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Dear Teacher,
This is a different Precalculus text. It contains all of the topics that
you would expect to find in a Precalculus text and more; but it is a
text written by COMAP and applications is our middle name. Thus
you will see the concepts and skills of Precalculus presented from
an applications and modeling point of view. Moreover, this is an
activity and problemsolving based book. We want students to experience the
mathematics they are learning in a way that will make both the mathematics
and the contemporary applications come alive.
We make serious use of graphing calculators and a variety of software,
including spreadsheets and geometric utility programs. We introduce and
make use of data analysis techniques. All of which permit us to analyze
deeper and more meaningful problems. And we have attempted to add
material that will in fact, as well as name, better prepare students for their
work in calculus—from our introductory work on functions to our final
chapter on finite difference equations. We use a spiraling approach, coming
back to earlier ideas in later chapters, so that we can keep those ideas,
concepts, and skills alive, reinforcing their importance as well as providing
additional practice.
This text follows on over twenty years of work by COMAP in curriculum
reform. As such there are a great many people whose work past and present
should be acknowledged. First and foremost, we wish to recognize the
author team led by Gary Froelich and Nancy Crisler. We also want to pay
special tribute to the COMAP production staff led by George Ward who
worked tirelessly, with unreasonable deadlines, to create this handsome text.
Solomon Garfunkel
EXECUTIVE DIRECTOR, COMAP
CHAPTER 1
Functions in Modeling
Introduction
LESSON 1.1
Functions as Models
LESSON 1.2
Creating a Mathematical Model
LESSON 1.3
Modeling Linear Patterns: Beginning the Tool Kit of Functions
LESSON 1.4
Expanding the Tool Kit of Functions
LESSON 1.5
Transformations of Functions
LESSON 1.6
Operations on Functions
CHAPTER 1 REVIEW
CHAPTER 2
The Exponential and Logarithmic Functions
LESSON 2.1
Exponential Functions
LESSON 2.2
Logarithmic Scale
LESSON 2.3
Changing Bases
LESSON 2.4
Logarithmic Functions
LESSON 2.5
Modeling with Exponential and Logarithmic Functions
LESSON 2.6
Composition and Inverses of Functions
CHAPTER 2 REVIEW
CHAPTER 3
Polynomial Models
LESSON 3.1
Modeling Falling Objects
LESSON 3.2
The Merits of Polynomial Models
LESSON 3.3
The Power of Polynomials
LESSON 3.4
Zeroing in on Polynomials
LESSON 3.5
Polynomial Divisions
LESSON 3.6
Polynomial Approximations
CHAPTER 4
Trigonometric Functions
LESSON 4.1
Oscillating Phenomena and Periodic Functions
LESSON 4.2
The Sine Function
LESSON 4.3
The Cosine Function
LESSON 4.4
The Tangent and Other Functions
CHAPTER 5
Triangle Trigonometry
LESSON 5.1
Right Triangles
LESSON 5.2
Inverses
LESSON 5.3
Oblique Triangles
CHAPTER 6
Coordinate Systems and Vectors
LESSON 6.1
Polar Coordinates
LESSON 6.2
Polar Form of Complex Numbers
LESSON 6.3
The Geometry of Vectors
LESSON 6.4
The Algebra of Vectors
LESSON 6.5
Vector and Parametric Equations in Two Dimensions
LESSON 6.6
Vector Equations in Three Dimensions
CHAPTER 6 REVIEW
CHAPTER 7
Matrices
LESSON 7.1
Matrix Basics
LESSON 7.2
The Multiplicative Inverse
LESSON 7.3
Systems of Equations in Three Variables
CHAPTER 8
Analytic Geometry
LESSON 8.1
Analytic Geometry and Loci
LESSON 8.2
Modeling with Circles
LESSON 8.3
Modeling with Parabolas
LESSON 8.4
Modeling with Ellipses
LESSON 8.5
Modeling with Hyperbolas
CHAPTER 8 REVIEW
CHAPTER 9
Counting and the Binomial Theorem
LESSON 9.1
Counting Basics
LESSON 9.2
Compound Events
LESSON 9.3
The Binomial Theorem
CHAPTER 10
Modeling Change with Discrete Dynamical Systems
LESSON 10.1
Modeling Change with Difference Equations
LESSON 10.2
Approximating Change with Difference Equations
LESSON 10.3
Numerical Solutions
LESSON 10.4
Systems of Difference Equations
Teacher’s Guide
Teacher’s Resources
Handouts
Assessment Problems
Transparencies
Software
Solutions Manual
Supplemental Activities
