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Chapter 1 Problem Solving 1
1-1 Introduction 1
How to Use This Chapter 1
Background 2
Chapter Objectives 2
Introductory Problem 2
1-2 Problem-Solving Concepts 4
Polya’s Four Phases 4
Rubinstein’s Anatomy of a Problem 5
Developing the Knack 8
Use It or Lose It 8
Choosing an Approach 9
Avoiding Conceptual Boxes 9
Problem-Solving Analogy 10
Take a Walk 11
1-3 The IPO Method 12
The IPO Worksheet 14
Applying the IPO Method 14
Problem Statement Section 17
Output Section 19
Input Section 21
Process Section 23
Solution Section 31
Check Section 33
1-4 Problem Solving with the IPO Method 35
Tips on Using the IPO Method 35
Example Problems 37
1-5 Study Materials 44
Chapter Summary 44
Review Questions 44
Problem Solutions 45
Chapter 2 Exponents 47
2-1 Introduction 47
How to Use This Chapter 47
Background 47
Chapter Objectives 47
Introductory Problem 48
2-2 Squares and Square Roots 49
Squares 49
Square Roots 50
2-3 Powers and Exponents 58
Powers 58
Rules of Exponents 60
Reciprocals and Negative Exponents 65
Roots and Fractional Exponents 69
Exponent Rules Summary 72
2-4 Problem Solving with Exponents 74
Scientific Notation 74
Exponential Curiosities 77
2-5 Study Materials 80
Chapter Summary 80
Review Questions 80
Problem Solutions 81
Chapter 3 Number Systems 83
3-1 Introduction 83
How to Use This Chapter 83
Background 83
Chapter Objectives 84
Introductory Problem 84
3-2 How Number Systems Work 85
Several Examples 85
The Decimal Number System 85
3-3 The Binary Number System 87
Binary Basics 87
Converting Binary to Decimal 88
Converting Decimal to Binary 91
3-4 The Hexadecimal Number System 93
Hexadecimal Basics 93
Converting Hexadecimal to Decimal 94
Converting Decimal to Hexadecimal 96
Converting Hexadecimal to Binary 98
Converting Binary to Hexadecimal 100
3-5 Problem Solving with Number Systems 102
Representing Numbers in Computer Memory 102
Memory Addressing in Computers 107
3-6 Study Materials 111
Chapter Summary 111
Review Questions 113
Problem Solutions 113
Chapter 4 Unit Analysis 115
4-1 Introduction 115
How to Use This Chapter 115
Background 115
Chapter Objectives 116
Introductory Problem 116
4-2 Types of Units 117
Physical Quantities 117
Simple Units 117
Composite Units 117
Rates 118
Conversion Factors 118
Units in Equations 118
Derived Units 119
Hidden Units 120
Weights vs. Mass 120
4-3 Unit Conversions 122
Equivalence Expressions and Conversion Factors 122
Conversion Examples 123
4-4 Prefixes 127
Decimal Prefixes 127
Binary Prefixes 127
Changing Prefixes 130
4-5 Problem Solving with Units 136
Problems with Several Conversion Factors 136
Unit Analysis Using the IPO Worksheet 139
4-6 Study Materials 160
Chapter Summary 160
Review Questions 161
Problem Solutions 161
Chapter 5 A Little Algebra 163
5-1 Introduction 163
How to Use This Chapter 163
Background 163
Chapter Objectives 164
Introductory Problem 164
5-2 Algebraic Equations 165
Components of an Equation 165
Solving Equations 169
Ratio Equations 170
Simple Equations with Two Variables 173
5-3 Problem Solving with Algebra 176
Translating Words into Equations 176
Percents 181
Percent Change 183
Proportions 186
5-4 Study Materials 188
Chapter Summary 188
Review Questions 189
Problem Solutions 189
Chapter 6 Graphing 191
6-1 Introduction 191
How to Use This Chapter 191
Background 191
Chapter Objectives 192
Introductory Problem 192
6-2 Spreadsheet Charts 194
