15 Math Competitions for High School Students
If you enjoy solving math problems and want to go beyond your school syllabus, math competitions are worth trying. These contests allow you to apply concepts from algebra, geometry, combinatorics, and number theory in ways you won't see in class. Such experiences can strengthen your CV and show a clear interest in the subject when you apply for colleges, research programs, or internships. Preparing for these contests will also help you stay consistent and improve your problem-solving speed. You can also use competition prep as a starting point for independent projects or research to include in your SOP later.
If you want to check out other competitions for high schoolers, check out art competitions here and for writing-based competitions, find a list here!
Why should I participate in a math competition in high school?
Participating in math competitions while you’re in high school allows you to learn to think through problems. Such contests can train you to approach questions from different angles and break them down into smaller, manageable steps. Scores and rankings will help you track your progress over time. You’ll also develop skills such as logical reasoning, writing clear solutions, and time management during tests. Even if you don't win, participating shows effort and curiosity, both of which matter when you’re building your academic profile.
Here are 15 math competitions for high school students worth checking out.
Key takeaways
This list rounds up 15 math competitions for high schoolers spanning online team contests, university-hosted tournaments, and national olympiad-style exams, with standout hosts including Harvard, MIT, Princeton, and Stanford.
Entry is free for many of these, including a couple of the most prestigious invite-only exams and several online contests, while a handful of university-hosted tournaments charge a modest per-student or per-team fee, and prize money ranges from a few hundred dollars up to a $250,000 scholarship for one video-based competition.
A couple of these are invite-only based on strong scores from earlier competitions, so it's worth building up through those first if Olympiad-level competitions are your goal, and one prize competition is specifically for girls and requires an official AMC score to qualify.
Most of these are open nationally or even internationally, with only a handful of university-hosted tournaments requiring in-person travel to a specific campus.
A few of the earliest registration windows open as early as May and June for a couple of the fall competitions, with several more opening through August and September, so it's worth planning ahead if you're eyeing one of the university-hosted tournaments.
1. Purple Comet! Math Meet!
Location: Virtual
Cost: Free
Acceptance rate/cohort size: Last year, over 12,000 students participated across more than 4,000 teams from 80 countries | This year, 4,804 teams registered from 86 countries
Dates: April 14 – 23
Registration Deadline: Registration remains open until the end of the contest
Eligibility: Middle and high school students | Non-competitive teams are open to anyone, and competitive teams are limited to students who have not graduated from high school and are under 20 at the time of the competition
The Purple Comet Math Meet is a free, international online team competition for middle and high school students focused on solving math problems. You can take part individually or as part of a team of up to six and work together during a ten-day contest window. You can choose a start time that fits your schedule. Once the timer begins, you can submit answers until the time runs out. The middle school level includes 20 problems in 60 minutes, while the high school level has 30 problems in 90 minutes, with difficulty ranging from easy to very challenging. Teams are grouped as large school, small school, mixed, or non-competitive, and an adult supervisor is required to register and start the contest. Competitive teams can earn certificates and rankings, and others receive recognition for participation.
2. Princeton University Math Competition (PUMaC)
Location: Princeton University in Princeton, NJ (Main Competition); the Power-round Only Competition can be completed online
Cost: $12.50 per student, totaling $100 per team or $12.50 for individual participants (Main Competition) | $5 per student, totaling $40 per team (Power-round Only Competition)
Acceptance rate/cohort size: PUMaC accepts about 70 teams each year for its on-site competition
Dates: November 21 (Main Competition) | November 13 – 20 (Power-round Only Competition)
Registration Deadline: September 9 – October 7; rolling admissions
Eligibility: High school students who are less than 20 years old
The Princeton University Math Competition (PUMaC) offers two options: the Main Competition, held on campus, and the Power-round Only Competition, in which teams complete only the proof-based Power Round, released about a week in advance and to be submitted by a set deadline. You’ll join a team of eight students from the same school or region, with an adult present, and take part in several math rounds. You’ll complete two 60-minute individual tests chosen from algebra, geometry, combinatorics, or number theory, each with eight problems. You’ll also work on a 30-minute team test with collaboration allowed and a longer, proof-based Power Round that requires creative thinking. Top scorers advance to a 90-minute proof-based individual final. Rankings for top teams and individuals are announced, and awards include trophies, medals, and cash certificates.
