Elementary Algebra For College Students

About our authors Allen Angel received his BS and MS in mathematics from SUNY at New Paltz. He completed additional graduate work at Rutgers University. He taught at Sullivan County Community College and Monroe Community College, where he served as chairperson of the Mathematics Department. He served as Assistant Director of the National Science Foundation at Rutgers University for the summers of 1967 - 1970. He was President of The New York State Mathematics Association of Two-Year Colleges (NYSMATYC). He also served as Northeast Vice President of the American Mathematics Association of Two-Year Colleges (AMATYC). Allen lives in Palm Harbor, Florida but spends his summers in Penfield, New York. He enjoys playing tennis and watching sports. He also enjoys traveling with his wife Kathy. Dennis Runde received his BS and MS in mathematics from the University of Wisconsin - Platteville and Milwaukee, respectively. He has a PhD in Mathematics Education from the University of South Florida. He has been teaching for 27 years at State College of Florida - Manatee - Sarasota. His interests include reading, history, fishing, trivia contests and cooking. He and his wife Kristin are the proud parents of their 3 sons Alex, Nick and Max.

Real Numbers

1.1 Study Skills for Success in Mathematics
1.2 Problem Solving
1.3 Fractions
1.4 The Real Number System
1.5 Inequalities and Absolute Value

Mid-Chapter Test: Sections 1.1—1.5


1.6 Addition of Real Numbers
1.7 Subtraction of Real Numbers
1.8 Multiplication and Division of Real Numbers
1.9 Exponents, Parentheses, and the Order of Operations
1.10 Properties of the Real Number System


Solving Linear Equations and Inequalities

2.1 Combining Like Terms
2.2 The Addition Property of Equality
2.3 The Multiplication Property of Equality
2.4 Solving Linear Equations with a Variable on Only One Side of the Equation

Mid-Chapter Test: Sections 2.1—2.4


2.5 Solving Linear Equations with the Variable on Both Sides of the Equation
2.6 Formulas
2.7 Ratios and Proportions
2.8 Inequalities in One Variable


Applications of Algebra

3.1 Changing Application Problems into Equations
3.2 Solving Application Problems

Mid-Chapter Test: Sections 3.1—3.2


3.3 Geometric Problems
3.4 Motion, Money, and Mixture Problems


Exponents and Polynomials

4.1 Exponents
4.2 Negative Exponents
4.3 Scientific Notation

Mid-Chapter Test: Sections 4.1—4.3


4.4 Addition and Subtraction of Polynomials
4.5 Multiplication of Polynomials
4.6 Division of Polynomials


Factoring

5.1 Factoring a Monomial from a Polynomial
5.2 Factoring by Grouping
5.3 Factoring Trinomials of the Form ax2 + bx + c, a = 1
5.4 Factoring Trinomials of the Form ax2 + bx + c, a ≠ 1

Mid-Chapter Test: Sections 5.1—5.4


5.5 Special Factoring Formulas and a General Review of Factoring
5.6 Solving Quadratic Equations Using Factoring
5.7 Applications of Quadratic Equations


Rational Expressions and Equations

6.1 Simplifying Rational Expressions
6.2 Multiplication and Division of Rational Expressions
6.3 Addition and Subtraction of Rational Expressions with a Common Denominator and Finding the Least Common Denominator
6.4 Addition and Subtraction of Rational Expressions

Mid-Chapter Test: Sections 6.1—6.4


6.5 Complex Fractions
6.6 Solving Rational Equations
6.7 Rational Equations: Applications and Problem Solving
6.8 Variation


Graphing Linear Equations

7.1 The Cartesian Coordinate System and Linear Equations in Two Variables
7.2 Graphing Linear Equations
7.3 Slope of a Line

Mid-Chapter Test: Sections 7.1—7.3


7.4 Slope-Intercept and Point-Slope Forms of a Linear Equation
7.5 Graphing Linear Inequalities
7.6 Functions


Systems of Linear Equations

8.1 Solving Systems of Equations Graphically
8.2 Solving Systems of Equations by Substitution
8.3 Solving Systems of Equations by the Addition Method

Mid-Chapter Test: Sections 8.1—8.3


8.4 Systems of Equations: Applications and Problem Solving
8.5 Solving Systems of Linear Inequalities


Roots and Radicals

9.1 Evaluating Square Roots
9.2 Simplifying Square Roots
9.3 Adding, Subtracting, and Multiplying Square Roots
9.4 Dividing Square Roots

Mid-Chapter Test: Sections 9.1—9.4


9.5 Solving Radical Equations
9.6 Radicals: Applications and Problem Solving
9.7 Higher Roots and Rational Exponents


Quadratic Equations

10.1 The Square Root Property
10.2 Solving Quadratic Equations by Completing the Square
10.3 Solving Quadratic Equations by the Quadratic Formula

Mid-Chapter Test: Sections 10.1—10.3


10.4 Graphing Quadratic Equations
10.5 Complex Numbers



Appendices

A. Review of Decimals and Percent
B. Geometry