Elementary & Intermediate Algebra

For more than twenty years, Jay Lehmann has taught at College of San Mateo, where he has received the Shiny Apple Award for excellence in teaching. He has worked on a NSF-funded grant to study classroom assessment and has performed research on collaborative directed-discovery learning. Jay has served as the newsletter editor for CMC3 (California Mathematics Council, Community College) for twelve years. He has presented at more than seventy-five conferences, including AMATYC, ICTCM, and T3, where he has discussed curve fitting and sung his "Number Guy" song.   Jay plays in a rock band called The Procrastinistas, who play at various clubs in the San Francisco Bay Area, where Jay, his wife Keri, and son Dylan reside. He plays a number of instruments including bass, guitar, piano, violin, and baritone. In addition to his elementary, intermediate, and combined algebra textbooks, Jay is currently writing a heist novel for high school students, which he hopes will be published before Dylan outgrows it. Dylan, a devoted drummer and artist, drafted many of the cartoons that are included in Jay's textbooks.   In the words of the author:             Before writing my algebra series, it was painfully apparent that my students couldn't relate to the applications in the course. I was plagued with the question, "What is this good for?" To try to bridge that gap, I wrote some labs, which facilitated my students in collecting data, finding models via curve fitting, and using the models to make estimates and predictions. My students really loved working with the current, compelling, and authentic data and experiencing how mathematics truly is useful.             My students' response was so strong that I decided to write an algebra series. Little did I know that to realize this goal, I would need to embark on a 15-year challenging journey, but the rewards of hearing such excitement from students and faculty across the country has made it all worthwhile! I'm proud to have played even a small role in raising peoples' respect and enthusiasm for mathematics.              have tried to honor my inspiration: by working with authentic data, students can experience the power of mathematics. A random-sample study at my college suggests that I am achieving this goal. The study concludes that students who used my series were more likely to feel that mathematics would be useful in their lives (P-value 0.0061) as well as their careers (P-value 0.024).             The series is excellent preparation for subsequent courses; in particular, because of the curve fitting and emphasis on interpreting the contextual meaning of parameters, it is an ideal primer for statistics. In addition to curve fitting, my approach includes other types of meaningful modeling, directed-discovery explorations, conceptual questions, and of course, a large bank of skill problems. The curve-fitting applications serve as a portal for students to see the usefulness of mathematics so that they become fully engaged in the class. Once involved, they are more receptive to all aspects of the course.

Preface

Acknowledgments

Index of Applications

 

1. Introduction To Modeling

1.1 Variables And Constants

1.2 Scattergrams

1.3 Exact Linear Relationships

1.4 Approximate Linear Relationships

Taking It To The Lab: Climate Change Lab * Volume Lab * Linear

Graphing Lab: Topic Of Your Choice

            Chapter Summary

            Key Points Of Chapter 1

            Chapter 1 Review Exercises

            Chapter 1 Test

 

2. Operations And Expressions

2.1 Expressions

2.2 Operations With Fractions

2.3 Adding Real Numbers

2.4 Change In A Quantity And Subtracting Real Numbers

2.5 Ratios, Percents, And Multiplying And Dividing Real Numbers

2.6 Exponents And Order Of Operations

Taking It To The Lab: Climate Change Lab * Stocks Lab

            Chapter Summary

            Key Points Of Chapter 2

            Chapter 2 Review Exercises

            Chapter 2 Test

            Cumulative Review Of Chapters 1 And 2

 

3. Using Slope To Graph Linear Equations

3.1 Graphing Equations Of The Form y = mx + b

3.2 Graphing Linear Models; Unit Analysis

3.3 Slope Of A Line

3.4 Using Slope To Graph Linear Equations

3.5 Rate Of Change

            Taking It To The Lab: Climate Change Lab * Workout

            Lab * Balloon Lab

            Chapter Summary

            Key Points Of Chapter 3

            Chapter 3 Review Exercises

            Chapter 3 Test

 

4. Simplifying Expressions And Solving Equations

4.1 Commutative, Associative, And Distributive Laws

4.2 Simplifying Expressions

4.3 Solving Linear Equations In One Variable

4.4 Solving More Linear Equations In One Variable

4.5 Comparing Expressions And Equations

4.6 Formulas

            Chapter Summary

            Key Points Of Chapter 4

            Chapter 4 Review Exercises

            Chapter 4 Test

            Cumulative Review Of Chapters 1—4

 

