Table of Contents

1 Prerequisites

1.1 Real Numbers: Algebra Essentials
 Real Numbers
 Evaluating Numerical Expressions Involving Exponents Using Order of Operations
 Applications of Using the Order of Operations
 The Identity and Inverse Properties of Addition and Multiplication
 Properties of Addition and Multiplication in Algebraic Expressions
 Evaluating Simple Algebraic Expressions
 Evaluating Simple and Rational Algebraic Expressions
 Simplifying Algebraic Expressions
 1.2 Exponents and Scientific Notation
 1.3 Radicals and Rational Expressions
 1.4 Polynomials
 1.5 Factoring Polynomials
 1.6 Rational Expressions

1.1 Real Numbers: Algebra Essentials

2 Equations and Inequalities
 2.1 The Rectangular Coordinate Systems and Graphs

2.2 Linear Equations in One Variable
 TwoStep Equations
 Solving Rational Equations Using the Least Common Denominator
 Rational Equations by Cross Multiplication
 Linear Equations with Variables on Both Sides
 Slope from Two Points
 Slopes and Intercepts of Linear Equations
 Equation of a Straight Line in Different Forms
 Equation of a Line through Two Points
 Slope–Intercept Form of a Line
 Equations of Vertical and Horizontal Lines
 Slope: Parallel & Perpendicular Lines
 Equations of Parallel and Perpendicular Lines
 2.3 Models and Applications
 2.4 Complex Numbers

2.5 Quadratic Equations
 Factoring Monic Quadratics
 Factoring by Grouping
 HigherDegree Polynomial Equations
 Solving Quadratics by Taking Square Roots
 Solving Quadratics by Completing the Square
 The Quadratic Formula
 Quadratic Formula
 Quadratic Equations with Complex Roots
 Properties of a Discriminant in a Quadratic Equation
 The Pythagorean Theorem
 Factoring Nonmonic Quadratics
 Factoring Difference of Two Squares
 2.6 Other Types of Equations
 2.7 Linear Inequalities and Absolute Value Inequalities

3 Functions

3.1 Functions and Function Notation
 Determining Whether a Relation Is a Function
 Recognizing Functions from Diagrams and Sets
 Evaluating a Polynomial Function for a Given Value
 Evaluating a Polynomial Function for Variables and Algebraic Expressions
 Writing an Equation to Represent a Function
 Finding the Value of Functions from Graphs
 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

3.1 Functions and Function Notation

4 Linear Functions

4.1 Linear Functions
 Linear and Nonlinear Functions
 Graphing Linear Functions Using Intercepts
 Slope and a Rate of Change
 Equation of a Line through Two Points
 Writing an Equation to Represent a Function
 Graphing Linear Functions Using Tables
 Graphing Linear Functions Using Intercepts
 Equations of Vertical and Horizontal Lines
 Slope: Parallel & 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
 Evaluating a Polynomial Function for Variables and Algebraic Expressions
 Polynomial Remainder Theorem: Checking Factors of Polynomials
 Polynomial Factorization into Linear and Irreducible Quadratic Factors
 Using Synthetic Division to Find the Zeros of a Polynomial
 The Linear Factorization Theorem in Polynomial Functions
 Descartes's Rule of Signs
 Polynomial Equations and the Rational Zeros Theorem
 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