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Contemporary Mathematics

Chapter Review

Contemporary MathematicsChapter Review
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Table of contents
  1. Preface
  2. 1 Sets
    1. Introduction
    2. 1.1 Basic Set Concepts
    3. 1.2 Subsets
    4. 1.3 Understanding Venn Diagrams
    5. 1.4 Set Operations with Two Sets
    6. 1.5 Set Operations with Three Sets
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  3. 2 Logic
    1. Introduction
    2. 2.1 Statements and Quantifiers
    3. 2.2 Compound Statements
    4. 2.3 Constructing Truth Tables
    5. 2.4 Truth Tables for the Conditional and Biconditional
    6. 2.5 Equivalent Statements
    7. 2.6 De Morgan’s Laws
    8. 2.7 Logical Arguments
    9. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Projects
      5. Chapter Review
      6. Chapter Test
  4. 3 Real Number Systems and Number Theory
    1. Introduction
    2. 3.1 Prime and Composite Numbers
    3. 3.2 The Integers
    4. 3.3 Order of Operations
    5. 3.4 Rational Numbers
    6. 3.5 Irrational Numbers
    7. 3.6 Real Numbers
    8. 3.7 Clock Arithmetic
    9. 3.8 Exponents
    10. 3.9 Scientific Notation
    11. 3.10 Arithmetic Sequences
    12. 3.11 Geometric Sequences
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  5. 4 Number Representation and Calculation
    1. Introduction
    2. 4.1 Hindu-Arabic Positional System
    3. 4.2 Early Numeration Systems
    4. 4.3 Converting with Base Systems
    5. 4.4 Addition and Subtraction in Base Systems
    6. 4.5 Multiplication and Division in Base Systems
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Projects
      5. Chapter Review
      6. Chapter Test
  6. 5 Algebra
    1. Introduction
    2. 5.1 Algebraic Expressions
    3. 5.2 Linear Equations in One Variable with Applications
    4. 5.3 Linear Inequalities in One Variable with Applications
    5. 5.4 Ratios and Proportions
    6. 5.5 Graphing Linear Equations and Inequalities
    7. 5.6 Quadratic Equations with Two Variables with Applications
    8. 5.7 Functions
    9. 5.8 Graphing Functions
    10. 5.9 Systems of Linear Equations in Two Variables
    11. 5.10 Systems of Linear Inequalities in Two Variables
    12. 5.11 Linear Programming
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  7. 6 Money Management
    1. Introduction
    2. 6.1 Understanding Percent
    3. 6.2 Discounts, Markups, and Sales Tax
    4. 6.3 Simple Interest
    5. 6.4 Compound Interest
    6. 6.5 Making a Personal Budget
    7. 6.6 Methods of Savings
    8. 6.7 Investments
    9. 6.8 The Basics of Loans
    10. 6.9 Understanding Student Loans
    11. 6.10 Credit Cards
    12. 6.11 Buying or Leasing a Car
    13. 6.12 Renting and Homeownership
    14. 6.13 Income Tax
    15. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  8. 7 Probability
    1. Introduction
    2. 7.1 The Multiplication Rule for Counting
    3. 7.2 Permutations
    4. 7.3 Combinations
    5. 7.4 Tree Diagrams, Tables, and Outcomes
    6. 7.5 Basic Concepts of Probability
    7. 7.6 Probability with Permutations and Combinations
    8. 7.7 What Are the Odds?
    9. 7.8 The Addition Rule for Probability
    10. 7.9 Conditional Probability and the Multiplication Rule
    11. 7.10 The Binomial Distribution
    12. 7.11 Expected Value
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Formula Review
      4. Projects
      5. Chapter Review
      6. Chapter Test
  9. 8 Statistics
    1. Introduction
    2. 8.1 Gathering and Organizing Data
    3. 8.2 Visualizing Data
    4. 8.3 Mean, Median and Mode
    5. 8.4 Range and Standard Deviation
    6. 8.5 Percentiles
    7. 8.6 The Normal Distribution
    8. 8.7 Applications of the Normal Distribution
    9. 8.8 Scatter Plots, Correlation, and Regression Lines
    10. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  10. 9 Metric Measurement
    1. Introduction
    2. 9.1 The Metric System
    3. 9.2 Measuring Area
    4. 9.3 Measuring Volume
    5. 9.4 Measuring Weight
    6. 9.5 Measuring Temperature
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  11. 10 Geometry
    1. Introduction
    2. 10.1 Points, Lines, and Planes
    3. 10.2 Angles
    4. 10.3 Triangles
    5. 10.4 Polygons, Perimeter, and Circumference
    6. 10.5 Tessellations
    7. 10.6 Area
    8. 10.7 Volume and Surface Area
    9. 10.8 Right Triangle Trigonometry
    10. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  12. 11 Voting and Apportionment
    1. Introduction
    2. 11.1 Voting Methods
    3. 11.2 Fairness in Voting Methods
    4. 11.3 Standard Divisors, Standard Quotas, and the Apportionment Problem
    5. 11.4 Apportionment Methods
    6. 11.5 Fairness in Apportionment Methods
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  13. 12 Graph Theory
    1. Introduction
    2. 12.1 Graph Basics
    3. 12.2 Graph Structures
    4. 12.3 Comparing Graphs
    5. 12.4 Navigating Graphs
    6. 12.5 Euler Circuits
    7. 12.6 Euler Trails
    8. 12.7 Hamilton Cycles
    9. 12.8 Hamilton Paths
    10. 12.9 Traveling Salesperson Problem
    11. 12.10 Trees
    12. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  14. 13 Math and...
    1. Introduction
    2. 13.1 Math and Art
    3. 13.2 Math and the Environment
    4. 13.3 Math and Medicine
    5. 13.4 Math and Music
    6. 13.5 Math and Sports
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Formula Review
      4. Projects
      5. Chapter Review
      6. Chapter Test
  15. A | Co-Req Appendix: Integer Powers of 10
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
  17. Index

