R. Review of Basic Concepts

• R.1. Fractions, Decimals, and Percents
• R.2. Sets and Real Numbers
• R.3. Real Number Operations and Properties
• R.4. Integer and Rational Exponents
• R.5. Polynomials
• R.6. Factoring Polynomials
• R.7. Rational Expressions
• R.8. Radical Expressions

1. Equations and Inequalities

• 1.1. Linear Equations
• 1.2. Applications and Modeling with Linear Equations
• 1.3. Complex Numbers
• 1.4. Quadratic Equations
• 1.5. Applications and Modeling with Quadratic Equations
• 1.6. Other Types of Equations and Applications
• 1.7. Inequalities
• 1.8. Absolute Value Equations and Inequalities

2. Graphs and Functions

• 2.1. Rectangular Coordinates and Graphs
• 2.2. Circles
• 2.3. Functions
• 2.4. Linear Functions
• 2.5. Equations of Lines and Linear Models
• 2.6. Graphs of Basic Functions
• 2.7. Graphing Techniques
• 2.8. Function Operations and Composition

3. Polynomial and Rational Functions

• 3.1. Quadratic Functions and Models
• 3.2. Synthetic Division
• 3.3. Zeros of Polynomial Functions
• 3.4. Polynomial Functions: Graphs, Applications, and Models
• 3.5. Rational Functions: Graphs, Applications, and Models
• 3.6. Polynomial and Rational Inequalities
• 3.7. Variation

4. Inverse, Exponential, and Logarithmic Functions

• 4.1. Inverse Functions
• 4.2. Exponential Functions
• 4.3. Logarithmic Functions
• 4.4. Evaluating Logarithms and the Change-of-Base Theorem
• 4.5. Exponential and Logarithmic Equations
• 4.6. Applications of Models of Exponential Growth and Decay

5. Trigonometric Functions

• 5.1. Angles
• 5.2. Trigonometric Functions
• 5.3. Trigonometric Function Values and Angle Measures
• 5.4. Solutions and Applications of Right Triangles

6. The Circular Functions and Their Graphs

• 6.1. Radian Measure
• 6.2. The Unit Circle and Circular Functions
• 6.3. Graphs of the Sine and Cosine Functions
• 6.4. Translations of the Graphs of the Sine and Cosine Functions
• 6.5. Graphs of the Tangent and Cotangent Functions
• 6.6. Graphs of the Secant and Cosecant Functions
• 6.7. Harmonic Motion

7. Trigonometric Identities and Equations

• 7.1. Fundamental Identities
• 7.2. Verifying Trigonometric Identities
• 7.3. Sum and Difference Identities
• 7.4. Double-Angle and Half-Angle Identities
• 7.5. Inverse Circular Functions
• 7.6. Trigonometric Equations
• 7.7. Equations Involving Inverse Trigonometric Functions

8. Applications of Trigonometry

• 8.1. The Law of Sines
• 8.2. The Law of Cosines
• 8.3. Geometrically Defined Vectors and Applications
• 8.4. Algebraically Defined Vectors and the Dot Product
• 8.5. Trigonometric (Polar) Form of Complex Numbers; Products and Quotients
• 8.6. De Moivres Theorem; Powers and Roots of Complex Numbers
• 8.7. Polar Equations and Graphs
• 8.8. Parametric Equations, Graphs, and Applications

9. Systems and Matrices

• 9.1. Systems of Linear Equations
• 9.2. Matrix Solution of Linear Systems
• 9.3. Determinant Solution of Linear Systems
• 9.4. Partial Fractions
• 9.5. Nonlinear Systems of Equations
• 9.6. Systems of Inequalities and Linear Programming
• 9.7. Properties of Matrices
• 9.8. Matrix Inverses

10. Analytic Geometry

• 10.1. Parabolas
• 10.2. Ellipses
• 10.3. Hyperbolas
• 10.4. Summary of the Conic Sections

11. Further Topics in Algebra

• 11.1. Sequences and Series
• 11.2. Arithmetic Sequences and Series
• 11.3. Geometric Sequences and Series
• 11.4. The Binomial Theorem
• 11.5. Mathematical Induction
• 11.6. Basics of Probability

• Appendix A Polar Form of Conic Sections
• Appendix B Rotation of Axes
• Appendix C Geometry Formulas