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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

Gathering and Organizing Data

Decide whether randomization is being used in the selection of these samples. If it is, identify the type of random sample (simple, systematic, cluster, or stratified).

1.
College students want to gauge interest in a new club they're thinking about starting. They choose three residence halls at random and slide a survey form under the door to every room.
2.
The managers of a campus dining hall want feedback on a new dish that is being served, so they ask the first 10 people who choose that dish what they think of it.
3.
The administration of a large university system with five campuses wants to administer a survey to students in the system. The administration chooses 50 students at random from each campus; the 250 students selected form thesample.

4.
A sample of college students were asked how many of their meals were provided by a campus dining hall on the previous day. Here are the results:
0 1 0 3 2 3 3
2 2 0 2 1 1 0
0 1 2 0 3 0 1
3 2 3 0 1 3 0

Create a frequency distribution for these data.

Visualizing Data
5.
Create a bar chart to visualize the data in question 4.
6.
Use the data in “MBB2019” on every school that fielded an NCAA Division I men’s basketball team in the 2018–2019 season, to create a histogram of the number of free throws made by each team (FT).
Mean, Median and Mode
7.
The data below show the top ten scorers (by points per game) in the National Basketball Association for the 2018–2019 season. Find the mode, median, and mean age of these players without technology.
Rank Player Age
1 James Harden 29
2 Paul George 28
3 Giannis Antetokounmpo 24
4 Joel Embiid 24
5 Stephen Curry 30
6 Devin Booker 22
7 Kawhi Leonard 27
8 Kevin Durant 30
9 Damian Lillard 28
10 Bradley Beal 25
Table 8.13 (source: https://www.basketball-reference.com/leagues/NBA_2019_leaders.html)
8.
Using the data in “MBB2019”, find the mean, median, and mode of the number of free throws made by each team (FT).
Range and Standard Deviation
9.
Using the data in “MBB2019”, find the range and standard deviation of the number of free throws made by each team (FT).
Percentiles

Use the data in “MBB2019”, to answer the following:

10.
What number of free throws (FT) is at the 40th percentile?
11.
At what percentile is Syracuse University, which made 480 free throws?
The Normal Distribution
12.
Identify the means and standard deviations of these normal distributions:
A graph shows a normal distribution curve and a negatively skewed distribution. The horizontal axis ranges from 0 to 14, in increments of 2. The normal distribution curve begins at 0, has a peak value at 7, and ends at 14. The negatively skewed distribution curve begins at 0, after point 4, the curve rises up and to the right, has a peak value at 10, and ends at 14. The skewed distribution curve has a large peak compared to the normal distribution.

Answer the following about data that are distributed normally with mean 200 and standard deviation 20:

13.
What proportion of the data are between 160 and 240?
14.
What’s the standardized score of the data value 235?
15.
At what percentile would the data value 187 fall?
16.
What data value would be at the 90th percentile?
Applications of the Normal Distribution

Use the data in “MBB2019” to answer the following:

17.
What is the standardized score for Purdue Universitiy’s number of free throws (FT = 461)?
18.
At what percentile would we estimate Purdue’s value of FT to fall, using the normal distribution?
19.
At what percentile does Purdue’s value of FT actually fall?
Scatter Plots, Correlation, and Regression Lines

For each of the following scatter plots, decide whether linear regression would be appropriate. If it is, classify the strength and direction of the relationship.

20.
A scatter plot. The x-axis ranges from 7 to 13, in increments of 1. The y-axis ranges from negative 4 to 8, in increments of 2. The points are scattered in a curved path. The points from 8 to 10 on the horizontal axis are in decreasing order and the points from 10 to 12 are in increasing order. Some of the points are as follows: (7.5, 7), (8, 5), (9, 2), (9.5, negative 1), (10, 0), (11, 1), and (12, 4). Note: all values are approximate.
21.
A scatter plot. The x-axis ranges from 7 to 13, in increments of 1. The y-axis ranges from 4 to 16, in increments of 2. The points are scattered in increasing order. Some of the points are as follows: (8, 7), (9, 9), (10, 10), (11, 12), and (11.5, 12). Note: all values are approximate.
22.
A scatter plot. The x-axis ranges from 7 to 13, in increments of 1. The y-axis ranges from negative 6 to negative 13, in increments of 1. The points are scattered in decreasing order. Some of the points are as follows: (8, negative 8), (9, negative 9), (10, negative 10), (11, negative 11), and (12, negative 12). Note: all values are approximate.
Use the data in “NBA2019” to answer the following:
23.
What is the correlation coefficient between the number of field goals attempted per game (FGA) and number of points scored per game (PTS)?
24.
What is the equation of the regression line we would use to predict PTS from FGA?
25.
Write a sentence to interpret the slope of the regression line.
26.
Predict the number of points per game for a player who attempts 16 field goals per game.
27.
Danilo Gallinari attempted 13 field goals per game, and averaged 19.8 points per game. Did he score more or fewer points per game than expected? By how much?
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