3. MAA American Mathematics Competitions (AMC)
Location: Multiple locations
Cost: $55–$115 registration fee, depending on the registration date
Acceptance rate/cohort size: No fixed cohort size; over 300,000 students participate in the AMC each year
Dates: November 5 (AMC 10 A and AMC 12 A) | November 13 (AMC 10 B and AMC 12 B) | January 21 – 27 (AMC 8)
Registration Deadline: AMC 10 and AMC 12: September 30 (early bird deadline) | October 15 (regular deadline) | October 28 (late deadline); AMC 8: October 28 (early bird deadline) | January 5 (regular deadline) | January 14 (late deadline)
Eligibility: Students in grade 8 or below and under 15.5 take the AMC 8, those in grade 10 or below and under 17.5 take the AMC 10, and students in grade 12 or below and under 19.5 take the AMC 12; Participants must be enrolled full-time at an accredited school or be homeschooled in the U.S. or Canada; Students and parents don’t register directly with the MAA, so you can check with your school, local colleges, universities, math circles, or learning centers to see if they are hosting the AMC
The AMC is a math competition for middle and high school students, with different levels based on grade and age. You can take the AMC 8 if you are in grade 8 or below, where you solve 25 questions in 40 minutes covering geometry, counting and probability, estimation, proportions, spatial reasoning, and interpreting graphs and tables. The AMC 10 is for students in grade 10 or below, with 25 multiple-choice questions in 75 minutes covering algebra, geometry, area and volume, number theory, and probability. The AMC 12 is also 25 questions in 75 minutes for students in grade 12 or below, covering trigonometry, advanced algebra, and geometry. The AMC 10 and 12 have A and B versions, and you can either try both or let competition managers choose dates. Students who perform well may be invited to additional competitions held in February and March.
4. USA Mathematical Talent Search (USAMTS)
Location: Virtual
Cost: Free
Acceptance rate/cohort size: Approximately 926 students participated in last year’s competition
Dates: The USAMTS runs from October to January with three rounds | Participants have one month to submit solutions for each round online, with deadlines on October 7 (Round 1), December 1 (Round 2), and January 5 (Round 3)
Registration Deadline: Students can register at any time during the year, even after the first round has been completed
Eligibility: U.S. middle and high school students
The USA Mathematical Talent Search is a free proof-based math contest for US middle and high school students. You’ll solve challenging problems and get written feedback on your work. You’ll take part in three rounds every year, and each round gives you at least a month to complete five problems made up of one puzzle and four proof-based questions with different difficulty levels. You must submit your solutions as a single PDF file. Graders will review your work, assign scores, and provide personalized feedback to help improve your math and writing skills. You can also use limited reference material while working. At the end of the year, about the top 45% of participants receive prizes such as math books, T-shirts, and sometimes Wolfram software subscriptions, with up to 500 winners total. Gold, silver, bronze, and honorable mention levels determine the number of books awarded, and scoring 68 or higher out of 75 can qualify you for the AIME, with further paths to USAJMO and USAMO.
5. Harvard–MIT Mathematics Tournament (HMMT)
Location: Harvard University, Cambridge, MA (HMMT November) | Massachusetts Institute of Technology, Cambridge, MA (HMMT February)
Cost: $80 per team application | $10 per individual application
Acceptance rate/cohort size: About 1,000 students participate in the competition each year
Dates: November 7 (Harvard) | February 13 (MIT); students can participate in only one tournament in a season, either in November or February
Registration Deadline: August 2 – September 20
Eligibility: High school students worldwide, including homeschooled students under 21 who have not earned a diploma or equivalent, can apply, but they cannot represent more than one organization in a season and must compete with their school team if their school applies
The Harvard MIT Mathematics Tournament is a high-level math competition in which you compete in individual and team rounds that focus on creative problem-solving. You can join a school team of 4–6 students in November or 6–8 in February. All members must attend the same school or live within 150 miles of each other and have an official school affiliation. Both tournaments include individual tests, a team round, and a guts round, though their formats differ. The November event at Harvard is similar to AMC and AIME levels, and the February event at MIT is more difficult, with subject tests in algebra, geometry, and combinatorics, and often requires proof-based solutions. You can only compete in one tournament per season. Awards are given to the top 10 individuals overall, the top scorers on each test, the top 5 teams in the team and Guts rounds, and the top 10 teams overall as Sweepstakes winners.
