High School Algebra II Unlocked: Your Key to Mastering Algebra II

635 Pages·2016·25.24 MB·English

by  Princeton Review

Acknowledgments
I first and foremost thank my family for always being supportive
of me in all my endeavors. My high school math teachers,
especially the talented Ed Davis, were inspiring and
encouraging, as was Ali, who believed I was capable of
studying graduate level math as an undergrad. I am grateful to
Sara for opening the door to the world of test preparation work
for me. Thanks to Aaron Riccio and the rest of the staff at The
Princeton Review for the tremendous amount of work they put
into the creation of this especially challenging book. I
appreciate all of the opportunities TPR has given me over the
years. Finally, I thank my wonderful husband, Takashi, whose
support and confidence have sustained me throughout this
process.
—Theresa Duhon
Additionally, The Princeton Review would like to emphatically
thank Theresa Duhon for her unwavering, above-and-beyond
commitment to this project, Maurice Kessler for his outstanding
attention to detail and design, Craig Patches and Scott Harris
for bearing with us through the art creation process, and
Deborah A. Silvestrini for her nonstop, can-do attitude toward
laying out this book. Special thanks also to Liz Rutzel and
Harmony Quiroz for reviewing this text.
Contents
Cover
Title Page
Copyright
Acknowledgments
Register Your Book Online!
About This Book
1 Complex Numbers and Polynomials
Lesson 1.1 Complex Numbers
Lesson 1.2 Operations with Polynomials
Lesson 1.3 Polynomial Identities
Lesson 1.4 Graphing Polynomials (Beyond Quadratics)
Lesson 1.5 Tips for Factoring Polynomials
Lesson 1.6 Polynomials in the Real World
2 Systems of Equations and Rational Expressions
Lesson 2.1 The Fundamental Theorem of Algebra
Lesson 2.2 Systems of Equations
Lesson 2.3 Variation Equations
Lesson 2.4 Rational Expressions
3 Radical and Rational Equations and Inequalities
Lesson 3.1 Rational Equations in One Variable
Lesson 3.2 Rational Inequalities in One Variable
Lesson 3.3 Rational Functions
Lesson 3.4 Radical Equations in One Variable
Lesson 3.5 Radical Inequalities in One Variable
Lesson 3.6 Radical Functions
4 Trigonometric Functions
Lesson 4.1 Trigonometric Ratios and Triangles
Lesson 4.2 Radians
Lesson 4.3 Trigonometric Functions and Circles
Lesson 4.4 Graphing Trigonometric Functions
Lesson 4.5 Trigonometric Function Identities
Lesson 4.6 Trigonometric Functions in Real Life
5 Logarithms
Lesson 5.1 Inverse Functions
Lesson 5.2 Logarithms
Lesson 5.3 Logarithmic Identities
Lesson 5.4 Logarithmic Functions
Lesson 5.5 Logarithms in the Real World
6 More Functions
Lesson 6.1 Cube Root Functions
Lesson 6.2 Piecewise-Defined Functions
Lesson 6.3 Exponential Functions
7 Making and Using Mathematical Models
Lesson 7.1 Manipulating Equations
Lesson 7.2 Interpreting Equations, Tables, and Graphs
Lesson 7.3 Modeling Situations with Equations and
Inequalities
Lesson 7.4 Modeling Situations with Graphs
8 Inferences and Conclusions from Data
Lesson 8.1 Data Collection
Lesson 8.2 Means and Measures of Variability
Lesson 8.3 Frequency Distributions
Lesson 8.4 Probability Distributions
Lesson 8.5 Sample Proportions and Sampling
Distributions
Lesson 8.6 Confidence Intervals and Margins of Error
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Online Practice
About This Book
WHY HIGH SCHOOL UNLOCKED?
It might not always seem that way, especially after a night of
endless homework assignments, but high school can fly by.
Classes are generally a little larger, subjects are more complex,
and not every student has had the same background for each
subject. Teachers don’t always have the time to re-explain a
topic, and worse, sometimes students don’t realize that there’s
a subject they don’t fully understand. This feeling of frustration
is a bit like getting to your locker and realizing that you’ve
forgotten a part of the combination to open it, only there’s no
math superintendent you can call to clip the lock open.
That’s why we at The Princeton Review, the leaders in test
prep, have built the High School Unlocked series. We can’t
guarantee that you won’t forget something along the way—
nobody can—but we can set the tools for unlocking problems at
your fingertips. That’s because this book not only covers all the
basics of Algebra II, but it also focuses on alternative
approaches and emphasizes how all of these techniques
connect with one another.
How to Use This Book
The speed at which you go through this material depends on
your personal needs. If you’re using this book to supplement
your daily high-school classes, we recommend that you stay at
your daily high-school classes, we recommend that you stay at
the pace of your class, and make a point out of solving
problems in both this book and your homework in as many
ways as you can. This is the most direct way to identify
effective (and practical) tools.
If, on the other hand, you’re using this book to review topics,
then you should begin by carefully reviewing the Goals listed at
the start of each chapter, and taking note of anything that
seems unfamiliar or difficult. Try answering some of the
example problems on your own, as you might just be a little
rusty. Applying math skills is a lot like riding a bike, in that it
comes back quickly—but that’s only true if you learned how in
the first place. Take as much time as you need, then, to
connect with this material. As a real test of your understanding,
try teaching one of these troublesome topics to someone else.
Ultimately, there’s no “wrong” way to use this book. You
wouldn’t have picked this up if you weren’t genuinely interested,
so the real key is that you remain patient and give yourself as
much time as you need before moving on. To aid in this, we’ve
carefully designed each chapter to break down each concept in
a series of consistent and helpful ways.
Goals and Reflect
Each chapter begins with a clear and specific list of objectives
that you should feel comfortable with by the end of the chapter.
This allows you not only to assess which sections of the book
you need to focus on, but also to clarify the underlying skills
that each example is helping to demonstrate. Think of this sort
of goal-based structure as a scavenger hunt: it’s generally more
efficient to find something if you know what you’re looking for.