Introductory and Intermediate Algebra

CONTENTS

 

A Brief Guide to Getting the Most from This Book

Preface

To The Student

About the Author

 

Chapter 1: The Real Number System

1.1 Fractions

1.2 The Real Numbers

1.3 Ordered Pairs and Graphs

1.4 Basic Rules of Algebra

Mid-Chapter Check Point

1.5 Addition of Real Numbers

1.6 Subtraction of Real Numbers

1.7 Multiplication and Division of Real Numbers

1.8 Exponents, Order of Operations, and Mathematical Models

Chapter 1 Group Project

Summary

Review Exercises

Chapter 1 Test


Chapter 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

2.5 An Introduction to Problem Solving

2.6 Problem Solving in Geometry

2.7 Solving Linear Inequalities

Chapter 2 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 2)

Chapter 2 Test


Chapter 3: Linear Equations in Two Variables

3.1 Graphing Equations in Two Variables

3.2 Graphing Linear Equations Using Intercepts

3.3 Slope                                                                       

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

Mid-Chapter Check Point

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

Chapter 3 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 3)

Chapter 3 Test


Chapter 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

4.4 Problem Solving Using Systems of Equations

4.5 Systems of Linear Equations in Three Variables

Chapter 4 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 4)

Chapter 4 Test


Chapter 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

5.5 Dividing Polynomials

5.6 Long Division of Polynomials; Synthetic Division

5.7 Negative Exponents and Scientific Notation

Chapter 5 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 5)

Chapter 5 Test


Chapter 6: Factoring Polynomials

6.1 The Greatest Common Factor and Factoring by Grouping

6.2 Factoring Trinomials Whose Leading Coefficient is One

6.3 Factoring Trinomials Whose Leading Coefficient Is Not One

Mid-Chapter Check Point

6.4 Factoring Special Forms

6.5 A General Factoring Strategy

6.6 Solving Quadratic Equations by Factoring

Chapter 6 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 6)

Chapter 6 Test


Chapter 7: Rational Expressions

7.1 Radical Expressions and Their Simplification

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions with the Same Denominators

7.4 Adding and Subtracting Rational Expressions with Different Denominators

Mid-Chapter Check Point

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

Summary

Cumulative Review Exercises (Chapters 1- 7)

Chapter 7 Test

 

Mid-Textbook Check Point


Chapter 8: Basics of Functions

8.1 Introduction to Functions

8.2 The Algebra of Functions

Mid-Chapter Check Point

8.3 Composite and Inverse Functions

Chapter 8 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 8)

Chapter 8 Test


Chapter 9: Inequalities and Problem Solving

9.1 Interval Notation and Business Applications Using Linear Inequalities

9.2 Compound Inequalities

9.3 Equations and Inequalities Involving Absolute Value

Mid-Chapter Check Point

9.4 Linear Inequalities in Two Variables

9.5 Linear Programming

Chapter 9 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 9)

Chapter 9 Test


Chapter 10: Radicals, Radical Functions, and Rational Exponents

10.1 Radical Expressions and Functions

10.2 Rational Expressions

10.3 Multiplying and Simplifying Radical Expressions

10.4 Adding, Subtracting, and Dividing Radical Expressions

Mid-Chapter Check Point

10.5 Multiplying with More Than One Term and Rationalizing Denominators

10.6 Radical Equalities

10.7 Complex Numbers

Chapter 10 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 10)

Chapter 10 Test

 

Chapter 11: Quadratic Equations and Functions

11.1 The Square Root Property and Completing the Square

11.2 The Quadratic Formula

11.3 Quadratic Functions and Their Graphs

Mid-Chapter Check Point

11.4 Equations Quadratic in Form

11.5 Polynomial and Rational Inequalities

Chapter 11 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 11)

Chapter 11 Test

 

Chapter 12: Exponential and Logarithmic Functions

12.1 Exponential Functions

12.2 Logarithmic Functions

12.3 Properties of Logarithms

Mid-Chapter Check Point

12.4 Exponential and Logarithmic Equations

12.5 Exponential Growth and Decay; Modeling Data

Chapter 12 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 12)

Chapter 12 Test

 

Chapter 13: Conic Sections and Systems of Nonlinear Equations 13.1 The Circle

13.2 The Ellipse

13.3 The Hyperbola

Mid-Chapter Check Point

13.4 The Parabola; Identifying Conic Sections

13.5 Systems of Nonlinear Equations in Two Variables

Chapter 13 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 13)

Chapter 13 Test

 

Chapter 14 Sequences, Induction, and Probability 14.1 Sequences and Summation Notation

14.2 Arithmetic Sequences

14.3 Geometric Sequences and Series

Mid-Chapter Check Points

14.4 The Binomial Theorem

14.5 Counting Principles, Permutations, and Combinations

14.6 Probability

Chapter 14 Group Project

Summary

Cumulative Review Exercises (Chapters 1- 14)

Chapter 14 Test

 

Appendices

            A: Matrix Solutions to Systems of Linear Equations

            B: Determinants and Cramer’s Rule

            C: Where Did That Come From? Selected Proofs

 

Answers to Selected Exercises

Graphing Answer Section

Applications Index

Subject Index

Photo Credits