The American Mathematics Competitions (AMC), one of the most widely recognized international math competitions in the world, has long been highly valued by international school students and parents alike. Participating in AMC not only helps students develop rigorous mathematical thinking and problem-solving skills, but also provides strong support for future overseas university applications.
The Massachusetts Institute of Technology (MIT) explicitly lists the AMC series as a recommended STEM extracurricular activity. Top universities such as the California Institute of Technology and Yale University also regard AMC results as an important reference when evaluating applicants’ academic potential.
For students and parents who are new to AMC, common questions often arise:
What exactly is the AMC competition?
What are the differences between AMC 8, AMC 10, and AMC 12?
Which competition should students at different stages choose?
This article provides a comprehensive explanation.
What Is the American Mathematics Competition (AMC)?
The American Mathematics Competition (AMC) is organized by the Mathematical Association of America (MAA). Each year, more than 300,000 students from over 6,000 schools worldwide participate, making it one of the most influential youth mathematics assessments globally.
The AMC competition system includes:
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AMC 8
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AMC 10
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AMC 12
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AIME (American Invitational Mathematics Examination)
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USA(J)MO / USAMO
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IMO (International Mathematical Olympiad)
For students in mainland China, AIME is typically the highest level they can reach.
Competition Progression Overview
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IMO
Promotes international exchange and development of mathematics education. -
USAMO / USAJMO
High scorers in AMC 12 + AIME are invited to USAMO.
High scorers in AMC 10 + AIME are invited to USAJMO. -
AIME
More challenging than AMC 10/12. Students with outstanding AMC 10/12 scores qualify for AIME. -
AMC 10 / AMC 12
AMC 10 focuses on junior high to early high school content.
AMC 12 covers the full high school math curriculum but excludes calculus. -
AMC 8
Designed primarily for students in Grade 8 and below, emphasizing interest-based mathematical exploration.
Key Differences Between AMC 8, AMC 10, and AMC 12
AMC 8
Target Students
Primarily for students in Grade 8 (middle school) and below. This is the entry-level competition in the AMC series.
Exam Time
January each year
Format
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Individual competition
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25 multiple-choice questions
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40 minutes
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Total score: 25 points (1 point per correct answer)
Content Coverage
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Algebra: Basic expressions, equations, inequalities
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Combinatorics: Fundamental counting principles
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Number Theory: Integer properties, factorization, congruences
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Geometry: Basic geometric properties and area calculations
Academic Value
Many top international schools in China—such as YK Pao School, Pinghe School, and World Foreign Language Academy—frequently include AMC 8 original or adapted problems in their entrance exams. Students with systematic AMC 8 preparation gain a significant advantage.
AMC 10 and AMC 12
Target Students
Better suited for middle and high school students in terms of difficulty, content, and recognition. These competitions are considered essential for students aiming at top overseas universities and serve as the gateway to AIME, USAJMO, and USAMO.
Exam Time
November each year
Format
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25 multiple-choice questions
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75 minutes
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Total score: 150 points
The difference lies in content depth and scope, with AMC 12 being broader and more challenging.
Content Coverage
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AMC 10
Covers Grades 9–10 mathematics, including:-
Plane geometry (Pythagorean theorem, area and volume)
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Intermediate algebra
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Combinatorics
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Functions
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Probability
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Sequences
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AMC 12
Covers the entire high school curriculum, including:-
Advanced inequalities
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Complex function problems
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Three-dimensional geometry and functional representations
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Quadratic and higher-order residues
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Random processes and expected value
(Calculus is not included.)
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AMC Preparation Roadmap by Grade Level
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Grades 5–6
Build sufficient English proficiency and strengthen fundamental math skills. -
Grades 7–8
Begin AMC 10 preparation in Grade 7 while studying Algebra I at school. -
Grade 9
Study Algebra II and Geometry in school; transition into AP-level coursework; focus on AMC 10. -
Grade 10
Study Pre-Calculus in school; begin AP Calculus for STEM-oriented students; aim for AMC 12. -
Grade 11
Advance in Calculus and higher-level mathematics; complete AP Calculus exams.
AMC 10 / AMC 12 Preparation Plan for 2026
January – June: Foundation Building
This stage is crucial for younger students or those who need to fill knowledge gaps. The goal is to ensure solid mastery of all foundational topics.
July – August: Intensive Skill Enhancement
Conduct topic-based training for AMC 10/12 content, focusing on problem-solving techniques, speed, and accuracy. Begin systematic practice with real AMC problems from the past 10–15 years to understand question styles and difficulty levels.
September – October: Mock Exam and Final Sprint
Use recent past papers as full mock exams. Identify and address weak areas from earlier stages. Complete 1–2 full 75-minute mock tests per week using problems from the last five years.