Beginning and Intermediate Algebra

by Miller, Julie; O'Neill, Molly; Hyde, Nancy

• ISBN13: 9780077350086
• ISBN10: 0077350081
• Edition: 3rd
• Format: Hardcover
• Copyright: 2010-01-28
• Publisher: McGraw-Hill Education

Summary

Miller/O'Neill/Hyde continues to offer an enlightened approach grounded in the fundamentals of classroom experience in Beginning and Intermediate 2e. The practice of many instructors in the classroom is to present examples and have their students solve similar problems. This is realized through the Skill Practice Exercises that directly follow the examples in the textbook. Throughout the text, the authors have integrated many Study Tips and Avoiding Mistakes hints, which are reflective of the comments and instruction presented to students in the classroom. In this way, the text communicates 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. The authors included in this edition, Problem-Recognition Exercises, that many instructors will likely identify to be similar to worksheets they have personally developed for distribution to students. The intent of the Problem-Recognition exercises, is to help students overcome what is sometimes a natural inclination toward applying problem-sovling algorithms that may not always be appropriate. In addition, the exercise sets have been revised to include even more core exercises than were present in the first edition. This permits instructors to choose from a wealth of problems, allowing ample opportunity for students to practice what they learn in lecture to hone their skills and develop the knowledge they need to make a successful transition into College Algebra. In this way, the book perfectly complements any learning platform, whether traditional lecture or distance-learning; its instruction is so reflective of what comes from lecture, that students will feel as comfortable outside of class, as they do inside class with their instructor. For even more support, students have access to a wealth of supplements, including McGraw-Hill's online homework management system, MathZone.

