Intermediate Algebra - 1st Edition - ISBN: 9780124847606, 9781483269221

Intermediate Algebra

1st Edition

Authors: Charles P. McKeague
eBook ISBN: 9781483269221
Imprint: Academic Press
Published Date: 1st January 1979
Page Count: 510
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Intermediate Algebra focuses on the principles, operations, and approaches involved in intermediate algebra.

The book first elaborates on basic properties and definitions, first-degree equations and inequalities, and exponents and polynomials. Discussions focus on the greatest common factor and factoring by grouping, factoring trinomials, special factoring, equations with absolute value, inequalities involving absolute value, formulas, first-degree equations, graphing simple and compound inequalities, and properties of real numbers. The text then takes a look at rational expressions, rational exponents and roots, and quadratic equations. Topics include solving quadratic equations by factoring, discriminant and the sum and product of solutions, multiplication and division of complex numbers, combinations of radical expressions, rational exponents, complex fractions, and multiplication and division of rational expressions. The manuscript elaborates on sequence and series, logarithms, relations and functions, and conic sections, including ellipses and hyperbolas, nonlinear systems, function and notation, algebra with functions, common logarithms and computations, and word problems.

The publication is a dependable reference for students and researchers interested in intermediate algebra.

Table of Contents

1 Basic Properties and Definitions

1.1 Basic Definitions

1.2 The Real Numbers, Opposites, Reciprocals, and Absolute Value

1.3 Graphing Simple and Compound Inequalities

1.4 Properties of Real Numbers

1.5 Addition and Subtraction of Real Numbers

1.6 Multiplication, Division, and Order of Operation for Real Numbers

Summary and Review


2 First-Degree Equations and Inequalities

2.1 First-Degree Equations

2.2 First-Degree Inequalities

2.3 Equations with Absolute Value

2.4 Inequalities Involving Absolute Value

2.5 Formulas

2.6 Word Problems

Summary and Review


3 Exponents and Polynomials

3.1 Properties of Exponents

3.2 Polynomials, Sums, and Differences

3.3 Multiplication of Polynomials

3.4 Division of Polynomials

3.5 The Greatest Common Factor and Factoring by Grouping

3.6 Factoring Trinomials

3.7 Special Factoring

Summary and Review


4 Rational Expressions

4.1 Basic Properties and Reducing to Lowest Terms

4.2 Multiplication and Division of Rational Expressions

4.3 Addition and Subtraction of Rational Expressions

4.4 Complex Fractions

4.5 Equations Involving Rational Expressions

4.6 Word Problems

Summary and Review


5 Rational Exponents and Roots

5.1 Rational Exponents

5.2 Simplified Form for Radicals

5.3 Combinations of Radical Expressions

5.4 Equations with Radicals

5.5 Addition and Subtraction of Complex Numbers

5.6 Multiplication and Division of Complex Numbers

Summary and Review


6 Quadratic Equations

6.1 Solving Quadratic Equations by Factoring

6.2 Completing the Square

6.3 The Quadratic Formula

6.4 The Discriminant and the Sum and Product of Solutions

6.5 Word Problems

Summary and Review


7 Linear Equations and Inequalities

7.1 Graphing in Two Dimensions

7.2 The Slope of a Line

7.3 The Equation of a Straight Line

7.4 Linear Inequalities in Two Variables

7.5 Variation

Summary and Review


8 Systems of Linear Equations

8.1 Systems of Linear Equations in Two Variables

8.2 Systems of Linear Equations in Three Variables

8.3 Introduction to Determinants

8.4 Cramer's Rule

8.5 Word Problems

Summary and Review


9 The Conic Sections

9.1 Graphing Parabolas

9.2 The Circle

9.3 Ellipses and Hyperbolas

9.4 Second-Degree Inequalities

9.5 Nonlinear Systems

Summary and Review


10 Relations and Functions

10.1 Relations and Functions

10.2 Function Notation

10.3 Algebra with Functions

10.4 Classification of Functions

10.5 The Inverse of a Function

Summary and Review


11 Logarithms

11.1 Logarithms Are Exponents

11.2 Properties of Logarithms

11.3 Common Logarithms and Computations

11.4 Exponential Equations and Change of Base

11.5 Word Problems

Summary and Review


12 Sequences and Series

12.1 Sequences

12.2 Series and Summation Notation

12.3 Arithmetic Progressions

12.4 Geometric Progressions

12.5 The Binomial Expansion

Summary and Review


Appendix A: Synthetic Division

Appendix B: Quadratic Inequalities in One Variable

Appendix C: Table of Powers, Roots, and Prime Factors

Appendix D: Table of Common Logarithms

Answers to Odd-Numbered Exercises and Chapter Tests



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© Academic Press 1979
Academic Press
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About the Author

Charles P. McKeague

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