5. Linear Functions And Linear Inequalities In One Variable

5.1 Graphing Linear Equations

5.2 Functions

5.3 Function Notation

5.4 Finding Linear Equations

5.5 Finding Equations Of Linear Models

5.6 Using Function Notation With Linear Models To Make Estimates And Predictions

5.7 Solving Linear Inequalities In One Variable

            Taking It To The Lab: Climate Change Lab * Golf Ball Lab *

            Rope Lab * Shadow Lab * Linear Lab: Topic Of Your Choice

            Chapter Summary

            Key Points Of Chapter 5

            Chapter 5 Review Exercises

            Chapter 5 Test

 

6. Systems Of Linear Equations And Systems Of Linear Inequalities

6.1 Using Graphs And Tables To Solve Systems

6.2 Using Substitution To Solve Systems

6.3 Using Elimination To Solve Systems

6.4 Using Systems To Model Data

6.5 Perimeter, Value, Interest, And Mixture Problems

6.6 Linear Inequalities In Two Variables; Systems Of Linear

            Inequalities In Two Variables

            Taking It To The Lab: Climate Change Lab * Sports Lab *

            Truck Lab

            Chapter Summary

            Key Points Of Chapter 6

            Chapter 6 Review Exercises

            Chapter 6 test 383

            Cumulative Review of Chapters 1—6

 

7. Polynomial Functions And Properties Of Exponents

7.1 Adding And Subtracting Polynomial Expressions And Functions

7.2 Multiplying Polynomial Expressions And Functions

7.3 Powers Of Polynomials; Product Of Binomial Conjugates

7.4 Properties Of Exponents

7.5 Dividing Polynomials: Long Division And Synthetic Division

            Taking It To The Lab: Climate Change Lab * Projectile Lab

            Chapter Summary

            Key Points Of Chapter 7

            Chapter 7 Review Exercises

            Chapter 7 Test

            Making Sure You’re Ready For Intermediate Algebra:

            A Review Of Chapters 1—7

 

8. Factoring Polynomials And Solving Polynomial Equations

8.1 Factoring Trinomials Of The Form x2 + bx + c And Differences of Two Squares

8.2 Factoring Out The GCF; Factoring By Grouping

8.3 Factoring Trinomials Of The Form ax2 + bx + c

8.4 Sums And Differences Of Cubes; A Factoring Strategy

8.5 Using Factoring To Solve Polynomial Equations

8.6 Using Factoring To Make Predictions With Quadratic Models

            Chapter Summary

            Key Points Of Chapter 8

            Chapter 8 Review Exercises

            Chapter 8 Test

            Making Sure You’re Ready For Intermediate Algebra:

            A Review Of Chapters 1—8

 

9. Quadratic Functions

9.1 Graphing Quadratic Functions In Vertex Form

9.2 Graphing Quadratic Functions In Standard Form

9.3 Simplifying Radical Expressions

9.4 Using The Square Root Property To Solve Quadratic Equations

9.5 Solving Quadratic Equations By Completing The Square

9.6 Using The Quadratic Formula To Solve Quadratic Equations

9.7 Solving Systems Of Linear Equations In Three Variables; Finding Quadratic Functions

9.8 Finding Quadratic Models

9.9 Modeling With Quadratic Functions

            Taking It To The Lab: Climate Change Lab * Projectile

            Lab * Projectile Lab (Using A CBR Or CBL) * Water Flow

            Lab * Quadratic Lab: Topic Of Your Choice

            Chapter Summary

            Key Points Of Chapter 9

            Chapter 9 Review Exercises

            Chapter 9 Test

            Cumulative Review Of Chapters 1—9

 

10. Exponential Functions

10.1 Integer Exponents

10.2 Rational Exponents

10.3 Graphing Exponential Functions

10.4 Finding Equations Of Exponential Functions

10.5 Using Exponential Functions To Model Data

            Taking It To The Lab: Stringed Instrument Lab * Cooling Water

            Lab * Exponential Lab: Topic Of Your Choice

            Chapter Summary

            Key Points Of Chapter 10

            Chapter 10 Review Exercises

            Chapter 10 Test

 

