Precalculus

Chapter 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
• • P.7 Equations
• • P.8 Modeling with Equations
• • P.9 Linear Inequalities and Absolute Value Inequalities
• • Summary, Review, and Test
• • Review Exercises
• • Chapter P Test

Chapter 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
• • 1.10 Modeling with Functions

Chapter 2: Polynomial and Rational Functions

• • 2.1 Complex Numbers
• • 2.2 Quadratic Functions
• • 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

Chapter 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

Chapter 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

Chapter 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

Chapter 6: Additional Topics in Trigonometry

• • 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

Chapter 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

Chapter 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

Chapter 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

Chapter 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

Chapter 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