Integrated Review Worksheets for Introductory Algebra

Description

Marvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University–Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled “Baseball and Mathematics.” His hobbies include hiking in Utah, baseball, golf, and bowling. In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.

Judy Beecher has an undergraduate degree in mathematics from Indiana University and a graduate degree in mathematics from Purdue University. She has taught at both the high school and college levels with many years of developmental math and precalculus teaching experience at Indiana University–Purdue University Indianapolis. In addition to her career in textbook publishing, she spends time traveling, enjoying her grandchildren, and promoting charity projects for a children’s camp.

Barbara Johnson has a BS in mathematics from Bob Jones University and a MS in mathematics from Clemson University, and she is currently pursuing a PhD in Educational Studies at Ball State University. She has taught high school and college math for 30 years, and she enjoys the challenge of helping each student grow in appreciation for and understanding of mathematics. As a Purdue Master Gardener, she also enjoys helping others learn gardening skills. Believing that the best teacher is always learning, she is also a student of karate.

Foundation: Studying the Concepts

• Updated – Structured, yet flexible, the updated learning path highlights author-created, faculty-vetted content — giving students what they need exactly when they need it.  The learning path directs students to resources such as videos and animations for just in time support.
• New – Just-in-Time Review modules at the beginning of the text and etext review the key topics from previous courses that are prerequisites for the new material in this course. Just-in-Time Review Videos in MyLab Math offer a concise presentation of each topic with additional examples.
• New – Skill Review, in nearly every section of the text and etext, reviews a previously presented skill at the objective level where it is key to learning the new material. In MyLab Math, Skill Review Videos, created by the authors, offer a concise, stepped-out solution for each Skill Review Exercise. 
• New – Chapter Opener applications with graphics use current data and applications to present the math in context. These applications are linked to exercises in the text and MyLab Math course to help students model, visualize, and learn the math. 
• New – Student Activities begin with real-world data and guide students to examine a key concept in each chapter, while analyzing the data and connecting other concepts. There is one activity per chapter and they are available in MyLab Math and in the printed MyMathGuide.
• New – Interactive Animations, available in MyLab Math, allow students to examine visual representations of concepts through both guided and open-ended exploration to further solidify their understanding of these concepts.
• New – Bittinger-specific Learning Catalytics questions are now available. Learning Catalytics is an interactive student response tool that uses students’ smartphones, tablets, or laptops to engage them in more sophisticated tasks and thinking.

Application: Reinforcing Understanding

• New – Check Your Understanding with Reading Check and Concept Check exercises at the beginning of each section exercise set gives students the opportunity to assess their grasp of the skills and concepts before they move on to the homework.
• Margin Exercises give students frequent opportunities to apply concepts just discussed by solving problems that parallel the text Examples.
• Section Exercises, including Skill Maintenance, Synthesis, and real-data Applications, offer abundant opportunities for practice, review, and development of critical-thinking skills. New! Guided Solutions exercises were added to MyLab Math to reinforce the step-by-step problem-solving process, while the new Drag & Drop functionality was applied to matching exercises throughout the course to better assess a student’s understanding of the concepts.

Retention: Carrying Success Forward

• New – Skill Builder offers adaptive practicethat is designed to increase students’ ability to complete their assignments. By monitoring student performance on their homework, Skill Builder adapts to each student’s needs and provides just-in-time, in-assignment practice to help them improve their proficiency of key learning objectives.
• Mid-Chapter Review with Concept Reinforcement, Guided Solutions, Mixed Review, and Understanding through Discussion and Writing allows student to pause and actively review halfway through the chapter in the text and MyLab Math
• Summary and Review is a comprehensive learning and review section at the end of each chapter with Vocabulary Reinforcement, Concept Reinforcement, Study Guide, Review Exercises, and Understanding through Writing and Discussion exercises. Chapter Tests, Chapter Test Prep videos, and Cumulative Review offer additional opportunities for review and reinforcement of skills and concepts in the text and MyLab Math.

Also available with MyLab Math 

MyLab™ is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab personalizes the learning experience and improves results for each student. Learn more about MyLab Math.

