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Pre-Calculus Math (MATH-2412) Syllabus and Course Structure

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Intro to Functions & Their Graphs

  • Finding the Domain and Range of a Graph
    5:10
  • Verifying if Equations are Functions
    5:38
  • Relations and Functions
    5:20

Common Functions

  • Graphs of Common Functions
    5:57

Transformations

  • Reflections of Functions Example 1
    01:09
  • Reflections of Functions
    5:00
  • Graphs of Shifted & Reflected Functions Example 1
    2:49

Function Operations

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

Function Composition

  • Decomposition of Functions
    4:07
  • Function Composition
    4:56
  • Domain Restrictions of Composed Functions
    3:51

Understanding Polynomial Functions

  • Guided course
    Introduction to Polynomial Functions
    06:04
  • Guided course
    Finding Zeros & Their Multiplicity
    03:42
  • Guided course
    End Behavior of Polynomial Functions
    06:08

Graphing Polynomial Functions

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

Rational Equations

  • Guided course
    Restrictions on Rational Equations
    05:21
  • Guided course
    Introduction to Rational Equations
    05:56

Introduction to Exponential Functions

  • Guided course
    Exponential Functions
    6:13

Graphing Exponential Functions

  • Guided course
    Transformations of Exponential Graphs Example 1
    4:12
  • Guided course
    Graphing Exponential Functions Example 1
    3:58
  • Guided course
    Graphs of Exponential Functions
    5:46

Introduction to Logarithms

  • Guided course
    Logarithms Introduction
    7:30
  • Guided course
    The Natural Log
    2:51
  • Guided course
    Evaluate Logarithms
    05:15

Graphing Logarithmic Functions

  • Guided course
    Transformations of Logarithmic Graphs
    4:37
  • Guided course
    Graphing Logarithmic Functions
    4:30
  • Guided course
    Graphs of Logarithmic Functions
    5:26

Properties of Logarithms

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

Solving Exponential and Logarithmic Equations

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

Angles in Standard Position

  • Drawing Angles in Standard Position
    5:50
  • Example 1
    3:59

Coterminal Angles

  • Example 1
    3:51
  • Guided course
    Coterminal Angles
    04:46

Radians

  • Converting between Degrees & Radians
    5:04

Defining the Unit Circle

  • Guided course
    Introduction to the Unit Circle
    06:11

Trigonometric Functions on the Unit Circle

  • Guided course
    Sine, Cosine, & Tangent on the Unit Circle
    6:34

Common Values of Sine, Cosine, & Tangent

  • Guided course
    Example 1
    6:04
  • Guided course
    Sine, Cosine, & Tangent of 30°, 45°, & 60°
    5:08

Reference Angles

  • Guided course
    Reference Angles on the Unit Circle
    5:31
  • Guided course
    Coterminal Angles on the Unit Circle
    3:47
  • Guided course
    Example 1
    3:03

Graphs of the Sine and Cosine Functions

  • Amplitude and Reflection of Sine and Cosine
    5:05
  • Example 1
    2:18
  • Graph of Sine and Cosine Function
    5:53

Graphs of Tangent and Cotangent Functions

  • Introduction to Cotangent Graph
    5:37
  • Example 1
    3:40
  • Introduction to Tangent Graph
    5:43

Graphs of Secant and Cosecant Functions

  • Graphs of Secant and Cosecant Functions
    6:22

Phase Shifts

  • Phase Shifts
    6:31
  • Example 1
    3:42

Inverse Sine, Cosine, & Tangent

  • Guided course
    Inverse Tangent
    3:17
  • Guided course
    Example 1
    1:08
  • Guided course
    Example 3
    1:25

Linear Trigonometric Equations

  • Guided course
    Example 3
    3:29
  • Guided course
    Example 2
    2:17
  • Guided course
    Introduction to Trig Equations
    4:25

Introduction to Trigonometric Identities

  • Guided course
    Simplifying Trig Expressions
    6:36
  • Guided course
    Example 1
    2:20
  • Guided course
    Example 4
    5:18

Sum and Difference Identities

  • Guided course
    Sum and Difference of Tangent
    4:47
  • Guided course
    Sum and Difference of Sine & Cosine Example 3
    2:42
  • Guided course
    Sum and Difference of Sine & Cosine
    06:14

Double Angle Identities

  • Guided course
    Double Angle Identities
    5:06
  • Guided course
    Double Angle Identities Example 1
    2:33
  • Guided course
    Double Angle Identities Example 2
    2:26

Solving Trigonometric Equations Using Identities

  • Guided course
    Solve Trig Equations Using Identity Substitutions
    4:42

Special Right Triangles

  • 45-45-90 Triangles
    04:39
  • Common Trig Functions For 30-60-90 Triangles
    6:24
  • 30-60-90 Triangles
    5:35

Law of Sines

  • Solving SSA Triangles ("Ambiguous" Case) Example 1
    4:02
  • Solving SSA Triangles ("Ambiguous" Case)
    9:50
  • Solving SAA & ASA Triangles
    7:23

Law of Cosines

  • Solving SAS & SSS Triangles
    7:50
  • Intro to Law of Cosines
    4:35

Sequences

  • Example 1
    05:52
  • Example 2
    04:19
  • Introduction to Sequences

Arithmetic Sequences

  • Example 1
    02:35
  • Arithmetic Sequences - General Formula
    05:17
  • Example 2
    07:00

Geometric Sequences

  • Geometric Sequences - General Formula
    04:45
  • Geometric Sequences - Recursive Formula
    04:18