Developmental Mathematics: Prealgebra, Elementary Algebra, and Intermediate Algebra

Developmental Mathematics: Prealgebra, Elementary Algebra, and Intermediate Algebra, 2nd edition

  • Michael Sullivan, 
  • Katherine R. Struve, 
  • Janet Mazzarella

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Overview

Known for its unique examples that provide extra step-by-step support, Developmental Mathematics utilizes the authors' hallmark engaging features to introduce the logic, precision and rigor of mathematics  -- while building a foundation for success in future math courses.

Published by Pearson (December 11th 2020) - Copyright © 2019

ISBN-13: 9780137398966

Subject: Developmental Math

Category: Combined Developmental Math (2 or 3 courses combined)

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; Exponents
Putting the Concepts Together (Sections 1.1 - 1.4)
1.5 Dividing Whole Numbers
1.6 Prime Numbers
1.7 Order of Operations
1 Review
1 Test
Getting Ready for 2: A Review of 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; Order of Operations
Putting the Concepts Together (Sections 2.1 - 2.4)
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
2 Review
2 Test
Getting Ready for 3: A Review of Chapters 1 and 2

3. Rational Numbers Expressed as Fractions
3.1 Fundamentals of Fractions
3.2 Multiplying and Dividing Fractions
3.3 Adding and Subtracting Like Fractions
Putting the Concepts Together (Sections 3.1 - 3.3)
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 That Contain Fractions
3 Review
3 Test
Getting Ready for 4: A Review of Chapters 1 - 3

4. Rational Numbers as Decimals
4.1 Fundamentals of Decimals
4.2 Adding and Subtracting Decimals
4.3 Multiplying Decimals
4.4 Dividing Decimals
Putting the Concepts Together (Sections 4.1 - 4.4)
4.5 Solving Equations That Contain Decimals
4 Review
4 Test
Getting Ready for 5: A Review of Chapters 1 - 4
Putting It Together: Real Numbers

5. Ratio, Proportion, and Percent
5.1 Ratios and Unit Rates
5.2 Proportions
5.3 Fundamentals of Percent Notation
Putting the Concepts Together (Sections 5.1 - 5.3)
5.4 Solving Percent Problems: Proportion Method
5.5 Solving Percent Problems: Equation Method
5.6 Applications Involving Percent
5 Review
5 Test
Getting Ready for 6: A Review of Chapters 1 - 5

6. Measurement and Geometry
6.1 The U.S. Standard (English) System of Measurement
6.2 The Metric System of Measurement
Putting the Concepts Together (Sections 6.1 - 6.2)
6.3 Fundamentals of Geometry
6.4 Introduction to Square Roots and the Pythagorean Theorem
6.5 Polygons
6.6 Perimeter and Area of Polygons and Circles
6.7 Volume and Surface Area
6 Review
6 Test
Getting Ready for 7: A Review of Chapters 1 - 6

7. Introduction to Statistics and the Rectangular Coordinate System
7.1 Tables and Graphs
7.2 Mean, Median, and Mode
Putting the Concepts Together (Sections 7.1 and 7.2)
7.3 The Rectangular Coordinate System and Equations in Two Variables
7.4 Graphing Equations in Two Variables
7 Review
7 Test
Getting Ready for Elementary Algebra: A Review of Chapters 1 - 7

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 Problem Solving: Direct Translation
8.6 Problem Solving: Problems Involving Percent
8.7 Problem Solving: Geometry and Uniform Motion
8.8 Solving Linear Inequalities in One Variable
8 Review
8 Test

9. Introduction to Graphing and Equations 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
Putting the Concepts Together (Sections 9.1 - 9.6)
9.7 Linear Inequalities in Two Variables
9 Activity: Graphing Practice
9 Review
9 Test
Cumulative Review Chapters 1 - 9

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
Putting the Concepts Together (Sections 10.1 - 10.3)
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
10 Activity: Find the Numbers
10 Review
10 Test

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
Putting the Concepts Together (Sections 11.1 - 11.4)
11.5 Dividing Polynomials
11.6 Applying Exponent Rules: Scientific Notation
11 Activity: What Is the Question?
11 Review
11 Test
Cumulative Review Chapters 1 - 11

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 837
12.5 Summary of Factoring Techniques
Putting the Concepts Together (Sections 12.1 - 12.5)
12.6 Solving Polynomial Equations by Factoring
12.7 Modeling and Solving Problems with Quadratic Equations
12 Activity: Which One Does Not Belong?
12 Review
12 Test
Getting Ready for Intermediate Algebra: A Review of Chapters 1 - 12

