, Team Round, Individual Round, Guts Round, and Opening and Award Ceremonies. Refer to the SMT website to find out how to register for the in-person competition as well as alternate online and asynchronous versions - the latter of which allows you to compete with a team of up to 8 students during a week-long window in April.

18. Tests of Engineering Aptitude, Mathematics, and Science (TEAMS)

Hosting institution: Technology Student Association

Awards: Certificates and trophies

Entry deadline: Late January

Competition date: Specific dates vary by state, but all are held in February and March

This unique competition has a wide variety of solution formats, including building and testing prototypes, answering multiple-choice questions, and writing an essay response to a themed engineering prompt. TEAMS is a US-based competition that invites teams of 2-4 high school students to compete in either the 9th/10th-grade or 11th/12th-grade levels. There are 3 distinct components to the contest: design/build; multiple choice; and essay. The questions are themed around real-life engineering problems. State teams who score among the top 20% are eligible to compete at the National TEAMS competition, which takes place for a week in late June.

19. Trig-Star

Hosting institution: National Society of Professional Surveyors (NSPS)

Awards: $500-$2000

Entry deadline: Early June

Competition date: Exact dates vary according to local chapters, but the national winners are announced in early July

Love trigonometry? This particular high school math competition is entirely dedicated to trigonometry and its use in the real world. To enter, you take the preliminary test at a participating high school. Local winners then move on to a state-level competition, and state winners move on to the national exam. To find a test site in your area, you can check out this list of Trig-Star area coordinators. Contest participants are also eligible for a $5,000 Trig-Star Scholarship. You can download sample tests for free on Trig-Star’s site

20. USA Mathematical Talent Search (USAMTS)

Hosting institution: The Art of Problem Solving Initiative, Inc.

Awards: Books and software

Entry deadline: Register ASAP to be emailed the problems at the start of Round 1

Competition date: 3 month-long rounds (1 in mid-September-mid-October, 2 in November, 3 in mid-December-mid-January)

Sometimes the deepest knowledge and thought need time. This is a good competition for those who love math but also don’t want the pressure of solving problems on the spot. USAMTS is a free mathematics competition that gives you the luxury of a full month to work out your solutions. There are three rounds of problems. Each round is a month-long and asks you to solve 5 problems. You can mail or upload your solutions. The aim of this competition is primarily about competing with yourself and it works on an honor system.

Your work will be graded by mathematicians and returned with comments, which are as valuable (if not more so) than any trophy. Participants must be U.S. high school students; this is not an international competition. Scoring well on this test also qualifies you to take the American Invitational Mathematics Examination (AIME), which is the second qualifier on your way to the USA Mathematical Olympiad Team.

How To Find More Math Competitions Specific to Your State?

The best way to get really good at math competitions is to take part in as many as you possibly can. You can get lots of additional information about the variety of student math competitions available to U.S. residents with this national high school mathematics competitions wiki.

How Should You Choose the Right Math Competition for You?

Choosing the right math competition can be as crucial as participating in one. It's essential to find a competition that aligns with your interests, skill level, and goals. Here's how to make the right choice:

  • Understand Your Goals: Determine what you want to achieve through math competitions. Is it to enhance your problem-solving skills, compete at the highest level, or improve your college applications? Knowing your objectives will guide your selection.

  • Assess Your Skill Level: Be realistic about your mathematical abilities. Some competitions are highly competitive and cater to advanced math enthusiasts, while others are more inclusive for a broader range of participants. Pick a competition that matches your proficiency.

  • Explore Various Formats: Math competitions come in various formats, including individual and team-based, on-site and virtual, and different rounds like multiple-choice, proof-writing, or modeling. Consider which format excites you and plays to your strengths.

  • Check Eligibility: Review eligibility criteria such as age, grade level, and prior qualification exams. Some competitions have specific requirements that you must meet to participate.

  • Research Past Questions: To get a sense of the competition's difficulty and style, look for past questions or sample problems. Solving these can help you gauge if the competition aligns with your interests and abilities.

  • Consider Location: Some competitions require physical attendance, while others are entirely virtual. Think about your availability and willingness to travel if needed.

  • Consult with Mentors: If you have mentors, teachers, or advisors who are experienced in math competitions, seek their guidance. They can provide valuable insights into which competitions align with your goals.

Research and Prepare for your Competition or Fair

Polygence pairs you with an expert mentor in your area of passion. Together, you work to create a high quality research project that is uniquely your own. Our highly-specialized mentors can help guide you to feel even more prepared for an upcoming fair or competion. We also offer options to explore multiple topics, or to showcase your final product!

Can Math Competitions Help Your College Applications?

Participating in math competitions offers several benefits for your college applications:

  • Demonstrated Passion: Engaging in math competitions showcases your genuine interest and passion for mathematics. Admissions committees appreciate applicants who are dedicated to their chosen field.

  • Strong Academic Record: Success in math competitions can strengthen your academic profile. It demonstrates your ability to excel in a challenging subject, which can be especially valuable for STEM-related majors.

  • Problem-Solving Skills: Math competitions sharpen your problem-solving skills, a quality highly sought after by colleges and employers alike.

  • Differentiation: Math competitions set you apart from other applicants. They show that you are willing to go the extra mile to pursue your interests and challenge yourself.

  • Networking: Participating in competitions connects you with like-minded peers and experts in the field. These connections can be valuable for mentorship and recommendation letters.

  • Scholarship Opportunities: Some math competitions offer cash prizes and scholarships. Winning or performing well can help you fund your college education.

  • College Essay Material: Your experiences in math competitions can serve as compelling material for college application essays. They provide anecdotes that demonstrate your growth and determination.

By carefully selecting math competitions that align with your goals and leveraging the advantages they offer, you can enhance your college applications and embark on a fulfilling mathematical journey.

Your Project Your Schedule - Your Admissions Edge!

Register to get paired with one of our expert mentors and to get started on exploring your passions today! And give yourself the edge you need to move forward!