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AMC Overview & Competition Path
The AMC (American Mathematics Competition) is the gateway to the prestigious US math olympiad pipeline. Top scorers advance through a series of increasingly difficult competitions:
AMC 8
Grades ≤ 8
25 questions, 40 min, no penalty
AMC 10
Grades ≤ 10
30 questions, 75 min, score 150
AMC 12
Grades ≤ 12
30 questions, 75 min, score 150
AIME
Top ~5%
15 questions, 3 hours, integer answers 0–999
USAMO
Top ~270
6 proof problems over 2 days
IMO
Top 6 (USA)
International Mathematical Olympiad
2026 AMC Dates: AMC 10A/12A — November 6, 2025. AMC 10B/12B — November 12, 2025. The 2026–2027 cycle begins in fall 2026. Register through your school's math teacher or AMC coordinator.
AMC 10 vs AMC 12
| Feature | AMC 10 | AMC 12 |
|---|
| Eligibility | Grades ≤ 10, age ≤ 17.5 | Grades ≤ 12 |
| Topics | Through precalculus (no trig, no complex) | Through precalculus + trig + complex numbers |
| AIME cutoff (typical) | ~100/150 | ~85/150 |
| Honor roll (top 1%) | ~120 | ~100 |
| Scoring | +6 correct, 0 blank, −1.5 wrong | +6 correct, 0 blank, −1.5 wrong |
If you're in grade 10 or below, you can take both the AMC 10 and AMC 12 on different test dates (A and B). Your best score qualifies you for AIME.
Topic Breakdown by Frequency
AMC 10/12 problems cluster around a core set of topics. Based on analysis of past exams (2000–2025):
| Topic Area | Questions per Exam | Priority |
|---|
| Algebra & expressions | 5–7 | 🔴 Critical |
| Number theory (divisibility, modular arithmetic) | 4–6 | 🔴 Critical |
| Geometry (areas, volumes, circles, similar triangles) | 5–7 | 🔴 Critical |
| Combinatorics & counting | 4–5 | 🟠 High |
| Probability | 3–4 | 🟠 High |
| Sequences & series | 2–3 | 🟡 Medium |
| Inequalities & optimization | 2–3 | 🟡 Medium |
| Complex numbers (AMC 12 only) | 2–3 | 🟡 Medium |
| Trigonometry (AMC 12 only) | 2–3 | 🟡 Medium |
| Logarithms & exponents | 1–2 | 🟢 Supporting |
Problem-Solving Strategy
AMC problems require creative thinking, not just formula recall. Here's a reliable approach:
The 5-Step AMC Method
- Read carefully. Identify exactly what the problem is asking. Many wrong answers come from misreading "maximum" vs "minimum" or "positive" vs "non-negative."
- Identify the structure. Is this a counting problem? A geometry problem? Does it involve modular arithmetic? Naming the type activates the right toolset.
- Try small cases or draw a picture. For combinatorics and number theory, testing small examples often reveals a pattern. For geometry, a careful diagram is essential.
- Work backwards from the answer choices. AMC is multiple choice — if a direct approach is stuck, try plugging in answer choices (especially for problems 1–15).
- Use the skip-and-return rule. If a problem takes more than 3 minutes, mark it and move on. Return after completing easier problems.
Scoring Strategy
The −1.5 penalty matters. With 5 answer choices, a random guess has an expected value of 6/5 − (4/5)(1.5) = 0 — exactly zero. Only guess when you've eliminated at least one answer choice. With two eliminated, expected value is positive.
Training Plan
For students targeting AIME qualification (top ~5%):
| Phase | Duration | Focus |
|---|
| Foundation | 3–4 months | Master the 6 core topics. Do AMC 10 problems 1–20 from older years (2015–2020). |
| Intermediate | 2–3 months | Focus on problems 21–30 (hard). Learn advanced techniques: Vieta's, PIE, Stewart's theorem, power of a point. |
| Simulation | 4–6 weeks before exam | Take timed full AMC exams. Review every wrong answer immediately. Track weak topic areas. |
Resources
- Art of Problem Solving (AoPS): The community forum has solutions to every AMC problem ever written. The AoPS textbook series (Prealgebra through Precalculus) is the standard curriculum for competition prep.
- MATHCOUNTS: If you're in middle school, MATHCOUNTS is excellent preparation for future AMC performance.
- Past exams: Available free at artofproblemsolving.com/wiki and maa.org/math-competitions/amc.
- MathHub competitions page: Our US competitions section has curated problem sets targeting AMC-style thinking.
Key insight: The single best predictor of AMC success is the volume of AMC-style problems you've solved. There is no shortcut — consistent daily practice (even 15–30 minutes) compounds dramatically over months.
Competition Math Tutoring
Our competition math tutors have AIME and USAMO experience. We specialize in the problem-solving techniques that move students from AMC to AIME qualification.
Get Competition Math Help
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