| Fundamentals | |
| Chapter Overview | |
| Real Numbers | |
| Exponents and Radicals | |
| Algebraic Expressions | |
| Fractional Expressions | |
| Equations | |
| Modeling with Equations | |
| Inequalities | |
| Coordinate Geometry | |
| Solving Equations and Inequalities Graphically | |
| Lines | |
| Modeling Variation | |
| Functions | |
| Chapter Overview | |
| What Is a Function? | |
| Graphs of Functions | |
| Getting Information from the Graph of a Function | |
| Average Rate of Change of a Function | |
| Transformations of Functions | |
| Combining Functions | |
| One-to-One Functions and Their Inverses | |
| Review | |
| TeSt. Focus on Modeling: Functions as Models | |
| Polynomial And Rational Functions | |
| Chapter Overview | |
| Quadratic Functions and Models | |
| Polynomial Functions and Their Graphs | |
| Dividing Polynomials | |
| Real Zeros of Polynomials | |
| Complex Numbers | |
| Complex Zeros and the Fundamental Theorem of Algebra | |
| Rational Functions | |
| Review | |
| TeSt. Focus on Modeling: Fitting Polynomial Curves to Data | |
| Exponential And Logarithmic Functions | |
| Chapter Overview | |
| Exponential Functions | |
| The Natural Exponential Function | |
| 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 | |
| Cumulative Review Test: Chapters 2, 3, and 4 | |
| Trigonometric Functions: Unit Circle Approach | |
| Chapter Overview | |
| The Unit Circle | |
| Trigonometric Functions of Real Numbers | |
| Trigonometric Graphs | |
| More Trigonometric Graphs | |
| Inverse Trigonometric Functions and Their Graphs | |
| Modeling Harmonic Motion | |
| Review | |
| TeSt. Focus on Modeling: Fitting Sinusoidal Curves to Data | |
| Trigonometric Functions: Right Triangle Approach | |
| Chapter Overview | |
| Angle Measure | |
| Trigonometry of Right Triangles | |
| Trigonometric Functions of Angles | |
| Inverse Trigonometric Functions and Triangles | |
| The Law of Sines | |
| The Law of Cosines | |
| Review | |
| TeSt. Focus on Modeling: Surveying | |
| Analytic Trigonometry | |
| Chapter Overview | |
| Trigonometric Identities | |
| Addition and Subtraction Formulas | |
| Double-Angle, Half-Angle, and Sum-Product Identities | |
| Basic Trigonometric Equations | |
| More Trigonometric Equations | |
| Review | |
| TeSt. Focus on Modeling: Traveling and Standing Waves | |
| Cumulative Review Test: Chapters 5, 6, and 7 | |
| Polar Coordinates And Parametric Equations | |
| Chapter Overview | |
| Polar Coordinates | |
| Graphs of Polar Equations | |
| Polar Form of Complex Numbers | |
| DeMoivre's Theorem | |
| Plane Curves and Parametric Equations | |
| Review | |
| TeSt. Focus on Modeling: The Path of a Projectile | |
| Vectors In Two And Three Dimensions | |
| Chapter Overview | |
| Vectors in Two Dimensions | |
| The Dot Product | |
| Three -Dimensional Coordinate Geometry | |
| Vectors in Three Dimensions | |
| The Cross Product | |
| Equations of Lines and Planes | |
| Review | |
| TeSt. Focus on Modeling: Vector Fields | |
| Cumulative Review Test: Chapters 8 and 9 | |
| Systems Of Equations And Inequalities | |
| Chapter Overview | |
| Systems of Linear Equations in Two Variables | |
| Systems of Linear Equations in Several Variables | |
| Systems of Linear Equations: Matrices | |
| The Algebra of Matrices | |
| Inverses of Matrices and Matrix Equations | |
| Determinants and Cramer's Rule | |
| Partial Fractions | |
| Systems of Non-Linear Equations | |
| Systems of Inequalities | |
| Review | |
| TeSt. Focus on Modeling: Linear Programming | |
| Analytic Geometry | |
| Overview | |
| Parabolas | |
| Ellipses | |
| Hyperbolas | |
| Shifted Conics | |
| Rotation of Axes | |
| Polar Equations of Conics | |
| Review | |
| TeSt. Focus on Modeling: Conics in Architecture | |
| Cumulative Review Test: Chapters 10 and 11 | |
| Sequences And Series | |
| Chapter Overview | |
| Sequences and Summation Notation | |
| Arithmetic Sequences | |
| Geometric Sequences | |
| Mathematics of Finance | |
| Mathematical Induction | |
| The Binomial Theorem | |
| Review | |
| TeSt. Focus on Modeling: Difference Equations | |
| Limits: A Preview Of Calculu.S | |
| Chapter Overview | |
| Finding Limits Numerically and Graphically | |
| Finding Limits Algebraically | |
| Tangent Lines and Derivatives | |
| Limits at Infinity: Limits of Sequences | |
| Areas | |
| Review | |
| TeSt. Appendix: Calculators and Calculations | |
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