Table of Contents

Chapter R: Reference

R.1 Study Tips

R.2 Fractions

R.3 Introduction to Geometry

Chapter 1: The Set of Real Numbers

1.1 Sets of Numbers and the Real Number Line

1.2 Order of Operations

1.3 Addition of Real Numbers

1.4 Subtraction of Real Numbers

Problem Recognition Exercises – Addition and Subtraction of Signed Numbers

1.5 Multiplication and Division of Real Numbers

1.6 Properties of Real Numbers and Simplifying Expressions

Chapter 1 Summary

Chapter 1 Review Exercises

Chapter 1 Test

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

2.4 Applications of Linear Equations: Introduction to Problem Solving

2.5 Applications Involving Percents

2.6 Formulas and Applications of Geometry

2.7 Linear Inequalities

Chapter 2 Summary

Chapter 2 Review Exercises

Chapter 2 Test

Cumulative Review Exercises Chapters 1 – 2

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

3.4 Slope-Intercept Form of a Line

3.5 Point-Slope Formula

3.6 Applications of Linear Equations

Chapter 3 Summary

Chapter 3 Review Exercises

Chapter 3 Test

Cumulative Review Exercises Chapters 1 – 3

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

4.4 Applications of Linear Equations in Two Variables

Chapter 4 Summary

Chapter 4 Review Exercises

Chapter 4 Test

Cumulative Review Exercises Chapters 1 – 4

Chapter 5: Polynomials and Properties of Exponents

5.1 Exponents: Multiplying and Dividing Common Bases

5.2 More Properties of Exponents

5.3 Definitions of b0 and b-n

5.4 Scientific NotationProblem Recognition Exercises – Properties of Exponents

5.5 Addition and Subtraction of Polynomials

5.6 Multiplication of Polynomials

5.7 Division of Polynomials

Problem Recognition Exercises – Operations on Polynomial

Chapter 5 Summary

Chapter 5 Review Exercises

Chapter 5 Test

Cumulative Review Exercises, Chapters 1-5

Chapter 6: Factoring Polynomials

6.1 Greatest Common Factor and Factoring by Grouping

6.2 Factoring Trinomials of the form x2 + bx + c (Optional)

6.3 Factoring Trinomials: Trial-and-Error Method

6.4 Factoring Trinomials: AC-Method

6.5 Factoring Binomials

6.6 General Factoring Summary

6.7 Solving Equations by Using the Zero Product Rule

Chapter 6 Summary

Chapter 6 Review Exercises

Chapter 6 Test

Cumulative Review Exercises Chapters 1 – 6

Chapter 7: Rational Expressions

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 on Rational Expressions

7.5 Complex Fractions

7.6 Rational EquationsProblem Recognition Exercises – Comparing Rational Equations and Rational Expressions

7.7 Applications of Rational Equations, Ratios and Proportions

7.8 Variation (Optional)

Chapter 7 Summary

Chapter 7 Review Exercises

Chapter 7 Test

Cumulative Review Exercises Chapters 1 – 7

Chapter 8: Introduction to Relations and Functions

8.1 Introduction to Relations

8.2 Introduction to Functions

8.3 Graphs of Functions

8.4 Variation

Chapter 8 Summary

Chapter 8 Review Exercises

Chapter 8 Test

Cumulative Review Exercises, Chapters 1 – 8

Chapter 9: Systems of Linear Equations in Three Variables

9.1 Systems of Linear Equations in Three Variables

9.2 Applications of Systems of Linear Equations in Three Variables

9.3 Solving systems of Linear Equations Using Matrices

9.4 Determinants and Cramer’s Rule

Chapter 9 Summary

Chapter 9 Review Exercises

Chapter 9 Test

Cumulative Review Exercises, Chapters 1 – 9

Chapter 10: More Equations and Inequalities

10.1 Compound Inequalities

10.2 Polynomial and Rational Inequalities

10.3 Absolute Value Equations

10.4 Absolute Value Inequalities

Problem Recognition Exercises – Equations and Inequalities

10.5 Linear Inequalities in Two Variables

Chapter 10 Summary

Chapter 10 Review Exercises

Chapter 10 Test

Cumulative Review Exercises, Chapters 1 – 10

Chapter 11: Radicals and Complex Numbers

11.1 Definition of an nth-Root

11.2 Rational Exponents

11.3 Simplifying Radical Expressions

11.4 Addition and Subtraction of Radicals

11.5 Multiplication of Radicals

11.6 Rationalization

Problem Recognition Exercises – Operations on Radicals

11.7 Radical Equations

11.8 Complex Numbers

Chapter 11 Summary

Chapter 11 Review Exercises

Chapter 11 Test

Cumulative Review Exercises, Chapters 1 – 11

Chapter 12: Quadratic Equations and Functions

12.1 Square Root Property and Completing the Square

12.2 Quadratic Formula

12.3 Equations in Quadratic Form

12.4 Graphs of Quadratic Functions

12.5 Vertex of a Parabola and Applications

Chapter 12 Summary

Chapter 12 Review Exercises

Chapter 12 Test

Cumulative Review Exercises, Chapters 1 – 12

Chapter 13: Exponential and Logarithmic Functions

13.1 Algebra and Composition of Functions

13.2 Inverse Functions

13.3 Exponential Functions

13.4 Logarithmic Functions

13.5 Properties of Logarithms

13.6 The Irrational Number, e

Problem Recognition Exercises - Logarithmic and Exponential Forms

13.7 Logarithmic and Exponential Equations

Chapter 13 Summary

Chapter 13 Review Exercises

Chapter 13 Test

Cumulative Review Exercises, Chapters 1 – 13

Chapter 14: Conic Sections and Nonlinear Systems

14.1 Distance Formulas and Circles

14.2 More on the Parabola

14.3 The Ellipse and Hyperbola

14.4 Nonlinear Systems of Equations in Two Variables

14.5 Nonlinear Inequalities and Systems of Inequalities

Chapter 14 Summary

Chapter 14 Review Exercises

Chapter 14 Test

Cumulative Review Exercises, Chapters 1 – 14

Beginning Algebra Review:

Review A Set of Real Numbers

Review B Linear Equations in One Variable

Review C Linear Equations in Two Variables

Review D Systems of Linear Equations in Two Variables

Review E Polynomials and Properties of Exponents

Review F Factoring Polynomials and Solving Quadratic Equations

Review G Rational Expressions

Appendix

A.1 Binomial Expansions

A.2 Sequences and Series

A.3 Arithmetic and Geometric Sequences and Series

Student Answer Appendix