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 SecondDegree 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: InputOutput 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 
