Preface VII
1 Basic Algebraic Operations 1
1.1 Numbers 2
1.2 Fundamental Operations of Algebra 6
1.3 Calculators and Approximate Numbers 12
1.4 Exponents and Unit Conversions 17
1.5 Scientific Notation 24
1.6 Roots and Radicals 27
1.7 Addition and Subtraction of Algebraic Expressions 29
1.8 Multiplication of Algebraic Expressions 33
1.9 Division of Algebraic Expressions 36
1.10 Solving Equations 39
1.11 Formulas and Literal Equations 43
1.12 Applied Word Problems 46
Key Formulas and Equations, Review Exercises, and Practice Test 50
2 Geometry 54
2.1 Lines and Angles 55
2.2 Triangles 58
2.3 Quadrilaterals 65
2.4 Circles 68
2.5 Measurement of Irregular Areas 72
2.6 Solid Geometric Figures 76
Key Formulas and Equations, Review Exercises, and Practice Test 80
3 Functions and Graphs 85
3.1 Introduction to Functions 86
3.2 More about Functions 89
3.3 Rectangular Coordinates 94
3.4 The Graph of a Function 96
3.5 Graphs on the Graphing Calculator 102
3.6 Graphs of Functions Defined by Tables of Data 107
Review Exercises and Practice Test 110
4 The Trigonometric Functions 113
4.1 Angles 114
4.2 Defining the Trigonometric Functions 117
4.3 Values of the Trigonometric Functions 120
4.4 The Right Triangle 124
4.5 Applications of Right Triangles 129
Key Formulas and Equations, Review Exercises, and Practice Test 134
5 Systems of Linear Equations; Determinants 140
5.1 Linear Equations and Graphs of Linear Functions 141
5.2 Systems of Equations and Graphical Solutions 147
5.3 Solving Systems of Two Linear Equations in Two Unknowns Algebraically 152
5.4 Solving Systems of Two Linear Equations in Two Unknowns by Determinants 159
5.5 Solving Systems of Three Linear Equations in Three Unknowns Algebraically 164
5.6 Solving Systems of Three Linear Equations in Three Unknowns by Determinants 169
Key Formulas and Equations, Review Exercises, and Practice Test 174
6 Factoring and Fractions 180
6.1 Factoring: Greatest Common Factor and Difference of Squares 181
6.2 Factoring Trinomials 186
6.3 The Sum and Difference of Cubes 193
6.4 Equivalent Fractions 195
6.5 Multiplication and Division of Fractions 200
6.6 Addition and Subtraction of Fractions 204
6.7 Equations Involving Fractions 210
Key Formulas and Equations, Review Exercises, and Practice Test 215
7 Quadratic Equations 219
7.1 Quadratic Equations; Solution by Factoring 220
7.2 Completing the Square 225
7.3 The Quadratic Formula 227
7.4 The Graph of the Quadratic Function 232
Key Formulas and Equations, Review Exercises, and Practice Test 237
8 Trigonometric Functions of Any Angle 240
8.1 Signs of the Trigonometric Functions 241
8.2 Trigonometric Functions of Any Angle 243
8.3 Radians 249
8.4 Applications of Radian Measure 253
Key Formulas and Equations, Review Exercises, and Practice Test 259
9 Vectors and Oblique Triangles 263
9.1 Introduction to Vectors 264
9.2 Components of Vectors 268
9.3 Vector Addition by Components 272
9.4 Applications of Vectors 277
9.5 Oblique Triangles, the Law of Sines 283
9.6 The Law of Cosines 290
Key Formulas and Equations, Review Exercises, and Practice Test 295
10 Graphs of the Trigonometric Functions 299
10.1 Graphs of y = a sin x and y = a cos x 300
10.2 Graphs of y = a sin bx and y = a cos bx 303
10.3 Graphs of y = a sin (bx + c) and y = a cos (bx + c) 306
10.4 Graphs of y = tan x, y = cot x, y = sec x, y = csc x 310
10.5 Applications of the Trigonometric Graphs 312
10.6 Composite Trigonometric Curves 315
Key Formulas and Equations, Review Exercises, and Practice Test 320
11 Exponents and Radicals 323
11.1 Simplifying Expressions with Integer Exponents 324
11.2 Fractional Exponents 328
11.3 Simplest Radical Form 332
11.4 Addition and Subtraction of Radicals 336
11.5 Multiplication and Division of Radicals 338
