Basics | |

The Real Number System | |

Special Topics: Decimal Representation of Real Numbers | |

Solving Equations Algebraically | |

Special Topics: Absolute Value Equations | |

Special Topics: Variation | |

The Coordinate Plane | |

Lines | |

Discovery Project: Modeling the Real World with Lines | |

Graphs and Technology | |

Graphs | |

Solving Equations Graphically and Numerically | |

Applications of Equations | |

Optimization Applications | |

Linear Models | |

Discovery Project: Supply and Demand | |

Functions and Graphs | |

Functions | |

Function Notation | |

Graphs of Functions | |

Special Topics: Graph Reading | |

Graphs and Transformations | |

Special Topics: Symmetry | |

Operations on Functions | |

Rates of Change | |

Inverse Functions | |

Discovery Project: Feedback: Good and Bad | |

Polynomial and Rational Functions | |

Quadratic Functions | |

Polynomial Functions | |

Special Topics: Synthetic Division | |

Real Roots of Polynomials | |

Graphs of Polynomial Functions | |

Special Topics: Polynomial Models | |

Rational Functions | |

Special Topics: Other Rational Functions | |

Polynomial and Rational Inequalities | |

Special Topics: Absolute Value Inequalities | |

Complex Numbers | |

Theory of Equations | |

Discovery Project: Architectural Arches | |

Exponential and Logarithmic Functions | |

Radicals and Rational Exponents | |

Special Topics: Radical Equations | |

Exponential Functions | |

Special Topics: Compound Interest and the Number e | |

Common and Natural Logarithmic Functions | |

Properties of Logarithms | |

Special Topics: Logarithmic Functions to Other Bases | |

Algebraic Solutions of Exponential and Logarithmic Equations | |

Exponential, Logarithmic, and Other Models | |

Discovery Project: Exponential and Logistic Modeling of Diseases | |

Trigonometric Functions | |

Angles and Their Measurement | |

The Sine, Cosine, and Tangent Functions | |

Alternate: The Sine, Cosine, and Tangent Functions | |

Algebra and Identities | |

Basic Graphs | |

Periodic Graphs and Simple Harmonic Motion | |

Special Topics: Other Trigonometric Graphs | |

Other Trigonometric Functions | |

Discovery Project: Pistons and Flywheels | |

Trigonometric Identities and Equations | |

Basic Identities and Proofs | |

Addition and Subtraction Identities | |

Special Topics: Lines and Angles | |

Other Identities | |

Inverse Trigonometric Functions | |

Trigonometric Equations | |

Discovery Project: The Sun and the Moon | |

Triangle Trigonometry | |

Trigonometric Functions of Angles | |

Alternate: Trigonometric Functions of Angles | |

Applications of Right Triangle Trigonometry | |

The Law of Cosines | |

The Law of Sines | |

Special Topics: The Area of a Triangle | |

Discovery Project: Life on a Sphere | |

Applications of Trigonometry | |

The Complex Plane and Polar Form for Complex Numbers | |

DeMoivre' s Theorem and nth Roots of Complex Numbers | |

Vectors in the Plane | |

The Dot Product | |

Discovery Project: Surveying | |

Analytic Geometry | |

Circles and Ellipses | |

Hyperbolas | |

Parabolas | |

Rotations and Second-Degree Equations | |

Special Topics: Rotation of Axes | |

Plane Curves and Parametric Equations | |

Polar Coordinates | |

Polar Equations of Conics | |

Discovery Project: Designing Machines to Make Designs | |

Systems of Equations | |

Systems of Linear Equations in Two Variables | |

Special Topics: Systems of Nonlinear Equations | |

Large Systems of Linear Equations | |

Matrix Methods for Square Systems | |

Discovery Project: Input-Output Analysis | |

Discrete Algebra | |

Sequences and Sums | |

Arithmetic Sequences | |

Geometric Sequences | |

Special Topics: Infinite Series | |

The Binomial Theorem | |

Mathematical Induction | |

Discovery Project: Taking Your Chances | |

Limits and Continuity | |

Limits of Functions | |

Properties of Limits | |

Special Topics: The Formal Definition of Limit | |

Continuity | |

Limits Involving Infinity | |

Discovery Project: Black Holes | |

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