## Table of Contents

**1. Variables, Real Numbers, and Mathematical Models**

1.1 Introduction to Algebra: Variables and Mathematical Models

1.2 Fractions in Algebra

1.3 The Real Numbers

1.4 Basic Rules of Algebra

Mid-Chapter Check Point Section 1.1–Section 1.4

1.5 Addition of Real Numbers

1.6 Subtraction of Real Numbers

1.7 Multiplication and Division of Real Numbers

1.8 Exponents and Order of Operations

Chapter 1 Group Project

Chapter 1 Summary

Chapter 1 Review Exercises

Chapter 1 Test

**2. Linear Equations and Inequalities in One Variable **

2.1 The Addition Property of Equality

2.2 The Multiplication Property of Equality

2.3 Solving Linear Equations

2.4 Formulas and Percents

Mid-Chapter Check Point Section 2.1–Section 2.4

2.5 An Introduction to Problem Solving

2.6 Problem Solving in Geometry

2.7 Solving Linear Inequalities

Chapter 2 Group Project

Chapter 2 Summary

Chapter 2 Review Exercises

Chapter 2 Test

Cumulative Review Exercises (Chapters 1–2)

**3. Linear Equations in Two Variables**

3.1 Graphing Linear Equations in Two Variables

3.2 Graphing Linear Equations Using Intercepts

3.3 Slope

3.4 The Slope-Intercept Form of the Equation of a Line

Mid-Chapter Check Point Section 3.1–Section 3.4

3.5 The Point-Slope Form of the Equation of a Line

Chapter 3 Group Project

Chapter 3 Summary

Chapter 3 Review Exercises

Chapter 3 Test

Cumulative Review Exercises (Chapters 1–3)

**4. Systems of Linear Equations **

4.1 Solving Systems of Linear Equations by Graphing

4.2 Solving Systems of Linear Equations by the Substitution Method

4.3 Solving Systems of Linear Equations by the Addition Method

Mid-Chapter Check Point Section 4.1–Section 4.3

4.4 Problem Solving Using Systems of Equations

4.5 Systems of Linear Equations in Three Variables

Chapter 4 Group Project

Chapter 4 Summary

Chapter 4 Review Exercises

Chapter 4 Test

Cumulative Review Exercises (Chapters 1–4)

**5. Exponents and Polynomials**

5.1 Adding and Subtracting Polynomials

5.2 Multiplying Polynomials

5.3 Special Products

5.4 Polynomials in Several Variables

Mid-Chapter Check Point Section 5.1–Section 5.4

5.5 Dividing Polynomials

5.6 Long Division of Polynomials; Synthetic Division

5.7 Negative Exponents and Scientific Notation

Chapter 5 Group Project

Chapter 5 Summary

Chapter 5 Review Exercises

Chapter 5 Test

Cumulative Review Exercises (Chapters 1–5)

**6. Factoring Polynomials**

6.1 The Greatest Common Factor and Factoring By Grouping

6.2 Factoring Trinomials Whose Leading Coefficient Is 1

6.3 Factoring Trinomials Whose Leading Coefficient Is Not 1

Mid-Chapter Check Point Section 6.1–Section 6.3

6.4 Factoring Special Forms

6.5 A General Factoring Strategy

6.6 Solving Quadratic Equations By Factoring

Chapter 6 Group Project

Chapter 6 Summary

Chapter 6 Review Exercises

Chapter 6 Test

Cumulative Review Exercises (Chapters 1–6)

**7. Rational Expressions**

7.1 Rational Expressions and Their Simplification

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions with the Same Denominator

7.4 Adding and Subtracting Rational Expressions with Different Denominators

Mid-Chapter Check Point Section 7.1–Section 7.4

7.5 Complex Rational Expressions

7.6 Solving Rational Equations

7.7 Applications Using Rational Equations and Proportions

7.8 Modeling Using Variation

Chapter 7 Group Project

Chapter 7 Summary

Chapter 7 Review Exercises

Chapter 7 Test

Cumulative Review Exercises (Chapters 1–7)

**8. Basics of Functions **

8.1 Introduction to Functions

8.2 Graphs of Functions

8.3 The Algebra of Functions

Mid-Chapter Check Point Section 8.1–Section 8.3

8.4 Composite and Inverse Functions

Chapter 8 Group Project

Chapter 8 Summary

Chapter 8 Review Exercises

Chapter 8 Test

Cumulative Review Exercises (Chapters 1–8)

**9. Inequalities and Problem Solving**

9.1 Reviewing Linear Inequalities and Using Inequalities in Business Applications

9.2 Compound Inequalities

9.3 Equations and Inequalities Involving Absolute Value

Mid-Chapter Check Point Section 9.1–Section 9.3

9.4 Linear Inequalities in Two Variables

Chapter 9 Group Project

Chapter 9 Summary

Chapter 9 Review Exercises

Chapter 9 Test

Cumulative Review Exercises (Chapters 1–9)

**10. Radicals, Radical Functions, and Rational Exponents **

10.1 Radical Expressions and Functions

10.2 Rational Exponents

10.3 Multiplying and Simplifying Radical Expressions

10.4 Adding, Subtracting, and Dividing Radical Expressions

Mid-Chapter Check Point Section 10.1–Section 10.4

10.5 Multiplying with More Than One Term and Rationalizing Denominators

10.6 Radical Equations

10.7 Complex Numbers

Chapter 10 Group Project

Chapter 10 Summary

Chapter 10 Review Exercises

Chapter 10 Test

Cumulative Review Exercises (Chapters 1–10)

**11. Quadratic Equations and Functions **

11.1 The Square Root Property and Completing the Square; Distance and Midpoint Formulas

11.2 The Quadratic Formula

11.3 Quadratic Functions and Their Graphs

Mid-Chapter Check Point Section 11.1–Section 11.3

11.4 Equations Quadratic in Form

11.5 Polynomial and Rational Inequalities

Chapter 11 Group Project

Chapter 11 Summary

Chapter 11 Review Exercises

Chapter 11 Test

Cumulative Review Exercises (Chapters 1–11)

**12. Exponential and Logarithmic Functions **

12.1 Exponential Functions

12.2 Logarithmic Functions

12.3 Properties of Logarithms

Mid-Chapter Check Point Section 12.1–Section 12.3

12.4 Exponential and Logarithmic Equations

12.5 Exponential Growth and Decay; Modeling Data

Chapter 12 Group Project

Chapter 12 Summary

Chapter 12 Review Exercises

Chapter 12 Test

Cumulative Review Exercises (Chapters 1–12)

**13. Conic Sections and Systems of Nonlinear Equations**

13.1 The Circle

13.2 The Ellipse

13.3 The Hyperbola

Mid-Chapter Check Point Section 13.1–Section 13.3

13.4 The Parabola; Identifying Conic Sections

13.5 Systems of Nonlinear Equations in Two Variables

Chapter 13 Group Project

Chapter 13 Summary

Chapter 13 Review Exercises

Chapter 13 Test

Cumulative Review Exercises (Chapters 1–13)

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

14.1 Sequences and Summation Notation

14.2 Arithmetic Sequences

14.3 Geometric Sequences and Series

Mid-Chapter Check Point Section 14.1–Section 14.3

14.4 The Binomial Theorem

Chapter 14 Group Project

Chapter 14 Summary

Chapter 14 Review Exercises

Chapter 14 Test

Cumulative Review Exercises (Chapters 1–14)

**Appendices**

**A. Mean, Median, and Mode**

**B. Matrix Solutions to Linear Systems**

**C. Determinants and Cramer's Rule**

**D. Where Did That Come From? Selected Proofs**