Algebra

Textbook – [PDF] | Prealgebra Review [PDF]

The videos below cover what is traditionally covered in Beginning and Intermediate Algebra. These courses are also often called Algebra I & II, or Elementary Algebra in high school.

Algebra Review

A quick overview of some things we will need to brush up on before we begin our Algebra class. If you feel comfortable with the basic operations related to numbers, including fractions, you may be able to skip this unit.

•  Set Notation
  
•  Various Sets of Numbers
  
•  Plot Values on a Number Line
  
•  Inequalities on a Number Line
  
•  Opposites
  
•  Absolute Value
  
•  Absolute Value: Example 1
  
•  Adding/Subtracting Integers
  
•  Minus a Negative Number
  
•  Addition/Subtraction: Example 1
  
•  Subtraction Using a Calculator
  
•  Products of Integers
  
•  Products With Many Negatives
  
•  Quotients
  
•  Multiplication/Division With Zero
  
•  Multiply/Divide on Calculator
  
•  Prime Numbers
  
•  Prime Factorization
  
•  Reduce Fractions
  
•  Improper vs. Mixed Number
  
•  Multiplying Fractions
  
•  Dividing Fractions
  
•  Multiply/Divide Fractions: Ex 1
  
•  Add/Subtract Fractions: Same Denominators
  
•  Add/Subtract Fractions: Different Denominators
  
•  Least Common Multiples (LCM)
  
•  Add/Subtract Decimals
  
•  Multiplying Decimals
  
•  Dividing Decimals
  
•  Decimals to Fractions
  
•  Fractions to Decimals
  
•  Fractions/Decimals on Calculator
  
•  Decimals vs. Percents
  
•  Percents vs Fractions
  
•  Basic Stats: Mean
  
•  Basic Stats: Median
  
•  Basic Stats: Mode
  
•  Midrange
  
•  Range
  
•  Basics of Exponents
  
•  Order of Operations
  
•  Order of Operation: Example 1
  
•  Order of Operations on Calculator
  
•  Constants, Variables, Expressions, Equations
  
•  Coefficients and Like Terms
  
•  Evaluate Variable Expressions
  
•  Distributive Property
  
•  Distributive Property: Example 1
  

Linear Equations: 1 Variable

In this unit, we look at the definition of a linear equation in one variable, as well as how to solve linear equations and inequalities. We also discuss how to solve linear equations related to real life applications.

•  Linear Equation: 1 Variable
  
•  Equation vs. Expression
  
•  Solution to 1 Variable Equation
  
•  Solution Set
  
•  Linear Equations – Addition Property
  
•  Linear Equations – Multiplication Property
  
•  One Step Linear Equations
  
•  Two Step Linear Equations
  
•  Solving Linear Equations
  
•  Linear Equations With Fractions
  
•  Linear Equation: Contradiction/Identity
  
•  Linear Examples: 1 Var. – Part 1
  
•  Linear Examples: 1 Var. – Part 2
  
•  Linear Examples: 1 Var. – Part 3
  
•  Linear Equation: How to Verify Answer
  
•  Literal Equations
  
•  Linear Equations: Word Problems
  
•  Sum of Consecutive Integers: Ex 1
  
•  Perimeter: Example 1
  
•  Complementary Angles: Ex 1
  
•  Sum of Angles: Example 1
  
•  Motion Problems: Example 1
  
•  Motion Problems: Example 2
  
•  Coins: Example 1
  
•  Percent Applications
  
•  Application of Percents: Example 1
  
•  Percent Increase/Decrease
  
•  Simple Interest
  
•  Simple Interest: Example 1
  
•  Mixture Problem: Example 1
  
•  Ratios
  
•  Proportions
  
•  Proportions: Example 1
  
•  Proportions: Example 2
  
•  Dimensional Analysis
  
•  Linear Inequalities: 1 Variable
  
•  Interval Notation
  
•  Linear Inequality: Example 1
  
•  Compound Inequality: And
  
•  Compound Inequality: Or
  

Linear Equations: 2 Variables

In this unit we take a look at different techniques for how to graph linear equations in two variables.