6. Rocket City Math League
Location: Online
Cost: Free
Acceptance rate/cohort size: Over 4,500 students participate annually
Dates: November 13 – December 3 (Interschool Contest) | Individual Rounds are held in the spring: January 14 – 28 (Round 1) | February 11 – 25 (Round 2) | March 11 – 25 (Round 3)
Registration Deadline: December 9 for interschool results and March 31 for individual round scores
Eligibility: Middle and high school students
The Rocket City Math League is a free, international, student-run competition held over four rounds for middle and high school students. You’ll take part through your school, where tests are sent by email, completed on site, and scores are submitted online for global ranking. The contest includes spring individual rounds with three 30-minute tests of 10 questions each across levels from pre-algebra to calculus, as well as an interschool team test of 15 questions. A teacher or coach is required to register, supervise, and upload results. You’ll compete in only one level to be eligible for awards, with levels ranging from Explorer through Discovery. Trophies are mailed to top students and schools at the end of the year.
7. American Invitational Mathematics Exam (AIME)
Location: Multiple locations; students take the AIME at the same location where they completed the AMC 10 or AMC 12
Cost: Free
Acceptance rate/cohort size: No fixed cohort size; about 12,000–15,000 students qualify for the AIME each year
Dates: February 5 (AIME I) | February 11 (AIME II)
Registration Deadline: There’s no registration deadline because this is an invite-only competition; you can check the details here
Eligibility: This is an invite-only competition for high school students who score very highly on the AMC 10 or AMC 12; the qualifying thresholds can be checked here
The American Invitational Mathematics Examination is a challenging math contest for high school students who perform very well on the AMC 10 or AMC 12. You take a 3-hour exam with 15 problems, and each answer is an integer from 0 to 999. The questions are more difficult than those on the AMC and require greater problem-solving skills. There are two testing dates, AIME I and AIME II, but you can take the exam only once, and taking both leads to disqualification. Eligibility usually includes around the top 2.5 percent of AMC 10 scorers and the top 5 percent of AMC 12 scorers, though cutoffs can change each year. You will take the test at the same location as the AMC or at another approved site with a Change of Venue form. Scores are released on the AMC Platform within 24 hours, and high scorers may qualify for the USA Mathematical Olympiad (USAMO) or the Junior Mathematical Olympiad (USAJMO).
8. Stanford Math Tournament (SMT) @ Stanford
Location: Stanford University, Stanford, CA
Cost: $30 per student; financial aid is available upon request
Acceptance rate/cohort size: Around 800 U.S. high school students
Dates: April 17 – 18
Registration Deadline: December 3 – February 18
Eligibility: High school students living in the United States can apply for the in-person competition
The Stanford Math Tournament (SMT) is a high school math competition run by Stanford students with help from the Stanford Undergraduate Mathematics Organization and the math department. You can participate individually or on a school team of exactly five or six students, all from the same school or organization. If your school registers for the competition, you cannot compete as part of another group. Individual participants are matched with teams before the event, and each team must have an adult chaperone. The competition includes several math rounds. You'll take a General Test with 25 short-answer questions over 110 minutes, which counts for 60% of the Subject Tests. You'll also tackle a Team Round with 15 questions, a proof-based Power Round, and a live-scored Guts Round that gets harder as it goes. For the Subject Tests, you can choose from algebra, calculus, discrete math, or geometry, each lasting 50 minutes.
9. Regeneron Science Talent Search (STS)
Location: Virtual; the finals take place in Washington, D.C.
Cost: Free
Acceptance rate/cohort size: About 2,600 students participate in the competition each year
Dates: Students submit research by November 5, the top 300 scholars are announced on January 7, the top 40 finalists are announced on January 21, and Finals Week takes place from March 11 to 17
Registration Deadline: June 1 – November 5
Eligibility: Students in their final year of high school in the U.S. or its territories can apply regardless of citizenship | U.S. citizens living abroad may also be eligible
Regeneron STS is a science competition for high school seniors where they present original research in science, math, or engineering. You’ll complete an independent project, write a report with data and results, and submit it with project details. It includes a research paper up to 20 pages, recommendations, essays, transcripts, and optional test scores. You can use work from any high school year if the data is clearly collected and explained. All entrants receive small rewards; about 300 scholars earn $2,000 with matching funds for their schools, and 40 finalists compete in Washington, D.C. for awards up to $250,000. Mathematics is a key category, with many participants conducting advanced research in areas like mathematical modeling, algorithm development, and pure mathematics. Recent finalists have earned awards for projects involving algorithms and models used to study electron density.
