Introductory Technical Mathematics

Cover......Page 1
Half Title......Page 2
Title......Page 4
Statement......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 17
Section I: Fundamentals of General Mathematics......Page 23
1–1 Place Value......Page 24
1–2 Expanding Whole Numbers......Page 25
1–3 Estimating (Approximating)......Page 26
1–4 Addition of Whole Numbers......Page 27
1–5 Subtraction of Whole Numbers......Page 29
1–6 Problem Solving—Word Problem Practical Applications......Page 31
1–7 Adding and Subtracting Whole Numbers in Practical Applications......Page 32
1–8 Multiplication of Whole Numbers......Page 34
1–9 Division of Whole Numbers......Page 38
1–10 Multiplying and Dividing Whole Numbers in Practical Applications......Page 41
1–11 Combined Operations of Whole Numbers......Page 44
1–12 Combined Operations of Whole Numbers in Practical Applications......Page 46
Unit Exercise and Problem Review......Page 49
1–13 Computing with a Calculator: Whole Numbers......Page 53
1–14 Computing with a Spreadsheet: Whole Numbers......Page 57
2–1 Definitions......Page 63
2–2 Fractional Parts......Page 64
2–4 Equivalent Fractions......Page 65
2–6 Expressing Mixed Numbers as Improper Fractions......Page 66
2–7 Expressing Improper Fractions as Mixed Numbers......Page 67
2–9 Use of Common Fractions in Practical Applications......Page 68
2–10 Addition of Common Fractions......Page 70
2–11 Subtraction of Common Fractions......Page 75
2–12 Adding and Subtracting Common Fractions in Practical Applications......Page 78
2–13 Multiplication of Common Fractions......Page 82
2–14 Multiplying Common Fractions in Practical Applications......Page 86
2–15 Division of Common Fractions......Page 89
2–16 Dividing Common Fractions in Practical Applications......Page 92
2–17 Combined Operations with Common Fractions......Page 95
2–18 Combined Operations of Common Fractions in Practical Applications......Page 97
Unit Exercise and Problem Review......Page 99
2–19 Computing with a Calculator: Fractions and Mixed Numbers......Page 104
2–20 Computing with a Spreadsheet: Fractions and Mixed Numbers......Page 110
Introduction......Page 117
3–2 Reading Decimal Fractions......Page 118
3–4 Writing Decimal Fractions......Page 119
3–6 Expressing Common Fractions as Decimal Fractions......Page 120
3–7 Expressing Decimal Fractions as Common Fractions......Page 121
3–8 Expressing Decimal Fractions in Practical Applications......Page 122
3–9 Adding Decimal Fractions......Page 123
3–10 Subtracting Decimal Fractions......Page 124
3–11 Adding and Subtracting Decimal Fractions in Practical Applications......Page 125
3–12 Multiplying Decimal Fractions......Page 128
3–13 Multiplying Decimal Fractions in Practical Applications......Page 131
3–14 Dividing Decimal Fractions......Page 134
3–15 Dividing Decimal Fractions in Practical Applications......Page 136
3–16 Powers and Roots of Decimal Fractions......Page 139
3–17 Decimal Fraction Powers and Roots in Practical Applications......Page 142
3–18 Table of Decimal Equivalents......Page 145
3–19 Combined Operations of Decimal Fractions......Page 148
3–20 Combined Operations of Decimal Fractions in Practical Applications......Page 150
Unit Exercise and Problem Review......Page 154
3–21 Computing with a Calculator: Decimals......Page 161
3-22 Computing with a Spreadsheet: Decimal Fractions......Page 167
4–1 Description of Ratios......Page 174
4–2 Order of Terms of Ratios......Page 175
4–3 Description of Proportions......Page 177
4–4 Direct Proportions......Page 180
4–5 Inverse Proportions......Page 181
Unit Exercise and Problem Review......Page 184
5–1 Definition of Percent......Page 188
5–3 Expressing Common Fractions and Mixed Numbers as Percents......Page 189