•  Cartesian Coordinate System
  
•  Def of Linear Equations: 2 variables
  
•  Intro to Linear Equations in 2 Variables
  
•  Graphing Linear Equations by Plotting Points
  
•  Graphing by Plotting Points: Example 1
  
•  x and y Intercepts
  
•  Graphing Lines Using Intercepts
  
•  Lines Thru Origin Using Intercepts
  
•  Standard Form of a Line
  
•  Horizontal & Vertical Lines
  
•  Intro to Slope of a Line
  
•  Slope Between Two Points
  
•  Slope Intercept Form
  
•  Graphing Using Slope Intercept Form
  
•  Slope Intercept Form: Example 1
  
•  Slope Intercept Form: Example 2
  
•  Slope Intercept Form: Example 3
  
•  Intro to Linear Functions
  
•  Evaluating Linear Functions
  
•  Linear Function Application: Ex 1
  
•  Graphing Linear Functions
  
•  Parallel Lines
  
•  Parallel Lines: Example 1
  
•  Perpendicular Lines
  
•  Perpendicular Lines: Example 1
  
•  Point Slope Form of a Line
  
•  Point Slope Form: Example 1
  
•  Point Slope Form: Example 2
  
•  Linear Inequalities – 2 Variables
  
•  Linear Inequality: Example 1
  

Exponents and Polynomials

In this unit we will begin with a brief overview of exponent properties. We will then transition into talking about polynomials – specifically, how to add, subtract, multiply, and divide polynomials.

•  Exponent Properties
  
•  Exponent Properties: Example 1
  
•  Exponent Properties: Example 2
  
•  Exponent Properties: Example 3
  
•  Exponent Properties: Example 4
  
•  Negative Exponents
  
•  Negative Exponents: Example 1
  
•  Negative Exponents: Example 2
  
•  Scientific Notation
  
•  Scientific Notation: Mult/Divide
  
•  Scientific Notation on a Calculator
  
•  Scientific Notation: Example 1
  
•  Scientific Notation: Example 2
  
•  Introduction to Polynomials
  
•  Polynomial Coefficient/Degree: Example 1
  
•  Evaluating a Polynomial
  
•  Monomials, Binomials & Trinomials
  
•  Polynomial Functions
  
•  Adding Polynomials
  
•  Subtracting Polynomials
  
•  Polynomial in Several Variables
  
•  Monomial Times a Polynomial
  
•  Binomial Times a Binomial – FOIL
  
•  FOIL – Example 1
  
•  Polynomial Times a Polynomial
  
•  Polynomial Divided by Monomial
  
•  Long Division of Polynomials
  
•  Long Division – Writing an Answer
  

Factoring and Quadratic Equations

In this unit we will look at different ways to factor polynomials, including greatest common factors, trial and error, factor by grouping, and special factoring forms. We will also focus more specifically at the end of the unit on quadratic equations.

•  Intro to Factoring Polynomials
  
•  Factoring – Greatest Common Factor
  
•  Factoring GCFs: Example 1
  
•  Factoring GCFs: Example 2
  
•  Factoring GCFs: Example 3
  
•  Factor by Grouping
  
•  Factoring Trinomials: x2+bx+c
  
•  Factoring Quadratic Trinomials: Ex1
  
•  Factoring Quadratic Trinomials: Ex2
  
•  Prime Polynomials
  
•  Factoring Trinomials: ax2+bx+c
  
•  Factoring Quadratic Trinomials: Ex3
  
•  Quadratic Trinomial – Factor by Grouping
  
•  Factor by Grouping: Example 1
  
•  Factoring Quadratic Trinomials: Ex4
  
•  Factoring – Difference of Squares
  
•  Factoring – Sum/Difference of Cubes
  
•  Factoring – General Strategy
  
•  Quadratic vs. Linear Equations
  
•  Solve Quadratic Equations by Factoring
  
•  Solve Quadratic by Factoring – Example 1
  
•  Solve Quadratic by Factoring – Example 2
  
•  Solve Quadratic by Factoring – Example 3
  
•  Solve Quadratic by Factoring – Example 4
  
•  Solve Quadratic by Factoring – Example 5
  
•  Solve Quadratic by Factoring – Example 6
  
•  Quadratic Equation With Fractions
  
•  Finding Quadratic With Given Solutions
  
•  Finding Quadratic With Given Solutions: Ex1
  
•  Quadratic Functions
  
•  Evaluate Quadratic Functions: Ex 1
  
•  Evaluate Quadratic Functions: Ex 2
  
•  Finding x Such That f(x)=0
  
•  Graphs of Quadratics – Parabolas
  
•  Solving f(x)=c Using Calculator
  

Absolute Value Functions

In this chapter, we study how to solve equations that contain absolute values. Extra caution must be taken when an equation contains absolute values, and one absolute value equation often requires us to solve multiple different linear or quadratic equations.

