Intermediate Algebra, 2nd Edition

R. Real Numbers and Algebraic Expressions

R.1 Success in Mathematics

R.2 Sets and Classification of Numbers

R.3 Operations on Signed Numbers; Properties of Real Numbers

R.4 Order of Operations

R.5 Algebraic Expressions

 

1. Linear Equations and Inequalities

Part I: Linear Equations and Inequalities in One Variable

1.1 Linear Equations in One Variable

1.2 An Introduction to Problem Solving

1.3 Using Formulas to Solve Problems

1.4 Linear Inequalities in One Variable

            Putting the Concepts Together (Sections 1.1—1.4)

Part II: Linear Equations and Inequalities in Two Variables

1.5 Rectangular Coordinates and Graphs of Equations

1.6 Linear Equations in Two Variables

1.7 Parallel and Perpendicular Lines

1.8 Linear Inequalities in Two Variables

            Chapter 1 Activity: Pass the Paper

            Chapter 1 Review

            Chapter 1 Test

            Cumulative Review Chapters R—1

 

2. Relations, Functions, and More Inequalities

2.1 Relations

2.2 An Introduction to Functions

2.3 Functions and Their Graphs

            Putting the Concepts Together (Sections 2.1—2.4)

2.4 Linear Functions and Models

2.5 Compound Inequalities

2.6 Absolute Value Equations and Inequalities

2.7 Variation

            Chapter 2 Activity: Shifting Discovery?

            Chapter 2 Review

            Chapter 2 Test

 

3. Systems of Linear Equations and Inequalities

3.1 Systems of Linear Equations in Two Variables

3.2 Problem Solving: Systems of Two Linear Equations Containing Two Unknowns

3.3 Systems of Linear Equations in Three Variables

            Putting the Concepts Together (Sections 3.1—3.3)

3.4 Using Matrices to Solve Systems

3.5 Determinants and Cramer's Rule

3.6 Systems of Linear Inequalities

            Chapter 3 Activity: Find the Numbers

            Chapter 3 Review

            Chapter 3 Test

            Cumulative Review Chapters R–3

 

Getting Ready for Chapter 4: Laws of Exponents and Scientific Notation

 

4. Polynomial and Polynomial Functions

4.1 Adding and Subtracting Polynomials

4.2 Multiplying Polynomials

4.3 Dividing Polynomials; Synthetic Division

            Putting the Concepts Together (Sections 4.1—4.3)

4.4 Greatest Common Factor; Factoring by Grouping

4.5 Factoring Trinomials

4.6 Factoring Special Products

4.7 Factoring: A General Strategy

4.8 Polynomial Equations

            Chapter 4 Activity: What Is the Question?

            Chapter 4 Review

            Chapter 4 Test

 

Getting Ready for Chapter 5: A Review of Operations on Rational Numbers

 

5. Rational Expressions and Rational Functions

5.1 Multiplying and Dividing Rational Expressions

5.2 Adding and Subtracting Rational Expressions

5.3 Complex Rational Expressions

            Putting the Concepts Together (Sections 5.1—5.3)

5.4 Rational Equations

5.5 Rational Inequalities

5.6 Models Involving Rational Expressions

            Chapter 5 Activity: Correct the Quiz

            Chapter 5 Review

            Chapter 5 Test

            Cumulative Review Chapters R–5

 

Getting Ready for Chapter 6: Square Roots

 

6. Radicals and Rational Exponents

6.1 nth Roots and Rational Exponents

6.2 Simplify Expressions Using the Law of Exponents

6.3 Simplify Radical Expressions Using Properties of Radicals

6.4 Adding, Subtracting, and Multiplying Radical Expressions

6.5 Rationalizing Radical Expressions

            Putting the Concepts Together (Sections 6.1—6.5)

6.6 Functions Involving Radicals

6.7 Radical Equations and Their Applications

6.8 The Complex Number System

            Chapter 6 Activity: Which One Does Not Belong?

            Chapter 6 Review

            Chapter 6 Test

 

7. Quadratic Equations and Functions

7.1 Solving Quadratic Equations by Completing the Square

7.2 Solving Quadratic Equations by the Quadratic Formula

7.3 Solving Equations Quadratic in Form

            Putting the Concepts Together (Sections 7.1—7.3)

7.4 Graphing Quadratic Functions Using Transformations

7.5 Graphing Quadratic Functions Using Properties

7.6 Quadratic Inequalities

            Chapter 7 Activity: Presidential Decision Making

            Chapter 7 Review

            Chapter 7 Test

            Cumulative Review Chapters R–7

 

8. Exponential and Logarithmic Functions

8.1 Composite Functions and Inverse Functions

8.2 Exponential Functions

8.3 Logarithmic Functions

            Putting the Concepts Together (Sections 8.1—8.3)

8.4 Properties of Logarithms

8.5 Exponential and Logarithmic Equations

            Chapter 8 Activity: Correct the Quiz

            Chapter 8 Review

            Chapter 8 Test

 

9. Conics

9.1 Distance and Midpoint Formulas

9.2 Circles

9.3 Parabolas

9.4 Ellipses

9.5 Hyperbolas

            Putting the Concepts Together (Sections 9.1—9.5)

9.6 Systems of Nonlinear Equations

            Chapter 9 Activity: How Do You Know That&.?

            Chapter 9 Review

            Chapter 9 Test

            Cumulative Review Chapters R–9

 

10. Sequences, Series, and the Binomial Theorem

10.1 Sequences

10.2 Arithmetic Sequences

10.3 Geometric Sequences and Series

            Putting the Concepts Together (Sections 10.1—10.3)

10.4 The Binomial Theorem

            Chapter 10 Activity: Discover the Relation

            Chapter 10 Review

            Chapter 10 Test

 

Answers to Selected Exercises

Graphing Answer Sections

Application Index

Subject Index

Photo Credits