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Precalculus Algebra and Trigonometry: Course Competencies and Study Guide

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Algebraic Expressions

  • Introduction to Algebraic Expressions
    05:09
  • Evaluating Algebraic Expressions
    03:11
  • Guided course
    Introduction to Exponents
    07:07

Exponents

  • Zero and Negative Rules
    6:37
  • Power Rules
    5:50
  • Simplifying Exponential Expressions
    6:39

Polynomials Intro

  • Adding and Subtracting Polynomials
    03:34
  • Standard Form of Polynomials
    05:16
  • Introduction to Polynomials
    05:13

Multiplying Polynomials

  • Multiply Polynomials Using the Distributive Property
    04:15
  • Special Products - Square Formulas
    04:14
  • Special Products - Cube Formulas
    03:41

Factoring Polynomials

  • Factor by Grouping
    04:36
  • Introduction to Factoring Polynomials
    07:30
  • Factor Using Special Product Formulas
    6:29

Rational Exponents

  • Rational Exponents
    04:06

Rationalize Denominator

  • Rationalizing Denominators
    2:58
  • Rationalizing Denominators Using Conjugates
    03:42

Linear Equations

  • Guided course
    Solving Linear Equations with Fractions
    04:02
  • Guided course
    Introduction to Solving Linear Equations
    07:48
  • Guided course
    Categorizing Linear Equations
    06:00

Intro to Quadratic Equations

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

The Square Root Property

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

Completing the Square

  • Guided course
    Solving Quadratic Equations by Completing the Square
    06:24

The Quadratic Formula

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

Complex Numbers

  • Guided course
    Introduction to Complex Numbers
    03:31
  • Guided course
    Dividing Complex Numbers
    04:22
  • Guided course
    Complex Conjugates
    05:33

Rational Equations

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

Choosing a Method to Solve Quadratics

  • Guided course
    Choosing a Method to Solve Quadratics
    04:03

Linear Inequalities

  • Guided course
    Interval Notation
    05:18
  • Guided course
    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

Two-Variable Equations

  • Equations with Two Variables
    05:28
  • Graphing Intercepts
    04:08
  • Graphing Equations of Two Variables by Plotting Points
    4:29

Lines

  • Standard Form of Line Equations
    05:39
  • Types of Slope
    5:17
  • Point-Slope Form
    05:46

Circles

  • Circles in Standard Form
    5:18
  • Circles in General Form
    06:20
  • Circles in Standard Form Example 1
    03:40

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

Quadratic Functions

  • Guided course
    Properties of Parabolas
    07:42
  • Guided course
    Vertex Form
    08:07
  • Guided course
    Example 1
    07:11

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

Introduction to Rational Functions

  • Guided course
    Intro to Rational Functions
    6:04

Asymptotes

  • Guided course
    Determining Horizontal Asymptotes
    4:48
  • Guided course
    Introduction to Asymptotes
    6:24
  • Guided course
    Determining Vertical Asymptotes
    3:12

Graphing Rational Functions

  • Guided course
    Example 1
    10:18
  • Guided course
    How to Graph Rational Functions
    8:19
  • Guided course
    Example 1
    3:08

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

The Number e

  • Guided course
    The Number e
    4:47

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

Complementary and Supplementary Angles

  • Solving Problems with Complementary & Supplementary Angles
    2:28
  • Example 1
    3:04
  • Intro to Complementary & Supplementary Angles
    3:35

Radians

  • Converting between Degrees & Radians
    5:04

Trigonometric Functions on Right Triangles

  • Introduction to Inverse Trig Functions
    4:28
  • Fundamental Trigonometric Identities
    5:32
  • Introduction to Trigonometric Functions
    6:04

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

Cofunctions of Complementary Angles

  • Using Cofunction Identities to Solve Equations
    4:42
  • Cofunction Identities
    6:30

Solving Right Triangles

  • Finding Missing Side Lengths
    4:18
  • Example 2
    3:22
  • Finding Missing Angles
    5:13

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

Reciprocal Trigonometric Functions on the Unit Circle

  • Guided course
    Secant, Cosecant, & Cotangent on the Unit Circle
    3:23

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 Secant and Cosecant Functions

  • Graphs of Secant and Cosecant Functions
    6:22

Graphs of Tangent and Cotangent Functions

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

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

Evaluate Composite Trig Functions

  • Guided course
    Example 1
    1:58
  • Guided course
    Example 3
    3:30
  • Guided course
    Example 2
    1:48

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

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

Area of SAS & ASA Triangles

  • Calculating Area of SAS Triangles Example 1
    5:30
  • Calculating Area of ASA Triangles
    4:30
  • Calculating Area of SAS Triangles
    4:02

Polar Coordinate System

  • Guided course
    Determining Different Coordinates for the Same Point Example 2
    3:00
  • Guided course
    Intro to Polar Coordinates Example 1
    2:13
  • Guided course
    Intro to Polar Coordinates
    5:32

