Ultimate Guide to Math Competitions for School Students!

Math competitions are an exciting way to challenge yourself, sharpen your math skills, and even earn scholarships. They’re also a great addition to your college application, helping you stand out from the crowd.

If you’ve been thinking about joining a math competition but don’t know where to start, you’re in the right place. This guide covers the 4 best high school math competitions - American Mathematics Competitions (AMC), Math Kangaroo, Math Counts, and MOEMS.

So, let’s dive in!

📌 AMC (American Mathematics Competitions)

The American Mathematics Competitions (AMCs) are the first of a series of competitions in secondary school mathematics that determine the United States of America's team for the International Mathematical Olympiad (IMO).

Eligibility Criteria

1. AMC 8:

• Grades: Open to middle school students, typically grades 6 through 8.

• Age: Students should be in middle school.

• Regular Registration Deadline: Dec. 23, 2024 ($73 registration fee)

• Late Registration Deadline: Jan. 15, 2025 ($113 registration fee)

• Competition Dates: Jan. 22 - 28, 2025

2. AMC 10:

• Grades: students in grades 10 and below.

• Age: Students must be under 17.5 years old on the day of the competition.

• Registration Deadline: October 2025 (Exact date to be announced)

• Competition Date: November 2025 (Exact date to be announced)

3. AMC 12:

• Grades: Students in grades 12 and below.

• Age: Students must be under 19.5 years old on the day of the competition.

• Registration Deadline: October 2025 (Exact date to be announced)

• Competition Date: November 2025 (Exact date to be announced)

Structure of the AMC Exams

1. AMC 8:

• Format: 25 multiple-choice questions.

• Time: 40 minutes.

• Scoring: A correct answer is worth 1 point, with no negative marking for incorrect answers. The maximum score is 25.

2. AMC 10 and AMC 12:

• Format: 25 multiple-choice questions.

• Time: 75 minutes.

• Scoring: Each correct answer is of  6 points, an unanswered question is worth 1.5 points, incorrect answer is worth 0 points. The maximum score is 150.

Criteria for Selection and Advancement

The American Mathematics Competitions (AMC) serve as a critical foundation for students aiming to participate in prestigious mathematics olympiads at regional, national, and international levels. Here's how the AMC connects to these stages:

1. Regional-Level Qualifier

• The AMC 10 and AMC 12 are open to high school students across the U.S. and serve as the first step in identifying mathematically talented individuals.

• High performers on the AMC are invited to take the American Invitational Mathematics Examination (AIME), a more challenging competition.

2. National-Level Pathway

• Students who achieve high combined scores on the AMC and AIME qualify for the USA Mathematical Olympiad (USAMO) or the USA Junior Mathematical Olympiad (USAJMO), depending on their grade level.

• The USAMO is the highest national-level math competition in the U.S., focusing on advanced problem-solving and proof-writing skills.

3. International Representation

• Top performers from the USAMO are selected to attend the Mathematical Olympiad Program (MOP), an intensive training camp.

• The MOP helps prepare students to represent the U.S. in the International Mathematical Olympiad (IMO), the world’s most prestigious high school math competition.

Summary of Progression:

AMC → AIME → USAMO/USAJMO → MOP → IMO

This structured pathway ensures that students gradually develop the skills needed to compete at the highest levels of mathematical excellence.

📌 Math Kangaroo

The Math Kangaroo USA is a prestigious international mathematics competition that has been inspiring students for over 26 years. It offers a platform for elementary, middle, and high school students to earn awards, gain special recognitions, and connect with like-minded peers. Held annually on the third Thursday of March.

Math Kangaroo is particularly beneficial for younger students looking to strengthen their extracurricular profiles or gain early exposure to academic competitions. To support participants, Math Kangaroo provides a wealth of resources, including lesson plans and practice materials, ensuring students have the tools they need to succeed.

Winning Criteria

Participants are scored based on the number of correct answers, with higher-point questions rewarding greater problem-solving skills. Scores are ranked at the national and state levels, with students competing within their respective grade categories.

The top 20 national scorers in each grade level are recognized for their exceptional performance. These students receive exclusive prizes and accolades for their achievements.

Prizes and Recognition

1. Top Performers:

   • National winners often receive medals, trophies, and certificates.

   • Some top scorers are awarded scholarships or monetary prizes.

2. Participation Awards:

   • All participants receive a certificate of participation and a small gift, fostering a spirit of inclusion and encouragement.

Eligibility

Math Kangaroo is open to students from Grades 1 to 12, regardless of their proficiency in math. The only prerequisite is an interest in problem-solving and a desire to challenge oneself. Students are categorized into grade-based levels, ensuring fair competition among peers.

Registration for Math Kangaroo 2025 was opened on September 15th and close on December 31st, 2024

Late registration will be available from January 1st to February 1st, 2025, with an increased registration fee applied during this period.

Structure of the Exam

1. Duration:

   • 75 minutes to solve all problems.

2. Number of Questions:

   • 24 questions for Grades 1-4.

   • 30 questions for Grades 5-12.

3. Question Types:

   • Multiple-choice questions with five answer options.

4. Scoring System:

   • Questions are divided into three levels of difficulty:

     • Easy Questions: 3 points each.

     • Medium Questions: 4 points each.

     • Hard Questions: 5 points each.

   • Maximum score depends on the grade:

     • Grades 1-4: 96 points (24 questions).

     • Grades 5-12: 120 points (30 questions).

