Pre-Calculus Workbook For Dummies

340 Pages·2011·36.11 MB·English

by  Michelle Rose Gilman

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School of Mathematical and Statistical Sciences
ISBN: 978-0-470-92322-1 Arizona State University
55
Michelle Rose Gilman
$16.99 US Kuang 88
President and Founder, Fusion Academy and
$19.99 CN
Gilman
Learning Center
£13.99 UK Mathematics/Calculus
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by Dr. Yang Kuang and Michelle Rose Gilman,
with Elleyne Kase
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Pre-Calculus Workbook For Dummies®, 2nd Edition
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Published simultaneously in Canada
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Library of Congress Control Number: 2011921773
ISBN: 978-0-470-92322-1
Manufactured in the United States of America
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About the Authors
Dr. Yang Kuang is a proud father of three: Youny, Foris, and Belany. He has been a
professor of mathematics at Arizona State University (ASU) since 1988. He entered the
University of Science and Technology of China in 1980, went to the University of Oxford
in 1984 for a Master’s degree and completed a PhD in mathematics at University of
Alberta (Canada) in 1988, becoming a mathematics professor at ASU in the same year.
Yang Kuang has published over 120 refereed publications and authored or edited many
books. He has directed a dozen PhD dissertations and many funded research projects
in mathematical biology and medicine. He founded and continues to edit the journal
Mathematical Biosciences and Engineering. He has given mathematical research talks all
over the world and has organized many international mathematical biology and medi-
cine meetings. He is well-known for his pioneer work in the application of delay differen-
tial equations in models of biology and medicine and his ongoing work in establishing a
solid foundation and framework for building accurate, dynamic, rich population models
that explicitly include resource quality dynamics.
His more recent interest is to formulate scientifi cally well-grounded and computation-
ally tractable mathematical models to describe the rich and intriguing dynamics of
various within-host diseases and their treatments, including various types of cancer,
diabetic diseases, and virus-induced diseases such as infl uenza and hepatitis B virus
(HBV) infection. He hopes that these models will help speed up the much-needed devel-
opment of personalized medicine.
Yang Kuang teaches and uses calculus all the time. He is keenly aware of the many chal-
lenges facing students and instructors. He hopes this book will be helpful to many of
those who want to confront those challenges.
Michelle Rose Gilman is the founder and CEO of Fusion Learning Center and Fusion
Academy, a private school and tutoring/test prep facility in Solana Beach, California.
She is the author of Pre-Calculus For Dummies, The ACT For Dummies, and other books
on self-esteem, writing, and motivational topics.
Elleyne Kase is a multidisciplined artist and graphics professional whose creative
expertise has been applied commercially in many different avenues, such as fi ne art
designs for the commercial interior design industry, Wayfi nding programs for large hos-
pital systems, 3D displays, Web site design, and national brand identity. A bachelor’s
degree in graphic design from San Jose State University began her professional career
in the San Francisco Bay Area, which continued in San Diego design agencies as her
family grew.
Book design, a favorite of hers, began early on in her career and has now been applied
to two of her own exam prep publications, Visual Quick Notes for Life Insurance and
Visual Quick Notes for Life and Health. Both use her new mind mapping system, an
evolution of her study on how the mind absorbs data, to explain simple terms and con-
cepts in an organized visual matrix of graphic elements and text that improves memory
retention.
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Authors’ Acknowledgments
From Yang:
I would like to thank Elleyne Kase for inviting me to take part in this unusual book
project and all the people involved in the process. It was a joy working with all of you.
I would also like to thank Professor Jamie Whittimore McGill and Dr. Scott Parsell for
providing a detailed technical review of this edition.
And last, but not least, I am forever grateful to my wife, Aijun, for her beautiful creation
of and the great attention she devotes to the family, so that I can have time to do my
work, including carrying out this project.
From Elleyne:
Throughout my varied career I have had the great pleasure of working with profes-
sionals of many disciplines. The For Dummies series combines the skills of many very
talented people. I want to express my gratitude to Bill Gladstone who gave me this rare
opportunity to participate; to the editors at Wiley — Lindsay Lefevere, Tracy Boggier,
Elizabeth Rea, and Christy Pingleton — for their professionalism, understanding, and
skill in bringing such a complex product to market; and to Yang Kuang who juggled his
demanding teaching schedule to accommodate this project.
Above all I want to thank my dear mother, who has always supported me in all my
varied interests, and my three children, Seth, Shane, and Mimi, who have grown to
become wonderful, nurturing, caring adults and my best friends.
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Contents at a Glance
Introduction ............................................................................1
Part I: Setting the Foundation: The Nuts and
Bolts of Pre-Calculus ...............................................................5
Chapter 1: Beginning at the Very Beginning: Pre-Pre-Calculus .......................................................7
Chapter 2: Real Numbers Come Clean .............................................................................................23
Chapter 3: Controlling Functions by Knowing Their Function .....................................................37
Chapter 4: Searching Roots to Get the Degree ...............................................................................69
