Developmental Mathematics with Applications and Visualization: Prealgebra, Beginning Algebra, and Intermediate Algebra, 2nd edition

Published by Pearson (March 29, 2017) © 2018
  • Gary K. Rockswold
  • Terry A. Krieger

Title overview

For courses in Prealgebra & Beginning Algebra.

Develop concepts in context

The Rockswold/Krieger algebra series fosters conceptual understanding through applications, multiple representations, and visualization; students make math part of their own experiences instead of just memorizing techniques. Developmental Mathematics with Applications and Visualization promotes conceptual understanding above procedural skills. Its emphasis on visualization empowers students with different learning styles to successfully absorb the information presented.

The 2nd Edition adds a wealth of new features including Connecting Concepts with Your Life, Math in Context, Online Exploration exercises, See the Concept, and more. Modeling data has been added to hundreds of exercises and examples and applications have been updated throughout.

Hallmark features of this title

  • Learning the Math from Multiple Perspectives presents concepts by means of verbal, graphical, numerical, and symbolic representations to support different learning styles and problem-solving methods.
  • New Vocabulary is listed at the start of every section, highlighting the math concepts that are introduced in that section and helping with test preparation. Putting It All Together boxes at the end of each section summarize techniques and reinforce the mathematical concepts presented in the section.
  • Reading Check questions appear alongside important concepts, ensuring that students understand the material they have just read. Making Connections throughout help students see how previous concepts are related to new concepts.
  • Graphing Calculator Exercise icons denote an optional exercise that requires students to have access to a graphing calculator. Technology Notes throughout the text are optional notes that offer students guidance, suggestions, and caution.
  • Multiple exercise types include Now Try, Critical Thinking, Concepts and Vocabulary, Checking Basic Concepts, Thinking Generally, and Writing about Mathematics.
  • Group Activities appear once or twice per chapter and provide an opportunity for students to work collaboratively on a problem that involves real-world data. Most activities can be completed with limited use of class time.

New to this edition

  • New Connecting Concepts with Your Life gives meaning to mathematics by relating common life experiences that students already understand. New See the Concept presents a concise, visual overview of topics that were previously written out as text.
  • New Math in Context connects mathematics to current and relevant topics. 
  • Updated applications include several new examples that discuss the mathematics of the Internet, social networking, tablets, and more.
  • Modeling data in hundreds of exercises and examples offer students the chance to model real and relevant data with their own functions.
  • New Online Exploration exercises invite students to find their own data online and use mathematics to analyze it.
  • New comment balloons appear next to steps and procedures to make them more (immediately) understandable.

Key features

Features of MyLab Math for the 2nd Edition

  • New See the Concept videos, created entirely by the authors, bring key concepts to life by providing a visual overview of each See the Concept feature in the text.
  • New Section Introduction videos, also created entirely by the authors, are available for every section of the text. These introduce the section’s concepts in a contextual setting, engaging students with a concrete introduction to topics.
  • New Video assessment questions are available for all See the Concept and Section Introduction videos; instructors can assign the video to help reinforce students' conceptual understanding.
  • Additional content from the text (including many of the Reading Checks, Making Connections, and Critical Thinking features) is available in MyLab Math for instructors to assign.
  • New Drag and Drop exercises allow students to manually select elements of the question, such as expressions, words, graphs, or images, and place them into a designated target area.
  • The new Guided Workbook is keyed to the text by section and objective, giving students the opportunity to record key information, work practice problems, and show/keep their work for reference.

