📏 Essential Formulas

Quick reference for all essential precalculus formulas with usage examples and micro-examples.

🎯 How to Use This Section

1. Quick Lookup - Find formulas by topic
2. Usage Examples - See how each formula applies
3. Memory Aids - Use patterns to remember formulas
4. Practice - Apply formulas to AMC problems

📚 Formula Categories

🔢 Complete Formula Bank

Comprehensive collection of all essential formulas organized by topic.

🎯 Quick Formula Finder

Functions & Transformations

• Domain restrictions, inverse functions, composition
• Transformations: shifts, scales, reflections

Polynomials & Rational Functions

• Vieta’s formulas, remainder theorem, factoring
• Asymptotes, partial fractions

Exponents & Logarithms

• Laws of exponents, logarithm properties
• Change of base, growth/decay formulas

Trigonometry

• Unit circle values, identities, laws of sines/cosines
• Addition formulas, double/half angles

Complex Numbers

• Polar form, De Moivre’s theorem, roots of unity
• Complex arithmetic, geometric interpretations

Sequences & Series

• Arithmetic/geometric sequences, telescoping
• Binomial theorem, partial sums

Coordinate Geometry

• Distance, midpoint, line equations
• Circle equations, area formulas

Inequalities

• AM-GM, Cauchy-Schwarz, triangle inequality
• Optimization techniques

💡 Formula Usage Tips

1. Memorize the essentials - Focus on most frequently used formulas
2. Understand the context - Know when to apply each formula
3. Practice applications - Work through examples to build fluency
4. Check your work - Verify formulas are applied correctly

📋 Study Strategy

• Week 1: Master basic formulas (functions, polynomials, trig basics)
• Week 2: Add advanced formulas (complex numbers, sequences, inequalities)
• Week 3: Practice applications and problem-solving
• Week 4: Review and refine formula usage

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