Chapter 5: Exponential and Logarithmic Functions .......................................................................87
Part II: Trig Is the Key: Basic Review,
the Unit Circle, and Graphs ................................................103
Chapter 6: Basic Trigonometry and the Unit Circle .....................................................................105
Chapter 7: Graphing and Transforming Trig Functions ...............................................................127
Part III: Digging into Advanced Trig: Identities,
Theorems, and Applications ..................................................143
Chapter 8: Basic Trig Identities .......................................................................................................145
Chapter 9: Advanced Identities .......................................................................................................161
Chapter 10: Solving Oblique Triangles ...........................................................................................177
Part IV: Poles, Cones, Variables, Sequences,
and Finding Your Limits .......................................................195
Chapter 11: Exploring Complex Numbers and Polar Coordinates .............................................197
Chapter 12: Conquering Conic Sections ........................................................................................213
Chapter 13: Finding Solutions for Systems of Equations .............................................................245
Chapter 14: Spotting Patterns in Sequences, Series, and Binomials .........................................277
Chapter 15: Previewing Calculus ....................................................................................................289
Part V: The Part of Tens .......................................................301
Chapter 16: Ten Uses for Parent Graphs .......................................................................................303
Chapter 17: Ten Missteps to Avoid in Pre-Calculus .....................................................................311
Index ..................................................................................315
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Table of Contents
Introduction .............................................................................1
About This Book .................................................................................................................1
Conventions Used in This Book ........................................................................................2
Foolish Assumptions ..........................................................................................................2
How This Book Is Organized .............................................................................................2
Part I: Setting the Foundation: The Nuts and Bolts of Pre-Calculus ...................2
Part II: Trig Is the Key: Basic Review, the Unit Circle, and Graphs ....................2
Part III: Digging into Advanced Trig: Identities,
Theorems, and Applications ................................................................................3
Part IV: Poles, Cones, Variables, Sequences, and Finding Your Limits..............3
Part V: The Part of Tens ...........................................................................................3
Icons Used in This Book ....................................................................................................3
Where to Go from Here ......................................................................................................4
Part I: Setting the Foundation: The Nuts and
Bolts of Pre-Calculus ................................................................5
Chapter 1: Beginning at the Very Beginning: Pre-Pre-Calculus. . . . . . . . . . . . . . .7
Reviewing Order of Operations: The Fun in Fundamentals ..........................................7
Keeping Your Balance While Solving Equalities ...........................................................10
When Your Image Really Counts: Graphing Equalities and Inequalities ...................12
Graphing with the plug-and-chug method ...........................................................12
Graphing by using the slope-intercept form .......................................................13
Graphing inequalities by either method ..............................................................14
Using Graphs to Find Distance, Midpoint, and Slope ..................................................15
Finding the distance ...............................................................................................15
Calculating the midpoint........................................................................................15
Discovering the slope .............................................................................................16
Answers to Problems on Fundamentals ........................................................................18
Chapter 2: Real Numbers Come Clean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
Solving Inequalities ..........................................................................................................23
Expressing Inequality Solutions in Interval Notation ..................................................26
Don’t Panic with Radicals and Exponents — Just Simplify! ........................................28
Getting Out of a Sticky Situation, or Rationalizing .......................................................31
Answers to Problems on Real Numbers ........................................................................33
Chapter 3: Controlling Functions by Knowing Their Function. . . . . . . . . . . . . . . .37
Using Both Faces of the Coin: Even and Odd ................................................................37
Leaving the Nest: Transforming Parent Graphs ...........................................................39
Quadratic functions ................................................................................................39
Square root functions .............................................................................................40
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