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Ebook Title: | Algebra Foundations: PrealgebraIntermediate AlgebraIntroductory Algebra |

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1. The Whole Numbers

1.1 Tips for Success in Mathematics

1.2 Place Value, Names for Numbers, and Reading Tables

1.3 Adding and Subtracting Whole Numbers, and Perimeter

1.4 Rounding and Estimating

1.5 Multiplying Whole Numbers and Area

1.6 Dividing Whole Numbers

Integrated Review–Operations on Whole Numbers

1.7 Exponents and Order of Operations

1.8 Introduction to Variables, Algebraic Expressions, and Equations

2. Integers and Introduction to Solving Equations

2.1 Introduction to Integers

2.2 Adding Integers

2.3 Subtracting Integers

2.4 Multiplying and Dividing Integers

Integrated Review–Integers

2.5 Order of Operations

2.6 Solving Equations: The Addition and Multiplication Properties

3. Solving Equations and Problem Solving

3.1 Simplifying Algebraic Expressions

3.2 Solving Equations: Review of the Addition and Multiplication Properties

Integrated Review–Expressions and Equations

3.3 Solving Linear Equations in One Variable

3.4 Linear Equations in One Variable and Problem Solving

4. Fractions and Mixed Numbers

4.1 Introduction to Fractions and Mixed Numbers

4.2 Factors and Simplest Form

4.3 Multiplying and Dividing Fractions

4.4 Adding and Subtracting Like Fractions, Least Common Denominator, and Equivalent Fractions

4.5 Adding and Subtracting Unlike Fractions

Integrated Review–Summary on Fractions and Operations on Fractions

4.6 Complex Fractions and Review of Order of Operations

4.7 Operations on Mixed Numbers

4.8 Solving Equations Containing Fractions

5. Decimals

5.1 Introduction to Decimals

5.2 Adding and Subtracting Decimals

5.3 Multiplying Decimals and Circumference of a Circle

5.4 Dividing Decimals

Integrated Review–Operations on Decimals

5.5 Fractions, Decimals, and Order of Operations

5.6 Solving Equations Containing Decimals

5.7 Decimal Applications: Mean, Median, and Mode

6. Ratio, Proportion, and Percent

6.1 Ratio and Proportion

6.2 Percents, Decimals, and Fractions

6.3 Solving Percent Problems with Equations

6.4 Solving Percent Problems with Proportions

Integrated Review–Ratio, Proportion, and Percent

6.5 Applications of Percent

6.6 Percent and Problem Solving: Sales Tax, Commission, and Discount

6.7 Percent and Problem Solving: Interest

7. Graphs and Triangle Applications

7.1 Reading Pictographs, Bar Graphs, Histograms, and Line Graphs

7.2 Reading and Drawing Circle Graphs

Integrated Review–Reading Graphs

7.3 Square Roots and the Pythagorean Theorem

7.4 Congruent and Similar Triangles

7.5 Counting and Introduction to Probability

8. Geometry and Measurement

8.1 Lines and Angles

8.2 Perimeter

8.3 Area, Volume, and Surface Area

Integrated Review–Geometry Concepts

8.4 Linear Measurement

8.5 Weight and Mass

8.6 Capacity

8.7 Temperature and Conversions Between the U.S. and Metric Systems

9. Equations, Inequalities, and Problem Solving

9.1 Symbols and Sets of Numbers

9.2 Properties of Real Numbers

9.3 Further Solving Linear Equations

Integrated Review–Real Numbers and Solving Linear Equations

9.4 Further Problem Solving

9.5 Formulas and Problem Solving

9.6 Linear Inequalities and Problem Solving

10. Graphs and Introduction to Functions

10.1 Reading Graphs and the Rectangular Coordinate System

10.2 Graphing Linear Equations

10.3 Intercepts

10.4 Slope and Rate of Change

Integrated Review–Summary on Slope and Graphing Linear Equations

10.5 Equation of Lines

10.6 Functions

11. Solving Systems of Linear Equations

11.1 Solving Systems of Linear Equations by Graphing

11.2 Solving Systems of Linear Equations by Substitution

11.3 Solving Systems of Linear Equations by Addition

Integrated Review–Solving Systems of Equations

11.4 Solving Systems of Linear Equations in Three Variables

11.5 Systems of Linear Equations and Problem Solving

12. Exponents and Polynomials

12.1 Exponents

12.2 Polynomial Functions and Adding and Subtracting Polynomials

12.3 Multiplying Polynomials

12.4 Special Products

Integrated Review–Exponents and Operations on Polynomials

