Elementary and Intermediate Algebra

by Carson, Tom; Jordan, Bill E.

• ISBN13: 9780321925145
• ISBN10: 0321925149
• Edition: 4th
• Format: Hardcover
• Copyright: 2014-01-13
• Publisher: Pearson

Summary

The Carson Algebra Series guides students to success by presenting the why behind understanding algebra, and includes the complete Carson Math Study System with a Learning Styles Inventory to address individual learning styles. The Carson Math Study System adapts to the way each student learns, and targeted learning strategies are presented throughout the program. The authors speak to students in everyday language and walk them through the concepts, explaining not only how to do the math, but also where the concepts come from and why they work to foster conceptual understanding.

 

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Author Biography

Tom Carson ’s first teaching experience was teaching guitar while an undergraduate student studying electrical engineering. That experience helped him to realize that his true gift and passion are for teaching. He earned his MAT in mathematics at the University of South Carolina. In addition to teaching at Midlands Technical College, Columbia State Community College, and Franklin Classical School, Tom has served on the faculty council and has been a board member of the South Carolina Association of Developmental Educators (SCADE). Ever the teacher, Tom teaches outside the classroom by presenting at conferences such as NADE, AMATYC, and ICTCM on topics such as Combating Innumeracy, Writing in Mathematics, and Implementing a Study System. In addition to his work on the Carson Developmental Algebra Series, Tom also is the author of Prealgebra, Fourth Edition.

 

Bill Jordan received his BS from Rollins College and his MAT from Tulane University. A decorated teacher for more than 40 years, Bill has served as the chair of the math department at Seminole Community College and has taught at Rollins College. He has been a member and leader of numerous professional organizations, including the Florida Two-Year College Mathematical Association (president), Florida Council of Teachers of Mathematics (district director), and others. In addition to his work on the Carson series, Bill is also the lead author of Integrated Algebra and Arithmetic, 2/e, also published by Pearson. In his spare time, he enjoys fishing, traveling, and hiking.

Table of Contents

1. Foundations of Algebra

1.1 Number Sets and the Structure of Algebra

1.2 Fractions

1.3 Adding and Subtracting Real Numbers; Properties of Real Numbers

1.4 Multiplying and Dividing Real Numbers; Properties of Real Numbers

1.5 Exponents, Roots, and Order of Operations

1.6 Translating Word Phrases to Expressions

1.7 Evaluating and Rewriting Expressions

 

2. Solving Linear Equations and Inequalities

2.1 Equations, Formulas, and the Problem-Solving Process

2.2 The Addition Principle of Equality

2.3 The Multiplication Principle of Equality

2.4 Applying the Principles to Formulas

2.5 Translating Word Sentences to Equations

2.6 Ratios and Proportions

2.7 Percents

2.8 Solving Linear Inequalities

 

3. Graphing Linear Equations and Inequalities

3.1 The Rectangular Coordinate System

3.2 Graphing Linear Equations

3.3 Graphing Using Intercepts

3.4 Slope–Intercept Form

3.5 Point–Slope Form

3.6 Graphing Linear Inequalities

3.7 Introduction to Functions and Function Notation

 

4. Systems of Linear Equations and Inequalities

4.1 Solving Systems of Linear Equations Graphically

4.2 Solving Systems of Linear Equations by Substitution; Applications

4.3 Solving Systems of Linear Equations by Elimination; Applications

4.4 Solving Systems of Linear Equations in Three Variables; Applications

4.5 Solving Systems of Linear Equations Using Matrices

4.6 Solving Systems of Linear Inequalities

 

5. Polynomials

5.1 Exponents and Scientific Notation

5.2 Introduction to Polynomials

5.3 Adding and Subtracting Polynomials

5.4 Exponent Rules and Multiplying Monomials

5.5 Multiplying Polynomials; Special Products

5.6 Exponent Rules and Dividing Polynomials

 

6. Factoring

6.1 Greatest Common Factor and Factoring by Grouping

6.2 Factoring Trinomials of the Form x ² + bx + c

6.3 Factoring Trinomials of the Form ax ² + bx + c, where a ≠ 1

6.4 Factoring Special Products

6.5 Strategies for Factoring

6.6 Solving Quadratic Equations by Factoring

6.7 Graphs of Quadratic Equations and Functions

 

7. Rational Expressions and Equations

7.1 Simplifying Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions with the Same Denominator

7.4 Adding and Subtracting Rational Expressions with Different Denominators

7.5 Complex Rational Expressions

7.6 Solving Equations Containing Rational Expressions

7.7 Applications with Rational Expressions, Including Variation

 

8. More on Inequalities, Absolute Value, and Functions

8.1 Compound Inequalities

8.2 Equations Involving Absolute Value; Absolute Value Functions

8.3 Inequalities Involving Absolute Value

 

9. Rational Exponents, Radicals, and Complex Numbers

9.1 Radical Expressions and Functions

9.2 Rational Exponents

9.3 Multiplying, Dividing, and Simplifying Radicals

9.4 Adding, Subtracting, and Multiplying Radical Expressions

9.5 Rationalizing Numerators and Denominators of Radical Expressions

9.6 Radical Equations and Problem Solving

9.7 Complex Numbers

 

10. Quadratic Equations and Functions

10.1 The Square Root Principle and Completing the Square

10.2 Solving Quadratic Equations Using the Quadratic Formula

10.3 Solving Equations That Are Quadratic in Form

10.4 Graphing Quadratic Functions

10.5 Solving Nonlinear Inequalities

10.6 Function Operations

 

11. Exponential and Logarithmic Functions

11.1 Composite and Inverse Functions

11.2 Exponential Functions

11.3 Logarithmic Functions

11.4 Properties of Logarithms

11.5 Common and Natural Logarithms

11.6 Exponential and Logarithmic Equations with Applications

 

12. Conic Sections

12.1 Parabolas and Circles

12.2 Ellipses and Hyperbolas

12.3 Nonlinear Systems of Equations

12.4 Nonlinear Inequalities and Systems of Inequalities

 

R. Elementary Algebra Review

 

Appendices

A.  Mean, Median, and Mode

B.  Arithmetic Sequences and Series

C.  Geometric Sequences and Series

D.  The Binomial Theorem

E.  Synthetic Division

F.  Solving Systems of Linear Equations Using Cramer’s Rule