🧭 Topic Guides

Detailed study guides for each major precalculus topic, designed specifically for AMC preparation. Each guide includes key concepts, examples, common traps, and AMC-style problems.

📚 Core Topics (AMC 10 & 12)

🔄 Functions & Transformations

Domains, ranges, inverses, shifts, scales, and symmetry. Essential foundation for all function work.

📊 Equations & Inequalities

Absolute value equations, systems, and basic inequality techniques including AM-GM.

🎯 Polynomials & Rational Functions

Factoring, Vieta’s formulas, asymptotes, and partial fractions.

🔢 Exponents & Logarithms

Laws, change-of-base, equation solving, and growth/decay applications.

📐 Trigonometry Basics

Unit circle, special angles, and right triangle relationships.

🔄 Trig Identities & Equations

Addition formulas, double/half angles, and equation solving techniques.

📐 Laws of Sines & Cosines

Triangle solving, area calculations, and the ambiguous case.

🎯 Advanced Topics (AMC 12 Focus)

🌀 Complex Numbers

Algebra, polar form, De Moivre’s theorem, and roots of unity.

🌀 Complex Plane Geometry

Rotations, loci, and geometric applications in the complex plane.

📈 Sequences & Series

Arithmetic, geometric, telescoping, and partial sums.

🎯 Binomial Theorem & Series

Expansions, coefficients, and estimation techniques.

📐 Coordinate Geometry

Lines, circles, distance, and basic conic sections.

🎯 Vectors (Light)

2D vectors, dot product, and projections.

🔄 Functional Equations (Light)

Substitutions, invariants, and common patterns.

🎯 Study Strategy

  1. Start with Core Topics - Master the fundamentals first
  2. Practice with Examples - Work through each topic’s examples
  3. Watch for Traps - Pay attention to common pitfalls
  4. Apply to AMC Problems - Use the worked examples as templates
  5. Connect Topics - See how different areas work together

📋 Topic Checklist

Next: Start with Functions & Transformations to build your foundation, or jump to any topic you need to review.

Next: Functions & Transformations | Back: Precalculus Mastery Guide