Table of Contents

1 Prerequisites
 1.1 Real Numbers: Algebra Essentials
 1.2 Exponents and Scientific Notation
 1.3 Radicals and Rational Expressions
 1.4 Polynomials
 1.5 Factoring Polynomials
 1.6 Rational Expressions

2 Equations and Inequalities
 2.1 The Rectangular Coordinate Systems and Graphs
 2.2 Linear Equations in One Variable
 2.3 Models and Applications
 2.4 Complex Numbers

2.5 Quadratic Equations
 Factoring Monic Quadratics
 Factoring by Grouping
 Polynomial Equations
 Solving Quadratic Equations: Taking Square Roots
 Solving Quadratics: Completing the Square
 Solving Quadratic Equations: Quadratic Formula
 Solving Quadratic Equation with Complex Roots
 Discriminants of Quadratics
 The Pythagorean Theorem
 2.6 Other Types of Equations
 2.7 Linear Inequalities and Absolute Value Inequalities

3 Functions
 3.1 Functions and Function Notation
 3.2 Domain and Range
 3.3 Rates of Change and Behavior of Graphs
 3.4 Composition of Functions
 3.5 Transformation of Functions
 3.6 Absolute Value Functions
 3.7 Inverse Functions

4 Linear Functions

4.1 Linear Functions
 Linear and Nonlinear Functions
 Slope and Rate of Change
 Equation of a Straight Line: General Form
 Equation of a Straight Line: Standard and Point–Slope Forms
 Equation of a Straight Line: Slope–Intercept Form
 Graphing Linear Functions
 Equations of Vertical and Horizontal Lines
 Slopes of Parallel and Perpendicular Lines
 Equations of Parallel and Perpendicular Lines
 4.2 Modeling with Linear Functions
 4.3 Fitting Linear Models to Data

4.1 Linear Functions

5 Polynomial and Rational Functions
 5.1 Quadratic Functions
 5.2 Power Functions and Polynomial Functions
 5.3 Graphs of Polynomial Functions
 5.4 Dividing Polynomials
 5.5 Zeros of Polynomial Functions
 5.6 Rational Functions
 5.7 Inverses and Radical Functions
 5.8 Modeling Using Variation

6 Exponential and Logarithmic Functions
 6.1 Exponential Functions
 6.2 Graphs of Exponential Functions
 6.3 Logarithmic Functions
 6.4 Graphs of Logarithmic Functions
 6.5 Logarithmic Properties
 6.6 Exponential and Logarithmic Equations
 6.7 Exponential and Logarithmic Models
 6.8 Fitting Exponential Models to Data

7 The Unit Circle: Sine and Cosine Functions
 7.1 Angles
 7.2 Right Triangle Trigonometry
 7.3 Unit Circle
 7.4 The Other Trigonometric Functions

8 Periodic Functions
 8.1 Graphs of the Sine and Cosine Functions
 8.2 Graphs of the Other Trigonometric Functions
 8.3 Inverse Trigonometric Functions

9 Trigonometric Identities
and Equations
 9.1 Solving Trigonometric Equations with Identities
 9.2 Sum and Difference Identities
 9.3 DoubleAngle, HalfAngle, and Reduction Formulas
 9.4 SumtoProduct and ProducttoSum Formulas
 9.5 Solving Trigonometric Equations

10 Further Applications of Trigonometry
 10.1 NonRight Triangles: Law of Sines
 10.2 NonRight Triangles: Law of Cosines
 10.3 Polar Coordinates
 10.4 Polar Coordinates: Graphs
 10.5 Polar Form of Complex Numbers
 10.6 Parametric Equations
 10.7 Parametric Equations: Graphs
 10.8 Vectors

11 Systems of Equations and Inequalities
 11.1 Systems of Linear Equations: Two Variables
 11.2 Systems of Linear Equations: Three Variables
 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables
 11.4 Partial Fractions
 11.5 Matrices and Matrix Operations
 11.6 Solving Systems with Gaussian Elimination
 11.7 Solving Systems with Inverses
 11.8 Solving Systems with Cramer’s Rule

12 Analytic Geometry
 12.1 The Ellipse
 12.2 The Hyperbola
 12.3 The Parabola
 12.4 Rotation of Axis
 12.5 Conic Sections in Polar Coordinates

13 Sequences, Probability and Counting Theory
 13.1 Sequences and Their Notations
 13.2 Arithmetic Sequences
 13.3 Geometric Sequences
 13.4 Series and Their Notations
 13.5 Counting Principles
 13.6 Binomial Theorem
 13.7 Probability