Beginning Algebra https://www.mheducation.com/cover-images/Jpeg_250-high/0073384488.jpeg 13 9780073384481
Beginning Algebra

Beginning Algebra

Grade Levels: 13
By Julie Miller and Molly O'Neill and Nancy Hyde
Copyright: 2014
Publication Date: January 4, 2013
MHID: 0073384488
ISBN 13: 9780073384481

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Key Features

Step-by-Step Worked Examples

The worked examples offer a clear, concise methodology that replicates the mathematical processes used in the authors’ classroom lectures.

Classroom Examples

To ensure that the classroom experience also matches the examples in the text and the practice exercises, the authors have included references to even-numbered exercises to be used as classroom examples. These exercises are highlighted in the Practice Exercises at the end of each section.

Chapter Openers

The chapter openers help students get better results through engaging Puzzles and Games that introduce the chapter concepts and ask ‘Are you prepared?’

Tip and Avoiding Mistakes Boxes

Tip and Avoiding Mistakes boxes have been created based on the authors’ classroom experiences and have been integrated into the worked examples. Thee pedagogical tools will help students get better results by learning how to work through a problem using clearly defined step-by-step methodology.

Problem Recognition Exercises

Problem Recognition Exercises present a collection of problems that look similar to a student upon first glance, but are actually quite different in the manner of their individual solutions. Students sharpen critical thinking skills and better develop their ‘solution recall’ to help them distinguish the method needed to solve an exercise, an essential skill in developmental mathematics.

Student Centered Applications

The Board of Advisors partnered with our authors to bring the best applications from every region in the country. These applications include real data and topics that are more relevant and interesting to today’s student.

Group Activities

Each chapter concludes with a Group Activity to promote classroom discussion and collaboration, helping students not only to solve problems but to explain their solutions for better mathematical mastery. Group Activities are great for both full-time and adjunct instructors, bringing a more interactive approach to teaching mathematics. All required materials, activity time, and suggested group sixes are provided in the end-of-chapter material.

Beginning Algebra

Beginning Algebra, Miller, O'Neill, Hyde, 4 edition

Chapter 1: The Set of Real Numbers

1.1 Fractions

1.2 Introduction to Algebra and the Set of Real Numbers

1.3 Exponents, Square Roots, and the 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 and Modeling

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 Linear Inequalities and Systems of Inequalities in Two 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 and 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 on 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

7.8 Variation

Chapter 8: Radicals

8.1 Introduction to Roots and Radicals

8.2 Simplifying Radicals

8.3 Addition and Subtraction of Radicals

8.4 Multiplication of Radicals

8.5 Division of Radicals and Rationalization

Problem Recognition Exercises—Operations on Radicals

8.6 Radical Equations

8.7 Rational Exponents

Chapter 9: Quadratic Equations, Complex Numbers, and Functions

9.1 The Square Root Property

9.2 Completing the Square

9.3 Quadratic Formula

Problem Recognition Exercises—Solving Different Types of Equations

9.4 Complex Numbers

9.5 Graphing Quadratic Equations

9.6 Introduction to Functions

Additional Topics Appendix

A.1 Decimals and Percents

A.2 Mean, Median, and Mode

A.3 Introduction to Geometry

A.4 Converting Units of Measurement

About the Author

Julie Miller

Julie Miller is from Daytona State College, where she has taught developmental and upper-level mathematics courses for 20 years. Prior to her work at Daytona State College, she worked as a software engineer for General Electric in the area of flight and radar simulation. Julie earned a bachelor of science in applied mathematics from Union College in Schenectady, New York, and a master of science in mathematics from the University of Florida. In addition to this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus, as well as several short works of fiction and nonfiction for young readers.
My father is a medical researcher, and I got hooked on math and science when I was young and would visit his laboratory. I can remember using graph paper to plot data points for his experiments and doing simple calculations. He would then tell me what the peaks and features in the graph meant in the context of his experiment. I think that applications and hands-on experience made math come alive for me and I’d like to see math come alive for my students.

Molly O'Neill

Molly ONeill is from Daytona State College, where she has taught for 22 years in the School of Mathematics. She has taught a variety of courses from developmental mathematics to calculus. Before she came to Florida, Molly taught as an adjunct instructor at the University of Michigan-Dearborn, Eastern Michigan University, Wayne State University, and Oakland Community College. Molly earned a bachelor of science in mathematics and a master of arts and teaching from Western Michigan University in Kalamazoo, Michigan. Besides this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus and has reviewed texts for developmental mathematics.
I differ from many of my colleagues in that math was not always easy for me. But in seventh grade I had a teacher who taught me that if I follow the rules of mathematics, even I could solve math problems. Once I understood this, I enjoyed math to the point of choosing it for my career. I now have the greatest job because I get to do math every day and I have the opportunity to influence my students just as I was influenced. Authoring these texts has given me another avenue to reach even more students.

Nancy Hyde

Nancy Hyde served as a full-time faculty member of the Mathematics Department at Broward College for 24 years. During this time she taught the full spectrum of courses from developmental math through differential equations. She received a bachelor of science degree in math education from Florida State University and a master’s degree in math education from Florida Atlantic University. She has conducted workshops and seminars for both students and teachers on the use of technology in the classroom. In addition to this textbook, she has authored a graphing calculator supplement for College Algebra.
I grew up in Brevard County, Florida, where my father worked at Cape Canaveral. I was always excited by mathematics and physics in relation to the space program. As I studied higher levels of mathematics I became more intrigued by its abstract nature and infinite possibilities. It is enjoyable and rewarding to convey this perspective to students while helping them to understand mathematics.