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IdahoAMC

AMC 12 lessons

Algebra & Number Theory

  1. Logarithms and Exponential Equations
  2. Polynomials: Factor Theorem, Rational Roots, and Vieta
  3. Symmetric Sums, Newton's Sums, and Root Transformations
  4. Complex Numbers: Modulus, Conjugates, and Polar Form
  5. Roots of Unity and Their Sums
  6. Sequences, Series, and Linear Recurrences
  7. Functions, Graphs, and Functional Equations
  8. Orders, Euler's Theorem, and Advanced Modular Arithmetic

Geometry

  1. Trigonometric Ratios and the Unit Circle
  2. The Laws of Sines and Cosines
  3. Trigonometric Identities and Equations
  4. Trigonometry in Triangles and Circles
  5. Analytic Geometry and Transformations
  6. Conic Sections
  7. Vectors and Complex Numbers as Geometry
  8. Three-Dimensional Geometry and Cross-Sections

Combinatorics

  1. Advanced Counting and Bijections
  2. Binomial Coefficients and Combinatorial Identities
  3. Inclusion-Exclusion and Derangements
  4. Recursion and Recurrence Relations
  5. States, Random Walks, and Transitions
  6. Conditional Probability and Independence
  7. Expected Value and Linearity
  8. Symmetry, Colorings, and Invariants