Beginning Algebra

1. Pre-Algebra Review

• 1.1 Introduction
  • 1.1.1 Beginning Algebra
  • 1.1.2 Review of Arithmetic: Addition and Subtraction
  • 1.1.3 Review of Arithmetic: Multiplication and Division
  • 1.1.4 Top Ten List of Mistakes

• 1.2 Factors and Fractions
  • 1.2.1 Factors and Primes
  • 1.2.2 Greatest Common Factor and Least Common Multiples
  • 1.2.3 Introduction to Fractions
  • 1.2.4 Multiplying Fractions
  • 1.2.5 Dividing Fractions
  • 1.2.6 Adding Fractions
  • 1.2.7 Subtracting Fractions
  • 1.2.8 Mixed Numbers
  • 1.2.9 Adding and Subtracting Mixed Numbers
  • 1.2.10 Multiplying and Dividing Mixed Numbers

• 1.3 Decimals
  • 1.3.1 Decimal Numbers
  • 1.3.2 Multiplying and Dividing Decimals
  • 1.3.3 Percent
  • 1.3.4 Conversion between Fractions, Percents, and Decimals

2. Foundations of Algebra

• 2.1 The Real Number System
  • 2.1.1 Real Numbers
  • 2.1.2 Ordering Real Numbers
  • 2.1.3 Arithmetic on the Number Line
  • 2.1.4 Multiplying Real Numbers
  • 2.1.5 Multiplying a Negative by a Negative: The Why
  • 2.1.6 Dividing Real Numbers
  • 2.1.7 Order of Operations
  • 2.1.8 Properties of Real Numbers

• 2.2 Exponents, Exponential Notation, and Scientific Notation
  • 2.2.1 Introduction to Exponents
  • 2.2.2 Evaluating Exponential Expressions
  • 2.2.3 Applying the Rules of Exponents
  • 2.2.4 Evaluating Expressions with Negative Exponents
  • 2.2.5 Converting between Decimal and Scientific Notation

• 2.3 Algebraic Expressions and the Language of Algebra
  • 2.3.1 Algebraic Expressions
  • 2.3.2 Introduction to Word Problems

3. Solving Equations

• 3.1 Introduction to Solving Equations
  • 3.1.1 Equations
  • 3.1.2 Addition Property of Equality
  • 3.1.3 Multiplication Property of Equality

• 3.2 Further Techniques for Solving Equations
  • 3.2.1 Solving Equations with the Variable on One Side
  • 3.2.2 Solving Equations with the Variable on Both Sides
  • 3.2.3 Equality or Identity?
  • 3.2.4 Equivalent Equations and Equations with No Solution

4. Linear Equations and Inequalities

• 4.1 Formulas and Word Problems
  • 4.1.1 Formulas
  • 4.1.2 Formulas: Temperature Conversion and Rate
  • 4.1.3 Ratios and Proportions
  • 4.1.4 More Ratios and Proportions
  • 4.1.5 Finding a Perimeter
  • 4.1.6 Solving a Linear Geometry Problem
  • 4.1.7 Solving for Constant Velocity
  • 4.1.8 Solving a Business Problem
  • 4.1.9 Solving a Mixture Problem
  • 4.1.10 Solving an Investment Problem
  • 4.1.11 Solving for Consecutive Numbers
  • 4.1.12 Finding an Average

• 4.2 Inequalities in One Variable
  • 4.2.1 Introduction to Inequalities
  • 4.2.2 Solving Inequalities
  • 4.2.3 Solving Word Problems with Inequalities

• 4.3 Compound Inequalities
  • 4.3.1 Sets, Intersections, and Unions
  • 4.3.2 Solving Compound Inequalities
  • 4.3.3 More On Compound Inequalities

• 4.4 Absolute-Value Equations
  • 4.4.1 Matching Number Lines with Absolute Value
  • 4.4.2 Solving Absolute-Value Equations
  • 4.4.3 Solving Equations with Two Absolute-Value Expressions

• 4.5 Absolute-Value Inequalities
  • 4.5.1 Solving Absolute-Value Inequalities
  • 4.5.2 Solving Absolute-Value Inequalities: More Examples

5. Polynomials

• 5.1 Polynomial Basics
  • 5.1.1 Determining Components and Degree
  • 5.1.2 Adding and Subtracting Polynomials
  • 5.1.3 Multiplying Polynomials

• 5.2 Techniques for Multiplying Polynomials
  • 5.2.1 The FOIL Method
  • 5.2.2 Multiplying Big Products
  • 5.2.3 Using Special Products

