Math competitions can be one of the most rewarding experiences a high school student can pursue. Beyond the college admissions boost, they push students to think in genuinely new ways, build real mathematical intuition, and connect with a community of peers who love problem-solving just as much as they do.

But with so many competitions out there — each with different formats, difficulty levels, and purposes — it can be hard to know where to start.

In this guide, we’ll walk you through the most important US math competitions for high school students: what they are, how they’re structured, and what it takes to qualify for each level.

This is Part 1 of our US Math Competition series, focusing on the flagship AMC pathway and several accessible competitions worth knowing about. Part 2 will cover additional competitions for middle and high school students.

The AMC Pathway: From AMC 10/12 to the International Stage

The most prestigious math competition pathway in the United States follows a clear progression: AMC → AIME → USAJMO/USAMO → MOP → IMO. Let’s walk through each step.

Competition	Who Can Enter	Format	Next Level
AMC 10	Grade 10 or below	25 questions, 75 min	AIME (top ~2.5%)
AMC 12	Grade 12 or below	25 questions, 75 min	AIME (top ~5%)
AIME	AMC qualifiers only	15 questions, 3 hrs	USAJMO / USAMO
USAJMO	AMC 10 + AIME top scores	6 questions, 2 days	MOP
USAMO	AMC 12 + AIME top scores	6 questions, 2 days	MOP / IMO Team

AMC 10 — Open to All, Grades 10 and Below

The AMC 10 (American Mathematics Competition 10) is the entry point of the flagship competition pathway. Any student in 10th grade or below can register — no invitation required.

The exam consists of 25 multiple-choice questions to be completed in 75 minutes. Questions start relatively straightforward and become significantly more challenging toward the end. The math involved stays within 10th-grade curriculum, but the hardest problems require creative thinking well beyond what’s typically taught in class.

Scoring: 6 points for each correct answer, 1.5 points for each blank, and 0 points for incorrect answers. The maximum score is 150.

AIME Qualification: Approximately the top 2.5% of AMC 10 participants earn an invitation to the AIME. For 2024–2025, the cutoff scores were 94.5 (AMC 10A) and 105 (AMC 10B).

When: The AMC 10 is now held in November each year (a change from the previous February schedule, effective 2024). Two versions — AMC 10A and 10B — are offered on different dates, and students may take one or both.

AMC 12 — Open to All, Grades 12 and Below

The AMC 12 follows the same format as the AMC 10 — 25 questions in 75 minutes — but draws from a broader range of topics including precalculus and more advanced algebra. Students in any grade through 12th grade can participate.

AIME Qualification: Approximately the top 5% of AMC 12 participants qualify for the AIME. For 2024–2025, cutoffs were 76.5 (AMC 12A) and 88.5 (AMC 12B).

A student can take both the AMC 10 and AMC 12 (or the A and B versions), but can only use one score to qualify for AIME.

AIME — Invitation Only

The American Invitational Mathematics Examination (AIME) is the next step for top AMC scorers. Unlike the AMC, which uses multiple choice, the AIME consists of 15 short-answer questions where answers are integers from 000 to 999. Students have 3 hours.

The AIME is significantly harder than the AMC — many participants finish with a score in the single digits. There are two versions each year (AIME I and AIME II), offered on different dates for flexibility. Students can only take one.

When: AIME I and II are typically held in February, following the November AMC exams.

USAJMO & USAMO — The Olympiad Level

After the AIME, the very top scorers (combining AMC + AIME scores) are invited to the USA Mathematical Olympiad (USAMO) or USA Junior Mathematical Olympiad (USAJMO).

• For students who qualified through AMC 10 + AIME. Think of this as the olympiad track for younger students.USAJMO:
• For students who qualified through AMC 12 + AIME. This is the top tier of US high school math competition.USAMO:

Both exams span two days, with 3 problems each day. Unlike the AMC or AIME, these are proof-based problems that require full written mathematical arguments. They’re extraordinarily challenging and a remarkable achievement to qualify for.

MOP & IMO — The Ultimate Goal

Top performers at USAJMO and USAMO are invited to the Mathematical Olympiad Program (MOP), a summer training camp where the US IMO team is selected.

The International Mathematical Olympiad (IMO) is the world’s most prestigious math competition for high school students. The US sends a team of 6 students to represent the country at the IMO each year.

To participate in USAJMO, USAMO, MOP, and IMO, students must be US citizens or permanent residents.

Other Competitions Worth Knowing About

Not every student is aiming for the IMO — and that’s completely fine. There are excellent competitions at every level, including some that are a great entry point for students newer to math competitions.

Math League — Open to All, K–12

Math League is a school-based competition program designed for students from elementary through high school. The goal is to develop mathematical thinking and problem-solving skills in an accessible, fun environment.

Students compete at the school, regional, state, and national levels. Top performers can advance to national and even international competitions.

How to register: Students typically register through their school. If your school doesn’t have a team, you can often find a local group or register independently. Check the Math League website or contact the coordinator in your region directly.

Schedule: Contests generally run from October through spring, with an international event in summer.

Caribou Contests — Open to All, Grades 9–12

Caribou Contests are a well-regarded international competition with a mission to inspire a love of mathematics. Students in grades 9–12 can participate individually or as a team.

The competition is accessible and encourages mathematical curiosity at all levels — not just for students already at the top of their class.

Math Kangaroo — Open to All, K–12

Math Kangaroo is one of the most widely recognized math competitions globally, available to students from kindergarten through 12th grade. The problems are designed to be engaging and thought-provoking — challenging without being intimidating.

It’s an excellent starting point for students who are curious about math competitions but haven’t competed before. The “Beginner” level is particularly accessible.

How to participate: Students must take the exam at an officially registered Math Kangaroo center. You can find nearby testing locations on the official Math Kangaroo website.

Why Math Competitions Matter

Beyond the trophies and certificates, math competitions develop something more valuable: the ability to think through hard problems with patience, creativity, and persistence.

Students who participate in math competitions regularly — even if they don’t reach the top levels — tend to develop stronger analytical skills, greater confidence in math, and a problem-solving mindset that serves them well in college and beyond.

And for students applying to competitive colleges, demonstrated achievement in math competitions is a genuine differentiator.

Ready to get started? The best time to begin is now. Even if your student has never competed before, starting with Math Kangaroo or Math League and working toward the AMC is a completely achievable path.

Stay tuned for Part 2, where we’ll cover more competitions for middle and high school students. And if you have questions about preparing for math competitions, we’re always happy to help.

— The ICM Math and Science Team