5. Penalty for Incorrect Answers:

   • No penalty for wrong answers; students are encouraged to attempt all questions.

Lets Unbound resources to learn for the Math Kangaroo exam:

📌 MATHCOUNTS

The MATHCOUNTS Competition Series is a prestigious math contest in the United States, designed to promote critical thinking and problem-solving skills among middle school students (grades 6–8). Launched in 1984, MATHCOUNTS has become a cornerstone program for students passionate about mathematics, offering a structured and competitive environment to showcase their talents.

Here’s the exam structure and criteria for students: 

Eligibility Criteria:

1. Grade Level: Mathcounts are typically open to students enrolled in grades 6-8 (middle school).

2. School Participation: Students participate through their school's MathCounts team. Schools must register with Math Counts to participate in the competitions.

3. Individual Registration: Individual students may be able to participate if their school does not have a team, though exceptions occur.

4. Citizenship: Students must be citizens or legal residents of the country where it's held.

Important Dates:

• Regular Registration Deadline: 16 December, 2025

• Competition Dates: Feb-March, 2025

📌 MOEMS

The Mathematical Olympiads for Elementary and Middle Schools (MOEMS) is a well-known international mathematics competition designed to develop problem-solving skills and foster a love for math among young students. It is conducted annually and provides an engaging platform for elementary and middle school students to test their critical thinking abilities in a competitive environment.

Eligibility

• Open to students in grades 4 to 8.

• Participants compete in two divisions:

  • Division E (Elementary): For students up to grade 6.

  • Division M (Middle): For students up to grade 8.

Schools, teams, and homeschool groups can register to participate, with teams comprising up to 35 students.

Winning Criteria and Recognition

• Individual Scoring:

  • Individual students earn certificates and awards based on their total scores.

• Team Scoring:

  • The top 10 scores from a team are combined to determine the team’s total score. Teams with high scores are recognized at the regional, national, and international levels.

General Format

1. Divisions:

   • Division E (Elementary): For students in grades 4-6.

   • Division M (Middle): For students in grades 6-8 (or advanced younger students).

2. Number of Contests:

   • Five contests are held during the academic year (November to March).

3. Duration:

   • Each contest lasts 30 minutes.

4. Number of Questions per Contest:

   • Each contest consists of 5 problems.

Why MOEMS Stands Out

MOEMS is not just a contest; it is a learning experience. It nurtures young minds by pushing them to think critically and creatively, setting them on a path of mathematical excellence. For schools and families, MOEMS serves as a valuable tool to inspire and prepare students for future success in both academics and beyond.

Important Dates:

• Registration Deadline: Closed, happens during November

• Competition Dates: January 19, 2025

Top 10 Tips for Math Competitions

1️⃣ Practice Past Problems

The best preparation is solving questions from previous competitions, as patterns and concepts often repeat. Familiarize yourself with common tricks and problem-solving techniques to handle challenging questions effectively.

Use resources like Art of Problem Solving and Lets Unbound YouTube Channel for access to past exams, solutions, and explanations.

2️⃣ Memorize Key Formulas and Facts

Learn essential formulas from resources like the Mathcounts Toolkit, which condenses key shortcuts and calculations. Additionally, know standard measurement systems (metric and imperial) for quick conversions.

For example, knowing the number of feet in a mile can save time on distance-related questions.

3️⃣ Strengthen Math Fundamentals

Many competition problems require solid skills in multiplication, division, and handling exponents or fractions. Practice these basics to build speed and accuracy.

Be mindful that complex problems often have elegant solutions, so avoid unnecessarily lengthy calculations.

4️⃣ Prepare Required Tools

Check the competition guidelines for items like pencils, scratch paper, and calculators.

Use mechanical pencils to avoid interruptions and graph paper (if allowed) for precise geometric diagrams. Ensure your calculator meets the competition's rules.

5️⃣ Manage Your Time Wisely

Develop a strategy to ensure you read and attempt all questions. Solve questions you’re confident about first, mark those you can revisit later, and skip the ones you find too challenging initially.

Use the remaining time to double-check your answers and make educated guesses for unanswered questions.

6️⃣ Simplify Long Questions

Lengthy problems are often easier than they appear when broken down. Create diagrams, tables, or equations to organize the given information systematically.

For instance, use a table for multi-step problems to make solving them more straightforward.

7️⃣ Draw Geometry Diagrams

If a geometry question lacks a diagram, draw one yourself—it often simplifies the solution.

Verify the accuracy of provided diagrams, as they can sometimes be misleading. Sketching accurately can save time and reduce errors.

8️⃣ Focus on What’s Asked

Pay close attention to the specific requirements of each question. Avoid common traps like calculating a value that isn’t the final answer being asked.

Double-check whether the question specifies units, forms (e.g., fractions or decimals), or other details.

9️⃣ Follow Formatting Guidelines

Use the expected format for answers. For example, reduce fractions, simplify radicals, and avoid adding unnecessary symbols like units or commas.

Misformatted answers, even if correct, may be marked wrong.

1️⃣0️⃣ Guess When There’s No Penalty

If guessing is allowed, never leave an answer blank. Use reasoning to make educated guesses, and if unsure, default to values like "0" or "1."

These are often used as answers for difficult questions toward the end of exams.

By combining smart preparation, clear strategies, and attention to detail, you can approach math competitions with confidence and perform your best.

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Amol & Nishant,

The College Crest - Powered by Lets Unbound,

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Resources for you to prepare for the exams: