Intermediate Algebra

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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0321915879 / 9780321915870 Intermediate Algebra

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.

Preface

To the Student

Learning Styles Inventory

The Carson Math Study System

1. Real Numbers and Expressions

1.1 Sets and the Structure of Algebra

1.2 Operations with Real Numbers; Properties of Real Numbers

1.3 Exponents, Roots, and Order of Operations

1.4 Evaluating and Rewriting Expressions

            Summary and Review Exercises

            Practice Test

2. Linear Equations and Inequalities in One Variable

2.1 Linear Equations and Formulas

2.2 Solving Problems

2.3 Solving Linear Inequalities

2.4 Compound Inequalities

2.5 Equations Involving Absolute Value; Absolute Value Functions

2.6 Inequalities Involving Absolute Value

            Summary and Review Exercises

            Practice Test

            Chapters 1 and 2 Cumulative Review Exercises

3. Equations and Inequalities in Two Variables; Functions

3.1 Graphing Linear Equations

3.2 The Slope of a Line

3.3 The Equation of a Line

3.4 Graphing Linear Inequalities

3.5 Introduction to Functions and Function Notation

            Summary and Review Exercises

            Practice Test

            Chapters 1–3 Cumulative Review Exercises

4. Systems of Linear Equations and Inequalities

4.1 Solving Systems of Linear Equations in Two Variables

4.2 Solving Systems of Linear Equations in Three Variables

4.3 Solving Applications Using Systems of Equations

4.4 Solving Systems of Linear Equations Using Matrices

4.5 Solving Systems of Linear Inequalities

            Summary and Review Exercises

            Practice Test

            Chapters 1–4 Cumulative Review Exercises

5. Exponents, Polynomials, and Polynomial Functions

5.1 Exponents and Scientific Notation

5.2 Polynomials and Polynomial Functions

5.3 Multiplying Polynomials

5.4 Dividing Polynomials

5.5 Synthetic Division and the Remainder

Theorem

            Summary and Review Exercises

            Practice Test

            Chapters 1–5 Cumulative Review Exercises

6. Factoring

6.1 Greatest Common Factor and Factoring by Grouping

6.2 Factoring Trinomials

6.3 Factoring Special Products and Factoring Strategies

6.4 Solving Equations by Factoring

            Summary and Review Exercises

            Practice Test

            Chapters 1–6 Cumulative Review Exercises

7. Rational Expressions and Equations

7.1 Simplifying, Multiplying, and Dividing Rational Expressions

7.2 Adding and Subtracting Rational Expressions

7.3 Simplifying Complex Rational Expressions

7.4 Solving Equations Containing Rational Expressions

7.5 Applications with Rational Expressions; Variation

            Summary and Review Exercises

            Practice Test

            Chapters 1–7 Cumulative Review Exercises

8. More on Inequalities Absolute Value, and Functions

8.1 Compound Inequalities

8.2 Equation Involving Absolute Value

8.3 Inequalities Involving Absolute Value

            Summary and Review Exercises

            Practice Test

            Chapters 1–8 Cumulative Review Exercises

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

            Summary and Review Exercises

            Practice Test

            Chapters 1–9 Cumulative Review Exercises

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

            Summary and Review Exercises

            Practice Test

            Chapters 1–10 Cumulative Review Exercises

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

            Summary and Review Exercises

            Practice Test

            Chapters 1–11 Cumulative Review Exercises

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

            Summary and Review Exercises

            Practice Test

            Chapters 1–12 Cumulative Review Exercises

Appendices

A. Arithmetic Sequences and Series APP-000

B. Geometric Sequences and Series APP-000

C. The Binomial Theorem APP-000

D. Cramer’s Rule

E. Permutations and Combinations (available online via MyMathLab)

F. Probability (available online via MyMathLab)

Answers

Glossary

Index of Applications

Index

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