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.   Bill Jordan received his BS from Rollins College and his MAT from Tulane University. A decorated teacher for more than 40 years, Jordan 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, Jordan 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.

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

 

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

2.6 Inequalities Involving Absolute Value

 

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

 

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 Equations Using Cramer’s Rule

4.6 Solving Systems of Linear Inequalities

 

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

 

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

 

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

 

8. Rational Exponents, Radicals, and Complex Numbers

8.1 Radical Expressions and Functions

8.2 Rational Exponents

8.3 Multiplying, Dividing, and Simplifying Radicals

8.4 Adding, Subtracting, and Multiplying Radical Expressions

8.5 Rationalizing Numerators and Denominators of Radical Expressions

8.6 Radical Equations and Problem Solving

8.7 Complex Numbers

 

9. Quadratic Equations and Functions

9.1 Completing the Square

9.2 Solving Quadratic Equations Using the Quadratic Formula

9.3 Solving Equations That Are Quadratic in Form

9.4 Graphing Quadratic Functions

9.5 Solving Nonlinear Inequalities

 

10. Exponential and Logarithmic Functions

10.1 Composite and Inverse Functions

10.2 Exponential Functions

10.3 Logarithmic Functions

10.4 Properties of Logarithms

10.5 Common and Natural Logarithms

10.6 Exponential and Logarithmic Equations with Applications

 

11. Conic Sections

11.1 Parabolas and the Circles

11.2 Ellipses and Hyperbolas

11.3 Nonlinear Systems of Equations

11.4 Nonlinear Inequalities and Systems of Inequalities

 

Appendices

A. Arithmetic Sequences and Series

B. Geometric Sequences and Series

C. The Binomial Theorem

D. Permutations and Combinations (available online via MyMathLab)

E. Probability (available online via MyMathLab)