## Table of Contents

Preface.

To the Student.

Prologue: Principles of Problem Solving.

P. PREREQUISITES.

P1. Modeling the Real-World with Algebra. P2. The Real Numbers. P3. Integer Exponents and Scientific Notation. P4. Rational Exponents and Radicals.

P5. Algebraic Expressions. P6. Factoring. P7. Rational Expressions. P8. Solving Basic Equations. P9. Modeling with Equations. Chapter P Review. Chapter P Test.

FOCUS ON MODELING: MAKING THE BEST DECISIONS.

1. EQUATIONS AND GRAPHS.

1.1 The Coordinate Plane. 1.2 Graphs of Equations in Two Variables; Circles. 1.3 Lines. 1.4 Solving Quadratic Equations. 1.5 Complex Numbers. 1.6 Solving Other Types of Equations. 1.7 Solving Inequalities. 1.8 Solving Absolute Value Equations and Inequalities. 1.9 Solving Equations and Inequalities Graphically. 1.10 Modeling Variations. Chapter 1 Review. Chapter 1 Test.

FOCUS ON MODELING: Fitting Lines to Data.

2. FUNCTIONS.

Chapter Overview.2.1 Functions. 2.2 Graphs of Functions. 2.3 Getting Information from the Graph of a Function. 2.4 Average Rate of Change of a Function. 2.5 Linear Functions and Models. 2.6 Transformations of Functions. 2.7 Combining Functions. 2.8 One-to-One Functions and Their Inverses. Chapter 2 Review. Chapter 2 Test.

FOCUS ON MODELING: MODELING WITH FUNCTIONS.

3. POLYNOMIAL AND RATIONAL FUNCTIONS.

Chapter Overview. 3.1. Quadratic Functions and Models. 3.2 Polynomial Functions and Their Graphs. 3.3 Dividing Polynomials. 3.4 Real Zeros of Polynomials. 3.5 Complex Zeros and the Fundamental Theorem of Algebra. 3.6 Rational Functions. 3.7 Polynomial and Rational Inequalities. Chapter 3 Review. Chapter 3 Test.

FOCUS ON MODELING: FITTING POLYNOMIAL CURVES TO DATA.

4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.

Chapter Overview. 4.1 Exponential Functions. 4.2 The Natural Exponential Function. 4.3 Logarithmic Functions. 4.4 Laws of Logarithms. 4.5 Exponential and Logarithmic Equations. 4.6 Modeling with Exponential Functions. 4.7 Logarithmic Scales. Chapter 4 Review. Chapter 4 Test.

FOCUS ON MODELING: FITTING EXPONENTIAL AND POWER CURVES TO DATA.

5. TRIGONOMETRIC FUNCTIONS: RIGHT TRIANGLE APPROACH.

Chapter Overview.

5.1 Angle Measure.

5.2 Trigonometry of Right Triangles.

5.3 Trigonometric Functions of Angles. 5.4 Inverse Trigonometric Functions and Triangles. 5.5 The Law of Sines. 5.6 The Law of Cosines. 5.7 Chapter 5 Review. Chapter 5 Test.

FOCUS ON MODELING: SURVEYING.

1. TRIGONOMETRIC FUNCTIONS: UNIT CIRCLE APPROACH.

Chapter Overview.

6.1 The Unit Circle. 6.2 Trigonometric Functions of Real Numbers. 6.3 Trigonometric Graphs. 6.4 More Trigonometric Graphs. 6.5 Inverse Trigonometric Functions and Their Graphs. 6.6 Modeling Harmonic Motion. Chapter 6 Review. Chapter 6 Test.

FOCUS ON MODELING: FITTING SINUSOIDAL CURVES TO DATA.

7. CONIC SECTIONS.

Chapter Overview.

7.1 Trigonometric Identities. 7.2 Addition and Subtraction Formulas. 7.3 Double-Angle, Half-Angle, and Sum-Product Formulas. 7.4 Basic Trigonometric Equations. 7.5 More Trigonometric Equations. Chapter 7 Review. Chapter 7 Test.

FOCUS ON MODELING: TRAVELING AND STANDING WAVES.

8. POLAR COORDINATES AND PARAMETRIC EQUATIONS.

Chapter Overview. 8.1 Polar Coordinates. 8.2 Graphs of Polar Equations. 8.3 Polar Form of Complex Numbers; De Moivre''s Theorem. 8.4 Plane Curves and Parametric Equations. Chapter 8 Review. Chapter 8 Test.

FOCUS ON MODELING: THE PATH OF A PROJECTILE.

9. VECTORS IN TWO AND THREE DIMENSIONS.

Chapter Overview. 9.1 Vectors in Two Dimensions. 9.2 The Dot Product. 9.3 Three–Dimensional Coordinate Geometry. 9.4 Vectors in Three Dimensions. 9.5 The Cross Product. 9.6 Equations of Lines and Planes. Chapter 9 Review. Chapter 9 Test.

FOCUS ON MODELING: VECTOR FIELDS.

10. SYSTEMS OF EQUATIONS AND INEQUALITIES.

10.1 Systems of Linear Equations in Two Variables. 10.2 Systems of Linear Equations in Several Variables. 10.3 Partial Fractions. 10.4 Systems of Nonlinear Equations. 10.5 Systems of Inequalities. Chapter 10 Review. Chapter 10 Test.

FOCUS ON MODELING: LINEAR PROGRAMMING.

11. MATRICES AND DETERMINANTS.

11.1 Matrices and Systems of Linear Equations. 11.2 The Algebra of Matrices. 11.3 Inverses of Matrices and Matrix Equations. 11.4 Determinants and Cramer''s Rule. Chapter 11 Review. Chapter 11 Test.

FOCUS ON MODELING: COMPUTER GRAPHICS.

12. CONIC SECTIONS.

Chapter Overview. 12.1 Parabolas. 12.2 Ellipses. 12.3 Hyperbolas. 12.4 Shifted Conics. 12.5 Rotation of Axes. 12.6 Polar Equations of Conics. Chapter 12 Review. Chapter 12 Test.

FOCUS ON MODELING: CONICS IN ARCHITECTURE.

13. SEQUENCES AND SERIES.

Chapter Overview. 13.1 Sequences and Summation Notation. 13.2 Arithmetic Sequences. 13.3 Geometric Sequences. 13.4 Mathematics of Finance. 13.5 Mathematical Induction. 13.6 The Binomial Theorem. Chapter 13 Review. Chapter 13 Test.

FOCUS ON MODELING: MODELING WITH RECURSIVE SEQUENCES.

14. COUNTING AND PROBABILITY.

14.1 Counting. 14.2 Probability. 14.3 Binomial Probability. 14.4 Expected Value. Chapter 14 Review. Chapter 14 Test.

FOCUS ON MODELING: THE MONTE CARLO METHOD.

APPENDIX A: Geometry Review.

APPENDIX B: Calculations and Significant Figures.

APPENDIX C: Graphing with a Graphing Calculator.

APPENDIX D: Using the TI-83/84 Graphing Calculator.