TOC & Index
Browse:
Topical Outline
Table of Contents
Index
Page
Topic
0
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Chapter 1: Calculation
0
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Chapter Opener
0
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Chapter Opener
1
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Chapter Opener
2
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1.1 Order of Operations & Formulas
2
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Example 1 − Using Order of Operations
3
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Example 2 − Using Order of Operations
4
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Example 3 − Using A Calculator
5
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Example 4 − Buying Floor Tiles
6
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Example 5 − Using the Distance Formula
7
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Example 6 − Comparing Job Offers
8
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Exercises for Examples 1 & 2
9
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Exercises for Examples 3 & 4
10
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Exercises for Examples 5 & 6
11
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Extending Concepts Exercises
12
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1.2 Rounding & Calculators
12
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Example 1 − Rounding Numbers in Context
13
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Example 2 − Comparing Annual Fuel Cost
14
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Example 3 − Describing Large and Small Numbers
15
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Example 4 − Comparing Hard Drive Storage
16
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Example 5 − Estimating the Accuracy of Measurements
17
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Example 6 − Writing Significant Digits
18
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Exercises for Examples 1 & 2
19
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Exercises for Examples 3 & 4
20
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Exercises for Examples 5 & 6
21
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Extending Concepts Exercises
22
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1.1−1.2 Quiz
22
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1.1−1.2 Quiz
23
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Chapter Project
23
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Project: Finding Patterns in Nature
24
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1.3 Using Percent
24
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Example 1 − Finding a Percent of a Number
25
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Example 2 − Finding Percents
26
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Example 3 − Comparing Two Numbers Using Percent
27
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Example 4 − Comparing Two Numbers Using Percent
28
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Example 5 − Using Percent to Describe an Increase
29
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Example 6 − Using Percent to Describe an Increase
30
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Exercises for Examples 1 & 2
31
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Exercises for Examples 3 & 4
32
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Exercises for Examples 5 & 6
33
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Extending Concepts Exercises
34
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1.4 Units & Conversions
34
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Example 1 − Using Unit Analysis
35
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Example 2 − Using Unit Analysis
36
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Example 3 − Converting Units
37
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Example 4 − Converting Units
38
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Example 5 − Converting Units
39
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Example 6 − Converting Temperature Units
40
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Exercises for Examples 1 & 2
41
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Exercises for Examples 3 & 4
42
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Exercises for Examples 5 & 6
43
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Extending Concepts Exercises
44
+
1.3−1.4 Quiz
44
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1.3−1.4 Quiz
45
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Chapter Summary
45
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Chapter Summary
46
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Chapter Review Exercises
46
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Review Exercises for Section 1.1
47
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Review Exercises for Section 1.2
48
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Review Exercises for Section 1.3
49
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Review Exercises for Section 1.4
50
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Chapter 2: Consumption
50
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Chapter Opener
50
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Chapter Opener
51
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Chapter Opener
52
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2.1 Unit Prices
52
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Example 1 − Finding a Unit Price
53
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Example 2 − Analyzing a Unit Price
54
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Example 3 − Comparing Unit Prices
55
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Example 4 − Comparing Unit Prices
56
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Example 5 − Finding the Annual Savings
57
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Example 6 − Eating In or Eating Out?
58
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Exercises for Examples 1 & 2
59
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Exercises for Examples 3 & 4
60
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Exercises for Examples 5 & 6
61
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Extending Concepts Exercises
62
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2.2 Markup & Discount
62
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Example 1 − Finding a Markup Percent
63
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Example 2 − Finding a Markup Percent
64
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Example 3 − Using Discounts and Markup
65
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Example 4 − Buying Generic Prescription Drugs
66
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Example 5 − Calculating Multiple Discounts
67
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Example 6 − Using Promotional Codes
68
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Exercises for Examples 1 & 2
69
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Exercises for Examples 3 & 4
70
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Exercises for Examples 5 & 6
71
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Extending Concepts Exercises
72
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2.1−2.2 Quiz
72
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2.1−2.2 Quiz
73
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Chapter Project
73
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Project: How Should I Exchange Currency?
74
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2.3 Consumption Taxes
74
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Example 1 − Finding Sales Tax
75
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Example 2 − Finding a Sales Tax Rate
76
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Example 3 − Estimating Excise Tax
77
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Example 4 − Finding Changes in Excise Taxes
78
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Example 5 − Comparing Sales Tax and Value-Added Tax
79
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Example 6 − Comparing Tax Revenue Sources
80
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Exercises for Examples 1 & 2
81
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Exercises for Examples 3 & 4
82
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Exercises for Examples 5 & 6
83
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Extending Concepts Exercises
84
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2.4 Budgeting
84
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Example 1 − Comparing Budgeted and Actual Expenses
85
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Example 2 − Balancing a Monthly Budget
86
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Example 3 − Keeping a Checkbook Registry
87
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Example 4 − Calculating Bad Check Penalties
88
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Example 5 − Analyzing Annual Expenses
89
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Example 6 − Qualifying for a Home Mortgage
90
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Exercises for Examples 1 & 2
91
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Exercises for Examples 3 & 4
92
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Exercises for Examples 5 & 6
93
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Extending Concepts Exercises
94
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2.3−2.4 Quiz
94
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2.3−2.4 Quiz
95
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Chapter Summary
95
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Chapter Summary
96
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Chapter Review
96
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Review Exercises for Section 2.1
97
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Review Exercises for Section 2.2
98
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Review Exercises for Section 2.3
99
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Review Exercises for Section 2.4
100
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Chapter 3: Logic & the Media
100
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Chapter Opener
100
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Chapter Opener
101
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Chapter Opener
102
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3.1 Sets & Set Diagrams
102
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Example 1 − Drawing a Set Diagram
103
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Example 2 − Describing Set Diagram Regions
104
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Example 3 − Using a Set Diagram
105
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Example 4 − Finding the Intersection of Sets
106
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Example 5 − Finding the Complement of a Set
107
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Example 6 − Finding the Complement of a Set
108
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Exercises for Examples 1 & 2
109
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Exercises for Examples 3 & 4
110
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Exercises for Examples 5 & 6
111
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Extending Concepts Exercises
112
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3.2 Statements & Negations
112
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Example 1 − Analyzing a Statement Involving All
113
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Example 2 − Analyzing a Statement Involving All
114
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Example 3 − Analyzing a Statement Involving Some
115
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Example 4 − Analyzing a Statement Involving Many
116
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Example 5 − Negating of a Statement Involving And
117
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Example 6 − Negating of a Statement Involving Or
118
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Exercises for Examples 1 & 2
119
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Exercises for Examples 3 & 4
120
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Exercises for Examples 5 & 6
121
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Extending Concepts Exercises
122
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3.1−3.2 Quiz
122
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3.1−3.2 Quiz
123
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Chapter Project
123
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Project: Organizing Real-Life Information
124
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3.3 Deductive & Inductive Reasoning
124
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Example 1 − Writing a Syllogism
125
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Example 2 − Writing a Syllogism
126
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Example 3 − Analyzing a Logical System
127
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Example 4 − Comparing Logical Systems
128
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Example 5 − Using Inductive Reasoning
129
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Example 6 − Using Inductive Reasoning
130
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Exercises for Examples 1 & 2
131
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Exercises for Examples 3 & 4
132
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Exercises for Examples 5 & 6
133
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Extending Concepts Exercises
134
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3.4 Fallacies in Logic
134
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Example 1 − Detecting a Fallacy
135
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Example 2 − Detecting a Fallacy
136
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Example 3 − Drawing a Set Diagram
137
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Example 4 − Drawing a Set Diagram
138
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Example 5 − Analyzing an Advertisement
139
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Example 6 − Analyzing Political Advertisements
140
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Exercises for Examples 1 & 2
141
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Exercises for Examples 3 & 4
142
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Exercises for Examples 5 & 6
143
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Extending Concepts Exercises
144
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3.3−3.4 Quiz
144
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3.3−3.4 Quiz
145
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Chapter Summary
145
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Chapter Summary
146
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Chapter Review
146
•
Review Exercises for Section 3.1
147
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Review Exercises for Section 3.2
148
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Review Exercises for Section 3.3
149
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Review Exercises for Section 3.4
150
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Chapter 4: Inflation & Depreciation
150
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Chapter Opener
150
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Chapter Opener
151
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Chapter Opener
152
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4.1 Exponential Growth
152
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Example 1 − Making a Table
153
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Example 2 − Using a Spreadsheet
