Intermediate Algebra

For courses in Intermediate Algebra.

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R. Review of the Real Number System

R.1 Basic Concepts

R.2 Operations on Real Numbers

R.3 Exponents, Roots, and Order of Operations

R.4 Properties of Real Numbers

Study Skills Using Your Math Text

Study Skills Reading Your Math Text

1. Linear Equations and Applications

1.1 Linear Equations in One Variable

Study Skills Completing Your Homework

1.2 Formulas and Percent

Study Skills Managing Your Time

1.3 Applications of Linear Equations

Study Skills Taking Lecture Notes

1.4 Further Applications of Linear Equations

Summary Exercises  Applying Problem-Solving Techniques

Study Skills Reviewing a Chapter

2. Linear Inequalities and Absolute Value

2.1 Linear Inequalities in One Variable

Study Skills Using Study Cards

2.2 Set Operations and Compound Inequalities

Study Skills Using Study Cards Revisited

2.3 Absolute Value Equations and Inequalities

Summary Exercises  Solving Linear and Absolute Value Equations and Inequalities 
Study Skills Taking Math Tests

3. Graphs, Linear Equations and Functions

3.1 The Rectangular Coordinate System

Study Skills Analyzing Your Test Results

3.2 Slope of a Line

3.3 Linear Equations in Two Variables

Summary Exercises  Finding Slopes and Equations of Lines

3.4 Linear Inequalities in Two Variables

3.5 Introduction to Relations and Functions

3.6 Function Notation and Linear Functions

4. Systems of Linear Equations

4.1 Systems of Linear Equations in Two Variables

Study Skills Preparing for Your Math Final Exam

4.2 Systems of Linear Equations in Three Variables

4.3 Applications of Systems of Linear Equations

5. Exponents, Polynomials, and Polynomial Functions

5.1 Integer Exponents

5.2 Scientific Notation

5.3 Adding and Subtracting Polynomials

5.4 Polynomial Functions and Graphs

5.5 Multiplying Polynomials

5.6 Dividing Polynomials

6. Factoring

6.1 Greatest Common Factors and Factoring by Grouping

6.2 Factoring Trinomials

6.3 Special Factoring

6.4 A General Approach to Factoring

6.5 Solving Equations Using the Zero-Factor Property

7. Rational Expressions and Functions

7.1 Rational Expressions and Functions; Multiplying and Dividing

7.2 Adding and Subtracting Rational Expressions

7.3 Complex Fractions

7.4 Equations with Rational Expressions and Graphs

Summary Exercises  Simplifying Rational Expressions vs. Solving Rational Equations

7.5 Applications of Rational Expressions

7.6 Variation

8. Roots, Radicals, and Root Functions

8.1 Radical Expressions and Graphs

8.2 Rational Exponents

8.3 Simplifying Radical Expressions

8.4 Adding and Subtracting Radical Expressions

8.5 Multiplying and Dividing Radical Expressions

Summary Exercises  Performing Operations with Radicals and Rational Exponents

8.6 Solving Equations with Radicals

8.7 Complex Numbers

9. Quadratic Equations, Inequalities, and Functions

9.1 The Square Root Property and Completing the Square

9.2 The Quadratic Formula

9.3 Equations Quadratic in Form

Summary Exercises  Applying Methods for Solving Quadratic Equations

9.4 Formulas and Further Applications

9.5 Graphs of Quadratic Functions

9.6 More about Parabolas and Their Applications

9.7 Polynomial and Rational Inequalities

10. Inverse, Exponential, and Logarithmic Functions

10.1 Composition of Functions

10.2 Inverse Functions

10.3 Exponential Functions

10.4 Logarithmic Functions

10.5 Properties of Logarithms

10.6 Common and Natural Logarithms

10.7 Exponential and Logarithmic Equations and Their Applications

11. Nonlinear Functions, Conic Sections, and Nonlinear Systems

11.1 Additional Graphs of Functions

11.2 Circles and Ellipses

11.3 Hyperbolas and Functions Defined by Radicals

11.4 Nonlinear Systems of Equations

11.5 Second-Degree Inequalities and Systems of Inequalities

Appendix A. Review of Fractions

Appendix B. Synthetic Division

Appendix C. Solving Systems of Linear Equations by Matrix Methods

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