Table of contents

1. Whole Numbers

  • 1.1 Introduction to Whole Numbers
  • 1.2 Adding and Subtracting Whole Numbers; Perimeter <
  • 1.3 Multiplying and Dividing Whole Numbers; Area
  • 1.4 Exponents, Variables, and Algebraic Expressions
  • 1.5 Rounding and Estimating; Square Roots
  • 1.6 Order of Operations
  • 1.7 More with Equations and Problem Solving

2. Integers

  • 2.1 Integers and the Number Line
  • 2.2 Adding Integers
  • 2.3 Subtracting Integers
  • 2.4 Multiplying and Dividing Integers
  • 2.5 Order of Operations; Averages
  • 2.6 Solving Equations That Have Integer Solutions

3. Algebraic Expressions and Linear Equations

  • 3.1 Simplifying Algebraic Expressions
  • 3.2 Translating Words to Expressions and Equations
  • 3.3 Properties of Equality
  • 3.4 Solving Linear Equations in One Variable
  • 3.5 Applications and Problem Solving

4. Fractions

  • 4.1 Introduction to Fractions and Mixed Numbers
  • 4.2 Prime Factorization and Lowest Terms
  • 4.3 Multiplying and Dividing Fractions
  • 4.4 Adding and Subtracting Fractions–Like Denominators
  • 4.5 Adding and Subtracting Fractions–Unlike Denominators
  • 4.6 Operations on Mixed Numbers
  • 4.7 Complex Fractions and Order of Operations
  • 4.8 Solving Equations Involving Fractions

5. Decimals

  • 5.1 Introduction to Decimals
  • 5.2 Adding and Subtracting Decimals
  • 5.3 Multiplying and Dividing Decimals
  • 5.4 Real Numbers, Square Roots, and Order of Operations
  • 5.5 Solving Equations Involving Decimals
  • 5.6 Applications from Geometry and Statistics

6. Ratios, Proportions, and Measurement

  • 6.1 Ratios and Rates
  • 6.2 Proportions and Similar Figures
  • 6.3 The U.S. System of Measurement
  • 6.4 The Metric System of Measurement
  • 6.5 U.S.-Metric Conversions; Temperature 6.6 Time and Speed

7. Percents

  • 7.1 Introduction to Percent; Circle Graphs
  • 7.2 Using Equations to Solve Percent Problems
  • 7.3 Using Proportions to Solve Percent Problems
  • 7.4 Applications: Sales Tax, Discounts, and Net Pay
  • 7.5 Applications: Simple and Compound Interest
  • 7.6 Probability and Percent Chance

8. Geometry

  • 8.1 Plane Geometry: Points, Lines, and Angles
  • 8.2 Triangles
  • 8.3 Polygons and Circles
  • 8.4 Perimeter and Circumference
  • 8.5 Area, Volume, and Surface Area

9. Linear Equations and Inequalities in One Variable

  • 9.1 Review of Linear Equations in One Variable
  • 9.2 Further Problem Solving
  • 9.3 Linear Inequalities in One Variable

10. Graphing Equations

  • 10.1 Introduction to Graphing
  • 10.2 Equations in Two Variables
  • 10.3 Intercepts; Horizontal and Vertical Lines
  • 10.4 Slope and Rates of Change
  • 10.5 Slope-Intercept Form
  • 10.6 Point-Slope Form
  • 10.7 Introduction to Modeling

11. Systems of Linear Equations in Two Variables

  • 11.1 Solving Systems of Linear Equations Graphically and Numerically
  • 11.2 Solving Systems of Linear Equations by Substitution
  • 11.3 Solving Systems of Linear Equations by Elimination
  • 11.4 Systems of Linear Inequalities

12. Polynomials and Exponents

  • 12.1 Rules for Exponents
  • 12.2 Addition and Subtraction of Polynomials
  • 12.3 Multiplication of Polynomials
  • 12.4 Special Products
  • 12.5 Integer Exponents and the Quotient Rule
  • 12.6 Division of Polynomials

13. Factoring Polynomials and Solving Equations

  • 13.1 Introduction to Factoring
  • 13.2 Factoring Trinomials I (x2 + bx + c)
  • 13.3 Factoring Trinomials II (ax2 + bx + c)
  • 13.4 Special Types of Factoring
  • 13.5 Summary of Factoring
  • 13.6 Solving Equations by Factoring I (Quadratics)
  • 13.7 Solving Equations by Factoring II (Higher Degree)

