BRIEF TABLE OF CONTENTS:

Review Chapter

• Equations, Inequalities, and Applications
• The Rectangular Coordinate System, Lines, and Circles
• Functions
• Polynomial and Rational Functions
• Exponential and Logarithmic Functions and Equations
• Conic Sections and Parametric Equations
• Systems of Equations and Inequalities
• Matrices
• Sequences and Series; Counting and Probability

Appendix: Conic Section Proofs

COMPREHENSIVE TABLE OF CONTENTS:

• Review Chapter
  • R.1 Real Numbers
  • R.2 The Order of Operations and Algebraic Expressions
  • R.3 The Laws of Exponents; Radicals
  • R.4 Polynomials
  • R.5 Operations with Radicals (New Section)
  • R.6 Factoring Polynomials
  • R.7 Rational Expressions

• Equations, Inequalities, and Applications

• 1.1 Linear and Rational Equations
• 1.2 Applications of Linear Equations and Rational Equation
• 1.3 Complex Numbers
• 1.4 Quadratic Equations
• 1.5 Applications of Quadratic Equations
• 1.6 Other Types of Equations
• 1.7 Linear Inequalities in One Variable
• 1.8 Absolute Value Equations and Inequalities
• 1.9 Polynomial and Rational Inequalities

• The Rectangular Coordinate System, Lines, and Circles

• 2.1 The Rectangular Coordinate System
• 2.2 Circles
• 2.3 Lines
• 2.4 Parallel and Perpendicular Lines

• Functions

• 3.1 Relations and Functions
• 3.2 Properties of a Function's Graph
• 3.3 Graphs of Basic Functions; Piecewise Functions
• 3.4 Transformations of Functions
• 3.5 The Algebra of Functions; Composite Functions
• 3.6 One-to-One Functions; Inverse Functions

• Polynomial and Rational Functions

• 4.1 Quadratic Functions
• 4.2 Applications and Modeling of Quadratic Functions
• 4.3 The Graphs of Polynomial Functions
• 4.4 Synthetic Division; The Remainder and Factor Theorems
• 4.5 The Zeros of Polynomial Functions; The Fundamental Theorem of Algebra
• 4.6 Rational Functions and Their Graphs
• 4.7 Variation

• Exponential and Logarithmic Functions and Equations

• 5.1 Exponential Functions
• 5.2 Logarithmic Functions
• 5.3 Properties of Logarithms
• 5.4 Exponential and Logarithmic Equations
• 5.5 Applications of Exponential and Logarithmic Functions

• Conic Sections and Parametric Equations

• 6.1 Introduction to Conic Sections
• 6.2 The Parabola
• 6.3 The Ellipse
• 6.4 The Hyperbola

• Systems of Equations and Inequalities

• 7.1 Solving Systems of Linear Equations in Two Variables
• 7.2 Solving Systems of Linear Equations in Three Variables Using the Elimination Method
• 7.3 Solving Systems of Linear Equations in Three Variables Using Gaussian Elimination and Gauss-Jordan Elimination
• 7.4 Partial Fraction Decomposition
• 7.5 Systems of Nonlinear Equations
• 7.6 Systems of Inequalities

• Matrices

• 8.1 Matrix Operations
• 8.2 Inverses of Matrices and Matrix Equations
• 8.3 Determinants and Cramer's Rule

• Sequences and Series; Counting and Probability

• 9.1 Introduction to Sequences and Series
• 9.2 Arithmetic Sequences and Series
• 9.3 Geometric Sequences and Series
• 9.4 The Binomial Theorem
• 9.5 Mathematical Induction
• 9.6 The Theory of Counting
• 9.7 An Introduction to Probability

Appendix: Conic Section Proofs