The American Mathematics Competitions (AMC) are a series of internationally recognized math contests organized by the Mathematical Association of America (MAA). Designed to inspire students’ interest in mathematics and develop problem-solving ability, AMC competitions are widely regarded as one of the most influential math contests for middle and high school students worldwide.
Based on age and academic level, AMC competitions are divided into AMC 8, AMC 10, and AMC 12, with advancement opportunities to AIME and ultimately USAMO / USAJMO. This article provides a comprehensive overview of each level, recommended grades, exam rules, preparation planning, and real exam strategies.
I. AMC Competition Levels and Recommended Grades
AMC 8
Target Students:
Students in Grade 8 or below, aged 15.5 or younger (under the updated age rule).
Recommended Starting Grade:
As early as Grade 5.
Exam Format:
25 multiple-choice questions completed in 40 minutes.
Scoring: 1 point for a correct answer, 0 points for blank or incorrect answers.
Maximum score: 25.
Test Content:
Middle school–level algebra, geometry, probability, and logical reasoning.
Value:
Ideal for introducing younger students to math competitions, strengthening logical reasoning, creative thinking, and problem decomposition. It also supports academic transitions such as middle school placement.
AMC 10
Target Students:
Students in Grade 10 or below, aged 17.5 or younger.
Recommended Grade:
Grade 8 and above.
Exam Format:
25 multiple-choice questions completed in 75 minutes.
Scoring: 6 points for a correct answer, 1.5 points for a blank answer, 0 points for an incorrect answer.
Maximum score: 150.
Test Content:
Covers mathematics from middle school through early high school, excluding calculus and trigonometry.
Value:
A significant academic credential for competitive university applications, especially for applicants to top institutions such as MIT and Stanford.
AMC 12
Target Students:
Students in Grade 12 or below, aged 19.5 or younger.
Recommended Grade:
Grades 10–11 are optimal.
Exam Format:
Same as AMC 10: 25 multiple-choice questions in 75 minutes, with a maximum score of 150.
Test Content:
Covers the full high school math curriculum, including trigonometry and advanced geometry, with a higher level of difficulty.
Value:
One of the primary qualification pathways to AIME and a strong academic indicator for STEM-focused university applications.
AIME (American Invitational Mathematics Examination)
Eligibility:
Top 2.5% of AMC 10 scorers and top 5% of AMC 12 scorers.
Exam Format:
15 questions completed in 3 hours.
Scoring: 1 point for a correct answer, 0 points otherwise.
Value:
AIME performance is essential for advancing to USAMO / USAJMO and serves as a highly respected academic credential for elite universities.
II. Why Is AMC Highly Recommended?
Strong Impact on College Applications
Top universities such as MIT, Stanford, and Cambridge explicitly encourage applicants to submit AMC and AIME scores. Qualification for AIME significantly strengthens an applicant’s academic profile.
For students applying to majors such as computer science, engineering, mathematics, or economics, AMC scores provide concrete evidence of advanced mathematical reasoning.
Development of Core Mathematical Skills
AMC emphasizes logical reasoning, creative problem-solving, and conceptual understanding rather than rote memorization.
The preparation process also improves students’ stress management, analytical thinking, and time management skills.
Globally Recognized Credentials
AMC certificates and scores are recognized worldwide, making them valuable not only within international education systems but also for domestic academic pathways.
A Clear, Progressive Learning Path
From AMC 8 → AMC 10 → AMC 12 → AIME → USAMO, AMC provides a structured, long-term progression that allows students to continuously develop their mathematical ability.
III. AMC Preparation Roadmap
Foundation Stage
Goal:
Master core concepts and avoid mistakes on basic problems (especially Questions 1–10).
Key Tasks:
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Study systematically across four modules: algebra, geometry, number theory, and combinatorics
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Identify and reinforce high-frequency concepts
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Use Art of Problem Solving (AoPS) materials to build a strong foundation
Skill Enhancement Stage
Goal:
Achieve at least 85% accuracy on mid-level questions (Questions 11–20).
Key Tasks:
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Practice AMC problems from the past 5–10 years by topic
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Focus on high-frequency question types (e.g., geometry applications in AMC 10, complex number integration in AMC 12)
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Build an error log and review it weekly
Intensive Mock Exam Stage
Goal:
Adapt fully to exam pace and target 105+ on AMC 10 (AIME cutoff) or 85+ on AMC 12.
Key Tasks:
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Complete 2–3 full-length mock exams per week under timed conditions
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Master test-taking techniques such as answer elimination and special-value substitution
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Allocate time wisely to ensure accuracy on the first 20 questions while attempting harder problems strategically
IV. Exam-Day Strategies
Tackle Easy Questions First
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Prioritize Questions 1–15 to secure accuracy
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Carefully work through Questions 16–20
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For Questions 21–25, attempt only those with a clear approach
Use Smart Techniques
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Substitute answer choices to verify equations and inequalities
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Apply special values to eliminate incorrect options
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Always draw diagrams for geometry problems, even rough sketches
Control Your Pace
Avoid getting stuck on a single problem. Leave time at the end to check calculations and answer sheet markings to prevent avoidable mistakes.