## Table of Contents

**1. Whole Numbers **

1.1 Success in Mathematics

1.2 Fundamentals of Whole Numbers

1.3 Adding and Subtracting Whole Numbers

1.4 Multiplying Whole Numbers; Exponents

Putting the Concepts Together (Sections 1.1—1.4)

1.5 Dividing Whole Numbers

1.6 Prime Numbers

1.7 Order of Operations

Chapter 1 Review

Chapter 1 Test

Getting Ready for Chapter 2: A Review of Whole Numbers

**2. Integers and an Introduction to Algebra**

2.1 Fundamentals of Integers

2.2 Adding and Subtracting Integers

2.3 Multiplying and Dividing Integers

2.4 Exponents; Order of Operations

Putting the Concepts Together (Sections 2.1—2.4)

2.5 Simplifying Algebraic Expressions

2.6 Linear Equations: The Addition and Multiplication Properties

2.7 Linear Equations: Using the Properties Together

2.8 Introduction to Problem Solving: Direct Translation Problems

Chapter 2 Review

Chapter 2 Test

Getting Ready for Chapter 3: A Review of Chapters 1 and 2

**3. Rational Numbers Expressed as Fractions**

3.1 Fundamentals of Fractions

3.2 Multiplying and Dividing Fractions

3.3 Adding and Subtracting Like Fractions

Putting the Concepts Together (Sections 3.1—3.3)

3.4 Adding and Subtracting Unlike Fractions

3.5 Order of Operations and Complex Fractions

3.6 Operations with Mixed Numbers

3.7 Solving Equations That Contain Fractions

Chapter 3 Review

Chapter 3 Test

Getting Ready for Chapter 4: A Review of Chapters 1—3

**4. Rational Numbers as Decimals**

4.1 Fundamentals of Decimals

4.2 Adding and Subtracting Decimals

4.3 Multiplying Decimals

4.4 Dividing Decimals

Putting the Concepts Together (Sections 4.1—4.4)

4.5 Solving Equations That Contain Decimals

Chapter 4 Review

Chapter 4 Test

Getting Ready for Chapter 5: A Review of Chapters 1—4

Putting It Together: Real Numbers

**5. Ratio, Proportion, and Percent**

5.1 Ratios and Unit Rates

5.2 Proportions

5.3 Fundamentals of Percent Notation

Putting the Concepts Together (Sections 5.1—5.3)

5.4 Solving Percent Problems: Proportion Method

5.5 Solving Percent Problems: Equation Method

5.6 Applications Involving Percent

Chapter 5 Review

Chapter 5 Test

Getting Ready for Chapter 6: A Review of Chapters 1—5

**6. Measurement and Geometry**

6.1 The U.S. Standard (English) System of Measurement

6.2 The Metric System of Measurement

Putting the Concepts Together (Sections 6.1—6.2)

6.3 Fundamentals of Geometry

6.4 Introduction to Square Roots and the Pythagorean Theorem

6.5 Polygons

6.6 Perimeter and Area of Polygons and Circles

6.7 Volume and Surface Area

Chapter 6 Review

Chapter 6 Test

Getting Ready for Chapter 7: A Review of Chapters 1—6

**7. Introduction to Statistics and the Rectangular Coordinate System**

7.1 Tables and Graphs

7.2 Mean, Median, and Mode

Putting the Concepts Together (Sections 7.1 and 7.2)

7.3 The Rectangular Coordinate System and Equations in Two Variables

7.4 Graphing Equations in Two Variables

Chapter 7 Review

Chapter 7 Test

Getting Ready for Elementary Algebra: A Review of Chapters 1—7

**8. Equations and Inequalities in One Variable**

8.1 Linear Equations: The Addition and Multiplication Properties of Equality

8.2 Linear Equations: Using the Properties Together

8.3 Solving Linear Equations Involving Fractions and Decimals; Classifying Equations

8.4 Evaluating Formulas and Solving Formulas for a Variable

8.5 Problem Solving: Direct Translation

8.6 Problem Solving: Problems Involving Percent

8.7 Problem Solving: Geometry and Uniform Motion

8.8 Solving Linear Inequalities in One Variable

Chapter 8 Review

Chapter 8 Test

**9. Introduction to Graphing and Equations of Lines**

9.1 The Rectangular Coordinate System and Equations in Two Variables

9.2 Graphing Equations in Two Variables

9.3 Slope

9.4 Slope-Intercept Form of a Line

9.5 Point-Slope Form of a Line

9.6 Parallel and Perpendicular Lines

Putting the Concepts Together (Sections 9.1—9.6)

