## Table of Contents

**Review Chapter**

R.1 Real Numbers

R.2 The Order of Operations and Algebraic Expressions

R.3 The Laws of Exponents; Radicals

R.4 Polynomials

R.5 Factoring Polynomials

R.6 Rational Expressions

**1. Equations, Inequalities, and Applications**

1.1 Linear Equations

1.2 Applications of Linear Equations

1.3 Complex Numbers

1.4 Quadratic Equations

1.5 Applications of Quadratic Equations

1.6 Other Types of Equations

1.7 Linear Inequalities

1.8 Absolute Value Equations and Inequalities

1.9 Polynomial and Rational Inequalities

**2. The Rectangular Coordinate System, Lines, and Circles**

2.1 The Rectangular Coordinate System

2.2 Circles

2.3 Lines

2.4 Parallel and Perpendicular Lines

**3. Functions**

3.1 Relations and Functions

3.2 Properties of a Function's Graph

3.3 Graphs of Basic Functions; Piecewise Functions

3.4 Transformations of Functions

3.5 The Algebra of Functions; Composite Functions

3.6 One-to-One Functions; Inverse Functions

**4. Polynomial and Rational Functions**

4.1 Quadratic Functions

4.2 Applications and Modeling of Quadratic Functions

4.3 The Graphs of Polynomial Functions

4.4 Synthetic Division; The Remainder and Factor Theorems

4.5 The Zeros of Polynomial Functions; The Fundamental Theorem of Algebra

4.6 Rational Functions and Their Graphs

4.7 Variation

**5. Exponential and Logarithmic Functions and Equations**

5.1 Exponential Functions

5.2 Logarithmic Functions

5.3 Properties of Logarithms

5.4 Exponential and Logarithmic Equations

5.5 Applications of Exponential and Logarithmic Functions

**6. An Introduction to Trigonometric Functions**

6.1 An Introduction to Angles: Degree and Radian Measure

6.2 Applications of Radian Measure

6.3 Triangles

6.4 Right Triangle Trigonometry

6.5 Trigonometric Functions of General Angles

6.6 The Unit Circle

**7. The Graphs of Trigonometric Functions**

7.1 The Graphs of Sine and Cosine

7.2 More on Graphs of Sine and Cosine; Phase Shift

7.3 The Graphs of the Tangent, Cosecant, Secant, and Cotangent Functions

7.4 Inverse Trigonometric Functions I

7.5 Inverse Trigonometric Functions II

**8. Trigonometric Identities, Formulas, and Equations**

8.1 Trigonometric Identities

8.2 The Sum and Difference Formulas

8.3 The Double-Angle and Half-Angle Formulas

8.4 The Product-to-Sum and Sum-to-Product Formulas

8.5 Trigonometric Equations

**9. Applications of Trigonometry**

9.1 Right Triangle Applications

9.2 The Law of Sines

9.3 The Law of Cosines

9.4 Area of Triangles

**10. Polar Equations, Complex Numbers, and Vectors**

10.1 Polar Coordinates and Polar Equations

10.2 Graphing Polar Equations

10.3 Complex Numbers in Polar Form; DeMoivre’s Theorem

10.4 Vectors

10.5 The Dot Product

**11. Conic Sections and Parametric Equations**

11.1 The Parabola

11.2 The Ellipse

11.3 The Hyperbola

11.4 Conic Sections in Polar Form

11.5 Parametric Equations

**12. Systems of Equations and Inequalities**

12.1 Solving Systems of Linear Equations in Two Variables

12.2 Solving Systems of Linear Equations in Three Variables Using the Elimination Method

12.3 Solving Systems of Linear Equations in Three Variables Using Gaussian Elimination and Gauss-Jordan Elimination

12.4 Partial Fraction Decomposition

12.5 Systems of Nonlinear Equations

12.6 Systems of Inequalities

**13. Matrices**

13.1 Matrix Operations

13.2 Inverses of Matrices and Matrix Equations

13.3 Determinants and Cramer's Rule

**14. Sequences and Series; Counting and Probability**

14.1 Introduction to Sequences and Series

14.2 Arithmetic Sequences and Series

14.3 Geometric Sequences and Series

14.4 The Binomial Theorem

14.5 Mathematical Induction

14.6 The Theory of Counting

14.7 An Introduction to Probability

**Appendix A: Degree, Minute, Second Form and Degree Decimal Form**

Appendix B: Conic Section Proofs