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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 |