Elementary and Intermediate Algebra

by Carson, Tom; Gillespie, Ellyn; Jordan, Bill E.

• ISBN13: 9780201729627
• ISBN10: 0201729628
• Format: Hardcover
• Copyright: 2005-01-01
• Publisher: Addison Wesley

Summary

Elementary and Intermediate Algebra is a book for the student. The authors' goal is to help build students' confidence, their understanding and appreciation of math, and their basic skills by presenting an extremely user-friendly text that models a framework in which students can succeed. Unfortunately, students who place into developmental math courses often struggle with math anxiety due to bad experiences in past math courses. Developmental students often have never developed nor applied a study system in mathematics. To address these needs, the authors have framed three goals for Elementary and Intermediate Algebra: 1) reduce math anxiety, 2) teach for understanding, and 3) foster critical thinking and enthusiasm. The authors' writing style is extremely student friendly. They talk to students in their own language and walk them through the concepts, explaining not only how to do the math, but also why it works and where it comes from, rather than using the "monkey-see, monkey-do" approach that some books take.

Table of Contents

Preface	vi
To the Student	xiii
Learning Styles Inventory	xix
Foundations of Algebra	1	(102)
Number Sets and the Structure of Algebra	2	(11)
Fractions	13	(14)
Adding and Subtracting Real Numbers; Properties of Real Numbers	27	(16)
Multiplying and Dividing Real Numbers; Properties of Real Numbers	43	(16)
Exponents, Roots, and Order of Operations	59	(14)
Translating Word Phrases to Expressions	73	(8)
Evaluating and Rewriting Expressions	81	(22)
Summary	91	(6)
Review Exercises	97	(4)
Practice Test	101	(2)
Solving Linear Equations and Inequalities	103	(88)
Equations, Formulas, and the Problem-Solving Process	104	(15)
The Addition Principle	119	(14)
The Multiplication Principle	133	(14)
Applying the Principles to Formulas	147	(7)
Translating Word Sentences to Equations	154	(12)
Solving Linear Inequalities	166	(25)
Summary	180	(5)
Review Exercises	185	(4)
Practice Test	189	(2)
Problem Solving	191	(76)
Ratios and Proportions	192	(15)
Percents	207	(15)
Problems with Two or More Unknowns	222	(14)
Rates	236	(8)
Investment and Mixture	244	(23)
Summary	252	(5)
Review Exercises	257	(5)
Practice Test	262	(2)
Chapters 1--3 Cumulative Review Exercises	264	(3)
Graphing Linear Equations and Inequalities	267	(110)
The Rectangular Coordinate System	268	(10)
Graphing Linear Equations	278	(12)
Graphing Using Intercepts	290	(10)
Slope-Intercept Form	300	(16)
Point-Slope Form	316	(12)
Graphing Linear Inequalities	328	(11)
Introduction to Functions and Function Notation	339	(38)
Summary	359	(8)
Review Exercises	367	(7)
Practice Test	374	(3)
Polynomials	377	(86)
Exponents and Scientific Notation	378	(12)
Introduction to Polynomials	390	(12)
Adding and Subtracting Polynomials	402	(11)
Exponent Rules and Multiplying Monomials	413	(12)
Multiplying Polynomials; Special Products	425	(12)
Exponent Rules and Dividing Polynomials	437	(26)
Summary	454	(3)
Review Exercises	457	(4)
Practice Test	461	(2)
Factoring	463	(82)
Greatest Common Factor and Factoring by Grouping	464	(13)
Factoring Trinomials of the Form x2 + bx + c	477	(7)
Factoring Trinomials of the Form ax2 + bx + c, where a ≠ 1	484	(9)
Factoring Special Products	493	(9)
Strategies for Factoring	502	(6)
Solving Quadratic Equations by Factoring	508	(12)
Graphs of Quadratic Equations and Functions	520	(25)
Summary	532	(5)
Review Exercises	537	(3)
Practice Test	540	(1)
Chapters 1--6 Cumulative Review Exercises	541	(4)
Rational Expressions and Equations	545	(98)
Simplifying Rational Expressions	546	(15)
Multiplying and Dividing Rational Expressions	561	(11)
Adding and Subtracting Rational Expressions with the Same Denominator	572	(7)
Adding and Subtracting Rational Expressions with Different Denominators	579	(12)
Complex Rational Expressions	591	(11)
Solving Equations Containing Rational Expressions	602	(12)
Applications with Rational Expressions	614	(29)
Summary	629	(6)
Review Exercises	635	(5)
Practice Test	640	(3)
More on Inequalities, Absolute Value, and Functions	643	(66)
Compound Inequalities	644	(15)
Equations Involving Absolute Value	659	(5)
Inequalities Involving Absolute Value	664	(9)
Functions and Graphing	673	(16)
Function Operations	689	(20)
Summary	697	(5)
Review Exercises	702	(5)
Practice Test	707	(2)
Systems of Equations	709	(108)
Solving Systems of Linear Equations Graphically	710	(12)
Solving Systems of Linear Equations by Substitution	722	(14)
Solving Systems of Linear Equations by Elimination	736	(18)
Solving Systems of Linear Equations in Three Variables	754	(13)
Solving Systems of Linear Equations Using Matrices	767	(11)
Cramer's Rule	778	(10)
Solving Systems of Linear Inequalities	788	(29)
Summary	799	(6)
Review Exercises	805	(5)
Practice Test	810	(2)
Chapters 1--9 Cumulative Review Exercises	812	(5)
Rational Exponents, Radicals, and Complex Numbers	817	(86)
Radical Expressions and Functions	818	(12)
Rational Exponents	830	(12)
Multiplying, Dividing, and Simplifying Radicals	842	(10)
Adding, Subtracting, and Multiplying Radical Expressions	852	(9)
Rationalizing Numerators and Denominators of Radical Expressions	861	(11)
Radical Equations and Problem Solving	872	(10)
Complex Numbers	882	(21)
Summary	890	(7)
Review Exercises	897	(5)
Practice Test	902	(1)
Quadratic Equations	903	(80)
Completing the Square	904	(15)
Solving Quadratic Equations Using the Quadratic Formula	919	(14)
Solving Equations That Are Quadratic in Form	933	(10)
Graphing Quadratic Functions	943	(15)
Solving Nonlinear Inequalities	958	(25)
Summary	971	(5)
Review Exercises	976	(4)
Practice Test	980	(3)
Exponential and Logarithmic Functions	983	(84)
Composite and Inverse Functions	984	(15)
Exponential Functions	999	(12)
Logarithmic Functions	1011	(10)
Properties of Logarithms	1021	(9)
Common and Natural Logarithms	1030	(7)
Exponential and Logarithmic Equations with Applications	1037	(30)
Summary	1050	(9)
Review Exercises	1059	(6)
Practice Test	1065	(2)
Conic Sections	1067
The Parabola and the Circle	1068	(16)
Ellipses and Hyperbolas	1084	(15)
Nonlinear Systems of Equations	1099	(8)
Nonlinear Inequalities and Systems of Inequalities	1107
Summary	1116	(8)
Review Exercises	1124	(6)
Practice Test	1130	(3)
Chapters 1--13 Cumulative Review Exercises	1133
Appendices A--E	1	(1)
Answers	1	(1)
Glossary	1	(1)
Index	1	(1)
Photograph Credits	1