10. ARML (American Regions Mathematics League)
Location: Multiple college and university campuses across the U.S.
Cost: $400 per team and $65–$75 per person, totaling $1,505 for a full team of 15 students and two coaches
Acceptance rate/cohort size: Over 128 teams from the United States, China, Canada, and South Korea are invited to compete in ARML | Last year, over 1,800 students participated in the competition
Dates: May 29 – 30 for the annual competition | ARML Local takes place from April 18 – 19
Registration Deadline: May 1 for the annual competition
Eligibility: Students in grade 12 or below, including middle school students, who are 18 or younger as of December 31 of the academic year
The American Regions Mathematics League is a high-level team competition that covers algebra, number theory, geometry, combinatorics, and probability, with challenging problems that may reward some calculus knowledge. You’ll compete on a team of 15 students from a defined, contiguous region, with two coaches. Teams are grouped into divisions based on regional performance. The contest includes four rounds. In the Individual Round, you’ll complete five sets of two questions for up to 10 points per person. The Team Round has 10 questions, each worth 5 points. The Power Round focuses on deeper problem-solving and is worth 50 points. The Relay Round rewards speed, with higher points for faster correct answers. Competitions are held at several U.S. universities on the same day, and top teams earn rankings and prizes such as books or software, as well as recognition at the awards ceremony.
11. USA Mathematical Olympiad and Junior Mathematical Olympiad (USAMO and USAJMO)
Location: Multiple locations
Cost: Free
Acceptance rate/cohort size: There are about 500–600 total participants in USAMO and USAJMO combined, with roughly 200–300 in each
Dates: March 20 – 21
Registration Deadline: There’s no registration deadline because this is an invite-only competition
Eligibility: This is an invite-only competition for high school students who score very highly on the AMC 10 or AMC 12 or perform well on the AIME | The selection indices can be checked here
The United States of America Mathematical Olympiad and the United States of America Junior Mathematical Olympiad are national-level, invite-only competitions and an important step in selecting the International Mathematical Olympiad team. You qualify based on strong AMC 10 or AMC 12 and AIME scores, with AMC 12 participants invited to USAMO and AMC 10 participants to USAJMO. You’ll take a two-day proof-based exam with six problems total, three each day, and 4.5 hours per session. They are held on two consecutive days at official sites across the US and Canada. Locations are assigned, but changes can be requested if needed. Awards include Gold for about 6% of participants, Silver for about 12%, and Bronze for about 18% in the USAMO. The USAJMO recognizes about 20% of entrants, with honorable mentions for strong scores.
12. Math Majors of America Tournament for High Schools
Location: Multiple college and university campuses across the U.S.
Cost: The registration fee is $15 per student if paid before the contest date through GiveButter or by check, and $20 if paid on site
Acceptance rate/cohort size: No fixed cohort size; maximum 6 students per team
Dates: November 15 (tentative)
Registration Deadline: Registrations typically close about one month before the competition date
Eligibility: High school students and some advanced middle school students
The Math Majors of America Tournament for High Schools is a fall math competition held at various US campuses, with all sites running it on the same day. It covers topics in algebra, number theory, geometry, and combinatorics. You’ll compete as part of a 6-person team, and members can come from different schools or be assigned if needed. The contest includes four rounds: an Individual Round with 12 problems in 75 minutes, a Team Round with 12 problems in 45 minutes, a Tiebreaker Round for top-tied individuals with 2–3 problems in 10 minutes, and a 27-question Guts Round split into timed sets. Individual scoring awards 1 point per problem, with tiebreaks based on difficulty, then on performance and speed. Team scores combine individual results plus 6 points per team problem, with adjustments for smaller teams. Awards are based on overall performance across rounds.