Reach every student with MyLab

• Deliver trusted content: You deserve teaching materials that meet your own high standards for your course. That’s why we partner with highly respected authors to develop interactive content and course-specific resources that you can trust – and that keep your students engaged. 
• Empower each learner: Each student learns at a different pace. Personalized learning pinpoints the precise areas where each student needs practice, giving all students the support they need – when and where they need it – to be successful.
• Teach your course your way: Your course is unique. So whether you’d like to build your own assignments, teach multiple sections, or set prerequisites, MyLab gives you the flexibility to easily create your course to fit your needs.
• Improve student results: When you teach with MyLab, student performance often improves. That’s why instructors have chosen MyLab for over 15 years, touching the lives of over 50 million students.

• Structured, yet flexible, the updated learning path highlights author-created, faculty-vetted content – giving students what they need exactly when they need it.  The learning path directs students to resources such as videos and animations for just in time support.
• Just-in-Time Review modules at the beginning of the text and etext review the key topics from previous courses that are prerequisites for the new material in this course. Just-in-Time Review Videos in MyLab™ Math offer a concise presentation of each topic with additional examples.
• Skill Review, in nearly every section of the text and etext, reviews a previously presented skill at the objective level where it is key to learning the new material. In MyLab Math, Skill Review Videos, created by the authors, offer a concise, stepped-out solution for each Skill Review Exercise. 
• Interactive Animations, available in MyLab Math, allow students to examine visual representations of concepts through both guided and open-ended exploration to further solidify their understanding of these concepts.
• Chapter Opener applications with graphics in the text use current data and applications to present the math in context. These applications are linked to additional examples and exercises  in the text and MyLab Math course to help students model, visualize, and learn the math. 
• Check Your Understanding with Reading Check and Concept Check exercises at the beginning of each section exercise set gives students the opportunity to assess their grasp of the skills and concepts before they move on to the homework.
• Skill Builder offers adaptive practice that is designed to increase students’ ability to complete their assignments. By monitoring student performance on their homework, Skill Builder adapts to each student’s needs and provides just-in-time, in-assignment practice to help them improve their proficiency of key learning objectives.
• Student Activities begin with real-world data and guide students to examine a key concept in each chapter, while analyzing the data and connecting other concepts. There is one activity per chapter and they are available in MyLab Math and the printed MyMathGuide workbook.
• Interactive exercises in MyLab Math help build problem-solving skills and foster conceptual understanding. For the 13th Edition, increased coverage of skill-building, conceptual, and applications exercises, and new problem types provide even more flexibility when creating homework. Guided Solutions exercises have been added to reinforce the step-by-step problem-solving process, while the new Drag & Drop functionality was added  throughout the course to better assess a student’s understanding of the concepts.

• A library of pre-made developmental math questions is available in Learning Catalytics, helping instructors to start using this new engagement tool. Learning Catalytics is an interactive student response tool that uses students’ smartphones, tablets, or laptops to engage them in more sophisticated tasks and thinking.  

• Index of Activities
• Index of Animations
• Preface
• Index of Applications
• Just-in-Time Review
  1. All Factors of a Number
  2. Prime Factorizations
  3. Greatest Common Factor
  4. Least Common Multiple
  5. Equivalent Expressions and Fraction Notation
  6. Mixed Numerals
  7. Simplify Fraction Notation
  8. Multiply and Divide Fraction Notation
  9. Add and Subtract Fraction Notation
  10. Convert from Decimal Notation to Fraction Notation
  11. Add and Subtract Decimal Notation
  12. Multiply and Divide Decimal Notation
  13. Convert from Fraction Notation to Decimal Notation
  14. Rounding with Decimal Notation
  15. Convert Between Percent Notation and Decimal Notation
  16. Convert Between Percent Notation and Fraction Notation
  17. Exponential Notation
  18. Order of Operations

