Introductory & Intermediate Algebra for College Students

Bob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob’s love for teaching mathematics was nourished for nearly 30 years at Miami Dade College, where he received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College and an endowed chair based on excellence in the classroom. In addition to Intermediate Algebra for College Students, Bob has written textbooks covering introductory algebra, college algebra, algebra and trigonometry, precalculus, and liberal arts mathematics, all published by Prentice Hall. When not secluded in his Northern California writer’s cabin, Bob can be found hiking the beaches and trails of Point Reyes National Seashore, and tending to the chores required by his beloved entourage of horses, chickens, and irritable roosters.

A Brief Guide to Getting the Most from This Book

Preface

To The Student

About the Author

 

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 Chapter 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)

 

Mid-Textbook Check Point


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 Business Applications Using Linear Inequalities

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 Systems of Linear Equations

C: Determinants and Cramer's Rule

D: Where Did That Come From? Selected Proofs

 

Answers to Selected Exercises

Graphing Answer Section (AIE only)

Applications Index

Subject Index

Photo Credits