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| 1. 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 | |
| 2. GRAPHS AND TECHNOLOGY | |
| Graphs | |
| Solving Equations Graphically and Numerically | |
| Applications of Equations | |
| Optimization Applications | |
| Linear Models | |
| Discovery Project: Supply and Demand | |
| 3. 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 | |
| 4. 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 | |
| 5. 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 | |
| 6. 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 | |
| 7. 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 | |
| 8. 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 | |
| 9. 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 | |
| 10. 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 | |
| 11. 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 | |
| 12. DISCRETE ALGEBRA | |
| Sequences and Sums | |
| Arithmetic Sequences | |
| Geometric Sequences | |
| Special Topics: Infinite Series | |
| The Binomial Theorem | |
| Mathematical Induction | |
| Discovery Project: Taking Your Chances | |
| 13. 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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