Chapter R Review
R.1 Real Numbers
R.2 Algebra Essentials
R.3 Geometry Essentials
R.4 Polynomials
R.5 Factoring Polynomials
R.6 Synthetic Division
R.7 Rational Expressions
R.8 nth Roots; Rational Exponents
Chapter 1 Equations and Inequalities
1.1 Rectangular Coordinates; Graphing Utilities; Introduction to Graphing Equations
1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations
1.3 Quadratic Equations
1.4 Complex Numbers; Quadratic Equations in the Complex Number System
1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations; Factorable Equations
1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Jobs
1.7 Solving Inequalities
Chapter 2 Graphs
2.1 Symmetry; Graphing Key Equations
2.2 Lines
2.3 Circles
2.4 Variation
Chapter 3 Functions and Their Graphs
3.1 Functions
3.2 The Graph of a Function
3.3 Properties of Functions
3.4 Library of Functions; Piecewise-defined Functions
3.5 Graphing Techniques: Transformations
3.6 Mathematical Models: Building Functions
Chapter 4 Linear and Quadratic Functions
4.1 Linear Functions, Their Properties, and Linear Models
4.2 Building Linear Models from Data; Direct Variation
4.3 Quadratic Functions and Their Properties
4.4 Building Quadratic Models from Verbal Descriptions and Data
4.5 Inequalities Involving Quadratic Functions
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions and Models
5.2 Properties of Rational Functions
5.3 The Graph of a Rational Function; Inverse and Joint Variation
5.4 Polynomial and Rational Inequalities
5.5 The Real Zeros of a Polynomial Function
5.6 Complex Zeros; Fundamental Theorem of Algebra
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions
6.2 One-to-One Functions; Inverse Functions
6.3 Exponential Functions
6.4 Logarithmic Functions
6.5 Properties of Logarithms
6.6 Logarithmic and Exponential Equations
6.7 Financial Models
6.8 Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models
6.9 Building Exponential, Logarithmic, and Logistic Models from Data
Chapter 7 Trigonometric Functions
7.1 Angles and Their Measure
7.2 Right Triangle Trigonometry
7.3 Evaluating Trigonometric Functions of Acute Angles
7.4 Evaluating Trigonometric Functions of General Angle
7.5 Unit Circle Approach; Properties of the Trigonometric Functions
7.6 Graphs of the Sine and Cosine Functions
7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
7.8 Phase Shift; Building Sinusoidal Models
Chapter 8 Analytic Trigonometry
8.1 The Inverse Sine, Cosine, and Tangent Functions
8.2 The Inverse Trigonometric Functions (Continued)
8.3 Trigonometric Identities
8.4 Sum and Difference Formulas
8.5 Double-angle and Half-angle Formulas
8.6 Product-to-Sum and Sum-to-Product Formulas
8.7 Trigonometric Equations (I)
8.8 Trigonometric Equations (II)
Chapter 9 Applications of Trigonometric Functions
9.1 Applications Involving Right Triangles
9.2 The Law of Sines
9.3 The Law of Cosines
9.4 Area of a Triangle
9.5 Simple Harmonic Motion; Damped Motion; Combining Waves
Chapter 10 Polar Coordinates; Vectors
10.1 Polar Coordinates
10.2 Polar Equations and Graphs
10.3 The Complex Plane; De Moivre's Theorem
10.4 Vectors
10.5 The Dot Product
Chapter 11 Analytic Geometry
11.1 Conics
11.2 The Parabola
11.3 The Ellipse
11.4 The Hyperbola
11.5 Rotation of Axes; General Form of a Conic
11.6 Polar Equations of Conics
11.7 Plane Curves and Parametric Equations
Chapter 12 Systems of Equations and Inequalities
12.1 Systems of Linear Equations: Substitution and Elimination
12.2 Systems of Linear Equations: Matrices
12.3 Systems of Linear Equations: Determinants
12.4 Matrix Algebra
12.5 Partial Fraction Decomposition
12.6 Systems of Nonlinear Equations
12.7 Systems of Inequalities
12.8 Linear Programming
Chapter 13 Sequences; Induction; the Binomial Theorem
13.1 Sequences
13.2 Arithmetic Sequences
13.3 Geometric Sequences; Geometric Series
13.4 Mathematical Induction
13.5 The Binomial Theorem
Chapter 14 Counting and Probability
14.1 Counting
14.2 Permutations and Combinations
14.3 Probability
