Do you love a good challenge that combines problem-solving with scientific knowledge?

If so, then mathematics competitions might be the perfect way for you to dive deeper into your passion and showcase your talent!

Some of these competitions also have significant prizes and recognition for those who succeed.

American Mathematics Competition (AMC) The American Mathematics Competition (AMC) is a series of exams designed to challenge and engage middle and high school students in the United States and Canada.

This is probably the most prestigious mathematics competition because it can lead to participation in the International Mathematical Olympiad (IMO).

Note that this is a challenging process involving a series of exams including the American Invitational Mathematics Examination (AIME) and the United States of America Mathematical Olympiad (USAMO).

The AMC Exams: There are three AMC exams offered at increasing difficulty levels: AMC 8: Designed for middle school students (grade 8 or below) AMC 10: Designed for high school students (grades 9 and 10) AMC 12: Designed for high school students (grades 11 and 12) Exam Format: Each AMC exam is a 25-question multiple-choice format with a 75-minute time limit.

Calculators are not allowed on the AMC 10 or 12 exams, placing emphasis on mental math and problem-solving strategies.

Exam Content: The AMC exams cover a variety of topics typically included in middle or high school math curriculums, depending on the exam level.

Here are some general areas: Algebra Geometry Combinatorics (counting problems) Number theory Probability Preparing for the AMC: The Mathematical Association of America (MAA), which administers the AMC, provides past exams and resources on their website: MAA AMC exams: https://maa-amc. org/students/study-space/ Reviewing past exams can familiarize you with the question format and level of difficulty.

Many math textbooks and online resources offer practice problems specifically designed for the AMC.

Joining a math club or finding a study partner can provide a collaborative learning environment to discuss problems and approaches.

Harvard/MIT Mathematics Tournament What is the HMMT?

It's a biannual (twice a year) team-based mathematics competition held in February and November at either Harvard University or MIT in Cambridge, Massachusetts.

It's known for attracting some of the brightest high school math students from around the world.

Why Participate?

It's an amazing opportunity to test your problem-solving skills and mathematical knowledge in a collaborative setting.

You'll get to compete with other talented students and experience the excitement of a high-level math competition.

Scoring well can open doors to scholarship opportunities and recognition in the mathematics community.

The HMMT Format: The HMMT consists of several rounds that test different aspects of mathematical ability: Individual Round: Tests individual skills in Algebra, Geometry, and Combinatorics.

Team Round: Challenges teams to work together on a problem-solving task.

Guts Round: A fast-paced round with short answer questions on a variety of math topics.

Eligibility: The HMMT is open to high school students around the world.

You can participate as part of a team with your school or form a team with other students.

Preparing for the HMMT: There are practice tests available at their website: Look for past problems (if available) to get a feel for the competition style.

Many math textbooks and online resources offer practice problems in these areas.

Purple Comet Math Meet The Purple Comet Math Meet is a fun and challenging competition designed to test your problem-solving skills and teamwork.

Here's your guide to participating: What is the Purple Comet Math Meet?

It's a free, online, international team math competition held annually.

Teams of 1 to 6 students work together to solve challenging math problems.

It's a great way to explore mathematics beyond the classroom and have fun with your peers.

Who Can Participate?

The competition is open to middle and high school students worldwide.

You can form a team with classmates or friends who share your love of math!

What to Expect: The competition offers various difficulty levels, so there's a challenge for everyone.

Teams are given a set of problems to solve within a specific timeframe.

Working together, you'll need to apply your math knowledge, critical thinking, and communication skills.

How to Prepare: There are practice tests available at their website Focus on areas typically covered in middle or high school math, like: Algebra Geometry Problem-solving strategies Many math textbooks and online resources offer practice problems in these areas.

Additional Tips: Communication and teamwork are key!

Discuss problem-solving approaches and delegate tasks effectively within your team.

Math Majors Tournament of America (MMATHS) What is MMATHS?

It's a team-based mathematics competition held annually across various colleges and universities in the United States.

Teams of students work together to solve challenging math problems in a fun and engaging environment.

Why Participate?

It's a fantastic opportunity to test your problem-solving skills and mathematical knowledge in a collaborative setting.

You'll get to compete with other talented students and experience the thrill of a math competition, in-person.

Scoring well can open doors to recognition in the mathematics community.

The MMATHS Format: The format may vary slightly depending on the host university, but it typically involves: Individual Round: Students work on a set of math problems individually Team Round: Teams work together on challenging math problems Tiebreaker Round: Special round for teams when there is a tie in the scoring.

Eligibility: MMATHS is open to high school students in the United States.

You can participate as part of a team with your school or form a team with students from other schools (check with your school's math department for details).

Preparing for MMATHS: Look at past problems to get a feel for the competition style Many math textbooks and online resources offer practice problems in these areas.

Princeton University Mathematics Competition (PUMaC) What is PUMaC?

It's a high school mathematics competition held annually by Princeton University students.

There are two divisions: Division A: Designed for experienced students who participate in math competitions Division B: Designed for newcomers to math competitions Why Participate?

It's a great way to challenge yourself and explore new areas of mathematics, with some of the most difficult questions available in a no-invite competition.

You'll get to compete with other math enthusiasts, in an in-person setting.

The PUMaC Format: Both divisions have a multiple-choice format with a time limit.

Calculators are not allowed, so focus on your mental math and problem-solving strategies.

Specific details like question count and time limit may vary slightly year to year.

Eligibility: PUMaC is open to high school students worldwide.

You participate as a team with your school.

Preparing for PUMaC: There are practice tests available on their website and you should also find resources to improve your skills in relevant areas: Use the practice tests from other competitions in this guide Consider forming a study group or club with other mathematically-inclined classmates, as you will need to find team members to participate.

USA Mathematical Talent Search (USAMTS) What is the USAMTS?

It's an online math competition open to middle and high school students in the United States.

Participants are given challenging problems to solve over a designated period spanning multiple weeks.

Why Participate?

It's a fantastic opportunity to test your problem-solving skills and mathematical knowledge in a unique format.

You'll get to explore new areas of mathematics beyond the typical curriculum.

You can qualify for the AIME through this, in lieu of the AMC.

The USAMTS Format: The USAMTS consists of three rounds with increasing difficulty levels.

Each round involves solving challenging math problems without a time limit, at home.

You can use any resources like textbooks or online references (with citation) Calculators and computers are permitted, so long as all work is your own.

Answer explanations and clear communication of your thought process are crucial for successful submissions.

Eligibility: The USAMTS is open to middle and high school students who are U.

S. citizens or residents.

Preparing for the USAMTS: There are past problems available at their website, but preparation is a little bit different than for a traditional timed exam, since you will have a lot of time to solve the questions.

Conclusions If you read this far, you are definitely interested in pursuing more STEM competitions throughout your high school career.

I would recommend that you learn about other options through Rishab’s Ultimate STEM Student Guide, which is available to anyone completely for free.

It has 50+ competitions for you to consider.

About Eashan Iyer: I am a founding member of The Qurios Institute (the company that runs this blog) and an incoming student at Brown University.

In 2023, I co-authored a research paper in the field of theoretical physics.

I am also an Eagle Scout and a senior at The Academy for Mathematics, Science, and Engineering in Rockaway, NJ.

Learn more about me at my website and LinkedIn.