•  Linear Equation: 1 Variable
  
•  Equation vs. Expression
  
•  Solution to 1 Variable Equation
  
•  Solution Set
  
•  Solving Linear Equations
  
•  Linear Equations With Fractions
  
•  Linear Equation: Contradiction/Identity
  
•  Linear Examples: 1 Var. – Part 1
  
•  Linear Examples: 1 Var. – Part 2
  
•  Linear Examples: 1 Var. – Part 3
  
•  Linear Equation: How to Verify Answer
  
•  Absolute Value Equations
  
•  Solving Abs Value Equations: Example 1
  
•  Solving Abs Value Equations: Example 2
  
•  Solving Abs Value Equations: Example 3
  
•  Solving Abs Value Equations: Example 4
  
•  Linear Inequalities: 1 Variable
  
•  Interval Notation
  
•  Linear Inequality: Example 1
  
•  Compound Inequality: And
  
•  Compound Inequality: Or
  
•  Cartesian Coordinate System
  
•  Intro to Linear Equations in 2 Variables
  
•  Graphing Linear Equations by Plotting Points
  
•  Graphing by Plotting Points: Example 1
  
•  x and y Intercepts
  
•  Graphing Lines Using Intercepts
  
•  Lines Thru Origin Using Intercepts
  
•  Standard Form of a Line
  
•  Horizontal & Vertical Lines
  
•  Intro to Slope of a Line
  
•  Slope Between Two Points
  
•  Slope Intercept Form
  
•  Graphing Using Slope Intercept Form
  
•  Slope Intercept Form: Example 1
  
•  Graphs of Absolute Value Functions
  
•  How to Graph Abs Value Functions: Part 1
  
•  How to Graph Abs Value Functions: Part 2
  
•  Graph Abs Value Using Calculator
  
•  Abs Value Domain & Range
  
•  Abs Value Domain & Range: Example 1
  
•  Absolute Value Graph: Example 1
  
•  Absolute Value Graph: Example 2
  

Rational Functions

Many algebra courses devote an entire unit to rational expressions. We will cover all the main topics you need to know regarding rational expressions, functions, and equations.

•  Introduction to Rational Expressions
  
•  Evaluating Rational Expressions
  
•  Rational Expressions – Undefined Values
  
•  Simplifying Rational Expressions
  
•  Rational Expressions – Opposite Factors
  
•  Domain of a Rational Function
  
•  Domain of a Rational Function: Example 1
  
•  Caution: Rational Function Domain
  
•  Multiplying Rational Expressions
  
•  Multiplying Rational Expressions: Example 1
  
•  Dividing Rational Expressions
  
•  Caution: Dividing Rational Expressions
  
•  Dividing Rational Expressions: Example 1
  
•  Dividing Two Rational Functions
  
•  Add Rational Expressions: Same Denom
  
•  Subtract Rational Expressions: Same Denom
  
•  Subtract Rational Expressions: Example 1
  
•  Add/Subtract Rat Expression: Opposite Denom
  
•  Simplifying Complex Fractions
  
•  Simplifying Complex Fractions: Example 1
  
•  Solving Rational Equations
  
•  Solving Rational Equations: Example 1
  
•  Solving Rational Equations: Example 2
  
•  Caution: LCDs for Rational Equations vs Expressions
  
•  Literal Equations
  
•  Applications of Rational Equations
  
•  Applications of Rational Equations: Reciprocals
  
•  Applications of Rational Equations: Work Rate Problem
  
•  Applications of Rational Equations: Motion Problems
  
•  Direct and Indirect Variation
  

Systems of Linear Equations

A system of equations is a combination of two or more equations. A solution to a system of equations must satisfy all of the equations at the same time. In this unit we discuss different methods to solve systems of equations.

•  Systems of Linear Equations
  
•  Solving Linear Systems by Graphing
  
•  Solving Linear Systems by Substitution
  
•  Solving Linear Systems by Addition Method
  
•  Solving Systems: Mixed Examples
  
•  Systems of Equations: Contradictions & Identities
  
•  App of Systems of Equations: Interest
  
•  App of Systems of Equations: Mixture Problems
  
•  Systems of Equations: 3 Variables
  
•  Systems of Linear Inequalities
  

Radical Equations

Radicals are a common algebra operation we see quite frequently. Common types of radicals include “square roots” and “cube roots”. In this unit we explore radicals and how to solve equations that include radicals.

•  Square Roots
  
•  nth Roots