154
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Example 3 − Graphing Exponential Growth
155
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Example 4 − Graphing Exponential Growth
156
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Example 5 − Finding an Exponential Growth Rate
157
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Example 6 − Finding an Exponential Growth Rate
158
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Exercises for Examples 1 & 2
159
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Exercises for Examples 3 & 4
160
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Exercises for Examples 5 & 6
161
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Extending Concepts Exercises
162
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4.2 Inflation & the Consumer Price Index
162
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Example 1 − Reading a Consumer Price Index
163
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Example 2 − Calculating an Inflated Price
164
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Example 3 − Graphing a Consumer Price Index
165
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Example 4 − Analyzing a Graph
166
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Example 5 − Graphing the Value of the Dollar
167
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Example 6 − Comparing Debt Between Two Years
168
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Exercises for Examples 1 & 2
169
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Exercises for Examples 3 & 4
170
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Exercises for Examples 5 & 6
171
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Extending Concepts Exercises
172
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4.1−4.2 Quiz
172
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4.1−4.2 Quiz
173
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Chapter Project
173
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Project: Comparing Costs of Living
174
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4.3 Exponential Decay
174
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Example 1 − Making a Table
175
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Example 2 − Graphing Exponential Decay
176
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Example 3 − Making a Table
177
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Example 4 − Carbon Dating a Skeleton
178
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Example 5 − Finding an Exponential Decay Rate
179
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Example 6 − Finding an Exponential Decay Rate
180
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Exercises for Examples 1 & 2
181
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Exercises for Examples 3 & 4
182
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Exercises for Examples 5 & 6
183
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Extending Concepts Exercises
184
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4.4 Depreciation
184
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Example 1 − Making a Depreciation Schedule
185
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Example 2 − Making a Depreciation Schedule
186
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Example 3 − Making a Depreciation Schedule
187
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Example 4 − Making a Depreciation Schedule
188
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Example 5 − Making a Depreciation Schedule
189
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Example 6 − Comparing Different Types of Depreciation
190
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Exercises for Examples 1 & 2
191
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Exercises for Examples 3 & 4
192
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Exercises for Examples 5 & 6
193
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Extending Concepts Exercises
194
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4.3−4.4 Quiz
194
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4.3−4.4 Quiz
195
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Chapter Summary
195
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Chapter Summary
196
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Chapter Review
196
•
Review Exercises for Section 4.1
197
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Review Exercises for Section 4.2
198
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Review Exercises for Section 4.3
199
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Review Exercises for Section 4.4
200
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Chapter 5: Taxation
200
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Chapter Opener
200
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Chapter Opener
201
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Chapter Opener
202
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5.1 Flat Tax & Political Philosophy
202
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Example 1 − Calculating a Flat Income Tax
203
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Example 2 − Determining Taxable Income
204
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Example 3 − Identifying Types of Taxes
205
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Example 4 − Identifying Types of Taxes
206
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Example 5 − Analyzing an Indirect Tax
207
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Example 6 − Analyzing Possible Effects of Taxes
208
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Exercises for Examples 1 & 2
209
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Exercises for Examples 3 & 4
210
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Exercises for Examples 5 & 6
211
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Extending Concepts Exercises
212
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5.2 Graduated Income Tax
212
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Example 1 − Calculating a Graduated Income Tax
213
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Example 2 − Calculating a Graduated Income Tax
214
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Example 3 − Analyzing a Graduated Tax System
215
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Example 4 − Analyzing Federal Tax Revenue
216
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Example 5 − Comparing Possible Systems
217
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Example 6 − Analyzing The Deficit
218
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Exercises for Examples 1 & 2
219
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Exercises for Examples 3 & 4
220
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Exercises for Examples 5 & 6
221
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Extending Concepts Exercises
222
+
5.1−5.2 Quiz
222
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5.1−5.2 Quiz
223
+
Chapter Project
223
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Project: Finding a Tax Freedom Day
224
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5.3 Property Tax
224
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Example 1 − Calculating a Property Tax
225
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Example 2 − Calculating Effective Rates
226
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Example 3 − Appealing an Assessed Value
227
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Example 4 − Applying a Tax Credit
228
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Example 5 − Estimating Lost Tax Revenue
229
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Example 6 − Analyzing the Value of an Exemption
230
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Exercises for Examples 1 & 2
231
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Exercises for Examples 3 & 4
232
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Exercises for Examples 5 & 6
233
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Extending Concepts Exercises
234
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5.4 Social Security & Payroll Taxes
234
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Example 1 − Calculating Total Payroll Taxes
235
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Example 2 − Calculating a Total Compensation Package
236
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Example 3 − Evaluating a Social Security Retirement
237
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Example 4 − Considering Retirement?
238
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Example 5 − Analyzing a Graph
239
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Example 6 − Looking into the Future
240
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Exercises for Examples 1 & 2
241
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Exercises for Examples 3 & 4
242
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Exercises for Examples 5 & 6
243
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Extending Concepts Exercises
244
+
5.3−5.4 Quiz
244
•
5.3−5.4 Quiz
245
+
Chapter Summary
245
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Chapter Summary
246
+
Chapter Review
246
•
Review Exercises for Section 5.1
247
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Review Exercises for Section 5.2
248
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Review Exercises for Section 5.3
249
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Review Exercises for Section 5.4
250
+
Chapter 6: Borrowing & Saving
250
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Chapter Opener
250
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Chapter Opener
251
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Chapter Opener
252
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6.1 Introduction to Lending
252
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Example 1 − Reading a Promissory Note
253
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Example 2 − Finding the Due Date and Total Amount Due
254
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Example 3 − Finding the Cost of Credit
255
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Example 4 − Applying the Truth in Lending Act
256
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Example 5 − Finding Simple Interest
257
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Example 6 − Finding the Annual Percentage Rate
258
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Exercises for Examples 1 & 2
259
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Exercises for Examples 3 & 4
260
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Exercises for Examples 5 & 6
261
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Extending Concepts Exercises
262
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6.2 Buying Now, Paying Later
262
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Example 1 − Creating a Compound Interest Table
263
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Example 2 − Using an Amortization Table
264
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Example 3 − Finding the Cost of Buying on Credit
265
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Example 4 − Comparing Rates
266
•
Example 5 − Tracking the Prime Interest Rate
267
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Example 6 − Comparing Two Levels of Indebtedness
268
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Exercises for Examples 1 & 2
269
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Exercises for Examples 3 & 4
270
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Exercises for Examples 5 & 6
271
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Extending Concepts Exercises
272
+
6.1−6.2 Quiz
272
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6.1−6.2 Quiz
273
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Chapter Project
273
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Project: How Much Car Can I Afford?
274
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6.3 Home Mortgages
274
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Example 1 − Comparing Rates for a Home Mortgage
275
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Example 2 − Comparing Terms for a Home Mortgage
276
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Example 3 − Analyzing the Effect of Principal Payments
277
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Example 4 − Analyzing the Cost of a Balloon Mortgage
278
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Example 5 − Comparing Buying and Renting
279
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Example 6 − Analyzing a Housing Bubble
280
•
Exercises for Examples 1 & 2
281
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Exercises for Examples 3 & 4
282
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Exercises for Examples 5 & 6
283
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Extending Concepts Exercises
284
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6.4 Savings & Retirement Plans
284
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Example 1 − Comparing Terms for a Savings Plan
285
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Example 2 − Calculating the Consequences of Franklin's Will
286
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Example 3 − Creating a Retirement Plan
287
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Example 4 − Creating a Retirement Plan
288
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Example 5 − Withdrawing from a Retirement Plan
289
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Example 6 − Analyzing a Defined Benefit Plan
290
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Exercises for Examples 1 & 2
291
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Exercises for Examples 3 & 4
292
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Exercises for Examples 5 & 6
293
•
Extending Concepts Exercises
294
+
6.3−6.4 Quiz
294
•
6.3−6.4 Quiz
295
+
Chapter Summary
295
•
Chapter Summary
296
+
Chapter Review
296
•
Review Exercises for Section 6.1
297
•
Review Exercises for Section 6.2
298
•
Review Exercises for Section 6.3
299
•
Review Exercises for Section 6.4
300
+
Chapter 7: Patterns & Nature
300
+
Chapter Opener
300
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Chapter Opener
301
•
Chapter Opener
302
+
7.1 Linear Patterns
302
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Example 1 − Recognizing a Linear Pattern
303
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Example 2 − Recognizing a Linear Pattern
304
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Example 3 − Predicting a Future Event
305
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Example 4 − Describing a Linear Pattern in Nature
306
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Example 5 − Recognizing a Proportional Pattern
307
•
Example 6 − Recognizing a Proportional Pattern
308
•
Exercises for Examples 1 & 2
309
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Exercises for Examples 3 & 4
310
•
Exercises for Examples 5 & 6
311
•
Extending Concepts Exercises
312
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7.2 Exponential Patterns
312
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Example 1 − Recognizing an Exponential Pattern
313
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Example 2 − Describing an Exponential Pattern
314
•
Example 3 − Predicting a Future Event
315
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Example 4 − Predicting a Future Event
316
•
Example 5 − Comparing Exponential and Logistic Growth
317
•
Example 6 − Comparing Logistic Patterns
318
•
Exercises for Examples 1 & 2
319
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Exercises for Examples 3 & 4
320
•
Exercises for Examples 5 & 6
321
•
Extending Concepts Exercises
322
+
7.1−7.2 Quiz
322
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7.1−7.2 Quiz
323
+
Chapter Project
323
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Project: Are We Running Out of Antibiotics?
