Intermediate Algebra, 9th Edition

Study Skills: Your Brain Can Learn Mathematics

 

1. Review of the Real Number System

1.1 Basic Concepts

1.2 Operations on Real Numbers

1.3 Exponents, Roots, and Order of Operations

1.4 Properties of Real Numbers

            Study Skills: Using Your Textbook

 

2. Linear Equations and Applications

2.1 Linear Equations in One Variable

            Study Skills: Homework: How, Why, When

2.2 Formulas and Percent

2.3 Applications of Linear Equations

            Study Skills: Taking Lecture Notes

2.4 Further Applications of Linear Equations

            Summary Exercises on Solving Applied Problems

            Study Skills: Reviewing a Chapter

            Study Skills: Preparing for Tests

 

3. Linear Inequalities and Absolute Value

3.1 Linear Inequalities in One Variable

            Study Skills: Using Study Cards

3.2 Set Operations and Compound Inequalities

            Study Skills: Using Study Cards Revisited

3.3 Absolute Value Equations and Inequalities

            Summary Exercises on Solving Linear and Absolute Value Equations and Inequalities

            Study Skills: Managing Your Time

            Study Skills: Tips for Taking Math Tests

 

4. Graphs, Linear Equations, and Functions

4.1 The Rectangular Coordinate System

4.2 Slope of a Line

4.3 Linear Equations in Two Variables

4.4 Linear Inequalities in Two Variables

4.5 Introduction to Functions

            Study Skills: Analyzing Your Test Results

 

5. Systems of Linear Equations

5.1 Systems of Linear Equations in Two Variables

5.2 Systems of Linear Equations in Three Variables

5.3 Applications of Linear Systems of Equations

5.4 Solving Linear Systems of Equations by Matrix Methods

 

6. Exponents, Polynomials, and Polynomial Functions

6.1 Integer Exponents and Scientific Notation

6.2 Adding and Subtracting Polynomials

6.3 Polynomial Functions

6.4 Multiplying Polynomials

6.5 Dividing Polynomials

 

7. Factoring

7.1 Greatest Common Factors; Factoring by Grouping

7.2 Factoring Trinomials

7.3 Special Factoring

7.4 A General Approach to Factoring

7.5 Solving Equations by Factoring

 

8. Rational Expressions

8.1 Rational Expressions and Functions; Multiplying and Dividing

            Study Skills: Making a Mind Map

8.2 Adding and Subtracting Rational Expressions

8.3 Complex Fractions

8.4 Equations with Rational Expressions and Graphs

            Summary Exercises on Operations and Equations with Rational Expressions

8.5 Applications of Rational Expressions

8.6 Variation

 

9. Roots, Radicals, and Root Functions

9.1 Rational Expressions and Graphs

9.2 Rational Exponents

9.3 Simplifying Radical Expressions

9.4 Adding and Subtracting Radical Expressions

9.5 Multiplying and Dividing Radical Expressions

            Summary Exercises on Operations with Radicals

9.6 Solving Equations with Radicals

9.7 Complex Numbers

            Study Skills: Preparing for Your Math Final

 

10. Quadratic Equations, Inequalities, and Functions

10.1 The Square Root Property and Completing the Square

10.2 The Quadratic Formula

10.3 Equations Quadratic in Form

            Summary Exercises on Solving Quadratic Equations

10.4 Formulas and Further Applications

10.5 Graphs of Quadratic Functions

10.6 More About Parabolas and Their Applications

10.7 Polynomial and Rational Inequalities

 

11. Inverse, Exponential, and Logarithmic Functions

11.1 Inverse Functions

11.2 Exponential Functions

11.3 Logarithmic Functions

11.4 Properties of Logarithms

11.5 Common and Natural Logarithms

11.6 Exponential and Logarithmic Equations; Further Applications

 

12. Nonlinear Functions, Conic Sections, and Nonlinear Systems

12.1 Additional Graphs of Functions; Composition

12.2 The Circle and the Ellipse

12.3 The Hyperbola, and Other Functions Defined by Radicals

12.4 Nonlinear Systems of Equations

12.5 Second-Degree Inequalities and Systems of Inequalities

 

Appendix A. Strategies for Problem Solving

Appendix B. Review of Fractions

Appendix C. Synthetic Division

 

Answers to Selected Exercises

Solutions to Selected Exercises

Index