Intermediate Algebra

An award-winning instructor and best-selling author, 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 developed an acclaimed series of lecture videos to support developmental mathematics students in their quest for success. These highly successful videos originally served as the foundation material for her texts. Today, the videos are specific to each book in the Martin-Gay series. Elayn also pioneered the Chapter Test Prep Video to help students as they prepare for a test–their most “teachable moment!”   Elayn’s experience has made her aware of how busy instructors are and what a difference quality support makes. For this reason, she created the Instructor-to-Instructor video series. These videos provide instructors with suggestions for presenting specific math topics and concepts in basic mathematics, Prealgebra, beginning algebra, and intermediate algebra. Seasoned instructors can use them as a source for alternate approaches in the classroom. New or adjunct faculty may find the CDs useful for review.   Her textbooks and acclaimed video program support Elayn's passion of helping every student to succeed.

1. Real Numbers and Algebraic Expressions

1.1 Tips for Success in Mathematics

1.2 Algebraic Expressions and Sets of Numbers

1.3 Operations on Real Numbers

            Integrated Review - Algebraic Expressions and Operations on Whole Numbers

1.4 Properties of Real Numbers

 

2. 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

 

3. 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

 

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 Systems of Linear Equations and Problem Solving

            Integrated Review - Systems of Linear Equations

4.4 Solving Systems of Equations by Matrices

4.5 Solving Systems of Linear Inequalities

 

5. 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

 

6. 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 Divisions 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

 

7. 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

 

8. 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

 

9. Exponential and Logarithmic Functions

9.1 The Algebra of Functions; Composite Functions

9.2 Inverse Functions

9.3 Exponential Functions

9.4 Logarithmic Functions

9.5 Properties of Logarithms

            Integrated Review - Functions and Properties of Logarithms

9.6 Common Logarithms, Natural Logarithms, and Change of Base

9.7 Exponential and Logarithmic Equations and Applications

 

10. 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

 

11. 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

A. The Bigger Picture/Practice Final Exam

B. Geometry

C. Stretching and Compressing Graphs of Absolute Value Functions

D. Solving Systems of Equations Using Determinants

E. An Introduction to Using a Graphing Utility