Precalculus

Table of Contents

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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 Moivre''s Theorem; Powers and Roots of Complex Numbers
• 8-7 Polar Equations and Graphs
• 8-8 Parametric Equations, Graphs, and Applications

• 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

• Analytic Geometry

• 10-1 Parabolas
• 10-2 Ellipses
• 10-3 Hyperbolas
• 10-4 Summary of the Conic Sections

• 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 Counting Theory
• 11-7 Basics of Probability

Appendix A Polar Form of Conic Sections

Appendix B Rotation of Axes

Appendix C Geometry Formulas