Developmental Mathematics

Note: every chapter ends with a chapter summary, review exercises, and a chapter test. Chapters 8 and 17 also have cumulative review exercises.


 

1. Whole Numbers

1.1 Reading and Writing Whole Numbers

1.2 Adding Whole Numbers

1.3 Subtracting Whole Numbers

1.4 Multiplying Whole Numbers

1.5 Dividing Whole Numbers

1.6 Long Division

1.7 Rounding Whole Numbers

1.8 Exponents, Roots, and Order of Operations

1.9 Reading Pictographs, Bar Graphs, and Line Graphs

1.10 Solving Application Problems

Summary

Review Exercises

Test

 

2. Multiplying and Dividing Fractions 

2.1 Basics of Fractions

2.2 Mixed Numbers

2.3 Factors

2.4 Writing a Fraction in Lowest Terms

2.5 Multiplying Fractions

2.6 Applications of Multiplication

2.7 Dividing Fractions

2.8 Multiplying and Dividing Mixed Numbers

Summary

Review Exercises

Test

 

3. Adding and Subtracting Fractions 

3.1 Adding and Subtracting Like Fractions

3.2 Least Common Multiples

3.3 Adding and Subtracting Unlike Fractions

3.4 Adding and Subtracting Mixed Numbers

3.5 Order Relations and the Order of Operations

Summary

Review Exercises

Test

 

4. Decimals 

4.1 Reading and Writing Decimals

4.2 Rounding Decimals

4.3 Adding and Subtracting Decimals

4.4 Multiplying Decimals

4.5 Dividing Decimals

4.6 Writing Fractions as Decimals

Summary

Review Exercises

Test

 

5. Ratio and Proportion

5.1 Ratios

5.2 Rates

5.3 Proportions

5.4 Solving Proportions

5.5 Solving Application Problems with Proportions

Summary

Review Exercises

Test

 

6. Percent 

6.1 Basics of Percent

6.2 Percents and Fractions

6.3 Using the Percent Proportion and Identifying the Components in a Percent Problem

6.4 Using Proportions to Solve Percent Problems

6.5 Using the Percent Equation

6.6 Solving Application Problems with Percent

6.7 Simple Interest

6.8 Compound Interest

Summary

Review Exercises

Test

 

7. Geometry  

7.1 Lines and Angles

7.2 Rectangles and Squares

7.3 Parallelograms and Trapezoids

7.4 Triangles

7.5 Circles

7.6 Volume and Surface Area

7.7 Pythagorean Theorem

7.8 Congruent and Similar Triangles

Summary

Review Exercises

Test

 

8. Statistics

8.1 Circle Graphs

8.2 Bar Graphs and Line Graphs

8.3 Frequency Distributions and Histograms

8.4 Mean, Median, and Mode

Summary

Review Exercises

Test

Cumulative Review Exercises

 

9. The Real Number System 

9.1 Exponents, Order of Operations, and Inequality

9.2 Variables, Expressions, and Equations

9.3 Real Numbers and the Number Line

9.4 Adding Real Numbers

9.5 Subtracting Real Numbers

9.6 Multiplying and Dividing Real Numbers

9.7 Properties of Real Numbers

9.8 Simplifying Expressions

Summary

Review Exercises

Test

 

10. Equations, Inequalities, and Applications

10.1 The Addition Property of Equality

10.2 The Multiplication Property of Equality

10.3 More on Solving Linear Equations

10.4 An Introduction to Applications of Linear Equations

10.5 Formulas and Applications from Geometry

10.6 Solving Linear Inequalities

Summary

Review Exercises

Test

 

11. Graphs of Linear Equations and Inequalities in Two Variables

11.1 Reading Graphs: Linear Equations in Two Variables

11.2 Graphing Linear Equations in Two Variables

11.3 Slope of a Line

11.4 Equations of Lines

11.5 Graphing Linear Inequalities in Two Variables

Summary

Review Exercises

Test

 

12. Exponents and Polynomials 

12.1 Adding and Subtracting Polynomials

12.2 The Product Rule and Power Rules for Exponents

12.3 Multiplying Polynomials

12.4 Special Products

12.5 Integer Exponents and the Quotient Rule

12.6 Dividing a Polynomial by a Monomial

12.7 Dividing a Polynomial by a Polynomial

12.8 An Application of Exponents: Scientific Notation

Summary

Review Exercises

Test

 

13. Factoring and Applications

13.1 Factors: The Greatest Common Factor

13.2 Factoring Trinomials

13.3 Factoring Trinomials by Grouping

13.4 Factoring Trinomials Using FOIL

13.5 Special Factoring Techniques

13.6 Solving Quadratic Equations by Factoring

13.7 Applications of Quadratic Equations

Summary

Review Exercises

Test

 

14. Rational Expressions and Applications

14.1 The Fundamental Property of Rational Expressions

14.2 Multiplying and Dividing Rational Expressions

14.3  Least Common Denominators

14.4 Adding and Subtracting Rational Expressions

14.5 Complex Fractions

14.6 Solving Equations with Rational Expressions

14.7 Applications of Rational Expressions

14.8 Variation

Summary

Review Exercises

Test

 

15. Systems of Linear Equations and Inequalities 

15.1 Solving Systems of Linear Equations by Graphing

15.2 Solving Systems of Linear Equations by Substitution

15.3 Solving Systems of Linear Equations by Elimination

15.4 Applications of Linear Systems

15.5 Solving Systems of Linear Inequalities

Summary

Review Exercises

Test

 

16. Roots and Radicals 

16.1 Evaluating Roots

16.2 Multiplying, Dividing, and Simplifying Radicals

16.3 Adding and Subtracting Radicals

16.4 Rationalizing the Denominator

16.5 More Simplifying and Operations with Radicals

16.6 Solving Equations with Radicals

Summary

Review Exercises

Test

 

17. Quadratic Equations

17.1 Solving Quadratic Equations by the Square Root Property

17.2 Solving Quadratic Equations by Completing the Square

17.3 Solving Quadratic Equations by the Quadratic Formula

17.4 Graphing Quadratic Equations and Inequalities

17.5 Introduction to Functions

Summary

Review Exercises

Test

Cumulative Review Exercises

 

Appendix A Measurement

1. Problem Solving with English Measurement

2. The Metric System Length

3. The Metric System Capacity and Weight (Mass)

4. Metric-English Conversions and Temperature

Appendix B Sets

Appendix C Further Algebra Topics

1. Absolute Value Equations and Inequalities

2. Midpoint and Distance Formulas 

3. Rational Exponents

Appendix D Inductive and Deductive Reasoning

Appendix E Preparing for THEA

1. THEA Test Mathematical Skills

2. THEA Practice Test

 

Answers to Selected Exercises

Index