What is the Syllabus for the AMC Maths Competition?

The American Mathematics Competitions (AMC) come in three levels: AMC 8, AMC 10, and AMC 12, and each one is designed for students at different stages. 

AMC 8 focuses on middle school math, AMC 10 covers high school math up to precalculus, and AMC 12 adds advanced topics like trigonometry and complex numbers.

Knowing the AMC syllabus helps you study smarter. Instead of wasting energy on topics that won’t even show up, you can focus on what really counts—and walk into the test with confidence.

AMC Syllabus (AMC 8, AMC 10, AMC 12)

The AMC math contests come in three levels: AMC 8, AMC 10, and AMC 12. Each one matches where you are in school and how much math you’ve covered.

Now, don’t worry—you won’t see calculus or crazy college math here. Every AMC sticks to pre-calculus topics. 

The twist is that the problems are super creative and tricky, so you’ll need to think outside the box, not just memorize formulas.

AMC 8 Syllabus (Middle School Level)

Eligibility: Grade 8 or below, under 14.5 years old

Topics Covered:

• Arithmetic & Pre-Algebra: fractions, decimals, ratios, percentages, simple algebraic expressions
• Geometry Basics: angles, perimeter, area, volume, Pythagorean theorem
• Number Theory: factors, multiples, primes, divisibility rules
• Counting & Probability: fundamental counting principles, basic probability
• Logical Reasoning & Patterns: simple combinatorics, spatial visualization, interpreting graphs and tables

Not Included:

• Trigonometry
• Advanced algebra (functions, polynomials, inequalities)
• Coordinate geometry beyond basics
• Calculus

AMC 10 Syllabus (High School Foundation Level)

Eligibility: Grade 10 or below, under 17.5 years old

Topics Covered:

• Algebra: linear and quadratic equations, inequalities, polynomials, functions
• Geometry: plane geometry, circles, triangles, quadrilaterals, coordinate geometry
• Number Theory: modular arithmetic, divisibility, basic Diophantine equations
• Probability & Counting: fundamental counting principles, binomial coefficients, simple combinatorics
• Pre-Calculus Basics: exponents, logarithms, sequences and series

Not Included:

• Advanced algebra beyond the above
• Trigonometry (identities, equations)
• Advanced geometry (3D, vector methods)
• Calculus

AMC 12 Syllabus (Advanced High School Level)

Eligibility: Grade 12 or below, under 19.5 years old

Topics Covered:

• Advanced Algebra: polynomial equations, inequalities, logarithms, functions
• Geometry: Euclidean and coordinate geometry, circle theorems, 3D geometry
• Trigonometry: identities, equations, and applications (law of sines, law of cosines)
• Number Theory: congruences, prime factorization, residues, Diophantine equations
• Probability & Combinatorics: advanced counting methods, permutations, combinations, pigeonhole principle

Not Included:

• Calculus (derivatives, integrals)
• College-level mathematics

In short: AMC 8 builds fundamentals, AMC 10 expands reasoning with algebra and precalculus, and AMC 12 challenges students with advanced problem-solving—all without calculus.

Key Differences Between AMC 8, 10, and 12 Syllabus

The three levels of the American Mathematics Competitions (AMC) are designed to match students’ grade levels and math maturity:

• AMC 8 → Foundation level for middle school (grade 8 and below). Focuses on core skills like arithmetic, pre-algebra, basic geometry, and problem-solving with middle school concepts.
• AMC 10 → Intermediate level for grade 10 and below. Introduces precalculus, deeper algebra, and more abstract reasoning. Serves as a bridge to higher math contests.
• AMC 12 → Advanced level for grade 12 and below. Covers trigonometry, complex numbers, and advanced algebra/geometry, preparing students for elite competitions.
  

Progression Pathway

Many students follow a journey: AMC → AIME → USAMO → IMO. Each step requires stronger problem-solving skills, deeper creativity, and a more advanced understanding of mathematics.

 In short: AMC 8 builds the basics, AMC 10 strengthens reasoning with higher-level topics, and AMC 12 challenges students with advanced math—positioning them for top-level competitions.

Preparation Tips Based on the AMC Syllabus

Smart preparation means focusing on what actually matters for the AMC. Here are key strategies to align your study plan with the syllabus:

• Practice with past AMC papers: This helps you understand the format, question style, and difficulty level for AMC 8, 10, and 12.
• Master the core topics: Algebra, geometry, number theory, and combinatorics appear across all levels and form the backbone of the exam.
• Focus for AMC 12: Add extra practice on trigonometry and complex numbers, as these are unique to this level.
• Skip what’s not tested: Don’t waste time on calculus or college-level math—they’re not part of the AMC syllabus.
• Learn from mistakes: Review errors carefully, keep an error log, and revisit weak areas until they’re solid.
• Simulate test conditions: Practice under timed, distraction-free settings to build pacing, endurance, and confidence.

By targeting the AMC syllabus directly, you’ll study more efficiently, strengthen problem-solving skills, and boost your chances of a higher score.

FAQs on the AMC Syllabus

🔹 Does AMC include calculus?
No. Calculus is not tested on AMC 8, AMC 10, or AMC 12. The exams focus on middle school and high school math up through precalculus.

🔹 Is trigonometry on AMC 10?
Only in a very limited way. The AMC 10 may include simple trigonometry within geometry problems, but advanced trigonometric identities and equations are saved for the AMC 12.

🔹 What’s the difference between AMC 10 and AMC 12 syllabus?

• AMC 10: Algebra, geometry, number theory, combinatorics, and basic probability (up to 10th grade level).
• AMC 12: All AMC 10 topics plus advanced algebra, trigonometry, complex numbers, and deeper problem-solving (up to 12th grade level).

🔹 Where can I find official AMC syllabus details?
The Mathematical Association of America (MAA) website provides official AMC resources, including past exams, scoring policies, and contest guidelines.

🔹 How do I know which AMC level to take?

• AMC 8: Middle school students (grade 8 and below).
• AMC 10: Students up to grade 10 who are comfortable with algebra and geometry.
• AMC 12: Students in grades 11–12 or those seeking an advanced challenge with topics like trigonometry and complex numbers.

Conclusion

The AMC syllabus grows with you: AMC 8 builds the basics, AMC 10 takes you into deeper algebra and precalculus, and AMC 12 adds advanced topics like trigonometry and higher-level problem solving. 

With steady practice and the right mindset, the AMC becomes more than a competition—it’s a chance to learn, grow, and discover the fun side of mathematics.