324
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7.3 Quadratic Patterns
324
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Example 1 − Recognizing a Quadratic Pattern
325
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Example 2 − Recognizing a Quadratic Pattern
326
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Example 3 − Predicting a Future Event
327
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Example 4 − Describing Lift for Airplanes
328
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Example 5 − Conducting an Experiment with Gravity
329
•
Example 6 − Describing Muscle Strength
330
•
Exercises for Examples 1 & 2
331
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Exercises for Examples 3 & 4
332
•
Exercises for Examples 5 & 6
333
•
Extending Concepts Exercises
334
+
7.4 Fibonacci & Other Patterns
334
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Example 1 − Recognizing a Fibonacci Pattern
335
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Example 2 − Recognizing a Fibonacci Pattern
336
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Example 3 − Drawing the Fibonacci Spiral
337
•
Example 4 − Using the Golden Ratio
338
•
Example 5 − Analyzing Kepler's Third Law
339
•
Example 6 − Analyzing Hours of Daylight
340
•
Exercises for Examples 1 & 2
341
•
Exercises for Examples 3 & 4
342
•
Exercises for Examples 5 & 6
343
•
Extending Concepts Exercises
344
+
7.3−7.4 Quiz
344
•
7.3−7.4 Quiz
345
+
Chapter Summary
345
•
Chapter Summary
346
+
Chapter Review
346
•
Review Exercises for Section 7.1
347
•
Review Exercises for Section 7.2
348
•
Review Exercises for Section 7.3
349
•
Review Exercises for Section 7.4
350
+
Chapter 8: Likelihood
350
+
Chapter Opener
350
•
Chapter Opener
351
•
Chapter Opener
352
+
8.1 Assigning a Measure to Likelihood
352
•
Example 1 − Describing Likelihoods
353
•
Example 2 − Putting Probability into Words
354
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Example 3 − Analyzing the Likelihood of a Risk
355
•
Example 4 − Comparing Significance and Risk
356
•
Example 5 − Using Actuarial Data
357
•
Example 6 − Analyzing an Actuarial Graph
358
•
Exercises for Examples 1 & 2
359
•
Exercises for Examples 3 & 4
360
•
Exercises for Examples 5 & 6
361
•
Extending Concepts Exercises
362
+
8.2 Estimating Likelihood
362
•
Example 1 − Finding a Theoretical Probability
363
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Example 2 − Finding a Theoretical Probability
364
•
Example 3 − Finding an Experimental Probability
365
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Example 4 − Finding an Experimental Probability
366
•
Example 5 − Interpreting a Historical Probability
367
•
Example 6 − Analyzing a Historical Probability
368
•
Exercises for Examples 1 & 2
369
•
Exercises for Examples 3 & 4
370
•
Exercises for Examples 5 & 6
371
•
Extending Concepts Exercises
372
+
8.1−8.2 Quiz
372
•
8.1−8.2 Quiz
373
+
Chapter Project
373
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Project: Modeling a Binomial Distribution
374
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8.3 Expected Value
374
•
Example 1 − Finding an Expected Value
375
•
Example 2 − Finding an Expected Value
376
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Example 3 − Comparing Two Expected Values
377
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Example 4 − Using a Decision Tree
378
•
Example 5 − Using Expected Value
379
•
Example 6 − Comparing Two Expected Values
380
•
Exercises for Examples 1 & 2
381
•
Exercises for Examples 3 & 4
382
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Exercises for Examples 5 & 6
383
•
Extending Concepts Exercises
384
+
8.4 Expecting the Unexpected
384
•
Example 1 − Finding the Probability of Independent Events
385
•
Example 2 − Using Independent Events to Detect Fraud
386
•
Example 3 − Finding the Probability of an Event
387
•
Example 4 − Finding the Probability of an Event
388
•
Example 5 − Finding a Counterintuitive Probability
389
•
Example 6 − Winning a Lottery Twice: Fraud?
390
•
Exercises for Examples 1 & 2
391
•
Exercises for Examples 3 & 4
392
•
Exercises for Examples 5 & 6
393
•
Extending Concepts Exercises
394
+
8.3−8.4 Quiz
394
•
8.3−8.4 Quiz
395
+
Chapter Summary
395
•
Chapter Summary
396
+
Chapter Review
396
•
Review Exercises for Section 8.1
397
•
Review Exercises for Section 8.2
398
•
Review Exercises for Section 8.3
399
•
Review Exercises for Section 8.4
400
+
Chapter 9: Description
400
+
Chapter Opener
400
•
Chapter Opener
401
•
Chapter Opener
402
+
9.1 Information Design
402
•
Example 1 − Reading a Stacked Area Graph
403
•
Example 2 − Interpreting a Stacked Area Graph
404
•
Example 3 − Reading a Radar Graph
405
•
Example 4 − Drawing an Area Graph
406
•
Example 5 − Animating Information
407
•
Example 6 − Reading a Design with Several Variables
408
•
Exercises for Examples 1 & 2
409
•
Exercises for Examples 3 & 4
410
•
Exercises for Examples 5 & 6
411
•
Extending Concepts Exercises
412
+
9.2 Describing "Average"
412
•
Example 1 − Estimating the Mean, Median, and Mode
413
•
Example 2 − Comparing Population Pyramids
414
•
Example 3 − Reading a Box-and-Whisker Plot
415
•
Example 4 − Reading Histograms
416
•
Example 5 − Analyzing Outliers and Averages
417
•
Example 6 − Analyzing Data
418
•
Exercises for Examples 1 & 2
419
•
Exercises for Examples 3 & 4
420
•
Exercises for Examples 5 & 6
421
•
Extending Concepts Exercises
422
+
9.1−9.2 Quiz
422
•
9.1−9.2 Quiz
423
+
Chapter Project
423
•
Project: Modeling a Presidential Election
424
+
9.3 Describing Dispersion
424
•
Example 1 − Describing Dispersion
425
•
Example 2 − Describing Dispersion
426
•
Example 3 − Analyzing a Famous Normal Distribution
427
•
Example 4 − Comparing Distributions
428
•
Example 5 − Comparing Distributions
429
•
Example 6 − Analyzing a Bimodal Distribution
430
•
Exercises for Examples 1 & 2
431
•
Exercises for Examples 3 & 4
432
•
Exercises for Examples 5 & 6
433
•
Extending Concepts Exercises
434
+
9.4 Describing by Sampling
434
•
Example 1 − Estimating a Population Mean by Sampling
435
•
Example 2 − Estimating by Sampling
436
•
Example 3 − Analyzing How a Poll Can Go Wrong
437
•
Example 4 − Analyzing Biased Samples
438
•
Example 5 − Determining a Sample Size
439
•
Example 6 − Analyzing a Historical Example of Sampling
440
•
Exercises for Examples 1 & 2
441
•
Exercises for Examples 3 & 4
442
•
Exercises for Examples 5 & 6
443
•
Extending Concepts Exercises
444
+
9.3−9.4 Quiz
444
•
9.3−9.4 Quiz
445
+
Chapter Summary
445
•
Chapter Summary
446
+
Chapter Review
446
•
Review Exercises for Section 9.1
447
•
Review Exercises for Section 9.2
448
•
Review Exercises for Section 9.3
449
•
Review Exercises for Section 9.4
450
+
Chapter 10: Fitness & Sports
450
+
Chapter Opener
450
•
Chapter Opener
451
•
Chapter Opener
452
+
10.1 Health & Fitness
452
•
Example 1 − Analyzing the Met Life Height-Weight Tables
453
•
Example 2 − Finding a Body Fat Percentage
454
•
Example 3 − Finding a Target Heart Rate
455
•
Example 4 − Using a Basal Metabolic Rate
456
•
Example 5 − Graphically Representing Health Claims
457
•
Example 6 − Describing Insulin and Glucose Interaction
458
•
Exercises for Examples 1 & 2
459
•
Exercises for Examples 3 & 4
460
•
Exercises for Examples 5 & 6
461
•
Extending Concepts Exercises
462
+
10.2 The Olympics
462
•
Example 1 − Analyzing Winning Times
463
•
Example 2 − Analyzing Winning Heights
464
•
Example 3 − Analyzing Winning Times
465
•
Example 4 − Analyzing Winning Times
466
•
Example 5 − Analyzing Olympic Scoring
467
•
Example 6 − Analyzing Olympic Scoring
468
•
Exercises for Examples 1 & 2
469
•
Exercises for Examples 3 & 4
470
•
Exercises for Examples 5 & 6
471
•
Extending Concepts Exercises
472
+
10.1−10.2 Quiz
472
•
10.1−10.2 Quiz
473
+
Chapter Project
473
•
Project: Modeling the Path of a Basketball
474
+
10.3 Professional Sports
474
•
Example 1 − Analyzing Batting Statistics
475
•
Example 2 − Analyzing the Strike Zone
476
•
Example 3 − Calculating Quarterback Ratings
477
•
Example 4 − Describing the Probability of Winning
478
•
Example 5 − Analyzing U.S. Open Wins and Losses
479
•
Example 6 − Analyzing Splits and Strikes
480
•
Exercises for Examples 1 & 2
481
•
Exercises for Examples 3 & 4
482
•
Exercises for Examples 5 & 6
483
•
Extending Concepts Exercises
484
+
10.4 Outdoor Sports
484
•
Example 1 − Comparing Grade and Speed
485
•
Example 2 − Analyzing UV Radiation
486
•
Example 3 − Analyzing a Graph
487
•
Example 4 − Analyzing Sail Designs
488
•
Example 5 − Describing a Bicycle Trip
489
•
Example 6 − Analyzing Energy Use in Outdoor Sports
490
•
Exercises for Examples 1 & 2
491
•
Exercises for Examples 3 & 4
492
•
Exercises for Examples 5 & 6
493
•
Extending Concepts Exercises
494
+
10.3−10.4 Quiz
494
•
10.3−10.4 Quiz
495
+
Chapter Summary
495
•
Chapter Summary
496
+
Chapter Review
496
•
Review Exercises for Section 10.1
497
•
Review Exercises for Section 10.2
498
•
Review Exercises for Section 10.3
498
•
Review Exercises for Section 10.3
+
Calculation
+
Order of Operations & Formulas
•
Equal-Payment Plan for Electric Bills (Using Order of Operations)
•
How Many Calories are in Mayonnaise? (Using Order of Operations)
•
Finding the Cost of a College Course (Using A Calculator)
•
Buying Floor Tiles
•
Calories Burned While Running (Using the Distance Formula)
•
Comparing Job Offers
+
Rounding & Calculators
•
Calculating Defense Spending per Person (Rounding Numbers in Context)
•
Comparing Annual Fuel Cost
•
Describing the Size of Bacteria Cells (Describing Large and Small Numbers)
•
Comparing Hard Drive Storage
•
Estimating the Accuracy of Measurements
•
What is the Area of the Vietnam Veterans Memorial Wall? (Writing Significant Digits)
+
Using Percent
•
How Much Land is Owned by Federal Government? (Finding a Percent of a Number)
•
Estimating Dog Ownership in the U.S. (Finding Percents)
•
Comparing SCRABBLE Tiles (Comparing Two Numbers Using Percent)
•
Calculating Body Fat Percentages (Comparing Two Numbers Using Percent)
•
Analyzing Life Expectancy Rates (Using Percent to Describe an Increase)
•
Calculating the Increase in Gold Prices (Using Percent to Describe an Increase)
+
Units & Conversion
•
Calculating Attorney Billing Rates (Using Unit Analysis)
•
Estimating Endangered Species Extinction Rates (Using Unit Analysis)
•
How Many Seconds are in a Calendar Year? (Converting Units)
•
Calculating the Velocity of a Parachutist (Converting Units)
•
Comparing Speed Limits (Converting Units)
•
Converting Temperature Units
+
Consumption
+
Unit Prices
•
Finding the Unit Price of Corn Grits (Finding a Unit Price)
•
Analyzing the Unit Price for Milk Earned by Dairy Farmers (Analyzing a Unit Price)
•
Comparing Unit Prices of Laundry Detergents (Comparing Unit Prices)
•
Comparing Unit Prices of Different Sizes of Pizzas (Comparing Unit Prices)
•
Estimating Annual Savings for a Family (Finding the Annual Savings)
•
Eating In or Eating Out?
