Review: Equations and Inequalities

0.1 Linear Equations

0.2 Quadratic Equations

0.3 Other Types of Equations

0.4 Inequalities

0.5 Graphing Equations

0.6 Lines

0.7 Modeling Variation

1 Functions and Their Graphs

1.1 Functions

1.2 Graphs of Functions

1.3 Graphing Techniques: Transformations

1.4 Combining Functions

1.5 One-to-One Functions and Inverse Functions

2 Polynomial and Rational Functions

2.1 Quadratic Functions

2.2 Polynomial Functions of Higher Degree

2.3 Dividing Polynomials

2.4 The Real Zeros of a Polynomial Function

2.5 Complex Zeros: The Fundamental Theorem of Algebra

2.6 Rational Functions

3 Exponential and Logarithmic Functions

3.1 Exponential Functions and Their Graphs

3.2 Logarithmic Functions and Their Graphs

3.3 Properties of Logarithms

3.4 Exponential and Logarithmic Equations

3.5 Exponential and Logarithmic Models

4 Trigonometric Functions of Angles

4.1 Angle Measure

4.2 Right Triangle Trigonometry

4.3 Trigonometric Functions of Angles

4.4 The Law of Sines

4.5 The Law of Cosines

5 Trigonometric Functions of Real Numbers

5.1 Trigonometric Functions: The Unit Circle Approach

5.2 Graphs of Sine and Cosine Functions

5.3 Graphs of Other Trigonometric Functions

6 Analytic Trigonometry

6.1 Verifying Trigonometric Identities

6.2 Sum and Difference Identities

6.3 Double-Angle and Half-Angle Identities

6.4 Product-to-Sum and Sum-to-Product Identities

6.5 Inverse Trigonometric Functions

6.6 Trigonometric Equations

7 Vectors, the Complex Plane, and Polar Coordinates

7.1 Vectors

7.2 The Dot Product

7.3 Polar (Trigonometric) Form of Complex Numbers

7.4 Products, Quotients, Powers, and Roots of Complex Numbers

7.5 Polar Coordinates and Graphs of Polar Equations

8 Systems of Linear Equations and Inequalities

8.1 Systems of Linear Equations in Two Variables

8.2 Systems of Linear Equations in Three Variables

8.3 Systems of Linear Equations and Matrices

8.4 Matrix Algebra

8.5 The Determinant of a Square Matrix and Cramer’s Rule

8.6 Partial Fractions

8.7 Systems of Linear Inequalities in Two Variables

9 Conics, Systems of Nonlinear Equations and Inequalities, and Parametric Equations

9.1 Conic Basics

9.2 The Parabola

9.3 The Ellipse

9.4 The Hyperbola

9.5 Systems of Nonlinear Equations

9.6 Systems of Nonlinear Inequalities

9.7 Rotation of Axes

9.8 Polar Equations of Conics

9.9 Parametric Equations and Graphs

10 Sequences and Series

10.1 Sequences and Series

10.2 Arithmetic Sequences and Series

10.3 Geometric Sequences and Series

10.4 Mathematical Induction

10.5 The Binomial Theorem

11 Limits: A Preview to Calculus 992

11.1 Introduction to Limits: Estimating Limits Numerically and Graphically

11.2 Techniques for Finding Limits

11.3 Tangent Lines and Derivatives

11.4 Limits at Infinity; Limits of Sequences

11.5 Finding the Area Under a Curve

Appendix Prerequisites: Fundamentals of Algebra

A.1 Real Numbers

A.2 Integer Exponents and Scientific Notation

A.3 Polynomials: Basic Operations

A.4 Factoring Polynomials

A.5 Rational Expressions

A.6 Rational Exponents and Radicals

A.7 Complex Numbers