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
• An Introduction to Trigonometric Functions
  • 6.1 An Introduction to Angles: Degree and Radian Measure
  • 6.2 Applications of Radian Measure
  • 6.3 Triangles
  • 6.4 Right Triangle Trigonometry
  • 6.5 Trigonometric Functions of General Angles
  • 6.6 The Unit Circle
• The Graphs of Trigonometric Functions
  • 7.1 The Graphs of Sine and Cosine
  • 7.2 More on Graphs of Sine and Cosine; Phase Shift
  • 7.3 The Graphs of the Tangent, Cotangent , Cosecant, and Secant Functions
  • 7.4 Inverse Trigonometric Functions I
  • 7.5 Inverse Trigonometric Functions II
• Trigonometric Identities, Formulas, and Equations
  • 8.1 Trigonometric Identities
  • 8.2 The Sum and Difference Formulas
  • 8.3 The Double-Angle and Half-Angle Formulas
  • 8.4 The Product-to-Sum and Sum-to-Product Formulas
  • 8.5 Trigonometric Equations
• Applications of Trigonometry
  • 9.1 Right Triangle Applications
  • 9.2 The Law of Sines
  • 9.3 The Law of Cosines
  • 9.4 Area of Triangles
• Polar Equations, Complex Numbers, and Vectors
  • 10.1 Polar Coordinates and Polar Equations
  • 10.2 Graphing Polar Equations
  • 10.3 Complex Numbers in Polar Form; DeMoivre''s Theorem
  • 10.4 Vectors
  • 10.5 The Dot Product
• Conic Sections and Parametric Equations
  • 11.1 Introduction to Conic Sections
  • 11.2 The Parabola
  • 11.3 The Ellipse
  • 11.4 The Hyperbola
  • 11.5 Conic Sections in Polar Form
  • 11.6 Parametric Equations
• Systems of Equations and Inequalities
  • 12.1 Solving Systems of Linear Equations in Two Variables
  • 12.2 Solving Systems of Linear Equations in Three Variables Using the Elimination Method
  • 12.3 Solving Systems of Linear Equations in Three Variables Using Gaussian Elimination and Gauss-Jordan Elimination
  • 12.4 Partial Fraction Decomposition
  • 12.5 Systems of Nonlinear Equations
  • 12.6 Systems of Inequalities
• Matrices
  • 13.1 Matrix Operations
  • 13.2 Inverses of Matrices and Matrix Equations
  • 13.3 Determinants and Cramer''s Rule
• Sequences and Series; Counting and Probability
  • 14.1 Introduction to Sequences and Series
  • 14.2 Arithmetic Sequences and Series
  • 14.3 Geometric Sequences and Series
  • 14.4 The Binomial Theorem
  • 14.5 Mathematical Induction
  • 14.6 The Theory of Counting
  • 14.7 An Introduction to Probability

• Appendix A: Degree, Minute, Second Form and Degree Decimal Form

  Appendix B: Conic Section Proofs