5–4 Expressing Percents as Decimal Fractions......Page 190
5–6 Types of Simple Percent Problems......Page 191
5–7 Finding Percentage in Practical Applications......Page 194
5–8 Finding Percent (Rate) in Practical Applications......Page 196
5–9 Finding the Base in Practical Applications......Page 198
5–10 More Complex Percentage Practical Applications......Page 199
Unit Exercise and Problem Review......Page 202
6–1 Meaning of Signed Numbers......Page 205
6–2 The Number Line......Page 207
6–4 Absolute Value......Page 208
6–5 Addition of Signed Numbers......Page 209
6–6 Subtraction of Signed Numbers......Page 213
6–7 Multiplication of Signed Numbers......Page 214
6–8 Division of Signed Numbers......Page 215
6–9 Powers of Signed Numbers......Page 217
6–10 Roots of Signed Numbers......Page 220
6–11 Combined Operations of Signed Numbers......Page 223
6–12 Scientific Notation......Page 226
6–13 Engineering Notation......Page 232
Unit Exercise and Problem Review......Page 235
Section II:  Measurement......Page 241
7–1 Exact and Approximate (Measurement) Numbers......Page 242
7–2 Degree of Precision of Measuring Instruments......Page 243
7–3 Common Linear Measuring Instruments......Page 244
7–4 Degree of Precision of a Measurement Number......Page 245
7–6 Significant Digits......Page 246
7–7 Accuracy......Page 247
7–8 Accuracy in Multiplying and Dividing Measurement Numbers......Page 248
7–9 Absolute and Relative Error......Page 249
7–10 Tolerance (Linear)......Page 250
7–11 Unilateral and Bilateral Tolerance with Clearance and Interference Fits......Page 251
Unit Exercise and Problem Review......Page 254
8–1 Customary Linear Units......Page 259
8–2 Expressing Equivalent Units of Measure......Page 260
8–3 Arithmetic Operations with Compound Numbers......Page 263
8–4 Customary Linear Measure Practical Applications......Page 266
8–5 Customary Units of Surface Measure (Area)......Page 270
8–6 Customary Area Measure Practical Applications......Page 271
8–7 Customary Units of Volume (Cubic Measure)......Page 272
8–9 Customary Units of Capacity......Page 274
8–10 Customary Capacity Practical Applications......Page 275
8–11 Customary Units of Weight (Mass )......Page 276
8–12 Customary Weight Practical Applications......Page 277
8–13 Compound Units......Page 278
8–14 Compound Units Practical Applications......Page 279
Unit Exercise and Problem Review......Page 281
9–1 Metric Units of Linear Measure......Page 284
9–2 Expressing Equivalent Units within the Metric System......Page 286
9–4 Metric Linear Measure Practical Applications......Page 288
9–5 Metric Units of Surface Measure (Area)......Page 289
9–6 Arithmetic Operations with Metric Area Units......Page 291
9–8 Metric Units of Volume (Cubic Measure)......Page 292
9–10 Metric Volume Practical Applications......Page 294
9–11 Metric Units of Capacity......Page 295
9–12 Metric Capacity Practical Applications......Page 296
9–13 Metric Units of Weight (Mass)......Page 297
9–15 Compound Units......Page 298
9–16 Compound Units Practical Applications......Page 300
9–17 Metric Prefixes Applied to Very Large and Very Small Numbers......Page 301
9–18 Conversion Between Metric and Customary Systems......Page 304
Unit Exercise and Problem Review......Page 308
10–2 Reading Fractional Measurements......Page 311
10–3 Measurements that do not Fall on Rule Graduations......Page 313
10–4 Reading Decimal-Inch Measurements......Page 314
10–5 Reading Metric Measurements......Page 315
10–6 Vernier Calipers: Types and Description......Page 316
10–7 Reading Measurements on a Customary Vernier Caliper......Page 318
10–8 Reading Measurements on a Metric Vernier Caliper......Page 320
10–9 Reading Digital Calipers......Page 322
Unit Exercise and Problem Review......Page 325
11–1 Description of a Customary Outside Micrometer......Page 327
