Intermediate Algebra

Elayn Martin-Gay has taught mathematics at the University of New Orleans for more than 25 years. Her numerous teaching awards include the local University Alumni Association’s Award for Excellence in Teaching, and Outstanding Developmental Educator at University of New Orleans, presented by the Louisiana Association of Developmental Educators. Prior to writing textbooks, Elayn Martin-Gay developed an acclaimed series of lecture videos to support developmental mathematics students. These highly successful videos originally served as the foundation materials for her texts. Today, the videos are specific to each book in her series. She has also created Chapter Test Prep Videos to help students during their most “teachable moment”–as they prepare for a test–along with Instructor-to-Instructor videos that provide teaching tips, hints, and suggestions for every developmental mathematics course, including basic mathematics, prealgebra, beginning algebra, and intermediate algebra. Elayn is the author of 12 published textbooks and numerous multimedia interactive products, all specializing in developmental mathematics courses. She has also published series in Algebra 1, Algebra 2, and Geometry. She has participated as an author across a broad range of educational materials: textbooks, videos, tutorial software, and courseware. This offers an opportunity for multiple combinations for an integrated teaching and learning package, offering great consistency for the student.

Table of Contents



Real Numbers and Algebraic Expressions

1.1 Study Skill Tips for Success in Mathematics
1.2 Algebraic Expressions and Sets of Numbers
1.3 Operations on Real Numbers and Order of Operations

Integrated Review—Algebraic Expressions and Operations on Whole Numbers


1.4 Properties of Real Numbers and Algebraic Expressions


Equations, Inequalities, and Problem Solving

2.1 Linear Equations in One Variable
2.2 An Introduction to Problem Solving
2.3 Formulas and Problem Solving
2.4 Linear Inequalities and Problem Solving

Integrated Review—Linear Equations and Inequalities


2.5 Compound Inequalities
2.6 Absolute Value Equations
2.7 Absolute Value Inequalities


Graphs and Functions

3.1 Graphing Equations
3.2 Introduction to Functions
3.3 Graphing Linear Functions
3.4 The Slope of a Line
3.5 Equations of Lines

Integrated Review—Linear Equations in Two Variables


3.6 Graphing Piecewise-Defined Functions and Shifting and Reflecting Graphs of Functions
3.7 Graphing Linear Inequalities


Systems of Equations

4.1 Solving Systems of Linear Equations in Two Variables
4.2 Solving Systems of Linear Equations in Three Variables
4.3 Systems of Linear Equations and Problem Solving

Integrated Review—Systems of Linear Equations


4.4 Solving Systems of Equations by Matrices
4.5 Systems of Linear Inequalities


Exponents, Polynomials, and Polynomial Functions

5.1 Exponents and Scientific Notation
5.2 More Work with Exponents and Scientific Notation
5.3 Polynomials and Polynomial Functions
5.4 Multiplying Polynomials
5.5 The Greatest Common Factor and Factoring by Grouping
5.6 Factoring Trinomials
5.7 Factoring by Special Products

Integrated Review—Operations on Polynomials and Factoring Strategies


5.8 Solving Equations by Factoring and Problem Solving


Rational Expressions

6.1 Rational Functions and Multiplying and Dividing Rational Expressions
6.2 Adding and Subtracting Rational Expressions
6.3 Simplifying Complex Fractions
6.4 Dividing Polynomials: Long Division and Synthetic Division
6.5 Solving Equations Containing Rational Expressions

Integrated Review—Expressions and Equations Containing Rational Expressions


6.6 Rational Equations and Problem Solving
6.7 Variation and Problem Solving


Rational Exponents, Radicals, and Complex Numbers

7.1 Radicals and Radical Functions
7.2 Rational Exponents
7.3 Simplifying Radical Expressions
7.4 Adding, Subtracting, and Multiplying Radical Expressions
7.5 Rationalizing Denominators and Numerators of Radical Expressions

Integrated Review—Radicals and Rational Exponents


7.6 Radical Equations and Problem Solving
7.7 Complex Numbers


Quadratic Equations and Functions

8.1 Solving Quadratic Equations by Completing the Square
8.2 Solving Quadratic Equations by the Quadratic Formula
8.3 Solving Equations by Using Quadratic Methods

Integrated Review—Summary on Solving Quadratic Equations


8.4 Nonlinear Inequalities in One Variable
8.5 Quadratic Functions and Their Graphs
8.6 Further Graphing of Quadratic Functions


Exponential and Logarithmic Functions

9.1 The Algebra of Functions; Composite Functions
9.2 Inverse Functions
9.3 Exponential Functions
9.4 Exponential Growth and Decay Functions
9.5 Logarithmic Functions
9.6 Properties of Logarithms

Integrated Review—Functions and Properties of Logarithms


9.7 Common Logarithms, Natural Logarithms, and Change of Base
9.8 Exponential and Logarithmic Equations and Problem Solving


Conic Sections

10.1 The Parabola and the Circle
10.2 The Ellipse and the Hyperbola

Integrated Review—Graphing Conic Sections


10.3 Solving Nonlinear Systems of Equations
10.4 Nonlinear Inequalities and Systems of Inequalities


Sequences, Series, and the Binomial Theorem

11.1 Sequences
11.2 Arithmetic and Geometric Sequences
11.3 Series

Integrated Review—Sequences and Series


11.4 Partial Sums of Arithmetic and Geometric Sequences
11.5 The Binomial Theorem



Appendices

Geometry
Stretching and Compressing Graphs of Absolute Value Functions
Solving Systems of Equations Using Determinants
An Introduction to Using a Graphing Utility

Student Resources Study Skills Builders Bigger Picture—Study Guide Outline Practice Final Exam