Introductory & Intermediate Algebra

Table of Contents

• R. Prealgebra Review
• R.1 Fractions
• R.2 Decimals and Percents
• Study Skills Using Your Math Text

1. The Real Number System
   • 1.1 Exponents, Order of Operations, and Inequality
     • Study Skills Taking Lecture Notes
   • 1.2 Variables, Expressions, and Equations
     • Study Skills Reading Your Math Text
   • 1.3 Real Numbers and the Number Line
     • Study Skills Using Study Cards
   • 1.4 Adding Real Numbers
   • 1.5 Subtracting Real Numbers
     • Study Skills Completing Your Homework
   • 1.6 Multiplying and Dividing Real Numbers
     • Summary Exercises Performing Operations with Real Numbers
   • 1.7 Properties of Real Numbers
   • 1.8 Simplifying Expressions
     • Study Skills Reviewing a Chapter
2. Equations, Inequalities, and Applications
   • 2.1 The Addition Property of Equality
     • Study Skills Managing Your Time
   • 2.2 The Multiplication Property of Equality
   • 2.3 More on Solving Linear Equations
     • Study Skills Using Study Cards Revisited
     • Summary Exercises Applying Methods for Solving Linear Equations
   • 2.4 An Introduction to Applications of Linear Equations
   • 2.5 Formulas and Additional Applications from Geometry
   • 2.6 Ratio, Proportion, and Percent
     • Summary Exercises Applying Problem-Solving Techniques
   • 2.7 Solving Linear Inequalities
     • Study Skills Taking Math Tests
3. Graphs of Linear Equations and Inequalities in Two Variables
   • 3.1 Linear Equations and Rectangular Coordinates
     • Study Skills Analyzing Your Test Results
   • 3.2 Graphing Linear Equations in Two Variables
   • 3.3 The Slope of a Line
   • 3.4 Slope-Intercept Form of a Linear Equation
   • 3.5 Point-Slope Form of a Linear Equation and Modeling
     • Summary Exercises Applying Graphing and
     • Equation-Writing Techniques for Lines
     • Study Skills Preparing for Your Math Final Exam
   • 3.6 Graphing Linear Inequalities in Two Variables
4. Systems of Linear Equations and Inequalities
   • 4.1 Solving Systems of Linear Equations by Graphing
   • 4.2 Solving Systems of Linear Equations by Substitution
   • 4.3 Solving Systems of Linear Equations by Elimination
     • Summary Exercises Applying Techniques for Solving Systems of Linear Equations
   • 4.4 Applications of Linear Systems
   • 4.5 Solving Systems of Linear Inequalities
5. Exponents and Polynomials
   • 5.1 The Product Rule and Power Rules for Exponents
   • 5.2 Integer Exponents and the Quotient Rule
     • Summary Exercises Applying the Rules for Exponents
   • 5.3 An Application of Exponents: Scientific Notation
   • 5.4 Adding and Subtracting Polynomials
   • 5.5 Multiplying Polynomials
   • 5.6 Special Products
   • 5.7 Dividing a Polynomial by a Monomial
   • 5.8 Dividing a Polynomial by a Polynomial
6. Factoring and Applications
   • 6.1 Greatest Common Factors; Factor by Grouping
   • 6.2 Factoring Trinomials
   • 6.3 Factoring Trinomials by Grouping
   • 6.4 Factoring Trinomials Using the FOIL Method
   • 6.5 Special Factoring Techniques
   • 6.6 A General Approach to Factoring
   • 6.7 Solving Quadratic Equations Using the Zero-Factor Property
   • 6.8 Applications of Quadratic Equations
7. Rational Expressions and Applications
   • 7.1 The Fundamental Property of Rational Expressions
   • 7.2 Multiplying and Dividing Rational Expressions
   • 7.3 Least Common Denominators
   • 7.4 Adding and Subtracting Rational Expressions
   • 7.5 Complex Fractions
   • 7.6 Solving Equations with Rational Expressions
     • Summary Exercises Simplifying Rational Expressions vs. Solving Rational Equations
   • 7.7 Applications of Rational Expressions
   • 7.8 Variation
8. Equations, Inequalities, Graphs, and Systems Revisited
   • 8.1 Review of Solving Linear Equations and Inequalities in one Variable
   • 8.2 Set Operations and Compound Inequalities
   • 8.3 Absolute Value Equations and Inequalities
     • Summary Exercises Solving Linear and Absolute Value Equations and Inequalities
   • 8.4 Review of Graphing Linear Equations in Two Variables; Slope
   • 8.6 Systems of Linear Equations in Three Variables; Applications
9. Relations and Functions
   • 9.1 Introduction to Relations and Functions
   • 9.2 Function Notation and Linear Functions
   • 9.3 Polynomial Functions, Operations, and Graphs
   • 9.4 Variation
10. Roots, Radicals, and Root Functions
    • 10.1 Radical Expressions and Graphs
    • 10.2 Rational Exponents
    • 10.3 Simplifying Radical Expressions
    • 10.4 Adding and Subtracting Radical Expressions
    • 10.5 Multiplying and Dividing Radical Expressions
      • Summary Exercises Performing Operations with Radicals and Rational Exponents
    • 10.6 Solving Equations with Radicals
    • 10.7 Complex Numbers
11. Quadratic Equations, Inequalities, and Functions
    • 11.1 Solving Quadratic Equations by the Square Root Property
    • 11.2 Solving Quadratic Equations by Completing the Square
    • 11.3 Solving Quadratic Equations by the Quadratic Formula
    • 11.4 Equations Quadratic in Form
      • Summary Exercises Applying Methods for Solving Quadratic Equations
    • 11.5 Formulas and Further Applications
    • 11.6 Graphs of Quadratic Functions
    • 11.7 More about Parabolas and Their Applications
    • 11.8 Polynomial and Rational Inequalities
12. Inverse, Exponential, and Logarithmic Functions
    • 12.1 Composition of Functions
    • 12.2 Inverse Functions
    • 12.3 Exponential Functions
    • 12.4 Logarithmic Functions
    • 12.5 Properties of Logarithms
    • 12.6 Common and Natural Logarithms
    • 12.7 Exponential and Logarithmic Equations and Their Applications
13. Nonlinear Functions, Conic Sections, and Nonlinear Systems
    • 13.1 Additional Graphs of Functions
    • 13.2 Circles and Ellipses
    • 13.3 Hyperbolas and Functions Defined by Radicals
    • 13.4 Nonlinear Systems of Equations
    • 13.5 Second-Degree Inequalities and Systems of Inequalities

Appendix A: Review of Exponents, Polynomials, and Factoring (Transition from Introductory to Intermediate Algebra)

Appendix B: Synthetic Division

Appendix C: Solving Systems of Linear Equations by Matrix Methods

Answers to Selected Exercises

Index