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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; Mon
ey

 
Distance/Rate/Time ExampleNumber, Rectangle and Money ExamplesMore 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
 

LectureExample

 

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:   LectureLecture
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


 

ExampleRectangle
Examples:  Number, Rectangle, Right Triangle
Example, ExampleProjectile

Equations in Quadratic Form

 
higher powers:  ExampleExample
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


LectureLecture
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