1. Algebraic Modeling

    1. Graphing Data
    2. Analyzing Data
    3. Solving Problems Algebraically and Graphically

  2. Functions Defined and Notation

    1. Domain
    2. Range
    3. Boundedness
    4. Local and Absolute Extrema
    5. Symmetry
    6. Asymptotes
    7. End Behavior
    8. Introduction to Twelve Basic Functions
    9. Function Composition
    10. Modeling with Functions

  3. Linear and Quadratic Functions

    1. Linear Functions and Graphs
    2. Average Rate of Change
    3. Linear Correlation and Modeling
    4. Graphing Quadratic Functions
    5. Applications of Quadratic Functions
    6. Linear and Quadratic Functions on a Graphing Calculator
    7. Completing the Square
    8. The Quadratic Formula

  4. Power Functions and Variation

    1. Graphing Power Functions
    2. Modeling with Power Functions
    3. Power Functions and Variation on a Graphing Calculator

  5. Polynomial Functions of Higher Degree

    1. Graphing Polynomial Functions
    2. End Behavior
    3. Zeros
    4. Intermediate Value Theorem
    5. Polynomial Functions of Higher Degree on a Graphing Calculator

  6. Real Zeros of Polynomials

    1. Zero Factor Property
    2. Long Division of Polynomials
    3. Remainder and Factor Theorems
    4. Synthetic Division
    5. Rational Zeros
    6. Upper and Lower Bounds
    7. Real Zeros of Polynomials on a Graphing Calculator

  7. Complex Zeros

    1. Fundamental Theorem of Algebra
    2. Complex Conjugate Zeros
    3. Factoring Real Number Coefficients
    4. Complex Zeros on a Graphing Calculator

  8. Graphing Rational Functions

    1. Transformations of the Reciprocal Function
    2. Limits - End Behavior and Asymptotes
    3. Graphing Rational Functions on a Graphing Calculator

  9. Solving Rational Equations

    1. Extraneous Solutions
    2. Solving Rational Equations on a Graphing Calculator

  10. Solving Rational Inequalities

    1. Sign Charts
    2. Polynomial Inequalities
    3. Solving Rational Inequalities on a Graphing Calculator

  11. Exponential and Logistic Functions

    1. Exponential and Logistic Graphs
    2. The Natural Base e
    3. Population Models
    4. Exponential and Logistic Functions on a Graphing Calculator
    5. Scientific Notation

  12. Exponential and Logistic Modeling

    1. Constant Percentage and Exponentials
    2. Exponential Growth and Decay
    3. Modeling Population with Regression on a Graphing Calculator
    4. Other Logistic Models
    5. Exponential and Logistic Modeling on a Graphing Calculator

  13. Properties of Logarithmic Functions

    1. Logarithm-- Inverse of an Exponential Function
    2. Common Logs
    3. Functions with Base b
    4. Natural Logs

  14. Solving Exponential and Logarithmic Equations

    1. Orders of Magnitude
    2. Logarithmic Models
    3. Newton's Law of Cooling

  15. Vectors in the Plane

    1. 2-D Vectors
    2. Vector Operations
    3. Unit Vectors
    4. Direction Angles

  16. Dot Product of Vectors

    1. The Dot Product
    2. Angle between Vectors
    3. Vector Projection
    4. Work

  17. Polar Coordinates

    1. The Polar Coordinate System
    2. Converting Coordinates from Rectangular to Polar
    3. Converting Coordinates from Polar to Rectangular
    4. Converting Equations from Polar to Rectangular
    5. Finding Distance Between Polar Coordinates
    6. Rose Curves
    7. Cardioid Curves
    8. Limacon Curves

  18. Complex Numbers in Trigonometric Form

    1. Complex Number Plane
    2. Trigonometric Form of Complex Numbers
    3. Multiplication of Complex Numbers
    4. Division of Complex Numbers
    5. Powers of Complex Numbers
    6. Roots of Complex Numbers

  19. Solving Systems of Two Equations

    1. Solving by Substitution
    2. Solving by Elimination
    3. Solving Graphically

  20. Matrix Algebra

    1. Addition of Matrices
    2. Subtraction of Matrices
    3. Multiplication of Matrices
    4. Identity Matrix
    5. Inverse Matrix
    6. Determinant of a Square Matrix
    7. Cramer's Rule

  21. Matrix Row Operations

    1. Gaussian Elimination
    2. Elementary Row Operations
    3. Reduced Row Echelon Form
    4. Solving a System of Equations Using a Matrix
    5. Partial Fraction Decomposition (Linear Denominators)
    6. Partial Fraction Decomposition (Irreducible Quadratic Denominators)

  22. Systems of Inequalities in Two Variables

    1. Graphing Systems of Inequalities
    2. Linear Programming

  23. Geometry of a Parabola

    1. Standard Form of the Equation
    2. Vertex Form of the Equation
    3. Identify Critical Points
    4. Graphing Parabolas

  24. Geometry of an Ellipse

    1. Standard Form of the Equation
    2. General Form of the Equation
    3. Identify Critical Points
    4. Graphing Ellipses

  25. Geometry of a Hyperbola

    1. Standard Form of the Equation
    2. General Form of the Equation
    3. Identify Critical Points
    4. Graphing Hyperbolas

  26. Translation and Rotation of Axis

    1. Graphing Conic Sections Algebraically
    2. Graphing Conic Sections on a Graphing Calculator
    3. Translation of a Conic Section
    4. Rotation of a Conic Section
    5. Finding the Angle of Rotation
    6. Finding the Coefficients for a Conic in a Rotated System

  27. Polar Equations of Conic Sections

    1. Writing Polar Equations for Conic Sections
    2. Analyzing Polar Equations for Conic Sections

  28. 3-D Cartesian Coordinate System

    1. 3-D Coordinates
    2. Finding Distance and Midpoint
    3. Equation of a Sphere
    4. Planes
    5. Vectors in Space
    6. Lines in Space

  29. The Binomial Theorem

    1. Powers of the Binomial
    2. Pascal's Triangle and Binomial Expansion
    3. The Binomial Theorem
    4. Factorial Identities

  30. Sequences

    1. Infinite Sequences
    2. Limits of Infinite Sequences
    3. Arithmetic Sequences
    4. Geometric Sequences
    5. Working with Sequences on a Graphing Calculator

  31. Series

    1. Summation Notation
    2. Sums of Arithmetic Sequences
    3. Sums of Geometric Sequences
    4. Infinite Series
    5. Convergence of Geometric Series

  32. Limits, Motion, and the Tangent Line

    1. Average Velocity
    2. Instantaneous Velocity
    3. The Derivative by Definition
    4. Definition of the Tangent Line

  33. Limits, Motion, and Areas

    1. Distance from a Constant Velocity
    2. Distance from a Changing Velocity
    3. Connection to Areas
    4. The Definite Integral

  34. Limits

    1. Concepts and Informal Definition of a Limit
    2. Properties of Limits
    3. Limits of Continuous Functions
    4. One-Sided Limits
    5. Two-Sided Limits
    6. Limits Involving Infinity

  35. Graphs of Trigonometric Functions

    1. Graphing Trigonometric Functions with Domain and Range
    2. Graphing Trigonometric Functions with Critical Points
    3. Graphing Trigonometric Functions with Translations and Asymptotes
    4. Graphing Sine and Cosine
    5. Translations of Sinusodial Graphs