11–2 Reading a Customary Micrometer......Page 328
11–3 The Customary Vernier Micrometer......Page 329
11–4 Reading a Customary Vernier Micrometer......Page 330
11–6 Reading a Metric Micrometer......Page 332
11–7 The Metric Vernier Micrometer......Page 333
11–8 Reading a Metric Vernier Micrometer......Page 334
11–9 Reading Digital Micrometers......Page 336
Unit Exercise and Problem Review......Page 338
Section III: Fundamentals of Algebra......Page 341
12–1 Symbolism......Page 342
12–2 Algebraic Expressions......Page 343
12–3 Evaluation of Algebraic Expressions......Page 345
Unit Exercise and Problem Review......Page 350
13–1 Definitions......Page 353
13–2 Addition......Page 354
13–3 Subtraction......Page 356
13–4 Multiplication......Page 358
13–5 Division......Page 362
13–6 Powers......Page 366
13–7 Roots......Page 369
13–8 Removal of Parentheses......Page 372
13–9 Combined Operations......Page 373
13–10 Basic Structure of the Binary Numeration System......Page 374
Unit Exercise and Problem Review......Page 378
14–1 Expression of Equality......Page 383
14–2 Writing Equations from Word Statements......Page 384
14–3 Checking the Equation......Page 386
14–5 Solution of Equations by the Subtraction Principle of Equality......Page 388
14–6 Solution of Equations by the Addition Principle of Equality......Page 391
14–7 Solution of Equations by the Division Principle of Equality......Page 394
14–8 Solution of Equations by the Multiplication Principle of Equality......Page 396
14–9 Solution of Equations by the Root Principle of Equality......Page 399
14–10 Solution of Equations by the Power Principle of Equality......Page 401
Unit Exercise and Problem Review......Page 402
15–1 Equations Consisting of Combined Operations......Page 405
15–2 Solving for the Unknown in Formulas......Page 408
15–3 Substituting Values Directly in Given Formulas......Page 409
15–4 Rearranging Formulas......Page 412
Unit Exercise and Problem Review......Page 416
16–1 Description of the Cartesian (Rectangular) Coordinate System......Page 418
16–2 Graphing a Linear Equation......Page 419
16–3 Slope of a Linear Equation......Page 422
16–5 Point-Slope Equation of a Straight Line......Page 423
16–6 Determining an Equation, Given Two Points......Page 424
16–7 Describing a Straight Line......Page 425
Unit Exercise and Problem Review......Page 428
Introduction......Page 430
17–1 Graphical Method of Solving Systems of Equations......Page 431
17–2 Substitution Method of Solving Systems of Equations......Page 432
17–3 Addition or Subtraction Method of Solving Systems of Equations......Page 433
17–4 Types of Systems of Equations......Page 437
17–5 Determinants......Page 438
17–6 Cramer’s Rule......Page 439
17–7 Writing and Solving Systems of Equations from Word Statements, Number Problems, and Practical Applications......Page 440
Unit Exercise and Problem Review......Page 446
18–1 General or Standard Form of Quadratic Equations......Page 449
18–2 Incomplete Quadratic Equations (ax2 = c)......Page 450
18–3 Complete Quadratic Equations......Page 454
18–4 Practical Applications of Complete Quadratic Equations. Equations Given......Page 458
18–5 Word Problems Involving Complete Quadratic Equations. Equations Not Given......Page 464
Unit Exercise and Problem Review......Page 468
Section IV: Fundamentals of Plane Geometry......Page 471
19–1 Plane Geometry......Page 472
19–2 Axioms and Postulates......Page 473
19–3 Points and Lines......Page 476
Unit Exercise and Problem Review......Page 477
20–1 Units of Angular Measure......Page 478
20–2 Units of Angular Measure in Degrees, Minutes, and Seconds......Page 479
20–3 Expressing Degrees, Minutes, and Seconds as Decimal Degrees......Page 480
