Intermediate Algebra

by Kaufmann, Jerome E.; Schwitters, Karen L.

• ISBN13: 9780534368265
• ISBN10: 0534368263
• Format: Hardcover
• Copyright: 1999-07-30
• Publisher: Brooks Cole

Summary

Thousands of students have learned algebra with the Kaufmann Solution. This text is written for college students who need an algebra course that bridges the gap between elementary algebra and the more advanced courses in precalculus mathematics. The basic concepts of intermediate algebra are presented in a simple, straight-forward manner. Algebraic ideas are developed in a logical sequence, through examples, continuously reinforced through additional examples, and then applied in a variety of problem-solving situations. In this edition, special efforts were made by the authors to incorporate improvements suggested by reviewers and by users to earlier editions, while at the same time preserving the book's many successful features.

Table of Contents

chapter 1 Basic Concepts and Properties	1	(43)
1.1 Sets, Real Numbers, and Numerical Expressions	2	(9)
1.2 Operations with Real Numbers	11	(10)
1.3 Properties of Real Numbers and the Use of Exponents	21	(8)
1.4 Algebraic Expressions	29	(10)
CHAPTER 1 SUMMARY	39	(2)
CHAPTER 1 REVIEW PROBLEM SET	41	(2)
CHAPTER 1 TEST	43	(1)
chapter 2 Equations, Inequalities, and Problem Solving	44	(61)
2.1 Solving First-Degree Equations	45	(7)
2.2 Equations Involving Fractional Forms	52	(8)
2.3 Equations Involving Decimals and Problem Solving	60	(7)
2.4 Formulas	67	(10)
2.5 Inequalities	77	(7)
2.6 More on Inequalities and Problem Solving	84	(9)
2.7 Equations and Inequalities Involving Absolute Value	93	(7)
CHAPTER 2 SUMMARY	100	(2)
CHAPTER 2 REVIEW PROBLEM SET	102	(2)
CHAPTER 2 TEST	104	(1)
chapter 3 Linear Equations and Inequalities in Two Variables	105	(55)
3.1 Rectangular Coordinate System	106	(13)
3.2 Linear Equations in Two Variables	119	(9)
3.3 Linear Inequalities in Two Variables	128	(5)
3.4 Distance and Slope	133	(10)
3.5 Determining the Equation of a Line	143	(12)
CHAPTER 3 SUMMARY	155	(2)
CHAPTER 3 REVIEW PROBLEM SET	157	(1)
CHAPTER 3 TEST	158	(2)
chapter 4 Polynomials	160	(58)
4.1 Polynomials: Sums and Differences	161	(6)
4.2 Products and Quotients of Monomials	167	(6)
4.3 Multiplying Polynomials	173	(9)
4.4 Factoring: Use of the Distributive Property	182	(7)
4.5 Factoring: Difference of Two Squares and Sum or Difference of Two Cubes	189	(7)
4.6 Factoring Trinomials	196	(8)
4.7 Equations and Problem Solving	204	(7)
CHAPTER 4 SUMMARY	211	(2)
CHAPTER 4 REVIEW PROBLEM SET	213	(2)
CHAPTER 4 TEST	215	(1)
CUMULATIVE REVIEW PROBLEM SET (Chapters 1-4)	216	(2)
chapter 5 Rational Expressions	218	(59)
5.1 Simplifying Rational Expressions	219	(6)
5.2 Multiplying and Dividing Rational Expressions	225	(6)
5.3 Adding and Subtracting Rational Expressions	231	(9)
5.4 More on Rational Expressions and Complex Fractions	240	(9)
5.5 Dividing Polynomials	249	(4)
5.6 Fractional Equations	253	(9)
5.7 More Fractional Equations and Applications	262	(10)
CHAPTER 5 SUMMARY	272	(1)
CHAPTER 5 REVIEW PROBLEM SET	273	(2)
