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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  
Fractions Review (Multiplication and Division)
Multiplication Example, Division Example
Fractions Review (Addition and Subtraction) 

Number Line and Absolute Value Review

Positive and Negative Numbers Review

Order of Operations

Lecture,   Examples With Fractions,   Example
Properties of Real Numbers


2. Expressions, Linear Equations and Inequalities in One Variable

Simplifying Expressions

Examples, Examples

Solving Linear Equations

Lecture and Examples

Clearing denominators:  Examples

Solving Formulas


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

Systems of Equations: 
       Solve by Substitution Method

Lecture, Examples
Systems of Equations: 
      Solve by Addition (Elimination) Method

Lecture Examples
Distance, Rate and Time; Number; Mon

Distance/Rate/Time ExampleNumber, Rectangle and Money ExamplesMore Examples
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
Polynomials Introduction
Add/Subtract Polynomials
Multiplying Polynomials
Examples, Example, Example, Example
Division of Polynomial by Monomial
Long Division of Polynomials
Lecture, Example, Example

Synthetic Division



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
Example, Example:  Difference of Squares
Example, Example:  Perfect Square Trinomials
Factoring Summary

Solving Equations By Factoring

Examples, Examples Examples

7. Rational Expressions

Defining Rational Expressions

Lecture, Examples
Multiplication and Division of Rational Expressions
Example (with opposite factors)
Addition and Subtraction of Rational Expressions

Example: Like Denominators
Example:  Unlike Denominators

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)
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 
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

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
Simplifying Radicals


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


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: 

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


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

Compound Interest: Examples

Logarithmic Functions 

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


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

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: