Math Notes (Work in progress)

Here you will find notes for AP Precalculus, Calculus AB/BC, and Competition Math. Note that competition math will not include calculus, but is still good to know calculus to excel at competition math.

AP Precalculus

Unit notes are listed on the AP Precalculus hub

AP Calculus AB/BC

Unit notes are listed on the AP Calculus AB/BC hub (under AP Notes).

Competition Math

Through my years of preparing for AMC 10/12, AIME, and USAJMO, here are some important concepts for competition math, list in order of increasing difficulty. On each topic, I will write the difficulty of the topic inside of the notes.

Algebra

Polynomials
Newton’s Sums
Summations
Inequalities
Functional equations
Recursion

Geometry

Circles
Inversion
Homothety

Number Theory

Fermat’s Little Theorem
Wilson’s Theorem
Lifting the Exponent (LTE) Lemma
Fermat’s Christmas Theorem

Combinatorics

Expected Value

Proof-writing

How to write your proofs!