Equations and Inequalities | |

Linear Equations, Formulas, and Problem Solving | |

Linear Inequalities in One Variable | |

Absolute Value Equations and Inequalities | |

Complex Numbers | |

Solving Quadratic Equations | |

Solving Other Types of Equations | |

Relations, Functions and Graphs | |

Rectangular Coordinates; Graphing Circles and Relations | |

Graphs of Linear Equations | |

Linear Equations and Rates of Change | |

Functions, Notation, and Graphs of Functions | |

Analyzing the Graph of a Function | |

Toolbox Functions and Transformations | |

Piecewise-Defined Functions | |

The Algebra and Composition of Functions | |

Polynomial and Rational Functions | |

Quadratic Functions and Applications | |

Synthetic Division; The Remainder and Factor Theorems | |

The Zeroes of Polynomial Functions | |

Graphing Polynomial Functions | |

Graphing Rational Functions | |

Additional Insights into Rational Functions | |

Polynomial and Rational Inequalities | |

Variation: Function Models in Action | |

Exponential and Logarithmic Functions | |

One-to-One and Inverse Functions | |

Exponential Functions | |

Logarithms and Logarithmic Functions | |

Properties of Logarithms; Solving Exponential and Logarithmic Equations | |

Applications from Business, Finance, and Science | |

Introduction to Trigonometric Functions | |

Angle Measure, Special Triangles, and Special Angles | |

Unit Circles and the Trigonometry of Real Numbers | |

Graphs of Sine and Cosine Functions; Cosecant and Secant Functions | |

Graphs of Tangent and Cotangent Functions | |

Transformations and Applications of Trigonometric Graphs | |

The Trigonometry of Right Triangles | |

Trigonometry and the Coordinate Plane | |

Trigonometric Identities, Inverses, and Equations | |

Fundamental Identities and Families of Identities | |

Constructing and Verifying Identities | |

The Sum and Difference Identities | |

Double Angle, Half Angle & Product-to-Sum Identities | |

The Inverse Trigonometric Functions and Their Applications | |

Solving Basic Trigonometric Equations | |

General Trigonometric Equations and Applications | |

Applications of Trigonometry | |

Oblique Triangles and the Law of Sines | |

The Law of Cosines; Area of a Triangle | |

Vectors and Vector Diagrams | |

Vector Applications and the Dot Product | |

Complex Numbers in Trigonometric Form | |

Demoivre’s Theorem and the Theorem on nth Roots | |

Systems of Equations and Inequalities | |

Linear Systems in Two Variables with Applications | |

Linear Systems in Three Variables with Applications | |

Partial Fraction Decomposition | |

Systems of Inequalities and Linear Programming | |

Solving Systems Using Matrices and Row Operations | |

The Algebra of Matrices | |

Solving Linear Systems Using Matrix Equations | |

Applications of Matrices and Determinants: Cramer's Rule, Geometry, and More | |

Analytical Geometry | |

Introduction to Analytic Geometry | |

The Circle and the Ellipse | |

The Hyperbola | |

The Analytic Parabola | |

Nonlinear Systems of Equations and Inequalities | |

Polar Coordinates, Equations, and Graphs | |

More on Conic Sections: Rotation of Axes and Polar Form | |

Parametric Equations and Graphs | |

Additional Topics in Algebra | |

Sequences and Series | |

Arithmetic Sequences | |

Geometric Sequences | |

Mathematical Induction | |

Counting Techniques | |

Introduction to Probability | |

The Binomial Theorem | |

Bridges to Calculus - An Introduction to Limits | |

Finding Limits Numerically and Graphically | |

Algebraic Methods for Finding Limits; One-Sided Limits and Continuity | |

Infinite Limits and Limits at Infinity | |

Applications of Limits: Instantaneous Rates of Change and the Area Under a Curve | |

Appendices | |

A Review of Basic Concepts and Skills | |

US Standard Units and the Metric System | |

Rational Expressions and the Least Common Denominator | |

Deriving the Equation of a Conic | |

More on Matrices | |

Deriving the Equation of a Conic | |

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