Beginning and Intermediate Algebra

- Includes Problem Recognition Exercises, designed to help students recognize which solution strategies are most appropriate for a given exercise. 
- Throughout, the authors communicate to students the very points their instructors are likely to make during lecture, helping to reinforce the concepts and provide instruction that leads students to mastery and success.
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Table of Contents

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Program Details

Beginning and Intermediate Algebra 5e

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

3.5 Point-Slope Formula

3.6 Applications of Linear Equations

Chapter 4: Systems of Linear Equations in Two Variables

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 Two 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 and Special Products

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 Versus Polynomial Equations

6.8 Applications of Quadratic Equations

Chapter 7: Rational Expressions and Equations

7.1 Introduction to 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 Inequalities and Systems of Linear 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 Radicals

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 and Functions

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: Identifying Graphs of Functions

12.4 Properties of Logarithms

12.5 The Irrational Number e and change of Base

Problem Recognition Exercises: Logarithmic and Exponential Forms

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 in Two Variables

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

Chapter 15 (Online): Transformations, Piecewise-Defined Functions, and Probability

15.1 Transformations of Graphs and Piecewise-Defined Functions

15.2 Fundamentals of Counting

15.3 Introduction to Probability

Additional Topics Appendix

A.1 Additional Factoring

A.2 Mean, Median, and Mode

A.3 Introduction to Geometry

A.4 Solving Systems of Linear Equations Using Matrices

A.5 Determinants and Cramer’s Rule

Online Appendix B

B.1 Review of the Set of Real Numbers

B.2 Review of Linear Equations and Linear Inequalities

B.3 Review of Graphing

B.4 Review of Systems of Linear Equations in Two Variables

B.5 Review of Polynomials and Properties of Exponents

B.6 Review of Factoring Polynomials and Solving Quadratic Equations

B.7 Review of Rational Expressions