CHAPTER 5 TEST	275	(2)
chapter 6 Exponents and Radicals	277	(48)
6.1 Using Integers as Exponents	278	(6)
6.2 Roots and Radicals	284	(11)
6.3 Combining Radicals and Simplifying Radicals That Contain Variables	295	(5)
6.4 Products and Quotients Involving Radicals	300	(5)
6.5 Equations Involving Radicals	305	(5)
6.6 Merging Exponents and Roots	310	(6)
6.7 Scientific Notation	316	(5)
CHAPTER 6 SUMMARY	321	(1)
CHAPTER 6 REVIEW PROBLEM SET	322	(2)
CHAPTER 6 TEST	324	(1)
chapter 7 Quadratic Equations and Inequalities	325	(54)
7.1 Complex Numbers	326	(7)
7.2 Quadratic Equations	333	(9)
7.3 Completing the Square	342	(5)
7.4 Quadratic Formula	347	(9)
7.5 More Quadratic Equations and Applications	356	(10)
7.6 Quadratic and Other Nonlinear Inequalities	366	(7)
CHAPTER 7 SUMMARY	373	(1)
CHAPTER 7 REVIEW PROBLEM SET	374	(2)
CHAPTER 7 TEST	376	(1)
CUMULATIVE REVIEW PROBLEM SET (Chapters 1-7)	377	(2)
chapter 8 Conic Sections	379	(35)
8.1 Graphing Parabolas	380	(10)
8.2 More Parabolas and Some Circles	390	(8)
8.3 Graphing Ellipses	398	(5)
8.4 Graphing Hyperbolas	403	(8)
CHAPTER 8 SUMMARY	411	(1)
CHAPTER 8 REVIEW PROBLEM SET	411	(2)
CHAPTER 8 TEST	413	(1)
chapter 9 Functions	414	(55)
9.1 Relations and Functions	415	(6)
9.2 Functions: Their Graphs and Applications	421	(14)
9.3 Graphing Made Easy Via Transformations	435	(9)
9.4 Composition of Functions	444	(6)
9.5 Inverse Functions	450	(8)
9.6 Direct and Inverse Variations	458	(7)
CHAPTER 9 SUMMARY	465	(2)
CHAPTER 9 REVIEW PROBLEM SET	467	(1)
CHAPTER 9 TEST	468	(1)
chapter 10 Systems of Equations	469	(63)
10.1 Systems of Two Linear Equations in Two Variables	470	(8)
10.2 Elimination-by-Addition Method	478	(10)
10.3 Systems of Three Linear Equations in Three Variables	488	(8)
10.4 Matrix Approach to Solving Systems	496	(6)
10.5 Determinants	502	(5)
10.6 3 X 3 Determinants and Systems of Three Linear Equations in Three Variables	507	(7)
10.7 Systems Involving Nonlinear Equations and Systems of Inequalities	514	(8)
CHAPTER 10 SUMMARY	522	(2)
CHAPTER 10 REVIEW PROBLEM SET	524	(2)
CHAPTER 10 TEST	526	(2)
CUMULATIVE REVIEW PROBLEM SET (Chapter 1-10)	528	(4)
chapter 11 Exponential and Logarithmic Functions	532	(45)
11.1 Exponents and Exponential Functions	533	(7)
11.2 Applications of Exponential Functions	540	(9)
11.3 Logarithms	549	(9)
11.4 Logarithmic Functions	558	(7)
11.5 Exponential Equations, Logarithmic Equations, and Problem Solving	565	(8)
CHAPTER 11 SUMMARY	573	(1)
CHAPTER 11 REVIEW PROBLEM SET	574	(2)
CHAPTER 11 TEST	576	(1)
chapter 12 Sequences and Series	577	(31)
12.1 Arithmetic Sequences	578	(5)
12.2 Arithmetic Series	583	(5)
12.3 Geometric Sequences and Series	588	(7)
12.4 Infinite Geometric Series	595	(5)
12.5 Binomial Expansions	600	(4)
CHAPTER 12 SUMMARY	604	(1)
CHAPTER 12 REVIEW PROBLEM SET	605	(1)
CHAPTER 12 TEST	606	(2)
Appendixes	608	(19)
A Synthetic Division and the Factor Theorem	609	(4)
B Common Logarithms	613	(12)
C Natural Logarithms	625	(2)
ANSWERS TO ODD-NUMBERED PROBLEMS AND ALL CHAPTER REVIEW, CHAPTER TEST, AND CUMULATIVE REVIEW PROBLEMS	627	(38)
INDEX	665