+
Markup & Discount
•
Finding a Markup Percent
•
Finding the Markup Percent for Handbags (Finding a Markup Percent)
•
Finding the Markup Percent for T-shirts (Using Discounts and Markup)
•
Buying Generic Prescription Drugs
•
What is the Final Price of a Pair of Jeans? (Calculating Multiple Discounts)
•
Finding the Price of a Rental Car after Using Promotional Codes (Using Promotional Codes)
+
Consumption Taxes
•
Finding Sales Tax
•
Finding the Sales Tax Rate of a Jacket (Finding a Sales Tax Rate)
•
Estimating the Amount of Excise Tax Generated by Cigarette Sales (Estimating Excise Tax)
•
Finding Changes in Excise Taxes
•
Comparing Sales Tax and Value-Added Tax
•
Comparing Tax Revenue Sources
+
Budgeting
•
Comparing Budgeted and Actual Expenses
•
Balancing a Monthly Budget
•
Finding the Balance in Your Checking Account (Keeping a Checkbook Registry)
•
Calculating Bad Check Penalties
•
Analyzing Annual Expenses
•
Do You Qualify for a Home Mortgage? (Qualifying for a Home Mortgage)
+
Logic & the Media
+
Sets & Set Diagrams
•
Drawing a Set Diagram of Bird and Cat Owners (Drawing a Set Diagram)
•
Describing Set Diagram Regions
•
Using a Set Diagram to Solve a Crime (Using a Set Diagram)
•
Using Fingerprint Data to Find the Intersection of Sets (Finding the Intersection of Sets)
•
Finding the Number of Employed People (Finding the Complement of a Set)
•
Examining Diversity Among Vertebrates (Finding the Complement of a Set)
+
Statements & Negations
•
Using a Set Diagram to Analyze the Declaration of Independence (Analyzing a Statement Involving All)
•
Using a Set Diagram to Analyze a Pet Policy (Analyzing a Statement Involving All)
•
Using a Set Diagram to Analyze a Statement about Presidential Elections (Analyzing a Statement Involving Some)
•
Using a Set Diagram to Analyze the Concept in a Paragraph (Analyzing a Statement Involving Many)
•
Using a Set Diagram to Analyze the Negation of a Wedding Vow (Negating of a Statement Involving And)
•
Using a Set Diagram to Analyze the Negation of a Statement (Negating of a Statement Involving Or)
+
Deductive & Inductive Reasoning
•
Writing a Syllogism about Aliens from Mars (Writing a Syllogism)
•
Writing a Syllogism about Women and Education (Writing a Syllogism)
•
Analyzing Euclid's Logical System (Analyzing a Logical System)
•
Comparing Euclid's Geometry with Spherical Geometry (Comparing Logical Systems)
•
Using Inductive Reasoning with Salk Vaccine Data (Using Inductive Reasoning)
•
Using Inductive Reasoning with Spawning Biomass Data (Using Inductive Reasoning)
+
Fallacies in Logic
•
Analyzing a Description of a Polygraph Test (Detecting a Fallacy)
•
Analyzing the Logic of a Quote (Detecting a Fallacy)
•
Analyzing the Conclusion of a Study on Cell Phone Use (Drawing a Set Diagram)
•
Analyzing the Logic of the Hollywood Blacklist (Drawing a Set Diagram)
•
Analyzing an Advertisement Featuring Marilyn Monroe (Analyzing an Advertisement)
•
Analyzing Political Advertisements
+
Inflation & Depreciation
+
Exponential Growth
•
Using the Growth Rate of Bacteria to Make a Table (Making a Table)
•
Using a Spreadsheet to Illustrate the Number of Dragon's Beard Noodles (Using a Spreadsheet)
•
Graphing the Exponential Growth of Mice (Graphing Exponential Growth)
•
Graphing the Exponential Growth of Moore's Law (Graphing Exponential Growth)
•
Finding the Exponential Growth Rate of Stocks (Finding an Exponential Growth Rate)
•
What is the Annual Rate of Growth Represented by Moore's Law? (Finding an Exponential Growth Rate)
+
Inflation & the Consumer Price Index
•
Analyzing the Great Depression Using a Consumer Price Index (Reading a Consumer Price Index)
•
Comparing the Value of Property to Inflation (Calculating an Inflated Price)
•
Describing the Rates of Inflation Over the Years (Graphing a Consumer Price Index)
•
Analyzing the Graph of a Consumer Price Index (Analyzing a Graph)
•
Graphing the Value of the Dollar
•
Comparing the U.S. Federal Debt Between Two Years (Comparing Debt Between Two Years)
+
Exponential Decay
•
Finding the Population of Salmon (Making a Table)
•
Estimating Atmospheric Pressure (Graphing Exponential Decay)
•
Finding the Amount of a Drug in Your Bloodstream (Making a Table)
•
Carbon Dating a Mastodon Skeleton (Carbon Dating a Skeleton)
•
Estimating Age Based on Basal Metabolic Rate (Finding an Exponential Decay Rate)
•
Estimating the Length of Time for Plutonium-239 to Decay (Finding an Exponential Decay Rate)
+
Depreciation
•
Using Straight-Line Depreciation for Office Furniture (Making a Depreciation Schedule)
•
Using Straight-Line Depreciation for a Grain Harvester (Making a Depreciation Schedule)
•
Using Double Declining-Balance Depreciation for Office Furniture (Making a Depreciation Schedule)
•
Using Double Declining-Balance Depreciation for Computer Servers (Making a Depreciation Schedule)
•
Using Sum of the Years-Digits Depreciation for Delivery Vans (Making a Depreciation Schedule)
•
Comparing Different Types of Depreciation
+
Taxation
+
Flat Tax & Political Philosophy
•
Calculating a Flat Income Tax
•
Determining Taxable Income
•
Identifying Regressive, Flat, and Progressive Taxes (Identifying Types of Taxes)
•
Identifying Regressive, Flat, and Progressive Taxes (Identifying Types of Taxes)
•
Analyzing an Indirect Tax
•
Analyzing Possible Effects of Taxes
+
Graduated Income Tax
•
Calculating a Graduated Income Tax
•
Calculating the Effective Tax Rate for a California Income (Calculating a Graduated Income Tax)
•
Analyzing the Income Tax System in the United States (Analyzing a Graduated Tax System)
•
Analyzing Federal Tax Revenue
•
Comparing Graduated and Flat Income Tax Systems (Comparing Possible Systems)
•
Analyzing the Deficit in the United States (Analyzing The Deficit)
+
Property Tax
•
Calculating a Property Tax
•
Calculating Effective Property Tax Rates (Calculating Effective Rates)
•
Appealing an Assessed Value
•
Applying a Tax Credit to Property Taxes (Applying a Tax Credit)
•
Estimating Property Tax Exemptions (Estimating Lost Tax Revenue)
•
Analyzing the Value of a Military Tax Exemption (Analyzing the Value of an Exemption)
+
Social Security & Payroll Taxes
•
Calculating Total Payroll Taxes
•
Calculating an Employee's Total Compensation Package (Calculating a Total Compensation Package)
•
Evaluating a Social Security Retirement
•
Considering Retirement?