• 5.3 Techniques for Factoring
  • 5.3.1 Factoring Using the Greatest Common Factor
  • 5.3.2 Factoring by Grouping
  • 5.3.3 Factoring Trinomials Completely
  • 5.3.4 Factoring Trinomials: The Guess and Check Method

• 5.4 Special Factoring
  • 5.4.1 Factoring Perfect-Square Trinomials
  • 5.4.2 Factoring the Difference of Two Squares
  • 5.4.3 Factoring the Sums and Differences of Cubes
  • 5.4.4 Factoring by Any Method

• 5.5 Solving Equations by Factoring
  • 5.5.1 The Zero Factor Property

• 5.6 Division of Polynomials
  • 5.6.1 Using Long Division with Polynomials
  • 5.6.2 Long Division: Another Example

• 5.7 Synthetic Division
  • 5.7.1 Using Synthetic Division with Polynomials
  • 5.7.2 More Synthetic Division

• 5.8 The Remainder Theorem
  • 5.8.1 Using the Remainder Theorem
  • 5.8.2 More on the Remainder Theorem

6. Rational Expressions

• 6.1 The Basics of Rational Expressions
  • 6.1.1 An Introduction to Rational Expressions
  • 6.1.2 Working with Fractions
  • 6.1.3 Writing Rational Expressions in Lowest Terms

• 6.2 Operations with Rationals
  • 6.2.1 Multiplying and Dividing Rational Expressions
  • 6.2.2 Adding and Subtracting Rational Expressions
  • 6.2.3 Rewriting Complex Fractions

• 6.3 Equations with Rationals
  • 6.3.1 Solving a Linear Equation with Rationals
  • 6.3.2 Solving a Linear Equation with Restrictions

• 6.4 Inequalities with Rationals
  • 6.4.1 Solving Rational Inequalities
  • 6.4.2 Solving Rational Inequalities: Another Example
  • 6.4.3 Determining Domain

• 6.5 Applications
  • 6.5.1 Solving a Problem about Work
  • 6.5.2 Resistors in Parallel

• 6.6 Variation
  • 6.6.1 An Introduction to Variation
  • 6.6.2 Direct Proportion
  • 6.6.3 Inverse Proportion
  • 6.6.4 Joint and Combined Proportion

7. Relations and Functions

• 7.1 The Rectangular Coordinate System
  • 7.1.1 Using the Cartesian System
  • 7.1.2 Thinking Visually

• 7.2 An Introduction to Functions
  • 7.2.1 Introducing Relations and Functions
  • 7.2.2 Functions and the Vertical-Line Test
  • 7.2.3 Function Notation and Values

• 7.3 Domain and Range
  • 7.3.1 Finding Domain and Range
  • 7.3.2 Domain and Range: An Explicit Example
  • 7.3.3 Satisfying the Domain of a Function
  • 7.3.4 Graphing Important Functions

• 7.4 The Algebra of Functions
  • 7.4.1 Operations on Functions
  • 7.4.2 Composite Functions
  • 7.4.3 Components of Composite Functions

• 7.5 The Slope of a Line
  • 7.5.1 An Introduction to Slope
  • 7.5.2 Finding the Slope Given Two Points

• 7.6 Graphing Linear Equations
  • 7.6.1 Using Intercepts to Graph Lines
  • 7.6.2 Working with Specific Lines
  • 7.6.3 Interpreting Slope from a Graph
  • 7.6.4 Graphing with a Point and the Slope

• 7.7 Linear Equations
  • 7.7.1 Writing an Equation in Slope-Intercept Form
  • 7.7.2 Writing an Equation Given Two Points
  • 7.7.3 Writing an Equation in Point-Slope Form
  • 7.7.4 Matching a Slope-Intercept Equation with Its Graph
  • 7.7.5 Slope for Parallel and Perpendicular Lines

• 7.8 Applications of Linear Concepts
  • 7.8.1 Constructing a Linear Model from a Set of Data
  • 7.8.2 Scatterplots and Predictions
  • 7.8.3 Interpreting Line Graphs
  • 7.8.4 Linear Cost and Revenue

8. Roots and Radicals

• 8.1 Rational Exponents and Radicals
  • 8.1.1 Converting Rational Exponents and Radicals
  • 8.1.2 Radical Notation and Properties of Roots
  • 8.1.3 Variables and Negative Values under a Radical

• 8.2 Simplifying Radical Expressions
  • 8.2.1 Simplifying Radicals
  • 8.2.2 Simplifying Radical Expressions with Variables

