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

1. Equations and Inequalities

1.1 Graphs and Graphing Utilities

1.2 Linear Equations and Rational Equations

1.3 Models and Applications

1.4 Complex Numbers

1.5 Quadratic Equations

1.6 Other Types of Equations

1.7 Linear Inequalities and Absolute Value Inequalities

2. Functions and Graphs

2.1 Basics of Functions and Their Graphs

2.2 More on Functions and Their Graphs

2.3 Linear Functions and Slope

2.4 More on Slope

2.5 Transformations of Functions

2.6 Combinations of Functions; Composite Functions

2.7 Inverse Functions

2.8 Distance and Midpoint Formulas; Circles

3. Polynomial and Rational Functions

3.1 Quadratic Functions

3.2 Polynomial Functions and Their Graphs

3.3 Dividing Polynomials; Remainder and Factor Theorems

3.4 Zeros of Polynomial Functions

3.5 Rational Functions and Their Graphs

3.6 Polynomial and Rational Inequalities

3.7 Modeling Using Variation

4. Exponential and Logarithmic Functions

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Properties of Logarithms

4.4 Exponential and Logarithmic Equations

4.5 Exponential Growth and Decay; Modeling Data

5. Systems of Equations and Inequalities

5.1 Systems of Linear Equations in Two Variables

5.2 Systems of Linear Equations in Three Variables

5.3 Partial Fractions

5.4 Systems of Nonlinear Equations in Two Variables

5.5 Systems of Inequalities

5.6 Linear Programming

6. Matrices and Determinants

6.1 Matrix Solutions to Linear Systems

6.2 Inconsistent and Dependent Systems and Their Applications

6.3 Matrix Operations and Their Applications

6.4 Multiplicative Inverses of Matrices and Matrix Equations

6.5 Determinants and Cramer’s Rule

7. Conic Sections

7.1 The Ellipse

7.2 The Hyperbola

7.3 The Parabola

8. Sequences, Induction, and Probability

8.1 Sequences and Summation Notation

8.2 Arithmetic Sequences

8.3 Geometric Sequences and Series

8.4 Mathematical Induction

8.5 The Binomial Theorem

8.6 Counting Principles, Permutations, and Combinations

8.7 Probability