1. Introduction to Real Numbers and Algebraic Expressions
   • 1.1 Introduction to Algebra
   • 1.2 The Real Numbers
   • 1.3 Addition of Real Numbers
   • 1.4 Subtraction of Real Numbers
     • Mid-Chapter Review
   • 1.5 Multiplication of Real Numbers
   • 1.6 Division of Real Numbers
   • 1.7 Properties of Real Numbers
   • 1.8 Simplifying Expressions; Order of Operations
   • Summary and Review
   • Test
2. Solving Equations and Inequalities
   • 2.1 Solving Equations: The Addition Principle
   • 2.2 Solving Equations: The Multiplication Principle
   • 2.3 Using the Principles Together
   • 2.4 Formulas
     • Mid-Chapter Review
   • 2.5 Applications of Percent
   • 2.6 Applications and Problem Solving
     • Translating for Success
   • 2.7 Solving Inequalities
   • 2.8 Applications and Problem Solving with Inequalities
   • Summary and Review
   • Test
   • Cumulative Review
3. Graphs of Linear Equations
   • 3.1 Graphs and Applications of Linear Equations
   • 3.2 More with Graphing and Intercepts
     • Visualizing for Success
   • 3.3 Slope and Applications
   • 3.4 Equations of Lines
     • Mid-Chapter Review
   • 3.5 Graphing Using the Slope and y-Intercept
   • 3.6 Parallel Lines and Perpendicular Lines
   • 3.7 Graphing Inequalities in Two Variables
   • Visualizing for Success
   • Summary and Review
   • Test
   • Cumulative Review
4. Polynomials: Operations
   • 4.1 Integers as Exponents
   • 4.2 Exponents and Scientific Notation
   • 4.3 Introduction to Polynomials
   • 4.4 Addition and Subtraction of Polynomials
     • Mid-Chapter Review
   • 4.5 Multiplication of Polynomials
   • 4.6 Special Products
     • Visualizing for Success
   • 4.7 Operations with Polynomials in Several Variables
   • 4.8 Division of Polynomials
   • Summary and Review
   • Test
   • Cumulative Review
5. Polynomials: Factoring
   • 5.1 Introduction to Factoring
   • 5.2 Factoring Trinomials of the Type x² + bx + c
   • 5.3 Factoring ax² + bx + c, a ≠ 1: The FOIL Method
   • 5.4 Factoring ax² + bx + c, a ≠ 1: The ac-Method
     • Mid-Chapter Review
   • 5.5 Factoring Trinomial Squares and Differences of Squares
   • 5.6 Factoring: A General Strategy
   • 5.7 Solving Quadratic Equations by Factoring
   • 5.8 Applications of Quadratic Equations
   • Translating For Success
   • Summary and Review
   • Test
   • Cumulative Review
6. Rational Expressions and Equations
   • 6.1 Multiplying and Simplifying Rational Expressions
   • 6.2 Division and Reciprocals
   • 6.3 Least Common Multiples and Denominators
   • 6.4 Adding Rational Expressions
   • 6.5 Subtracting Rational Expressions
     • Mid-Chapter Review
   • 6.6 Complex Rational Expressions
   • 6.7 Solving Rational Equations
   • 6.8 Applications Using Rational Equations and Proportions
     • Translating for Success
   • 6.9 Direct Variation and Inverse Variation
   • Summary and Review
   • Test
   • Cumulative Review
7. Systems of Equations
   • 7.1 Systems of Equations in Two Variables
   • 7.2 The Substitution Method
   • 7.3 The Elimination Method
     • Mid-Chapter Review
   • 7.4 Applications and Problem Solving
   • 7.5 Applications with Motion
   • Translating for Success
   • Summary and Review
   • Test
   • Cumulative Review
8. Radical Expressions and Equations
   • 8.1 Introduction to Radical Expressions
   • 8.2 Multiplying and Simplifying with Radical Expressions
   • 8.3 Quotients Involving Radical Expressions
     • Mid-Chapter Review
   • 8.4 Addition, Subtraction, and More Multiplication
   • 8.5 Radical Equations
   • 8.6 Applications with Right Triangles
   • Translating for Success
   • Summary and Review
   • Test
   • Cumulative Review
9. Quadratic Equations
   • 9.1 Introduction to Quadratic Equations
   • 9.2 Solving Quadratic Equations by Completing the Square
   • 9.3 The Quadratic Formula
     • Mid-Chapter Review
   • 9.4 Formulas
   • 9.5 Applications and Problem Solving
     • Translating for Success
   • 9.6 Graphs of Quadratic Equations
     • Visualizing for Success
   • 9.7 Functions
   • Summary and Review
   • Test
   • Cumulative Review

APPENDICES

• A. Factoring Sums or Differences of Cubes
• B. Finding Equations of Lines: Point—Slope Equation
• C. Higher Roots
• D. Sets
• E. Mean, Median, and Mode
• F. Inequalities and Interval Notation

• Answers
• Guided Solutions
• Glossary
• Index

Additional information