## Table of Contents

**Module 1: Whole Numbers and Introduction to Algebra**

1.1: Understanding Whole Numbers

1.2: Adding Whole Number Expressions

1.3: Subtracting Whole Number Expressions

1.4: Multiplying Whole Number Expressions

1.5: Dividing Whole Number Expressions

1.6: Exponents and the Order of Operations

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How Am I Doing? Topics 1.1—1.6

1.7: More on Algebraic Expressions

1.8: Introduction to Solving Linear Equations

1.9: Solving Applied Problems Using Several Operations

Module 1 Organizer

Module 1 Review Problems

How Am I Doing? Module 1 Test

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**Module 2: Integers**

2.1: Understanding Integers

2.2: Adding Integers

2.3: Subtracting Integers

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How Am I Doing? Topics 2.1—2.3

2.4: Multiplying and Dividing Integers

2.5: The Order of Operations and Applications Involving Integers

2.6: Simplifying and Evaluating Algebraic Expressions

Module 2 Organizer

Module 2 Review Problems

How Am I Doing? Module 2 Test

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**Module 3: Introduction to Equations and Algebraic Expressions**

3.1: Equations of the form *x* + *a* = *c* and *x* - *a* = *c*

3.2: Equations of the form *ax* = *c*

How Am I Doing? Topics 3.1—3.2

3.3: Equations and Geometric Formulas

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3.4: Performing Operations with Exponents

Module 3 Organizer

Module 3 Review Problems

How Am I Doing? Module 3 Test

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**Module 4: Fractions, Ratio, and Proportions**

4.1: Factoring Whole Numbers

4.2: Understanding Fractions

4.3: Simplifying Fractional Expressions

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How Am I Doing? Topics 4.1—4.3

4.4: Simplifying Fractional Expressions with Exponents

4.5: Ratios and Rates

4.6: Proportions and Applications

Module 4 Organizer

Module 4 Review Problems

How Am I Doing? Module 4 Test

Math Coach

**Module 5: Operations on Fractional Expressions**

5.1: Multiplying and Dividing Fractional Expressions

5.2: Least Common Multiples of Algebraic Expressions

5.3: Adding and Subtracting Fractional Expressions

5.4: Operations with Mixed Numbers

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How Am I Doing? Topics 5.1—5.4

5.5: Order of Operations and Complex Fractions

5.6: Solving Applied Problems Involving Fractions

5.7: The Multiplication Principle of Equality

Module 5 Organizer

Module 5 Review Problems

How Am I Doing? Module 5 Test

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**Module 6: Decimals and Percents**

6.1: Understanding Decimal Fractions

6.2: Adding and Subtracting Decimal Expressions

6.3: Multiplying and Dividing Decimal Expressions

How Am I Doing? Topics 6.1—6.3

6.4: Estimating with Percents

6.5: Percents

6.6: Solving Percent Problems Using Equations

6.7: Solving Percent Problems Using Proportions

6.8: Solving Applied Problems Involving Percents

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Module 6 Organizer

Module 6 Review Problems

How Am I Doing? Module 6 Test

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**Module 7: Measurement and Geometric Figures**

7.1: Using Unit Fractions with U.S. and Metric Units

7.2: Converting Between the U.S. and Metric Systems

7.3: Angles

How Am I Doing? Topics 7.1—7.3

7.4: The Circle

7.5: Volume

7.6: Similar Geometric Figures

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Module 7 Organizer

Module 7 Review Problems

How Am I Doing? Module 7 Test

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**Module 8: Introduction to Polynomials**

8.1: Adding and Subtracting Polynomials

8.2: Multiplying Polynomials

How Am I Doing? Topics 8.1—8.2

8.3: Translate from English to Algebra

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8.4: Factoring Using the Greatest Common Factor

Module 8 Organizer

Module 8 Review Problems

How Am I Doing? Module 8 Test

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**Module 9: Equations, Inequalities, and Applications**

9.1: Addition and Multiplication Principles of Equality

9.2: Using Both Principles of Equality Together

9.3: Solving Equations with Fractions

How Am I Doing? Topics 9.1—9.3

9.4: Formulas

9.5: Using Equations to Solve Word Problems

9.6: Solving Word Problems Involving Money and Percents

9.7: Solving Inequalities in One Variable

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Module 9 Organizer

Module 9 Review Problems

How Am I Doing? Module 9 Test

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**Module 10: Graphing and Functions**

10.1: The Rectangular Coordinate System

10.2: Graphing Linear Equations

10.3: The Slope of a Line

How Am I Doing? Topics 10.1—10.3

10.4: Writing the Equation of a Line

10.5: Graphing Linear Inequalities

10.6: Functions

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Module 10 Organizer

Module 10 Review Problems

How Am I Doing? Module 10 Test

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**Module 11: Systems of Linear Equations and Inequalities**

