Elementary and 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. 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 Solving Linear Inequalities

 

3. Problem Solving

3.1 Ratios and Proportions

3.2 Percents

3.3 Problems with Two or More Unknowns

3.4 Rates

3.5 Investment and Mixture

 

4. Graphing Linear Equations and Inequalities

4.1 The Rectangular Coordinate System

4.2 Graphing Linear Equations

4.3 Graphing Using Intercepts

4.4 Slope-Intercept Form

4.5 Point-Slope Form

4.6 Graphing Linear Inequalities

4.7 Introduction to Functions and Function Notation

 

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 x2 + bx + c

6.3 Factoring Trinomials of the Form ax2 + 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

8.3 Inequalities Involving Absolute Value

8.4 Functions and Graphing

8.5 Function Operations 

 

9. Systems of Linear Equations and Inequalities

9.1 Solving Systems of Linear Equations Graphically

9.2 Solving Systems of Linear Equations by Substitution; Applications

9.3 Solving Systems of Linear Equations by Elimination; Applications

9.4 Solving Systems of Linear Equations in Three Variables

9.5 Solving Systems of Linear Equations Using Matrices

9.6 Solving Systems of Linear Equations Using Cramer’s Rule

9.7 Solving Systems of Linear Inequalities

 

10. Rational Exponents, Radicals, and Complex Numbers

10.1 Radical Expressions and Functions

10.2 Rational Exponents

10.3 Multiplying, Dividing, and Simplifying Radicals

10.4 Adding, Subtracting, and Multiplying Radical Expressions

10.5 Rationalizing Numerators and Denominators of Radical Expressions

10.6 Radical Equations and Problem Solving

10.7 Complex Numbers

 

11. Quadratic Equations and Functions

11.1 Completing the Square

11.2 Solving Quadratic Equations Using the Quadratic Formula

11.3 Solving Equations That Are Quadratic in Form

11.4 Graphing Quadratic Functions

11.5 Solving Nonlinear Inequalities

 

12. Exponential and Logarithmic Functions

12.1 Composite and Inverse Functions

12.2 Exponential Functions

12.3 Logarithmic Functions

12.4 Properties of Logarithms

12.5 Common and Natural Logarithms

12.6 Exponential and Logarithmic Equations with Applications

 

13. Conic Sections

13.1 The Parabola and Circle

13.2 Ellipses and Hyperbolas

13.3 Nonlinear Systems of Equations

13.4 Nonlinear Inequalities and Systems of Inequalities

 

Elementary Algebra Review

 

Appendices

A Arithmetic Sequences and Series

B Geometric Sequences and Series

C The Binomial Series

D Synthetic Division

E Mean, Median, and Mode (if room)