Thanks to Evan Chen for his .sty file which is used for all the handouts here. It can be found here.

The handout covers the basics of manipulating algebraic equations in math competitions. Its mainly for the AMC 12 and AIME but includes a few easy olympiad problems. It includes factoring, logarithms, exponents, and SSFT. It is quite short but includes a good amount of problems. (01/06/2025)
Factoring and Manipulating Algebraic Equations

The handout covers the basics of orders and primitive roots in general. (01/25/2025)
An Introduction to Orders and Primitive Roots