Math Competitions for High School Students
Math competitions are the rare opportunity where preparation is fully in your control. There's no essay, no interview, and no recommendation letter — you register, you practice, and your score is your score. That makes them one of the fairest ways for a strong math student to build a record.
They also differ enormously in commitment. Some are single sittings you can enter with a few weeks of practice; others are multi-round contests where the first round is usually taken at your own school, which means you may need a teacher willing to proctor it.
A practical note: many of these have registration windows that close months before the contest date, and school-based rounds often have an earlier internal deadline. If a competition looks interesting, check the deadline now rather than in the spring.
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USA Mathematical Talent Search
Free, proof-based math contest you complete from home over several weeks, with detailed written feedback on every solution you submit.
AMC 10/12
The nation's largest high school math competition, and the first step toward AIME, USAMO, and the IMO team. Register through your school's math department.
Regeneron Science Talent Search
The nation's oldest and most prestigious science research competition for seniors, judging original independent research. Top awards exceed $250,000.
F=ma Exam & USA Physics Olympiad
Take the F=ma exam at your school in February; top scorers advance to USAPhO and possibly the U.S. Physics Team camp. Your school registers, not you, and there's a school plus per-student fee.
USA Astronomy & Astrophysics Olympiad
Three-round astronomy competition starting with a proctored first round in February and a national round in April. Registration is $30 per student, discounted for groups, with financial aid available.
USA/North America AI Olympiad
Multi-round AI competition with a February first round of non-coding and Colab coding tasks, an invitational second round, and a June camp that selects Team USA. Exams are proctored at your school or a test site.
Davidson Fellows
Scholarship competition awarding $25,000 to $100,000 to students 18 or younger for a significant, original piece of work in science, technology, math, literature, music, or philosophy. No fee to apply.
MathWorks Math Modeling Challenge
Teams of three to five get a single 14-hour window to build and write up a mathematical model of a real-world problem, competing for over $100,000 in scholarships. Free, but a teacher must register the team.
PhysicsBowl
A 40-question, 45-minute multiple-choice physics exam given at participating schools each spring, split into first-year and second-year divisions and scored individually and by team. Enter through a teacher.
Regeneron International Science and Engineering Fair
The world's largest pre-college science fair. You qualify by winning at an affiliated regional or state fair, not by applying directly.
High School Terminal
Free, virtual, round-robin team coding competition where students build algorithms for finance and data-driven problems, with cash prizes and Citadel recruiting exposure.
Breakthrough Junior Challenge
Submit an original two-minute video explaining a concept in physics, life sciences, or math, competing for a $250,000 college scholarship. Finalists also peer-review at least five other entries.
American Regions Mathematics League
Team mathematics competition where regional teams of fifteen compete across individual, relay, and team rounds. Students join through a regional or school team rather than registering alone.
American Rocketry Challenge
The world's largest student rocket contest: teams of three to twenty-five design, build, and launch a model rocket meeting a specific altitude and flight-time target for a chance to compete nationally.
Berkeley Math Tournament
Student-run math tournament at UC Berkeley with individual and team rounds, including a novice division for students newer to competition mathematics.
eCYBERMISSION
Free virtual STEM competition for teams in grades 6–9. Teams identify a problem in their own community, work through the scientific or engineering method, and compete for state, regional and national awards.
Harvard-MIT Mathematics Tournament
Two competitions a year — one at Harvard in November and one at MIT in February — with individual and team rounds across algebra, geometry, and combinatorics.
National Economics Challenge
Team economics competition testing students on economic reasoning, current events, microeconomics, macroeconomics, and international economics.
National Science Bowl
Fast-paced buzzer competition covering math and all sciences, run by the U.S. Department of Energy from regional events through a national finals in Washington, D.C. Teams register through their school.
picoCTF
Free cybersecurity capture-the-flag competition and year-round practice platform built by Carnegie Mellon for middle and high school students, covering cryptography, forensics, and web exploitation.
Princeton University Mathematics Competition (PUMaC)
Student-run math contest at Princeton. Teams come from high schools or well-defined regions.
Purple Comet! Math Meet
Free online team mathematics contest held each spring, with a high school division and problems designed for collaboration. An adult coach registers the team.
Stanford Math Tournament
Student-run math competition on the Stanford campus with individual, team, and relay rounds, plus a novice division and practice problems published online.
The Stock Market Game
Ten-week online investing simulation where teams manage a virtual portfolio and compete against other schools. Participants learn research, diversification, and risk through a teacher-registered session.
Wharton High School Data Science Competition
Free sports analytics contest from Wharton. You use real data to answer a sports question.