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College Algebra Final Exam Review: Comprehensive Study Notes

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Complex Numbers

  • Dividing Complex Numbers
    04:22
  • Introduction to Complex Numbers
    03:31
  • Adding and Subtracting Complex Numbers
    03:18

The Imaginary Unit

  • Square Roots of Negative Numbers
    05:02

Powers of i

  • Higher Powers of i
    05:10
  • Powers of i
    04:10

Intro to Quadratic Equations

  • Introduction to Quadratic Equations
    05:35
  • Solving Quadratic Equations by Factoring
    06:08

The Square Root Property

  • Imaginary Roots with the Square Root Property
    02:20
  • Solving Quadratic Equations by the Square Root Property
    06:12

Completing the Square

  • Solving Quadratic Equations by Completing the Square
    06:24

The Quadratic Formula

  • Solving Quadratic Equations Using The Quadratic Formula
    06:36
  • The Discriminant
    04:11

Choosing a Method to Solve Quadratics

  • Choosing a Method to Solve Quadratics
    04:03

Lines

  • Point-Slope Form
    05:46
  • Graphing Lines in Slope-Intercept Form
    02:35
  • Types of Slope
    05:17

Linear Inequalities

  • Interval Notation
    05:18
  • Linear Inequalities with Fractions & Variables on Both Sides
    03:42
  • Linear Inequalities
    06:07

Graphs and Coordinates

  • Graphs and Coordinates - Example
    02:16
  • Graphs & the Rectangular Coordinate System
    05:10

Function Operations

  • Adding & Subtracting Functions
    5:56
  • Adding & Subtracting Functions Example 1
    4:46
  • Multiplying & Dividing Functions
    7:24

Function Composition

  • Evaluating Composed Functions
    4:26
  • Decomposition of Functions Example 1
    1:46
  • Domain Restrictions of Composed Functions
    3:51

Quadratic Functions

  • Converting Standard Form to Vertex Form
    04:34
  • Vertex Form
    08:07
  • Example 2
    7:49

Graphing Polynomial Functions

  • Example 1
    09:43
  • Identifying Intervals of Unknown Behavior
    05:01
  • Graphing Polynomial Functions
    05:25

Zeros of Polynomial Functions

    Introduction to Rational Functions

    • Intro to Rational Functions
      6:04

    Asymptotes

    • Introduction to Asymptotes
      6:24
    • Determining Horizontal Asymptotes
      4:48
    • Determining Removable Discontinuities (Holes)
      3:34

    Graphing Rational Functions

    • Graphing Rational Functions Using Transformations
      5:31
    • Example 1
      3:08
    • Example 1
      10:18

    Sequences

    • Example 2
      4:19
    • Example 1
      5:52
    • Introduction to Sequences
      8:22

    Arithmetic Sequences

    • Example 2
      7:00
    • Example 1
      2:35
    • Arithmetic Sequences - Recursive Formula
      6:40

    Geometric Sequences

    • Geometric Sequences - General Formula
      4:45
    • Geometric Sequences - Recursive Formula
      4:18

    Factorials

    • Factorials
      5:22

    Combinatorics

    • Permutations vs. Combinations
      3:18
    • Fundamental Counting Principle
      4:04
    • Permutations of Non-Distinct Objects
      6:37

    Probability

    • Probability of Non-Mutually Exclusive Events Example
      2:57
    • Probability of Multiple Independent Events
      5:54
    • Probability of Non-Mutually Exclusive Events
      5:14

    Introduction to Logarithms

    • Evaluate Logarithms
      5:14
    • Logarithms Introduction
      7:30
    • The Natural Log
      2:51

    Properties of Logarithms

    • Change of Base Property
      5:36
    • Product, Quotient, and Power Rules of Logs
      3:49
    • Expand & Condense Log Expressions
      4:22

    Solving Exponential and Logarithmic Equations

    • Solving Exponential Equations Using Logs
      5:47
    • Solving Exponential Equations Using Like Bases
      4:46
    • Solving Logarithmic Equations
      5:02