High School Math Competitions: A Comprehensive Guide

Math competitions serve as a fantastic extracurricular activity for high school students, providing a platform to hone problem-solving abilities, boost self-confidence, and enhance communication skills. These competitions offer students the opportunity to challenge themselves beyond the classroom, preparing them for future academic and professional endeavors. This article provides a detailed overview of various math competitions available for high school students, helping them decide which ones align with their interests and goals.

Why Participate in Math Competitions?

Participating in high school math competitions can significantly benefit students in several ways:

College Applications: Math competitions look great on high school resumes and college applications, especially for students applying to selective colleges and universities. Demonstrating excellence in math through competitions showcases a student's dedication and talent.
Standardized Test Success: Math competitions provide practice in solving problems under time and resource constraints, helping students develop the ability to think clearly under pressure - a valuable skill for standardized tests like the SAT and ACT.
Scholarship Opportunities: Many math competitions offer cash prizes to winning participants, providing financial assistance for college.
Skill Development: Preparing for math competitions enhances problem-solving abilities, critical thinking skills, and mathematical knowledge.
Networking: Math competitions provide opportunities to meet other students who share a passion for mathematics, fostering a sense of community and collaboration.

Types of Math Competitions

The landscape of math competitions is diverse, offering something for every kind of math student. Here's a breakdown of some popular types:

American Mathematics Competitions (AMC)

Founded in 1950, the American Mathematics Competitions (AMC) are preeminent math competitions for students in grades K-12. The AMC program is a national effort to strengthen the mathematical capabilities of the next generation.

AMC 8: A 25-question, 40-minute competition designed for students in grade 8 and below. The competition focuses on middle school mathematics topics, including counting and probability, estimation, proportional reasoning, elementary geometry (including the Pythagorean Theorem), spatial visualization, and interpreting graphs and tables. Some of the later questions may touch on beginning algebra topics, such as linear or quadratic functions and coordinate geometry.
AMC 10: A 25-question, 75-minute multiple-choice competition designed for students in grades 10 and below. The content covers mathematical topics such as elementary algebra, basic geometry, area and volume formulas, elementary number theory, and elementary probability. The AMC 10 offers two versions of the test, the 'A' and 'B' competitions.
AMC 12: A 25-question, 75-minute multiple-choice competition designed for students in grades 12 and below. It covers the full high school mathematics curriculum, including trigonometry, advanced algebra, and advanced geometry. The AMC 12 offers two versions of the test, the 'A' and 'B' competitions.

The AMC 10 and AMC 12 are the first exams in a series of math exams that progress from the local, to the national, to the international level. Taking the AMC 10/12 is a crucial step toward eligibility for other math competitions and scholarships. High achievement in the AMC can lead to the American Invitational Mathematics Examination (AIME).

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American Invitational Mathematics Examination (AIME)

The American Invitational Mathematics Examination (AIME) is an intermediate examination between the AMC 10 or AMC 12 and the USA Mathematical Olympiad. Students are selected for the AIME based on their scores in the AMC 10 (top 2.5% of students) or AMC12 (top 5% of students). The AIME is a 15 question, 3-hour examination, with each answer being an integer number between 0 to 999. The questions on the AIME are much more difficult than those on the AMC 10 and AMC 12 competitions.

American Regions Mathematics League (ARML)

The American Regions Mathematics League (ARML) is a highly competitive, international high school mathematics competition. Teams can have up to 15 members, and students from all over the world may compete. The ARML covers a wide range of topics such as algebra, geometry, number theory, combinatorics, probability, and inequalities. The focus is to check speed and accuracy in mathematical problem-solving. Members will answer questions in teams and individually.

Harvard/MIT Mathematics Tournament (HMMT)

The Harvard/MIT Mathematics Tournament (HMMT) is one of the largest and most prestigious high school competitions in the world. High school students around the world can compete individually or in teams of 4-6. Each tournament draws close to 1,000 students from around the globe, including top scorers at national and international olympiads. There are two competitions each year (November and the following February) and the competitions are significantly different from one another.

Stanford Math Tournament (SMT)

The Stanford Math Tournament (SMT) is an annual, student-run math competition for high school students. Students can form 8-member teams. SMT aims to encourage interest in math by providing students an opportunity to work on fun and challenging problems and to meet other students interested in math. Students can choose subject tests (up to 2) and general tests. The Subject Tests are 50-minute exams with 10 short answer questions. The subjects covered are algebra, combinatorics, number theory and geometry. The General Tests are 110-minute exams with 25 short answer questions and designed for a wider pool of students who may not have subject-level mastery but would like a more well-rounded question paper.

Caribou Math Contests

The Caribou Mathematics Competition or Caribou Cup is the largest online math contest that is conducted globally and is held six times over the school year. High school students can participate in levels for grades 9/10 and 11/12. If you like to have fun with math then gear up to solve some incredible logic-oriented questions and puzzles. This contest is not based purely on concepts or memorizing formulas but instead on flexible thinking, creativity, logic, and common sense, applicable in the real world.

