ALGEBRA FOR COLLEGE STUDENTS
by Jerome E. Kaufmann & Karen L. Schwitters
Pages count :920 pages
Size :10719 Ko
ALGEBRA FOR
COLLEGE STUDENTS
Jerome E. Kaufmann
Karen L. Schwitters
Seminole Community College
CONTENTS
1- Basic Concepts and Properties 1
1.1 Sets, Real Numbers, and Numerical Expressions 2
1.2 Operations with Real Numbers 11
1.3 Properties of Real Numbers and the Use of Exponents 22
1.4 Algebraic Expressions 30
Chapter 1 Summary 40
Chapter 1 Review Problem Set 41
Chapter 1 Test 43
2- Equations, Inequalities, and Problem Solving 44
2.1 Solving First-Degree Equations 45
2.2 Equations Involving Fractional Forms 53
2.3 Equations Involving Decimals and Problem Solving 61
2.4 Formulas 69
2.5 Inequalities 80
2.6 More on Inequalities and Problem Solving 87
2.7 Equations and Inequalities Involving Absolute Value 96
Chapter 2 Summary 103
Chapter 2 Review Problem Set 104
Chapter 2 Test 107
3- Polynomials 108
3.1 Polynomials: Sums and Differences 109
3.2 Products and Quotients of Monomials 115
3.3 Multiplying Polynomials 122
3.4 Factoring: Use of the Distributive Property 129
3.5 Factoring: Difference of Two Squares and Sum or Difference
of Two Cubes 137
3.6 Factoring Trinomials 143
3.7 Equations and Problem Solving 151
4- Rational Expressions 165
4.1 Simplifying Rational Expressions 166
4.2 Multiplying and Dividing Rational Expressions 172
4.3 Adding and Subtracting Rational Expressions 177
4.4 More on Rational Expressions and Complex Fractions 185
4.5 Dividing Polynomials 195
4.6 Fractional Equations 201
4.7 More Fractional Equations and Applications 209
Chapter 4 Summary 220
Chapter 4 Review Problem Set 221
Chapter 4 Test 223
5- Exponents and Radicals 224
5.1 Using Integers as Exponents 225
5.2 Roots and Radicals 232
5.3 Combining Radicals and Simplifying Radicals That
Contain Variables 244
5.4 Products and Quotients Involving Radicals 250
5.5 Equations Involving Radicals 256
5.6 Merging Exponents and Roots 261
5.7 Scientific Notation 268
Chapter 5 Summary 274
Chapter 5 Review Problem Set 275
Chapter 5 Test 277
6- Quadratic Equations and Inequalities 278
6.1 Complex Numbers 279
6.2 Quadratic Equations 287
6.3 Completing the Square 295
6.4 Quadratic Formula 300
6.5 More Quadratic Equations and Applications 308
6.6 Quadratic and Other Nonlinear Inequalities 320
Chapter 6 Summary 327
Chapter 6 Review Problem Set 328
Chapter 6 Test 330
Cumulative Review Problem Set (Chapters 1– 6) 331
7- Linear Equations and Inequalities in Two Variables 333
7.1 Rectangular Coordinate System and Linear Equations 334
7.2 Graphing Nonlinear Equations 349
7.3 Linear Inequalities in Two Variables 357
7.4 Distance and Slope 362
7.5 Determining the Equation of a Line 374
Chapter 7 Summary 387
Chapter 7 Review Problem Set 388
Chapter 7 Test 390
8- Functions 391
8.1 Concept of a Function 392
8.2 Linear Functions and Applications 402
8.3 Quadratic Functions 410
8.4 More Quadratic Functions and Applications 421
8.5 Transformations of Some Basic Curves 431
8.6 Combining Functions 442
8.7 Direct and Inverse Variation 450
Chapter 8 Summary 459
Chapter 8 Review Problem Set 460
Chapter 8 Test 462
9- Polynomial and Rational Functions 463
9.1 Synthetic Division 464
9.2 Remainder and Factor Theorems 469
9.3 Polynomial Equations 474
9.4 Graphing Polynomial Functions 486
9.5 Graphing Rational Functions 497
9.6 More on Graphing Rational Functions 508
Chapter 9 Summary 517
Chapter 9 Review Problem Set 518
9- Test 519
10- Exponential and Logarithmic Functions 520
10.1 Exponents and Exponential Functions 521
10.2 Applications of Exponential Functions 529
10.3 Inverse Functions 541
10.4 Logarithms 552
10.5 Logarithmic Functions 562
10.6 Exponential Equations, Logarithmic Equations, and Problem Solving 570
