If your child is preparing for the American Mathematics Competitions, the single most useful thing you can do is understand exactly what the contest tests, and the AMC syllabus is more focused than most families expect.
The AMC, run by the Mathematical Association of America, is the entry point to the most respected math competition pathway in the United States. There is no single official document titled "AMC syllabus," but the topics drawn upon are well established and consistent year to year. Below is a practical, accurate breakdown of what each level covers, so you can prepare with intention rather than guesswork.
AMC format and eligibility at a glance
The AMC has three levels, each tied to grade and age limits. Always confirm current age cutoffs, dates and fees on the official site, but the structure is stable:
- AMC 8 — for students in grade 8 and below: 25 multiple-choice questions in 40 minutes. It is a standalone contest and does not lead directly to the next round.
- AMC 10 — for students in grade 10 and below: 25 multiple-choice questions in 75 minutes.
- AMC 12 — for students in grade 12 and below: 25 multiple-choice questions in 75 minutes.
On the AMC 10 and 12, correct answers earn 6 points, unanswered questions earn 1.5 points, and wrong answers earn 0. That scoring rewards disciplined guessing strategy. High scorers on the AMC 10 and 12 qualify for the American Invitational Mathematics Examination (AIME), the next step toward the USA Mathematical Olympiad.
The AMC topic checklist by level
AMC 8 topics
- Arithmetic, fractions, ratios and percentages
- Introductory algebra and linear equations
- Basic geometry: angles, area, perimeter and volume
- Counting principles and elementary probability
- Logic and pattern recognition
AMC 10 topics (adds to the AMC 8 foundation)
- Algebra: quadratics, factoring, systems of equations and algebraic manipulation
- Geometry: similarity, congruence, the Pythagorean theorem and coordinate geometry
- Number theory: divisibility, primes, modular thinking and integer properties
- Combinatorics and probability: permutations, combinations and counting techniques
Trigonometry and calculus are not required for the AMC 10.
AMC 12 topics (adds to the AMC 10 syllabus)
- Advanced algebra: polynomials, Vieta's formulas, logarithms, exponentials, and function composition and inverses
- Complex numbers and sequences and series
- Trigonometry: the unit circle, the six trig functions, and the laws of sines and cosines, mostly inside geometry problems
- Harder number theory and combinatorics: inclusion-exclusion, conditional probability and expected value
The AMC 12 spans the full high school curriculum, but breadth alone is not the challenge. The difficulty lives in combining familiar ideas in unfamiliar ways under time pressure.
How to actually prepare
A topic list is only a map. Real progress comes from a structured loop: learn a concept, drill targeted problems, then take timed past papers to build pacing and accuracy. Because the AMC rewards clever insight over raw content, the most effective preparation emphasizes technique: case analysis, working backward from answer choices, and recognizing when a problem hides a simpler structure.
Pacing matters too. With 25 questions and limited time, students should secure the early problems quickly, then invest remaining minutes in the harder back half. Practicing this allocation is as important as knowing the math itself.
At BIAA's AMC program, we group students by level and target the exact gaps that hold them back, then track progress through full timed simulations. Strong AMC training also reinforces the analytical thinking that powers our broader math enrichment track and feeds naturally into other rigorous academic competitions.
Ready to turn this checklist into a clear, level-appropriate study plan? Explore BIAA's AMC preparation program and give your student a focused path from first practice set to AIME qualification.