Understanding Elementary Algebra with Geometry A Course for College Students (with CD-ROM and iLrn™ Tutorial)

by Hirsch, Lewis R.; Goodman, Arthur

• ISBN13: 9780534999728
• ISBN10: 0534999727
• Edition: 6th
• Format: Hardcover
• Copyright: 2005-09-19
• Publisher: Brooks Cole

Summary

Hirsch and Goodman offer a mathematically sound, rigorous text to those instructors who believe students should be challenged. The text prepares students for future study in higher-level courses by gradually building 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 variety of situations. This author team carefully prepares students to succeed in higher-level mathematics.

Table of Contents

The Integers	1	(46)
What Is Algebra? Introduction and Basic Notation	2	(8)
Integers	10	(7)
Adding Integers	17	(6)
Subtracting Integers	23	(7)
Multiplying and Dividing Integers	30	(7)
The Real Number System	37	(10)
Chapter 1 Summary	42	(1)
Chapter 1 Review Exercises	43	(1)
Chapter 1 Practice Test	44	(3)
Algebraic Expressions	47	(48)
Variables and Exponents	48	(8)
Algebraic Substitution	56	(11)
The Distributive Property and Combining Like Terms	67	(7)
Simplifying Algebraic Expressions	74	(6)
Translating Phrases and Sentences Algebraically	80	(15)
Chapter 2 Summary	91	(1)
Chapter 2 Review Exercises	92	(1)
Chapter 2 Practice Test	93	(2)
First-Degree Equations and Inequalities	95	(52)
Types of Equations	96	(4)
Solving First-Degree Equations in One Variable and Applications	100	(11)
More First-Degree Equations and Applications	111	(15)
Types of Inequalities and Basic Properties of Inequalities	126	(8)
Solving First-Degree Inequalities in One Variable and Applications	134	(13)
Chapter 3 Summary	142	(1)
Chapter 3 Review Exercises	143	(1)
Chapter 3 Practice Test	144	(1)
Chapters 1--3 Cumulative Review	145	(1)
Chapters 1--3 Cumulative Practice Test	146	(1)
Rational Expressions	147	(60)
Fundamental Principle of Fractions	148	(7)
Multiplying and Dividing Rational Expressions	155	(9)
Adding and Subtracting Rational Expressions	164	(9)
Solving Fractional Equations and Inequalities	173	(8)
Ratio and Proportion	181	(10)
Applications	191	(16)
Chapter 4 Summary	201	(3)
Chapter 4 Review Exercises	204	(1)
Chapter 4 Practice Test	205	(2)
Graphing Straight Lines	207	(56)
The Rectangular (Cartesian) Coordinate System	208	(8)
Graphing a Linear Equation in Two Variables	216	(14)
The Slope	230	(15)
The Equation of a Line	245	(18)
Chapter 5 Summary	257	(2)
Chapter 5 Review Exercises	259	(1)
Chapter 5 Practice Test	260	(3)
Interpreting Graphs and Systems of Linear Equations	263	(44)
Interpreting Graphs	264	(10)
Solving Systems of Linear Equations: Graphical Method	274	(7)
Solving Systems of Linear Equations: Algebraic Methods	281	(9)
Applications	290	(17)
Chapter 6 Summary	298	(1)
Chapter 6 Review Exercises	299	(2)
Chapter 6 Practice Test	301	(2)
Chapters 4--6 Cumulative Review	303	(2)
Chapters 4--6 Cumulative Practice Test	305	(2)
Exponents and Polynomials	307	(50)
Exponent Rules	308	(7)
Zero and Negative Exponents	315	(9)
Scientific Notation	324	(7)
Introduction to Polynomials	331	(8)
Multiplying Polynomials	339	(7)
Special Products	346	(11)
Chapter 7 Summary	351	(2)
Chapter 7 Review Exercises	353	(2)
Chapter 7 Practice Test	355	(2)
Factoring	357	(36)
Common Factors	358	(5)
Factoring Trinomials	363	(7)
More Factoring	370	(7)
Solving Polynomial Equations by Factoring	377	(8)
Dividing Polynomials	385	(8)
Chapter 8 Summary	390	(1)
Chapter 8 Review Exercises	391	(1)
Chapter 8 Practice Test	392	(1)
More Rational Expressions	393	(50)
Reducing Rational Expressions	394	(5)
Multiplying and Dividing Rational Expressions	399	(5)
Adding and Subtracting Rational Expressions	404	(10)
Fractional Equations	414	(9)
Literal Equations	423	(4)
Applications	427	(16)
Chapter 9 Summary	435	(2)
Chapter 9 Review Exercises	437	(1)
Chapter 9 Practice Test	438	(1)
Chapters 7--9 Cumulative Review	439	(2)
Chapters 7--9 Cumulative Practice Test	441	(2)
Radical Expressions and Equations	443	(38)
Definitions and Basic Notation	444	(5)
Properties of Radicals and Simplest Radical Form	449	(10)
Adding and Subtracting Radical Expressions	459	(4)
Multiplying and Dividing Radical Expressions	463	(7)
Radical Equations	470	(11)
Chapter 10 Summary	477	(1)
Chapter 10 Review Exercises	478	(1)
Chapter 10 Practice Test	479	(2)
Quadratic Equations	481	(50)
The Factoring and Square Root Methods	482	(10)
The Method of Completing the Square	492	(5)
The Quadratic Formula	497	(7)
Choosing a Method	504	(5)
Applications	509	(6)
Graphing Quadratic Equations	515	(16)
Chapter 11 Summary	525	(2)
Chapter 11 Review Exercises	527	(1)
Chapter 11 Practice Test	528	(1)
Chapters 10--11 Cumulative Review	529	(1)
Chapters 10--11 Cumulative Practice Test	530	(1)
G. Geometry	531	(84)
Angles	532	(9)
Triangles	541	(7)
Congruence	548	(7)
Similarity	555	(12)
Quadrilaterals	567	(8)
Perimeter and Area	575	(12)
Circles	587	(8)
Solid Geometry	595	(20)
Chapter G Review Exercises	606	(6)
Chapter G Practice Test	612	(3)
Appendixes
A. A Review of Arithmetic	615	(22)
Fractions	615	(5)
Multiplying and Dividing Fractions	620	(4)
Adding and Subtracting Fractions	624	(5)
Decimals	629	(3)
Percents	632	(5)
B. Using a Scientific Calculator	637	(6)
C. Using a Graphing Calculator	643	(6)
D. Introduction to Functions	649
Answers to Selected Exercises and Chapter Tests	1	(1)
Index	1