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*For courses in * *Intermediate Algebra.*

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Table of Contents

**R. Review of the Real Number System**

**R.1 **Basic Concepts

**R.2 **Operations on Real Numbers

**R.3 **Exponents, Roots, and Order of Operations

**R.4 **Properties of Real Numbers

**Study Skills **Using Your Math Text

**Study Skills **Reading Your Math Text

**1. Linear Equations and Applications**

**1.1 **Linear Equations in One Variable

**Study Skills **Completing Your Homework

**1.2 **Formulas and Percent

**Study Skills **Managing Your Time

**1.3 **Applications of Linear Equations

**Study Skills **Taking Lecture Notes

**1.4 **Further Applications of Linear Equations

** Summary Exercises **

*Applying Problem-Solving Techniques*

**Study Skills **Reviewing a Chapter

**2. Linear Inequalities and Absolute Value**

**2.1 **Linear Inequalities in One Variable

**Study Skills **Using Study Cards

**2.2 **Set Operations and Compound Inequalities

**Study Skills **Using Study Cards Revisited

**2.3 **Absolute Value Equations and Inequalities

** Summary Exercises **

*Solving Linear and Absolute Value Equations and Inequalities*

**Taking Math Tests**

Study Skills

Study Skills

**3. Graphs, Linear Equations and Functions**

**3.1 **The Rectangular Coordinate System

**Study Skills **Analyzing Your Test Results

**3.2 **Slope of a Line

**3.3 **Linear Equations in Two Variables

** Summary Exercises **

*Finding Slopes and Equations of Lines*

**3.4 **Linear Inequalities in Two Variables

**3.5 **Introduction to Relations and Functions

**3.6 **Function Notation and Linear Functions

**4. Systems of Linear Equations**

**4.1 **Systems of Linear Equations in Two Variables

**Study Skills **Preparing for Your Math Final Exam

**4.2 **Systems of Linear Equations in Three Variables

**4.3 **Applications of Systems of Linear Equations

**5. Exponents, Polynomials, and Polynomial Functions**

**5.1 **Integer Exponents

**5.2 **Scientific Notation

**5.3 **Adding and Subtracting Polynomials

**5.4 **Polynomial Functions and Graphs

**5.5 **Multiplying Polynomials

**5.6 **Dividing Polynomials

**6. Factoring**

**6.1 **Greatest Common Factors and Factoring by Grouping

**6.2 **Factoring Trinomials

**6.3 **Special Factoring

**6.4 **A General Approach to Factoring

**6.5 **Solving Equations Using the Zero-Factor Property

**7. Rational Expressions and Functions**

**7.1 **Rational Expressions and Functions; Multiplying and Dividing

**7.2 **Adding and Subtracting Rational Expressions

**7.3 **Complex Fractions

**7.4 **Equations with Rational Expressions and Graphs

** Summary Exercises **

*Simplifying Rational Expressions vs. Solving Rational Equations*

**7.5 **Applications of Rational Expressions

**7.6 **Variation

**8. Roots, Radicals, and Root Functions**

**8.1 **Radical Expressions and Graphs

**8.2 **Rational Exponents

**8.3 **Simplifying Radical Expressions

**8.4 **Adding and Subtracting Radical Expressions

**8.5 **Multiplying and Dividing Radical Expressions

** Summary Exercises **

*Performing Operations with Radicals and Rational Exponents*

**8.6 **Solving Equations with Radicals

**8.7 **Complex Numbers

**9. Quadratic Equations, Inequalities, and Functions**

**9.1 **The Square Root Property and Completing the Square

**9.2 **The Quadratic Formula

**9.3 **Equations Quadratic in Form

** Summary Exercises **

*Applying Methods for Solving Quadratic Equations*

**9.4 **Formulas and Further Applications

**9.5 **Graphs of Quadratic Functions

**9.6 **More about Parabolas and Their Applications

**9.7 **Polynomial and Rational Inequalities

**10. Inverse, Exponential, and Logarithmic Functions**

**10.1 **Composition of Functions

**10.2 **Inverse Functions

**10.3 **Exponential Functions

**10.4 **Logarithmic Functions

**10.5 **Properties of Logarithms

**10.6 **Common and Natural Logarithms

**10.7 **Exponential and Logarithmic Equations and Their Applications

**11. Nonlinear Functions, Conic Sections, and Nonlinear Systems**

**11.1 **Additional Graphs of Functions

**11.2 **Circles and Ellipses

**11.3 **Hyperbolas and Functions Defined by Radicals

**11.4 **Nonlinear Systems of Equations

**11.5 **Second-Degree Inequalities and Systems of Inequalities

**Appendix A. Review of Fractions**

**Appendix B. Synthetic Division**

**Appendix C. Solving Systems of Linear Equations by Matrix Methods**