Data Series 194
Pie Charts 194
Bar Charts 195
Line Charts 196
x-y Charts 196
6-3 Graphing Equations 198
Rectangular Coordinate System 198
The Slope-Intercept Form of a Linear Equation 203
Solving Two Linear Equations 209
6-4 Problem Solving with Graphing 211
The Shortest Distance Between Two Points 211
Computer Graphing Coordinates 215
6-5 Study Materials 217
Chapter Summary 217
Review Questions 218
Problem Solutions 219
Chapter 7 Computer Programming Concepts 223
7-1 Introduction 223
How to Use This Chapter 223
Background 224
Chapter Objectives 224
Introductory Problem 224
7-2 Beginning Definitions 227
What Is a Computer? 227
Computer Variables 227
Arithmetic and Logic 229
7-3 A Simple Programming Language 231
INPUT Statement 231
OUTPUT Statement 232
LET Statement 233
IF-THEN-ELSE Statement 234
LOOP Statement 236
7-4 Building and Checking Simple Programs 241
Important Assignment Tasks 241
Desk Checking 247
7-5 Problem Solving with Computer Programs 250
Evolution of a Simple Program 250
7-6 Study Materials 257
Chapter Summary 257
Review Questions 257
Problem Solutions 258
Chapter 8 Computer Logic 261
8-1 Introduction 261
How to Use This Chapter 261
Background 261
Chapter Objectives 262
Introductory Problem 262
8-2 Operators and Expressions 263
Relational Operators 263
Conditional Expressions 265
Logical Operators 266
Combined Expressions 269
Removing NOTs 273
8-3 Problem Solving with Computer Logic 279
Testing Ranges 279
Boolean Variables and Flags 282
8-4 Study Materials 288
Chapter Summary 288
Review Questions 289
Problem Solutions 289
Chapter 9 Structured Program Design 291
9-1 Introduction 291
How to Use This Chapter 291
Background 291
Chapter Objectives 293
Introductory Problem 293
9-2 Algorithm Design Tools 295
Algorithms 295
IPO Charts 296
Pseudocode 299
Flowcharts 300
9-3 Program Design Concepts 310
Background 310
Top-Down Development 310
Modular Design 310
The Structure Theorem 311
Beyond Structured Programming 312
9-4 Problem Solving with Structured Design 314
Program Development 314
Modular Design 314
9-5 Study Materials 322
Chapter Summary 322
Review Questions 322
Problem Solutions 323
Appendix A Arithmetic Review 327
A-1 Introduction 327
How to Use This Appendix 327
Background 327
Self-Test 328
A-2 Arithmetic Operations 329
A-3 Real Numbers 332
The Number Line 332
Other Definitions 335
Properties of Numbers 338
A-4 Manipulating Fractions 341
A-5 Decimal Numbers 346
Positional Notation 346
Significant Digits and Rounding 346
Percents, Decimals, and Fractions 352
A-6 Problem Solving with Arithmetic 356
Averages 356
A-7 Study Materials 361
Problem Solutions 361
Appendix B More Algebra 363
B-1 Introduction 363
How to Use This Appendix 363
Background 363
Introductory Problem 363
B-2 Simultaneous Linear Equations 364
Solving Linear Equations Using Algebra 364
B-3 Problem Solving with Algebra 368
Time-Rate-Distance Problems 368
Linear Interpolation 374
B-4 Study Materials 380
Problem Solutions 380
Appendix C Geometry 381
C-1 Introduction 381
How to Use This Appendix 381
Background 381
Introductory Problem 382
C-2 Beginning Definitions 383
C-3 Triangles 385
Right Triangles 385
Similar Triangles 388
C-4 Circles and Ellipses 390
Circles 390
The Value of Pi 390
Ellipses 390
C-5 Other Plane Figures 393
C-6 Solid Figures 396
C-7 Problem Solving with Geometry 399
C-8 Study Materials 406
Problem Solutions 406
Glossary 407
Index 419