**Basic Algebra/Precalculus**

**Basic College Algebra**

BCA2.0. Review: Manipulating Equalities

BCA2.1. Linear Equations in Two Variables

BCA2.3. Slope-Intercept Equation of a Line

BCA2.4. Point-Slope Equation of a Line

BCA3.1. SLE 1 - The Graphing Method

BCA3.2. SLE 2 - Substitution Method

BCA3.3. SLE 3 - Addition Method

BCA4.1.1. Polynomial Example: Subtraction with Parentheses

BCA4.2. Polynomials: Multiplication

BCA4.4. Factoring: Greatest Common Factor and Grouping

BCA4.5. Factoring: Quadratics 1

BCA4.5. Factoring: Quadratics 2: Difference of Two Squares

BCA4.5.X. Factoring Example: DO2S x 2

BCA4.6. Solving Quadratic Equations Using Zero Product Rule

BCA4.6.X Example 1: Solving Quadratics Equations Using ZPR

BCA4.6.X. Example 2: Solving Quadratic Equations

BCA5.1. Simplifying Rational Expressions

BCA5.2. Rational Expressions: Multiplication and Division

BCA5.3. Rational Expressions: Addition and Subtraction

BCA5.4. Solving Rational Equations

BCA5.4.X. Example: Solving a Rational Equation

BCA6.1. Definition of Square Root

BCA6.2. Simplifying Radical Expressions

**Basic Algebra II**

**Precalculus**

Example of Arithmetic Sequence

Geometric Proof of Integer Sum Formula

Example of Proof By Induction 1: Sum 3n+2 = n(3n+7)/2

Example of Proof by Induction 2: 3 divides 5^n-2^n

Example of Proof by Induction 3: n! <= n^n

Example of Proof by Induction 4: Increasing Sequence (Hard)

Example of a Piecewise-Defined Function

Domain of sqrt(x+1) - 1/sqrt(9-x^2)

Example of Composition of Functions

Inverse Function for f(x) = (x-2)/(x+2)

Using Synthetic Division to Evaluate a Polynomial

Fast Factorization of Polynomial

Complex Conjugate Roots of a Real Polynomial

Factoring 3x^4-2x^3+3x-2 Over The Complex Numbers

Domain and Range of 1/(x^2-2x-8)

Partial Fraction Expansion of (x^4+x^3+1)/(x(x^2+1)^2)

Domain of ln((x+1)/(x-1)) +ln(x-1)-ln(x+1)

Evaluation of 3ln(2e^2) + 2ln(3/e) - ln(72e)

Solving an Exponential Equation

Example of Exponential Growth - Two Populations

Examples of Values of Trig Functions

Examples of Inverse Trig Evaluations

Graph of y = 2 sec(pi x - pi/3)

Example of Converting to Polar Coordinates

Example of Graph of Polar Equation

Example of Proof of Trig Identity

Example of Double Angle Formulas

Trig Values for Multiples of pi/5