**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. Equations and Inequalities**

- 1.1 Graphs and Graphing Utilities
- 1.2 Linear Equations and Rational Equations
- 1.3 Models and Applications
- 1.4 Complex Numbers
- 1.5 Quadratic Equations
- 1.6 Other Types of Equations
- 1.7 Linear Inequalities and Absolute Value Inequalities

**2. Functions and Graphs**

- 2.1 Basics of Functions and Their Graphs
- 2.2 More on Functions and Their Graphs
- 2.3 Linear Functions and Slope
- 2.4 More on Slope
- 2.5 Transformations of Functions
- 2.6 Combinations of Functions; Composite Functions
- 2.7 Inverse Functions
- 2.8 Distance and Midpoint Formulas; Circles

**3. Polynomial and Rational Functions**

- 3.1 Quadratic Functions
- 3.2 Polynomial Functions and Their Graphs
- 3.3 Dividing Polynomials; Remainder and Factor Theorems
- 3.4 Zeros of Polynomial Functions
- 3.5 Rational Functions and Their Graphs
- 3.6 Polynomial and Rational Inequalities
- 3.7 Modeling Using Variation

**4. Exponential and Logarithmic Functions**

- 4.1 Exponential Functions
- 4.2 Logarithmic Functions
- 4.3 Properties of Logarithms
- 4.4 Exponential and Logarithmic Equations
- 4.5 Exponential Growth and Decay; Modeling Data

**5. Trigonometric Functions**

- 5.1 Angles and Radian Measure
- 5.2 Right Triangle Trigonometry
- 5.3 Trigonometric Functions of Any Angle
- 5.4 Trigonometric Functions of Real Numbers; Periodic Functions
- 5.5 Graphs of Sine and Cosine Functions
- 5.6 Graphs of Other Trigonometric Functions
- 5.7 Inverse Trigonometric Functions
- 5.8 Applications of Trigonometric Functions

**6. Analytic Trigonometry**

- 6.1 Verifying Trigonometric Identities
- 6.2 Sum and Difference Formulas
- 6.3 Double-Angle, Power-Reducing, and Half-Angle Formulas
- 6.4 Product-to-Sum and Sum-to-Product Formulas
- 6.5 Trigonometric Equations

**7. Additional Topics in Trigonometry**

- 7.1 The Law of Sines
- 7.2 The Law of Cosines
- 7.3 Polar Coordinates
- 7.4 Graphs of Polar Equations
- 7.5 Complex Numbers in Polar Form; DeMoivre's Theorem
- 7.6 Vectors
- 7.7 The Dot Product

**8. Systems of Equations and Inequalities**

- 8.1 Systems of Linear Equations in Two Variables
- 8.2 Systems of Linear Equations in Three Variables
- 8.3 Partial Fractions
- 8.4 Systems of Nonlinear Equations in Two Variables
- 8.5 Systems of Inequalities
- 8.6 Linear Programming

**9. Matrices and Determinants**

- 9.1 Matrix Solutions to Linear Systems
- 9.2 Inconsistent and Dependent Systems and Their Applications
- 9.3 Matrix Operations and Their Applications
- 9.4 Multiplicative Inverses of Matrices and Matrix Equations
- 9.5 Determinants and Cramer's Rule

**10. Conic Sections and Analytic Geometry**

- 10.1 The Ellipse
- 10.2 The Hyperbola
- 10.3 The Parabola
- 10.4 Rotation of Axes
- 10.5 Parametric Equations
- 10.6 Conic Sections in Polar Coordinates

**11. Sequences, Induction, and Probability**

- 11.1 Sequences and Summation Notation
- 11.2 Arithmetic Sequences
- 11.3 Geometric Sequences and Series
- 11.4 Mathematical Induction
- 11.5 The Binomial Theorem
- 11.6 Counting Principles, Permutations, and Combinations
- 11.7 Probability

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