Math League High School Contest

The Math League sponsors a number of high school contests that are held throughout the school year. This is a high school program that consists of a series of contests held throughout the school year, culminating in a National/International Championship. Top-scoring students in qualifying rounds are invited to compete in their State Championship contest (or their National Championship, for schools outside the US), held in April. Winners of each State Championship are invited to compete in the US National High School Championship in May. Winners of each non-US National Championship are invited to compete in the International Championship in May. Problems draw from a wide range of high school topics: geometry, algebra, trigonometry, logarithms, series, sequences, exponents, roots, integers, real numbers, combinations, probability, coordinate geometry, and more. No knowledge of calculus is required to solve any of these problems. The questions from this contest are known to be great for SAT prep!

Math Majors of America Tournament for High Schools (MMATHS)

High school students can participate in MMATHS individually or in teams of up to 6 (from the same or different high schools). The individual round is a 12-question, 75-minute test. All of the questions are weighted equally and have only numerical answers. In the mathathon round, teams work together to solve small packets of questions. Upon submitting final answers to one packet, the team can move to the next one. The point values for each question increase, and so does the difficulty. The team will have 75 minutes to get through as many packets as it can.

Purple Comet Math Meet

The Purple Comet Math Meet is an international math competition with a dedicated track for high school students. High school students across the world can compete as individuals or in teams. The competition has 30 problems that need to be solved in 90 minutes! The questions range from very easy to extremely difficult, but students can pick a convenient start time within a 10-day competition window and participate! This competition is known for its flexibility in having competitive and non-competitive teams. Students competing on a competitive team must qualify by satisfying age, grade, and school criteria. Non-competitive teams have no age, grade, or school restrictions.

Mu Alpha Theta Mathematical Minutes Video Contest

The Mu Alpha Theta Mathematical Minutes Video Contest combines a solid understanding of math with creativity. High school students who are members of Mu Alpha Theta can participate. Students select a math topic and create a fun, informative, 2-5-minute video that would be relevant for other high school students. The videos are submitted on YouTube and judged on quality of information and video.

Other Notable Competitions

Math Kangaroo: A math contest with many puzzles and logic style problems.
Pi Math Contest (PiMC): Organized by AlphaStar Academy, this contest is for students in 3rd-12th grades and is offered online annually as a single-round individual contest.
Annual Mathematics Competition: An annual, student-run online math competition and event for high school and advanced middle school students.
United Kingdom Mathematics Trust (UKMT) Challenges: A set of challenges for students in England and Wales.
Berkeley Math Tournament (BMT): Organized by the Berkeley Math Tournament Group at the University of California-Berkeley.
Princeton University Mathematics Competition (PUMaC): An annual competition run by the Princeton University Math Club.
USA Mathematical Talent Search (USAMTS): A competition that allows students a full month or more to work out their solutions.
Bay Area Mathematical Olympiad (BAMO): Consists of two exams, one for students in 8th grade and under, and the other for students in 12th grade and under.
US Ersatz Math Olympiad (USEMO): A proof-based competition open to all US middle and high school students.
International Mathematical Olympiad (IMO): The pinnacle of all high school mathematics competitions.
MATHCOUNTS Competition Series: Has 4 levels of competition-school, chapter, state and national.
SIGMA: Provides students the opportunity to compete nationally as individuals, as teams, and as schools.

Colorado-Specific Competitions

For students in Colorado, there are several state-level math competitions to consider:

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The Annual Secondary School State Mathematics Contest: Sponsored by the University of Northern Colorado since 1992, this contest is for students in grades 7-12. The contest consists of two rounds: a 90-minute First Round, done remotely, and a three-hour Final Round at UNC.
The Soifer Mathematical Olympiad: Founded in 1984 by Dr. Alexander Soifer at the University of Colorado Colorado Springs (UCCS), this is for Colorado students in grades 5-12. Participants may use calculators but not the internet. Students are asked to solve five problems in four hours, presenting their results in essay-type solutions.
Colorado State University Math Day: Held annually at CSU in Fort Collins, this event includes a lecture, a quiz-bowl-style tournament involving three-member teams, student math projects, and other activities.
CSU-Pueblo Math Day: Includes both the Swanson and Math Bowl competitions on the CSU-Pueblo campus. The Swanson Competition is a rigorous exam, and the Math Bowl Competition is a fast-paced, head-to-head contest between two 3-person teams.
Colorado Mathematics League: One of several state math leagues supported administratively by The Math League. Six monthly high school contests are given nationwide.
Colorado MATHCOUNTS: Schools register with MATHCOUNTS to receive coaching and testing materials and begin in September preparing for regional competition that is held in February. Top teams are invited to the state competition in March.
AreteLabs Competition: Hosts a competition each fall for students in 3rd through 12th grade.
Colorado Math Awards: Recognizes outstanding performance in national and international mathematics competitions and contests by Colorado middle school, high school, and college students.

Tips for Choosing the Right Competition

The best way to choose a math competition to participate in is to think about your goals and how they intersect with your day-to-day life. Consider the following factors:

Your Interests: Different math competitions focus on different areas of mathematics. Choose competitions that align with your strengths and interests.
Your Skill Level: Some competitions are highly competitive and require extensive preparation. Assess your current skill level and choose competitions that are challenging but not overwhelming.
Time Commitment: Consider the time commitment required for preparation and participation. Choose competitions that fit into your schedule.
Travel Requirements: Some competitions are international or national events and may require traveling. Consider your ability to travel before committing to a competition.
Competition Format: Some competitions are individual events, while others are team-based. Choose a format that you enjoy and that suits your strengths.

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