🧩 Problem Types

Master the art of pattern recognition! This section provides templates and strategies for common AMC precalculus problem types.

🎯 Pattern Recognition Strategy

1. Read the problem - What’s being asked?
2. Identify the pattern - Which type does this match?
3. Apply the template - Use the standard approach
4. Check your work - Verify the solution makes sense

📚 Problem Type Categories

🔄 Trigonometric Problems

• Solving trigonometric equations
• Identity manipulation techniques
• Inverse trigonometric constraints

📊 Logarithm & Exponential

• Equation solving strategies
• Domain and range considerations
• Growth and decay applications

🎯 Polynomial Manipulation

• Vieta’s formula applications
• Root relationship problems
• Parameter sweeps

🌀 Complex Number Geometry

• Roots of unity problems
• De Moivre’s theorem applications
• Complex plane geometry

📐 Coordinate Geometry

• Locus problems
• Distance and area calculations
• Conic section applications

⚖️ Inequality Techniques

• AM-GM applications
• Cauchy-Schwarz inequality
• Optimization problems

🎯 Quick Recognition Guide

Trig Problems

• Look for: $\sin$, $\cos$, $\tan$, angle relationships
• Common patterns: identities, equations, inverse functions

Log/Exp Problems

• Look for: $\log$, $\ln$, $e^x$, growth/decay
• Common patterns: equation solving, domain restrictions

Polynomial Problems

• Look for: roots, coefficients, Vieta’s relationships
• Common patterns: symmetric sums, parameter sweeps

Complex Problems

• Look for: $i$, polar form, rotations, roots of unity
• Common patterns: geometric interpretations, De Moivre’s

Coordinate Problems

• Look for: points, distances, areas, conic sections
• Common patterns: locus problems, geometric relationships

Inequality Problems

• Look for: maximum/minimum, optimization, AM-GM
• Common patterns: equality conditions, constraint optimization

📋 Problem-Solving Checklist

• Identify the pattern - Which problem type?
• Check constraints - Domain, range, special cases
• Apply template - Use standard approach
• Simplify - Look for shortcuts and identities
• Verify - Check answer makes sense
• Consider alternatives - Is there a simpler approach?

🎯 AMC Success Tips

1. Practice pattern recognition - The more problems you see, the faster you’ll recognize types
2. Master the templates - Know the standard approaches by heart
3. Watch for traps - Common pitfalls in each problem type
4. Time management - Some patterns are faster to solve than others
5. Check your work - AMC problems often have elegant solutions

Next: Start with Trigonometric Problems or jump to any pattern you need to practice.