Understanding Elementary Algebra With Geometry

by Hirsch, Lewis; Goodman, Arthur

• ISBN13: 9780534381240
• ISBN10: 0534381243
• Edition: CD
• Format: Hardcover
• Copyright: 2001-10-01
• Publisher: Cengage Learning

Summary

Helping students grasp the "why" of algebra through patient explanations, Hirsch and Goodman gradually build students' confidence without sacrificing rigor. To help students move beyond the "how" of algebra (computational proficiency) to the "why" (conceptual understanding), the authors introduce topics at an elementary level and return to them at increasing levels of complexity. Their gradual introduction of concepts, rules, and definitions through a wealth of illustrative examples-both numerical and algebraic-helps students compare and contrast related ideas and understand the sometimes-subtle distinctions among a wide variety of situations. This author team carefully prepares students to succeed in higher level mathematics.

Table of Contents

The Integers	1	(44)
What Is Algebra? Introduction and Basic Notation	2	(7)
Integers	9	(7)
Adding Integers	16	(6)
Subtracting Integers	22	(6)
Multiplying and Dividing Integers	28	(8)
The Real Number System	36	(9)
Chapter 1 Summary	40	(1)
Chapter 1 Review Exercises	41	(1)
Chapter 1 Practice Test	42	(3)
Algebraic Expressions	45	(48)
Variables and Exponents	46	(7)
Algebraic Substitution	53	(12)
The Distributive Property and Combining Like Terms	65	(7)
Simplifying Algebraic Expressions	72	(6)
Translating Phrases and Sentences Algebraically	78	(15)
Chapter 2 Summary	88	(1)
Chapter 2 Review Exercises	89	(2)
Chapter 2 Practice Test	91	(2)
First-Degree Equations and Inequalities	93	(52)
Types of Equations	94	(4)
Solving First-Degree Equations in One Variable and Applications	98	(11)
More First-Degree Equations and Applications	109	(14)
Types of Inequalities and Basic Properties of Inequalities	123	(7)
Solving First-Degree Inequalities in One Variable and Applications	130	(15)
Chapter 3 Summary	138	(2)
Chapter 3 Review Exercises	140	(1)
Chapter 3 Practice Test	141	(1)
Chapters 1-3 Cumulative Review	141	(1)
Chapters 1-3 Cumulative Practice Test	142	(3)
Rational Expressions	145	(58)
Fundamental Principle of Fractions	146	(7)
Multiplying and Dividing Rational Expressions	153	(9)
Adding and Subtracting Rational Expressions	162	(9)
Solving Fractional Equations and Inequalities	171	(8)
Ratio and Proportion	179	(9)
Applications	188	(15)
Chapter 4 Summary	198	(2)
Chapter 4 Review Exercises	200	(2)
Chapter 4 Practice Test	202	(1)
Graphing Straight Lines	203	(52)
The Rectangular (Cartesian) Coordinate System	204	(7)
Graphing a Linear Equation in Two Variables	211	(14)
The Slope	225	(13)
The Equation of a Line	238	(17)
Chapter 5 Summary	250	(1)
Chapter 5 Review Exercises	251	(2)
Chapter 5 Practice Test	253	(2)
Interpreting Graphs and Systems of Linear Equations	255	(42)
Interpreting Graphs	256	(10)
Solving Systems of Linear Equations: Graphical Method	266	(6)
Solving Systems of Linear Equations: Algebraic Methods	272	(9)
Applications	281	(16)
Chapter 6 Summary	288	(1)
Chapter 6 Review Exercises	289	(3)
Chapter 6 Practice Test	292	(1)
Chapters 4-6 Cumulative Review	293	(2)
Chapters 4-6 Cumulative Practice Test	295	(2)
Exponents and Polynomials	297	(48)
Exponent Rules	298	(7)
Zero and Negative Exponents	305	(9)
Scientific Notation	314	(7)
Introduction to Polynomials	321	(7)
Multiplying Polynomials	328	(7)
Special Products	335	(10)
Chapter 7 Summary	340	(2)
Chapter 7 Review Exercises	342	(2)
Chapter 7 Practice Test	344	(1)
Factoring	345	(36)
Common Factors	346	(5)
Factoring Trinomials	351	(6)
More Factoring	357	(7)
Solving Polynomial Equations by Factoring	364	(8)
Dividing Polynomials	372	(9)
Chapter 8 Summary	376	(1)
Chapter 8 Review Exercises	377	(1)
Chapter 8 Practice Test	378	(3)
More Rational Expressions	381	(48)
Reducing Rational Expressions	382	(5)
Multiplying and Dividing Rational Expressions	387	(4)
Adding and Subtracting Rational Expressions	391	(10)
Fractional Equations	401	(8)
Literal Equations	409	(4)
Applications	413	(16)
Chapter 9 Summary	421	(1)
Chapter 9 Review Exercises	422	(2)
Chapter 9 Practice Test	424	(1)
Chapters 7-9 Cumulative Review	424	(3)
Chapters 7-9 Cumulative Practice Test	427	(2)
Radical Expressions and Equations	429	(36)
Definitions and Basic Notation	430	(5)
Properties of Radicals and Simplest Radical Form	435	(9)
Adding and Subtracting Radical Expressions	444	(5)
Multiplying and Dividing Radical Expressions	449	(7)
Radical Equations	456	(9)
Chapter 10 Summary	462	(1)
Chapter 10 Review Exercises	463	(1)
Chapter 10 Practice Test	464	(1)
Quadratic Equations	465	(48)
The Factoring and Square Root Methods	466	(8)
The Method of Completing the Square	474	(5)
The Quadratic Formula	479	(8)
Choosing a Method	487	(4)
Applications	491	(7)
Graphing Quadratic Equations	498	(15)
Chapter 11 Summary	507	(2)
Chapter 11 Review Exercises	509	(1)
Chapter 11 Practice Test	510	(1)
Chapters 10-11 Cumulative Review	510	(1)
Chapters 10-11 Cumulative Practice Test	511	(2)
Geometry	513	(82)
Angles	514	(9)
Triangles	523	(7)
Congruence	530	(7)
Similarity	537	(12)
Quadrilaterals	549	(8)
Perimeter and Area	557	(11)
Circles	568	(8)
Solid Geometry	576	(19)
Chapter G Review Exercises	587	(6)
Chapter G Practice Test	593	(2)
APPENDIX A A Review of Arithmetic	595	(22)
A.1 Fractions	596	(4)
A.2 Multiplying and Dividing Fractions	600	(4)
A.3 Adding and Subtracting Fractions	604	(5)
A.4 Decimals	609	(3)
A.5 Percents	612	(5)
APPENDIX B Using a Scientific Calculator	617	(6)
APPENDIX C Using a Graphing Calculator	623	(6)
APPENDIX D Introduction to Functions	629	(6)
Answers to Selected Exercises and Chapter Tests	635	(28)
Index	663