| 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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