Chapter Review

The Metric System
For the following exercises, determine the base unit of the metric system described: liter, gram, or meter.
1.
amount of juice in a carton
2.
weight of a puppy
3.
height of a wall
For the following exercises, choose the smaller of the two units.
4.
hectogram or centigram
5.
decameter or kilometer
6.
milliliter or deciliter
7.
Convert 236 cm to meters (m).
8.
Convert 137.5 mg to grams (g).
9.
You purchase 15 kg of birdseed. You divide the birdseed into 10 bags. How many grams of birdseed are in each bag?
10.
A track is 650 m long. If you run 8 laps around the track, how many kilometers did you run?
Measuring Area
For the following exercises, determine the most reasonable value for each area.
11.
bedroom floor
12 km2
12 m2
12 cm2
12 mm2
12.
nature preserve
800 km2
800 m2
800 cm2
800 mm2
13.
desk surface
0.125 km2
0.125 m2
0.125 cm2
0.125 mm2
For the following exercises, convert the given area to the units shown.
14.
650,000 cm2 = __________ m2
15.
17 m2 = __________ cm2
16.
759 cm2 = __________ mm2
17.
A laptop is 30 cm by 20 cm. A sticker on the laptop cover measures 15 mm by 15 mm. How many square centimeters of the laptop cover is still visible?
18.
A dining room wall is 2.75 m by 2.25 m. A window on the wall is 0.75 m by 1.5 m. How many square meters is the surface of the wall?
19.
A floor is 6 m by 4 m. A rug on the floor measures 200 cm by 100 cm. How much of the floor, in m2, is not covered by the rug?
20.
A ceiling is 4 m by 2.5 m. A skylight in the ceiling measures 75 cm by 80 cm. How much of the ceiling, in m2, would need to be painted if you decide to change the color of the ceiling?
Measuring Volume
For the following exercises, determine the most reasonable value for each volume.
21.
aquarium
65,750 km3
65,750 m3
65,750 cm3
65,750 mm3
22.
carton of soup
94,000 L
94 L
940,000 mL
940 mL
23.
gift box
6,250 km3
6,250 m3
6,250 cm3
6,250 mm3
For the following exercises, convert the given volume to the units shown.
24.
59,837 mm3 = __________ cm3
25.
12.5 dm3 = __________ mL
26.
368 cm3 = __________ mm3
27.
A box has dimensions of 15\,{\text{cm}} \times 10\,{\text{cm}} \times 25\,{\text{cm}}. The box currently holds 1,750 cm3 of black beans. How many cubic centimeters of black beans are needed to completely fill the box?
28.
The dimensions of a small storage unit are 3\,{\text{m}} \times 3{\text{m}} \times 3\,{\text{m}}. What is the volume of a medium storage area with dimensions twice the size of the small unit?
29.
How much liquid, in liters, can a container with dimensions of 35\,{\text{cm}} \times 15\,{\text{cm}} \times 20\,{\text{cm}} hold?
30.
A box is 20 cm long and 15 cm wide. The volume of the box is 2,100 cm3. What is the height of the box?
Measuring Weight
31.
What is the most reasonable estimate for the weight of a small stack of coins?
120 mg
12 g
1.2 kg
0.12 mt
For the following exercises, convert the given weight to the units shown.
32.
7,900 g = __________ kg
33.
81 g = __________ mg
34.
0.12 kg = __________ g
For the following exercises, determine the total weight in the units shown.
35.
four 450 mg tablets ________ g
36.
six 45 g candy bars ________ kg
37.
seven 1.5 g buttons ________ mg
38.
A box of chocolate weighs 2.75 kg. If you share the candy bar equally with 5 friends, how many grams of chocolate does each person get?
39.
You purchase 15 tomatoes that weigh 100 grams each. If tomatoes cost $1.18 per kilogram, how much did you pay?
40.
A value-size package of ground chicken costs $23.00. The package weighs 2.5 kg. What is the cost per gram of the chicken?
Measuring Temperature
For the following exercises, convert the temperatures to the nearest degree.
41.
365 °F = __________ °C
42.
42 °C = __________ °F
43.
575 °F = __________ °C
44.
135 °C = __________ °F
45.
–20 °F = __________ °C
46.
73 °C = __________ °F
47.
The temperature of a welder’s torch increases 1,112 ºF every 3 minutes. About how many minutes does it take for the torch to increase 1,200 ºC?
48.
A substance is heated to 302 ºF. As the substance cools the temperature drops 4 ºC every 3 minutes. How many minutes until the temperature of the water reaches 130 ºC?
49.
On November 1 the temperature was 40 ºF. On December 1 the temperature was 7 ºC. Which day was cooler?
50.
The instructions to cook lasagna say to set the oven at 475 ºF. To the nearest degree, what is the temperature in degrees Celsius?
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