Table of Contents

P. Prerequisites: Fundamental Concepts of Algebra

P.1 Algebraic Expressions, Mathematical Models, and Real Numbers 

P.2 Exponents and Scientific Notation 

P.3 Radicals and Rational Exponents 

P.4 Polynomials 

P.5 Factoring Polynomials 

P.6 Rational Expressions 

P.7 Equations 

P.8 Modeling with Equations 

P.9 Linear Inequalities and Absolute Value Inequalities 

 

1. Functions and Graphs

1.1 Graphs and Graphing Utilities 

1.2 Basics of Functions and Their Graphs 

1.3 More on Functions and Their Graphs 

1.4 Linear Functions and Slope 

1.5 More on Slope 

1.6 Transformations of Functions 

1.7 Combinations of Functions; Composite Functions 

1.8 Inverse Functions 

1.9 Distance and Midpoint Formulas; Circles 

1.10 Modeling with Functions 

 

2. Polynomial and Rational Functions

2.1 Complex Numbers 

2.2 Quadratic Functions 

2.3 Polynomial Functions and Their Graphs 

2.4 Dividing Polynomials; Remainder and Factor Theorems 

2.5 Zeros of Polynomial Functions 

2.6 Rational Functions and Their Graphs 

2.7 Polynomial and Rational Inequalities 

2.8 Modeling Using Variation 

 

3. Exponential and Logarithmic Functions

3.1 Exponential Functions 

3.2 Logarithmic Functions 

3.3 Properties of Logarithms 

3.4 Exponential and Logarithmic Equations 

3.5 Exponential Growth and Decay; Modeling Data 

 

4. Trigonometric Functions

4.1 Angles and Radian Measure 

4.2 Trigonometric Functions: The Unit Circle 

4.3 Right Triangle Trigonometry 

4.4 Trigonometric Functions of Any Angle 

4.5 Graphs of Sine and Cosine Functions 

4.6 Graphs of Other Trigonometric Functions 

4.7 Inverse Trigonometric Functions 

4.8 Applications of Trigonometric Functions 

 

5. Analytic Trigonometry

5.1 Verifying Trigonometric Identities 

5.2 Sum and Difference Formulas 

5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas 

5.4 Product-to-Sum and Sum-to-Product Formulas 

5.5 Trigonometric Equations 

 

6. Additional Topics in Trigonometry

6.1 The Law of Sines 

6.2 The Law of Cosines 

6.3 Polar Coordinates 

6.4 Graphs of Polar Equations 

6.5 Complex Numbers in Polar Form; DeMoivre's Theorem 

6.6 Vectors 

6.7 The Dot Product 

 

7. Systems of Equations and Inequalities

7.1 Systems of Linear Equations in Two Variables 

7.2 Systems of Linear Equations in Three Variables 

7.3 Partial Fractions 

7.4 Systems of Nonlinear Equations in Two Variables 

7.5 Systems of Inequalities 

7.6 Linear Programming 

 

8. Matrices and Determinants

8.1 Matrix Solutions to Linear Systems 

8.2 Inconsistent and Dependent Systems and Their Applications 

8.3 Matrix Operations and Their Applications 

8.4 Multiplicative Inverses of Matrices and Matrix Equations 

8.5 Determinants and Cramer's Rule 

 

9. Conic Sections and Analytic Geometry

9.1 The Ellipse 

9.2 The Hyperbola 

9.3 The Parabola 

9.4 Rotation of Axes 

9.5 Parametric Equations 

9.6 Conic Sections in Polar Coordinates 

 

10. Sequences, Induction, and Probability

10.1 Sequences and Summation Notation 

10.2 Arithmetic Sequences 

10.3 Geometric Sequences and Series 

10.4 Mathematical Induction 

10.5 The Binomial Theorem 

10.6 Counting Principles, Permutations, and Combinations 

10.7 Probability 

 

11. Introduction to Calculus

11.1 Finding Limits Using Tables and Graphs 

11.2 Finding Limits Using Properties of Limits 

11.3 Limits and Continuity 

11.4 Introduction to Derivatives