This manual provides solutions to odd-numbered exercises in the exercise sets, the Extensions, and the Appendix exercises, as well as solutions for all the Chapter Test exercises. Chapter summaries review key points in the text, providing extra examples, and enumerate major topic objectives.
1 The Art of Problem Solving
1.1 Solving Problems by Inductive Reasoning
1.2 An Application of Inductive Reasoning: Number Patterns
1.3 Strategies for Problem Solving
1.4 Calculating, Estimating, and Reading Graphs
Extension: Using Writing to Learn About Mathematics
Collaborative Investigation: Discovering Patterns in Pascal’s Triangle
Chapter 1 Test
2 The Basic Concepts of Set Theory
2.1 Symbols and Terminology
2.2 Venn Diagrams and Subsets
2.3 Set Operations and Cartesian Products
2.4 Surveys and Cardinal Numbers
2.5 Infinite Sets and Their Cardinalities
Collaborative Investigation: Surveying the Members of your Class
Chapter 2 Test
3 Introduction to Logic
3.1 Statements and Quantifiers
3.2 Truth Tables and Equivalent Statements
3.3 The Conditional and Circuits
3.4 More on the Conditional
3.5 Analyzing Arguments with Euler Diagrams
Extension: Logic Problems and Sodoku
3.6 Analyzing Arguments with Truth Tables
Collaborative Investigation: Logic Problems and Sodoku Revisited
Chapter 3 Test
4 Numeration and Mathematical Systems
4.1 Historical Numeration Systems
4.2 Arithmetic in the Hindu-Arabic System
4.3 Conversion between Number Bases
4.4 Clock Arithmetic and Modular Systems
4.5 Properties of Mathematical Systems
4.6 Groups
Collaborative Investigation: A Perpetual Calendar Algorithm
Chapter 4 Test
5 Number Theory
5.1 Prime and Composite Numbers
5.2 Selected Topics from Number Theory
5.3 Greatest Common Factor and Least Common Multiple
Extension: Modern Cryptography
5.4 The Fibonacci Sequence and the Golden Ratio
Extension: Magic Squares
Collaborative Investigation: Investigating an Interesting Property of Number Squares
Chapter 5 Test
6 The Real Numbers and Their Representations
6.1 Real Numbers, Order, and Absolute Value
6.2 Operations, Properties, and Applications of Real Numbers
6.3 Rational Numbers and Decimal Representation
6.4 Irrational Numbers and Decimal Representation
6.5 Applications of Decimals and Percents
Extension: Complex Numbers
Collaborative Investigation: Budgeting to Buy a Car
Chapter 6 Test
7 The Basic Concepts of Algebra
7.1 Linear Equations
7.2 Applications of Linear Equations
7.3 Ratio, Proportion, and Variation
7.4 Linear Inequalities
7.5 Properties of Exponents and Scientific Notation
7.6 Polynomials and Factoring
7.7 Quadratic Equations and Applications
Collaborative Investigation: How Does Your Walking Rate Compare to That of Olympic Race-walkers?
Chapter 7 Test
8 Graphs, Functions, and Systems of Equations and Inequalities
8.1 The Rectangular Coordinate System and Circles
8.2 Lines and Their Slopes
8.3 Equations of Lines and Linear Models
8.4 An Introduction to Functions: Linear Functions, Applications, and Models
8.5 Quadratic Functions, Applications, and Models
8.6 Exponential and Logarithmic Functions, Applications, and Models
8.7 Systems of Equations and Applications
Extension: Using Matrix Row Operations to Solve Systems
8.8 Linear Inequalities, Systems, and Linear Programming
Collaborative Investigation: Living with AIDS
Chapter 8 Test
9 Geometry
9.1 Points, Lines, Planes, and Angles
9.2 Curves, Polygons, and Circles
Extension: Geometric Constructions
9.3 Perimeter, Area, and Circumference
9.4 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem
9.5 Space Figures, Volume, and Surface Area
9.6 Transformational Geometry
9.7 Non-Euclidean Geometry, Topology, and Networks
9.8 Chaos and Fractal Geometry
Collaborative Investigation: Generalizing the Angle Sum Concept
Chapter 9 Test
10 Trigonometry
10.1 Angles and Their Measures
10.2 Trigonometric Functions of Angles
10.3 Trigonometric Identities
10.4 Right Triangles and Function Values
10.5 Applications of Right Triangles
10.6 The Laws of Sines and Cosines: Area Formulas
Collaborative Investigation: Making a Point about Trigonometric Function Values
Chapter 10 Test
11 Counting Methods
11.1 Counting by Systematic Listing
11.2 Using the Fundamental Counting Principle
11.3 Using Permutations and Combinations
11.4 Using Pascal’s Triangle
11.5 Counting Problems Involving “Not” and “Or”
Collaborative Investigation: Solving a Traveling Salesman Problem
Chapter 11 Test
12 Probability
12.1 Basic Concepts
12.2 Events Involving “Not” and “Or”
12.3 Conditional Probability; Events Involving “And”
12.4 Binomial Probability
12.5 Expected Value
Extension: Estimating Probabilities by Simulation
Collaborative Investigation: Finding Empirical Values of π
Chapter 12 Test
13 Statistics
13.1 Frequency Distributions and Graphs
13.2 Measures of Central Tendency
13.3 Measures of Dispersion
13.4 Measures of Position
13.5 The Normal Distribution
Extension: How to Lie with Statistics
13.6 Regression and Correlation
Collaborative Investigation: Combining Sets of Data
Chapter 13 Test
14 Personal Financial Management
14.1 The Time Value of Money
Extension: Annuities
14.2 Installment Buying
14.3 Truth in Lending
14.4 The Costs and Advantages of Home Ownership
14.5 Investing
Collaborative Investigation: To Buy or to Rent?
Chapter 14 Test
15 Graph Theory
15.1 Basic Concepts
15.2 Euler Circuits
15.3 Hamilton Circuits and Algorithms
15.4 Minimum Spanning Trees
Collaborative Investigation: Finding the Number of Edges in a Complete Graph
Chapter 15 Test
16 Voting and Apportionment
16.1 The Possibilities of Voting
16.2 The Impossibilities of Voting
16.3 The Possibilities of Apportionment
16.4 The Impossibilities of Apportionment
Collaborative Investigation: Class Favorites, An Election Exploration
Chapter 16 Test