Table of Contents

R.   Review

R.1 Real Numbers

R.2 Algebra Essentials

R.3 Geometry Essentials

R.4 Polynomials

R.5 Factoring Polynomials

R.6 Synthetic Division

R.7 Rational Expressions

R.8 nth Roots; Rational Exponents


1.    Equations and Inequalities

1.1  Linear Equations

1.2  Quadratic Equations

1.3  Complex Numbers; Quadratic Equations in the Complex Number System

1.4  Radical Equations; Equations Quadratic in Form; Factorable Equations

1.5  Solving Inequalities

1.6  Equations and Inequalities Involving Absolute Value

1.7  Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications

Chapter 1 Review, Test, and Projects


2.    Graphs

2.1  The Distance and Midpoint Formulas

2.2  Graphs of Equations in Two Variables; Intercepts; Symmetry

2.3  Lines

2.4  Circles

2.5  Variation

Chapter 2 Review, Test, and Projects


3.    Functions and Their Graphs

3.1  Functions

3.2  The Graph of a Function

3.3  Properties of Functions

3.4  Library of Functions; Piecewise-defined Functions

3.5  Graphing Techniques: Transformations

3.6  Mathematical Models: Building Functions

Chapter 3 Review, Test, and Projects


4.     Linear and Quadratic Functions

4.1  Properties of Linear Functions and Linear Models

4.2  Building Linear Models from Data

4.3  Quadratic Functions and Their Properties

4.4  Build Quadratic Models from Verbal Descriptions and from Data

4.5  Inequalities Involving Quadratic Functions

Chapter 4 Review, Test, and Projects


5.     Polynomial and Rational Functions

5.1  Polynomial Functions

5.2  Graphing Polynomials Functions; Models

5.3  Properties of Rational Functions

5.4  The Graph of a Rational Function

5.5  Polynomial and Rational Inequalities

5.6  The Real Zeros of a Polynomial Function

Chapter 5 Review, Test, and Projects


6.     Exponential and Logarithmic Functions

6.1  Composite Functions

6.2  One-to-One Functions; Inverse Functions

6.3  Exponential Functions

6.4  Logarithmic Functions

6.5  Properties of Logarithms

6.6  Logarithmic and Exponential Equations

6.7  Financial Models

6.8  Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models

6.9  Building Exponential, Logarithmic, and Logistic Models from Data

Chapter 6 Review, Test, and Projects


7.    Trigonometric Functions

7.1  Angles, Arc, Length, and Circular Motion

7.2  Right Triangle Trigonometry

7.3  Computing the Values of Trigonometric Functions of Acute Angles

7.4  Trigonometric Functions of Any Angle

7.5  Unit Circle Approach; Properties of the Trigonometric Functions

7.6  Graphs of the Sine and Cosine Functions

7.7  Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions

7.8  Phase Shift; Sinusoidal Curve Fitting

Chapter 7 Review, Test, and Projects


8.     Analytic Trigonometry

8.1  The Inverse Sine, Cosine, and Tangent Functions

8.2  The Inverse Trigonometric Functions (Continued)

8.3  Trigonometric Equations

8.4  Trigonometric Identities

8.5  Sum and Difference Formulas

8.6  Double-angle and Half-angle Formulas

8.7  Product-to-Sum and Sum-to-Product Formulas

Chapter 8 Review, Test, and Projects


9.    Applications of Trigonometric Functions

9.1  Applications Involving Right Triangles

9.2  The Law of Sines

9.3  The Law of Cosines

9.4  Area of a Triangle

9.5 Simple Harmonic Motion; Damped Motion; Combining Waves

Chapter 9 Review, Test, and Projects


10.  Polar Coordinates; Vectors

10.1  Polar Coordinates

10.2  Polar Equations and Graphs

10.3  The Complex Plane; De Moivre’s Theorem

10.4  Vectors

10.5  The Dot Product

Chapter 10 Review, Test, and Projects


11.  Analytic Geometry

11.1  Conics

11.2  The Parabola

11.3  The Ellipse

11.4  The Hyperbola

11.5  Rotation of Axes; General Form of a Conic

11.6  Polar Equations of Conics

11.7  Plane Curves and Parametric Equations

Chapter 11 Review, Test, and Projects


12.  Systems of Equations and Inequalities

12.1  Systems of Linear Equations: Substitution and Elimination

12.2  Systems of Linear Equations: Matrices

12.3  Systems of Linear Equations: Determinants

12.4  Matrix Algebra

12.5  Partial Fraction Decomposition

12.6  Systems of Nonlinear Equations

12.7  Systems of Inequalities

12.8  Linear Programming

Chapter 12 Review, Test, and Projects      


13.  Sequences; Induction; the Binomial Theorem

13.1  Sequences

13.2  Arithmetic Sequences

13.3  Geometric Sequences; Geometric Series

13.4  Mathematical Induction

13.5  The Binomial Theorem

 Chapter 13 Review, Test, and Projects


14.  Counting and Probability

14.1  Counting

14.2  Permutations and Combinations

14.3  Probability

Chapter 14 Review, Test, and Projects


Appendix: Graphing Utilities

A.1 The Viewing Rectangle

A.2 Using a Graphing Utility to Graph Equations

A.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry

A.4 Using a Graphing Utility to Solve Equations

A.5 Square Screens

A.6 Using a Graphing Utility to Graph Inequalities

A.7 Using a Graphing Utility to Solve Systems of Linear Equations

A.8 Using a Graphing Utility to Graph a Polar Equation

A.9 Using a Graphing Utility to Graph Parametric Equations