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
Putting the Concepts Together (Sections 13.1 - 13.6)
13.7 Rational Equations
13.8 Models Involving Rational Equations
13 Activity: Correct the Quiz
13 Review
13 Test
Cumulative Review Chapters 1 - 13
Getting Ready for Intermediate Algebra: A Review of Chapters 1 - 13
Getting Ready for 14: Interval Notation

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
Putting the Concepts Together (Sections 14.1 - 14.4)
14.5 Linear Functions and Models
14.6 Compound Inequalities
14.7 Absolute Value Equations and Inequalities
14.8 Variation
14 Activity: Shifting Discovery
14 Review
14 Test

15. Radicals and Rational Exponents
15.1 Square Roots
15.2nth Roots and Rational Exponents
15.3 Simplifying Expressions Using the Laws of Exponents
15.4 Simplifying Radical Expressions Using Properties of Radicals
15.5 Adding, Subtracting, and Multiplying Radical Expressions
15.6 Rationalizing Radical Expressions
Putting the Concepts Together (Sections 15.1 - 15.6)
15.7 Functions Involving Radicals
15.7.4 Graph Functions Involving Cube Roots
15.8 Radical Equations and Their Applications
15.9 The Complex Number System
15 Activity: Correct the Quiz
15 Review
15 Test
Cumulative Review Chapters 1 - 15

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
Putting the Concepts Together (Sections 16.1 - 16.3)
16.4 Graphing Quadratic Functions Using Transformations
16.5 Graphing Quadratic Functions Using Properties
16.6 Polynomial Inequalities
16.7 Rational Inequalities
16 Activity: Presidential Decision Making
16 Review
16 Test

17. Exponential and Logarithmic Functions
17.1 Composite Functions and Inverse Functions
17.2 Exponential Functions
17.3 Logarithmic Functions
Putting the Sections Together (17.1 - 17.3)
17.4 Properties of Logarithms
17.5 Exponential and Logarithmic Equations
17 Activity: Correct the Quiz
17 Review
17 Test
Cumulative Review Chapters 1 - 15

18. Conics
18.1 Distance and Midpoint Formulas
18.2 Circles
18.3 Parabolas
18.4 Ellipses
18.5 Hyperbolas
Putting the Concepts Together (Sections 18.1 - 18.5)
18.6 Systems of Nonlinear Equations
18.6.1 Solve a System of Nonlinear Equations Using Substitution
18.6.2 Solve a System of Nonlinear Equations Using Elimination
18 Activity: How Do You Know That …?
18 Review
18 Test

19. Sequences, Series, and the Binomial Theorem
19.1 Sequences
19.2 Arithmetic Sequences
19.3 Geometric Sequences and Series
Putting the Concepts Together (Sections 19.1 - 19.3)
19.4 The Binomial Theorem
19 Activity: Discover the Relation
19 Review
19 Test
Cumulative Review Chapters 1 - 19

APPENDICES
Appendix A. Synthetic Division
A.1.1 Divide Polynomials Using Synthetic Division
A.1.2 Use the Remainder and Factor Theorems
Appendix B. More on Systems of Linear Equations
B.1 A Review of Systems of Linear Equations in Two Variables
B.1.1 Determine Whether an Ordered Pair Is a Solution of a System of Linear Equations
B.1.2 Solve a System of Two Linear Equations by Graphing
B.1.3 Solve a System of Two Linear Equations by Substitution
B.1.4 Solve a System of Two Linear Equations by Elimination
B.1.5 Identify Inconsistent Systems
B.1.6 Write the Solution of a System with Dependent Equations
B.2 Systems of Linear Equations in Three Variables
B.2.1 Solve Systems of Three Linear Equations
B.2.2 Identify Inconsistent Systems
B.2.3 Write the Solution of a System with Dependent Equations
B.2.4 Model and Solve Problems Involving Three Linear Equations
B.3 A Using Matrices to Solve Systems
B.3.1 Write the Augmented Matrix of a System
B.3.2 Write the System from the Augmented Matrix
B.3.3 Perform Row Operations on a Matrix
B.3.4 Solve Systems Using Matrices
B.3.5 Solve Consistent Systems with Dependent Equations and Solve Inconsistent Systems
B.4 Determinants and Cramer's Rule
B.4.1 Evaluate the Determinant of a 2 x 2 Matrix
B.4.2 Use Cramer's Rule to Solve a System of Two Equations
B.4.3 Evaluate the Determinant of a 3 x 3 Matrix
B.4.4 Use Cramer's Rule to Solve a System of Three Equations

Appendix C. Table of Square Roots

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