11. Logarithmic Functions

11.1 Composite Functions

11.2 Inverse Functions

11.3 Logarithmic Functions

11.4 Properties Of Logarithms

11.5 Using The Power Property With Exponential Models To Make Predictions

11.6 More Properties Of Logarithms

11.7 Natural Logarithms

            Taking It To The Lab: China And India Populations Lab * Folding

            Paper Lab * Exponential/Logarithmic Lab: Topic Of Your Choice

            Chapter Summary

            Key Points Of Chapter 11

            Chapter 11 Review Exercises

            Chapter 11 Test

            Cumulative Review Of Chapters 1—11

 

12. Rational Functions

12.1 Finding The Domains Of Rational Functions And Simplifying Rational Expressions

12.2 Multiplying And Dividing Rational Expressions; Converting Units

12.3 Adding And Subtracting Rational Expressions

12.4 Simplifying Complex Rational Expressions

12.5 Solving Rational Equations

12.6 Modeling With Rational Functions

12.7 Proportions; Similar Triangles

12.8 Variation

            Taking It To The Lab: Climate Change Lab * Illumination

            Lab * Boyle’s Law Lab * Estimating P Lab

            Chapter Summary

            Key Points Of Chapter 12

            Chapter 12 Review Exercises

            Chapter 12 Test

 

13. Radical Functions

13.1 Simplifying Radical Expressions

13.2 Adding, Subtracting, And Multiplying Radical Expressions

13.3 Rationalizing Denominators And Simplifying Quotients Of Radical Expressions

13.4 Graphing And Combining Square Root Functions

13.5 Solving Radical Equations

13.6 Modeling With Square Root Functions

            Taking It To The Lab: Pendulum Lab

            Chapter Summary

            Key Points Of Chapter 13

            Chapter 13 Review Exercises

            Chapter 13 Test

 

14. Sequences And Series

14.1 Arithmetic Sequences

14.2 Geometric Sequences

14.3 Arithmetic Series

14.4 Geometric Series

Taking It To The Lab: Bouncing Ball Lab * Stacked Cups Lab

            Chapter Summary

            Key Points Of Chapter 14

            Chapter 14 Review Exercises

            Chapter 14 Test

            Cumulative Review Of Chapters 1—14

 

15. Additional Topics

15.1 Absolute Value: Equations And Inequalities

            Key Points Of Section 15.1

15.2 Performing Operations With Complex Numbers

            Key Points Of Section 15.2

15.3 Pythagorean Theorem, Distance Formula, And Circles

            Key Points Of Section 15.3

15.4 Ellipses And Hyperbolas

            Key Points Of Section 15.4

15.5 Solving Nonlinear Systems Of Equations

            Key Points Of Section 15.5

 

A. Using A TI-83 Or TI-84 Graphing Calculator (Available Online Only)

A.1 Turning A Graphing Calculator On Or Off

A.2 Making The Screen Lighter Or Darker

A.3 Entering An Equation

A.4 Graphing An Equation

A.5 Tracing A Curve Without A Scattergram

A.6 Zooming

A.7 Setting The Window Format

A.8 Plotting Points In A Scattergram

A.9 Tracing A Scattergram

A.10 Graphing Equations With A Scattergram

A.11 Tracing A Curve With A Scattergram

A.12 Turning A Plotter On Or Off

A.13 Creating A Table

A.14 Creating A Table For Two Equations

A.15 Using “Ask” In A Table

A.16 Finding The Regression Curve For Some Data

A.17 Plotting Points In Two Scattergrams

A.18 Finding The Intersection Point(S) Of Two Curves

A.19 Finding The Minimum Point(S) Or Maximum Point(S) Of A Curve

A.20 Storing A Value

A.21 Finding Any X-Intercepts Of A Curve

A.22 Turning An Equation On Or Off

A.23 Finding Coordinates Of Points

A.24 Graphing Equations With Axes “Turned Off”

A.25 Entering An Equation By Using Yn References

A.26 Responding To Error Messages

 

Answers To Odd-Numbered Exercises

Index