20–4 Expressing Decimal Degrees as Degrees, Minutes, and Seconds......Page 481
20–5 Arithmetic Operations on Angular Measure in Degrees, Minutes, and Seconds......Page 483
20–6 Simple Semicircular Protractor......Page 490
Unit Exercise and Problem Review......Page 494
21–2 Types of Angles......Page 497
21–3 Angles Formed by a Transversal......Page 498
21–4 Theorems and Corollaries......Page 500
Unit Exercise and Problem Review......Page 506
Introduction......Page 509
22–1 Types of Triangles......Page 510
22–2 Angles of a Triangle......Page 512
22–4 Isosceles Triangle Practical Applications......Page 516
22–5 Equilateral Triangle Practical Applications......Page 517
22–7 Pythagorean Theorem Practical Applications......Page 518
Unit Exercise and Problem Review......Page 521
23–1 Congruent Figures......Page 525
23–2 Similar Figures......Page 527
23–3 Practical Applications of Similar Triangles......Page 530
Unit Exercise and Problem Review......Page 536
24–1 Types of Polygons......Page 539
24–2 Types of Quadrilaterals......Page 541
24–3 Polygon Interior and Exterior Angles......Page 542
24–4 Practical Aplications of Polygon Interior and Exterior Angles......Page 543
24–5 Practical Applications of Trapezoid Median......Page 548
Unit Exercise and Problem Review......Page 550
25–1 Definitions......Page 553
25–2 Circumference Formula......Page 555
25–3 Arc Length Formula......Page 556
25–4 Radian Measure......Page 558
25–5 Circle Postulates......Page 561
25–6 Chords, Arcs, and Central Angles......Page 562
25–7 Practical Applications of Circle Chord Bisector......Page 563
25–8 Circle Tangents and Chord Segments......Page 566
25–10 Practical Applications of Tangents from a Common Point......Page 567
25–11 Angles Formed Inside and on a Circle......Page 570
25–12 Practical Applications of Inscribed Angles......Page 571
25–13 Practical Applications of Tangent and Chord......Page 572
25–14 Angles Outside a Circle......Page 574
25–15 Internally and Externally Tangent Circles......Page 576
25–16 Practical Applications of Internally Tangent Circles......Page 577
25–17 Practical Applications of Externally Tangent Circles......Page 578
Unit Exercise and Problem Review......Page 582
Section V: Geometric Figures: Areas and Volumes......Page 589
26–1 Areas of Rectangles......Page 590
26–2 Areas of Parallelograms......Page 594
26–3 Areas of Trapezoids......Page 598
26–4 Areas of Triangles Given the Base and Height......Page 601
26–5 Areas of Triangles Given Three Sides......Page 603
Unit Exercise and Problem Review......Page 607
27–1 Areas of Circles......Page 612
27–2 Ratio of Two Circles......Page 613
27–3 Areas of Sectors......Page 616
27–4 Areas of Segments......Page 618
27–5 Areas of Ellipses......Page 620
Unit Exercise and Problem Review......Page 622
28–2 Volumes of Prisms......Page 626
28–4 Volumes of Cylinders......Page 630
28–5 Computing Heights and Bases of Prisms and Cylinders......Page 632
28–6 Lateral Areas and Surface Areas of Right Prisms and Cylinders......Page 634
Unit Exercise and Problem Review......Page 637
29–1 Pyramids......Page 639
29–3 Volumes of Regular Pyramids and Right Circular Cones......Page 640
29–4 Computing Heights and Bases of Regular Pyramids and Right Circular Cones......Page 642
29–5 Lateral Areas and Surface Areas of Regular Pyramids and Right Circular Cones......Page 643
29–6 Frustums of Pyramids and Cones......Page 646
29–7 Volumes of Frustums of Regular Pyramids and Right Circular Cones......Page 647
29–8 Lateral Areas and Surface Areas of Frustums of Regular Pyramids and Right Circular Cones......Page 649
Unit Exercise and Problem Review......Page 653
30–1 Spheres......Page 655
30–3 Volume of a Sphere......Page 656
30–4 Volumes and Surface Areas of Composite Solid Figures......Page 658
