Fundamentals | |

Overview | |

Real Numbers | |

Exponents and Radicals | |

Algebraic Expressions | |

Discovery Project: Visualizing a Formula | |

Fractional Expressions | |

Equations | |

Modeling with Equations | |

Discovery Project: Equations through the Ages | |

Inequalities | |

Coordinate Geometry | |

Graphing Calculators: Solving Equations and Inequalities Graphically | |

Lines | |

Modeling Variation | |

Review | |

Test | |

Focus on Problem Solving: General Principles | |

Functions | |

Overview | |

What is a Function? Graphs of Functions | |

Discovery Project: Relations and Functions | |

Increasing and Decreasing Functions: Average Rate of Change | |

Transformations of Functions | |

Quadratic Functions: Maxima and Minima | |

Modeling with Functions | |

Combining Functions | |

Discovery | |

Project: Iteration and Chaos | |

One-to-One Functions and Their Inverses Review | |

Test | |

Focus on Modeling: Fitting Lines to Data | |

Polynomial and Rational Functions | |

Overview | |

Polynomial Functions and Their Graphs | |

Dividing Polynomials | |

Real Zeros of Polynomials | |

Discovery Project: Zeroing in on a Zero | |

Complex Numbers | |

Complex Zeros and the Fundamental Theorem of Algebra | |

Rational Functions | |

Review | |

Test | |

Focus on Modeling: Fitting Polynomials to Data | |

Exponential and Logarithmic Functions | |

Overview | |

Exponential Functions | |

Discovery Project: Exponential Explosion | |

Logarithmic Functions | |

Laws of Logarithms | |

Exponential and Logarithmic Equations | |

Modeling with Exponential and Logarithmic Functions | |

Review | |

Test | |

Focus on Modeling: Fitting Exponential and Power Curves to Data | |

Trigonometric Functions of Real Numbers | |

Overview | |

The Unit Circle | |

Trigonometric Functions of Real Numbers | |

Trigonometric Graphs | |

Discovery Project: Predator-Prey Models | |

More Trigonometric Graphs | |

Modeling Harmonic Motion | |

Review | |

Test | |

Focus on Modeling: Fitting Sinusoidal Curves to Data | |

Trigonometric Functions of Angles | |

Overview | |

Angle Measure | |

Trigonometry of Right Triangles | |

Discovery Project: Similarity | |

Trigonometric Functions of Angles | |

The Law of Sines | |

The Law of Cosines | |

Review | |

Test | |

Focus on Modeling:Surveying | |

Analytic Trigonometry | |

Overview | |

Trigonometric Identities | |

Addition and Subtraction Formulas | |

Double-Angle, Half-Angle, and Sum-Product Identities | |

Inverse Trigonometric Functions | |

Discovery Project: Where to Sit at the Movies | |

Trigonometric Equations | |

Review | |

Test | |

Focus on Modeling: Traveling and Standing Waves | |

Polar Coordinates and Vectors | |

Overview | |

Polar Coordinates | |

Graphs of Polar Equations | |

Polar Form of Complex Numbers | |

DeMoivre's Theorem | |

Discovery Project: Fractals | |

Vectors | |

The Dot Product | |

Discovery Project: Sailing Against the Wind | |

Review | |

Test | |

Focus on Modeling: Mapping the World | |

Systems of Equations and Inequalities | |

Overview | |

Systems of Equations | |

Systems of Linear Equations in Two Variables | |

Systems of Linear Equations in Several Variables | |

Discovery Project: Best Fit versus Exact Fit | |

Systems of Linear Equations: Matrices | |

The Algebra of Matrices | |

Discovery Project: Will the Species Survive? Inverses of Matrices and Matrix Equations | |

Discovery Project: Computer Graphics | |

I Determinants and Cramer's Rule | |

Partial Fractions | |

Systems of Inequalities | |

Review | |

Test | |

Focus on Modeling: Linear Programming | |

Analytic Geometry | |

Overview | |

Parabolas | |

Ellipses | |

Hyperbolas | |

Discovery Project: Conics in Architecture Shifted Conics | |

Rotation of Axes | |

Discovery Project: Computer Graphics II | |

Polar Equations of Conics | |

Plane Curves and Parametric Equations | |

Review | |

Test | |

Focus on Modeling: The Path of a Projectile | |

Sequences and Series | |

Overview | |

Sequences and Summation Notation | |

Arithmetic Sequences | |

Geometric Sequences | |

Discovery Project: Finding Patterns | |

Mathematical Finance | |

Mathematical Induction | |

The Binomial Theorem | |

Review | |

Test | |

Focus on Modeling: Modeling with Recursive Sequences | |

Limits: A Preview of Calculus | |

Overview | |

Finding Limits Numerically and Graphically | |

Finding Limits Algebraically | |

Tangent Lines and Derivatives | |

Discovery Project: Designing a Roller Coaster | |

Limits at | |

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