Chapter 10 Summary 580
Chapter 10 Review Problem Set 581
Chapter 10 Test 584
Cumulative Review Problem Set (Chapters 1–10) 585
11- Systems of Equations 589
11.1 Systems of Two Linear Equations in Two Variables 590
11.2 Systems of Three Linear Equations in Three Variables 602
11.3 Matrix Approach to Solving Linear Systems 609
11.4 Determinants 620
11.5 Cramer’s Rule 630
11.6 Partial Fractions (optional) 637
Chapter 11 Summary 643
Chapter 11 Review Problem Set 644
Chapter 11 Test 646
12- Algebra of Matrices 648
12.1 Algebra of 2x2 Matrices 649
12.2 Multiplicative Inverses 655
12.3 mxn Matrices 662
12.4 Systems of Linear Inequalities: Linear Programming 671
Chapter 12 Summary 682
Chapter 12 Review Problem Set 683
Chapter 12 Test 685
13- Conic Sections 686
13.1 Circles 687
13.2 Parabolas 695
13.3 Ellipses 704
13.4 Hyperbolas 713
13.5 Systems Involving Nonlinear Equations 724
Chapter 13 Summary 731
Chapter 13 Review Problem Set 732
Chapter 13 Test 733
14- Sequences and Mathematical Induction 734
14.1 Arithmetic Sequences 735
14.2 Geometric Sequences 743
14.3 Another Look at Problem Solving 752
14.4 Mathematical Induction 758
Chapter 14 Summary 764
Chapter 14 Review Problem Set 765
Chapter 14 Test 767
15- Counting Techniques, Probability, and the Binomial Theorem 768
15.1 Fundamental Principle of Counting 769
15.2 Permutations and Combinations 775
15.3 Probability 784
15.4 Some Properties of Probability: Expected Values 790
15.5 Conditional Probability: Dependent and Independent Events 801
15.6 Binomial Theorem 810
Chapter 15 Summary 815
Chapter 15 Review Problem Set 816
Chapter 15 Test 818
Appendix A: Prime Numbers and Operations with Fractions 819
Answers to Odd-Numbered Problems and All Chapter Review,
Chapter Test, Cumulative Review, and Appendix A Problems 831
Answers to Selected Even-Numbered Problems 881
Index I-1
COLLEGE STUDENTS
Jerome E. Kaufmann
Karen L. Schwitters
Seminole Community College
CONTENTS
1- Basic Concepts and Properties 1
1.1 Sets, Real Numbers, and Numerical Expressions 2
1.2 Operations with Real Numbers 11
1.3 Properties of Real Numbers and the Use of Exponents 22
1.4 Algebraic Expressions 30
Chapter 1 Summary 40
Chapter 1 Review Problem Set 41
Chapter 1 Test 43
2- Equations, Inequalities, and Problem Solving 44
2.1 Solving First-Degree Equations 45
2.2 Equations Involving Fractional Forms 53
2.3 Equations Involving Decimals and Problem Solving 61
2.4 Formulas 69
2.5 Inequalities 80
2.6 More on Inequalities and Problem Solving 87
2.7 Equations and Inequalities Involving Absolute Value 96
Chapter 2 Summary 103
Chapter 2 Review Problem Set 104
Chapter 2 Test 107
3- Polynomials 108
3.1 Polynomials: Sums and Differences 109
3.2 Products and Quotients of Monomials 115
3.3 Multiplying Polynomials 122
3.4 Factoring: Use of the Distributive Property 129
3.5 Factoring: Difference of Two Squares and Sum or Difference
of Two Cubes 137
3.6 Factoring Trinomials 143
3.7 Equations and Problem Solving 151
4- Rational Expressions 165
4.1 Simplifying Rational Expressions 166
4.2 Multiplying and Dividing Rational Expressions 172
4.3 Adding and Subtracting Rational Expressions 177
4.4 More on Rational Expressions and Complex Fractions 185
4.5 Dividing Polynomials 195
4.6 Fractional Equations 201
4.7 More Fractional Equations and Applications 209
Chapter 4 Summary 220
Chapter 4 Review Problem Set 221
Chapter 4 Test 223
5- Exponents and Radicals 224
5.1 Using Integers as Exponents 225
5.2 Roots and Radicals 232
5.3 Combining Radicals and Simplifying Radicals That
Contain Variables 244
5.4 Products and Quotients Involving Radicals 250
5.5 Equations Involving Radicals 256
5.6 Merging Exponents and Roots 261
