P. Prerequisites: Fundamental Concepts of Algebra

• P.1 Algebraic Expressions, Mathematical Models, and Real Numbers
• P.2 Exponents and Scientific Notation
• P.3 Radicals and Rational Exponents
• P.4 Polynomials
• P.5 Factoring Polynomials
• P.6 Rational Expressions

1. Functions and Graphs

• 1.1 Graphs and Graphing Utilities
• 1.2 Basics of Functions and Their Graphs
• 1.3 More on Functions and Their Graphs
• 1.4 Linear Functions and Slope
• 1.5 More on Slope
• 1.6 Transformations of Functions
• 1.7 Combinations of Functions; Composite Functions
• 1.8 Inverse Functions
• 1.9 Distance and Midpoint Formulas; Circles

2. Polynomial and Rational Functions

• 2.1 Complex Numbers
• 2.3 Polynomial Functions and Their Graphs
• 2.4 Dividing Polynomials; Remainder and Factor Theorems
• 2.5 Zeros of Polynomial Functions
• 2.6 Rational Functions and Their Graphs
• 2.7 Polynomial and Rational Inequalities
• 2.8 Modeling Using Variation

3. Exponential and Logarithmic Functions

• 3.1 Exponential Functions
• 3.2 Logarithmic Functions
• 3.3 Properties of Logarithms
• 3.4 Exponential and Logarithmic Equations
• 3.5 Exponential Growth and Decay; Modeling Data

4. Trigonometric Functions

• 4.1 Angles and Radian Measure
• 4.2 Trigonometric Functions: The Unit Circle
• 4.3 Right Triangle Trigonometry
• 4.4 Trigonometric Functions of Any Angle
• 4.5 Graphs of Sine and Cosine Functions
• 4.6 Graphs of Other Trigonometric Functions
• 4.7 Inverse Trigonometric Functions
• 4.8 Applications of Trigonometric Functions

5. Analytic Trigonometry

• 5.1 Verifying Trigonometric Identities
• 5.2 Sum and Difference Formulas
• 5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas
• 5.4 Product-to-Sum and Sum-to-Product Formulas
• 5.5 Trigonometric Equations

• 6.1 The Law of Sines
• 6.2 The Law of Cosines
• 6.3 Polar Coordinates
• 6.4 Graphs of Polar Equations
• 6.5 Complex Numbers in Polar Form; DeMoivre's Theorem
• 6.6 Vectors
• 6.7 The Dot Product

7. Systems of Equations and Inequalities

• 7.1 Systems of Linear Equations in Two Variables
• 7.2 Systems of Linear Equations in Three Variables
• 7.3 Partial Fractions
• 7.4 Systems of Nonlinear Equations in Two Variables
• 7.5 Systems of Inequalities
• 7.6 Linear Programming

8. Matrices and Determinants

• 8.1 Matrix Solutions to Linear Systems
• 8.2 Inconsistent and Dependent Systems and Their Applications
• 8.3 Matrix Operations and Their Applications
• 8.4 Multiplicative Inverses of Matrices and Matrix Equations
• 8.5 Determinants and Cramer's Rule

9. Conic Sections and Analytic Geometry

• 9.1 The Ellipse
• 9.2 The Hyperbola
• 9.3 The Parabola
• 9.4 Rotation of Axes
• 9.5 Parametric Equations
• 9.6 Conic Sections in Polar Coordinates

10. Sequences, Induction, and Probability

• 10.1 Sequences and Summation Notation
• 10.2 Arithmetic Sequences
• 10.3 Geometric Sequences and Series
• 10.4 Mathematical Induction
• 10.5 The Binomial Theorem
• 10.6 Counting Principles, Permutations, and Combinations
• 10.7 Probability

11. Introduction to Calculus

• 11.1 Finding Limits Using Tables and Graphs
• 11.2 Finding Limits Using Properties of Limits
• 11.3 Limits and Continuity
• 11.4 Introduction to Derivatives