•
Analyzing Economic Dependency Ratios on a Graph (Analyzing a Graph)
•
Analyzing the Future of Social Security (Looking into the Future)
+
Borrowing & Saving
+
Introduction to Lending
•
Reading a Promissory Note
•
Finding the Due Date and Total Amount Due for a Loan (Finding the Due Date and Total Amount Due)
•
Finding the Cost of a Loan for a Refrigerator (Finding the Cost of Credit)
•
Completing the Truth in Lending Act Disclosure for a Washer and Dryer (Applying the Truth in Lending Act)
•
Using a Spreadsheet to Find Interest for Various Terms and Rates (Finding Simple Interest)
•
Finding the Annual Percentage Rate for a Cash Advance (Finding the Annual Percentage Rate)
+
Buying Now, Paying Later
•
Using a Table to See How the Balance of a Loan Decreases (Creating a Compound Interest Table)
•
Using a Table to Find the Remaining Balance of a Loan (Using an Amortization Table)
•
Finding the Amount of Interest on a Loan for a Plasma Television (Finding the Cost of Buying on Credit)
•
Finding the Amount of Interest Saved with a Higher Credit Score (Comparing Rates)
•
Why do Interest Rates Increase and Decrease? (Tracking the Prime Interest Rate)
•
Comparing Total Consumer Credit in the U.S. from 1952 through 2008 (Comparing Two Levels of Indebtedness)
+
Home Mortgages
•
Comparing Annual Percentage Rates for a Home Mortgage (Comparing Rates for a Home Mortgage)
•
Comparing Terms for a Home Mortgage
•
Analyzing the Effect of Principal Payments on a Home Mortgage (Analyzing the Effect of Principal Payments)
•
Analyzing the Cost of a Balloon Mortgage
•
Comparing Buying and Renting a Home (Comparing Buying and Renting)
•
Why were there a Record Number of Foreclosures in 2007? (Analyzing a Housing Bubble)
+
Savings & Retirement Plans
•
Comparing Terms for a Savings Plan
•
Calculating the Consequences of a Will over Time (Calculating the Consequences of Franklin's Will)
•
Comparing Balances of Retirement Packages (Creating a Retirement Plan)
•
What is your Retirement Package Worth? (Creating a Retirement Plan)
•
Withdrawing from a Retirement Plan
•
Analyzing a Defined Benefit Plan
+
Patterns & Nature
+
Linear Patterns
•
Finding a Person's Height Using a Linear Pattern (Recognizing a Linear Pattern)
•
Finding a Person's Shoe Size Using a Linear Pattern (Recognizing a Linear Pattern)
•
Predicting the Ages of Women at Their First Marriage (Predicting a Future Event)
•
Describing the Migration of Canadian Geese (Describing a Linear Pattern in Nature)
•
Describing the Distance a Spring can Stretch (Recognizing a Proportional Pattern)
•
Is a Human's Skull Proportional to its Total Height as He Grows? (Recognizing a Proportional Pattern)
+
Exponential Patterns
•
Describing the Pattern for the Number of Chambers in a Shell (Recognizing an Exponential Pattern)
•
Describing the Exponential Growth of Earth's Population (Describing an Exponential Pattern)
•
Predicting the Number of Bald Eagle Nesting Pairs (Predicting a Future Event)
•
Analyzing an Exponential Pattern from a Graph (Predicting a Future Event)
•
Describing the Growth of the Number of Yeast Cells in Grape Juice (Comparing Exponential and Logistic Growth)
•
Comparing Logistic Patterns of Seals' Location Strategies (Comparing Logistic Patterns)
+
Quadratic Patterns
•
Describing the Pattern of a Hit Baseball (Recognizing a Quadratic Pattern)
•
Describing and Graphing the Quadratic Pattern of an Oil Spill (Recognizing a Quadratic Pattern)
•
Predicting the Levels of Carbon Dioxide in Earth's Atmosphere (Predicting a Future Event)
•
Describing the Pattern of Lift and Speed for Airplanes (Describing Lift for Airplanes)
•
Exploring the Concept of Gravity (Conducting an Experiment with Gravity)
•
Describing the Pattern of Muscle Strength and Upper Arm Circumference (Describing Muscle Strength)
+
Fibonacci & Other Patterns
•
Recognizing a Fibonacci Pattern in a Rabbit Population (Recognizing a Fibonacci Pattern)
•
Recognizing a Fibonacci Pattern in an X-Ray (Recognizing a Fibonacci Pattern)
•
Drawing the Fibonacci Spiral
•
Using the Fibonacci Sequence to Find the Golden Ratio (Using the Golden Ratio)
•
Finding the Mathematical Pattern in Kepler's Third Law (Analyzing Kepler's Third Law)
•
Analyzing the Hours of Daylight
+
Likelihood
+
Assigning a Measure to Likelihood
•
What is the Likelihood of an Asteroid or Meteoroid Hitting Earth? (Describing Likelihoods)
•
Describing the Likelihood a Hurricane Passing through a Region (Putting Probability into Words)
•
Analyzing the Likelihood of a Risk
•
Comparing Significance and Risk
•
Using an Actuarial Table for Life Expectancy (Using Actuarial Data)
•
Analyzing an Actuarial Graph
+
Estimating Likelihood
•
Find the Probability of Winning the Daily Number (Finding a Theoretical Probability)
•
Finding the Probability of the Order of the NBA Draft Lottery (Finding a Theoretical Probability)
•
Finding the Probability of Inheriting Eye Color (Finding an Experimental Probability
•
Finding the Probability of Different Genders Buying Fast Food (Finding an Experimental Probability)
•
Is a Bee Sting or Bicycle Accident more Fatal? (Estimating a Probability Using Historical Results)
•
Finding the Probability of Snow on December 25 (Analyzing a Historical Probability)
+
Expected Value
•
Finding the Expected Value of a Lottery Game (Finding an Expected Value)
•
Finding the Expected Value of a Fire Insurance Policy (Finding an Expected Value)
•
Comparing Two Expected Values
•
Using a Decision Tree
•
Relating Expected Value and Investment (Using Expected Value)
•
Comparing Speculative and Conservative Investments (Comparing Two Expected Values)
+
Expecting the Unexpected
•
What is the Probability of Rolling a Yahtzee? (Finding the Probability of Independent Events)
•
Using Independent Events to Detect Fraud
•
Finding the Probability You Share Your Birthday with a Classmate (Finding the Probability of an Event)
•
Finding the Probability of a Spouse's Life Expectancy (Finding the Probability of an Event)
•
The "Let's Make a Deal Problem" (Finding a Counter-Intuitive Probability)
•
Winning a Lottery Twice: Fraud?
+
Description
+
Information Design
•
Reading a Stacked Area Graph of Motor Vehicle Accident Fatalities (Reading a Stacked Area Graph)
•
Interpreting a Stacked Area Graph
•
Describing the Percent of 18-Year-Olds in School (Reading a Radar Graph)
•
Drawing an Area Graph of Facebook Relationship Status Updates (Drawing an Area Graph)
•
Animating Life Expectancy Data (Animating Information)
•
Analyzing a Stream Graph of Box Office Hits (Reading a Design with Several Variables)
+
Describing "Average"
•
Estimating the Mean, Median, and Mode of an Age Distribution Chart (Estimating the Mean, Median, and Mode)
•
Comparing Expansive, Constrictive, and Stationary Population Pyramids (Comparing Population Pyramids)
•
Using a Box-and-Whisker Plot to Analyze the Chicago Bears' Players' Weights (Reading a Box-and-Whisker Plot)
•
Reading a Histogram of Professional Athletes' Weights (Reading a Histogram)
•
Analyzing Annual Income in the U.S. (Analyzing Outliers and Averages)
•
Analyzing the IQs of Recent U.S. Presidents (Analyzing Data)
+
Describing Dispersion
•
Describing the Distribution of the Lengths of Cuckoo Eggs (Describing Dispersion)
•
Describing the Distribution of the Mean Daily Temperature at McGuire Air Force Base (Describing Dispersion)
•
Analyzing a Normal Distribution of Scottish Men's Chest Sizes (Analyzing a Famous Normal Distribution)
•
Comparing Distributions of Adult Male Heights to Adult Female Heights (Comparing Distributions)
•
Comparing Distributions of the Number of Moves in Board Games (Comparing Distributions)
•
Analyzing a Bimodal Distribution of Full-Time Salaries (Analyzing a Bimodal Distribution)
+
Describing by Sampling
•
Estimating a Population Mean of Black Bears' Shoulder Height by Sampling (Estimating a Population Mean by Sampling)
•
Estimating the Speed of Light by Sampling (Estimating by Sampling)
•
Analyzing How a Poll Can Go Wrong
•
Analyzing Biased Samples
•
Determining a Sample Size for a Men's Personal Care Product (Determining a Sample Size)
•
Analyzing Historical Examples of Sampling
+
Fitness & Sports
+
Health & Fitness
•
Analyzing the Met Life Height-Weight Tables
•
