Back to my Home Page

Video Tutorials for Introductory and Intermediate Algebra

These videos are arranged by topic following the chapter outline from Blitzer's combination Introductory and Intermediate Algebra textbook.  I screened many YouTube videos and selected the ones I thought had the best combination of the following criteria:
    1.  clarity and quality of presentation  
    2.  same methods/techniques and types of examples we use in our class   

The highlighted videos are the the ones I made and want my students to be able to identify.  

These video links will take you to a website that is not affiliated with Cuesta College.  Cuesta is not responsible for the content or the functionality of these links.
 

1. Review:  Fractions, Real Numbers, Order of Operations

Primes,  LCM  
 		 Lecture
Fractions Review (Multiplication and Division)
 		 Multiplication Example, Division Example
Fractions Review (Addition and Subtraction) 
 		 Lecture/Examples

Number Line and Absolute Value Review
 

 Lecture
Positive and Negative Numbers Review
 		 Examples 

Order of Operations
 

 Lecture,   Examples With Fractions,   Example
Properties of Real Numbers
 		 Lecture

 

2. Expressions, Linear Equations and Inequalities in One Variable

Simplifying Expressions
 

 Examples, Examples

Solving Linear Equations
 

 Lecture and Examples

Clearing denominators:  Examples
Solving Formulas
 		 Examples
Applications

Lecture/Examples 

Number Problems:  Examples

Geometry Problems:  Rectangle, Triangle, Triangle

Consecutive Integers:  Lecture, Example, Example

Solving Linear Inequalities

*Note:  This is the first section of chapter 9 in Blitzer, I copied it here also because some texts put it here.

 Example with Graph, Examples

                

3. Linear Equations and Inequalities in Two Variables:  Equations of Lines

Cartesian Coordinate System
 		 Lecture,   Lecture
Graphing Linear Equations
 
Lecture: Table of Values and Intercepts
Example:  Table of Values
Example:  Intercepts
 
Slope-Intercept Form
 		 Lecture:  Slope and Slope-Intercept Form
Examples: Slope Formula
Examples:  Graphing given y = mx + b
Examples, Examples:  Rewrite in y = mx + b form, then graph
 
Point-Slope Form

 

 Lecture Part 1:  Point and Slope, Two Points
Lecture Part 2: Point and Parallel/Perpendicular Line
Lecture,   Example,
3 Examples:  given 2 points, parallel line, perpendicular line
 
Graphing Linear Inequalities
*Note:  This is the last section of chapter 9 in Blitzer, I copied it here also because some texts put it here.		 Lecture, Examples

 

4. Systems of Linear Equations and Inequalities in Two Variables

Systems of Equations: 
        Solve by Graphing Method
 		 Lecture
Systems of Equations: 
       Solve by Substitution Method
 		 Lecture, Examples
Systems of Equations: 
      Solve by Addition (Elimination) Method
 		 Lecture,  Examples
Applications: 
Distance, Rate and Time; Number; Money
 		 Distance/Rate/Time Example,  Number, Rectangle and Money Examples,  More Examples
Applications: 
Interest and Mixture Problems
 		 Interest/Mixture Examples,    Mixture Example

Systems of Three-Variable Equations


 		 |
Example:  Consistent System
Example: Consistent System
Lecture:  Consistent System
Example: Inconsistent System
 

Systems of Linear Inequalities

*Note:  This is the last section of chapter 9 in Blitzer, I copied it here also because some texts put it here.

 		Examples, Example

 

5. Exponents and Polynomials

Integer Exponents I
 		 Lecture,   Example
Integer Exponents II
 		 Lecture, Example, Example
Scientific Notation
 		 Lecture/Examples
Polynomials Introduction
 		 Lecture
Add/Subtract Polynomials
 		 Example  
Multiplying Polynomials
 		 Examples, Example, Example, Example
Division of Polynomial by Monomial
 		 Example
Long Division of Polynomials
 		 Lecture, Example, Example

Synthetic Division
 

 		Lecture,  Example

 

6. Factoring Polynomials

Factoring out GCF
 		 Example, Example
Factoring by Grouping
 		 Example, Example
Factoring Trinomials By Trial and Error
 		 Lecture/Examples,   Not Factorable Example, Example, Example
Factoring Perfect Square Trinomials and Difference of Squares
 		 Lecture/Examples 
Example, Example:  Difference of Squares
Example, Example:  Perfect Square Trinomials
 
Factoring Summary
 		 Lecture/Examples

Solving Equations By Factoring
 

 		Examples, Examples , Examples



7. Rational Expressions

Defining Rational Expressions
 

 Lecture, Examples
Multiplication and Division of Rational Expressions
 		 Lecture
Example,
Example (with opposite factors)
Addition and Subtraction of Rational Expressions
 
Example: Like Denominators
Example:  Unlike Denominators
Lecture,
Example
 
Complex Fractions
 		 Method 1:  Example, Example, Example
Method 2:  Examples, Examples, Example
 