Convert Points Between Polar and Rectangular Coordinates

  • Guided course
    Convert Points from Rectangular to Polar Example 1
    2:21
  • Guided course
    Convert Points from Polar to Rectangular
    6:17
  • Guided course
    Convert Points from Rectangular to Polar
    6:58

Convert Equations Between Polar and Rectangular Forms

  • Guided course
    Convert Equations from Polar to Rectangular
    6:50
  • Guided course
    Convert Equations from Rectangular to Polar Example 1
    3:28
  • Guided course
    Convert Equations from Polar to Rectangular Example 2
    3:03

Graphing Other Common Polar Equations

  • Guided course
    Lemniscates
    02:33
  • Guided course
    Introduction to Common Polar Equations
    3:47
  • Guided course
    Limacons Example 2
    2:52

Graphing Complex Numbers

  • How To Plot Complex Numbers
    03:47

Polar Form of Complex Numbers

  • Converting Complex Numbers from Polar to Rectangular Form
    03:58
  • Complex Numbers In Polar Form
    04:47

Products and Quotients of Complex Numbers

  • Quotients of Complex Numbers in Polar Form
    03:40
  • Products of Complex Numbers in Polar Form
    04:46

Powers of Complex Numbers (DeMoivre's Theorem)

  • Powers Of Complex Numbers In Polar Form (DeMoivre's Theorem) Example 1
    03:05
  • Powers Of Complex Numbers In Polar Form (DeMoivre's Theorem)
    03:41
  • Complex Roots
    07:37

Geometric Vectors

  • Multiplying Vectors By Scalars
    05:05
  • Multiplying Vectors By Scalars Example 1
    03:12
  • Adding Vectors Geometrically
    05:29

Vectors in Component Form

  • Finding Magnitude of a Vector Example 1
    02:26
  • Algebraic Operations on Vectors Example 1
    03:11
  • Position Vectors & Component Form Example 1
    01:36

Direction of a Vector

  • Finding Direction of a Vector Example 1
    04:19
  • Finding Direction of a Vector
    05:13
  • Finding Components from Direction and Magnitude
    04:55

Unit Vectors and i & j Notation

  • Unit Vector in the Direction of a Given Vector Example 1
    02:17
  • i & j Notation
    06:01
  • Unit Vector in the Direction of a Given Vector Example 2
    05:21

Dot Product

  • Introduction to Dot Product
    5:40
  • Find the Angle Between Vectors
    04:33

Introduction to Conic Sections

  • Geometries from Conic Sections
    3:08

Parabolas

  • Parabolas as Conic Sections
    05:33
  • Horizontal Parabolas
    05:28
  • Parabolas as Conic Sections Example 1
    07:12

Ellipses: Standard Form

  • Graph Ellipses at Origin
    05:12
  • Graph Ellipses NOT at Origin
    04:50
  • Foci and Vertices of an Ellipse
    05:30

Hyperbolas at the Origin

  • Graph Hyperbolas at the Origin
    04:20
  • Graphing Hyperbolas at the Origin Example 1
    03:58
  • Introduction to Hyperbolas
    06:15

Hyperbolas NOT at the Origin

  • Graph Hyperbolas NOT at the Origin
    05:59

Graphing Parametric Equations

  • Introduction to Parametric Equations
    04:47

Eliminate the Parameter

  • Equations with Trigonometric Functions Example 3
    04:39
  • Eliminating the Parameter
    05:59
  • Equations with Trigonometric Functions
    04:11

Writing Parametric Equations

  • Parameterizing Equations
    08:02
  • Equations of Circles & Ellipses
    06:03
  • Parameterizing Equations Example 1
    04:26

Two Variable Systems of Linear Equations

  • Example 2
    3:31
  • Solving Systems of Equations - Elimination
    6:48
  • Introduction to Systems of Linear Equations
    4:27

Introduction to Matrices

  • Example 1
    13:06
  • Guided course
    Example 2
    11:24
  • Introduction to Matrices
    4:35

Determinants and Cramer's Rule

  • Determinants of 2×2 Matrices
    4:36
  • Determinants of 3×3 Matrices
    7:25
  • Cramer's Rule - 2 Equations with 2 Unknowns
    6:54

Graphing Systems of Inequalities

  • Systems of Inequalities
    6:19
  • Example 1
    3:55
  • Example 2
    4:37

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

Factorials

  • Guided course
    Factorials
    05:22

Combinatorics

  • Guided course
    Permutations of Non-Distinct Objects
    06:37
  • Guided course
    Introduction to Permutations
    07:11
  • Guided course
    Permutations vs. Combinations
    03:18

Probability

  • Guided course
    Probability of Non-Mutually Exclusive Events Example
    02:57
  • Guided course
    Complementary Events
    04:23
  • Guided course
    Introduction to Probability Example
    03:59