Developmental Mathematics

Table of Contents

1. Whole Numbers

1.1 Success in Mathematics

1.2 Fundamentals of Whole Numbers

1.3 Adding and Subtracting Whole Numbers

1.4 Multiplying Whole Numbers and Exponents

1.5 Dividing Whole Numbers

1.6 Prime Numbers

1.7 Order of Operations Using Whole Numbers

2. Integers and an Introduction to Algebra

2.1 Fundamentals of Integers

2.2 Adding and Subtracting Integers

2.3 Multiplying and Dividing Integers

2.4 Exponents and Order of Operations

2.5 Simplifying Algebraic Expressions

2.6 Linear Equations: The Addition and Multiplication Properties

2.7 Linear Equations: Using the Properties Together

2.8 Introduction to Problem Solving: Direct Translation Problems

3. Fractions

3.1 Fundamentals of Fractions

3.2 Multiplying and Dividing Fractions

3.3 Adding and Subtracting Like Fractions

3.4 Adding and Subtracting Unlike Fractions

3.5 Order of Operations and Complex Fractions

3.6 Operations with Mixed Numbers

3.7 Solving Equations Containing Fractions

4. Decimals

4.1 Fundamentals of Decimals

4.2 Adding and Subtracting Decimals

4.3 Multiplying Decimals

4.4 Dividing Decimals

4.5 Solving Equations Containing Decimals

5. Ratio, Proportion, and Percent

5.1 Ratios and Unit Rates

5.2 Proportions

5.3 Fundamentals of Percent Notation

5.4 Solving Percent Problems: Proportion Method

5.5 Solving Percent Problems: Equation Method

5.6 Applications Involving Percent

6. Measurement and Geometry

6.1 The U.S. Standard (English) System of Measurement

6.2 The Metric System of Measurement

6.3 Fundamentals of Geometry

6.4 Polygons

6.5 Perimeter and Area of Polygons and Circles

6.6 Volume and Surface Area

7. Introduction to Statistics and the Rectangular Coordinate System

7.1 Tables and Graphs

7.2 Mean, Median, and Mode

7.3 The Rectangular Coordinate System and Equations in Two Variables

7.4 Graphing Equations in Two Variables

8. Equations and Inequalities in One Variable

8.1 Linear Equations: The Addition and Multiplication Properties of Equality

8.2 Linear Equations: Using the Properties Together

8.3 Solving Linear Equations Involving Fractions and Decimals; Classifying Equations

8.4 Evaluating Formulas and Solving Formulas for a Variable

8.5 Introduction to Problem Solving: Direct Translation Problems

8.6 Problem Solving: Direct Translation Problems Involving Percent

8.7 Problem Solving: Geometry and Uniform Motion

8.8 Solving Linear Inequalities in One Variable

9. Introduction to Graphing and Equation of Lines

9.1 The Rectangular Coordinate System and Equations in Two Variables

9.2 Graphing Equations in Two Variables

9.3 Slope

9.4 Slope-Intercept Form of a Line

9.5 Point-Slope Form of a Line

9.6 Parallel and Perpendicular Lines

9.7 Linear Inequalities in Two Variables

10. Systems of Linear Equations and Inequalities

10.1 Solving Systems of Linear Equations by Graphing

10.2 Solving Systems of Linear Equations Using Substitution

10.3 Solving Systems of Linear Equations Using Elimination

10.4 Solving Direct Translation, Geometry, and Uniform Motion Problems Using Systems of Linear Equations

10.5 Solving Mixture Problems Using Systems of Linear Equations

10.6 Systems of Linear Inequalities

11. Exponents and Polynomials

11.1 Adding and Subtracting Polynomials

11.2 Multiplying Monomials: The Product and Power Rules

11.3 Multiplying Polynomials

11.4 Dividing Monomials: The Quotient Rule and Integer Exponents

11.5 Dividing Polynomials

11.6 Applying Exponent Rules: Scientific Notation

12. Factoring Polynomials

12.1 Greatest Common Factor and Factoring by Grouping

12.2 Factoring Trinomials of the Form x²+bx+c

12.3 Factoring Trinomials of the Form ax²+bx+c, a≠1

12.4 Factoring Special Products

12.5 Summary of Factoring Techniques

12.6 Solving Polynomial Equations by Factoring

12.7 Modeling and Solving Problems with Quadratic Equations

13. Rational Expressions and Equations

13.1 Simplifying Rational Expressions

13.2 Multiplying and Dividing Rational Expressions

13.3 Adding and Subtracting Rational Expressions with a Common Denominator

13.4 Finding the Least Common Denominator and Forming Equivalent Rational Expressions

13.5 Adding and Subtracting Rational Expressions with Unlike Denominators

13.6 Complex Rational Expressions

13.7 Rational Equations

13.8 Models Involving Rational Equations

14. Graphs, Relations, and Functions

14.1 Graphs of Equations

14.2 Relations

14.3 An Introduction to Functions

14.4 Functions and Their Graphs

14.5 Linear Equations and Models

14.6 Compound Inequalities

14.7 Absolute Value Equations and Inequalities

14.8 Variation

15. Radicals and Rational Exponents

15.1 Square Roots

15.2 nth Roots and Rational Exponents

15.3 Simplify Expressions Using the Laws of Exponents

15.4 Simplify Radical Expressions Using Properties of Radicals

15.5 Adding, Subtracting, and Multiplying Radical Expressions

15.6 Rationalizing Radical Expressions

15.7 Functions Involving Radicals

15.8 Radical Equations and Their Applications

15.9 The Complex Number System

16. Quadratic Equations and Functions

16.1 Solving Quadratic Equations by Completing the Square

16.2 Solving Quadratic Equations by the Quadratic Formula

16.3 Solving Equations Quadratic in Form

16.4 Graphing Quadratic Functions Using Transformations

16.5 Graphing Quadratic Functions Using Properties

16.6 Polynomial Inequalities

16.7 Rational Inequalities

17. Exponential and Logarithmic Functions

17.1 Composite Functions and Inverse Functions

17.2 Exponential Functions

17.3 Logarithmic Functions

17.4 Properties of Logarithms

17.5 Exponential and Logarithmic Equations

18. Conics

18.1 Distance and Midpoint Formulas

18.2 Circles

18.3 Parabolas

18.4 Ellipses

18.5 Hyperbolas

18.6 Systems of Nonlinear Equations

19. Sequences, Series, and the Binomial Theorem

19.1 Sequences

19.2 Arithmetic Sequences

19.3 Geometric Sequences and Series

19.4 The Binomial Theorem

Appendix A: Synthetic Division

Appendix B: More on Systems of Linear Equations