11.1: Systems of Linear Equations in Two Variables

11.2: Systems of Linear Equations in Three Variables

How Am I Doing? Topics 11.1—11.2

11.3: Applications of Systems of Linear Equations

11.4: Systems of Linear Inequalities

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Module 11 Organizer

Module 11 Review Problems

How Am I Doing? Module 11 Test

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**Module 12: Exponents and Polynomials**

12.1: The Rules of Exponents

12.2: Negative Exponents and Scientific Notation

12.3: Fundamental Polynomial Operations

How Am I Doing? Topics 12.1—12.3

12.4: Multiplying Polynomials

12.5: Multiplication -Special Cases

12.6: Dividing Polynomials

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Module 12 Organizer

Module 12 Review Problems

How Am I Doing? Module 12 Test

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**Module 13: Factoring**

13.1: Removing a Common Factor

13.2: Factoring by Grouping

13.3: Factoring Trinomials When *a* = 1

13.4: Factoring Trinomials When *a* ≠ 1

How Am I Doing? Topics 13.1—13.4

13.5: Special Cases of Factoring

13.6: A Brief Review of Factoring

13.7: Solving Quadratic Equations by Factoring

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Module 13 Organizer

Module 13 Review Problems

How Am I Doing? Module 13 Test

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**Module 14: Rational Expressions and Equations**

14.1: Simplifying Rational Expressions

14.2: Multiplying and Dividing Rational Expressions

14.3: Adding and Subtracting Rational Expressions

How Am I Doing? Topics 14.1—14.3

14.4: Simplifying Complex Rational Expressions

14.5: Solving Equations Involving Rational Expressions

14.6: Ratio, Proportion, and Other Applied Problems

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Module 14 Organizer

Module 14 Review Problems

How Am I Doing? Module 14 Test

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**Module 15: Rational Exponents and Radicals**

15.1: Rational Exponents

15.2: Radical Expressions and Functions

15.3: Simplifying, Adding, and Subtracting Radicals

15.4: Multiplying and Dividing Radicals

How Am I Doing? Topics 15.1—15.3

15.5: Radical Equations

15.6: Complex Numbers

15.7: Variation

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Module 15 Organizer

Module 15 Review Problems

How Am I Doing? Module 15 Test

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**Module 16: Quadratic Equations**

16.1: Quadratic Equations

16.2: Solutions to Quadratic Equations-Quadratic Formula

16.3: Solving Equations That Are Quadratic in Form

How Am I Doing? Topics 16.1—16.3

16.4: Formulas and Applications

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Module 16 Organizer

Module 16 Review Problems

How Am I Doing? Module 16 Test

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**Module 17: The Conic Sections**

17.1: The Distance Formula and the Circle

17.2: The Parabola

17.3: The Ellipse

How Am I Doing? Topics 17.1—17.3

17.4: The Hyperbola

17.5: Nonlinear Systems of Equations

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Module 17 Organizer

Module 17 Review Problems

How Am I Doing? Module 17 Test

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**Module 18: Additional Properties of Functions**

18.1: Function Notation

18.2: General Graphing Procedures for Functions

How Am I Doing? Topics 18.1—18.2

18.3: Algebraic Operations on Functions

18.4: Inverse of a Function

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Module 18 Organizer

Module 18 Review Problems

How Am I Doing? Module 18 Test

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**Module 19: Logarithmic and Exponential Functions**

19.1: The Exponential Function

19.2: The Logarithmic Function

19.3: Properties of Logarithms

How Am I Doing? Topics 19.1—19.3

19.4: Common and Natural Logarithms; Change of Base

19.5: Exponential and Logarithmic Equations

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Module 19 Organizer

Module 19 Review Problems

How Am I Doing? Module 19 Test

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**Module 20: Additional Topics**

20.1: Quadratic Functions

20.2: Compound and Quadratic Inequalities

20.3: Absolute Value Equations and Inequalities

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Module 20 Organizer

Module 20 Review Problems

How Am I Doing? Module 20 Test

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**Appendices**

Appendix A: Consumer Finance Applications

Appendix B: Introduction to U.S. and Metric Units of Measurement

Appendix C: Additional Arithmetic Practice

Appendix D: Foundations for Intermediate Algebra: A Transition from Beginning to Intermediate Algebra

Appendix E: Determinants and Cramer's Rule

Appendix F: Solving Systems of Linear Equations Using Matrices

Appendix G: Sets