P. Prerequisites | |

Modeling the Real World | |

Real Numbers | |

Integer Exponents | |

Rational Exponents and Radicals | |

Algebraic Expressions | |

Discovery Project: Visualizing a Formula | |

Factoring Algebraic Expressions | |

Rational Expressions | |

Chapter P Review | |

Chapter P Test | |

Focus on Problem Solving: General Principles | |

Equations and Inequalities | |

Basic Equations | |

Modeling with Linear Equations | |

Discovery Project: Equations Through the Ages | |

Quadratic Equations | |

Complex Numbers | |

Other Types of Equations | |

Inequalities | |

Absolute Value Equations and Inequalities | |

Chapter 1 Review | |

Chapter 1 Test | |

Focus on Modeling: Making the Best Decisions | |

Coordinates and Graphs | |

The Coordinate Plane | |

Discovery Project: Visualizing Data | |

Graphs of Equations in Two Variables | |

Graphing Calculators: Solving Equations and Inequalities Graphically | |

Lines | |

Modeling: Variation | |

Chapter 2 Review | |

Chapter 2 Test | |

Focus on Modeling: Fitting Lines to Data | |

Functions | |

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 | |

Combining Functions | |

Discovery Project: Iteration and Chaos | |

One-to-One Functions and Their Inverses | |

Chapter 3 Review | |

Chapter 3 Test | |

Focus on Modeling: Modeling With Functions | |

Polynomial and Rational Functions | |

Polynomial Functions and Their Graphs | |

Dividing Polynomials | |

Real Zeros of Polynomials | |

Discovery Project: Zeroing in on a Zero | |

Complex Zeros and the Fundamental Theorem of Algebra | |

Rational Functions | |

Chapter 4 Review | |

Chapter 4 Test | |

Focus on Modeling: Fitting Polynomial Curves to Data | |

Exponential and Logarithmic Functions | |

Exponential Functions | |

Discovery Project: Exponential Explosion | |

Logarithmic Functions | |

Laws of Logarithms | |

Exponential and Logarithmic Equations | |

Modeling with Exponential and Logarithmic Functions | |

Chapter 5 Review | |

Chapter 5 Test | |

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

Trigonometric Functions of Angles | |

Angle Measure | |

Trigonometry of Right Triangles | |

Trigonometric Functions of Angles | |

Discovery Project: Similarity | |

The Law of Sines | |

The Law of Cosines | |

Chapter 6 Review | |

Chapter 6 Test | |

Focus on Modeling: Surveying | |

Trigonometric Functions of Real Numbers | |

The Unit Circle | |

Trigonometric Functions of Real Numbers | |

Trigonometric Graphs | |

Discovery Project: Predator-Prey Models | |

More Trigonometric Graphs | |

Modeling Harmonic Motion | |

Chapter 7 Review | |

Chapter 7 Test | |

Focus on Modeling: Fitting Sinusoidal Curves to Data | |

Analytic Trigonometry | |

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 | |

Chapter 8 Review | |

Chapter 8 Test | |

Focus on Modeling: Traveling and Standing Waves | |

Polar Coordinates and Vectors | |

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 | |

Chapter 9 Review | |

Chapter 9 Test | |

Focus on Modeling: Mapping the World | |

Systems of Equations and Inequalities | |

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 Determinantsand Cramer's Rule | |

Partial Fractions | |

Systems of Inequalities | |

Chapter 10 Review | |

Chapter 10 Test | |

Focus on Modeling: Linear Programming | |

Analytic Geometry | |

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 | |

Chapter 11 Review | |

Chapter 11 Test | |

Focus on Modeling: The Path of a Projectile | |

Sequences And Series | |

Sequences and Summation Notation | |

Arithmetic Sequences | |

Geometric Sequences | |

Discovery Project: Finding Patterns | |

Mathematics of Finance | |

Mathematical Induction | |

The Binomial Theorem | |

Chapter 12 Review | |

Chapter 12 Test | |

Focus on Modeling: Modeling with Recursive Sequences | |

Counting And Probability | |

Counting Principles | |

Permutations and Combinations | |

Probability | |

Discovery Project: Small Samples, Big Results | |

Binomial Probability | |

Expected Value | |

Chapter 13 Review | |

Chapter 13 Test | |

Focus on Modeling: The Monte Carlo Method | |

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