Solving Rational Equations
 		 Lecture/Examples (ignore the graphing calculator part)
Example, Example
 
Applications of Rational Expressions
 		 Distance/Rate/Time:  Example, Example
Current/Wind:  Example
Work:  Example, Example, Example  (method 1:   t/rate1 + t/rate2 = 1)
 
Variation
 		 Direct Variation:  Lecture/Examples
Inverse Variation:  Lecture/Examples
Jointly and Combined:  Example, Example
 



 

8. Functions

Functions and Function Notation
 

  Lecture:  Part 1, Part 2, Part 3, Part 4
Algebra of Functions 
 		 Examples, 
Examples
Composition of Functions
 		 Composition of Functions:  Lecture,  Examples
 
Inverse Functions Inverse Functions:  Lecture, Lecture
   One-to-One Functions:  Lecture
   Find Inverse of Given Function:  Examples, Examples




9. Inequalities

Linear Inequalities
 

  Example with Graph, Examples
 Interval Notation:   Lecture,  Lecture
Compound Inequalities 
 		 Lecture, Examples
Absolute Value Equations and Inequalities
 		 Equations:  Example,   Example,   Example ,   Example(2 absolute values)

Inequalities:  Examples, Examples
 
Linear Inequalities in 2 Variables Lecture, Examples

Systems:   Examples, Example


 

10. Radicals

Introduction to Radicals

 
 

 Square Roots, Cube Roots: Lecture
Square Roots:  Examples 

Rational Exponents
 

 Lecture,   Lecture ,  Examples ,

Simplifying Expressions with Rational Exponents:
Examples,  Examples
Simplifying Radicals

 

 Product/Quotient Rules for Radicals:  Lecture,    
Simplifying Square Roots:  Lecture,  
Simplifying Cube Roots: Lecture

Examples  
 

Addition and Subtraction of Radicals

Multiplication of Radicals
 

Example:  Addition/Subtraction

Example:  Multiplication
Example:  Multiplication and Division
Rationalizing Denominators
 

Example ,  Example,  Example

Solving Equations with Radicals

 		 One Square Root: Lecture,
Two Square Roots:  Examples,  
Examples   

Complex Numbers
 

 Introduction:  Lecture
Operations and Powers of i :  Lecture
Addition/Subtraction: Examples, Examples
Multiplication/Division:  Examples
 

 

11. Quadratic Equations and Functions

Square Root Property

 

 Examples , Examples
Completing the Square

 

 Lecture:  Part 1 , Part 2 , Part 3

The Quadratic Formula
 

Two real solutions:  Lecture
No real solutions, Discriminant:  Lecture

Derivation of Formula:  Version 1,   Version 2

3 Examples ,  Example ,   Example

Applications of Quadratic Equations


 

Example:  Rectangle
Examples:  Number, Rectangle, Right Triangle
 Example, Example:  Projectile

Equations in Quadratic Form

  		 higher powers:  Example ,  Example
square roots:  Example
rational exponents:  Example , Example
negative exponents:  Example
Quadratic Functions, Parabolas
 		 Vertex Form ( y = a(x-h)^2+k):  Lecture/Examples

General Form (y = ax^2 + bx + c): 
    Method 1.  Complete the Square:  Example, Example*, Example
    Method 2.  Vertex Formula:  Example, Example

Max/Min Applications:  2nd half of Example* above, Examples



12. Exponential and Logarithmic Functions

Exponential Functions
Lecture,  Lecture
Compound Interest: Examples
 

Logarithmic Functions 
 

 Lecture,
Exponential Form to Log Form:  Examples
Log Form to Exponential Form:  Examples
Graph:  Example

Properties of Logarithms


 		 Expanding logs:  Examples
Condensing logs:  Examples, Examples
Both:  Examples
Change of Base:   Proof/Examples , Proof/Examples

Common Logarithms, Natural Logarithms
 

 Lecture

Logarithmic and Exponential Equations
 
Exponential Equations: 
    Using Common Base:  Examples
    Using Logarithms: Examples,   Examples
    Both Methods:  Examples
Logarithmic Equations:  Examples, Examples
 

Applications of  Exponential and Log Equations

 

 		 Compound Interest: Example  
Exponential Growth/Decay:  Examples



14. Sequences, Series, The Binomial Theorem
 

Sequences
 		 General Sequences:   Lecture
Find first 4 terms, find nth term:  Examples

Special Sequences
  1. Arithmetic Sequences:  Lecture
  2. Geometric Sequences:  Lecture
 
Series, Sigma Notation
 
General Series:  Lecture

Special Cases
  1. Arithmetic Series:  Lecture
  2. Geometric Series:  Lecture
 
Binomial Theorem and Pascal's Triangle
 		 Expanding Binomials Using Pascal's Triangle: 
      Lecture