I'm going to list what I believe are the key concepts that you need to master across different math subjects. These are the tools that I have to use most often in order to solve problems, so you should get very familiar with the theory behind them and very comfortable with applying them.

**Algebra 1:**

- order of operation (PEMDAS)
- solving equations
- slope-intercept form of linear equations
- point-slope form of linear equations
- systems of linear equations (elimination and substitution methods)
- inequalities
- domain and range
- undefined and imaginary expressions
- asymptotes (horizontal and vertical)
- discontinuities (removable and non-removable)
- rational expressions
- factoring
- quadratic formula
- radical properties
- exponent properties
- transformations and translations of functions

**Algebra 2:**

1. recognizing and factoring the three most common polynomial forms:

- quadratic equations
- common factor expressions
- difference of square expressions

2. synthetic division

3. Descartes's Rule of Signs

4. Rational Zero Theorem

5. Long division of polynomials

6. Factoring by grouping

7. Using the Quadratic Formula

**Trigonometry:**

- understanding and using the unit circle
- trig identities
- definitions of the trig functions "Soh-Cah-Toa"
- factoring quadratic equations (using the quadratic formula, etc.)

**Calculus:**

- the power rule
- the chain rule: du/dx = du/dy*dy/dx
- product rule
- quotient rule
- u-substitution
- integration by parts
- the disk, washer, and shell methods for finding volumes of solids of revolution
- limits
- L'Hopital's rule
- separation of variables
- trig substitution
- partial fractions
- implicit differentiation
- Taylor polynomials
- LaGrange remainders