🗺️ AMC 10 vs AMC 12 Scope Map
This matrix shows which counting and probability topics are essential for each contest level.
| Topic | AMC 10 | AMC 12 | Notes |
|---|---|---|---|
| Basic Counting | |||
| Addition Principle | ✅ Core | ✅ Core | Fundamental counting rule |
| Multiplication Principle | ✅ Core | ✅ Core | Sequential counting |
| Complement Counting | ✅ Core | ✅ Core | “At least” problems |
| Permutations & Combinations | |||
| Permutations | ✅ Core | ✅ Core | Arrangements |
| Combinations | ✅ Core | ✅ Core | Selections |
| Permutations with Repetition | ✅ Often | ✅ Core | Letters in words |
| Combinations with Repetition | ⚠️ Stretch | ✅ Often | Stars and bars |
| Circular Permutations | ⚠️ Stretch | ✅ Often | Ring arrangements |
| Advanced Counting | |||
| Inclusion-Exclusion | ⚠️ Stretch | ✅ Often | 2-3 sets max |
| Pigeonhole Principle | ⚠️ Stretch | ✅ Often | Bounds and colorings |
| Stars and Bars | ⚠️ Stretch | ✅ Often | Integer solutions |
| Derangements | ❌ No | ✅ Stretch | AMC 12 only |
| Probability Basics | |||
| Basic Probability | ✅ Core | ✅ Core | Fractions and ratios |
| Conditional Probability | ✅ Often | ✅ Core | Given information |
| Independence | ✅ Often | ✅ Core | Event relationships |
| Law of Total Probability | ⚠️ Stretch | ✅ Often | Tree diagrams |
| Bayes’ Theorem | ❌ No | ⚠️ Stretch | AMC 12 only |
| Expected Value | |||
| Expected Value Definition | ⚠️ Stretch | ✅ Often | Weighted average |
| Linearity of Expectation | ❌ No | ✅ Often | AMC 12 only |
| Indicators | ❌ No | ✅ Often | AMC 12 only |
| Distributions | |||
| Binomial Distribution | ⚠️ Stretch | ✅ Often | Success/failure |
| Geometric Distribution | ❌ No | ⚠️ Stretch | AMC 12 only |
| Hypergeometric Distribution | ❌ No | ⚠️ Stretch | AMC 12 only |
| Problem Types | |||
| Seating Problems | ✅ Core | ✅ Core | Adjacency constraints |
| Word Rearrangements | ✅ Core | ✅ Core | Letter arrangements |
| Committee Selection | ✅ Core | ✅ Core | Role assignments |
| Grid Paths | ✅ Often | ✅ Core | Lattice walks |
| Balls in Bins | ⚠️ Stretch | ✅ Often | Integer solutions |
| Digit Counting | ✅ Often | ✅ Core | Divisibility rules |
🎯 Legend
- ✅ Core: Essential for this level, appears frequently
- ✅ Often: Important but less frequent, good to know
- ⚠️ Stretch: Advanced topic, appears occasionally
- ❌ No: Not tested at this level
📊 Study Priorities
AMC 10 Focus
- Basic counting principles (addition, multiplication, complement)
- Permutations and combinations (with and without repetition)
- Basic probability (fractions, conditional, independence)
- Common problem types (seating, words, committees, grids)
AMC 12 Focus
- Everything from AMC 10 (assumed knowledge)
- Advanced counting (inclusion-exclusion, pigeonhole, stars and bars)
- Expected value and linearity
- Probability distributions (binomial, geometric, hypergeometric)
- Advanced problem types (derangements, complex probability chains)
🚀 Contest Strategy
- AMC 10: Master the “Core” and “Often” topics, skip “Stretch”
- AMC 12: Cover all “Core” and “Often” topics, study “Stretch” for harder problems
- Time allocation: Focus 80% of study time on “Core” topics for your level
Next: Notation Cheatsheet → Concept Atlas