How do you Find a Body Fat Percentage? (Finding a Body Fat Percentage)
•
Finding a Target Heart Rate
•
Using a Basal Metabolic Rate to Determine Your Daily Calorie Needs (Using a Basal Metabolic Rate)
•
Graphically Representing Health Claims
•
Describing Insulin and Glucose Interaction
+
The Olympics
•
Analyzing Winning Times for Men's 200-Meter Freestyle (Analyzing Winning Times)
•
Examining Winning Heights for Men's Pole Vaulting (Analyzing Winning Times)
•
Investigating Winning Times for Men's 1500-Meter Speed Skating (Analyzing Winning Times)
•
Analyzing Winning Times for Men's Downhill Skiing (Analyzing Winning Times)
•
Investigating Olympic Scoring for Women's Diving (Analyzing Olympic Scoring)
•
Analyzing Olympic Scoring Rules for Ski Jumping (Analyzing Olympic Scoring)
+
Professional Sports
•
Analyzing Batting Averages and Earned Run Averages (Analyzing Batting Statistics)
•
Examining the Strike Zone in Baseball (Analyzing the Strike Zone)
•
Calculating Quarterback Ratings using a Formula (Calculating Quarterback Ratings)
•
Describing the Probability of an NFL Team Winning a Game (Describing the Probability of Winning)
•
Analyzing the Top Four Seeds in the U.S. Tennis Open (Analyzing U.S. Open Wins and Losses)
•
Investigating Splits and Strikes in Bowling (Analyzing Splits and Strikes)
+
Outdoor Sports
•
Comparing Grade and Speed for Hiking (Comparing Grade and Speed)
•
Analyzing UV Radiation at Various Elevations (Analyzing UV Radiation)
•
Comparing Grade and Speed for Kayaking (Analyzing a Graph)
•
Analyzing Sail Design
•
Describing a Cyclist's Trip using his Heart Rate and Elevation (Describing a Bicycle Trip)
•
Analyzing Energy Use in Outdoor Sports
Index
A
B
C
D
E
F
G
H
I
L
M
N
O
P
Q
R
S
T
U
V
W
A
Actuary
defined,
356
Amount financed,
See
Principal
Annual percentage rate
defined,
256
finding,
257
Annuity,
See also
Savings account(s)
decreasing
defined,
288
increasing
defined,
286
formula for balance of,
286
Area
formula for
circle,
5
,
55
rectangle,
5
square,
5
triangle,
5
using,
5
Argument(s)
defined,
112
Assessed value,
See
Property tax
Average(s),
See also
Mean, Median, Mode
graphing,
412 - 421
outliers effect on,
416 - 417
defined,
416>
B
Balloon mortgage(s)
defined,
277
Balloon payment(s)
defined,
277
Bayes' Theorem,
393
Biased sample
defined,
437
Bimodal distribution,
428 - 429
Budget(s),
84 - 93
analyzing,
88
balancing,
84 - 85
checks,
86 - 87
bad checks,
87
defined,
86
defined,
84
mortgages
debt-to-income ratio,
89
C
Calculators
order of operations,
4
rounding and,
12-21
Capacity,
See
Volume
Capital gains,
See
Income
Categorical syllogism(s)
defined,
124
Change
percent of,
28-29
Charts,
See
Graph(s)
Chebyshev's inequality,
424
Check(s),
86 - 87
bad checks,
87
defined,
87
checkbook registry,
86 - 87
balancing,
86 - 87
defined,
86
Circle(s)
area of,
5
,
55
Complement
of a set,
106 - 107
defined,
106
finding,
106 - 107
Compound interest
defined,
262
formula for,
284
Computer storage
units of,
15
Consumer price index,
162 - 171
calculating,
163
defined,
162
graphing,
164 - 165
inflation and,
162 - 171
Consumption taxes,
See also
Taxes
,
74 - 83
defined,
74
excise
defined,
76
finding,
76 - 77
sales
finding,
74 - 75
value-added,
78
defined,
78
Converting
unit prices,
54 - 55
units of measure,
34 - 43
common,
36
currency,
43
described,
36
distance,
36
,
38
temperature,
38
,
39
volume,
36
,
38
weight,
36
,
38
Cost of credit,
See
Credit
Credit,
See also
Loan(s)
,
262-271
amortization table,
262-263
cost of,
254
,
264 -265
defined,
254
finding formula for,
254
defined,
254
prime interest rate,
266
Currency
converting units of,
43
Customary system of measurement
conversion,
36
,
38
D
Data
displaying
with animation,
406
area graphs,
405
box-and-whisker plots,
414
candlestick chart,
410
histograms,
415
life charts,
411
radar graphs,
404
stacked area graphs,
402 - 403
stream graphs,
407
distribution of
bimodal,
428 - 429
flat,
428
normal,
426 - 427
right-skewed,
428
health,
452 - 461
mean
defined,
412
graphing,
412- 421
median
defined,
412
graphing,
412 - 421
mode
defined,
412
graphing,
412 - 421
sports
interpreting,
462 - 465
,
474 - 475
,
477- 479
Olympic,
462 - 471
outliers
defined,
416
effect on averages,
416 - 417
professional,
474 - 483
standard deviation of,
424 - 433
Chebyshev's inequality,
424
defined,
424
displaying,
424 - 433
formula for,
433
Debt-to-income ratio,
89
28% Rule,
89
36% Rule,
89
Decay
depreciation,
184 - 193
double declining-balance,
186 - 187
formula for,
184>,
186
,
188
straight-line,
184 - 185
sum of the years-digits,
188
exponential,
174 - 183
defined,
174
finding rate of,
178-179
formula for,
174
graphing,
175
rate of,
178 - 179
half-life,
176 - 177
defined,
176
formula for,
176
Deductive reasoning,
124 - 127
defined,
124
fallacies,
134 - 143
defined,
134
syllogisms,
124
categorical,
124
writing,
124 - 125
systems,
126 - 127
Depreciation,
184 - 193
accelerated,
189
defined,
184
double declining-balance,
186 - 187
defined,
186
formula for,
186
formula for,
184
,
186
,
188
recovery period,
185
straight-line,
184 - 185
sum of the years-digits,
188
defined,
188
useful life,
186
Devaluation
defined,
166
Diagram(s)
set,
102 - 111
complement of,
106 -107
intersection of,
104 -105
union of,
102
using,
102 - 121
using to detect fallacies,
136 - 137
Discount,
See also
Price(s)
,
62 - 71
defined,
64
finding,
64 - 66
Dispersion,
See
Standard deviation
Distance
converting units,
36
,
38
formula for,
6
using,
6
Distribution,
424 - 433
bimodal,
428 - 429
flat,
428
normal,
426 - 427
defined,
426
right-skewed,
428
Division
fractions
Invert and Multiply Rule,
35
Dollar(s),
See also
Inflation
,
Price(s)
devaluation of,
166 - 167
formula for,
166
inflation and,
166
Double declining-balance depreciation,
186
E
Earnings
formula for,
7
Economic dependency ratio
defined,
238
formula for,
238
Effective tax rate,
See
Income Tax
Effective tax rate,
See
Property Tax
Equity
defined,
276
Estimation
rounding,
12 - 21
Event(s)
Bayes' Theorem,
393
expected values of,
374 - 383
defined,
374
finding,
374 - 377
using,
378
independent,
384 - 385
defined,
384
finding,
386
formula for,
384
using,
385
probability of,
352 - 361
,
384 - 393
probability of not occurring,
386 - 387
formula for,
386
Expected value(s),
374 - 383
defined,
374
finding
of multiple events,
376 - 377
of two events,
374 - 375
of investments,
378 - 379
using,
378
Expense(s)
analyzing,
88
budgets,
84 - 93
balancing,
84 - 85
depreciation,
184 - 193
defined,
184
double declining-balance,
186 - 187
straight-line,
184 - 185
sum of the years-digits,
188
Experiment(s),
See
Expected value(s)
,
Probability
Experimental probability,
See also
Probability
defined,
362
finding,
364 - 365
Exponential decay,
See also
Exponential pattern(s)
,
174 - 183
defined,
174
finding rate of,
178-179
formula for,
174
graphing,
175
half-life,
176 - 177
defined,
176
formula for,
176
rate of,
178-179
Exponential growth,
See also
Exponential pattern(s)
,
152 - 161
defined,
152
finding rate of,
156 - 157
formula for,
152
graphing,
154 - 155
Moore's Law,
155
,
157
rate of,
156 - 157
Exponential notation,
14 - 15
defined,
14
Exponential pattern(s),
See also
Exponential growth
,
312 - 321
compared to logistic growth,
316
defined,
312
recognizing,
312
,
328-329
regression,
314
using,
314 - 315
F
Fallacy
ad hominem,
143
ad populum,
143
appeal to authority,
138
appeal to emotion,
139
appeal to novelty,
143
begging the question,
139
composition,
143
deductive,
134 - 143
in advertisements,
138 - 139
defined,
134
denying the antecedent,
135
false cause,
136
false dilemma,
143
non sequitur,
136
self-refuting idea,
143
undistributed middle,
137
defined,
134
inductive,
134 - 143
defined,
134
Fibonacci sequence,
334 - 343
defined,
334
in geometric figures,
336 - 337
golden ratio,
337
golden triangle,
343
recognizing,
334 - 335
Finance charge(s)
defined,
255
Flat distribution,
428
Flat tax,
See
Income tax
Formula(s),
2 - 11
area
of a circle,
5
,
55
of a rectangle,
5
of a square,
5
of a triangle,
5
compound interest,
284
conversion
of temperature,
39
cost of credit,
254
defined,
5
depreciation,
184
double declining-balance,
186
straight-line,
186 - 187
sum of the years-digits,
188
devaluation of dollar,
166
distance,
6
earnings,
7
economic dependency ratio,
238
