🧭 Tactics by Topic

Master specialized problem-solving techniques for each major mathematical topic. These tactics provide targeted approaches for specific types of problems you’ll encounter in AMC 10/12 contests.

🎯 Topic-Specific Strategies

🔢 Algebra Tactics

• Algebra Tactics - Substitutions, discriminants, conjugates, and algebraic manipulation techniques
• Key focus: Equations, functions, inequalities, and algebraic relationships

🔢 Number Theory Tactics

• Number Theory Tactics - Modular arithmetic, divisibility, prime factorization, and number properties
• Key focus: Divisibility, remainders, primes, and number patterns

📐 Geometry Tactics

• Geometry Tactics - Similar triangles, power of a point, coordinate geometry, and geometric relationships
• Key focus: Shapes, angles, areas, and spatial relationships

🎲 Counting & Probability Tactics

• Counting & Probability Tactics - Combinatorics, probability calculations, and counting techniques
• Key focus: Arrangements, combinations, and likelihood calculations

📊 Precalculus Tactics (AMC 12)

• Precalculus Tactics - Trigonometry, logarithms, and advanced function techniques
• Key focus: Trig identities, log properties, and function analysis

🎯 How to Use These Tactics

Problem-Solving Process

1. Identify the topic: Use topic routing heuristics
2. Select appropriate tactics: Choose from topic-specific techniques
3. Apply systematically: Follow the tactical approach
4. Verify your answer: Use sanity checks and verification

Cross-Topic Integration

• Many problems combine topics: Don’t limit yourself to one approach
• Use multiple tactics: Apply different techniques as needed
• Stay flexible: Adapt your approach based on what works
• Learn connections: Understand how topics relate

📊 Topic Distribution

AMC 10/12 Typical Distribution

• Algebra: 30-40% of problems
• Geometry: 25-35% of problems
• Number Theory: 15-25% of problems
• Counting/Probability: 15-25% of problems
• Precalculus: 10-20% of problems (AMC 12 only)

Strategic Focus

• Master all topics: Don’t neglect any area
• Identify strengths: Focus on your strong topics
• Improve weaknesses: Work on challenging areas
• Practice integration: Solve problems that combine topics

🚀 Quick Reference

Topic Identification:

• Algebra: Variables, equations, functions
• Number Theory: Divisibility, remainders, primes
• Geometry: Shapes, angles, coordinates
• Counting/Probability: Arrangements, combinations
• Precalculus: Trig, logs, advanced functions

Tactical Approach:

• Read the problem: Understand what’s being asked
• Identify the topic: Use signal words and patterns
• Select tactics: Choose appropriate techniques
• Apply systematically: Follow the tactical approach
• Verify answer: Check your work

Next: Algebra Tactics | Back to: Strategy Guide