5.7 Scientific Notation 268
Chapter 5 Summary 274
Chapter 5 Review Problem Set 275
Chapter 5 Test 277
6- Quadratic Equations and Inequalities 278
6.1 Complex Numbers 279
6.2 Quadratic Equations 287
6.3 Completing the Square 295
6.4 Quadratic Formula 300
6.5 More Quadratic Equations and Applications 308
6.6 Quadratic and Other Nonlinear Inequalities 320
Chapter 6 Summary 327
Chapter 6 Review Problem Set 328
Chapter 6 Test 330
Cumulative Review Problem Set (Chapters 1– 6) 331
7- Linear Equations and Inequalities in Two Variables 333
7.1 Rectangular Coordinate System and Linear Equations 334
7.2 Graphing Nonlinear Equations 349
7.3 Linear Inequalities in Two Variables 357
7.4 Distance and Slope 362
7.5 Determining the Equation of a Line 374
Chapter 7 Summary 387
Chapter 7 Review Problem Set 388
Chapter 7 Test 390
8- Functions 391
8.1 Concept of a Function 392
8.2 Linear Functions and Applications 402
8.3 Quadratic Functions 410
8.4 More Quadratic Functions and Applications 421
8.5 Transformations of Some Basic Curves 431
8.6 Combining Functions 442
8.7 Direct and Inverse Variation 450
Chapter 8 Summary 459
Chapter 8 Review Problem Set 460
Chapter 8 Test 462
9- Polynomial and Rational Functions 463
9.1 Synthetic Division 464
9.2 Remainder and Factor Theorems 469
9.3 Polynomial Equations 474
9.4 Graphing Polynomial Functions 486
9.5 Graphing Rational Functions 497
9.6 More on Graphing Rational Functions 508
Chapter 9 Summary 517
Chapter 9 Review Problem Set 518
9- Test 519
10- Exponential and Logarithmic Functions 520
10.1 Exponents and Exponential Functions 521
10.2 Applications of Exponential Functions 529
10.3 Inverse Functions 541
10.4 Logarithms 552
10.5 Logarithmic Functions 562
10.6 Exponential Equations, Logarithmic Equations, and Problem Solving 570
Chapter 10 Summary 580
Chapter 10 Review Problem Set 581
Chapter 10 Test 584
Cumulative Review Problem Set (Chapters 1–10) 585
11- Systems of Equations 589
11.1 Systems of Two Linear Equations in Two Variables 590
11.2 Systems of Three Linear Equations in Three Variables 602
11.3 Matrix Approach to Solving Linear Systems 609
11.4 Determinants 620
11.5 Cramer’s Rule 630
11.6 Partial Fractions (optional) 637
Chapter 11 Summary 643
Chapter 11 Review Problem Set 644
Chapter 11 Test 646
12- Algebra of Matrices 648
12.1 Algebra of 2x2 Matrices 649
12.2 Multiplicative Inverses 655
12.3 mxn Matrices 662
12.4 Systems of Linear Inequalities: Linear Programming 671
Chapter 12 Summary 682
Chapter 12 Review Problem Set 683
Chapter 12 Test 685
13- Conic Sections 686
13.1 Circles 687
13.2 Parabolas 695
13.3 Ellipses 704
13.4 Hyperbolas 713
13.5 Systems Involving Nonlinear Equations 724
Chapter 13 Summary 731
Chapter 13 Review Problem Set 732
Chapter 13 Test 733
14- Sequences and Mathematical Induction 734
14.1 Arithmetic Sequences 735
14.2 Geometric Sequences 743
14.3 Another Look at Problem Solving 752
14.4 Mathematical Induction 758
Chapter 14 Summary 764
Chapter 14 Review Problem Set 765
Chapter 14 Test 767
15- Counting Techniques, Probability, and the Binomial Theorem 768
15.1 Fundamental Principle of Counting 769
15.2 Permutations and Combinations 775
15.3 Probability 784
15.4 Some Properties of Probability: Expected Values 790
15.5 Conditional Probability: Dependent and Independent Events 801
15.6 Binomial Theorem 810
Chapter 15 Summary 815
Chapter 15 Review Problem Set 816
Chapter 15 Test 818
Appendix A: Prime Numbers and Operations with Fractions 819
Answers to Odd-Numbered Problems and All Chapter Review,
Chapter Test, Cumulative Review, and Appendix A Problems 831
Answers to Selected Even-Numbered Problems 881
Index I-1
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