Beginning and Intermediate Algebra 4e

Chapter 1: Set of Real Numbers

1.1 Fractions

1.2 Introduction to Algebra and the Set of Real Numbers

1.3 Exponents, Square Roots, and Order of Operations

1.4 Addition of Real Numbers

1.5 Subtraction of Real Numbers

Problem Recognition Exercises—Addition and Subtraction of Real Numbers

1.6 Multiplication and Division of Real Numbers

Problem Recognition Exercises—Adding, Subtracting, Multiplying and Dividing Real Numbers

1.7 Properties of Real Numbers and Simplifying Expressions

Chapter 2: Linear Equations and Inequalities

2.1 Addition, Subtraction, Multiplication, and Division Properties of Equality

2.2 Solving Linear Equations

2.3 Linear Equations: Clearing Fractions and Decimals

Problem Recognition Exercises—Equations vs.Expressions

2.4 Applications of Linear Equations: Introduction to Problem Solving

2.5 Applications Involving Percents

2.6 Formulas and Applications of Geometry

2.7 Mixture Applications and Uniform Motion

2.8 Linear Inequalities

Chapter 3: Graphing Linear Equations in Two Variables

3.1 Rectangular Coordinate System

3.2 Linear Equations in Two Variables

3.3 Slope of a Line and Rate of Change

3.4 Slope-Intercept Form of a Linear Equation

Problem Recognition Exercises-Linear Equations in Two Variables

Point-Slope Formula

Applications of Linear Equations

Chapter 4: Systems of Linear Equations

4.1 Solving Systems of Equations by the Graphing Method

4.2 Solving Systems of Equations by the Substitution Method

4.3 Solving Systems of Equations by the Addition Method

Problem Recognition Exercises: Systems of Equations

4.4 Applications of Linear Equations in Three Variables

4.5 Systems of Linear Equations in Three Variables

4.6 Applications of Systems of Linear Equations in Three Variables

Chapter 5: Polynomials and Properties of Exponents

5.1 Multiplying and Dividing Expressions with Common Bases

5.2 More Properties of Exponents

5.3 Definitions of b^0 and b^-n

Problem Recognition Exercises-Properties of Exponents

5.4 Scientific Notation

5.5 Addition and Subtraction of Polynomials

5.6 Multiplication of Polynomials

5.7 Division of Polynomials

Problem Recognition Exercises-Operations on Polynomials

Chapter 6: Factoring Polynomials

6.1 Greatest Common Factor and Factoring by Grouping

6.2 Factoring Trinomials of the Form x^2 + bx + c

6.3 Factoring Trinomials: Trial-and-Error Method

6.4 Factoring Trinomials: AC-Method

6.5 Difference of Squares and Perfect Square Trinomials

6.6 Sum and Difference of Cubes

Problem Recognition Exercises-Factoring Strategy

6.7 Solving Equations Using the Zero Product Rule

Problem Recognition Exercises-Polynomial Expressions and Polynomial Equations

6.8 Applications of Quadratic Equations

Chapter 7: Rational Expressions and Equations

7.1 Introduction of Rational Expressions

7.2 Multiplication and Division of Rational Expressions

7.3 Least Common Denominator

7.4 Addition and Subtraction of Rational Expressions

Problem Recognition Exercises-Operations of Rational Expressions

7.5 Complex Fractions

7.6 Rational Equations

Problem Recognition Exercises-Comparing Rational Equations and Rational Expressions

7.7 Applications of Rational Equations and Proportions

Chapter 8: Relations and Functions

8.1 Introduction of Relations

8.2 Introduction of Functions

8.3 Graphs of Functions

Problem Recognition Exercises: Characteristics of Relations

8.4 Alebra of Functions and Composition

8.5 Variation

Chapter 9: More Equations and Inequalities

9.1 Compound Inequalities

9.2 Polynomial and Rational Enequalities

9.3 Absolute Value Equations

9.4 Absolute Value Inequalities

Problem Recognition Exercises: Equations and Inequalities

9.5 Linear and Compound Inequalities in Two Variables

Chapter 10: Radicals and Complex Numbers

10.1 Definition of an nth Root

10.2 Rational Exponents

10.3 Simplifying Radical Expressions

10.4 Addition and Subtraction of Radicals

10.5 Multiplication of Radical

Problem Recognition Exercises: Simplifying Radical Expressions

10.6 Division of Radicals and Rationalization

10.7 Solving Radical Equations

10.8 Complex Numbers

Chapter 11: Quadratic Equations, Functions and Inequalities

11.1 Square Root Property and Completing the Square

11.2 Quadratic Formula

11.3 Equations in Quadratic Form

Problem Recognition Exercises: Quadratic and Quadratic Type Equations

11.4 Graphs of Quadratic Functions

11.5 Vertex of a Parabola: Applications and Modeling

Chapter 12: Exponential and Logarithmic Functions and Applications

12.1 Inverse Functions

12.2 Exponential Functions

12.3 Logarithmic Functions

Problem Recognition Exercises: Logarithmic and Exponential Forms

12.4 Properties of Logarithms

12.5 The Irrational Number and change of Base

12.6 Logarithmic and Exponential Equations and Applications

Chapter 13: Conic Sections

13.1 Distance Formula, Midpoint Formula, and Circles

13.2 More on the Parabola

13.3 The Ellipse and Hyperbola

Problem Recognition Exercises: Formulas and Conic Sections

13.4 Nonlinear Systems of Equation in Two Variables

13.5 Nonlinear Inequalities and Systems of Inequalities

Chapter 14: Binomial Expansions, Sequences, and Series

14.1 Binomial Expansions

14.2 Sequences and Series

14.3 Arithmetic Sequences and Series

14.4 Geometric Sequences and Series

Problem Recognition Exercises: Identifying Arithmetic and Geometric Series

Additional Topics Appendix

A.1 Mean, Median, and Mode

A.2 Introduction to Geometry

A.3 Solving Systems of Linear Equations Using Matrices

A.4 Determinants and Cramer’s Rule