Key Formulas and Equations, Review Exercises, and Practice Test 342
12 Complex Numbers 345
12.1 Basic Definitions 346
12.2 Basic Operations with Complex Numbers 349
12.3 Graphical Representation of Complex Numbers 352
12.4 Polar Form of a Complex Number 354
12.5 Exponential Form of a Complex Number 356
12.6 Products, Quotients, Powers, and Roots of Complex Numbers 358
12.7 An Application to Alternating-current (ac) Circuits 364
Key Formulas and Equations, Review Exercises, and Practice Test 370
13 Exponential and Logarithmic Functions 373
13.1 Exponential Functions 374
13.2 Logarithmic Functions 376
13.3 Properties of Logarithms 380
13.4 Logarithms to the Base 10 385
13.5 Natural Logarithms 388
13.6 Exponential and Logarithmic Equations 391
13.7 Graphs on Logarithmic and Semilogarithmic Paper 395
Key Formulas and Equations, Review Exercises, and Practice Test 400
14 Additional Types of Equations and Systems of Equations 403
14.1 Graphical Solution of Systems of Equations 404
14.2 Algebraic Solution of Systems of Equations 407
14.3 Equations in Quadratic Form 411
14.4 Equations with Radicals 414
Review Exercises and Practice Test 418
15 Equations of Higher Degree 420
15.1 The Remainder and Factor Theorems; Synthetic Division 421
15.2 The Roots of an Equation 426
15.3 Rational and Irrational Roots 431
Key Formulas and Equations, Review Exercises, and Practice Test 436
16 Matrices; Systems of Linear Equations 439
16.1 Matrices: Definitions and Basic Operations 440
16.2 Multiplication of Matrices 444
16.3 Finding the Inverse of a Matrix 449
16.4 Matrices and Linear Equations 453
16.5 Gaussian Elimination 457
16.6 Higher-order Determinants 461
Key Formulas and Equations, Review Exercises, and Practice Test 466
17 Inequalities 470
17.1 Properties of Inequalities 471
17.2 Solving Linear Inequalities 475
17.3 Solving Nonlinear Inequalities 480
17.4 Inequalities Involving Absolute Values 486
17.5 Graphical Solution of Inequalities with Two Variables 489
17.6 Linear Programming 492
Key Formulas and Equations, Review Exercises, and Practice Test 496
18 Variation 499
18.1 Ratio and Proportion 500
18.2 Variation 504
Key Formulas and Equations, Review Exercises, and Practice Test 510
19 Sequences and the Binomial Theorem 514
19.1 Arithmetic Sequences 515
19.2 Geometric Sequences 519
19.3 Infinite Geometric Series 522
19.4 The Binomial Theorem 526
Key Formulas and Equations, Review Exercises, and Practice Test 531
20 Additional Topics in Trigonometry 535
20.1 Fundamental Trigonometric Identities 536
20.2 The Sum and Difference Formulas 542
20.3 Double-Angle Formulas 547
20.4 Half-Angle Formulas 551
20.5 Solving Trigonometric Equations 554
20.6 The Inverse Trigonometric Functions 558
Key Formulas and Equations, Review Exercises, and Practice Test 564
21 Plane Analytic Geometry 568
21.1 Basic Definitions 569
21.2 The Straight Line 573
21.3 The Circle 579
21.4 The Parabola 584
21.5 The Ellipse 588
21.6 The Hyperbola 593
21.7 Translation of Axes 599
21.8 The Second-degree Equation 602
21.9 Rotation of Axes 605
21.10 Polar Coordinates 609
21.11 Curves in Polar Coordinates 612
Key Formulas and Equations, Review Exercises, and Practice Test 616
22 Introduction to Statistics 621
22.1 Graphical Displays of Data 622
22.2 Measures of Central Tendency 626
22.3 Standard Deviation 630
22.4 Normal Distributions 633
22.5 Statistical Process Control 637
22.6 Linear Regression 642
22.7 Nonlinear Regression 647
Key Formulas and Equations, Review Exercises, and Practice Test 650
Appendix A Solving Word Problems A.1
Appendix B Units of Measurement A.2
Photo Credits A.4
Answers to Odd-Numbered Exercises and Chapter Review Exercises B.1
Solutions to Practice Test Problems C.1
Index of Applications D.1
Index E.1
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