13. Breakthrough Junior Challenge
Location: Online
Cost: Free
Acceptance rate/cohort size: Typically, 2,300–2,500+ students participate each year
Dates: September 17 to 30 (Peer-to-Peer Review) | October 1 – 3 (Administrative Review) | October 4 – 25 (Evaluation Panel Review) | October 26 – November 18 (Finalist Verification) | November 24 – December 9 (Popular Vote Challenge). Finalists, Popular Vote winners, and Regional Champions are announced on December 10
Registration Deadline: May 11 – September 15
Eligibility: Students aged 13–18 can apply, including homeschooled students, students with disabilities, and students from around the world
The Breakthrough Junior Challenge is an annual competition for students aged 13–18, in which they create a short, original video of up to 2 minutes that explains a concept in physics, mathematics, or life sciences. You can pick a challenging math idea like a theory, concept, or formula, and present it clearly and creatively by using demonstrations, animations, or documentary-style explanations. The challenge focuses on communicating complex mathematics rather than solving problems. Judges evaluate how engaging, creative, clear, and challenging the explanation is. After submitting a YouTube link, you’ll take part in peer review by evaluating other entries. This is followed by judging, finalist verification, and a popular vote phase. Results are usually announced in December. The winner receives a $250,000 scholarship, a $50,000 prize for a teacher, and $100,000 for a science lab.
14. Trig-Star
Location: Held annually at participating local high schools across the U.S. | State winners compete remotely, and the overall winner is awarded at the National Society of Professional Surveyors spring meeting, in the Washington, D.C. area
Cost: Free
Acceptance rate/cohort size: No fixed cohort size; students participate individually
Dates: State winners must be submitted to NSPS by May 1 to enter the national competition | National testing takes place between May 1 and 31, and results must be submitted to NSPS by June 1 to qualify for the National Trig-Star and Teaching Excellence Awards
Registration Deadline: May 1 for the National competition
Eligibility: High school students who win local or school-level contests can participate in the state level and potentially the national competition
Trig-Star is a math competition sponsored by the National Society of Professional Surveyors that recognizes high school students and their teachers for strong performance in trigonometry and highlights real-world uses of math in surveying and engineering. You’ll solve timed trigonometry problems on circle formulas, the Law of Sines and Cosines, right triangles, and angle measurements in degrees, minutes, and seconds. The contest runs at two levels: local school competitions, where winners move forward, and state competitions, where winners are chosen based on individual performance. Those state winners can move on to the national competition to compete for the Trig-Star title. At the national level, top students and their teachers receive awards, including $4,000 for first place, $2,000 for second, and $1,000 for third, with teachers earning $1,250, $750, and $500, respectively.
15. Advantage Testing Foundation/Jane Street Math Prize for Girls
Location: Massachusetts Institute of Technology, Cambridge, MA
Cost: Free
Acceptance rate/cohort size: Around 250 girls
Dates: October 10 – 11
Registration Deadline: May 31
Eligibility: Female students in grade 11 or below as of March 1 who are U.S. or Canadian citizens or permanent residents, or who live in the United States or Canada, and who have taken an official AMC 10 or AMC 12 exam in November of the competition cycle
The Advantage Testing Foundation and Jane Street Math Prize for Girls is the largest math prize for girls in the world, held each fall at MIT. You’ll take a 2.5-hour exam with 20 challenging numerical problems based on high school math, with no calculus, designed to test creative problem solving. Eligibility requires taking an official AMC exam in November of the previous year, and selection is based on AMC and other scores, with about the top 300 applicants invited and cutoff scores usually just above AIME level. You’ll compete for a total of $100,000 in prizes, including $50,000 for first, $20,000 for second, $10,000 for third, $4,000 for fourth and fifth, $2,000 for sixth through tenth, plus a $2,000 youth prize for the top 9th grader or below. About 25 others receive honorable mentions with possible $500 MathCamp scholarships, and the top 35 performers may be invited to a proof-based Olympiad.
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Questions students often ask about these competitions
1. Do I need to already be advanced in math to enter these competitions?
No, several of these are designed for a wide range of skill levels and welcome students newer to competition math. The most advanced, invite-only competitions do require strong prior scores, but there's a clear on-ramp through the more accessible contests first.
2. A couple of these competitions are invite-only. How do I qualify for those?
You typically need to score well on an earlier qualifying exam, like the AMC, to receive an invitation to the more advanced competitions. Building up through the accessible, open-entry contests first is the most common path there.
3. Can I compete individually, or do I need to join a team first?
It varies by competition. Several allow individual participation, while others require a school or regional team to register. Check the format details for each one before assuming you need a team lined up in advance.