14. Rational Expressions

  • 14.1 Introduction to Rational Expressions
  • 14.2 Multiplication and Division of Rational Expressions
  • 14.3 Addition and Subtraction with Like Denominators
  • 14.4 Addition and Subtraction with Unlike Denominators
  • 14.5 Complex Fractions
  • 14.6 Rational Equations and Formulas
  • 14.7 Proportions and Variation

15. Introduction to Functions

  • 15.1 Functions and Their Representations
  • 15.2 Linear Functions
  • 15.3 Compound Inequalities and Piecewise-Defined Functions
  • 15.4 Other Functions and Their Properties
  • 15.5 Absolute Value Equations and Inequalities

16. Systems of Linear Equations

  • 16.1 Systems of Linear Equations in Three Variables
  • 16.2 Matrix Solutions of Linear Systems
  • 16.3 Determinants

17. Radical Expressions and Functions

  • 17.1 Radical Expressions and Functions
  • 17.2 Rational Exponents
  • 17.3 Simplifying Radical Expressions
  • 17.4 Operations on Radical Expressions
  • 17.5 More Radical Functions
  • 17.6 Equations Involving Radical Expressions
  • 17.7 Complex Numbers

18. Quadratic Functions and Equations

  • 18.1 Quadratic Functions and Their Graphs
  • 18.2 Transformations and Translations of Parabolas
  • 18.3 Quadratic Equations
  • 18.4 The Quadratic Formula
  • 18.5 Quadratic Inequalities
  • 18.6 Equations in Quadratic Form

19. Exponential and Logarithmic Functions

  • 19.1 Composite and Inverse Functions
  • 19.2 Exponential Functions
  • 19.3 Logarithmic Functions
  • 19.4 Properties of Logarithms
  • 19.5 Exponential and Logarithmic Equations

20. Conic Sections

  • 20.1 Parabolas and Circles
  • 20.2 Ellipses and Hyperbolas
  • 20.3 Nonlinear Systems of Equations and Inequalities

21. Sequences and Series

  • 21.1 Sequences
  • 21.2 Arithmetic and Geometric Sequences
  • 21.3 Series
  • 21.4 The Binomial Theorem

Appendices

  • A: Using the Graphing Calculator
  • B: Sets
  • C: Linear Programming
  • D: Synthetic Division
  • E: Using a Calculator

Author bios

About our authors

Gary Rockswold has been a professor and teacher of mathematics, computer science, astronomy, and physical science for over 35 years. Not only has he taught at the undergraduate and graduate college levels, but he has also taught middle school, high school, vocational school, and adult education. He received his BA degree with majors in mathematics and physics from St. Olaf College and his PhD in applied mathematics from Iowa State University. He has been a principal investigator at the Minnesota Supercomputer Institute, publishing research articles in numerical analysis and parallel processing. He is currently an emeritus professor of mathematics at Minnesota State University–Mankato. He is an author for Pearson Education and has numerous textbooks at the developmental and precalculus levels. Making mathematics accessible to students and professing the power of mathematics are special passions for Gary. He frequently gives keynote and invited addresses at regional, national, and international math conferences. In his spare time he enjoys sailing, doing yoga, hiking, and spending time with his family.

Terry Krieger has taught mathematics for over 20 years at the middle school, high school, vocational, community college, and university levels. His undergraduate degree in secondary education is from Bemidji State University in Minnesota, where he graduated summa cum laude. He received his MA in mathematics from Minnesota State University–Mankato. In addition to his teaching experience in the United States, Terry has taught mathematics in Tasmania, Australia, and in a rural school in Swaziland, Africa, where he served as a Peace Corps volunteer. Terry has been involved with various aspects of mathematics textbook publication throughout his career. In his free time, Terry enjoys spending time with his wife and 2 boys, physical fitness, wilderness camping, and trout fishing.

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