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More About This Textbook
Overview
Algebra: A Combined Approach is intended for a 2semester sequence of Introductory and Intermediate Algebra where students get a solid foundation in algebra, including exposure to functions, which prepares them for success in College Algebra or their next math course.
Prealgebra Review; Real Numbers and Introduction to Algebra; Equations, Inequalities, and Problem Solving; Graphing Equations and Inequalities; Systems of Equations; Exponents and Polynomials; Factoring Polynomials; Rational Expressions; Graphs and Functions; Systems of Equations and Inequalities, and Variation; Rational Exponents, Radicals and Complex Numbers; Quadratic Equations and Functions; Exponential and Logarithmic Functions; Conic Sections
For all readers interested in algebra.
Product Details
Meet the Author
Elayn MartinGay, University of New Orleans
An awardwinning instructor and bestselling author, Elayn MartinGay 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.
Prentice Hall is pleased to announce the new Third Editions of Basic College Mathematics, Introductory Algebra, Intermediate Algebra, and Algebra A Combined Approach and two new first editions, Basic College Mathematics with Early Integers, and Developmental Mathematics. Elayn MartinGay also authors a bestselling ©2005 hardback series in developmental mathematics.
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 MartinGay series. Elayn also originated the Chapter Test Prep Video CDs to help students during their most “teachable moment” as they prepare for a test.
Elayn’s experience has made her aware of how busy instructors are and what a difference quality supports make. For this reason, she created the InstructortoInstructor video series. These videos provide instructors with suggestions for presenting specific math topic 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. They are a great resource for suggestions regarding areas they may wish to emphasize, or common trouble areas students experience, that instructors my wish to highlight.
With her textbooks series, the Chapter Test Prep Video Cd, and CD Lecture series, Elayn has sought to put success within the reach of every student and instructor.
Table of Contents
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 Numbers
1.5 Subtracting Real Numbers
Integrated Review–Operations on Real Numbers
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–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 Solving Linear Inequalities
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–Summary of Linear Equations
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–Summary on Solving Systems of Equations
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–Exponents and Operations on Polynomials
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 Grouping
6.5 Factoring Special Products
Integrated Review–Choosing a Factoring Strategy
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–Summary on Rational Expressions
7.6 Proportion and Problem Solving with Rational Expressions
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–Linear Equations in Two Variables
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 and Problem Solving in Three Variables
9.2 Solving Systems of Equations Using Matrices
Integrated Review–Systems of Linear Equations
9.3 Systems of Linear Inequalities
9.4 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–Radicals and Rational Exponents
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–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
Chapter 12 Exponential and Logarithmic Functions
12.1 The Algebra of 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 Problem Solving
Chapter 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
Appendices
A Transition Review: Exponents, Polynomials and Factoring Strategies
B Transition Review: Solving Linear and Quadratic Equations
C The Bigger Picture–Simplifying Expressions and Solving Equations
D Sets and Compound Inequalities
E Absolute Value Equations and Inequalities
F Determinants and Cramer’s Rule
G Review of Angles, Lines and Special Triangles
H An Introduction to Using a Graphing Utility
I. Stretching Graphs of Absolute Value Functions