# Major Math Concepts: Algebra 1, Algebra 2, Trigonometry, Calculus

**Algebra 1:**

Algebra 1 includes among other things expressions, systems of equations, functions, real numbers, inequalities, exponents, polynomials, radical and rational expressions.

- 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:**

Algebra 2 will cover among other things linear equations, inequalities, graphs, matrices, polynomials and radical expressions, quadratic equations, functions, exponential and logarithmic expressions, sequences and series, probability and trigonometry.

- recognizing and factoring the three most common polynomial forms:
- quadratic equations

- common factor expressions
- difference of square expressions

- synthetic division
- Descartes’s Rule of Signs
- Rational Zero Theorem
- Long division of polynomials
- Factoring by grouping
- Using the Quadratic Formula

**Trigonometry:**

In trigonometry, you learn functions that relate one non-right angle of a right triangle to the ratio of the lengths of any two sides of the triangle (or vice versa).

- 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:**

Calculus has two main parts: differential calculus and integral calculus. Differential calculus studies the derivative and integral calculus studies the integral. The derivative and integral are linked in that they are both defined via the concept of the limit: they are inverse operations of each other (a fact sometimes known as the fundamental theorem of 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