• 8.3 Operations with Radical Expressions
  • 8.3.1 Adding and Subtracting Radical Expressions
  • 8.3.2 Rationalizing Denominators

• 8.4 Equations with Radicals
  • 8.4.1 Extraneous Roots
  • 8.4.2 Solving an Equation Containing a Radical
  • 8.4.3 Solving Equations with Two Radical Expressions
  • 8.4.4 Solving an Equation with Rational Exponents

• 8.5 Complex Numbers
  • 8.5.1 Introducing and Writing Complex Numbers
  • 8.5.2 Rewriting Powers of i
  • 8.5.3 Adding and Subtracting Complex Numbers
  • 8.5.4 Multiplying Complex Numbers
  • 8.5.5 Dividing Complex Numbers

• 8.6 Applications
  • 8.6.1 Finding the Length of the Diagonal of a Cube
  • 8.6.2 Finding the Distance and the Midpoint between Two Points
  • 8.6.3 Applications in Meteorology

9. Quadratic Equations

• 9.1 The Basics of Quadratics
  • 9.1.1 An Introduction to Quadratics
  • 9.1.2 Solving Quadratics by Factoring

• 9.2 Graphs of Quadratics
  • 9.2.1 Finding x- and y-intercepts
  • 9.2.2 Nice-Looking Parabolas
  • 9.2.3 Graphing Parabolas

• 9.3 Solving by Completing the Square
  • 9.3.1 Solving by Completing the Square
  • 9.3.2 Completing the Square: Another Example
  • 9.3.3 Finding the Vertex by Completing the Square

• 9.4 Writing Quadratic Equations
  • 9.4.1 Using the Vertex to Write the Equation
  • 9.4.2 Building a Polynomial Equation from Its Solutions

• 9.5 Solving with the Quadratic Formula
  • 9.5.1 Proving the Quadratic Formula
  • 9.5.2 Using the Quadratic Formula
  • 9.5.3 Predicting Types of Solutions From the Discriminant
  • 9.5.4 Using the Discriminant to Graph Parabolas

• 9.6 Equations Quadratic in Form
  • 9.6.1 Solving for a Squared Variable
  • 9.6.2 Finding Real-Number Restrictions
  • 9.6.3 Solving Fancy Quadratics
  • 9.6.4 Horizontal Parabolas

• 9.7 Formulas and Applications
  • 9.7.1 Solving a Quadratic Geometry Problem
  • 9.7.2 Solving with the Pythagorean Theorem
  • 9.7.3 Solving a Motion Problem
  • 9.7.4 Solving a Projectile Problem
  • 9.7.5 Solving Other Problems

• 9.8 Nonlinear Inequalities
  • 9.8.1 Solving Quadratic Inequalities
  • 9.8.2 Solving Quadratic Inequalities: Another Example

10. Systems of Equations

• 10.1 Linear Systems in Two Variables
  • 10.1.1 An Introduction to Linear Systems
  • 10.1.2 Solving a System by Graphing
  • 10.1.3 Solving a System by Substitution
  • 10.1.4 Solving a System by Elimination

• 10.2 Linear Systems in Three Variables
  • 10.2.1 An Introduction to Systems in Three Variables
  • 10.2.2 Solving Systems with Three Variables
  • 10.2.3 Solving Inconsistent Systems
  • 10.2.4 Solving Dependent Systems
  • 10.2.5 Solving Systems with Two Equations

• 10.3 Applications of Linear Systems
  • 10.3.1 Investments
  • 10.3.2 Partial Fractions

• 10.4 Solutions by Matrix Methods
  • 10.4.1 An Introduction to Matrices
  • 10.4.2 Using the Gauss-Jordan Method
  • 10.4.3 Using Gauss-Jordan: Another Example

• 10.5 Determinants
  • 10.5.1 Evaluating 2x2 Determinants
  • 10.5.2 Evaluating nxn Determinants

• 10.6 Cramer's Rule
  • 10.6.1 Using Cramer's Rule
  • 10.6.2 Using Cramer's Rule in a 3x3 Matrix

• 10.7 Working with Inequalities
  • 10.7.1 An Introduction to Graphing Linear Inequalities
  • 10.7.2 Graphing Linear Inequalities
  • 10.7.3 Graphing a System of Inequalities

• 10.8 Systems of Nonlinear Equations
  • 10.8.1 Solving a Nonlinear System by Elimination
  • 10.8.2 Solving a Nonlinear System by Substitution