American Mathematics Competition (AMC)

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Overview:

The AMC 10 and AMC 12 (American Mathematics Competitions) are national mathematics contests administered by the Mathematical Association of America (MAA). These prestigious exams are designed to promote problem-solving skills and identify talented students for advanced mathematical competitions such as the AIME and USA(J)MO.

AMC 10: For students in 10th grade or below and under 17.5 years old

AMC 12: For students in 12th grade or below and under 19.5 years old

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Format:

• Number of Questions: 25 multiple-choice questions

• Duration: 75 minutes

• Scoring:

  • +6 points for each correct answer

  • 0 points for incorrect answers

  • +1.5 points for each unanswered question

• Maximum score: 150

• Calculator: Not allowed

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Content Focus:

• AMC 10 Content (up to 10th-grade math):

  • Algebra (linear & quadratic equations, inequalities, exponents)

  • Geometry (Euclidean, coordinate, similarity, area, volume)

  • Number theory (divisibility, primes, modular arithmetic)

  • Counting & probability

  • Logic and problem-solving strategies

  • Basic trigonometry (at most)

• AMC 12 Content (up to 12th-grade math):

  • All AMC 10 topics, plus:

  • Advanced algebra (complex numbers, functions)

  • Trigonometry (identities, equations)

  • Pre-calculus topics (polynomials, logarithms, sequences)

  • Some basic topics from calculus (limits, derivatives in concept only)

American Invitational Mathematics Examination (AIME)

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Overview:

The AIME (American Invitational Mathematics Examination) is a prestigious national math competition in the USA Mathematical Olympiad (USAMO) selection process, administered by the Mathematical Association of America (MAA). It serves as the second round following the AMC 10 or AMC 12 and is intended for students who demonstrate exceptional problem-solving ability.

Eligibility: By invitation only – top scorers on the AMC 10 or AMC 12

Audience: High school students (grades 9–12), and exceptional middle schoolers

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Format:

• Number of Questions: 15

• Duration: 3 hours

• Answer Format: Each answer is a whole number from 0 to 999

• Scoring:

  • +1 point per correct answer

  • No penalty for incorrect or blank answers

  • Maximum score: 15

• Calculator: Not allowed

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Content Focus:

• Algebra (functions, equations, polynomials, inequalities)

• Geometry (coordinate and Euclidean, circles, triangles, 3D shapes)

• Number theory (divisibility, modular arithmetic, primes)

• Combinatorics (counting, binomial coefficients, probability)

• Sequences and series

• Logic and clever techniques (e.g., invariants, recursion)

USA Junior Mathematical Olympiad (JMO)
USA Mathematical Olympiad (AMO)

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Overview:

The USAJMO (USA Junior Mathematical Olympiad) and USAMO (USA Mathematical Olympiad) are the final rounds in the U.S. math competition pathway, administered by the Mathematical Association of America (MAA). These prestigious, proof-based contests are designed to identify the top mathematical problem solvers in the nation and serve as the gateway to the Mathematical Olympiad Summer Program (MOSP) and the U.S. IMO Team.

Eligibility:

USAJMO: Based on performance in AMC 10 + AIME

USAMO: Based on performance in AMC 12 + AIME

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Format:

• Duration: 2 consecutive days

• Time: 4.5 hours per day

• Questions: 3 proof-based problems each day (6 total)

• Scoring:

  • Each problem is scored from 0 to 7 points

  • Maximum score: 42

• Calculator: Not allowed

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Content Focus:

• Algebra

• Geometry (including synthetic and Olympiad-style problems)

• Number theory

• Combinatorics

• Mathematical reasoning and creativity

International Mathematical Olympiad (IMO)

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The International Mathematical Olympiad (IMO) is the most prestigious global mathematics competition for high school students. Held annually since 1959, the IMO brings together top young mathematicians from over 100 countries to compete in a challenging two-day exam. Each day, students tackle three complex proof-based problems over 4.5 hours, testing deep understanding, creativity, and advanced problem-solving skills in areas such as algebra, geometry, number theory, and combinatorics. Earning a medal at the IMO is one of the highest honors in high school mathematics, and the competition serves as a launching pad for future careers in STEM, research, and innovation.

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