12.5 Negative Exponents and Scientific Notation

12.6 Dividing Polynomials

12.7 Synthetic Division and the Remainder Theorem

13. Factoring Polynomials

13.1 The Greatest Common Factor and Factoring by Grouping

13.2 Factoring Trinomials of the Form x2 + bx + c

13.3 Factoring Trinomials of the Form ax2 + bx + c and Perfect Square Trinomials

13.4 Factoring Trinomials of the Form ax2 + bx + c by Grouping

13.5 Factoring Binomials

Integrated Review–Choosing a Factoring Strategy

13.6 Solving Quadratic Equations by Factoring

13.7 Quadratic Equations and Problem Solving

14. Rational Expressions

14.1 Rational Functions and Simplifying Rational Expressions

14.2 Multiplying and Dividing Rational Expressions

14.3 Adding and Subtracting Rational Expressions with Common Denominators and Least Common Denominator

14.4 Adding and Subtracting Rational Expressions with Unlike Denominators

14.5 Solving Equations Containing Rational Expressions

Integrated Review–Summary on Rational Expressions

14.6 Proportion and Problem Solving with Rational Equations

14.7 Simplifying Complex Fractions

15. More on Functions and Graphs

15.1 Graphing and Writing Linear Functions

15.2 Function Notation Review and Graphing Nonlinear Functions

Integrated Review–Summary on Functions

15.3 Graphing Piecewise-Defined Functions and Shifting and Reflecting Graphs of Functions

15.4 Variation and Problem Solving

16. Inequalities and Absolute Value

16.1 Compound Inequalities

16.2 Absolute Value Equations

16.3 Absolute Value Inequalities

Integrated Review–Solving Equations and Inequalities

16.4 Linear Inequalities in Two Variables and Systems of Linear Inequalities

17. Rational Exponents, Radicals, and Complex Numbers

17.1 Radicals and Radical Functions

17.2 Rational Exponents

17.3 Simplifying Radical Expressions

17.4 Adding and Subtracting and Multiplying Radical Expressions

17.5 Rationalizing Denominators and Numerators of Radical Expressions

Integrated Review–Radicals and Rational Exponents

17.6 Radical Equations and Problem Solving

17.7 Complex Numbers

18. Quadratic Equations and Functions

18.1 Solving Quadratic Equations by Completing the Square

18.2 Solving Quadratic Equations by the Quadratic Formula

18.3 Solving Equations by Using Quadratic Methods

Integrated Review–Summary on Solving Quadratic Equations

18.4 Nonlinear Inequalities in One Variable

18.5 Quadratic Functions and Their Graphs

18.6 Further Graphing of Quadratic Functions

19. Exponential and Logarithmic Functions

19.1 The Algebra of Functions: Composite Functions

19.2 Inverse Functions

19.3 Exponential Functions

19.4 Exponential Growth and Decay Functions

19.5 Logarithmic Functions

19.6 Properties of Logarithms

Integrated Review–Functions and Properties of Logarithms

19.7 Common Logarithms, Natural Logarithms, and Change of Base

19.8 Exponential and Logarithmic Equations and Problem Solving

20. Conic Sections

20.1 The Parabola and the Circle

20.2 The Ellipse and the Hyperbola

Integrated Review–Graphing Conic Sections

20.3 Solving Nonlinear Systems of Equations

20.4 Nonlinear Inequalities and Systems of Inequalities

21. Sequences, Series, and the Binomial Theorem

21.1 Sequences

21.2 Arithmetic and Geometric Sequences

21.3 Series

Integrated Review–Sequences and Series

21.4 Partial Sums of Arithmetic and Geometric Sequences

21.5 The Binomial Theorem

Appendices

Appendix A Operations on Decimals/ Tables and Formulas

A.1 Table of Percent, DecimalGeometric Figures

A.2 Table of Percents, Decimals, and Fraction Equivalents

A.3 Table on Finding Common Percents of a Number

A.4 Table of Squares and Square Roots

A.5 Geometric Formulas

Appendix B Review of Algebra Topics

B.1 Equations (Linear and Quadratic Solved by Factoring)

B.2 Mixture and Uniform Motion Problem Solving

B.3 Graphing

B.4 Polynomials and Factoring

B.5 Rational Expressions

Appendix C. An Introduction to Using a Graphing Utility

Appendix D. Solving Systems of Equations by Matrices

Appendix E. Solving Systems of Equations by Determinants

Appendix F. Mean, Median, and Mode

Appendix G. Review of Angles, Lines, and Special Triangles

Appendix H. Contents of Student Resources

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