9.7 Linear Inequalities in Two Variables

Chapter 9 Activity: Graphing Practice

Chapter 9 Review

Chapter 9 Test

Cumulative Review Chapters 1—9

**10. Systems of Linear Equations and Inequalities**

10.1 Solving Systems of Linear Equations by Graphing

10.2 Solving Systems of Linear Equations Using Substitution

10.3 Solving Systems of Linear Equations Using Elimination

Putting the Concepts Together (Sections 10.1—10.3)

10.4 Solving Direct Translation, Geometry, and Uniform Motion Problems Using Systems of Linear Equations

10.5 Solving Mixture Problems Using Systems of Linear Equations

10.6 Systems of Linear Inequalities

Chapter 10 Activity: Find the Numbers

Chapter 10 Review

Chapter 10 Test

**11. Exponents and Polynomials**

11.1 Adding and Subtracting Polynomials

11.2 Multiplying Monomials: The Product and Power Rules

11.3 Multiplying Polynomials

11.4 Dividing Monomials: The Quotient Rule and Integer Exponents

Putting the Concepts Together (Sections 11.1—11.4)

11.5 Dividing Polynomials

11.6 Applying Exponent Rules: Scientific Notation

Chapter 11 Activity: What Is the Question?

Chapter 11 Review

Chapter 11 Test

Cumulative Review Chapters 1—11

**12. Factoring Polynomials**

12.1 Greatest Common Factor and Factoring by Grouping

12.2 Factoring Trinomials of the Form x2 + bx + c

12.3 Factoring Trinomials of the Form ax2 + bx + c, a 1

12.4 Factoring Special Products 837

12.5 Summary of Factoring Techniques

Putting the Concepts Together (Sections 12.1—12.5)

12.6 Solving Polynomial Equations by Factoring

12.7 Modeling and Solving Problems with Quadratic Equations

Chapter 12 Activity: Which One Does Not Belong?

Chapter 12 Review

Chapter 12 Test

Getting Ready for Intermediate Algebra: A Review of Chapters 1—12

**13. Rational Expressions and Equations**

13.1 Simplifying Rational Expressions

13.2 Multiplying and Dividing Rational Expressions

13.3 Adding and Subtracting Rational Expressions with a Common Denominator

13.4 Finding the Least Common Denominator and Forming Equivalent Rational Expressions

13.5 Adding and Subtracting Rational Expressions with Unlike Denominators

13.6 Complex Rational Expressions

Putting the Concepts Together (Sections 13.1—13.6)

13.7 Rational Equations

13.8 Models Involving Rational Equations

Chapter 13 Activity: Correct the Quiz

Chapter 13 Review

Chapter 13 Test

Cumulative Review Chapters 1—13

Getting Ready for Intermediate Algebra: A Review of Chapters 1—13

Getting Ready for Chapter 14: Interval Notation

**14. Graphs, Relations, and Functions**

14.1 Graphs of Equations

14.2 Relations

14.3 An Introduction to Functions

14.4 Functions and Their Graphs

Putting the Concepts Together (Sections 14.1—14.4)

14.5 Linear Functions and Models

14.6 Compound Inequalities

14.7 Absolute Value Equations and Inequalities

14.8 Variation

Chapter 14 Activity: Shifting Discovery

Chapter 14 Review

Chapter 14 Test

**15. Radicals and Rational Exponents**

15.1 Square Roots

15.2 *n*th Roots and Rational Exponents

15.3 Simplifying Expressions Using the Laws of Exponents

15.4 Simplifying Radical Expressions Using Properties of Radicals

15.5 Adding, Subtracting, and Multiplying Radical Expressions

15.6 Rationalizing Radical Expressions

Putting the Concepts Together (Sections 15.1—15.6)

