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 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.

Chapter R: Prealgebra Review                        

R.1 Factors and the Least Common Multiple

R.2 Fractions                                        

R.3 Decimals and Percents                                

 

Chapter 1: Real Numbers and Introduction to Algebra                                              

1.1 Tips for Success in Mathematics               

1.2 Symbols and Sets of Numbers                    

1.3 Exponents, Order of Operations, and Variable Expressions                   

1.4 Adding Real Number                                

1.5 Subtracting Real Numbers                           

Integrated Review                                              

1.6 Multiplying and Dividing Real Numbers  

1.7 Properties of Real Numbers                         

1.8 Simplifying Expressions                                                                                               

 

Chapter 2: Equations, Inequalities, and Problem Solving                                          

2.1 The Addition Property of Equality            

2.2 The Multiplication Property of Equality   

2.3 Further Solving Linear Equations              

Integrated Review                                              

2.4 An Introduction to Problem Solving         

2.5 Formulas and Problem Solving                   

2.6 Percent and Mixture Problem Solving       

2.7 Linear Inequalities and Problem Solving                                                                                   

 

Chapter 3: Graphing Equations and Inequalities                                                         

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                                              

3.5 Equations of Lines                                        

3.6 Graphing Linear Inequalities in Two Variables                                                                        

 

Chapter 4: Systems of 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                                              

4.4 Systems of Linear Equations and Problem Solving                                 

 

Chapter 5: Exponents and Polynomials          

5.1 Exponents                                                      

5.2 Negative Exponents and Scientific Notation

5.3 Introduction to Polynomials                       

5.4 Adding and Subtracting Polynomials       

5.5 Multiplying Polynomials                             

5.6 Special Products                                           

Integrated Review                                              

5.7 Dividing Polynomials

 

Chapter 6: Factoring Polynomials  

6.1 The Greatest Common Factor                     

6.2 Factoring Trinomials of the Form x2 + bx + c

6.3 Factoring Trinomials of the Form ax2 + bx + c

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

6.5 Factoring by Special Products                    

Integrated Review                                              

6.6 Solving Quadratic Equations by Factoring

6.7 Quadratic Equations and Problem Solving

 

 Chapter 7: Rational Expressions                    

7.1 Simplifying Rational Expressions               

7.2 Multiplying and Dividing Rational Expressions                                      

7.3 Adding and Subtracting Rational Expressions with the Same

Denominator and Least Common Denominator

7.4 Adding and Subtracting Rational Expressions with Different Denominators

7.5 Solving Equations Containing Rational Expressions                                              

Integrated Review                                              

7.6 Proportions and Problem Solving with Rational Equations                   

7.7 Simplifying Complex Fractions                                                                                   

 

Chapter 8: Graphs and Functions   

8.1 Review of Equations of Lines and Writing Parallel and Perpendicular Lines     

8.2 Introduction to Functions                           

8.3 Polynomial and Rational Functions

Integrated Review                                              

8.4     Interval Notation, Finding Domains and Ranges from

Graphs and Graphing Piecewise-Defined Functions                                     

8.5 Shifting and Reflecting Graphs of Functions                           

 

Chapter 9: Systems of Equations and Inequalities and Variation

9.1 Solving Systems of Linear Equations in Three Variables and Problem Solving

9.2 Solving Systems of Equations Using Matrices

Integrated Review

9.3 Systems of Linear Inequalities

Variation and Problem Solving

 

Chapter 10: Rational Exponents, Radicals, and Complex Numbers                         

10.1   Radical Expressions and Radical Functions

10.2   Rational Exponents                                    

10.3   Simplifying Radical Expressions              

10.4   Adding, Subtracting, and Multiplying Radical Expressions                               

10.5   Rationalizing Numerators and Denominators of Radical Expressions               

Integrated Review

10.6   Radical Equations and Problem Solving

10.7   Complex Numbers                                                                                                      

 

Chapter 11: Quadratic Equations and Functions

11.1   Solving Quadratic Equations by Completing the Square                    

11.2   Solving Quadratic Equations by Using the Quadratic Formula         

11.3   Solving Equations by Using Quadratic Methods  Integrated Review             

11.4   Nonlinear Inequalities in One Variable   

11.5   Quadratic Functions and Their Graphs  

11.6   Further Graphing of Quadratic Functions

 

Chapter 12: Exponential and Logarithmic Functions                                                 

12.1 The Algebra of Functions                         

12.2 Inverse Functions                                       

12.3 Exponential Functions                               

12.4 Exponential Growth and Decay Functions

12.5 Logarithmic Functions

Integrated Review                              

12.6 Properties of Logarithms                           

12.7 Common Logarithms, Natural Logarithms, and Change of Base         

12.8 Exponential and Logarithmic Equations and Problem Solving            

 

Chapter 13: Conic Sections                             

13.1 The Parabola and the Circle                      

13.2 The Ellipse and the Hyperbola 

Integrated Review              

13.3 Solving Nonlinear Systems of Equations

13.4 Nonlinear Inequalities and Systems of Inequalities                                              

 

Appendices

A Transition Review: Exponents, Polynomials, and Factoring Strategies

B. Transition Review: Solving Linear and Quadratic Equations

C.  Sets and Compound Inequalities

D.  Absolute Value Equations and Inequalities

E. Determinants and Cramer’s Rule

F. Review of Angles, Lines, and Special Triangles

G.  Stretching and Compressing Graphs of Absolute Value Functions

H. An Introduction to Using a Graphing Utility

 

Student Resources
Study Skills Builders

Bigger Picture Study Guide Outline

Practice Final Exam

Answers to Selected Exercises