evaluating with order of operations,
2 - 11
exponential decay,
174
exponential growth,
152
football passer rating,
476
half-life,
176
health related
basal metabolic rate,
455
,
461
body fat percentage,
453
body mass index,
453
Halls,
452
Hamwi,
452
Katch-McArdle,
461
maximum heart rate,
454
Mifflin-St. Jeor,
455
Robinson,
458
increasing annuities,
286
loans
cost of credit,
254
installment,
262
interest on,
256 - 257
period of,
256 - 257
principal,
256 - 257
rate of,
256 - 257
logistic growth,
321
Olympic scoring
diving,
466
ski jumping,
467
on-base percentage,
480
probability
of event not occurring,
386
independent event,
384
theoretical,
362
property tax rates,
233
simple interest,
256
slugging percentage,
480
Social Security benefits,
241
standard deviation,
433
unit analysis of,
34 - 35
weight
Halls,
452
Hamwi,
452
Robinson,
458
Fractions
division of
Invert and Multiply Rule,
35
G
Geometry
area
of a circle,
5
,
55
of a rectangle,
5
of a square,
5
of a triangle,
5
Fibonacci patterns,
336
Pythagorean Theorem,
157
Graduated income tax,
See
Income tax
Graph(s),
See also
Graphing
animating,
406
area,
405
box-and-whisker plots,
414
candlestick charts,
410
histograms,
415
interpreting,
452
,
457
,
474 - 475
,
477 - 479
,
484
,
486
,
488
life charts,
411
radar,
404
stacked area,
402 - 403
interpreting,
403
reading,
402
stream,
407
Graphing
averages,
412 - 421
mean,
412 - 421
median,
412 - 421
mode,
412 - 421
bubble graphs,
366
consumer price index,
164 - 165
devaluation of dollar,
166
exponential decay,
175
exponential growth,
154 - 155
Growth
exponential,
152 - 161
defined,
152
finding,
157
formula for,
152
graphing,
154 - 155
rate of,
156 - 157
Growth rate(s)
exponential,
156 - 157
logistic,
161
H
Half-life,
176 - 177
defined,
176
formula for,
176
Health and fitness,
452 - 461
,
456
data
interpreting,
452
,
457
formulas
basal metabolic rate,
455
,
461
body fat percentage,
453
body mass index,
453
Halls,
452
Hamwi,
452
Katch-McArdle,
461
maximum health rate,
454
Mifflin-St. Jeor,
455
Robinson,
458
weight,
452
,
458
Historical probability,
See also
Probability
,
366 - 367
defined,
362
Home mortgage,
See
Mortgage(s)
Home ownership
housing bubbles,
279
mortgages,
274 - 283
balloon,
277
balloon payments,
277
comparing,
274 - 275
defined,
274
discount points,
283
equity,
276
market value,
276
principal balance,
276
renting compared with buying,
278
I
Income,
See also
Income tax
,
Savings account(s)
budgets,
84 - 93
balancing,
84 - 85
capital gains,
221
debt-to-income ratio
defined,
89
Income tax,
202 - 221
capital gains,
221
credits,
211
deductions,
211
effective rate,
212
flat rate,
202 - 211
calculating,
202
compared to graduated,
216
defined,
202
graduated,
204
,
212 - 221
calculating,
212 - 213
compared to flat rate,
216
defined,
212
marginal rate,
212 - 213
defined,
212
negative,
211
philosophy of,
202 - 211
progressive
defined,
204
regressive
defined,
204
Independent event,
See
Event(s)
Indirect tax,
See
Taxes
Inductive reasoning,
128 - 129
defined,
128
fallacies,
134 - 143
defined,
134
Inflation,
162 - 171
consumer price index,
162 - 171
calculating,
163
defined,
162
graphing,
164 - 165
defined,
162
devaluation of dollar,
166
dollar value and,
166
Information design,
See also
Data
,
Graphs
,
402 - 411
defined,
402
Installment loan(s)
defined,
253
Interest
compound
defined,
262
formula for,
284
simple
annual percentage rate,
256
defined,
256
formula for,
256
Intersection
of sets,
104 - 105
defined,
104
finding,
104 - 105
Invert and Multiply Rule,
35
Investments,
See also
Savings account(s)
expected values of,
378 - 379
speculative,
379
Investments,
See
Savings plan(s)
L
Lending,
See
Loan(s)
Likelihood,
See
Probability
Linear pattern(s),
302 - 311
defined,
302
in health data,
452
interpreting,
452
,
462
proportional
defined,
306
recognizing,
306 - 307
,
328 - 329
regression,
304
using,
304 - 305
Loan(s),
252 - 261
amortized,
262 - 263
amount financed,
255
annual percentage rates
defined,
256
finding,
257
credit,
264 - 267
cost of,
254
defined,
254
prime interest rate,
266
finance charges
defined,
255
formula for
installment,
262
interest on,
257
period of,
257
rate of,
257
time of,
257
installment
defined,
253
interest
compound,
262
formula for,
256 - 257
prime rate,
266
simple,
256 - 257
loan proceeds
defined,
252
mortgages,
274 - 283
balloon,
277
balloon payments,
277
compared with renting,
278
comparing,
274 - 275
debt-to-income ratio,
89
defined,
274
discount points,
283
equity,
276
market value,
276
principal balance,
276
principal
defined,
255
formula for,
257
promissory notes
defined,
252
term
defined,
252
total amount due
defined,
252
finding,
253
Loan proceeds
defined,
252
Logic
argument
defined,
112
defined,
112
fallacies,
134 - 143
ad hominem,
143
ad populum,
143
in advertisements,
138 - 139
appeal to authority,
138
appeal to emotion,
139
appeal to novelty,
143
begging the question,
139
composition,
143
deductive,
134 - 143
defined,
134
denying the antecedent,
135
false cause,
136
false dilemma,
143
inductive,
134 - 143
non sequitur,
136
self-refuting idea,
143
undistributed middle,
137
reasoning,
124 - 133
deductive,
124 - 127
,
134 - 143
inductive,
128 - 129
,
134 - 143
systems,
126 - 127
set diagrams,
102 - 111
using,
102 - 121
using to detect fallacies,
136 - 137
statements,
112 - 121
defined,
112
negating,
116 - 117
Logistic growth,
161
,
316 - 317
compared to exponential,
316
defined,
316
formula for rate of,
321
M
Mapping
probability,
353
Marginal tax rate,
See
Income tax
Market research,
See
Sampling
Market value
defined,
276
Markup,
See also
Price(s)
,
62 - 71
defined,
62
finding,
62 - 63
percent of,
62 - 63
Mass,
See
Weight
Mean
defined,
412
graphing,
412 - 421
Measurement
estimating,
16 - 17
unit conversion,
34 - 43
Median
defined,
412
graphing,
412 - 421
Medicare tax,
See
Social Security tax
Metric system of measurements
conversion,
36
,
38
Mill(s),
See
Property tax
Mode
defined,
412
graphing,
412 - 421
Money
lending,
252 - 261
amount financed,
255
compound interest,
262
credit,
254
,
264 -267
finance charges,
255
installment loans,
253
loan proceeds,
252
mortgages,
274 - 283
prime interest rate,
266
principal,
255
promissory note,
252
term,
252
total amount due,
252
Moore's Law,
155
,
157
Mortgage(s),
See also
Loan(s)
,
274 - 283
balloon
defined,
277
balloon payments
defined,
277
compared with renting,
278
comparing,
274 - 275
debt-to-income ratio,
89
defined,
274
discount points,
283
equity
defined,
276
market value
defined,
276
principal balance
defined,
276
N
Negation(s),
See
Statement(s)
Normal distribution,
426 - 427
defined,
426
Numbers
compared using percent,
26 - 27
in exponential notation,
14 - 15
finding percent of,
24 - 25
rounding,
12 - 21
in scientific notation,
14 - 15
O
Olympic sports,
462 - 471
data
interpreting,
462 - 465
linear,
462
scoring formulas
diving,
466
ski jumping,
467
Order of operations,
2 - 11
calculators and,
4
defined,
2
evaluating formulas with,
2 - 11
study tip,
2
using,
2 - 3
Outdoor sports,
484 - 493
data
interpreting,
484
,
486
,
488
Outlier(s)
defined,
416
effect on averages,
416 - 417
P
Parallel Postulate,
126
,
127
Pattern(s),
302 - 343
exponential,
312 - 321
compared to logistic,
316
defined,
312
recognizing,
312
regression,
314
using,
314 - 315
Fibonacci sequence,
334 - 343
defined,
334
in geometric figures,
336 - 337
golden ratio,
337
golden triangle,
343
recognizing,
334 - 335
inductive reasoning,
128
interpreting,
462 - 465
linear,
302 - 311
defined,
302
in health data,
452
interpreting,
452
,
462
recognizing,
306 - 307
using,
304 - 305
logistic,
161
,
316 - 317
compared to exponential,
316
defined,
316
formula for,
321
proportional,
306 - 307
defined,
306
recognizing,
306 - 307
quadratic,
324 - 333
defined,
324
recognizing,
324 - 325
,
328 - 329
using,
326 - 327
recognizing models of,
328 - 329
sine wave,
339
Payroll tax,
See
Social Security tax
Pension(s),
See
Retirement plan(s)
Percent,
24 - 33
of change,
28 - 29
as a decimal,
24
defined,
24
finding,
24 - 25
using
to compare numbers,
26 - 27
to represent change,
28
Price(s),
See also
Unit price(s)
consumer price index,
162 - 171
calculating,
163
defined,
162
graphing,
164 - 165
inflation and,
162 - 171
devaluation of dollar,
166
discounts,
62 - 71
defined,
64
finding,
