College Algebra With Trigonometry

Chapter R: Basic Algebraic Operations

R-1 Algebra and Real Numbers

R-2 Exponents

R-3 Radicals

R-4 Polynomials: Basic Operations

R-5 Polynomials: Factoring

R-6 Rational Expressions: Basic Operations

Chapter R Review

Chapter R Group Activity: Rational Number Representations

Chapter 1: Equations and Inequalities

1-1 Linear Equations and Applications

1-2 Linear Inequalities

1-3 Absolute Value

1-4 Complex Numbers

1-5 Quadratic Equations and Applications

1-6 Equations Involving Radicals

Chapter 1 Review

Chapter 1 Group Activity: Solving a Cubic Equation

Chapter 2: Graphs

2-1 Cartesian Coordinate system

2-2 Distance in the Plane

2-3 Equations of a line

2-4 Linear Equations and Models

Chapter 2 Review

Chapter 2 Group Activity: Rates of Change

Chapter 3: Functions

3-1 Functions

3-2 Graphing Functions

3-3 Transformations of Functions

3-4 Quadratic Functions

3-5 Combining Functions; Composition

3-6 Inverse Functions

Chapter 3 Review

Chapter 3 Group Activity: Mathematical Modeling: Choosing a Long-Distance Calling Plan

Chapters 1-3 Cumulative Review Exercises

Chapter 4: Polynomials and Rational Functions

4-1 Polynomial Functions and Models

4-2 Real Zeros and Polynomial Inequalities

4-3 Complex Zeros and Rational Zeros of Polynomials

4-4 Rational Functions and Inequalities

4-5 Variation and Modeling

Chapter 4 Review

Chapter 4 Group Activity: Interpolating Polynomials

Chapter 5: Exponential and Logarithmic Functions

5-1 Exponential Functions

5-2 Exponential Models

5-3 Logarithmic Functions

5-4 Logarithmic Models

5-5 Exponential and Logarithmic Equations

Chapter 5 Review

Chapter 5 Group Activity: Growth of Increasing Functions

Chapters 4-5 Cumulative Review Exercises

Chapter 6: Trigonometric Functions

6-1 Angles and Their Measure

6-2 Right-Triangle Trigonometry

6-3 Trigonometric Functions: A Unit Circle Approach

6-4 Trigonometric Functions: Properties and Graphs

6-5 More General Trigonometric Functions

6-6 Inverse Trigonometric Functions

Chapter 6 Review

Chapter 6 Group Activity: A Predator-Prey Analysis Involving Mountain Lions and Deer

Chapter 7: Trigonometric Identities and Conditional Equations

7-1 Basic Identities and Their Use

7-2 Sum, Difference, and Cofunction Identities

7-3 Double-Angle and Half-Angle Identities

7-4 Product-Sum and Sum-Product Identities

7-5 Trigonometric Equations

Chapter 7 Review

Chapter 7 Group Activity: From M sin Bt + N cos Bt to A sin(Bt + C): A Harmonic Analysis Tool

Chapter 8: Additional Topics in Trigonometry

8-1 Law of Sines

8-2 Law of Cosines

8-3 Vectors in the Plane

8-4 Polar Coordinates and Graphs

8-5 Complex Numbers and De Moivre's Theorem

Chapter 8 Review

Chapter 8 Group Activity: Conic Sections and Planetary Orbits

Chapters 6-8 Cumulative Review Exercises

Chapter 9: Additional Topics in Analytic Geometry

9-1 Conic Sections; Parabolas

9-2 Ellipses

9-3 Hyperbolas

9-4 Rotation of Axes

Chapter 9 Review

Chapter 9 Group Activity: Focal Chords

Chapter 10: Systems of Equations and Inequalities; Matrices

10-1 Systems of Linear Equations: Graphing and Substitution

10-2 Systems of Linear Equations: Elimination

10-3 Systems of Linear Equations: Gauss-Jordan Elimination

10-4 Matrices: Basic Operations

10-5 Systems of Linear Equations: Matrix Inverse Methods

10-6 Systems of Nonlinear Equations

10-7 Systems of Linear Inequalities in Two Variables

10-8 Linear Programming

Chapter 10 Review

Chapter 10 Group Activity: Modeling With Systems of Linear Equations

Chapter 11: Sequences and Series

11-1 Sequences and Series

11-2 Mathematical Induction

11-3 Arithmetic and Geometric Sequences

11-4 Counting Techniques: Multiplication Principle, Permutations, and Combinations

11-5 Sample Spaces and Probability

11-6 Binomial Formula

Chapter 11 Review

Chapter 11 Group Activity: Sequences Specified by Recursion Formulas

Chapters 9-11 Cumulative Review Exercises

Appendix A: Special Topics

A-1 Scientific Notation and Significant Digits

A-2 Partial Fractions

A-3 Parametric Equations

Appendix B: Geometric Formulas