Student Solutions Manual for Developmental Mathematics

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 math from Clemson University. She has taught high school and college math for 30  years, and 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 recently earned a black belt in karate.  

1. Whole numbers

1.1 Standard Notation; Order

1.2 Addition and Subtraction

1.3 Multiplication and Division; Rounding and Estimating

1.4 Solving Equations

            Mid-Chapter Review

1.5 Applications and Problem Solving

            Translating for Success

1.6 Exponential Notation and Order of Operations

1.7 Factorizations

1.8 Divisibility

1.9 Least Common Multiples

            Summary and Review

            Test

 

2. Fraction Notation

2.1 Fraction Notation and Simplifying 

2.2 Multiplication and Division

2.3 Addition and Subtraction; Order

            Mid-Chapter Review

2.4 Mixed Numerals

2.5 Applications and Problem Solving

            Translating for Success

2.6 Order of Operations and Estimation

            Summary and Review

            Test

 

3. Decimal Notation

3.1 Decimal Notation, Order, and Rounding

3.2 Addition and Subtraction

3.3 Multiplication

3.4 Division

            Mid-Chapter Review

3.5 Converting from Fraction Notation to Decimal Notation

3.6 Estimating

3.7 Applications and Problem Solving

            Translating for Success

            Summary and Review

            Test

 

4. Percent Notation

4.1 Ratio and Proportion

4.2 Percent Notation

4.3 Percent Notation and Fraction Notation

4.4 Solving Percent Problems Using Percent Equations

4.5 Solving Percent Problems Using Proportions

            Mid-Chapter Review

4.6 Applications of Percent

            Translation for Success

4.7 Sales Tax, Commission, and Discount

4.8 Simple Interest and Compound Interest; Credit Cards

            Summary and Review

            Test

 

5. Data, Graphs, and Statistics

5.1 Averages, Medians, and Modes

5.2 Interpreting Data from Tables and Graphs

            Mid-Chapter Review

5.3 Interpreting and Drawing Bar Graphs and Line Graphs

5.4 Interpreting and Drawing Circle Graphs

            Translating for Success

            Summary and Review

            Test

 

6. Geometry

6.1 Basic Geometric Figures

6.2 Perimeter

6.3 Area

6.4 Circles

            Mid-Chapter Reviews

6.5 Volume and Surface Area

6.6 Relationships Between Angle Measures

6.7 Congruent Triangles and Properties of Parallelograms

6.8 Similar Triangles

            Translating for Success

            Summary and Review

            Test

 

7. Introduction to Real Numbers and Algebraic Expressions

7.1 Introduction to Algebra

7.2 The Real Numbers

7.3 Addition of Real Numbers

7.4 Subtraction of Real Numbers

            Mid-Chapter Review

7.5 Multiplication of Real Numbers

7.6 Division of Real Numbers

7.7 Properties of Real Numbers

7.8 Simplifying Expressions; Order of Operations

            Summary and Review

            Test

 

8. Solving Equations and Inequalities

8.1 Solving Equations: The Addition Principle

8.2 Solving Equations: The Multiplication Principle

8.3 Using the Principles Together

8.4 Formulas

            Mid-Chapter Review

8.5 Applications of Percent

8.6 Applications and Problem Solving

            Translating for Success

8.7 Solving Inequalities

8.8 Applications and Problem Solving with Inequalities

            Summary and Review

            Test

 

9. Graphs of Linear Equations

9.1 Graphs and Applications of Linear Equations

9.2 More with Graphing and Intercepts

            Visualizing for Success

9.3 Slope and Applications

9.4 Equations of Lines

            Mid-Chapter Review

9.5 Graphing Using the Slope and the y-Intercept

9.6 Parallel Lines and Perpendicular Lines

9.7 Graphing Inequalities in Two Variables

            Visualizing for Success

            Summary and Review

            Test

 

10. Polynomials: Operations

10.1 Integers as Exponents

10.2 Exponents and Scientific Notation

10.3 Introduction to Polynomials

10.4 Addition and Subtraction of Polynomials

            Mid-Chapter Review

10.5 Multiplication of Polynomials

10.6 Special Products

            Visualizing for Success

10.7 Operations with Polynomials in Several Variables

10.8 Division of Polynomials

            Summary and Review

            Test

 

11. Polynomials: Factoring

11.1 Introduction to Factoring

11.2 Factoring Trinomials of the Type x2 + bx + c

11.3 Factoring ax2 + bx + c, a ≠ 1: the FOIL Method

11.4 Factoring ax2 + bx + c, a ≠ 1: the ac-Method

            Mid-Chapter Review

11.5 Factoring Trinomial Squares and Differences of Squares

11.6 Factoring: A General Strategy

11.7 Solving Quadratic Equations by Factoring

11.8 Applications of Quadratic Equations

            Translating for Success

            Summary and Review

            Test

 

12. Rational Expressions and Equations

12.1 Multiplying and Simplifying Rational Expressions

12.2 Division and Reciprocals

12.3 Least Common Multiples and Denominators

12.4 Adding Rational Expressions

12.5 Subtracting Rational Expressions

            Mid-Chapter Review

12.6 Complex Rational Expressions

12.7 Solving Rational Equations

12.8 Applications Using Rational Equations and Proportions

            Translating for Success

12.9 Direct Variation and Inverse Variation

            Summary and Review

            Test

 

13. Systems of Equations

13.1 Systems of Equations in Two Variables

13.2 The Substitution Method

13.3 The Elimination Method

            Mid-Chapter Review

13.4 Applications and Problem Solving

13.5 Applications with Motion

            Translating for Success

            Summary and Review

            Test

 

14. Radical Expressions and Equations

14.1 Introduction to Radical Expressions

14.2 Multiplying and Simplifying with Radical Expressions

14.3 Quotients Involving Radical Expressions

            Mid-Chapter Review

14.4 Addition, Subtraction, and More Multiplication

14.5 Radical Equations

14.6 Applications with Right Triangles

            Translating for Success

            Summary and Review

            Test

 

15. Quadratic Equations

15.1 Introduction to Quadratic Equations

15.2 Solving Quadratic Equations by Completing the Square

15.3 The Quadratic Formula

            Mid-Chapter Review

15.4 Formulas

15.5 Applications and Problem Solving

            Translating for Success

15.6 Graphs for Quadratic Equations

            Visualizing for Success

15.7 Functions

            Summary and Review

            Test

 

Appendixes

A. Linear Measures: American Units and Metric Units

B. Weight and Mass; Medical Applications

C. Capacity; Medical Applications

D. Time and Temperature

E. Sets

F. Factoring Sums or Differences of Cubes

G. Finding Equations of Lines: Point-Slope Equation

H. Equations Involving Absolute Value

I. The Distance Formula and Midpoints

J. Higher Roots, and Rational Numbers as Exponents

K. Inequalities and Interval Notation

L. Nonlinear Inequalities

M. Systems of Linear Inequalities

N. Probability

O. The Complex Numbers

 

Answers

Guided Solutions

Glossary

Index