Beginning & 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 originated 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. Review of Real Numbers

1.1 Tips for Success in Mathematics

1.2 Symbols and Sets of Numbers

1.3 Fractions

1.4 Introduction to Variable Expressions and Equations

1.5 Adding Real Numbers

1.6 Subtracting Real Numbers

            Integrated Review - Operations on Real Numbers

1.7 Multiplying and Dividing Real Numbers

1.8 Properties of Real Numbers

 

2. Equations and Problem Solving

2.1 Simplifying Expressions

2.2 The Addition and Multiplication Properties of Equality

2.3 Solving Linear Equations

            Integrated Review - Solving Linear Equations

2.4 An Introduction to Problem Solving

2.5 Formulas and Problem Solving

2.6 Percent and Mixture Problem Solving

2.7 Further Problem Solving

2.8 Solving Linear Inequalities

 

3. Graphing

3.1 Reading Graphs and the Rectangular Coordinate System

3.2 Graphing Linear Equations

3.3 Intercepts

3.4 Slope and Rate of Change

            Integrated Review - Summary on Slope and Graphing Linear Equations

3.5 The Slope-Intercept Form

3.6 The Point-Slope Form

3.7 Functions

 

4. Systems of Linear Equations

4.1 Solving Systems of Linear Equations by Graphing

4.2 Solving Systems of Linear Equations by Substitution

4.3 Solving Systems of Linear Equations by Addition

            Integrated Review - Solving Systems of Equations

4.4 Solving Systems of Linear Equations in Three Variables

4.5 Systems of Linear Equations and Problem Solving

 

5. Exponents and Polynomials

5.1 Exponents

5.2 Polynomial Functions and Adding and Subtracting Polynomials

5.3 Multiplying Polynomials

5.4 Special Products

            Integrated Review - Exponents and Operations on Polynomials

5.5 Negative Exponents and Scientific Notation

5.6 Dividing Polynomials

5.7 Synthetic Division and the Remainder Theorem

 

6. Factoring Polynomials

6.1 The 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 and Perfect Square Trinomials

6.4 Factoring Trinomials of the Form ax2 + bx + c by Grouping

6.5 Factoring Binomials

            Integrated Review-Choosing a Factoring Strategy

6.6 Solving Quadratic Equations by Factoring

6.7 Quadratic Equations and Problem Solving

 

7. Rational Expressions

7.1 Rational Functions and Simplifying Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions with Common Denominators and Least Common Denominator

7.4 Adding and Subtracting Rational Expressions with Unlike  Denominators

7.5 Solving Equations Containing Rational Expressions

            Integrated Review-Summary on Rational Expressions

7.6 Proportion and Problem Solving with Rational Equations

7.7 Simplifying Complex Fractions

 

8. More on Functions and Graphs

8.1 Graphing and Writing Linear Functions

8.2 Graphing Nonlinear Functions

            Integrated Review - Summary on Functions and Equations of Lines

8.3 Graphing Piecewise-Defined Functions and Shifting and Reflecting Graphs of Functions

8.4 Variation and Problem Solving

 

9. Inequalities and Absolute Value

9.1 Compound Inequalities

9.2 Absolute Value Equations

9.3 Absolute Value Inequalities

            Integrated Review -  Solving Compound Inequalities and Absolute Value Equations and Inequalities

9.4 Linear Inequalities in Two Variables and Systems of Linear Inequalities

 

10. Rational Exponents, Radicals, and Complex Numbers   

10.1 Radicals and Radical Functions

10.2 Rational Exponents

10.3 Simplifying Radical Expressions

10.4 Adding, Subtracting, and Multiplying Radical Expressions

10.5 Rationalizing Denominators and Numerators of Radical Expressions

            Integrated Review - Radicals and Rational Exponents

10.6 Radical Equations and Problem Solving

10.7 Complex Numbers

 

11. Quadratic Equations and Functions

11.1 Solving Quadratic Equations by Completing the Square

11.2 Solving Quadratic Equations by the Quadratic Formula

11.3 Solving Equations by Using Quadratic Methods

            Integrated Review-Summary on Solving Quadratic Equations

11.4 Nonlinear Inequalities in One Variable

11.5 Quadratic Functions and Their Graphs

11.6 Further Graphing of Quadratic Functions

 

12. Exponential and Logarithmic Functions

12.1 The Algebra of Functions; Composite Functions

12.2 Inverse Functions

12.3 Exponential Functions

12.4 Logarithmic Functions

12.5 Properties of Logarithms

            Integrated Review - Functions and Properties of Logarithms

12.6 Common Logarithms, Natural Logarithms, and Change of Base

12.7 Exponential and Logarithmic Equations and Applications

 

13. Conic Sections

13.1 The Parabola and the Circle

13.2 The Ellipse and the Hyperbola

            Integrated Review - Graphing Conic Sections

13.3 Solving Nonlinear Systems of Equations

13.4 Nonlinear Inequalities and Systems of Inequalities

 

14. Sequences, Series, and the Binomial Theorem

14.1 Sequences

14.2 Arithmetic and Geometric Sequences

14.3 Series

            Integrated Review - Sequences and Series

14.4 Partial Sums of Arithmetic and Geometric Sequences

14.5 The Binomial Theorem

 

Appendices

A. The Bigger Picture/Practice Final Exams

B. Operations on Decimals/ Percent, Decimal, and Fraction Table

C. Review of Algebra Topics

            C-1 Equations (Linear and Quadratic Solved by Factoring)

            C-2 Problem Solving

            C-3 Graphing

            C-4 Polynomials and Factoring

            C-5 Rational Expressions

D. An Introduction to Using a Graphing Utility

E. Solving Systems of Equations by Matrices

F. Solving Systems of Equations by Determinants

G. Mean, Median, and Mode

H. Review of Angles, Lines, and Special Triangles