15.7 Functions Involving Radicals

15.7.4 Graph Functions Involving Cube Roots

15.8 Radical Equations and Their Applications

15.9 The Complex Number System

Chapter 15 Activity: Correct the Quiz

Chapter 15 Review

Chapter 15 Test

Cumulative Review Chapters 1—15

**16. Quadratic Equations and Functions**

16.1 Solving Quadratic Equations by Completing the Square

16.2 Solving Quadratic Equations by the Quadratic Formula

16.3 Solving Equations Quadratic in Form

Putting the Concepts Together (Sections 16.1—16.3)

16.4 Graphing Quadratic Functions Using Transformations

16.5 Graphing Quadratic Functions Using Properties

16.6 Polynomial Inequalities

16.7 Rational Inequalities

Chapter 16 Activity: Presidential Decision Making

Chapter 16 Review

Chapter 16 Test

**17. Exponential and Logarithmic Functions**

17.1 Composite Functions and Inverse Functions

17.2 Exponential Functions

17.3 Logarithmic Functions

Putting the Sections Together (17.1—17.3)

17.4 Properties of Logarithms

17.5 Exponential and Logarithmic Equations

Chapter 17 Activity: Correct the Quiz

Chapter 17 Review

Chapter 17 Test

Cumulative Review Chapters 1—15

**18. Conics**

18.1 Distance and Midpoint Formulas

18.2 Circles

18.3 Parabolas

18.4 Ellipses

18.5 Hyperbolas

Putting the Concepts Together (Sections 18.1—18.5)

18.6 Systems of Nonlinear Equations

18.6.1 Solve a System of Nonlinear Equations Using Substitution

18.6.2 Solve a System of Nonlinear Equations Using Elimination

Chapter 18 Activity: How Do You Know That …?

Chapter 18 Review

Chapter 18 Test

**19. Sequences, Series, and the Binomial Theorem**

19.1 Sequences

19.2 Arithmetic Sequences

19.3 Geometric Sequences and Series

Putting the Concepts Together (Sections 19.1—19.3)

19.4 The Binomial Theorem

Chapter 19 Activity: Discover the Relation

Chapter 19 Review

Chapter 19 Test

Cumulative Review Chapters 1—19

**APPENDICES**

Appendix A. Synthetic Division

A.1.1 Divide Polynomials Using Synthetic Division

A.1.2 Use the Remainder and Factor Theorems

Appendix B. More on Systems of Linear Equations

B.1 A Review of Systems of Linear Equations in Two Variables

B.1.1 Determine Whether an Ordered Pair Is a Solution of a System of Linear Equations

B.1.2 Solve a System of Two Linear Equations by Graphing

B.1.3 Solve a System of Two Linear Equations by Substitution

B.1.4 Solve a System of Two Linear Equations by Elimination

B.1.5 Identify Inconsistent Systems

B.1.6 Write the Solution of a System with Dependent Equations

B.2 Systems of Linear Equations in Three Variables

B.2.1 Solve Systems of Three Linear Equations

B.2.2 Identify Inconsistent Systems

B.2.3 Write the Solution of a System with Dependent Equations

B.2.4 Model and Solve Problems Involving Three Linear Equations

B.3 A Using Matrices to Solve Systems

B.3.1 Write the Augmented Matrix of a System

B.3.2 Write the System from the Augmented Matrix

B.3.3 Perform Row Operations on a Matrix

B.3.4 Solve Systems Using Matrices

B.3.5 Solve Consistent Systems with Dependent Equations and Solve Inconsistent Systems

B.4 Determinants and Cramer’s Rule

B.4.1 Evaluate the Determinant of a 2 x 2 Matrix

B.4.2 Use Cramer’s Rule to Solve a System of Two Equations

B.4.3 Evaluate the Determinant of a 3 x 3 Matrix

B.4.4 Use Cramer’s Rule to Solve a System of Three Equations

**Appendix C. Table of Square Roots**