Algebra for College Students

Note: each chapter concludes with a Group Activity, Chapter Summary, Chapter Review Exercises, Chapter Test, and after Chapter 1, a set of Cumulative Review Exercises.

 

Chapter 1: Review of the Real Number System

1.1 Basic Concepts

1.2 Operations on Real Numbers

1.3 Exponents, Roots, and Order of Operations

1.4 Properties of Real Numbers

 

Chapter 2: Linear Equations, Inequalities, and Applications

2.1 Linear Equations in One Variable

2.2 Formulas

2.3 Applications of Linear Equations

2.4 Further Applications of Linear Equations

Summary Exercises on Solving Applied Problems

2.5 Linear Inequalities in One Variable

2.6 Set Operations and Compound Inequalities

2.7 Absolute Value Equations and Inequalities

Summary Exercises on Solving Linear and Absolute Value Equations and Inequalities

 

Chapter 3: Graphs, Linear Equations, and Functions

3.1 The Rectangular Coordinate System

3.2 The Slope of a Line

3.3 Linear Equations in Two Variables

Summary Exercises on Slopes and Equations of Lines

3.4 Linear Inequalities in Two Variables

3.5 Introduction to Functions

 

Chapter 4: Systems of Linear Equations

4.1 Systems of Linear Equations in Two Variables

4.2 Systems of Linear Equations in Three Variables

4.3 Applications of Systems of Linear Equations

4.4 Solving Systems of Linear Equations by Matrix Methods

 

Chapter 5: Exponents, Polynomials, and Polynomial Functions

5.1 Integer Exponents and Scientific Notation

5.2 Adding and Subtracting Polynomials

5.3 Polynomial Functions, Graphs, and Composition

5.4 Multiplying Polynomials

5.5 Dividing Polynomials

 

Chapter 6: Factoring

6.1 Greatest Common Factors; Factoring by Grouping

6.2 Factoring Trinomials

6.3 Special Factoring

6.4 A General Approach to Factoring

6.5 Solving Equations by Factoring

 

Chapter 7: Rational Expressions and Functions

7.1 Rational Expressions and Functions; Multiplying and Dividing

7.2 Adding and Subtracting Rational Expressions

7.3 Complex Fractions

7.4 Equations with Rational Expressions and Graphs

Summary Exercises on Rational Expressions and Equations

7.5 Applications of Rational Expressions

7.6 Variation

 

Chapter 8: Roots, Radicals, and Root Functions

8.1 Radical Expressions and Graphs

8.2 Rational Exponents

8.3 Simplifying Radical Expressions

8.4 Adding and Subtracting Radical Expressions

8.5 Multiplying and Dividing Radical Expressions

Summary Exercises on Operations with Radicals and Rational Exponents

8.6 Solving Equations with Radicals

8.7 Complex Numbers

 

Chapter 9: Quadratic Equations and Inequalities

9.1 The Square Root Property and Completing the Square

9.2 The Quadratic Formula

9.3 Equations Quadratic in Form

Summary Exercises on Solving Quadratic Equations

9.4 Formulas and Further Applications

9.5 Quadratic and Rational Inequalities

 

Chapter 10: Additional Graphs of Functions and Relations

10.1 Review of Operations and Composition

10.2 Graphs of Quadratic Functions

10.3 More about Parabolas and Their Applications

10.4 Symmetry; Increasing and Decreasing Functions

10.5 Piecewise Linear Functions

 

Chapter 11: Inverse, Exponential, and Logarithmic Functions

11.1 Inverse Functions

11.2 Exponential Functions

11.3 Logarithmic Functions

11.4 Properties of Logarithms

11.5 Common and Natural Logarithms

11.6 Exponential and Logarithmic Equations; Further Applications

 

Chapter 12: Polynomial and Rational Functions

12.1 Synthetic Division

12.2 Zeros of Polynomial Functions

12.3 Graphs and Applications of Polynomial Functions

Summary Exercises on Polynomial Functions and Graphs

12.4 Graphs and Applications of Rational Functions

 

Chapter 13: Conic Sections and Systems of Inequalities

13.1 The Circle and the Ellipse

13.2 The Hyperbola and Functions Defined by Radicals

13.3 Nonlinear Systems of Equations

13.4 Second-Degree Inequalities, Systems of Inequalities, and Linear Programming

 

Chapter 14: Further Topics in Algebra

14.1 Sequences and Series

14.2 Arithmetic Sequences

14.3 Geometric Sequences

14.4 The Binomial Theorem

14.5 Mathematical Induction

14.6 Counting Theory

14.7 Basics of Probability

 

Appendixes

A: An Introduction to Calculators

B: Properties of Matrices

C: Matrix Inverses

D: Determinants and Cramer's Rule