Here you will find notes for AP Precalculus, Calculus AB/BC, and Competition Math.
AP Precalculus
Section titled “AP Precalculus”Unit notes are listed on the AP Precalculus hub
AP Calculus AB/BC
Section titled “AP Calculus AB/BC”Unit notes are listed on the AP Calculus AB/BC hub (under AP Notes).
Competition Math
Section titled “Competition Math”Through my years of preparing for AMC 10/12, AIME, and USAJMO, here are some important concepts for competition math, listed roughly in order of increasing difficulty. On each topic, I will write the difficulty of the topic inside of the notes.
Algebra
Section titled “Algebra”- Algebraic Identities and Equations
- Polynomials
- Summations
- Complex Numbers
- Inequalities
- Recursion
- Functional Equations
Geometry
Section titled “Geometry”- Triangles
- Circles and Cyclic Quadrilaterals
- Triangle Centers and Concurrency
- Coordinate Geometry
- Complex Geometry
- Solid (3D) Geometry
- Homothety
- Radical Axes and Inversion
Number Theory
Section titled “Number Theory”- Divisibility and Prime Factorization
- Modular Arithmetic
- Diophantine Equations
- Fermat’s Little Theorem and Orders
- Prime Exponents and LTE
- Quadratic Residues
- Advanced Diophantine Equations
Combinatorics
Section titled “Combinatorics”- Counting Fundamentals
- Distributions and Lattice Paths
- Principle of Inclusion–Exclusion
- Probability and Expected Value
- Pigeonhole Principle
- Invariants, Coloring, and Games
- Graph Theory
Multivariable Calculus
Section titled “Multivariable Calculus”bum bum bum USAPhO ahh
Proof-writing
Section titled “Proof-writing”- How to write your proofs!