Solutions Manual for A Survey of Mathematics with Applications 9th Edition by Allen Angel (Author), Christine Abbott (Author), Dennis Runde (Author), Tamsen Herrick (Author) Updated 2026/2027

SOLUTIONS
MANUAL
l




TAMSEN HERRICK l




A SURVEY OF MATHEMATICS
l l l




WITH A PPLICATIONS
l l




NINTH EDITION l




By

Allen R. Angel l l




l ChristineD.Abbott l l




Dennis C. Runde
l l l

, Table of Contents l l




CHAPTER 1 CRITICAL THINKING SKILLS
l l l


1.1 Inductive Reasoning 1 l


1.2 Estimation 3
1.3 Problem Solving 5 l


Review Exercises 12
l l


Chapter Test 14
l l


Group Projects 16
l l




CHAPTER 2 SETS
l


2.1 Set Concepts 17
l


2.2 Subsets 19
2.3 Venn Diagrams and Set Operations
l 21 l l l


2.4 Venn Diagrams With Three Sets and Verification of Equality of Sets
l l l l l l l l l l 27
2.5 Applications of Sets 37 l l


2.6 Infinite Sets 40 l l


Review Exercises 41 l


Chapter Test 44 l


Group Projects 46 l




CHAPTER 3 LOGIC
l


3.1 Statements and Logical Connectives 47 l l l


3.2 Truth Tables for Negation, Conjunction, and Disjunction
l l l l l l 49
3.3 Truth Tables for the Conditional and Biconditional
l 56 l l l l l


3.4 Equivalent Statements 64 l


3.5 Symbolic Arguments 73 l


3.6 Euler Diagrams and Syllogistic Arguments
l 80 l l l


3.7 Switching Circuits 82 l


Review Exercises 85
l l


Chapter Test 92
l l


Group Projects 94
l l




CHAPTER 4 SYSTEMS OF NUMERATION
l l l


4.1 Additive, Multiplicative, and Ciphered Systems of Numeration
l l l l l l 95
4.2 Place-Value or Positional-Value Numeration Systems 98 l l l l


4.3 Other Bases 101 l


4.4 Computation in Other Bases 108 l l l


4.5 Early Computational Methods
l 111 l


Review Exercises 115 l


Chapter Test 119 l


Group Projects 121 l




CHAPTER 5 NUMBER THEORY AND THE REAL NUMBER SYSTEM
l l l l l l l


5.1 Number Theory 123 l


5.2 The Integers 127
l


5.3 The Rational Numbers 129
l l


5.4 The Irrational Numbers and the Real Number System
l 135 l l l l l l


5.5 Real Numbers and Their Properties
l 138 l l l


5.6 Rules of Exponents and Scientific Notation
l 140
l l l l


5.7 Arithmetic and Geometric Sequences 144 l l l


5.8 Fibonacci Sequence 148 l


Review Exercises 150
l l


Chapter Test 153
l l


Group Projects 153 l

,CHAPTER 6 ALGEBRA, GRAPHS, AND FUNCTIONS
l l l l


6.1 Order of Operations 155
l l


6.2 Linear Equations in One Variable
l 157 l l l


6.3 Formulas 166
6.4 Applications of Linear Equations in One Variable 176 l l l l l l


6.5 Variation 182
6.6 Linear Inequalities 187 l


6.7 Graphing Linear Equations 193 l l


6.8 Linear Inequalities in Two Variables
l 203 l l l


6.9 Solving Quadratic Equations by Using Factoring and by Using
l l l l l l l l


the Quadratic Formula 209
l l l


6.10 Functions and Their Graphs 215 l l l


Review Exercises 226 l


Chapter Test 238 l


Group Projects 241 l




CHAPTER 7 SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES
l l l l l l


7.1 Systems of Linear Equations 243 l l l


7.2 Solving Systems of Equations by the Substitution and Addition
l l l l l l l l


Methods 250
l


7.3 Matrices 257
7.4 Solving Systems of Equations by Using Matrices
l 265 l l l l l


7.5 Systems of Linear Inequalities 268 l l l


7.6 Linear Programming 271 l


Review Exercises 275
l l


Chapter Test 280
l l


Group Projects 283 l




CHAPTER 8 THE METRIC SYSTEM
l l l


8.1 Basic Terms and Conversions Within the Metric System
l 285 l l l l l l


8.2 Length, Area, and Volume 286 l l l


8.3 Mass and Temperature
l 288 l


8.4 Dimensional Analysis and Conversions to and from the Metric System l l l l l l l l l 290
Review Exercises 295 l


Chapter Test 297 l


Group Projects 298 l




CHAPTER 9 GEOMETRY
l


9.1 Points, Lines, Planes, and Angles
l 301 l l l


9.2 Polygons 305
9.3 Perimeter and Area 310 l l


9.4 Volume and Surface Area 314 l l l


9.5 Transformational Geometry, Symmetry, and Tessellations l l l l 318
9.6 Topology 322
9.7 Non-Euclidean Geometry and Fractal Geometry 323 l l l l


Review Exercises 325 l


Chapter Test 329 l


Group Projects 330 l




CHAPTER 10 MATHEMATICAL SYSTEMS
l l


10.1 Groups 331
10.2 Finite Mathematical Systems 332
l l


10.3 Modular Arithmetic 336 l


Review Exercises 340
l l


Chapter Test 343
l l


Group Projects 345 l

, CHAPTER 11 CONSUMER MATHEMATICS
l l


11.1 Percent 347
11.2 Personal Loans and Simple Interest 350 l l l l


11.3 Compound Interest 353 l


11.4 Installment Buying 356 l


11.5 Buying a House with a Mortgage 363 l l l l l


11.6 Ordinary Annuities, Sinking Funds, l l l


and Retirement Investments
l l 367 l


Review Exercises 368
l l


Chapter Test 372 l


Group Projects 373 l




CHAPTER 12 PROBABILITY
l


12.1 The Nature of Probability
l 375 l l


12.2 Theoretical Probability 376 l


12.3 Odds 379
12.4 Expected Value (Expectation) 382 l l


12.5 Tree Diagrams 386 l


12.6 Or and And Problems
l 390 l l


12.7 Conditional Probability 394 l


12.8 The Counting Principle and Permutations
l 397 l l l


12.9 Combinations 399
12.10 Solving Probability Problems by Using Combinationsl l l l l 402
12.11 Binomial Probability Formula 406 l l


Review Exercises 407 l


Chapter Test 410 l


Group Projects 412 l




CHAPTER 13 STATISTICS
l


13.1 Sampling Techniques 413 l


13.2 The Misuses of Statistics
l 413 l l


13.3 Frequency Distributions and Statistical Graphs l l l l 415
13.4 Measures of Central Tendency 423 l l l


13.5 Measures of Dispersion 427 l l


13.6 The Normal Curve 433
l l


13.7 Linear Correlation and Regression l 439 l l


Review Exercises 450 l


Chapter Test 455 l


Group Projects 457 l




CHAPTER 14 GRAPH THEORY
l l


14.1 Graphs, Paths, and Circuits 459 l l l


14.2 Euler Paths and Euler Circuits
l 462 l l l


14.3 Hamilton Paths and Hamilton Circuits l l l l 466
14.4 Trees 472
Review Exercises 483 l


Chapter Test 488 l


Group Projects 489 l




CHAPTER 15 VOTING AND APPORTIONMENT
l l l


15.1 Voting Systems 491 l


15.2 Flaws of Voting 496 l l


15.3 Apportionment Methods 500 l


15.4 Flaws of Apportionment Methodsl506 l l


Review Exercises 510 l


Chapter Test 514 l