Unit Exercise and Problem Review......Page 663
Section VI: Basic Statistics......Page 665
31–1 Types and Structure of Graphs......Page 666
31–2 Reading Bar Graphs......Page 667
31–3 Drawing Bar Graphs......Page 672
31–4 Drawing Bar Graphs with a Spreadsheet......Page 674
31–5 Circle Graphs......Page 679
31–6 Drawing Circle Graphs with a Spreadsheet......Page 683
31–7 Line Graphs......Page 685
31–8 Reading Line Graphs......Page 686
31–9 Reading Combined-Data Line Graphs......Page 688
31–11 Drawing Broken-Line Graphs......Page 692
31–12 Drawing Broken-Line Graphs with a Spreadsheet......Page 694
31–13 Drawing Straight-Line Graphs......Page 696
31–14 Drawing Curved-Line Graphs......Page 697
Unit Exercise and Problem Review......Page 701
32–1 Probability......Page 705
32–2 Independent Events......Page 707
32–3 Mean Measurement......Page 709
32–4 Other Average Measurements......Page 712
32–5 Quartiles and Percentiles......Page 713
32–6 Grouped Data......Page 716
32–7 Variance and Standard Deviation......Page 721
32–8 Statistical Process Control: X-Bar Charts......Page 727
32–9 Statistical Process Control: R Charts......Page 731
Unit Exercise and Problem Review......Page 735
Section VII: Fundamentals of Trigonometry......Page 737
33–1 Ratio of Right Triangle Sides......Page 738
33–2 Identifying Right Triangle Sides by Name......Page 739
33–3 Trigonometric Functions: Ratio Method......Page 740
33–5 Determining Functions of Given Angles and Determining Angles of Given Functions......Page 742
Unit Exercise and Problem Review......Page 748
34–1 Variation of Functions......Page 750
34–2 Functions of Complementary Angles......Page 752
34–3 Determining an Unknown Angle When Two Sides of a Right Triangle Are Known......Page 754
34–4 Determining an Unknown Side When an Acute Angle and One Side of a Right Triangle Are Known......Page 757
Unit Exercise and Problem Review......Page 760
35–1 Solving Problems Stated in Word Form......Page 762
35–2 Solving Problems Given in Picture Form That Require Auxiliary Lines......Page 767
35–3 Solving Complex Problems That Require Auxiliary Lines......Page 776
Unit Exercise and Problem Review......Page 786
36–1 Cartesian (Rectangular) Coordinate System......Page 790
36–2 Determining Functions of Angles in Any Quadrant......Page 791
36–3 Alternating Current Applications......Page 794
36–4 Determining Functions of Angles Greater Than 360°......Page 797
36–5 Instantaneous Voltage Related to Time Application......Page 799
36–6 Solving Oblique Triangles......Page 800
36–8 Solving Problems Given Two Angles and a Side, Using the Law of Sines......Page 801
36–9 Solving Problems Given Two Sides and an Angle Opposite One of the Given Sides, Using the Law of Sines......Page 803
36–11 Solving Problems Given Two Sides and the Included Angle, Using the Law of Cosines......Page 807
36–12 Law of Cosines (Given Three Sides)......Page 810
36–13 Solving Problems Given Three Sides, Using the Law of Cosines......Page 811
36–14 Practical Applications of Oblique Triangles......Page 815
Unit Exercise and Problem Review......Page 823
37–2 Description and Naming of Vectors......Page 828
37–3 Vector Ordered Pair Notation......Page 829
37–5 Adding Vectors......Page 830
37–6 Graphic Addition of Vectors......Page 832
37–7 Addition of Vectors Using Trigonometry......Page 836
37–8 General (Component Vector) Procedure for Adding Vectors Using Trigonometry......Page 842
Unit Exercise and Problem Review......Page 847
Appendix A: United States Customary and Metric Units of Measure......Page 851
Appendix B: Formulas for Areas (A) of Plane Figures......Page 853
Appendix C: Formulas for Volumes and Areas of Solid Figures......Page 854
Appendix D: Answers to Odd-Numbered Exercises......Page 855
Index......Page 893