64 - 66
percent of,
64 - 66
inflation,
162 - 171
calculating,
163
defined,
162
markups,
62 - 71
defined,
62
finding,
62 - 63
percent of,
62 - 63
Prime interest rate
defined,
266
Principal,
See also
Loan(s)
balance
defined,
276
defined,
255
Probability,
352 - 371
actuary,
356 - 357
defined,
356
Bayes' Theorem,
393
counterintuitive,
388 - 389
defined,
352
estimating,
362 - 371
events,
384 - 393
expected values of,
374 - 383
finding,
374 - 377
formula of,
384
independent,
384 - 385
not occurring,
386 - 387
using,
378
of events,
352 - 361
risk maps,
355
significance,
355
expected value,
374 - 383
defined,
374
finding,
374 - 377
of two events,
374 - 375
using,
378
experimental
defined,
362
finding,
364 - 365
historical,
366 - 367
defined,
362
mapping,
353
theoretical
defined,
362
finding,
362
formula for,
362
using,
356
Professional sports,
474 - 483
data
interpreting,
474 - 475
,
477 - 479
formulas
football passer rating,
476
on-base percentage,
480
slugging percentage,
480
Progressive tax,
See
Income tax
Promissory note(s)
defined,
252
reading,
252
Property,
See
Property tax
Property tax,
205
,
224 -233
assessed value
defined,
224
,
226
calculating,
233
credits,
227
defined,
224
effective rate,
225
exemptions,
227
,
228 - 229
market value
defined,
226
mills
defined,
224
rates
formula for,
233
written as decimal,
224 - 225
Proportional pattern(s),
See also
Linear pattern(s)
defined,
306
recognizing,
306 - 307
Pythagorean Theorem,
157
Q
Quadratic pattern(s),
324 - 333
defined,
324
recognizing,
324 - 325
,
328 - 329
using,
326 - 327
R
Rate(s)
exponential decay,
178 - 179
exponential growth,
156 - 157
maximum heart,
454
mortgage,
274
property tax,
233
Ratio(s)
debt-to-income,
89
economic dependency,
238
golden ratio,
337
golden triangle,
343
price-to-rent,
278
Reasoning,
124 - 133
deductive,
124 - 127
defined,
124
fallacies,
134 - 143
systems,
126 - 127
fallacies,
134 - 143
ad hominem,
143
ad populum,
143
appeal to authority,
138
appeal to emotion,
139
appeal to novelty,
143
begging the question,
139
composition,
143
defined,
134
denying the antecedent,
135
false cause,
136
false dilemma,
143
non sequitur,
136
self-refuting idea,
143
undistributed middle,
137
inductive,
128 - 129
defined,
128
fallacies,
134 - 143
syllogisms
categorical,
124
defined,
124
writing,
124 - 125
Rectangle(s)
area of,
5
Regressive tax,
See
Income tax
Representative sample(s),
434 - 437
defined,
434
Retirement plans,
See also
Savings account(s)
,
236 - 237
annuities,
286 - 288
decreasing,
288
increasing,
286
pension plans,
289
Right-skewed distribution,
428
Risk,
See
Probability
Rounding
and calculators,
12 - 21
in context,
12-13
defined,
12
Rule of 72,
284
S
Sampling,
434 - 443
biased,
436 - 437
defined,
437
market research
field trials,
438
focus groups,
438
interviews,
438
observation,
438
surveys,
438
representative,
434 - 437
defined,
434
statistical inference,
434 - 436
defined,
435
Savings account(s),
284 -293
annuities
decreasing,
288
increasing,
286
balance of,
284 - 285
compound interest,
284
expected values of,
378 - 379
finding balance of,
284
retirement,
236 - 237
pension plans,
289
retirement plans,
286 - 289
annuities,
286 - 288
Rule of 72,
284
Savings plan(s),
See
Savings account(s)
Scientific notation,
14 - 15
Set(s),
102 - 111
complement of,
106 - 107
defined,
106
finding,
106 - 107
diagrams,
102 - 111
using,
102 - 121
using to detect fallacies,
136 - 137
intersection of,
104 - 105
defined,
104
finding,
104 - 105
union of,
102
,
104
defined,
102
Significant digit(s),
16 - 17
described,
16
rule,
16
writing,
17
Simple interest
annual percentage rate
defined,
256
finding,
257
defined,
256
finding,
256
formula for
interest,
256 - 257
period of,
256 - 257
principal,
256 - 257
rate of,
256 - 257
Sine wave,
339
Social Security tax,
234 - 243
benefits formula,
241
defined,
234
economic dependency ratio
defined,
238
formula for,
238
rates,
234
Solar year
defined,
36
Speed of light,
10
Sports,
See
Olympic sports
;
Outdoor sports
;
Professional sports
Square(s)
area of,
5
Standard deviation,
424 - 433
Chebyshev's inequality,
424
defined,
424
displaying,
424 - 425
formula for,
433
and normal distribution,
426 - 427
Statement(s),
112 - 121
argument
defined,
112
defined,
112
negating,
116 -117
Statistical inference,
434 - 436
defined,
435
Statistics
distribution
bimodal,
428 - 429
flat,
428
normal,
426 - 427
right-skewed,
428
sampling,
434 - 443
biased,
436 - 437
market research,
438
representative,
434 - 437
standard deviation,
424 - 433
Chebyshev's inequality,
424
defined,
424
displaying,
424 - 425
formula for,
433
statistical inference,
434 - 436
defined,
435
Straight-line depreciation,
184
Study tip
amortization,
262
annual percentage rate,
257
,
264
area of a rectangle,
5
averages,
412
bubble graphs,
366
budgets,
84
,
85
calculators,
4
Chebyshev's inequality,
424
credit,
266
credit cards,
264
decay
depreciation,
184
,
186
,
188
exponential,
174
half-life,
176
rate of,
178
depreciation,
184
,
185
,
186
double declining-balance,
188
straight-line,
188
sum of the years-digits,
188
determining units,
13
economic dependency ratio,
238
expenses,
184
exponential decay,
174
,
178
half-life,
176
exponential growth,
152
,
156
,
174
exponential notation,
14
exponential patterns,
312
,
314
fallacies
affirming the consequent,
134
appeal to authority,
138
denying the antecedent,
135
false cause,
136
non sequitur,
136
Fibonacci sequence,
334
formulas,
7
golden ratio,
337
growth
exponential,
156
,
174
health data,
452
income taxes,
202
,
212
,
234
linear patterns,
302
,
312
linear regression,
304
loans,
266
amortization,
262
annual percentage rate (APR),
257
,
264
foreclosures,
279
mortgages,
274
,
276
,
277
promissory note,
252
term of,
256
logic
fallacies,
134 - 136
,
138
terms,
112
mean,
412
measurement,
16
median,
412
mode,
412
mortgages,
274,
276,
277
balloon,
277
foreclosures,
279
price-to-rent ratio,
278
order of operations,
2
patterns
exponential,
312
,
314
Fibonacci sequence,
334
linear,
302
,
312
quadratic,
324
percent,
27
of change,
28
as a decimal,
24
price-to-rent ratio,
278
prices
markup and discount,
64
wholesale,
63
probability,
362
,
366
promissory note,
252
quadratic patterns,
324
reasoning,
134 - 136
,
138
retirement plans,
287
,
289
Rule of 72,
284
sampling,
434
,
438
savings accounts,
284
,
287
,
289
scientific notation,
14
sets
complement of,
106
intersection of,
104
union of,
102
,
104
square root of
2
,
157
standard deviation,
424
statistics,
424
sampling,
434
,
438
standard deviation,
424
taxes
exemptions,
227
income,
202
,
212
,
234
payroll,
235
property,
224
,
227 - 229
sales,
74
Social Security,
234
,
235
,
236
unit analysis,
34
,
36
,
37
unit conversion,
38
unit prices,
53
converting,
54
Sum of the years-digits depreciation,
188
Syllogism(s)
categorical
defined,
124
defined,
124
writing,
124 - 125
T
Tax credits,
See
Property tax
Taxes
consumption,
74 - 83
defined,
74
credits,
227
excise,
204
defined,
76
finding,
76 - 77
income
capital gains,
221
comparing systems,
216
credit,
211
deductions,
211
effective rate,
212
flat rate,
202 - 211
defined,
202
graduated,
204
,
211 - 212
marginal rate,
212-213
negative,
211
progressive,
204
regressive,
204
indirect,
206
defined,
206
philosophy of,
202 - 211
property,
205
,
224 - 233
assessed value,
224
,
226
defined,
224
effective rate,
225
market value,
226
rate written as decimal,
224 - 225
sales,
204 - 205
finding,
74 - 75
Social Security,
234 - 243
benefits formula,
241
defined,
234
economic dependency ratio,
238
rates,
234
value-added,
78
defined,
78
Temperature
converting units,
38
,
39
Term
defined,
252
Theoretical probability,
See also
Probability
defined,
362
finding,
362 - 363
formula for,
362
Total amount due
defined,
252
finding,
253
Triangle(s)
area of,
5
golden,
343
U
Union
of sets
defined,
102
Unit analysis,
34 - 35
defined,
34
using,
34 - 35
Unit price(s),
52 - 61
comparing,
54 - 57
defined,
52
finding,
52
using,
56
Units of measure
of computer storage,
15
converting,
34 - 43
described,
36
distance,
36
,
38
temperature,
38
,
39
volume,
36
,
38
weight,
36
,
38
customary,
36
defined,
34
determining,
13
metric,
36
unit analysis,
34 - 35
defined,
34
V
Venn diagram,
See
Set(s)
Volume
converting units,
36
,
38
W
Weight
converting units,
36
,
38